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We develop a linear theory of very weak solutions for nonlocal eigenvalue problems $\mathcal L u = \lambda u + f$ involving integro-differential operators posed in bounded domains with homogeneous Dirichlet exterior condition, with and…

Accurate segmentation of myocardial scar from late gadolinium enhanced (LGE) cardiac MRI is essential for evaluating tissue viability, yet remains challenging due to variable contrast and imaging artifacts. Electrocardiogram (ECG) signals…

We propose an exhaustive methodology that leverages all levels of feature abstraction, targeting an enhancement in the generalizability of image classification to unobserved hospitals. Our approach incorporates augmentation-based…

Tensor non-Gaussianity represents an important future probe of the physics of inflation. Inspired by recent works, we elaborate further on the possibility of significant primordial tensor non-Gaussianities sourced by extra fields during…

Given a reducible Galois representation $\overline{\rho}: G_{\mathbb{Q}} \rightarrow GL_2( \mathbb{F}_q)$ we show there exists an irreducible deformation $\rho : G_{\mathbb{Q}} \rightarrow GL_2 (\mathbb{W} [[T_1, T_2,.., T_r,....,]])$ of…

In this note we introduce some nonlinear extremal nonlocal operators that approximate the, so called, truncated Laplacians. For these operators we construct representation formulas that lead to the construction of what, with an abuse of…

Thurston introduced \emph{invariant (quadratic) laminations} in his 1984 preprint as a vehicle for understanding the connected Julia sets and the parameter space of quadratic polynomials. Important ingredients of his analysis of the angle…

Inference over tails is performed by applying only the results of extreme value theory. Whilst such theory is well defined and flexible enough in the univariate case, multivariate inferential methods often require the imposition of…

We introduce a new class of algebras called Poisson orders. This class includes the symplectic reflection algebras of Etingof and Ginzburg, many quantum groups at roots of unity, and enveloping algebras of restricted Lie algebras in…

This is a systematic introduction for physicists to the theory of algebras and groups with braid statistics, as developed over the last three years by the author. There are braided lines, braided planes, braided matrices and braided groups…

Differential cross section measurements are the currency of scientific exchange in particle and nuclear physics. A key challenge for these analyses is the correction for detector distortions, known as deconvolution or unfolding. Binned…

In this investigation we focus on the problem of mapping the ground reflectivity with multiple laser scanners mounted on mobile robots/vehicles. The problem originates because regions of the ground become populated with a varying number of…

Let $G$ be a split reductive group over a number field $F$. We consider the computation of the inner product of two $K$-spherical pseudo Eisenstein series of $G$ supported in $[T,\mathcal{O}(1)]$ by means of residues, following a classical…

Let $G=Sp(4,\mathbb{R})$ and let $\pi$ be an irreducible, unitary representation of $G$ which is cohomological with respect to trivial coefficients. Using the inclusion from $SO(5,\mathbb{C})$ to $GL(5,\mathbb{C})$, we transfer $\pi$ to an…

We study the middle convolution of local systems on the punctured affine line in the setting of singular cohomology and in the setting of \'etale cohomology. We derive a formula to compute the topological monodromy of the middle convolution…

We probe the theoretical connection among three different approaches to analyze the entanglement of identical particles, i.e., the first quantization language (1QL), elementary-symmetric/exterior products (which has the mathematical…

Constructing disentangled representations is known to be a difficult task, especially in the unsupervised scenario. The dominating paradigm of unsupervised disentanglement is currently to train a generative model that separates different…

Let $G$ and $\tilde G$ be reductive groups over a local field $F$. Let $\eta : \tilde G \to G$ be a $F$-homomorphism with commutative kernel and commutative cokernel. We investigate the pullbacks of irreducible admissible…

Many complex problems encountered in both production and daily life can be conceptualized as combinatorial optimization problems (COPs) over graphs. Recent years, reinforcement learning (RL) based models have emerged as a promising…

Rare diseases dominate the diagnostic challenge in medical imaging yet are severely underrepresented in clinical datasets, causing classifiers to fail on exactly the conditions where reliable detection matters most. Generative augmentation…