Scaling laws at the critical point

There are two independent critical exponents that describe the behavior of systems near their critical point. However, at the critical point only the exponent $\eta$, which describes the decay of the correlation function, is usually discussed. We emphasize that there is a second independent exponent $\eta'$ that describes the decay of the fourth-order correlation function. The exponent $\eta'$ is related to the exponents determining the behavior of thermodynamic functions near criticality via a fluctuation-response equation for the specific heat. We also discuss a scaling law for $\eta'$.Comment: Revised version, 1 added figure, 3 pages, 1 tabl

The upper critical magnetic field of holographic superconductor with conformally invariant power-Maxwell electrodynamics

The properties of $(d-1)$-dimensional $s$-wave holographic superconductor in the presence of power-Maxwell field is explored. We study the probe limit in which the scalar and gauge fields do not backreact on the background geometry. Our study is based on the matching of solutions on the boundary and on the horizon at some intermediate point. At first, the case without external magnetic field is considered, and the critical temperature is obtained in terms of the charge density, the dimensionality, and the power-Maxwell exponent. Then, a magnetic field is turned on in the $d$-dimensional bulk which can influence the $(d-1)$-dimensional holographic superconductor at the boundary. The phase behavior of the corresponding holographic superconductor is obtained by computing the upper critical magnetic field in the presence of power-Maxwell electrodynamics, characterized by the power exponent $q$. Interestingly, it is observed that in the presence of magnetic field, the physically acceptable phase behavior of the holographic superconductor is obtained for $q={d}/{4}$, which guaranties the conformal invariance of the power-Maxwell Lagrangian. The case of physical interest in five spacetime dimensions ($d=5$, and $q=5/4$) is considered in detail, and compared with the results obtained for the usual Maxwell electrodynamics $q=1$ in the same dimensions.Comment: 12 pages, 1 table, 5 figure

Critical behavior of the geometrical spin clusters and interfaces in the two-dimensional thermalized bond Ising model

The fractal dimensions and the percolation exponents of the geometrical spin clusters of like sign at criticality, are obtained numerically for an Ising model with temperature-dependent annealed bond dilution, also known as the thermalized bond Ising model (TBIM), in two dimensions. For this purpose, a modified Wolff single-cluster Monte Carlo simulation is used to generate equilibrium spin configurations on square lattices in the critical region. A tie-breaking rule is employed to identify non-intersecting spin cluster boundaries along the edges of the dual lattice. The values obtained for the fractal dimensions of the spanning geometrical clusters $D_{c}$, and their interfaces $D_{I}$, are in perfect agreement with those reported for the standard two-dimensional ferromagnetic Ising model. Furthermore, the variance of the winding angles, results in a diffusivity $\kappa=3$ for the two-dimensional thermalized bond Ising model, thus placing it in the universality class of the regular Ising model. A finite-size scaling analysis of the largest geometrical clusters, results in a reliable estimation of the critical percolation exponents for the geometrical clusters in the limit of an infinite lattice size. The percolation exponents thus obtained, are also found to be consistent with those reported for the regular Ising model. These consistencies are explained in terms of the Fisher renormalization relations, which express the thermodynamic critical exponents of systems with annealed bond dilution in terms of those of the regular model system.Comment: 12 pages, 7 figures, accepted for publication in J. Stat. Mech. (2012

On the static length of relaxation and the origin of dynamic heterogeneity in fragile glass-forming liquids

The most puzzling aspect of the glass transition observed in laboratory is an apparent decoupling of dynamics from structure. In this paper we recount the implication of various theories of glass transition for the static correlation length in an attempt to reconcile the dynamic and static lengths associate with the glass problem. We argue that a more recent characterization of the static relaxation length based on the bond ordering scenario, as the typical length over which the energy fluctuations are correlated, is more consistent with, and indeed in perfect agreement with the typical linear size of the dynamically heterogeneous domains observed in deeply supercooled liquids. The correlated relaxation of bonds in terms of energy is therefore identified as the physical origin of the observed dynamic heterogeneity.Comment: 6 pages, 1 figur

Identifying specific prefrontal neurons that contribute to autism-associated abnormalities in physiology and social behavior.

Functional imaging and gene expression studies both implicate the medial prefrontal cortex (mPFC), particularly deep-layer projection neurons, as a potential locus for autism pathology. Here, we explored how specific deep-layer prefrontal neurons contribute to abnormal physiology and behavior in mouse models of autism. First, we find that across three etiologically distinct models-in utero valproic acid (VPA) exposure, CNTNAP2 knockout and FMR1 knockout-layer 5 subcortically projecting (SC) neurons consistently exhibit reduced input resistance and action potential firing. To explore how altered SC neuron physiology might impact behavior, we took advantage of the fact that in deep layers of the mPFC, dopamine D2 receptors (D2Rs) are mainly expressed by SC neurons, and used D2-Cre mice to label D2R+ neurons for calcium imaging or optogenetics. We found that social exploration preferentially recruits mPFC D2R+ cells, but that this recruitment is attenuated in VPA-exposed mice. Stimulating mPFC D2R+ neurons disrupts normal social interaction. Conversely, inhibiting these cells enhances social behavior in VPA-exposed mice. Importantly, this effect was not reproduced by nonspecifically inhibiting mPFC neurons in VPA-exposed mice, or by inhibiting D2R+ neurons in wild-type mice. These findings suggest that multiple forms of autism may alter the physiology of specific deep-layer prefrontal neurons that project to subcortical targets. Furthermore, a highly overlapping population-prefrontal D2R+ neurons-plays an important role in both normal and abnormal social behavior, such that targeting these cells can elicit potentially therapeutic effects

Relation between positional specific heat and static relaxation length: Application to supercooled liquids

A general identification of the {\em positional specific heat} as the thermodynamic response function associated with the {\em static relaxation length} is proposed, and a phenomenological description for the thermal dependence of the static relaxation length in supercooled liquids is presented. Accordingly, through a phenomenological determination of positional specific heat of supercooled liquids, we arrive at the thermal variation of the static relaxation length $\xi$, which is found to vary in accordance with $\xi \sim (T-T_0)^{-\nu}$ in the quasi-equilibrium supercooled temperature regime, where $T_0$ is the Vogel-Fulcher temperature and exponent $\nu$ equals unity. This result to a certain degree agrees with that obtained from mean field theory of random-first-order transition, which suggests a power law temperature variation for $\xi$ with an apparent divergence at $T_0$. However, the phenomenological exponent $\nu = 1$, is higher than the corresponding mean field estimate (becoming exact in infinite dimensions), and in perfect agreement with the relaxation length exponent as obtained from the numerical simulations of the same models of structural glass in three spatial dimensions.Comment: Revised version, 7 pages, no figures, submitted to IOP Publishin

Molecular Control Of Synaptic Efficacy Within Striatal Circuits

As the input nucleus of the basal ganglia, the striatum integrates diverse excitatory projections governing cognitive and motor control. Over the last decade, substantial progress has been made in the identification of striatal cell-types, distinguishing their molecular profiles and local connectivity patterns. Nevertheless, our understanding of the functional organization of striatal circuits remains limited. The studies presented in this thesis focus on delineating the synaptic properties of excitatory inputs originating from dorsal prefrontal cortex and parafascicular thalamus innervating neuronal populations within dorsal medial striatum. In these studies, we use quantitative optogenetic measures to investigate striatal projections in an input-specific manner onto distinct striatal neuronal populations. In the first study, we find a divergence between cell-type specific anatomical connectivity and measures of excitatory strength. Furthermore, we find that synaptic strength is modified according to both presynaptic region and postsynaptic cell type. As a substantial degree of synaptic function is determined by the molecular composition of individual neurons and their synapses, the second study examines the role of a cell-adhesion molecule, Neurexin1ɑ, at these synapses. We found Neurexin1ɑ, a gene with broad neuropsychiatric disease association, regulates synaptic efficacy at these synapses in an input- and postsynaptic cell type manner. Together, these studies demonstrate a significant amount of diversity observed in physiological connectivity can be attributed to presynaptic-postsynaptic interactions and their underlying molecular composition. Ultimately, forming a comprehensive map of striatal circuits will be essential in understanding how the convergence of inputs from various sources convey information for distinct behavioral functions

Isomorph invariance of Couette shear flows simulated by the SLLOD equations of motion

Non-equilibrium molecular dynamics simulations were performed to study the thermodynamic, structural, and dynamical properties of the single-component Lennard-Jones and the Kob-Andersen binary Lennard-Jones liquids. Both systems are known to be strongly correlating, i.e., have strong correlations between equilibrium thermal fluctuations of virial and potential energy. Such systems have good isomorphs, i.e., curves in the thermodynamic phase diagram along which structural, dynamical, and some thermodynamic quantities are invariant when expressed in reduced units. The SLLOD equations of motion were used to simulate Couette shear flows of the two systems. We show analytically that these equations are isomorph invariant provided the reduced strain rate is fixed along the isomorph. Since isomorph invariance is generally only approximate, a range of shear rates were simulated to test for the predicted invariance, covering both the linear and non-linear regimes. For both systems, when represented in reduced units the radial distribution function and the intermediate scattering function collapse for state points that are isomorphic. The strain-rate dependence of the viscosity, which exhibits shear thinning, is also invariant along an isomorph. Our results extend the isomorph concept to the state-state non-equilibrium situation of a shear flow, in which the phase diagram is three dimensional because the shear rate defines the third dimension

Brain-wide representations of prior information in mouse decision-making.

The neural representations of prior information about the state of the world are poorly understood1. Here, to investigate them, we examined brain-wide Neuropixels recordings and widefield calcium imaging collected by the International Brain Laboratory. Mice were trained to indicate the location of a visual grating stimulus, which appeared on the left or right with a prior probability alternating between 0.2 and 0.8 in blocks of variable length. We found that mice estimate this prior probability and thereby improve their decision accuracy. Furthermore, we report that this subjective prior is encoded in at least 20% to 30% of brain regions that, notably, span all levels of processing, from early sensory areas (the lateral geniculate nucleus and primary visual cortex) to motor regions (secondary and primary motor cortex and gigantocellular reticular nucleus) and high-level cortical regions (the dorsal anterior cingulate area and ventrolateral orbitofrontal cortex). This widespread representation of the prior is consistent with a neural model of Bayesian inference involving loops between areas, as opposed to a model in which the prior is incorporated only in decision-making areas. This study offers a brain-wide perspective on prior encoding at cellular resolution, underscoring the importance of using large-scale recordings on a single standardized task

Molecular Control of Synaptic Efficacy Within Striatal Circuits

As the input nucleus of the basal ganglia, the striatum integrates diverse excitatory projections governing cognitive and motor control. Over the last decade, substantial progress has been made in the identification of striatal cell-types, distinguishing their molecular profiles and local connectivity patterns. Nevertheless, our understanding of the functional organization of striatal circuits remains limited. The studies presented in this thesis focus on delineating the synaptic properties of excitatory inputs originating from dorsal prefrontal cortex and parafascicular thalamus innervating neuronal populations within dorsal medial striatum. In these studies, we use quantitative optogenetic measures to investigate striatal projections in an input-specific manner onto distinct striatal neuronal populations. In the first study, we find a divergence between cell-type specific anatomical connectivity and measures of excitatory strength. Furthermore, we find that synaptic strength is modified according to both presynaptic region and postsynaptic cell type. As a substantial degree of synaptic function is determined by the molecular composition of individual neurons and their synapses, the second study examines the role of a cell-adhesion molecule, Neurexin1ɑ, at these synapses. We found Neurexin1ɑ, a gene with broad neuropsychiatric disease association, regulates synaptic efficacy at these synapses in an input- and postsynaptic cell type manner. Together, these studies demonstrate a significant amount of diversity observed in physiological connectivity can be attributed to presynaptic-postsynaptic interactions and their underlying molecular composition. Ultimately, forming a comprehensive map of striatal circuits will be essential in understanding how the convergence of inputs from various sources convey information for distinct behavioral functions