Trial-by-trial variability in cortical responses exhibits scaling of spatial correlations predicted from critical dynamics.

In the mammalian cortex, even simple sensory inputs or movements activate many neurons, with each neuron responding variably to repeated stimuli-a phenomenon known as trial-by-trial variability. Understanding the spatial patterns and dynamics of this variability is challenging. Using cellular 2-photon imaging, we study visual and auditory responses in the primary cortices of awake mice. We focus on how individual neurons' responses differed from the overall population. We find consistent spatial correlations in these differences that are unique to each trial and linearly scale with the cortical area observed, a characteristic of critical dynamics as confirmed in our neuronal simulations. Using chronic multi-electrode recordings, we observe similar scaling in the prefrontal and premotor cortex of non-human primates during self-initiated and visually cued motor tasks. These results suggest that trial-by-trial variability, rather than being random noise, reflects a critical, fluctuation-dominated state in the cortex, supporting the brain's efficiency in processing information.

Scale-free correlations in the dynamics of a small (N∼10000) cortical network.

The advent of novel optogenetics technology allows the recording of brain activity with a resolution never seen before. The characterization of these very large data sets offers new challenges as well as unique theory-testing opportunities. Here we discuss whether the spatial and temporal correlations of the collective activity of thousands of neurons are tangled as predicted by the theory of critical phenomena. The analysis shows that both the correlation length ξ and the correlation time τ scale as predicted as a function of the system size. With some peculiarities that we discuss, the analysis uncovers evidence consistent with the view that the large-scale brain cortical dynamics corresponds to critical phenomena.

Finite-size correlation behavior near a critical point: A simple metric for monitoring the state of a neural network.

In this article, a correlation metric κ_{c} is proposed for the inference of the dynamical state of neuronal networks. κ_{C} is computed from the scaling of the correlation length with the size of the observation region, which shows qualitatively different behavior near and away from the critical point of a continuous phase transition. The implementation is first studied on a neuronal network model, where the results of this new metric coincide with those obtained from neuronal avalanche analysis, thus well characterizing the critical state of the network. The approach is further tested with brain optogenetic recordings in behaving mice from a publicly available database. Potential applications and limitations for its use with currently available optical imaging techniques are discussed.

Learning by mistakes in memristor networks.

Recent results revived the interest in the implementation of analog devices able to perform brainlike operations. Here we introduce a training algorithm for a memristor network which is inspired by previous work on biological learning. Robust results are obtained from computer simulations of a network of voltage-controlled memristive devices. Its implementation in hardware is straightforward, being scalable and requiring very little peripheral computation overhead.

Box scaling as a proxy of finite size correlations.

The scaling of correlations as a function of size provides important hints to understand critical phenomena on a variety of systems. Its study in biological structures offers two challenges: usually they are not of infinite size, and, in the majority of cases, dimensions can not be varied at will. Here we discuss how finite-size scaling can be approximated in an experimental system of fixed and relatively small extent, by computing correlations inside of a reduced field of view of various widths (we will refer to this procedure as "box-scaling"). A relation among the size of the field of view, and measured correlation length, is derived at, and away from, the critical regime. Numerical simulations of a neuronal network, as well as the ferromagnetic 2D Ising model, are used to verify such approximations. Numerical results support the validity of the heuristic approach, which should be useful to characterize relevant aspects of critical phenomena in biological systems.

Lissencephaly in an epilepsy cohort: Molecular, radiological and clinical aspects.

INTRODUCTION: Lissencephaly is a rare malformation of cortical development due to abnormal transmantle migration resulting in absent or reduced gyration. The lissencephaly spectrum consists of agyria, pachygyria and subcortical band heterotopia. In this study we compared genetic aetiology, neuroradiology, clinical phenotype and response to antiepileptic drugs in patients with epilepsy and lissencephaly spectrum malformations. METHODS: The study group consisted of 20 patients - 13 males and 7 females, aged 18 months to 21 years at the time of data collection. Genetic testing was performed by oligonucleotide array comparative genomic hybridization (microarray), multiplex ligation-dependent probe amplification (MLPA), targeted gene panels and whole exome/genome sequencing. All neuroradiological investigations were re-evaluated and the malformations were classified by the same neuroradiologist. Clinical features and response to anti-epileptic drugs (AEDs) were evaluated by retrospective review of medical records. RESULTS: In eleven patients (55%) mutations in PAFAH1B1 (LIS1) or variable microdeletions of 17p13.3 including the PAFAH1B1 gene were detected. Four patients (20%) had tubulin encoding gene mutations (TUBA1A, TUBG1 and TUBGCP6). Mutations in DCX, DYNC1H1, ADGRG1 and WDR62 were identified in single patients. In one patient, a possibly pathogenic intragenic deletion in TRIO was detected. A clear radiologic distinction could be made between tubulinopathies and PAFAH1B1 related lissencephaly. The majority of the patients had therapy resistant epilepsy and epileptic spasms was the most prominent seizure type. The best therapeutic response to seizure control in our cohort was obtained by the ketogenic diet, vigabatrin, clobazam, phenobarbital and valproate. CONCLUSION: The most common genetic aetiologies in our cohort of 20 individuals with epilepsy and lissencephaly spectrum were intragenic deletions or single nucleotide mutations in PAFAH1B1 or larger deletions in 17p13.3, encompassing PAFAH1B1, followed by mutations in tubulin encoding genes. Radiological findings could reliably predict molecular results only in agyria with a posterior to anterior gradient. Radiological and molecular findings did not correlate consistently with severity of clinical outcome or therapeutic response.

Similar local neuronal dynamics may lead to different collective behavior.

This report is concerned with the relevance of the microscopic rules that implement individual neuronal activation, in determining the collective dynamics, under variations of the network topology. To fix ideas we study the dynamics of two cellular automaton models, commonly used, rather in-distinctively, as the building blocks of large-scale neuronal networks. One model, due to Greenberg and Hastings (GH), can be described by evolution equations mimicking an integrate-and-fire process, while the other model, due to Kinouchi and Copelli (KC), represents an abstract branching process, where a single active neuron activates a given number of postsynaptic neurons according to a prescribed "activity" branching ratio. Despite the apparent similarity between the local neuronal dynamics of the two models, it is shown that they exhibit very different collective dynamics as a function of the network topology. The GH model shows qualitatively different dynamical regimes as the network topology is varied, including transients to a ground (inactive) state, continuous and discontinuous dynamical phase transitions. In contrast, the KC model only exhibits a continuous phase transition, independently of the network topology. These results highlight the importance of paying attention to the microscopic rules chosen to model the interneuronal interactions in large-scale numerical simulations, in particular when the network topology is far from a mean-field description. One such case is the extensive work being done in the context of the Human Connectome, where a wide variety of types of models are being used to understand the brain collective dynamics.

Controlling a complex system near its critical point via temporal correlations.

Many complex systems exhibit large fluctuations both across space and over time. These fluctuations have often been linked to the presence of some kind of critical phenomena, where it is well known that the emerging correlation functions in space and time are closely related to each other. Here we test whether the time correlation properties allow systems exhibiting a phase transition to self-tune to their critical point. We describe results in three models: the 2D Ising ferromagnetic model, the 3D Vicsek flocking model and a small-world neuronal network model. We demonstrate that feedback from the autocorrelation function of the order parameter fluctuations shifts the system towards its critical point. Our results rely on universal properties of critical systems and are expected to be relevant to a variety of other settings.

Stability limits for the supercooled liquid and superheated crystal of Lennard-Jones particles.

We have studied the limits of stability in the first order liquid-solid phase transition in a Lennard-Jones system by means of the short-time relaxation method and using the bond-orientational order parameter Q6. These limits are compared with the melting line. We have paid special attention to the supercooled liquid, comparing our results with the point where the free energy cost of forming a nucleating droplet goes to zero. We also indirectly estimate the dimension associated to the critical nucleus at the spinodal, expected to be fractal according to mean field theories of nucleation.

The ketogenic diet compensates for AGC1 deficiency and improves myelination.

The brain aspartate-glutamate carrier (AGC1) is specifically expressed in neurons, where it transports aspartate from the mitochondria to the cytosol, and plays a role in transfer of nicotinamide adenine dinucleotide (NADH)-reducing equivalents into the mitochondria as a part of the malate-aspartate shuttle. Deficient function of AGC1 underlies an inborn error of metabolism that presents with severe hypotonia, arrested psychomotor development, and seizures from a few months of age. In AGC1 deficiency, there is secondary hypomyelination due to lack of N-acetylaspartate (NAA), which is normally generated by acetylation of aspartate in the neuron and required for fatty acid synthesis by the adjacent oligodendrocyte. Based on experiences from AGC2 deficiency, we predicted that reduced glycolysis should compensate for the metabolic defect and allow resumed myelination in AGC1 deficiency. Carbohydrate restriction was therefore initiated in a patient with AGC1 deficiency at 6 years of age by introducing a ketogenic diet. The response was dramatic, clinically as well as radiologically. Psychomotor development showed clear improvement, and magnetic resonance imaging (MRI) indicated resumed myelination. This is the first successful treatment of secondary hypomyelination reported. Because AGC1 is driven by the proton gradient generated by the neuronal mitochondrial respiratory chain, the results have potential relevance for secondary hypomyelination in general.

Specific Heat Anomaly in a Supercooled Liquid with Amorphous Boundary Conditions.

We study the specific heat of a model supercooled liquid confined in a spherical cavity with amorphous boundary conditions. We find the equilibrium specific heat has a cavity-size-dependent peak as a function of temperature. The cavity allows us to perform a finite-size scaling (FSS) analysis, which indicates that the peak persists at a finite temperature in the thermodynamic limit. We attempt to collapse the data onto a FSS curve according to different theoretical scenarios, obtaining reasonable results in two cases: a "not-so-simple" liquid with nonstandard values of the exponents α and ν, and random first-order theory, with two different length scales.

Illustrated approach to imaging and staging of nodal disease in the neck.

This article provides a review of the anatomic classification and staging of nodal disease in the neck through the use of tables, illustrations, and sample imaging cases. The article reinforces knowledge of nodal disease in the neck while reviewing imaging examples of common and uncommon disease entities in this region. We review nodal disease in the neck using American Joint Committee on Cancer staging criteria. We illustrate anatomy of the nodal levels of the neck with accompanying examples of selected cases. These are presented in an integrated manner, highlighting items of importance to radiologists. The accompanying images and clinical scenarios aid recognition with an emphasis on differential diagnosis. Case examples include a broad range of pathologically and clinically proven disease entities involving lymph node disease in the neck accumulated from 1999 to 2008 at a tertiary referral center. The anatomical relationships and major disease processes for this location are reviewed and illustrated with example images from commonly used imaging modalities for this region. Examples of cases discussed include lymphoma, metastatic neoplasms such as head/neck squamous cell carcinoma and esthesioneuroblastoma, and inflammatory and infectious processes such as mononucleosis. The reader will gain or refresh information about the anatomical relationships and demarcations of the nodal levels of the neck as well as disease entities that frequently present with neck adenopathy. This information is useful both in clinical practice and in preparation for certifying examinations. The images provided aid recognition with an emphasis on clinical context and differential diagnosis. A succinct review of patterns of nodal disease of the neck with anatomic orientation using illustrations of typical and atypical disease entities in this region enhance and reinforce understanding of this often complex area of imaging.

Cavity equations for a positive- or negative-refraction-index material with electric and magnetic nonlinearities.

We study evolution equations for electric and magnetic field amplitudes in a ring cavity with plane mirrors. The cavity is filled with a positive or negative-refraction-index material with third-order effective electric and magnetic nonlinearities. Two coupled nonlinear equations for the electric and magnetic amplitudes are obtained. We prove that the description can be reduced to one Lugiato-Lefever equation with generalized coefficients. A stability analysis of the homogeneous solution, complemented with numerical integration, shows that any combination of the parameters should correspond to one of three characteristic behaviors.