Scaling of a large-scale simulation of synchronous slow-wave and asynchronous awake-like activity of a cortical model with long-range interconnections. (arXiv:1902.08410v2 [cs.NE] UPDATED)

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Cortical synapse organization supports a range of dynamic states on multiple spatial and temporal scales, from synchronous slow wave activity (SWA), characteristic of deep sleep or anesthesia, to fluctuating, asynchronous activity during wakefulness (AW). Such dynamic diversity poses a challenge for producing efficient large-scale simulations that embody realistic metaphors of short- and long-range synaptic connectivity.…

Segmentation of lesioned brain anatomy with deep volumetric neural networks and multiple spatial priors achieves human-level performance. (arXiv:1905.10010v3 [eess.IV] UPDATED)

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Conventional automated segmentation of MRI of the brain and head distinguishes different tissues based on image intensities and prior tissue probability maps (TPM). This works well for normal head anatomies, but fails in the presence of unexpected lesions. Deep convolutional neural networks leverage instead spatial patterns and can learn to segment lesions, but have thus…

Constant order multiscale reduction for stochastic reaction networks. (arXiv:1909.11916v3 [math.PR] UPDATED)

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Stochastic models of chemical reaction networks are an important tool to describe and analyze noise effects in cell biology. In this paper, we consider a particular multiscaling limit for a class of stochastic reaction systems, with the property that all reactions initially take place at an approximately constant rate. It is known that the model…

The distribution of the $L_4$ norm of Littlewood polynomials. (arXiv:1911.11246v1 [math.NT])

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Classical conjectures due to Littlewood, Erd\H{o}s and Golay concern the asymptotic growth of the $L_p$ norm of a Littlewood polynomial (having all coefficients in $\{1, -1\}$) as its degree increases, for various values of $p$. Attempts over more than fifty years to settle these conjectures have identified certain classes of the Littlewood polynomials as particularly…

All $2$-transitive groups have the EKR-module property. (arXiv:1911.11252v1 [math.CO])

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We prove that every 2-transitive group has a property called the EKR-module property. This property gives a characterization of the maximum intersecting sets of permutations in the group. Specifically, the characteristic vector of any maximum intersecting set in a 2-transitive group is the linear combination of the characteristic vectors of the stabilizers of a points…

Graph isomorphism in quasipolynomial time parameterized by treewidth. (arXiv:1911.11257v1 [cs.DS])

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We extend Babai’s quasipolynomial-time graph isomorphism test (STOC 2016) and develop a quasipolynomial-time algorithm for the multiple-coset isomorphism problem. The algorithm for the multiple-coset isomorphism problem allows to exploit graph decompositions of the given input graphs within Babai’s group theoretic framework. We use it to develop a graph isomorphism test that runs in time $n^{\operatorname{polylog}(k)}$…

Point defects in 2-D liquid crystals with singular potential: profiles and stability. (arXiv:1911.11258v1 [math.AP])

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We study radial symmetric point defects with degree $\frac {k}{2}$ in 2D disk or $\mathbb{R}^2$ in $Q$-tensor framework with singular bulk energy, which is defined by Bingham closure. First, we obtain the existence of solutions for the profiles of radial symmetric point defects with degree $\frac k2$ in 2D disk or $\mathbb{R}^2$. Then we prove…

Decomposing the classifying diagram in terms of classifying spaces of groups. (arXiv:1911.11268v1 [math.AT])

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The classifying diagram was defined by Rezk and is a generalization of the nerve of a category; in contrast to the nerve, the classifying diagram of two categories is equivalent if and only if the categories are equivalent. In this paper we prove that the classifying diagram of any category is characterized in terms of…

Global gauge conditions in the Batalin-Vilkovisky formalism. (arXiv:1911.11269v1 [math-ph])

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In the Batalin-Vilkovisky formalism, gauge conditions are expressed as Lagrangian submanifolds in the space of fields and antifields. We discuss a way of patching together gauge conditions over different parts of the space of fields, and apply this method to extend the light-cone gauge for the superparticle to a conic neighbourhood of the forward light-cone…

Financial accumulation implies ever-increasing wealth inequality. (arXiv:1809.08681v3 [q-fin.GN] UPDATED)

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Wealth inequality is an important matter for economic theory and policy. Ongoing debates have been discussing recent rise in wealth inequality in connection with recent development of active financial markets around the world. Existing literature on wealth distribution connects the origins of wealth inequality with a variety of drivers. Our approach develops a minimalist modelling…