The Determining Role of Covariances in Large Networks of Stochastic Neurons

Biological neural networks are notoriously hard to model due to their stochastic behavior and high dimensionality. We tackle this problem by constructing a dynamical model of both the expectations and covariances of the fractions of active and refractory neurons in the network's populations. We do so by describing the evolution of the states of individual neurons with a continuous-time Markov chain, from which we formally derive a low-dimensional dynamical system. This is done by solving a moment closure problem in a way that is compatible with the nonlinearity and boundedness of the activation function. Our dynamical system captures the behavior of the high-dimensional stochastic model even in cases where the mean-field approximation fails to do so. Taking into account the second-order moments modifies the solutions that would be obtained with the mean-field approximation and can lead to the appearance or disappearance of fixed points and limit cycles. We moreover perform numerical experiments where the mean-field approximation leads to periodically oscillating solutions, while the solutions of the second-order model can be interpreted as an average taken over many realizations of the stochastic model. Altogether, our results highlight the importance of including higher moments when studying stochastic networks and deepen our understanding of correlated neuronal activity.

Predicting cognitive decline in a low-dimensional representation of brain morphology

Identifying early signs of neurodegeneration due to Alzheimer's disease (AD) is a necessary first step towards preventing cognitive decline. Individual cortical thickness measures, available after processing anatomical magnetic resonance imaging (MRI), are sensitive markers of neurodegeneration. However, normal aging cortical decline and high inter-individual variability complicate the comparison and statistical determination of the impact of AD-related neurodegeneration on trajectories. In this paper, we computed trajectories in a 2D representation of a 62-dimensional manifold of individual cortical thickness measures. To compute this representation, we used a novel, nonlinear dimension reduction algorithm called Uniform Manifold Approximation and Projection (UMAP). We trained two embeddings, one on cortical thickness measurements of 6237 cognitively healthy participants aged 18-100 years old and the other on 233 mild cognitively impaired (MCI) and AD participants from the longitudinal database, the Alzheimer's Disease Neuroimaging Initiative database (ADNI). Each participant had multiple visits ([Formula: see text]), one year apart. The first embedding's principal axis was shown to be positively associated ([Formula: see text]) with participants' age. Data from ADNI is projected into these 2D spaces. After clustering the data, average trajectories between clusters were shown to be significantly different between MCI and AD subjects. Moreover, some clusters and trajectories between clusters were more prone to host AD subjects. This study was able to differentiate AD and MCI subjects based on their trajectory in a 2D space with an AUC of 0.80 with 10-fold cross-validation.

Zebrafish brain atlases: a collective effort for a tiny vertebrate brain

In the past two decades, digital brain atlases have emerged as essential tools for sharing and integrating complex neuroscience datasets. Concurrently, the larval zebrafish has become a prominent vertebrate model offering a strategic compromise for brain size, complexity, transparency, optogenetic access, and behavior. We provide a brief overview of digital atlases recently developed for the larval zebrafish brain, intersecting neuroanatomical information, gene expression patterns, and connectivity. These atlases are becoming pivotal by centralizing large datasets while supporting the generation of circuit hypotheses as functional measurements can be registered into an atlas' standard coordinate system to interrogate its structural database. As challenges persist in mapping neural circuits and incorporating functional measurements into zebrafish atlases, we emphasize the importance of collaborative efforts and standardized protocols to expand these resources to crack the complex codes of neuronal activity guiding behavior in this tiny vertebrate brain.

Dimension matters when modeling network communities in hyperbolic spaces

Over the last decade, random hyperbolic graphs have proved successful in providing geometric explanations for many key properties of real-world networks, including strong clustering, high navigability, and heterogeneous degree distributions. These properties are ubiquitous in systems as varied as the internet, transportation, brain or epidemic networks, which are thus unified under the hyperbolic network interpretation on a surface of constant negative curvature. Although a few studies have shown that hyperbolic models can generate community structures, another salient feature observed in real networks, we argue that the current models are overlooking the choice of the latent space dimensionality that is required to adequately represent clustered networked data. We show that there is an important qualitative difference between the lowest-dimensional model and its higher-dimensional counterparts with respect to how similarity between nodes restricts connection probabilities. Since more dimensions also increase the number of nearest neighbors for angular clusters representing communities, considering only one more dimension allows us to generate more realistic and diverse community structures.

Dimension reduction of dynamics on modular and heterogeneous directed networks

Dimension reduction is a common strategy to study nonlinear dynamical systems composed by a large number of variables. The goal is to find a smaller version of the system whose time evolution is easier to predict while preserving some of the key dynamical features of the original system. Finding such a reduced representation for complex systems is, however, a difficult task. We address this problem for dynamics on weighted directed networks, with special emphasis on modular and heterogeneous networks. We propose a two-step dimension-reduction method that takes into account the properties of the adjacency matrix. First, units are partitioned into groups of similar connectivity profiles. Each group is associated to an observable that is a weighted average of the nodes' activities within the group. Second, we derive a set of equations that must be fulfilled for these observables to properly represent the original system's behavior, together with a method for approximately solving them. The result is a reduced adjacency matrix and an approximate system of ODEs for the observables' evolution. We show that the reduced system can be used to predict some characteristic features of the complete dynamics for different types of connectivity structures, both synthetic and derived from real data, including neuronal, ecological, and social networks. Our formalism opens a way to a systematic comparison of the effect of various structural properties on the overall network dynamics. It can thus help to identify the main structural driving forces guiding the evolution of dynamical processes on networks.

Beyond Wilson-Cowan dynamics: oscillations and chaos without inhibition

Fifty years ago, Wilson and Cowan developed a mathematical model to describe the activity of neural populations. In this seminal work, they divided the cells in three groups: active, sensitive and refractory, and obtained a dynamical system to describe the evolution of the average firing rates of the populations. In the present work, we investigate the impact of the often neglected refractory state and show that taking it into account can introduce new dynamics. Starting from a continuous-time Markov chain, we perform a rigorous derivation of a mean-field model that includes the refractory fractions of populations as dynamical variables. Then, we perform bifurcation analysis to explain the occurrence of periodic solutions in cases where the classical Wilson-Cowan does not predict oscillations. We also show that our mean-field model is able to predict chaotic behavior in the dynamics of networks with as little as two populations.

Toward an integrative neurovascular framework for studying brain networks

Brain functional connectivity based on the measure of blood oxygen level-dependent (BOLD) functional magnetic resonance imaging (fMRI) signals has become one of the most widely used measurements in human neuroimaging. However, the nature of the functional networks revealed by BOLD fMRI can be ambiguous, as highlighted by a recent series of experiments that have suggested that typical resting-state networks can be replicated from purely vascular or physiologically driven BOLD signals. After going through a brief review of the key concepts of brain network analysis, we explore how the vascular and neuronal systems interact to give rise to the brain functional networks measured with BOLD fMRI. This leads us to emphasize a view of the vascular network not only as a confounding element in fMRI but also as a functionally relevant system that is entangled with the neuronal network. To study the vascular and neuronal underpinnings of BOLD functional connectivity, we consider a combination of methodological avenues based on multiscale and multimodal optical imaging in mice, used in combination with computational models that allow the integration of vascular information to explain functional connectivity.

Sensory Afferents Use Different Coding Strategies for Heat and Cold

Primary afferents transduce environmental stimuli into electrical activity that is transmitted centrally to be decoded into corresponding sensations. However, it remains unknown how afferent populations encode different somatosensory inputs. To address this, we performed two-photon Ca²⁺ imaging from thousands of dorsal root ganglion (DRG) neurons in anesthetized mice while applying mechanical and thermal stimuli to hind paws. We found that approximately half of all neurons are polymodal and that heat and cold are encoded very differently. As temperature increases, more heating-sensitive neurons are activated, and most individual neurons respond more strongly, consistent with graded coding at population and single-neuron levels, respectively. In contrast, most cooling-sensitive neurons respond in an ungraded fashion, inconsistent with graded coding and suggesting combinatorial coding, based on which neurons are co-activated. Although individual neurons may respond to multiple stimuli, our results show that different stimuli activate distinct combinations of diversely tuned neurons, enabling rich population-level coding.

A Type 1 Diabetes Genetic Risk Score Predicts Progression of Islet Autoimmunity and Development of Type 1 Diabetes in Individuals at Risk

OBJECTIVE

We tested the ability of a type 1 diabetes (T1D) genetic risk score (GRS) to predict progression of islet autoimmunity and T1D in at-risk individuals.

RESEARCH DESIGN AND METHODS

We studied the 1,244 TrialNet Pathway to Prevention study participants (T1D patients' relatives without diabetes and with one or more positive autoantibodies) who were genotyped with Illumina ImmunoChip (median [range] age at initial autoantibody determination 11.1 years [1.2-51.8], 48% male, 80.5% non-Hispanic white, median follow-up 5.4 years). Of 291 participants with a single positive autoantibody at screening, 157 converted to multiple autoantibody positivity and 55 developed diabetes. Of 953 participants with multiple positive autoantibodies at screening, 419 developed diabetes. We calculated the T1D GRS from 30 T1D-associated single nucleotide polymorphisms. We used multivariable Cox regression models, time-dependent receiver operating characteristic curves, and area under the curve (AUC) measures to evaluate prognostic utility of T1D GRS, age, sex, Diabetes Prevention Trial-Type 1 (DPT-1) Risk Score, positive autoantibody number or type, HLA DR3/DR4-DQ8 status, and race/ethnicity. We used recursive partitioning analyses to identify cut points in continuous variables.

RESULTS

Higher T1D GRS significantly increased the rate of progression to T1D adjusting for DPT-1 Risk Score, age, number of positive autoantibodies, sex, and ethnicity (hazard ratio [HR] 1.29 for a 0.05 increase, 95% CI 1.06-1.6; P = 0.011). Progression to T1D was best predicted by a combined model with GRS, number of positive autoantibodies, DPT-1 Risk Score, and age (7-year time-integrated AUC = 0.79, 5-year AUC = 0.73). Higher GRS was significantly associated with increased progression rate from single to multiple positive autoantibodies after adjusting for age, autoantibody type, ethnicity, and sex (HR 2.27 for GRS >0.295, 95% CI 1.47-3.51; P = 0.0002).

CONCLUSIONS

The T1D GRS independently predicts progression to T1D and improves prediction along T1D stages in autoantibody-positive relatives.

Finite-size analysis of the detectability limit of the stochastic block model

It has been shown in recent years that the stochastic block model is sometimes undetectable in the sparse limit, i.e., that no algorithm can identify a partition correlated with the partition used to generate an instance, if the instance is sparse enough and infinitely large. In this contribution, we treat the finite case explicitly, using arguments drawn from information theory and statistics. We give a necessary condition for finite-size detectability in the general SBM. We then distinguish the concept of average detectability from the concept of instance-by-instance detectability and give explicit formulas for both definitions. Using these formulas, we prove that there exist large equivalence classes of parameters, where widely different network ensembles are equally detectable with respect to our definitions of detectability. In an extensive case study, we investigate the finite-size detectability of a simplified variant of the SBM, which encompasses a number of important models as special cases. These models include the symmetric SBM, the planted coloring model, and more exotic SBMs not previously studied. We conclude with three appendices, where we study the interplay of noise and detectability, establish a connection between our information-theoretic approach and random matrix theory, and provide proofs of some of the more technical results.

Supersymmetric Ruijsenaars-Schneider model

An integrable supersymmetric generalization of the trigonometric Ruijsenaars-Schneider model is presented whose symmetry algebra includes the super Poincaré algebra. Moreover, its Hamiltonian is shown to be diagonalized by the recently introduced Macdonald superpolynomials. Somewhat surprisingly, the consistency of the scalar product forces the discreteness of the Hilbert space.

Choriocarcinoma metastatic to the lung. A cytologic study with identification of human choriogonadotropin with an immunoperoxidase technique

A case of choriocarcinoma metastatic to the lung following a previous hydatidiform mole is presented. It was possible to make definitive identification of trophoblastic elements on a needle aspiration biopsy using an immunoperoxidase staining technique, thus avoiding diagnostic thoracotomy prior to therapeutic intervention. A method of immunoperoxidase staining of previously fixed and Papanicolaou-stained needle aspiration biopsy specimens is also described, and other uses of the immunoperoxidase technique on needle biopsy specimens are discussed.

Giant-cell carcinoma of the lung. A cytologic study

A case of giant-cell carcinoma of the lung, confirmed at autopsy, is presented. The cytologic features seen in sputum samples, bronchial washings and brushings and fine needle aspiration biopsy material as well as the histologic findings are described. The possible relationship to bronchioloalveolar carcinoma is discussed. The cytologic features of giant-cell carcinoma of the lung, when seen in the context of the clinical and radiologic setting, should allow the cytologic identification of the tumor prior to surgical intervention.