Publications of Joshua Socolar    :chronological  alphabetical  combined listing:

%% Papers Published   
@article{fds326695,
   Author = {Pham, AT and Zhuang, Y and Detwiler, P and Socolar, JES and Charbonneau,
             P and Yellen, BB},
   Title = {Phase diagram and aggregation dynamics of a monolayer of
             paramagnetic colloids.},
   Journal = {Physical review. E},
   Volume = {95},
   Number = {5-1},
   Pages = {052607},
   Year = {2017},
   Month = {May},
   url = {http://dx.doi.org/10.1103/physreve.95.052607},
   Abstract = {We have developed a tunable colloidal system and a
             corresponding theoretical model for studying the phase
             behavior of particles assembling under the influence of
             long-range magnetic interactions. A monolayer of
             paramagnetic particles is subjected to a spatially uniform
             magnetic field with a static perpendicular component and a
             rapidly rotating in-plane component. The sign and strength
             of the interactions vary with the tilt angle θ of the
             rotating magnetic field. For a purely in-plane field,
             θ=90^{∘}, interactions are attractive and the
             experimental results agree well with both equilibrium and
             out-of-equilibrium predictions based on a two-body
             interaction model. For tilt angles 50^{∘}≲θ≲55^{∘},
             the two-body interaction gives a short-range attractive and
             long-range repulsive interaction, which predicts the
             formation of equilibrium microphases. In experiments,
             however, a different type of assembly is observed. Inclusion
             of three-body (and higher-order) terms in the model does not
             resolve the discrepancy. We further characterize the
             anomalous regime by measuring the time-dependent cluster
             size distribution.},
   Doi = {10.1103/physreve.95.052607},
   Key = {fds326695}
}

@article{fds325483,
   Author = {Oğuz, EC and Socolar, JES and Steinhardt, PJ and Torquato,
             S},
   Title = {Hyperuniformity of quasicrystals},
   Journal = {Physical Review B},
   Volume = {95},
   Number = {5},
   Year = {2017},
   Month = {February},
   url = {http://dx.doi.org/10.1103/PhysRevB.95.054119},
   Doi = {10.1103/PhysRevB.95.054119},
   Key = {fds325483}
}

@article{fds325482,
   Author = {Socolar, JES and Lubensky, TC and Kane, CL},
   Title = {Mechanical graphene},
   Journal = {New Journal of Physics},
   Volume = {19},
   Number = {2},
   Pages = {025003-025003},
   Year = {2017},
   Month = {February},
   url = {http://dx.doi.org/10.1088/1367-2630/aa57bb},
   Doi = {10.1088/1367-2630/aa57bb},
   Key = {fds325482}
}

@article{fds323248,
   Author = {Rutkowski, DM and Marcoux, C and Socolar, JES and Hall,
             CK},
   Title = {Formation of limit-periodic structures by quadrupole
             particles confined to a triangular lattice},
   Journal = {Physical review. E},
   Volume = {95},
   Number = {1},
   Publisher = {American Physical Society},
   Year = {2017},
   Month = {January},
   url = {http://dx.doi.org/10.1103/PhysRevE.95.012604},
   Abstract = {We have performed Monte Carlo (MC) simulations on
             two-dimensional systems of quadrupole particles confined to
             a triangular lattice in order to determine the conditions
             that permit the formation of a limit-periodic phase. We have
             found that limit-periodic structures form only when the
             rotations of the particles are confined to a set of six
             orientations aligned with the lattice directions. Related
             structures including striped and unidirectional rattler
             phases form when π/6 rotations or continuous rotations are
             allowed. Order parameters signaling the formation of the
             limit-periodic structure and related structures are measured
             as a function of temperature. Our findings on the formation
             of the limit-periodic structure elucidate features relevant
             to the experimental creation of such a structure, which is
             expected to have interesting vibrational and electromagnetic
             modes.},
   Doi = {10.1103/PhysRevE.95.012604},
   Key = {fds323248}
}

@article{fds315560,
   Author = {Hann, CT and Socolar, JES and Steinhardt, PJ},
   Title = {Local growth of icosahedral quasicrystalline
             tilings},
   Journal = {Physical Review B},
   Volume = {94},
   Number = {1},
   Year = {2016},
   Month = {July},
   url = {http://arxiv.org/abs/1604.02479v1},
   Abstract = {Icosahedral quasicrystals (IQCs) with extremely high degrees
             of translational order have been produced in the laboratory
             and found in naturally occurring minerals, yet questions
             remain about how IQCs form. In particular, the fundamental
             question of how locally determined additions to a growing
             cluster can lead to the intricate long-range correlations in
             IQCs remains open. In answer to this question, we have
             developed an algorithm that is capable of producing a
             perfectly ordered IQC, yet relies exclusively on local rules
             for sequential, face-to-face addition of tiles to a cluster.
             When the algorithm is seeded with a special type of cluster
             containing a defect, we find that growth is forced to
             infinity with high probability and that the resultant IQC
             has a vanishing density of defects. The geometric features
             underlying this algorithm can inform analyses of
             experimental systems and numerical models that generate
             highly ordered quasicrystals.},
   Doi = {10.1103/PhysRevB.94.014113},
   Key = {fds315560}
}

@article{fds311986,
   Author = {Marcoux, C and Socolar, JES},
   Title = {Sparse phonon modes of a limit-periodic structure},
   Journal = {Physical Review B - Condensed Matter and Materials
             Physics},
   Volume = {93},
   Number = {17},
   Publisher = {American Physical Society},
   Year = {2016},
   Month = {May},
   ISSN = {0163-1829},
   url = {http://journals.aps.org/prb/abstract/10.1103/PhysRevB.93.174102},
   Abstract = {Limit-periodic structures are well ordered but nonperiodic,
             and hence have nontrivial vibrational modes. We study a ball
             and spring model with a limit-periodic pattern of spring
             stiffnesses and identify a set of extended modes with
             arbitrarily low participation ratios, a situation that
             appears to be unique to limit-periodic systems. The balls
             that oscillate with large amplitude in these modes live on
             periodic nets with arbitrarily large lattice constants. By
             studying periodic approximants to the limit-periodic
             structure, we present numerical evidence for the existence
             of such modes, and we give a heuristic explanation of their
             structure.},
   Doi = {10.1103/PhysRevB.93.174102},
   Key = {fds311986}
}

@article{fds311987,
   Author = {Fu, L and Steinhardt, W and Zhao, H and Socolar, JES and Charbonneau,
             P},
   Title = {Hard sphere packings within cylinders.},
   Journal = {Soft Matter},
   Volume = {12},
   Number = {9},
   Pages = {2505-2514},
   Year = {2016},
   Month = {March},
   ISSN = {1744-683X},
   url = {http://dx.doi.org/10.1039/c5sm02875b},
   Abstract = {Arrangements of identical hard spheres confined to a
             cylinder with hard walls have been used to model
             experimental systems, such as fullerenes in nanotubes and
             colloidal wire assembly. Finding the densest configurations,
             called close packings, of hard spheres of diameter σ in a
             cylinder of diameter D is a purely geometric problem that
             grows increasingly complex as D/σ increases, and little is
             thus known about the regime for D > 2.873σ. In this work,
             we extend the identification of close packings up to D =
             4.00σ by adapting Torquato-Jiao's adaptive-shrinking-cell
             formulation and sequential-linear-programming (SLP)
             technique. We identify 17 new structures, almost all of them
             chiral. Beyond D ≈ 2.85σ, most of the structures consist
             of an outer shell and an inner core that compete for being
             close packed. In some cases, the shell adopts its own
             maximum density configuration, and the stacking of core
             spheres within it is quasiperiodic. In other cases, an
             interplay between the two components is observed, which may
             result in simple periodic structures. In yet other cases,
             the very distinction between the core and shell vanishes,
             resulting in more exotic packing geometries, including some
             that are three-dimensional extensions of structures obtained
             from packing hard disks in a circle.},
   Doi = {10.1039/c5sm02875b},
   Key = {fds311987}
}

@article{fds312774,
   Author = {Marcoux, C and Byington, TW and Qian, Z and Charbonneau, P and Socolar,
             JES},
   Title = {Erratum: Emergence of limit-periodic order in tiling models
             [Phys. Rev. E 90 , 012136 (2014)]},
   Journal = {Physical review. E},
   Volume = {93},
   Number = {2},
   Year = {2016},
   Month = {February},
   ISSN = {2470-0045},
   url = {http://dx.doi.org/10.1103/PhysRevE.93.029902},
   Doi = {10.1103/PhysRevE.93.029902},
   Key = {fds312774}
}

@article{fds248310,
   Author = {Yang, Y and Fu, L and Marcoux, C and Socolar, JES and Charbonneau, P and Yellen, BB},
   Title = {Phase transformations in binary colloidal
             monolayers.},
   Journal = {Soft Matter},
   Volume = {11},
   Number = {12},
   Pages = {2404-2415},
   Year = {2015},
   Month = {March},
   ISSN = {1744-683X},
   url = {http://dx.doi.org/10.1039/c5sm00009b},
   Abstract = {Phase transformations can be difficult to characterize at
             the microscopic level due to the inability to directly
             observe individual atomic motions. Model colloidal systems,
             by contrast, permit the direct observation of individual
             particle dynamics and of collective rearrangements, which
             allows for real-space characterization of phase transitions.
             Here, we study a quasi-two-dimensional, binary colloidal
             alloy that exhibits liquid-solid and solid-solid phase
             transitions, focusing on the kinetics of a diffusionless
             transformation between two crystal phases. Experiments are
             conducted on a monolayer of magnetic and nonmagnetic spheres
             suspended in a thin layer of ferrofluid and exposed to a
             tunable magnetic field. A theoretical model of hard spheres
             with point dipoles at their centers is used to guide the
             choice of experimental parameters and characterize the
             underlying materials physics. When the applied field is
             normal to the fluid layer, a checkerboard crystal forms;
             when the angle between the field and the normal is
             sufficiently large, a striped crystal assembles. As the
             field is slowly tilted away from the normal, we find that
             the transformation pathway between the two phases depends
             strongly on crystal orientation, field strength, and degree
             of confinement of the monolayer. In some cases, the pathway
             occurs by smooth magnetostrictive shear, while in others it
             involves the sudden formation of martensitic
             plates.},
   Doi = {10.1039/c5sm00009b},
   Key = {fds248310}
}

@article{fds248311,
   Author = {Sun, M and Cheng, X and Socolar, JES},
   Title = {Regulatory logic and pattern formation in the early sea
             urchin embryo.},
   Journal = {Journal of Theoretical Biology},
   Volume = {363},
   Pages = {80-92},
   Year = {2014},
   Month = {December},
   ISSN = {0022-5193},
   url = {http://dx.doi.org/10.1016/j.jtbi.2014.07.023},
   Abstract = {We model the endomesoderm tissue specification process in
             the vegetal half of the early sea urchin embryo using
             Boolean models with continuous-time updating to represent
             the regulatory network that controls gene expression. Our
             models assume that the network interaction rules remain
             constant over time and the dynamics plays out on a
             predetermined program of cell divisions. An exhaustive
             search of two-node models, in which each node may represent
             a module of several genes in the real regulatory network,
             yields a unique network architecture that can accomplish the
             pattern formation task at hand--the formation of three
             latitudinal tissue bands from an initial state with only two
             distinct cell types. Analysis of an eight-gene model
             constructed from available experimental data reveals that it
             has a modular structure equivalent to the successful
             two-node case. Our results support the hypothesis that the
             gene regulatory network provides sufficient instructions for
             producing the correct pattern of tissue specification at
             this stage of development (between the fourth and tenth
             cleavages in the urchin embryo).},
   Doi = {10.1016/j.jtbi.2014.07.023},
   Key = {fds248311}
}

@article{PhysRevE.90.012136,
   Author = {Marcoux, C and Byington, TW and Qian, Z and Charbonneau, P and Socolar,
             JES},
   Title = {Emergence of limit-periodic order in tiling
             models.},
   Journal = {Physical Review E - Statistical, Nonlinear, and Soft Matter
             Physics},
   Volume = {90},
   Number = {1},
   Pages = {012136},
   Publisher = {American Physical Society},
   Year = {2014},
   Month = {July},
   ISSN = {1539-3755},
   url = {http://link.aps.org/doi/10.1103/PhysRevE.90.012136},
   Abstract = {A two-dimensional (2D) lattice model defined on a triangular
             lattice with nearest- and next-nearest-neighbor interactions
             based on the Taylor-Socolar monotile is known to have a
             limit-periodic ground state. The system reaches that state
             during a slow quench through an infinite sequence of phase
             transitions. We study the model as a function of the
             strength of the next-nearest-neighbor interactions and
             introduce closely related 3D models with only
             nearest-neighbor interactions that exhibit limit-periodic
             phases. For models with no next-nearest-neighbor
             interactions of the Taylor-Socolar type, there is a large
             degenerate class of ground states, including crystalline
             patterns and limit-periodic ones, but a slow quench still
             yields the limit-periodic state. For the Taylor-Socolar
             lattic model, we present calculations of the diffraction
             pattern for a particular decoration of the tile that permits
             exact expressions for the amplitudes and identify domain
             walls that slow the relaxation times in the ordered phases.
             For one of the 3D models, we show that the phase transitions
             are first order, with equilibrium structures that can be
             more complex than in the 2D case, and we include a proof of
             aperiodicity for a geometrically simple tile with only
             nearest-neighbor matching rules.},
   Doi = {10.1103/physreve.90.012136},
   Key = {PhysRevE.90.012136}
}

@article{fds248313,
   Author = {Cheng, X and Lyons, DC and Socolar, JES and McClay,
             DR},
   Title = {Delayed transition to new cell fates during cellular
             reprogramming.},
   Journal = {Developmental Biology},
   Volume = {391},
   Number = {2},
   Pages = {147-157},
   Year = {2014},
   Month = {July},
   ISSN = {0012-1606},
   url = {http://www.sciencedirect.com/science/article/pii/S001216061400222X},
   Abstract = {In many embryos specification toward one cell fate can be
             diverted to a different cell fate through a reprogramming
             process. Understanding how that process works will reveal
             insights into the developmental regulatory logic that
             emerged from evolution. In the sea urchin embryo, cells at
             gastrulation were found to reprogram and replace missing
             cell types after surgical dissections of the embryo.
             Non-skeletogenic mesoderm (NSM) cells reprogrammed to
             replace missing skeletogenic mesoderm cells and animal caps
             reprogrammed to replace all endomesoderm. In both cases
             evidence of reprogramming onset was first observed at the
             early gastrula stage, even if the cells to be replaced were
             removed earlier in development. Once started however, the
             reprogramming occurred with compressed gene expression
             dynamics. The NSM did not require early contact with the
             skeletogenic cells to reprogram, but the animal cap cells
             gained the ability to reprogram early in gastrulation only
             after extended contact with the vegetal halves prior to that
             time. If the entire vegetal half was removed at early
             gastrula, the animal caps reprogrammed and replaced the
             vegetal half endomesoderm. If the animal caps carried
             morpholinos to either hox11/13b or foxA (endomesoderm
             specification genes), the isolated animal caps failed to
             reprogram. Together these data reveal that the emergence of
             a reprogramming capability occurs at early gastrulation in
             the sea urchin embryo and requires activation of early
             specification components of the target tissues.},
   Doi = {10.1016/j.ydbio.2014.04.015},
   Key = {fds248313}
}

@article{fds248315,
   Author = {Sun, M and Cheng, X and Socolar, JES},
   Title = {Causal structure of oscillations in gene regulatory
             networks: Boolean analysis of ordinary differential equation
             attractors.},
   Journal = {Chaos},
   Volume = {23},
   Number = {2},
   Pages = {025104},
   Year = {2013},
   Month = {June},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/23822502},
   Abstract = {A common approach to the modeling of gene regulatory
             networks is to represent activating or repressing
             interactions using ordinary differential equations for
             target gene concentrations that include Hill function
             dependences on regulator gene concentrations. An alternative
             formulation represents the same interactions using Boolean
             logic with time delays associated with each network link. We
             consider the attractors that emerge from the two types of
             models in the case of a simple but nontrivial network: a
             figure-8 network with one positive and one negative feedback
             loop. We show that the different modeling approaches give
             rise to the same qualitative set of attractors with the
             exception of a possible fixed point in the ordinary
             differential equation model in which concentrations sit at
             intermediate values. The properties of the attractors are
             most easily understood from the Boolean perspective,
             suggesting that time-delay Boolean modeling is a useful tool
             for understanding the logic of regulatory
             networks.},
   Doi = {10.1063/1.4807733},
   Key = {fds248315}
}

@article{fds304616,
   Author = {Cheng, X and Sun, M and Socolar, JES},
   Title = {Autonomous Boolean modelling of developmental gene
             regulatory networks.},
   Journal = {Journal of the Royal Society Interface},
   Volume = {10},
   Number = {78},
   Pages = {20120574},
   Year = {2013},
   Month = {January},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/23034351},
   Abstract = {During early embryonic development, a network of regulatory
             interactions among genes dynamically determines a pattern of
             differentiated tissues. We show that important timing
             information associated with the interactions can be
             faithfully represented in autonomous Boolean models in which
             binary variables representing expression levels are updated
             in continuous time, and that such models can provide a
             direct insight into features that are difficult to extract
             from ordinary differential equation (ODE) models. As an
             application, we model the experimentally well-studied
             network controlling fly body segmentation. The Boolean model
             successfully generates the patterns formed in normal and
             genetically perturbed fly embryos, permits the derivation of
             constraints on the time delay parameters, clarifies the
             logic associated with different ODE parameter sets and
             provides a platform for studying connectivity and robustness
             in parameter space. By elucidating the role of regulatory
             time delays in pattern formation, the results suggest new
             types of experimental measurements in early embryonic
             development.},
   Doi = {10.1098/rsif.2012.0574},
   Key = {fds304616}
}

@article{fds248342,
   Author = {Byington, T and Socolar, JES},
   Title = {Hierarchical freezing of limit-periodic structure},
   Journal = {Physical Review E},
   Year = {2012},
   Month = {November},
   Key = {fds248342}
}

@article{fds248340,
   Author = {Gong, X and Socolar, JES},
   Title = {Quantifying the complexity of random Boolean
             networks.},
   Journal = {Physical Review E - Statistical, Nonlinear, and Soft Matter
             Physics},
   Volume = {85},
   Number = {6 Pt 2},
   Pages = {066107},
   Year = {2012},
   Month = {June},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/23005162},
   Abstract = {We study two measures of the complexity of heterogeneous
             extended systems, taking random Boolean networks as
             prototypical cases. A measure defined by Shalizi et al. for
             cellular automata, based on a criterion for optimal
             statistical prediction [Shalizi et al., Phys. Rev. Lett. 93,
             118701 (2004)], does not distinguish between the spatial
             inhomogeneity of the ordered phase and the dynamical
             inhomogeneity of the disordered phase. A modification in
             which complexities of individual nodes are calculated yields
             vanishing complexity values for networks in the ordered and
             critical regimes and for highly disordered networks, peaking
             somewhere in the disordered regime. Individual nodes with
             high complexity are the ones that pass the most information
             from the past to the future, a quantity that depends in a
             nontrivial way on both the Boolean function of a given node
             and its location within the network.},
   Doi = {10.1103/PhysRevE.85.066107},
   Key = {fds248340}
}

@article{fds248347,
   Author = {Khalil, KS and Sagastegui, A and Li, Y and Tahir, MA and Socolar, JES and Wiley, BJ and Yellen, BB},
   Title = {Binary colloidal structures assembled through Ising
             interactions.},
   Journal = {Nature Communications},
   Volume = {3},
   Pages = {794},
   Year = {2012},
   Month = {April},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/22531179},
   Abstract = {New methods for inducing microscopic particles to assemble
             into useful macroscopic structures could open pathways for
             fabricating complex materials that cannot be produced by
             lithographic methods. Here we demonstrate a colloidal
             assembly technique that uses two parameters to tune the
             assembly of over 20 different pre-programmed structures,
             including kagome, honeycomb and square lattices, as well as
             various chain and ring configurations. We programme the
             assembled structures by controlling the relative
             concentrations and interaction strengths between spherical
             magnetic and non-magnetic beads, which behave as
             paramagnetic or diamagnetic dipoles when immersed in a
             ferrofluid. A comparison of our experimental observations
             with potential energy calculations suggests that the lowest
             energy configuration within binary mixtures is determined
             entirely by the relative dipole strengths and their relative
             concentrations.},
   Doi = {10.1038/ncomms1798},
   Key = {fds248347}
}

@article{fds248341,
   Author = {Durrett, R and Gleeson, JP and Lloyd, AL and Mucha, PJ and Shi, F and Sivakoff, D and Socolar, JES and Varghese, C},
   Title = {Graph fission in an evolving voter model.},
   Journal = {Proceedings of the National Academy of Sciences of
             USA},
   Volume = {109},
   Number = {10},
   Pages = {3682-3687},
   Year = {2012},
   Month = {March},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/22355142},
   Abstract = {We consider a simplified model of a social network in which
             individuals have one of two opinions (called 0 and 1) and
             their opinions and the network connections coevolve. Edges
             are picked at random. If the two connected individuals hold
             different opinions then, with probability 1 - α, one
             imitates the opinion of the other; otherwise (i.e., with
             probability α), the link between them is broken and one of
             them makes a new connection to an individual chosen at
             random (i) from those with the same opinion or (ii) from the
             network as a whole. The evolution of the system stops when
             there are no longer any discordant edges connecting
             individuals with different opinions. Letting ρ be the
             fraction of voters holding the minority opinion after the
             evolution stops, we are interested in how ρ depends on α
             and the initial fraction u of voters with opinion 1. In case
             (i), there is a critical value α(c) which does not depend
             on u, with ρ ≈ u for α > α(c) and ρ ≈ 0 for
             α < α(c). In case (ii), the transition point α(c)(u)
             depends on the initial density u. For α > α(c)(u),
             ρ ≈ u, but for α < α(c)(u), we have
             ρ(α,u) = ρ(α,1/2). Using simulations and approximate
             calculations, we explain why these two nearly identical
             models have such dramatically different phase
             transitions.},
   Doi = {10.1073/pnas.1200709109},
   Key = {fds248341}
}

@article{fds248343,
   Author = {Byington, TW and Socolar, JES},
   Title = {Hierarchical freezing in a lattice model.},
   Journal = {Physical Review Letters},
   Volume = {108},
   Number = {4},
   Pages = {045701},
   Year = {2012},
   Month = {January},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/22400863},
   Abstract = {A certain two-dimensional lattice model with nearest and
             next-nearest neighbor interactions is known to have a
             limit-periodic ground state. We show that during a slow
             quench from the high temperature, disordered phase, the
             ground state emerges through an infinite sequence of phase
             transitions. We define appropriate order parameters and show
             that the transitions are related by renormalizations of the
             temperature scale. As the temperature is decreased,
             sublattices with increasingly large lattice constants become
             ordered. A rapid quench results in a glasslike state due to
             kinetic barriers created by simultaneous freezing on
             sublattices with different lattice constants.},
   Doi = {10.1103/PhysRevLett.108.045701},
   Key = {fds248343}
}

@article{fds248331,
   Author = {Sun, M and Socolar, JES},
   Title = {Comparison of autonomous Boolean network dynamics and ODE
             models},
   Journal = {Chaos},
   Year = {2012},
   Key = {fds248331}
}

@article{fds248344,
   Author = {Socolar, JES and Taylor, JM},
   Title = {Forcing Nonperiodicity with a Single Tile},
   Journal = {The Mathematical Intelligencer},
   Volume = {34},
   Number = {1},
   Pages = {18-28},
   Year = {2012},
   Month = {Spring},
   ISSN = {0343-6993},
   url = {http://dx.doi.org/10.1007/s00283-011-9255-y},
   Abstract = {An aperiodic prototile is a shape for which infinitely many
             copies can be arranged to fill Euclidean space completely
             with no overlaps, but not in a periodic pattern. Tiling
             theorists refer to such a prototile as an "einstein" (a
             German pun on "one stone"). The possible existence of an
             einstein has been pondered ever since Berger's discovery of
             large set of prototiles that in combination can tile the
             plane only in a nonperiodic way. In this article we review
             and clarify some features of a prototile we recently
             introduced that is an einstein according to a reasonable
             definition.},
   Doi = {10.1007/s00283-011-9255-y},
   Key = {fds248344}
}

@article{fds248346,
   Author = {Cheng, X and Sun, M and Socolar, JES},
   Title = {Autonomous Boolean modelling of developmental gene
             regulatory networks},
   Journal = {J. Royal Soc. Interface},
   Volume = {10},
   Number = {78},
   Pages = {20120574},
   Year = {2012},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/23034351},
   Abstract = {During early embryonic development, a network of regulatory
             interactions among genes dynamically determines a pattern of
             differentiated tissues. We show that important timing
             information associated with the interactions can be
             faithfully represented in autonomous Boolean models in which
             binary variables representing expression levels are updated
             in continuous time, and that such models can provide a
             direct insight into features that are difficult to extract
             from ordinary differential equation (ODE) models. As an
             application, we model the experimentally well-studied
             network controlling fly body segmentation. The Boolean model
             successfully generates the patterns formed in normal and
             genetically perturbed fly embryos, permits the derivation of
             constraints on the time delay parameters, clarifies the
             logic associated with different ODE parameter sets and
             provides a platform for studying connectivity and robustness
             in parameter space. By elucidating the role of regulatory
             time delays in pattern formation, the results suggest new
             types of experimental measurements in early embryonic
             development.},
   Doi = {10.1098/​rsif.2012.0574},
   Key = {fds248346}
}

@article{fds248332,
   Author = {Socolar, JES},
   Title = {Local action, global impact: forcing nonperiodicity with a
             single structural unit.},
   Journal = {Chaos},
   Volume = {21},
   Number = {4},
   Pages = {041106},
   Year = {2011},
   Month = {December},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/22225336},
   Abstract = {This is a presentation, with explanation, of an image of a
             nonperiodic tiling whose structure is forced by local rules
             governing how nearest and next-nearest neighbors can
             align.},
   Doi = {10.1063/1.3668192},
   Key = {fds248332}
}

@article{Socolar:2011:AHT:2027468.2027502,
   Author = {Socolar, JES and Taylor, JM},
   Title = {An aperiodic hexagonal tile},
   Journal = {Journal of Combinatorial Theory, Series A},
   Volume = {118},
   Number = {8},
   Pages = {2207-2231},
   Publisher = {Academic Press, Inc.},
   Address = {Orlando, FL, USA},
   Year = {2011},
   ISSN = {0097-3165},
   url = {http://dx.doi.org/10.1016/j.jcta.2011.05.001},
   Keywords = {Aperiodic, Matching rules, Substitution,
             Tiling},
   Abstract = {We show that a single prototile can fill space uniformly but
             not admit a periodic tiling. A two-dimensional, hexagonal
             prototile with markings that enforce local matching rules is
             proven to be aperiodic by two independent methods. The
             space-filling tiling that can be built from copies of the
             prototile has the structure of a union of honeycombs with
             lattice constants of 2na, where a sets the scale of the most
             dense lattice and n takes all positive integer values. There
             are two local isomorphism classes consistent with the
             matching rules and there is a nontrivial relation between
             these tilings and a previous construction by Penrose.
             Alternative forms of the prototile enforce the local
             matching rules by shape alone, one using a prototile that is
             not a connected region and the other using a
             three-dimensional prototile. © 2011 Elsevier
             Inc.},
   Doi = {10.1016/j.jcta.2011.05.001},
   Key = {Socolar:2011:AHT:2027468.2027502}
}

@article{fds248334,
   Author = {Cavalcante, HLDDS and Gauthier, DJ and Socolar, JES and Zhang,
             R},
   Title = {On the origin of chaos in autonomous Boolean
             networks.},
   Journal = {Philosophical Transactions A},
   Volume = {368},
   Number = {1911},
   Pages = {495-513},
   Year = {2010},
   Month = {January},
   ISSN = {1364-503X},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/20008414},
   Abstract = {We undertake a systematic study of the dynamics of Boolean
             networks to determine the origin of chaos observed in recent
             experiments. Networks with nodes consisting of ideal logic
             gates are known to display either steady states, periodic
             behaviour or an ultraviolet catastrophe where the number of
             logic-transition events circulating in the network per unit
             time grows as a power law. In an experiment, the non-ideal
             behaviour of the logic gates prevents the ultraviolet
             catastrophe and may lead to deterministic chaos. We identify
             certain non-ideal features of real logic gates that enable
             chaos in experimental networks. We find that short-pulse
             rejection and asymmetry between the logic states tend to
             engender periodic behaviour, at least for the simplest
             networks. On the other hand, we find that a memory effect
             termed 'degradation' can generate chaos. Our results
             strongly suggest that deterministic chaos can be expected in
             a large class of experimental Boolean-like networks. Such
             devices may find application in a variety of technologies
             requiring fast complex waveforms or flat power spectra, and
             can be used as a test-bed for fundamental studies of
             real-world Boolean-like networks.},
   Doi = {10.1098/rsta.2009.0235},
   Key = {fds248334}
}

@article{fds248345,
   Author = {Sevim, V and Gong, X and Socolar, JES},
   Title = {Reliability of transcriptional cycles and the yeast
             cell-cycle oscillator.},
   Journal = {PLoS computational biology},
   Volume = {6},
   Number = {7},
   Pages = {e1000842},
   Year = {2010},
   ISSN = {1553-7358},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/20628620},
   Abstract = {A recently published transcriptional oscillator associated
             with the yeast cell cycle provides clues and raises
             questions about the mechanisms underlying autonomous cyclic
             processes in cells. Unlike other biological and synthetic
             oscillatory networks in the literature, this one does not
             seem to rely on a constitutive signal or positive
             auto-regulation, but rather to operate through stable
             transmission of a pulse on a slow positive feedback loop
             that determines its period. We construct a continuous-time
             Boolean model of this network, which permits the modeling of
             noise through small fluctuations in the timing of events,
             and show that it can sustain stable oscillations. Analysis
             of simpler network models shows how a few building blocks
             can be arranged to provide stability against fluctuations.
             Our findings suggest that the transcriptional oscillator in
             yeast belongs to a new class of biological
             oscillators.},
   Doi = {10.1371/journal.pcbi.1000842},
   Key = {fds248345}
}

@article{fds248335,
   Author = {Zhang, R and de S Cavalcante and HLD and Gao, Z and Gauthier, DJ and Socolar, JES and Adams, MM and Lathrop, DP},
   Title = {Boolean chaos.},
   Journal = {Physical Review E - Statistical, Nonlinear, and Soft Matter
             Physics},
   Volume = {80},
   Number = {4 Pt 2},
   Pages = {045202},
   Year = {2009},
   Month = {October},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/19905381},
   Abstract = {We observe deterministic chaos in a simple network of
             electronic logic gates that are not regulated by a clocking
             signal. The resulting power spectrum is ultrawide band,
             extending from dc to beyond 2 GHz. The observed behavior is
             reproduced qualitatively using an autonomously updating
             Boolean model with signal propagation times that depend on
             the recent history of the gates and filtering of pulses of
             short duration, whose presence is confirmed experimentally.
             Electronic Boolean chaos may find application as an
             ultrawide-band source of radio waves.},
   Doi = {10.1103/PhysRevE.80.045202},
   Key = {fds248335}
}

@article{fds248336,
   Author = {Norrell, J and Socolar, JE},
   Title = {Boolean modeling of collective effects in complex
             networks.},
   Journal = {Physical Review E - Statistical, Nonlinear, and Soft Matter
             Physics},
   Volume = {79},
   Number = {6},
   Pages = {nihpa131303},
   Year = {2009},
   Month = {June},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/19649269},
   Abstract = {Complex systems are often modeled as Boolean networks in
             attempts to capture their logical structure and reveal its
             dynamical consequences. Approximating the dynamics of
             continuous variables by discrete values and Boolean logic
             gates may, however, introduce dynamical possibilities that
             are not accessible to the original system. We show that
             large random networks of variables coupled through
             continuous transfer functions often fail to exhibit the
             complex dynamics of corresponding Boolean models in the
             disordered (chaotic) regime, even when each individual
             function appears to be a good candidate for Boolean
             idealization. A suitably modified Boolean theory explains
             the behavior of systems in which information does not
             propagate faithfully down certain chains of nodes. Model
             networks incorporating calculated or directly measured
             transfer functions reported in the literature on
             transcriptional regulation of genes are described by the
             modified theory.},
   Doi = {10.1103/PhysRevE.79.061908},
   Key = {fds248336}
}

@article{fds248339,
   Author = {Orlando, DA and Lin, CY and Bernard, A and Wang, JY and Socolar, JES and Iversen, ES and Hartemink, AJ and Haase, SB},
   Title = {Global control of cell-cycle transcription by coupled CDK
             and network oscillators.},
   Journal = {Nature},
   Volume = {453},
   Number = {7197},
   Pages = {944-947},
   Year = {2008},
   Month = {June},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/18463633},
   Abstract = {A significant fraction of the Saccharomyces cerevisiae
             genome is transcribed periodically during the cell division
             cycle, indicating that properly timed gene expression is
             important for regulating cell-cycle events. Genomic analyses
             of the localization and expression dynamics of transcription
             factors suggest that a network of sequentially expressed
             transcription factors could control the temporal programme
             of transcription during the cell cycle. However, directed
             studies interrogating small numbers of genes indicate that
             their periodic transcription is governed by the activity of
             cyclin-dependent kinases (CDKs). To determine the extent to
             which the global cell-cycle transcription programme is
             controlled by cyclin-CDK complexes, we examined genome-wide
             transcription dynamics in budding yeast mutant cells that do
             not express S-phase and mitotic cyclins. Here we show that a
             significant fraction of periodic genes are aberrantly
             expressed in the cyclin mutant. Although cells lacking
             cyclins are blocked at the G1/S border, nearly 70% of
             periodic genes continued to be expressed periodically and on
             schedule. Our findings reveal that although CDKs have a
             function in the regulation of cell-cycle transcription, they
             are not solely responsible for establishing the global
             periodic transcription programme. We propose that periodic
             transcription is an emergent property of a transcription
             factor network that can function as a cell-cycle oscillator
             independently of, and in tandem with, the CDK
             oscillator.},
   Doi = {10.1038/nature06955},
   Key = {fds248339}
}

@article{fds248314,
   Author = {Socolar, JES},
   Title = {Time-Delay Control for Discrete Maps},
   Pages = {29-45},
   Year = {2008},
   Month = {May},
   url = {http://dx.doi.org/10.1002/9783527622313.ch2},
   Abstract = {This chapter is intended as a pedagogical introduction to
             discrete time delayed feedback methods. It is neither a
             comprehensive review, nor a presentation of dramatic new
             results. It does, on the other hand, organize known results
             in a self-contained manner that emphasizes the conceptual
             points that have proven to be important, where much of the
             original literature focuses on historically important points
             and rigorous mathematical proofs. The present work also
             contains examples and one generalization that have not
             appeared elsewhere. The goal is to provide a conceptual
             foundation for readers who wonder whether discrete time
             delay feedback methods are up to the task they have in mind.
             Since the study of discrete methods foreshadows many (but
             not all!) of the important questions that arise in studies
             of continuous versions of delayed feedback control, the
             present chapter may also serve as a useful prequel to
             chapters on continuous methods. © 2008 Wiley-VCH Verlag
             GmbH & Co. KGaA.},
   Doi = {10.1002/9783527622313.ch2},
   Key = {fds248314}
}

@article{fds145241,
   Author = {D.A. Orlando and C.Y. Lin and A. Bernard and J.Y. Wang and J.E.S.
             Socolar, E.S. Iversen and A.J. Hartemink and S.B.
             Haase},
   Title = {Global control of cell-cycle transcription by coupled CDK
             and network oscillators},
   Journal = {Nature},
   Year = {2008},
   Month = {May},
   url = {http://dx.doi.org/doi:10.1038/nature06955},
   Doi = {doi:10.1038/nature06955},
   Key = {fds145241}
}

@article{fds248337,
   Author = {Tighe, BP and Socolar, JES},
   Title = {Nonlinear elastic stress response in granular
             packings.},
   Journal = {Physical Review E - Statistical, Nonlinear, and Soft Matter
             Physics},
   Volume = {77},
   Number = {3 Pt 1},
   Pages = {031303},
   Year = {2008},
   Month = {March},
   ISSN = {1539-3755},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/18517366},
   Abstract = {We study the nonlinear elastic response of a two-dimensional
             material to a localized boundary force, with the particular
             goal of understanding the differences observed between
             isotropic granular materials and those with hexagonal
             anisotropy. Corrections to the classical Boussinesq result
             for the stresses in an infinite half space of a linear,
             isotropic material are developed in a power series in
             inverse distance from the point of application of the force.
             The breakdown of continuum theory on scales of order of the
             grain size is modeled with phenomenological parameters
             characterizing the strengths of induced multipoles near the
             point of application of the external force. We find that the
             data of Geng [Phys. Rev. Lett. 87, 035506 (2001)] on
             isotropic and hexagonal packings of photoelastic grains can
             be fitted within this framework. Fitting the hexagonal
             packings requires a choice of elastic coefficients with
             hexagonal anisotropy stronger than that of a simple
             ball-and-spring model. For both the isotropic and hexagonal
             cases, induced dipole and quadrupole terms produce
             propagation of stresses away from the vertical direction
             over short distances. The scale over which such propagation
             occurs is significantly enhanced by the nonlinearities that
             generate hexagonal anisotropy.},
   Doi = {10.1103/PhysRevE.77.031303},
   Key = {fds248337}
}

@article{fds248338,
   Author = {Ribeiro, AS and Kauffman, SA and Lloyd-Price, J and Samuelsson, B and Socolar, JES},
   Title = {Mutual information in random Boolean models of regulatory
             networks.},
   Journal = {Physical Review E - Statistical, Nonlinear, and Soft Matter
             Physics},
   Volume = {77},
   Number = {1 Pt 1},
   Pages = {011901},
   Year = {2008},
   Month = {January},
   ISSN = {1539-3755},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/18351870},
   Abstract = {The amount of mutual information contained in the time
             series of two elements gives a measure of how well their
             activities are coordinated. In a large, complex network of
             interacting elements, such as a genetic regulatory network
             within a cell, the average of the mutual information over
             all pairs, <I>, is a global measure of how well the system
             can coordinate its internal dynamics. We study this average
             pairwise mutual information in random Boolean networks
             (RBNs) as a function of the distribution of Boolean rules
             implemented at each element, assuming that the links in the
             network are randomly placed. Efficient numerical methods for
             calculating <I> show that as the number of network nodes, N,
             approaches infinity, the quantity N<I> exhibits a
             discontinuity at parameter values corresponding to critical
             RBNs. For finite systems it peaks near the critical value,
             but slightly in the disordered regime for typical parameter
             variations. The source of high values of N<I> is the
             indirect correlations between pairs of elements from
             different long chains with a common starting point. The
             contribution from pairs that are directly linked approaches
             zero for critical networks and peaks deep in the disordered
             regime.},
   Doi = {10.1103/PhysRevE.77.011901},
   Key = {fds248338}
}

@inbook{fds70496,
   Author = {J.E.S. Socolar},
   Title = {Time-delay control for discrete maps},
   Booktitle = {Handbook of Chaos Control},
   Publisher = {Wiley-VCH Verlag GmbH},
   Editor = {E. Scholl and H. G. Schuster},
   Year = {2007},
   Month = {December},
   url = {http://www.wiley.com/WileyCDA/WileyTitle/productCd-3527406050,descCd-tableOfContents.html},
   Abstract = {A pedagogical introduction to discrete time-delayed feedback
             methods. It is neither a comprehensive review, nor a
             presentation of dramatic new results. It does, on the other
             hand, organize known results in a self-contained manner that
             emphasizes the conceptual points that have proven to be
             important, where much of the original literature focuses on
             historically important points and rigorous mathematical
             proofs. The present work also contains examples and one
             generalization that have not appeared elsewhere.},
   Key = {fds70496}
}

@article{fds248349,
   Author = {Norrell, J and Samuelsson, B and Socolar, JES},
   Title = {Attractors in continuous and Boolean networks.},
   Journal = {Physical Review E - Statistical, Nonlinear, and Soft Matter
             Physics},
   Volume = {76},
   Number = {4 Pt 2},
   Pages = {046122},
   Year = {2007},
   Month = {October},
   ISSN = {1539-3755},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/17995075},
   Abstract = {We study the stable attractors of a class of continuous
             dynamical systems that may be idealized as networks of
             Boolean elements, with the goal of determining which Boolean
             attractors, if any, are good approximations of the
             attractors of generic continuous systems. We investigate the
             dynamics in simple rings and rings with one additional
             self-input. An analysis of switching characteristics and
             pulse propagation explains the relation between attractors
             of the continuous systems and their Boolean approximations.
             For simple rings, "reliable" Boolean attractors correspond
             to stable continuous attractors. For networks with more
             complex logic, the qualitative features of continuous
             attractors are influenced by inherently non-Boolean
             characteristics of switching events.},
   Doi = {10.1103/PhysRevE.76.046122},
   Key = {fds248349}
}

@article{fds248351,
   Author = {Berger, CM and Cain, JW and Socolar, JES and Gauthier,
             DJ},
   Title = {Control of electrical alternans in simulations of paced
             myocardium using extended time-delay autosynchronization.},
   Journal = {Physical Review E - Statistical, Nonlinear, and Soft Matter
             Physics},
   Volume = {76},
   Number = {4 Pt 1},
   Pages = {041917},
   Year = {2007},
   Month = {October},
   ISSN = {1539-3755},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/17995036},
   Abstract = {Experimental studies have linked alternans, an abnormal
             beat-to-beat alternation of cardiac action potential
             duration, to the genesis of lethal arrhythmias such as
             ventricular fibrillation. Prior studies have considered
             various closed-loop feedback control algorithms for
             perturbing interstimulus intervals in such a way that
             alternans is suppressed. However, some experimental cases
             are restricted in that the controller's stimuli must preempt
             those of the existing waves that are propagating in the
             tissue, and therefore only shortening perturbations to the
             underlying pacing are allowed. We present results
             demonstrating that a technique known as extended time-delay
             autosynchronization (ETDAS) can effectively control
             alternans locally while operating within the above
             constraints. We show that ETDAS, which has already been used
             to control chaos in physical systems, has numerous
             advantages over previously proposed alternans control
             schemes.},
   Doi = {10.1103/PhysRevE.76.041917},
   Key = {fds248351}
}

@article{fds248348,
   Author = {Shreim, A and Grassberger, P and Nadler, W and Samuelsson, B and Socolar, JES and Paczuski, M},
   Title = {Network analysis of the state space of discrete dynamical
             systems.},
   Journal = {Physical Review Letters},
   Volume = {98},
   Number = {19},
   Pages = {198701},
   Year = {2007},
   Month = {May},
   ISSN = {0031-9007},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/17677672},
   Abstract = {We study networks representing the dynamics of elementary 1D
             cellular automata (CA) on finite lattices. We analyze
             scaling behaviors of both local and global network
             properties as a function of system size. The scaling of the
             largest node in-degree is obtained analytically for a
             variety of CA including rules 22, 54, and 110. We further
             define the path diversity as a global network measure. The
             coappearance of nontrivial scaling in both the hub size and
             the path diversity separates simple dynamics from the more
             complex behaviors typically found in Wolfram's class IV and
             some class III CA.},
   Doi = {10.1103/PhysRevLett.98.198701},
   Key = {fds248348}
}

@article{fds248328,
   Author = {Socolar, JES},
   Title = {Erratum: The hexagonal parquet tiling, k-isohedral monotiles
             with arbitrarily large k (The Mathematical Intelligencer
             29:2 (33-38))},
   Journal = {The Mathematical Intelligencer},
   Volume = {29},
   Number = {4},
   Pages = {6-},
   Year = {2007},
   ISSN = {0343-6993},
   url = {http://dx.doi.org/10.1007/BF02986167},
   Doi = {10.1007/BF02986167},
   Key = {fds248328}
}

@article{fds248350,
   Author = {Socolar, JES},
   Title = {The hexagonal parquet tiling k-isohedral monotiles with
             arbitrarily large k},
   Journal = {The Mathematical Intelligencer},
   Volume = {29},
   Number = {2},
   Pages = {33-38},
   Year = {2007},
   ISSN = {0343-6993},
   url = {http://www.phy.duke.edu/~socolar/hexparquet.pdf},
   Abstract = {The interplay between local constraints and global structure
             of mathematical and physical systems is both subtle and
             important. This paper shows how to construct a single tile
             that can fill the Euclidean plane only with a tiling that
             contains k distinct isohedral sets of tiles, where k can be
             made arbitrarily large. It is shown that the construction
             cannot work for a simply connected 2D tile with matching
             rules for adjacent tiles enforced by shape alone. It is also
             shown that any of the following modifications allows the
             construction to work: (1) coloring the edges of the tiling
             and imposing rules on which colors can touch; (2) allowing
             the tile to be multiply connected; (3) requiring maximum
             density rather than space-filling; (4) allowing the tile to
             have a thickness in the third dimension.},
   Doi = {10.1007/BF02986203},
   Key = {fds248350}
}

@article{fds248352,
   Author = {Foster, DV and Kauffman, SA and Socolar, JES},
   Title = {Network growth models and genetic regulatory
             networks.},
   Journal = {Physical Review E - Statistical, Nonlinear, and Soft Matter
             Physics},
   Volume = {73},
   Number = {3 Pt 1},
   Pages = {031912},
   Year = {2006},
   Month = {March},
   ISSN = {1539-3755},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/16605563},
   Abstract = {We study a class of growth algorithms for directed graphs
             that are candidate models for the evolution of genetic
             regulatory networks. The algorithms involve partial
             duplication of nodes and their links, together with the
             innovation of new links, allowing for the possibility that
             input and output links from a newly created node may have
             different probabilities of survival. We find some
             counterintuitive trends as the parameters are varied,
             including the broadening of the in-degree distribution when
             the probability for retaining input links is decreased. We
             also find that both the scaling of transcription factors
             with genome size and the measured degree distributions for
             genes in yeast can be reproduced by the growth algorithm if
             and only if a special seed is used to initiate the
             process.},
   Doi = {10.1103/PhysRevE.73.031912},
   Key = {fds248352}
}

@inbook{fds26115,
   Author = {J.E.S. Socolar},
   Title = {Nonlinear Dynamical Systems},
   Booktitle = {Complex Systems Science and Biomedicine},
   Publisher = {Kluwer},
   Editor = {Deisboeck and Kresh},
   Year = {2006},
   Month = {February},
   Key = {fds26115}
}

@article{fds248353,
   Author = {Samuelsson, B and Socolar, JES},
   Title = {Exhaustive percolation on random networks},
   Journal = {Physical Review E - Statistical, Nonlinear, and Soft Matter
             Physics},
   Volume = {74},
   Number = {3},
   Pages = {031912},
   Year = {2006},
   ISSN = {1539-3755},
   url = {http://link.aps.org/abstract/PRE/v74/e036113},
   Abstract = {We consider propagation models that describe the spreading
             of an attribute, called "damage," through the nodes of a
             random network. In some systems, the average fraction of
             nodes that remain undamaged vanishes in the large system
             limit, a phenomenon we refer to as exhaustive percolation.
             We derive scaling law exponents and exact results for the
             distribution of the number of undamaged nodes, valid for a
             broad class of random networks at the exhaustive percolation
             transition and in the exhaustive percolation regime. This
             class includes processes that determine the set of frozen
             nodes in random Boolean networks with in-degree
             distributions that decay sufficiently rapidly with the
             number of inputs. Connections between our calculational
             methods and previous studies of percolation beginning from a
             single initial node are also pointed out. Central to our
             approach is the observation that key aspects of damage
             spreading on a random network are fully characterized by a
             single function, specifying the probability that a given
             node will be damaged as a function of the fraction of
             damaged nodes. In addition to our analytical investigations
             of random networks, we present a numerical example of
             exhaustive percolation on a directed lattice. © 2006 The
             American Physical Society.},
   Doi = {10.1103/PhysRevE.74.036113},
   Key = {fds248353}
}

@article{fds248355,
   Author = {Tighe, BP and Socolar, JES and Schaeffer, DG and Mitchener, WG and Huber, ML},
   Title = {Force distributions in a triangular lattice of rigid
             bars.},
   Journal = {Physical Review E - Statistical, Nonlinear, and Soft Matter
             Physics},
   Volume = {72},
   Number = {3 Pt 1},
   Pages = {031306},
   Year = {2005},
   Month = {September},
   ISSN = {1539-3755},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/16241425},
   Abstract = {We study the uniformly weighted ensemble of force balanced
             configurations on a triangular network of nontensile contact
             forces. For periodic boundary conditions corresponding to
             isotropic compressive stress, we find that the probability
             distribution for single-contact forces decays faster than
             exponentially. This superexponential decay persists in
             lattices diluted to the rigidity percolation threshold. On
             the other hand, for anisotropic imposed stresses, a broader
             tail emerges in the force distribution, becoming a pure
             exponential in the limit of infinite lattice size and
             infinitely strong anisotropy.},
   Doi = {10.1103/PhysRevE.72.031306},
   Key = {fds248355}
}

@article{fds248354,
   Author = {Dealy, S and Kauffman, S and Socolar, J},
   Title = {Modeling pathways of differentiation in genetic regulatory
             networks with Boolean networks},
   Journal = {Complexity},
   Volume = {11},
   Number = {1},
   Pages = {52-60},
   Year = {2005},
   ISSN = {1076-2787},
   url = {http://dx.doi.org/10.1002/cplx.20100},
   Abstract = {We have carried out the first examination of pathways of
             cell differentiation in model genetic networks in which cell
             types are assumed to be attractors of the nonlinear
             dynamics, and differentiation corresponds to a transition of
             the cell to a new basin of attraction, which may be induced
             by a signal or noise perturbation. The associated flow along
             a transient to a new attractor corresponds to a pathway of
             differentiation. We have measured a variety of features of
             such model pathways of differentiation, most of which should
             be observable using gene array techniques. © 2005 Wiley
             Periodicals, Inc.},
   Doi = {10.1002/cplx.20100},
   Key = {fds248354}
}

@article{fds248377,
   Author = {Harrington, I and Socolar, JES},
   Title = {Design and robustness of delayed feedback controllers for
             discrete systems},
   Journal = {Phys. Rev. E},
   Volume = {69},
   Number = {5 1},
   Pages = {56207},
   Year = {2004},
   ISSN = {1539-3755},
   Abstract = {A matrix form of time-delay feedback control in the context
             of discrete time maps of high dimension was studied.
             Time-delay feedback controllers containing only static
             elements can be designed to achieve identical linear
             stability properties, in almost all cases where standard
             proportional feedback control methods can achieve control.
             This control was a generalization of a method called
             'extended time-delay autosynchronization' (ETDAS). Analysis
             of an example involving a ring of coupled maps that can be
             controlled at only two sites demonstrated that the
             time-delay controller equivalent to a standard optimal
             controller can be equally robust in the presence of
             noise.},
   Key = {fds248377}
}

@article{fds304615,
   Author = {Harrington, I and Socolar, JES},
   Title = {Design and robustness of delayed feedback controllers for
             discrete systems},
   Journal = {Physical Review E - Statistical, Nonlinear, and Soft Matter
             Physics},
   Volume = {69},
   Number = {5 1},
   Pages = {056207-1-056207-8},
   Year = {2004},
   ISSN = {1539-3755},
   Abstract = {A matrix form of time-delay feedback control in the context
             of discrete time maps of high dimension was studied.
             Time-delay feedback controllers containing only static
             elements can be designed to achieve identical linear
             stability properties, in almost all cases where standard
             proportional feedback control methods can achieve control.
             This control was a generalization of a method called
             'extended time-delay autosynchronization' (ETDAS). Analysis
             of an example involving a ring of coupled maps that can be
             controlled at only two sites demonstrated that the
             time-delay controller equivalent to a standard optimal
             controller can be equally robust in the presence of
             noise.},
   Key = {fds304615}
}

@article{fds248378,
   Author = {Hövel, P and Socolar, JES},
   Title = {Stability domains for time-delay feedback control with
             latency.},
   Journal = {Physical Review E - Statistical, Nonlinear, and Soft Matter
             Physics},
   Volume = {68},
   Number = {3 Pt 2},
   Pages = {036206},
   Year = {2003},
   Month = {September},
   ISSN = {1539-3755},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/14524867},
   Abstract = {We generalize a known analytical method for determining the
             stability of periodic orbits controlled by time-delay
             feedback methods when latencies associated with the
             generation and injection of the feedback signal cannot be
             ignored. We discuss the case of extended time-delay
             autosynchronization and show that nontrivial qualitative
             features of the domain of control observed in experiments
             can be explained by taking into account the effects of both
             the unstable eigenmode and a single stable eigenmode in the
             Floquet theory.},
   Doi = {10.1103/PhysRevE.68.036206},
   Key = {fds248378}
}

@article{fds248386,
   Author = {Socolar, JES and Kauffman, SA},
   Title = {Scaling in ordered and critical random boolean
             networks.},
   Journal = {Physical Review Letters},
   Volume = {90},
   Number = {6},
   Pages = {068702},
   Year = {2003},
   Month = {February},
   ISSN = {0031-9007},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/12633339},
   Abstract = {Random Boolean networks, originally invented as models of
             genetic regulatory networks, are simple models for a broad
             class of complex systems that show rich dynamical
             structures. From a biological perspective, the most
             interesting networks lie at or near a critical point in
             parameter space that divides "ordered" from "chaotic"
             attractor dynamics. We study the scaling of the average
             number of dynamically relevant nodes and the median number
             of distinct attractors in such networks. Our calculations
             indicate that the correct asymptotic scalings emerge only
             for very large systems.},
   Doi = {10.1103/PhysRevLett.90.068702},
   Key = {fds248386}
}

@article{fds318470,
   Author = {Hövel, P and Socolar, JES},
   Title = {Stability domains for time-delay feedback control with
             latency},
   Journal = {Physical Review E - Statistical Physics, Plasmas, Fluids,
             and Related Interdisciplinary Topics},
   Volume = {68},
   Number = {3 2},
   Pages = {362061-362067},
   Year = {2003},
   Abstract = {The stability of periodic orbits controlled by time-delay
             feedback methods with latency was determined. Floquet theory
             and first order theory were used to derive nonlinear shapes
             from parametrized plane. It was found that Floquet modes,
             that contributed significantly to the overall stability
             picture, reduced the domain control substantially.},
   Key = {fds318470}
}

@article{fds248326,
   Author = {Otto, M and Bouchaud, J-P and Claudin, P and Socolar,
             JES},
   Title = {Anisotropy in granular media: Classical elasticity and
             directed-force chain network},
   Journal = {Physical Review E - Statistical Physics, Plasmas, Fluids,
             and Related Interdisciplinary Topics},
   Volume = {67},
   Number = {3 1},
   Pages = {031302/1-031302/24},
   Year = {2003},
   ISSN = {1063-651X},
   url = {http://arxiv.org/abs/cond-mat/0211015v2},
   Abstract = {A general framework that covers both classical anisotropic
             elasticity theory and a generally anisotropic
             "pseudoelasticity" theory, that appears within a linearized
             treatment of directed-force chain networks is presented. It
             is shown how the formalism applies to the example of a
             triangular ball-and-spring network, indicating how spring
             stiffnesses must be chosen to access all possible regions of
             the general parameter space.},
   Doi = {10.1103/PhysRevE.67.031302},
   Key = {fds248326}
}

@article{fds248385,
   Author = {Socolar, JES},
   Title = {Discrete models of force chain networks},
   Journal = {Discrete and Continuous Dynamical Systems - Series
             B},
   Volume = {3},
   Number = {4},
   Pages = {601-618},
   Year = {2003},
   ISSN = {1531-3492},
   url = {http://xxx.lanl.gov/abs/cond-mat/0212162},
   Abstract = {A fundamental property of any material is its response to a
             localized stress applied at a boundary. For granular
             materials consisting of hard, cohesionless particles, not
             even the general form of the stress response is known.
             Directed force chain networks (DFCNs) provide a theoretical
             frame-work for addressing this issue, and analysis of
             simplified DFCN models reveal both rich mathematical
             structure and surprising properties. We review some basic
             elements of DFCN models and present a class of homogeneous
             solutions for cases in which force chains are restricted to
             lie on a discrete set of directions.},
   Key = {fds248385}
}

@article{fds324423,
   Author = {Socolar, JES and Schaeffer, DG and Claudin, P},
   Title = {Erratum to: Directed force chain networks and stress
             response in static granular materials},
   Journal = {The European Physical Journal E - Soft Matter and Biological
             Physics},
   Volume = {8},
   Number = {4},
   Pages = {453-453},
   Year = {2002},
   Month = {July},
   url = {http://dx.doi.org/10.1140/epje/i2002-10030-4},
   Doi = {10.1140/epje/i2002-10030-4},
   Key = {fds324423}
}

@article{fds248323,
   Author = {Socolar, JES and Schaeffer, DG and Claudin, P},
   Title = {Erratum: Directed force chain networks and stress response
             in static granular materials (The European Physical Journal
             E (2002) 7 (353-370))},
   Journal = {European Physical Journal E},
   Volume = {8},
   Number = {4},
   Pages = {453-},
   Year = {2002},
   Key = {fds248323}
}

@article{fds248389,
   Author = {Socolar, JES and Schaeffer, DG and Claudin, P},
   Title = {Directed force chain networks and stress response in static
             granular materials},
   Journal = {European Physical Journal E},
   Volume = {7},
   Number = {4},
   Pages = {353-370},
   Year = {2002},
   url = {http://xxx.lanl.gov/abs/cond-mat/0201242},
   Abstract = {A theory of stress fields in two-dimensional granular
             materials based on directed force chain networks is
             presented. A general Boltzmann equation for the densities of
             force chains in different directions is proposed and a
             complete solution is obtained for a special case in which
             chains lie along a discrete set of directions. The analysis
             and results demonstrate the necessity of including nonlinear
             terms in the Boltzmann equation. A line of nontrivial
             fixed-point solutions is shown to govern the properties of
             large systems. In the vicinity of a generic fixed point, the
             response to a localized load shows a crossover from a
             single, centered peak at intermediate depths to two
             propagating peaks at large depths that broaden
             diffusively.},
   Key = {fds248389}
}

@article{fds304614,
   Author = {Beck, O and Amann, A and Schöll, E and Socolar, JES and Just,
             W},
   Title = {Comparison of time-delayed feedback schemes for
             spatiotemporal control of chaos in a reaction-diffusion
             system with global coupling},
   Journal = {Physical Review E - Statistical, Nonlinear, and Soft Matter
             Physics},
   Volume = {66},
   Number = {1},
   Pages = {016213/1-016213/6},
   Year = {2002},
   ISSN = {1539-3755},
   url = {http://dx.doi.org/10.1103/PhysRevE.66.016213},
   Abstract = {Time-delayed feedback control for stabilizing time periodic
             spatial patterns is investigated in a generic
             reaction-diffusion system with global coupling. We focus on
             the case of low-dimensional chaos where unstable patterns
             admit only a single unstable mode. Spatial degrees of
             freedom are taken into account to define different control
             schemes. The efficiency of these schemes is discussed, where
             control forces are motivated by physical requirements as
             well as by the possibility of obtaining analytically exact
             results. We find that control schemes that contain the full
             feedback of the inhibitor variable may finally destroy the
             control performance. Thus schemes that omit the inhibitor
             might be more efficient. Our numerical findings are
             explained in terms of Floquet spectra and compared with
             analytical solutions of particular coupling schemes. © 2002
             The American Physical Society.},
   Doi = {10.1103/PhysRevE.66.016213},
   Key = {fds304614}
}

@article{fds248383,
   Author = {Harrington, I and Socolar, JE},
   Title = {Limitation on stabilizing plane waves via time-delay
             feedback.},
   Journal = {Physical Review E - Statistical, Nonlinear, and Soft Matter
             Physics},
   Volume = {64},
   Number = {5 Pt 2},
   Pages = {056206},
   Year = {2001},
   Month = {November},
   ISSN = {1539-3755},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/11736053},
   Abstract = {Previous work has demonstrated the possibility of
             stabilizing plane wave solutions of one-dimensional systems
             using a spatially local form of time-delayed feedback. We
             show that the natural extension of this method to
             two-dimensional systems fails due to the presence of
             torsion-free unstable perturbations. Linear stability
             analysis of the complex Ginzburg-Landau equation reveals
             that long wavelength, transverse wave instabilities cannot
             be suppressed by the method of extended time-delay
             autosynchronization. The conclusion follows from symmetry
             considerations and therefore applies to a wide class of
             models with simple plane wave solutions.},
   Doi = {10.1103/PhysRevE.64.056206},
   Key = {fds248383}
}

@article{fds3758,
   Author = {J.E.S Socolar},
   Title = {Chaos},
   Series = {3rd Edition},
   Booktitle = {Encyclopedia of Physical Science and Technology},
   Publisher = {Academic Press},
   Editor = {R. Meyers},
   Year = {2001},
   Key = {fds3758}
}

@article{fds248322,
   Author = {Socolar, JES and Richards, S and Wilson, WG},
   Title = {Evolution in a spatially structured population subject to
             rare epidemics},
   Journal = {Physical Review E - Statistical, Nonlinear, and Soft Matter
             Physics},
   Volume = {63},
   Number = {4 I},
   Pages = {419081-419088},
   Year = {2001},
   Abstract = {A model that gave rise to inhomogenous population densities
             in a system of host individuals was studied. The model
             consisted of rules of reproduction, and natural death.
             Behavior observed in simulations of a one-dimensional system
             was accounted by a mean-field analysis, were the stable
             state corresponded to the solution of straightforward
             optimization problem.},
   Key = {fds248322}
}

@article{fds248382,
   Author = {Bleich, ME and Socolar, JES},
   Title = {Delayed feedback control of a paced excitable
             oscillator},
   Journal = {International Journal of Bifurcation and Chaos in Applied
             Sciences and Engineering},
   Volume = {10},
   Number = {3},
   Pages = {603-609},
   Year = {2000},
   Abstract = {A simple numerical experiment on Fitzhugh-Nagumo equations
             demonstrates that time-delay feedback methods can stabilize
             regular behavior in a paced, excitable oscillator without
             using large applied pulses. The method is robust against
             slow variations in the pacing rate and can be used to track
             an orbit into a parameter regime where it is unstable.
             Moreover, the method requires no information about the
             desired orbit other than period, which is determined
             directly by the observation of the pacing signal. Results
             are presented for feedback stabilization of a nonspiking
             orbit in the rapid pacing regime.},
   Key = {fds248382}
}

@article{fds248388,
   Author = {Richards, SA and Wilson, WG and Socolar, JE},
   Title = {Selection for intermediate mortality and reproduction rates
             in a spatially structured population.},
   Journal = {Proceedings of the Royal Society of London: Biological
             Sciences},
   Volume = {266},
   Number = {1436},
   Pages = {2383-2388},
   Year = {1999},
   Month = {December},
   ISSN = {0962-8452},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/10643082},
   Abstract = {How local interactions influence both population and
             evolutionary dynamics is currently a key topic in
             theoretical ecology. We use a 'well-mixed' analytical model
             and spatially explicit individual-based models to
             investigate a system where a population is subject to rare
             disturbance events. The disturbance can only propagate
             through regions of the population where the density of
             individuals is sufficiently high and individuals affected by
             the disturbance die shortly after. We find that populations
             where individuals are sessile often exhibit very different
             dynamic behaviour when compared to populations where
             individuals are mobile and spatially well mixed. When
             mutations are allowed which affect either offspring birth
             rates or mortality rates, the well-mixed populations always
             evolve to a state where a single disturbance event leads to
             extinction. Populations often persist substantially longer
             if individuals are sessile and they disperse their offspring
             locally. We also find that for sessile populations selection
             may favour short-lived individuals with limited offspring
             production. Population dynamics are found to be strongly
             influenced by the host characters that are evolving and the
             rate at which host variation is introduced into the
             system.},
   Doi = {10.1098/rspb.1999.0935},
   Key = {fds248388}
}

@article{fds248381,
   Author = {Sexton, MG and Socolar, JE and Schaeffer, DG},
   Title = {Force distribution in a scalar model for noncohesive
             granular material.},
   Journal = {Physical Review E - Statistical Physics, Plasmas, Fluids,
             and Related Interdisciplinary Topics},
   Volume = {60},
   Number = {2 Pt B},
   Pages = {1999-2008},
   Year = {1999},
   Month = {August},
   ISSN = {1063-651X},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/11969992},
   Abstract = {We study a scalar lattice model for intergrain forces in
             static, noncohesive, granular materials, obtaining two
             primary results: (i) The applied stress as a function of
             overall strain shows a power law dependence with a
             nontrivial exponent, which moreover varies with system
             geometry; and (ii) probability distributions for forces on
             individual grains appear Gaussian at all stages of
             compression, showing no evidence of exponential tails. With
             regard to both results, we identify correlations responsible
             for deviations from previously suggested
             theories.},
   Key = {fds248381}
}

@article{fds248379,
   Author = {Egolf, DA and Socolar, JES},
   Title = {Failure of linear control in noisy coupled map
             lattices},
   Journal = {Physical Review E - Statistical Physics, Plasmas, Fluids,
             and Related Interdisciplinary Topics},
   Volume = {57},
   Number = {5 SUPPL. A},
   Pages = {5271-5275},
   Year = {1998},
   Abstract = {We study a one-dimensional ring of diffusively coupled
             logistic maps in the vicinity of an unstable, spatially
             homogeneous fixed point. The failure of linear controllers
             due to additive noise is discussed with the aim of
             clarifying the failure mechanism. A criterion is suggested
             for estimating the noise level that can be tolerated by the
             given controller. The criterion implies the loss of control
             for surprisingly low noise levels in certain cases of
             interest, and accurately accounts for the results of
             numerical experiments over a broad range of parameter
             values. Previous results of Grigoriev et al. [Phys. Rev.
             Lett. 79, 2795 (1997)] are reviewed and compared with our
             numerical and analytic results.},
   Key = {fds248379}
}

@article{fds248380,
   Author = {Socolar, JES and Gauthier, DJ},
   Title = {Analysis and comparison of multiple-delay schemes for
             controlling unstable fixed points of discrete
             maps},
   Journal = {Physical Review E - Statistical Physics, Plasmas, Fluids,
             and Related Interdisciplinary Topics},
   Volume = {57},
   Number = {6},
   Pages = {6589-6595},
   Year = {1998},
   Abstract = {We investigate theoretically the stabilization of a fixed
             point of a discrete one-dimensional nonlinear map by
             applying small perturbations to an accessible system
             parameter or variable. The size of the perturbations is
             determined in real time using feedback schemes incorporating
             only the dynamical state of the system and its state at
             previous iterates without making a comparison to a reference
             state. In particular, we compare and contrast two
             algorithms: extended time-delay autosynchronization, which
             uses an infinite series of past iterates with weights that
             decay by a factor of R with each time step, and N-time-delay
             autosynchronization, which uses an average of N past
             iterates with equal weights. The range of feedback
             parameters that successfully stabilize the fixed point and
             the robustness of the schemes to noise are determined. It is
             found that the domain of control for the two schemes is
             similar for appropriately matched values of R and N, and
             that N-time-delay autosynchronization tends to be less
             sensitive to noise.},
   Key = {fds248380}
}

@article{fds248374,
   Author = {Sukow, DW and Bleich, ME and Gauthier, DJ and Socolar,
             JES},
   Title = {Controlling chaos in a fast diode resonator using extended
             time-delay autosynchronization: Experimental observations
             and theoretical analysis.},
   Journal = {Chaos},
   Volume = {7},
   Number = {4},
   Pages = {560-576},
   Year = {1997},
   Month = {December},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/12779682},
   Abstract = {We stabilize unstable periodic orbits of a fast diode
             resonator driven at 10.1 MHz (corresponding to a drive
             period under 100 ns) using extended time-delay
             autosynchronization. Stabilization is achieved by feedback
             of an error signal that is proportional to the difference
             between the value of a state variable and an infinite series
             of values of the state variable delayed in time by integral
             multiples of the period of the orbit. The technique is easy
             to implement electronically and it has an all-optical
             counterpart that may be useful for stabilizing the dynamics
             of fast chaotic lasers. We show that increasing the weights
             given to temporally distant states enlarges the domain of
             control and reduces the sensitivity of the domain of control
             on the propagation delays in the feedback loop. We determine
             the average time to obtain control as a function of the
             feedback gain and identify the mechanisms that destabilize
             the system at the boundaries of the domain of control. A
             theoretical stability analysis of a model of the diode
             resonator in the presence of time-delay feedback is in good
             agreement with the experimental results for the size and
             shape of the domain of control. (c) 1997 American Institute
             of Physics.},
   Doi = {10.1063/1.166256},
   Key = {fds248374}
}

@article{fds303753,
   Author = {Socolar, JES},
   Title = {Average stresses and force fluctuations in non-cohesive
             granular materials},
   Volume = {57},
   Pages = {3204},
   Year = {1997},
   Month = {October},
   url = {http://arxiv.org/abs/cond-mat/9710089v1},
   Abstract = {A lattice model is presented for investigating the
             fluctuations in static granular materials under
             gravitationally induced stress. The model is similar in
             spirit to the scalar q-model of Coppersmith et al., but
             ensures balance of all components of forces and torques at
             each site. The geometric randomness in real granular
             materials is modeled by choosing random variables at each
             site, consistent with the assumption of cohesionless grains.
             Configurations of the model can be generated rapidly,
             allowing the statistical study of relatively large systems.
             For a 2D system with rough walls, the model generates
             configurations consistent with continuum theories for the
             average stresses (unlike the q-model) without requiring the
             assumption of a constitutive relation. For a 2D system with
             periodic boundary conditions, the model generates
             single-grain force distributions similar to those obtained
             from the q-model with a singular distribution of
             q's.},
   Doi = {10.1103/PhysRevE.57.3204},
   Key = {fds303753}
}

@article{fds248375,
   Author = {Bleich, ME and Hochheiser, D and Moloney, JV and Socolar,
             JES},
   Title = {Controlling extended systems with spatially filtered,
             time-delayed feedback},
   Journal = {Physical Review E - Statistical Physics, Plasmas, Fluids,
             and Related Interdisciplinary Topics},
   Volume = {55},
   Number = {3 SUPPL. A},
   Pages = {2119-2126},
   Year = {1997},
   Abstract = {We investigate a control technique for spatially extended
             systems combining spatial filtering with a previously
             studied form of time-delay feedback. The scheme is naturally
             suited to real-time control of optical systems. We apply the
             control scheme to a model of a transversely extended
             semiconductor laser in which a desirable, coherent
             traveling-wave state exists, but is a member of a nowhere
             stable family. Our scheme stabilizes this state and directs
             the system towards it from realistic, distant, and noisy
             initial conditions. As confirmed by numerical simulation, a
             linear stability analysis about the controlled state
             accurately predicts when the scheme is successful and
             illustrates some key features of the control including the
             individual merit of, and interplay between, the spatial and
             temporal degrees of freedom in the control.},
   Key = {fds248375}
}

@article{fds248387,
   Author = {Gauthier, DJ and Socolar, JES},
   Title = {Comment on Dynamic Control of Cardiac Alternans},
   Journal = {Physical Review Letters},
   Volume = {79},
   Number = {24},
   Pages = {4938},
   Year = {1997},
   url = {http://dx.doi.org/10.1103/PhysRevLett.79.4938},
   Doi = {10.1103/PhysRevLett.79.4938},
   Key = {fds248387}
}

@article{fds248373,
   Author = {Bleich, ME and Socolar, JE},
   Title = {Controlling spatiotemporal dynamics with time-delay
             feedback.},
   Journal = {Physical Review E - Statistical Physics, Plasmas, Fluids,
             and Related Interdisciplinary Topics},
   Volume = {54},
   Number = {1},
   Pages = {R17-R20},
   Year = {1996},
   Month = {July},
   ISSN = {1063-651X},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/9965164},
   Key = {fds248373}
}

@article{fds248372,
   Author = {Bleich, ME and Socolar, JES},
   Title = {Stability of periodic orbits controlled by time-delay
             feedback},
   Journal = {Physics Letters, Section A: General, Atomic and Solid State
             Physics},
   Volume = {210},
   Number = {1-2},
   Pages = {87-94},
   Year = {1996},
   Abstract = {Extended time-delay auto-synchronization (ETDAS) is a
             promising technique for stabilizing unstable periodic orbits
             in low-dimensional dynamical systems. The technique involves
             continuous feedback of signals delayed by multiples of the
             orbit's period in a manner that is especially well-suited
             for fast systems and optical implementation. We show how to
             analyze the stability of a given implementation of ETDAS
             without explicit integration of time-delay equations. To
             illustrate the method and point out some nontrivial features
             of ETDAS, we obtain the domain of control for a period-one
             orbit of the driven, damped pendulum.},
   Key = {fds248372}
}

@article{fds248371,
   Author = {Socolar, JE and Sukow, DW and Gauthier, DJ},
   Title = {Stabilizing unstable periodic orbits in fast dynamical
             systems.},
   Journal = {Physical Review E - Statistical Physics, Plasmas, Fluids,
             and Related Interdisciplinary Topics},
   Volume = {50},
   Number = {4},
   Pages = {3245-3248},
   Year = {1994},
   Month = {October},
   ISSN = {1063-651X},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/9962372},
   Key = {fds248371}
}

@article{fds248370,
   Author = {Gauthier, DJ and Sukow, DW and Concannon, HM and Socolar,
             JE},
   Title = {Stabilizing unstable periodic orbits in a fast diode
             resonator using continuous time-delay autosynchronization.},
   Journal = {Physical Review E - Statistical Physics, Plasmas, Fluids,
             and Related Interdisciplinary Topics},
   Volume = {50},
   Number = {3},
   Pages = {2343-2346},
   Year = {1994},
   Month = {September},
   ISSN = {1063-651X},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/9962244},
   Key = {fds248370}
}

@article{fds248369,
   Author = {Grinstein, G and Jayaprakash, C and Socolar, JE},
   Title = {Scale invariance of nonconserved quantities in driven
             systems.},
   Journal = {Physical Review E - Statistical Physics, Plasmas, Fluids,
             and Related Interdisciplinary Topics},
   Volume = {48},
   Number = {2},
   Pages = {R643-R646},
   Year = {1993},
   Month = {August},
   ISSN = {1063-651X},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/9960763},
   Key = {fds248369}
}

@article{fds248368,
   Author = {Socolar, JE and Grinstein, G and Jayaprakash, C},
   Title = {On self-organized criticality in nonconserving
             systems.},
   Journal = {Physical Review E - Statistical Physics, Plasmas, Fluids,
             and Related Interdisciplinary Topics},
   Volume = {47},
   Number = {4},
   Pages = {2366-2376},
   Year = {1993},
   Month = {April},
   ISSN = {1063-651X},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/9960267},
   Key = {fds248368}
}

@article{fds303752,
   Author = {Krug, J and Socolar, JE and Grinstein, G},
   Title = {Surface fluctuations and criticality in a class of
             one-dimensional sandpile models.},
   Journal = {Physical Review A - Atomic, Molecular, and Optical
             Physics},
   Volume = {46},
   Number = {8},
   Pages = {R4479-R4482},
   Year = {1992},
   Month = {October},
   ISSN = {1050-2947},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/9908766},
   Key = {fds303752}
}

@article{fds248366,
   Author = {Krug, J and Socolar, JE},
   Title = {Comment on "Scalings of growing self-organized
             surfaces"},
   Journal = {Physical Review Letters},
   Volume = {68},
   Number = {5},
   Pages = {722},
   Year = {1992},
   Month = {February},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/10045973},
   Doi = {10.1103/PhysRevLett.68.722},
   Key = {fds248366}
}

@article{fds248365,
   Author = {Socolar, JES},
   Title = {Theory of Packings of Identical Hard Disks Generated by
             Ballistic Deposition},
   Journal = {Europhys. Lett.},
   Volume = {18},
   Pages = {39},
   Year = {1992},
   Key = {fds248365}
}

@article{fds37538,
   Author = {J.E.S. Socolar},
   Title = {Growth Rules for Quasicrystals},
   Booktitle = {Quasicrystals: The State of the Art},
   Publisher = {World Scientific, Singapore},
   Editor = {D. DiVincenzo and P. Steinhardt},
   Year = {1991},
   Key = {fds37538}
}

@article{fds37539,
   Author = {J.E.S. Socolar},
   Title = {The Alternation Condition and 2D Quasicrystals},
   Volume = {93},
   Series = {Springer Series in Solid-State Sciences},
   Booktitle = {Quasicrystals},
   Publisher = {Springer-Verlag, Berlin},
   Editor = {T. Fujiwara and T. Ogawa},
   Year = {1990},
   Key = {fds37539}
}

@article{fds248364,
   Author = {Socolar, JES},
   Title = {Weak matching rules for quasicrystals},
   Journal = {Communications in Mathematical Physics},
   Volume = {129},
   Number = {3},
   Pages = {599-619},
   Year = {1990},
   ISSN = {0010-3616},
   url = {http://dx.doi.org/10.1007/BF02097107},
   Abstract = {Weak matching rules for a quasicrystalline tiling are local
             rules that ensure that fluctuations in "perp-space" are
             uniformly bounded. It is shown here that weak matching rules
             exist for N-fold symmetric tilings, where N is any integer
             not divisible by four. The result suggests that, contrary to
             previous indications, quasicrystalline ground states are not
             confined to those symmetries for which the incommensurate
             ratios of wavevectors are quadratic irrationals. An explicit
             method of constructing weak matching rules for N-fold
             symmetric tilings in two dimensions is presented. It is
             shown that the generalization of the construction yields
             weak matching rules in the case of icosahedral symmetry as
             well. © 1990 Springer-Verlag.},
   Doi = {10.1007/BF02097107},
   Key = {fds248364}
}

@article{fds248363,
   Author = {Socolar, JE},
   Title = {Simple octagonal and dodecagonal quasicrystals.},
   Journal = {Physical Review B - Condensed Matter and Materials
             Physics},
   Volume = {39},
   Number = {15},
   Pages = {10519-10551},
   Year = {1989},
   Month = {May},
   ISSN = {0163-1829},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/9947860},
   Key = {fds248363}
}

@article{fds303751,
   Author = {Onoda, G and Steinhardt, PJ and DiVincenzo, D and Socolar,
             JE},
   Title = {Onoda etal. reply.},
   Journal = {Physical Review Letters},
   Volume = {62},
   Number = {10},
   Pages = {1210},
   Year = {1989},
   Month = {March},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/10039608},
   Doi = {10.1103/PhysRevLett.62.1210},
   Key = {fds303751}
}

@article{fds37541,
   Author = {J.E.S. Socolar},
   Title = {Locality Constraints and 2D Quasicrystals},
   Booktitle = {Quasicrystals - Adriatico Anniversary Research
             Conference},
   Publisher = {World Scientific, Singapore},
   Editor = {M.V. Jaric and S. Lundqvist},
   Year = {1989},
   Key = {fds37541}
}

@article{fds248361,
   Author = {Onoda, GY and Steinhardt, PJ and DiVincenzo, DP and Socolar,
             JE},
   Title = {Growing perfect quasicrystals.},
   Journal = {Physical Review Letters},
   Volume = {60},
   Number = {25},
   Pages = {2653-2656},
   Year = {1988},
   Month = {June},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/10038414},
   Doi = {10.1103/PhysRevLett.60.2653},
   Key = {fds248361}
}

@article{fds248360,
   Author = {Socolar, JE and Wright, DC},
   Title = {Explanation of peak shapes observed in diffraction from
             icosahedral quasicrystals.},
   Journal = {Physical Review Letters},
   Volume = {59},
   Number = {2},
   Pages = {221-224},
   Year = {1987},
   Month = {July},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/10035483},
   Doi = {10.1103/PhysRevLett.59.221},
   Key = {fds248360}
}

@article{fds248358,
   Author = {Lubensky, TC and Socolar, JE and Steinhardt, PJ and Bancel, PA and Heiney, AP},
   Title = {Distortion and peak broadening in quasicrystal diffraction
             patterns.},
   Journal = {Physical Review Letters},
   Volume = {57},
   Number = {12},
   Pages = {1440-1443},
   Year = {1986},
   Month = {September},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/10033450},
   Doi = {10.1103/PhysRevLett.57.1440},
   Key = {fds248358}
}

@article{fds248357,
   Author = {Socolar, JE and Lubensky, TC and Steinhardt, PJ},
   Title = {Phonons, phasons, and dislocations in quasicrystals.},
   Journal = {Physical Review B - Condensed Matter and Materials
             Physics},
   Volume = {34},
   Number = {5},
   Pages = {3345-3360},
   Year = {1986},
   Month = {September},
   ISSN = {0163-1829},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/9940073},
   Key = {fds248357}
}

@article{fds248319,
   Author = {Socolar, JE and Steinhardt, PJ},
   Title = {Quasicrystals. II. Unit-cell configurations.},
   Journal = {Physical Review B - Condensed Matter and Materials
             Physics},
   Volume = {34},
   Number = {2},
   Pages = {617-647},
   Year = {1986},
   Month = {July},
   ISSN = {0163-1829},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/9939668},
   Key = {fds248319}
}

@article{fds248359,
   Author = {Socolar, JES},
   Title = {Phason Strain in Quasicrystals},
   Journal = {Journal de Physique},
   Volume = {C3},
   Pages = {217-227},
   Year = {1986},
   Key = {fds248359}
}

@article{fds248318,
   Author = {Socolar, JE and Steinhardt, PJ and Levine, D},
   Title = {Quasicrystals with arbitrary orientational
             symmetry.},
   Journal = {Physical Review B - Condensed Matter and Materials
             Physics},
   Volume = {32},
   Series = {Rapid Communication},
   Number = {8},
   Pages = {5547-5550},
   Year = {1985},
   Month = {October},
   ISSN = {0163-1829},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/9937798},
   Key = {fds248318}
}

@article{fds248316,
   Author = {MELE, EJ and SOCOLAR, J},
   Title = {NUMERICAL-INTEGRATION OF THE TIME EVOLUTION OPERATOR -
             EXCITED-STATE DYNAMICS IN CONJUGATED MOLECULES},
   Journal = {International Journal of Quantum Chemistry},
   Volume = {18},
   Series = {Quantum Chemistry Symposium},
   Pages = {347-358},
   Year = {1984},
   ISSN = {0020-7608},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1984ACF7600031&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Key = {fds248316}
}

@booklet{Gollub80,
   Author = {Gollub, JP and Romer, EJ and Socolar, JE},
   Title = {Trajectory divergence for coupled relaxation oscillators:
             Measurements and models},
   Journal = {Journal of Statistical Physics},
   Volume = {23},
   Number = {3},
   Pages = {321-333},
   Year = {1980},
   ISSN = {0022-4715},
   url = {http://dx.doi.org/10.1007/BF01011372},
   Abstract = {The exponential divergence of nearby phase space
             trajectories is a hallmark of nonperiodic (chaotic) behavior
             in dynamical systems. We present the first laboratory of
             measurements of divergence rates (or characteristic
             exponents), using a system of coupled tunnel diode
             relaxation oscillators. This property of sensitive
             dependence on initial conditions is reliably associated with
             broadband spectra, and both methods are used to characterize
             the motion as a function of the coupling strength and
             natural frequency ratio of the two oscillators. A simple
             piecewise linear model correctly predicts the major periodic
             and non-periodic regions of the parameter space, thus
             confirming that the chaotic behavior involves only a few
             degrees of freedom. © 1980 Plenum Publishing
             Corporation.},
   Doi = {10.1007/BF01011372},
   Key = {Gollub80}
}


%% Papers Submitted   
@article{fds225655,
   Author = {Y. Yang and L. Fu and C. Marcoux and J. E. S. Socolar and P.
             Charbonneau, B. B. Yellen},
   Title = {Martensitic transformations in binary colloidal
             monolayers},
   Journal = {PNAS},
   Year = {2014},
   Month = {October},
   Key = {fds225655}
}