Eigenvalue spectral properties of sparse random matrices obeying Dale's law

Understanding the dynamics of large networks of neurons with heterogeneous connectivity architectures is a complex physics problem that demands novel mathematical techniques. Biological neural networks are inherently spatially heterogeneous, making them difficult to mathematically model. Random recurrent neural networks capture complex network connectivity structures and enable mathematically tractability. Our paper generalises previous classical results to sparse connectivity matrices which have distinct excitatory (E) or inhibitory (I) neural populations. By investigating sparse networks we construct our analysis to examine the impacts of all levels of network sparseness, and discover a novel nonlinear interaction between the connectivity matrix and resulting network dynamics, in both the balanced and unbalanced cases. Specifically, we deduce new mathematical dependencies describing the influence of sparsity and distinct E/I distributions on the distribution of eigenvalues (eigenspectrum) of the networked Jacobian. Furthermore, we illustrate that the previous classical results are special cases of the more general results we have described here. Understanding the impacts of sparse connectivities on network dynamics is of particular importance for both theoretical neuroscience and mathematical physics as it pertains to the structure-function relationship of networked systems and their dynamics. Our results are an important step towards developing analysis techniques that are essential to studying the impacts of larger scale network connectivity on network function, and furthering our understanding of brain function and dysfunction.Comment: 18 pages, 6 figure

Neural Field Models: A mathematical overview and unifying framework

Rhythmic electrical activity in the brain emerges from regular non-trivial interactions between millions of neurons. Neurons are intricate cellular structures that transmit excitatory (or inhibitory) signals to other neurons, often non-locally, depending on the graded input from other neurons. Often this requires extensive detail to model mathematically, which poses several issues in modelling large systems beyond clusters of neurons, such as the whole brain. Approaching large populations of neurons with interconnected constituent single-neuron models results in an accumulation of exponentially many complexities, rendering a realistic simulation that does not permit mathematical tractability and obfuscates the primary interactions required for emergent electrodynamical patterns in brain rhythms. A statistical mechanics approach with non-local interactions may circumvent these issues while maintaining mathematically tractability. Neural field theory is a population-level approach to modelling large sections of neural tissue based on these principles. Herein we provide a review of key stages of the history and development of neural field theory and contemporary uses of this branch of mathematical neuroscience. We elucidate a mathematical framework in which neural field models can be derived, highlighting the many significant inherited assumptions that exist in the current literature, so that their validity may be considered in light of further developments in both mathematical and experimental neuroscience.Comment: 55 pages, 10 figures, 2 table

Autoregressive models for biomedical signal processing

Autoregressive models are ubiquitous tools for the analysis of time series in many domains such as computational neuroscience and biomedical engineering. In these domains, data is, for example, collected from measurements of brain activity. Crucially, this data is subject to measurement errors as well as uncertainties in the underlying system model. As a result, standard signal processing using autoregressive model estimators may be biased. We present a framework for autoregressive modelling that incorporates these uncertainties explicitly via an overparameterised loss function. To optimise this loss, we derive an algorithm that alternates between state and parameter estimation. Our work shows that the procedure is able to successfully denoise time series and successfully reconstruct system parameters. This new paradigm can be used in a multitude of applications in neuroscience such as brain-computer interface data analysis and better understanding of brain dynamics in diseases such as epilepsy

Path Signatures for Seizure Forecasting

Forecasting the state of a system from an observed time series is the subject of research in many domains, such as computational neuroscience. Here, the prediction of epileptic seizures from brain measurements is an unresolved problem. There are neither complete models describing underlying brain dynamics, nor do individual patients exhibit a single seizure onset pattern, which complicates the development of a `one-size-fits-all' solution. Based on a longitudinal patient data set, we address the automated discovery and quantification of statistical features (biomarkers) that can be used to forecast seizures in a patient-specific way. We use existing and novel feature extraction algorithms, in particular the path signature, a recent development in time series analysis. Of particular interest is how this set of complex, nonlinear features performs compared to simpler, linear features on this task. Our inference is based on statistical classification algorithms with in-built subset selection to discern time series with and without an impending seizure while selecting only a small number of relevant features. This study may be seen as a step towards a generalisable pattern recognition pipeline for time series in a broader context

Genomic, Pathway Network, and Immunologic Features Distinguishing Squamous Carcinomas

This integrated, multiplatform PanCancer Atlas study co-mapped and identified distinguishing molecular features of squamous cell carcinomas (SCCs) from five sites associated with smokin

Pan-Cancer Analysis of lncRNA Regulation Supports Their Targeting of Cancer Genes in Each Tumor Context

Long noncoding RNAs (lncRNAs) are commonly dys-regulated in tumors, but only a handful are known toplay pathophysiological roles in cancer. We inferredlncRNAs that dysregulate cancer pathways, onco-genes, and tumor suppressors (cancer genes) bymodeling their effects on the activity of transcriptionfactors, RNA-binding proteins, and microRNAs in5,185 TCGA tumors and 1,019 ENCODE assays.Our predictions included hundreds of candidateonco- and tumor-suppressor lncRNAs (cancerlncRNAs) whose somatic alterations account for thedysregulation of dozens of cancer genes and path-ways in each of 14 tumor contexts. To demonstrateproof of concept, we showed that perturbations tar-geting OIP5-AS1 (an inferred tumor suppressor) andTUG1 and WT1-AS (inferred onco-lncRNAs) dysre-gulated cancer genes and altered proliferation ofbreast and gynecologic cancer cells. Our analysis in-dicates that, although most lncRNAs are dysregu-lated in a tumor-specific manner, some, includingOIP5-AS1, TUG1, NEAT1, MEG3, and TSIX, synergis-tically dysregulate cancer pathways in multiple tumorcontexts

Pan-cancer Alterations of the MYC Oncogene and Its Proximal Network across the Cancer Genome Atlas

Although theMYConcogene has been implicated incancer, a systematic assessment of alterations ofMYC, related transcription factors, and co-regulatoryproteins, forming the proximal MYC network (PMN),across human cancers is lacking. Using computa-tional approaches, we define genomic and proteo-mic features associated with MYC and the PMNacross the 33 cancers of The Cancer Genome Atlas.Pan-cancer, 28% of all samples had at least one ofthe MYC paralogs amplified. In contrast, the MYCantagonists MGA and MNT were the most frequentlymutated or deleted members, proposing a roleas tumor suppressors.MYCalterations were mutu-ally exclusive withPIK3CA,PTEN,APC,orBRAFalterations, suggesting that MYC is a distinct onco-genic driver. Expression analysis revealed MYC-associated pathways in tumor subtypes, such asimmune response and growth factor signaling; chro-matin, translation, and DNA replication/repair wereconserved pan-cancer. This analysis reveals insightsinto MYC biology and is a reference for biomarkersand therapeutics for cancers with alterations ofMYC or the PMN

Spatial Organization and Molecular Correlation of Tumor-Infiltrating Lymphocytes Using Deep Learning on Pathology Images

Beyond sample curation and basic pathologic characterization, the digitized H&E-stained images of TCGA samples remain underutilized. To highlight this resource, we present mappings of tumorinfiltrating lymphocytes (TILs) based on H&E images from 13 TCGA tumor types. These TIL maps are derived through computational staining using a convolutional neural network trained to classify patches of images. Affinity propagation revealed local spatial structure in TIL patterns and correlation with overall survival. TIL map structural patterns were grouped using standard histopathological parameters. These patterns are enriched in particular T cell subpopulations derived from molecular measures. TIL densities and spatial structure were differentially enriched among tumor types, immune subtypes, and tumor molecular subtypes, implying that spatial infiltrate state could reflect particular tumor cell aberration states. Obtaining spatial lymphocytic patterns linked to the rich genomic characterization of TCGA samples demonstrates one use for the TCGA image archives with insights into the tumor-immune microenvironment

Societal-level versus individual-level predictions of ethical behavior: a 48-society study of collectivism and individualism

Is the societal-level of analysis sufficient today to understand the values of those in the global workforce? Or are individual-level analyses more appropriate for assessing the influence of values on ethical behaviors across country workforces? Using multi-level analyses for a 48-society sample, we test the utility of both the societal-level and individual-level dimensions of collectivism and individualism values for predicting ethical behaviors of business professionals. Our values-based behavioral analysis indicates that values at the individual-level make a more significant contribution to explaining variance in ethical behaviors than do values at the societal-level. Implicitly, our findings question the soundness of using societal-level values measures. Implications for international business research are discussed