Highlights d Low-dimensional shared variability can be generated in spatial network models d Synaptic spatial and temporal scales determine the dimensions of shared variability d Depolarizing inhibitory neurons suppresses the populationwide fluctuations d Modeling the attentional modulation of variability within and between brain areas

A pervasive yet puzzling feature of cortical circuits is that despite their complex wiring, population-wide shared spiking variability is low dimensional.Neuronal variability is often used as a probe to understand how recurrent circuitry supports network dynamics. However, current models cannot internally produce low dimensional shared variability, and rather assume that it is inherited from outside the circuit. We analyze population recordings from the visual pathway where directed attention differentially modulates shared variability within and between areas, which is difficult to explain with externally imposed variability. We show that if the spatial and temporal scales of inhibitory coupling match physiology, network models capture the low dimensional shared 1 . CC-BY-NC-ND 4.0 International license peer-reviewed) is the author/funder. It is made available under aThe copyright holder for this preprint (which was not . http://dx.doi.org/10.1101/217976 doi: bioRxiv preprint first posted online Nov. 11, 2017; variability of our population data. Our theory provides a critical link between measured cortical circuit structure and recorded population activity.One Sentence Summary: Circuit models with spatio-temporal excitatory and inhibitory interactions generate population variability that captures recorded neuronal activity across cognitive states. IntroductionThe trial-to-trial variability of neuronal responses gives a critical window into how the circuit structure connecting neurons drives brain activity. This idea combined with the widespread use of population recordings has prompted a deep interest in how variability is distributed over a population (1, 2). There has been a proliferation of data sets where the shared variability over a population is low dimensional (3-7), meaning that neuronal activity waxes and wanes as a group. How cortical networks generate low dimensional shared variability is currently unknown.Theories of cortical variability can be broadly separated into two categories: ones where variability is internally generated through recurrent network interactions ( Fig. 1Ai) and ones where variability originates external to the network (Fig. 1Aii). Networks of spiking neuron models where strong excitation is balanced by opposing recurrent inhibition produce high single neuron variability through internal mechanisms (8-10). However, these networks famously enforce an asynchronous solution, and as such fail to explain population-wide shared variability (11)(12)(13). This lack of success is contrasted with the ease of producing arbitrary correlation structure from external sources. Indeed, many past cortical models assume a global fluctuation from an external source (2,7,(14)(15)(16), and accurately capture the structure of population data.However, such phenomenological models are circular, with an assumption of variability from 2 . CC-BY-NC-ND 4.0 International license peer-reviewed) is the author/funder. It is made available under a The copyright holder for this preprint (which was not . http...

Supplementary data are available at Bioinformatics online.

The increasing quality and the reducing cost of high-throughput sequencing technologies for 16S rRNA gene profiling enable researchers to directly analyze microbe communities in natural environments. The direct interactions among microbial species of a given ecological system can help us understand the principles of community assembly and maintenance under various conditions. Compositionality and dimensionality of microbiome data are two main challenges for inferring the direct interaction network of microbes. In this article, we use the logistic normal distribution to model the background mechanism of microbiome data, which can appropriately deal with the compositional nature of the data. The direct interaction relationships are then modeled via the conditional dependence network under this logistic normal assumption. We then propose a novel penalized maximum likelihood method called gCoda to estimate the sparse structure of inverse covariance for latent normal variables to address the high dimensionality of the microbiome data. An effective Majorization-Minimization algorithm is proposed to solve the optimization problem in gCoda. Simulation studies show that gCoda outperforms existing methods (e.g., SPIEC-EASI) in edge recovery of inverse covariance for compositional data under a variety of scenarios. gCoda also performs better than SPIEC-EASI for inferring direct microbial interactions of mouse skin microbiome data.