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Topological correctness plays a critical role in many image segmentation tasks, yet most networks are trained using pixel-wise loss functions, such as Dice, neglecting topological accuracy. Existing topology-aware methods often lack robust…

We introduce a new theoretical framework for deriving lower bounds on data movement in bilinear algorithms. Bilinear algorithms are a general representation of fast algorithms for bilinear functions, which include computation of matrix…

Accurate segmentation and classification of nuclei in histology images is critical but challenging due to nuclei heterogeneity, staining variations, and tissue complexity. Existing methods often struggle with limited dataset variability,…

A topology preserving skeleton is a synthetic representation of an object that retains its topology and many of its significant morphological properties. The process of obtaining the skeleton, referred to as skeletonization or thinning, is…

The structural and spatial arrangements of cells within tissues represent their functional states, making graph-based learning highly suitable for histopathology image analysis. Existing methods often rely on fixed graphs with predefined…

Given an open cover of a paracompact topological space X, there are two natural ways to construct a map from the cohomology of the nerve of the cover to the cohomology of X. One of them is based on a partition of unity, and is more…

Robotic systems with redundant degrees of freedom can achieve the same task outcome using multiple configurations, resulting in solution sets that form manifolds in the configuration space. Existing approaches typically exploit such…

We adapt the bialgebra and Hopf relations to expose internal structure in the ground state of a Hamiltonian with $Z_2$ topological order. Its tensor network description allows for exact contraction through simple diagrammatic rewrite rules.…

We present a method that connects a well-established nonlinear (bilinear) identification method from time-domain data with neural network (NNs) advantages. The main challenge for fitting bilinear systems is the accurate recovery of the…

In a preceding paper we introduced a notion of compatibility between a Jacobi structure and a Riemannian structure on a smooth manifold. We proved that in the case of fundamental examples of Jacobi structures : Poisson structures, contact…

In this article we provide a Hamilton-Jacobi formalism in locally conformally symplectic manifolds. Our interest in the Hamilton-Jacobi theory comes from the suitability of this theory as an integration method for dynamical systems, whilst…

Biomolecular structure comparison not only reveals evolutionary relationships, but also sheds light on biological functional properties. However, traditional definitions of structure or sequence similarity always involve superposition or…

The statistical mechanical approach to complex networks is the dominant paradigm in describing natural and societal complex systems. The study of network properties, and their implications on dynamical processes, mostly focus on locally…

In this paper we introduce the notion of infinite dimensional Jacobi structure to describe the geometrical structure of a class of nonlocal Hamiltonian systems which appear naturally when applying reciprocal transformations to Hamiltonian…

We introduce a method for learning chaotic maps using an improved autoencoder neural network that incorporates a conjugacy layer in the latent space. The added conjugacy layer transforms nonlinear maps into a simple piecewise linear map…

White matter tract segmentation is crucial for studying brain structural connectivity and neurosurgical planning. However, segmentation remains challenging due to issues like class imbalance between major and minor tracts, structural…

We develop techniques, based on differential geometry, to compute holomorphic Yukawa couplings for heterotic line bundle models on Calabi-Yau manifolds defined as complete intersections in projective spaces. It is shown explicitly how these…

We propose a novel approach to contact Hamiltonian mechanics which, in contrast to the one dominating in the literature, serves also for non-trivial contact structures. In this approach Hamiltonians are no longer functions on the contact…

As networks grow in size and complexity, backbones become an essential network representation. Indeed, they provide a simplified yet informative overview of the underlying organization by retaining the most significant and structurally…

This paper explores the point set representation for tubular structure extraction tasks. Compared with the traditional mask representation, the point set representation enjoys its flexibility and representation ability, which would not be…