arXiv preprints from January 1, 2026 through September 19, 2026 — 06:25:35 EST
Correlation geometry and topology in a random, scalar beam carrying Orbital Angular Momentum (OAM) in $L$ modes are shown to be linked to the real and imaginary parts, respectively, of its orbitalization matrix (OM). The OM is obtained by filtering the cross-spectral density in the polar Fourier basis at a given cross-section and...
Distributed quantum sensing is an emerging application of quantum networking, where entangled probe states are employed to sense combinations of delocalized parameters with enhanced precision relative to using separable states. Squeezed states of light are a prime resource for experimental demonstrations of entanglement-enhanced...
A long-standing goal across heterogeneous catalysis, materials science, and condensed matter physics is to design alloys with prescribed local atomic arrangements. Recent experiments show that dilute trimetallic alloys unlock chemistries inaccessible to bimetallics, but realizing this potential requires knowing which dopant structures...
We study how $SL(2,\mathbb Z)$ transformations act on pole-truncated linear-response effective theories in $(2+1)$ dimensions. For correlators meromorphic within a finite low-frequency domain, the EFT data include both derivative-expanded transport coefficients and the retained non-hydrodynamic poles. Since the $S$-trans\-for\-mation...
The traditional $α$ effect is extended by the first temporal derivative, so that in turbulent flows the magnetic field entering the induction process is effectively sampled in the past. As a consequence, dynamo excitation becomes easier and cycle times are prolonged relative to solutions obtained from the local standard formulation....
In particle collider experiments, event reconstruction is the task of inferring the kinematics of short-lived particles produced in the hard scatter from the stable final states recorded by detectors. We decompose event reconstruction into two primary tasks: assigning measured jets and charged leptons to parent particles, and...
Soft materials store, dissipate and release mechanical stresses through relaxation processes that often span many orders of magnitude in time. Such relaxation spectra are widely used to infer internal material dynamics and are usually regarded as fingerprints of microscopic complexity, disorder, or heterogeneity. Here we show that a...
We compute exactly the acceptance and logical error rates for the distance $d=3$ and $d=5$ magic state cultivation circuits from Clifft [arXiv:2604.27058] and SOFT [arXiv:2512.23037] using Pauli propagation and binary tensor contraction. Actual $T$ gates are studied, not the $S$-gate proxy used for sampling. The calculation includes...
Three-dimensional CFD-DEM simulations were used to investigate the influence of fluidizing medium on the hydrodynamics and mixing of a binary fluidized bed containing equal-density 3 and 4 mm particles. Water and air were compared using identical geometry, particle properties, and initial conditions over matched normalized superficial...
Crises and population responses can form coupled dynamical systems, with crisis conditions shaping protective behaviours and collective responses altering the crisis trajectory. Existing models rarely capture both evolving crisis conditions and the reinforcement-dependent spread of competing behaviours. We propose a complex contagion...
We study complete two-sided constant-mean-curvature hypersurfaces of dimensions $2\le n\le6$ and finite Morse index in simply connected space forms. In the round sphere the immersed domain is compact; in Euclidean space every noncompact example is minimal; in hyperbolic space of curvature $-1$ we obtain compactness under explicit...
In this paper we affirmatively resolve the singularity conjecture for finitely supported non-degenerate random walks on cocompact Fuchsian groups. The method we use is based on constructing a pair of geodesic currents, one for the Lebesgue measure and one for the random walk measure, and checking that they are different by using...
A prime circle of order $2n$ is a circular ordering of $1,\ldots,2n$ such that the sum of every two adjacent terms is prime. We prove that a prime circle exists for every sufficiently large $n$. The proof is based on a perfect matching and robust expansion. We also study Hamilton cycles in graphs and digraphs defined by primitive sums...
We establish an upper bound for the symmetry rank of closed, simply connected, almost non-negatively curved manifolds of dimension 4 through 9 and in the case of maximal symmetry rank provide an equivariant diffeomorphism classification of this class of manifolds in dimensions 4, 5, and 6.
We consider solving (convex) conic linear optimization problems, at the scale where matrix-factorization-free methods are attractive or necessary. The restarted primal-dual hybrid gradient method (rPDHG) -- with heuristic enhancements and GPU implementation -- has been very successful in solving huge-scale linear optimization problems...
We study robust bond valuation with endogenous short-rate feedback under volatility uncertainty. Within the $G$-expectation framework, the dependence of the short rate on the bond price yields a nonlinear fixed-point problem, represented by a quadratic $G$-BSDE for the logarithmic price. Under suitable assumptions, we establish...
Let $q$ be a prime power and $\mathbb{F}_{q^2}$ be the finite fields of $q^2$ elements. The Hermitian function field $H=\mathbb{F}_{q^2}(x,y)$ defined by $y^q+y=x^{q+1}$ is a well-known maximal function field with the largest possible genus. Let $A(P_\infty)$ be the decomposition group of the infinity place $P_\infty$ of $H$ which is...
Given a finite dimensional Lie algebra $L$ on a finite field $\mathbb{F}_{p^n}$ of prime power order $p^n$ (with $n$ positive integer and $p$ prime), we consider the number of modular pairs $(A,B)$ in the lattice of all subalgebras $\mathcal{L}(L)$ and introduce the notion of ``subalgebra commutativity degree'' of $L$. This represents...
We study the $θ$-congruent number problem for $\cosθ=\pm3/5$ and $\pm4/5$ using the generalized theta series construction of Sirolli--Tornaría. We describe its specialization to newforms of weight $2$ over $\mathbb Q$ with nontrivial square-free odd part of the level, and explain the reduction of quadratic twists to odd fundamental...
We study an uncountable system of McKean-Vlasov SDEs with coefficients of Nemytskii-type which are driven by a family of essentially pairwise independent Wiener processes. These SDEs interact through a Graphon kernel by means of their one-dimensional time marginal law densities evaluated in the spatial coordinate. We prove the...
Kernel methods, and Gaussian Processes (GPs) in particular, require a Hilbertian distance measure---one whose square is conditionally negative definite (CND)---to guarantee positive semi-definiteness (PSD) of the kernel matrix; a condition that fails for many natural input spaces, including smooth manifolds and spaces of probability...
For a semisimple Lie group $G$ satisfying the equal rank condition, the most basic family of unitary irreducible representations is the Discrete Series found by Harish-Chandra. In this paper, we study the structure of symmetry breaking operators for Discrete Series when restricted to a subgroup $H$ of the same type by combining...
As robot capabilities increase, quadratic programming (QP)-based controllers must account for a similarly increasing number of constraints to ensure safe, reliable operation. Yet, with each added constraint, this introduces more chances of momentary conflict: in which case, a QP solver that returns an "infeasible" status leaves the...
We propose a notion of simplicity for Cayley permutations that is compatible with inflation. We prove that Cayley permutations admit a substitution decomposition analogous to that of permutations and use it to enumerate simple Cayley permutations, primitive simple Cayley permutations, and simple restricted growth functions. We also...
The test error of a model plotted against its number of parameters $d$ falls, peaks when the model can just fit the training data, and falls again, exhibiting the double descent phenomenon. We explain the phenomenon with statistical mechanics. The training trajectory of a stochastic gradient-based method is a particle wandering over...