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We consider coherent and cohesive sheaves of $\cO$--modules over open sets $\Omega\subset\bC^n$. We prove that coherent sheaves, and certain other sheaves derived from them, are cohesive; and conversely, certain sheaves derived from…
We consider an algebraic variety X together with the choice of a subvariety Z. We show that any coherent sheaf on X can be constructed out of a coherent sheaf on the formal neighborhood of Z, a coherent sheaf on the complement of Z, and an…
We introduce and study a one-parameter family of fidelity-type quantities based on the weighted spectral geometric mean, which we call the \emph{weighted spectral fidelity} \(…
For a scheme X, we construct a sheaf C of complexes on X such that for every quasi-compact open subset U of X, C(U) is quasi-isomorphic to the Hochschild complex of the scheme U. Since C is moreover acyclic for taking sections on…
Virtual cell (VC) models aim to predict cellular responses to any perturbations in silico and have emerged as a promising approach for drug discovery and precision medicine. Yet, a clear gap still remains: while models routinely reported…
Let R be a commutative ring with identity and Specs(M) denote the set all second submodules of an R-module M. In this paper, we construct and study a sheaf of modules, denoted by O(N; M), on Specs(M) equipped with the dual Zariski topology…
Generative models are increasingly deployed as substitutes for real data in downstream scientific workflows, yet standard evaluation criteria remain focused on marginal distribution matching. We argue that this represents a fundamental gap:…
The sheaf-theoretic structure is useful in classifying no-go theorems related to non-locality and contextuality. It provides a new point of view different from conventional formularization of quantum mechanics. First, we examine a…
We prove two general results concerning spectral sequences of $\mathbf{FI}$-modules. These results can be used to significantly improve stable ranges in a large portion of the stability theorems for $\mathbf{FI}$-modules currently in the…
In this report, we present work towards a framework for modeling and checking behavior of spatially distributed component systems. Design goals of our framework are the ability to model spatial behavior in a component oriented, simple and…
Visual perception, the brain's construction of a stable world from sensory data, faces several long-standing, fundamental challenges. While often studied separately, these problems have resisted a single, unifying computational framework.…
We explain that spectral networks are a unifying framework that incorporates both shear (Fock-Goncharov) and length-twist (Fenchel-Nielsen) coordinate systems on moduli spaces of flat SL(2,C) connections, in the following sense. Given a…
Ascertaining causal direction from observational data is a fundamental challenge in scientific inquiry. Of particular interest is the problem of covariate-adjusted bivariate causal discovery, i.e., determining the causal direction between X…
We introduce a new neural architecture and an unsupervised algorithm for learning invariant representations from temporal sequence of images. The system uses two groups of complex cells whose outputs are combined multiplicatively: one that…
Beams made from thin-walled elements, whilst very efficient in terms of the structural strength and stiffness to weight ratios, can be susceptible to highly complex instability phenomena. A nonlinear analytical formulation based on…
Functional-structural models provide detailed representations of tree growth and their application to forestry seems full of prospects. However, owing to the complexity of tree architecture, parametric identification of such models remains…
A coupled cell network is a model for many situations such as food webs in ecosystems, cellular metabolism, economical networks... It consists in a directed graph $G$, each node (or cell) representing an agent of the network and each…
A fibration of graphs is an homomorphism that is a local isomorphism of in-neighbourhoods, much in the same way a covering projection is a local isomorphism of neighbourhoods. Recently, it has been shown that graph fibrations are useful…
Subsequence matching has appeared to be an ideal approach for solving many problems related to the fields of data mining and similarity retrieval. It has been shown that almost any data class (audio, image, biometrics, signals) is or can be…
This report proposes a novel framework for a rigorous robustness analysis of stochastic biochemical systems. The technique is based on probabilistic model checking. We adapt the general definition of robustness introduced by Kitano to the…