Kathryn Hess Bellwald

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Let X be a simplicial set. We construct a novel adjunction be- tween the categories RX of retractive spaces over X and ComodX+ of X+- comodules, then apply recent work on left-induced model category structures [5], [16] to establish the existence of a left ...

The organizational principles that distinguish the human brain from those of other species have been a long-standing enigma in neuroscience. Here, we leverage advances in algebraic topology to uncover the structural properties of the human brain at subcellular resolution. First, we reveal a much higher perisomatic branching density in pyramidal neurons when comparing homologous cortical regions in humans and mice. Traditional scaling methods consistently fail to interpret this difference, suggesting a disti

Establishing with precision the quantity and identity of the cell types of the brain is a prerequisite for a detailed compendium of gene and protein expression in the central nervous system (CNS). Currently, however, strict quantitation of cell numbers has ...

In this paper we elaborate a general homotopy-theoretic framework in which to study problems of descent and completion and of their duals, codescent and cocompletion. Our approach to homotopic (co)descent and to derived (co)completion can be viewed as $\in ...

Given any twisting cochain t:C→A , where C is a connected, coaugmented chain coalgebra and A is an augmented chain algebra over an arbitrary commutative ring R, we construct a twisted extension of chain complexes Full-size image (1 K) of which both the wel ...

We introduce the notion of a strongly homotopy-comultiplicative resolution of a module coalgebra over a chain Hopf algebra, which we apply to proving a comultiplicative enrichment of a well-known theorem of Moore concerning the homology of quotient spaces ...

The function of the neocortex is fundamentally determined by its repeating microcircuit motif, but also by its rich, interregional connectivity. We present a data-driven computational model of the anatomy of non-barrel primary somatosensory cortex of juvenile rat, integrating whole-brain scale data while providing cellular and subcellular specificity. The model consists of 4.2 million morphologically detailed neurons, placed in a digital brain atlas. They are connected by 14.2 billion synapses, comprising l

We define twisted composition products of symmetric sequences via classifying morphisms rather than twisting cochains. Our approach allows us to establish an adjunction that simultaneously generalizes a classic one for algebras and coalgebras, and the bar- ...

Hopf-Galois extensions of rings generalize Galois extensions, with the coaction of a Hopf algebra replacing the action of a group. Galois extensions with respect to a group

G

are the Hopf-Galois extensions with respect to the dual of the group algebra of ...

Rational homotopy theory is the study of topological spaces “modulo torsion”. When rational homotopy theorists calculate algebraic invariants of a topological space, such as its homotopy or homology groups, they retain only the nontorsion information. Algebraic models of topological spaces are the most important tools of the rational homotopy theorist.

Twisted topological Hochschild homology of Cn-equivariant spectra was introduced by Angeltveit, Blumberg, Gerhardt, Hill, Lawson, and Mandell, building on the work of Hill, Hopkins, and Ravenel on norms in equivariant homotopy theory. In this paper we intr ...

Standard single-cell RNA-seq analysis frameworks aggregate over-lapping biological processes and impose a single parametrization, conflating distinct programs. Here, we introduce a topological framework that detects and disentangles multiple cyclic processes directly from single-cell transcriptomic data. We validate this approach on synthetic datasets and scRNA-seq profiles of human dermal fibroblasts under control conditions and following androgen receptor (AR) silencing, as well as in vivo mouse prostate

We show that the configuration spaces of a product of parallelizable manifolds may be recovered from those of the factors as the Boardman-Vogt tensor product of right modules over the operads of little cubes of the appropriate dimension. We also discuss an ...

The bedrock of persistence theory over a single parameter is decomposition of persistence modules into intervals. In [HLM24], the authors leveraged interval decomposition to produce a cell decomposition of the minimal model of a simply connected copersistent space. The key tool was a technique called interval surgery, which involves the gluing of intervals to a persistent CDGA by means of algebraic cell attachments. In this article, we define a compact, combinatorial model categorical structure that context

Motivation: Unbiased clustering methods are needed to analyze growing numbers of complex data sets. Currently available clustering methods often depend on parameters that are set by the user, they lack stability, and are not applicable to small data sets. ...

A key player in the formation of endoplasmic reticulum sheets is CLIMP-63, but mechanistic details remained elusive. Here authors combined cellular experiments and mathematical modelling to show that S-acylation of CLIMP-63 regulates its function by mediat ...

Environmental cues influence the highly dynamic morphology of microglia. Strategies to characterize these changes usually involve user-selected morphometric features, which preclude the identification of a spectrum of context-dependent morphological phenot ...

We construct a spectral sequence converging to the homology of the ordered configuration spaces of a product of parallelizable manifolds. To identify the second page of this spectral sequence, we introduce a version of the Boardman-Vogt tensor product for ...

To distinguish between subpopulations, we developed a metric based on the mathematical theory of simplicial complexes that captures the complexity of their connectivity by contrasting its higher-order structure to a random control and confirmed its relevan ...

We prove existence results à la Jeff Smith for left-induced model category structures, of which the injective model structure on a diagram category is an important example. We further develop the notions of fibrant generation and Postnikov presentation fro ...

Kathryn Hess Bellwald

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Waldhausen K-theory of spaces via comodules

Of mice and men: Increased dendritic complexity gives rise to unique human networks

Intact Drosophila central nervous system cellular quantitation reveals sexual dimorphism

A general framework for homotopic descent and codescent

The Hochschild complex of a twisting cochain

Multiplicative structure in equivariant cohomology

Modeling and simulation of neocortical micro- and mesocircuitry (Part I, anatomy)

Twisting structures and morphisms up to strong homotopy

Homotopic Hopf-Galois extensions: foundations and examples

A history of rational homotopy theory

Computational tools for twisted topological Hochschild homology of equivariant spectra

Topology identifies concurrent cyclic processes in single-cell transcriptomics and androgen receptor function

Configuration Spaces Of Products

Interval-sphere model structures

Two-Tier Mapper, an unbiased topology-based clustering method for enhanced global gene expression analysis

Dynamics of CLIMP-63 S-acylation control ER morphology

A tool for mapping microglial morphology, morphOMICs, reveals brain-region and sex-dependent phenotypes

A Künneth theorem for configuration spaces

Heterogeneous and higher-order cortical connectivity undergirds efficient, robust, and reliable neural codes

Left-induced model structures and diagram categories