Collections of measures on compact metric spaces form a model category (“data complexes”), whose morphisms are marginalization integrals. The fibrant objects in this category represent collections of measures in which there is a measure on a product space that marginalizes to any measures on pairs of its factors. The homotopy and homology for this category…
Brain connectivity with functional Magnetic Resonance Imaging (fMRI) is a popular approach for detecting differences between healthy and clinical populations. Before creating a functional brain network, the fMRI time series must undergo several preprocessing steps to control for artifacts and to improve data quality. However, preprocessing may affect the results in an undesirable way. Spatial…
Opers were introduced by Beilinson-Drinfeld [BD93, BD91], and in [Bis03] a higher rank analog was considered, where the successive quotients of the oper filtration are allowed to have higher rank. We dedicate this paper to introducing generalized B-opers (where “B” stands for “bilinear”), obtained by endowing the underlying vector bundle, in the set-up of [Bis03],…
In the design of artificially sentient robots, an obstacle always has been that conventional computers cannot really process information in parallel, whereas the human affective system is capable of producing experiences of emotional concurrency (e.g., happy and sad). Another schism that has been in the way is the persistent Cartesian divide between cognition and affect,…
Increasing rates of global trade and travel, as well as changing climatic patterns, have led to more frequent outbreaks of plant disease epidemics worldwide. Mathematical modelling is a key tool in predicting where and how these new threats will spread, as well as in assessing how damaging they might be. Models can also be used…
We construct super Hamiltonian integrable systems within the theory of Supersymmetric Poisson vertex algebras (SUSY PVAs). We provide a powerful tool for the understanding of SUSY PVAs called the super master formula. We attach some Lie superalgebraic data to a generalized SUSY W-algebra and show that it is equipped with two compatible SUSY PVA brackets.…
We provide computational tools to calculate the strict units of commutative ring spectra. We describe the Goerss-Hopkins-Miller spectral sequence for computing strict units of $E_\infty$-$H\mathbb{F}_p$-algebras, and use it to compute the strict units of polynomial and truncated polynomial rings, whose Postnikov towers we also analyze. We then sketch the calculation of the strict units of…
We present a practical health-theme machine learning (ML) application concerning `AI for social good’ domain for `Producing Good Outcomes’ track. In particular, the solution is concerning the problem of a potential elderly adult dementia onset prediction in aging societies. The paper discusses our attempt and encouraging preliminary study results of behavioral responses analysis in a…
Inspired by the first-order method of Malitsky and Pock, we propose a novel variational framework for compressed MR image reconstruction which introduces the application of a rotation-invariant discretization of total variation functional into MR imaging while exploiting BM3D frame as a sparsifying transform. The proposed model is presented as a constrained optimization problem, however, we…
Over 50% of the world population is at risk of mosquito-borne diseases. Female Ae. aegypti mosquito species transmit Zika, Dengue, and Chikungunya. The spread of these diseases correlate positively with the vector population, and this population depends on biotic and abiotic environmental factors including temperature, vegetation condition, humidity and precipitation. To combat virus outbreaks, information…