arXiv preprints from January 1, 2026 through July 21, 2026 — 05:04:16 EST
We study the entanglement complexity of a system consisting of two simple-closed curves (self-avoiding polygons) that span a lattice tube, referred to as a 2SAP. 2SAPs are of interest as the first known model of confined ring polymers where the linking probability goes to 1 exponentially with the size of the system. Atapour et al...
In many real-world applications of data assimilation (DA), the strategic placement of observers is crucial for effective and efficient forecasting. Motivated by practical constraints in sensor deployment, we show that global recovery of the flow field can be achieved using observations available only in a subregion of the domain,...
In this work, we extend the notion of supershifts and superoscillation sequence to fractional Fock spaces based on Gelfond-Leontiev fractional derivatives. We first introduce the fractional supershifts sequence, and then discuss the associated evolution Cauchy problem with the fractional supershifts as initial condition.
We study the Euler Alignment system of collective behavior, equipped with `topological' interaction protocols, which were introduced to the mathematical literature by Shvydkoy and Tadmor. Interactions subject to these protocols may depend on both the Euclidean distance between agents and on the mass distribution between them -- the...
We propose a high-order version of the augmented Lagrangian method for solving convex optimization problems with linear constraints, which achieves arbitrarily fast -- and even superlinear -- convergence rates. First, we analyze the convergence rates of the high-order proximal point method under certain uniform convexity assumptions...
We consider probability measures on $A^N$, the set of sequences of symbols on a finite alphabet $A$ of length $N$, that give a weight to each sequence in terms of a collection of matrices with non-negative entries and having rows and columns labeled by a finite or countable set $B$. We prove for such kind of measures large deviations...
For actions of amenable groups, mean equicontinuity-a natural relaxation of equicontinuity obtained by averaging metrics along orbits-is well known to yield a maximal mean equicontinuous factor. In 2021, Li and Yu introduced the notion of weak sensitivity in the mean for actions of $\mathbb{Z}$ to gain a deeper understanding of this...
We formulate a relative analogue of the Clemens conjectures for 1/2-log Calabi-Yau threefold pairs (X,Y) (where K_X+2Y is isomorphic to O_X). This framework rests on the restoration of a perfect deformation/obstruction duality specific to the 1/2-log CY threefold setting. Based on this duality, we conjecture that for a generic...
Following previous work, we continue the study of infinitesimal methods in mixed Hodge theory. In the first part, inspired by the deformation theory of curves on Calabi-Yau threefolds, we study deformations of smooth $\mathbb{Q}$-log Calabi-Yau pairs $(X,Y)$. We prove unobstructedness results for these pairs under Fano hypotheses. We...
In a recent work of the authors, we proved the generic positivity of the Beilinson-Bloch heights of the Gross-Schoen and Ceresa cycles. The geometric part of the proof was to prove the maximality of the rank of the associated normal function and the Zariski closedness of the Betti strata. In this paper, we generalize these geometric...
We study a dynamical system modeling the Theory of Planned Behavior (TPB) in which each individual's behavioral intention evolves continuously under an ODE driven by internal attitudes, perceived social norms, and perceived behavioral control. Actions occur as discrete threshold events: when intention reaches a fixed threshold it is...
We study large traveling surface waves within a two-dimensional finite depth, free boundary, homogeneous, incompressible and viscous fluid governed by Darcy's law. The fluid is bound by a gravitational force to a flat rigid bottom and meets an atmosphere of constant pressure at the top with its free surface, where it does not...
Assuming a mild non-degeneracy condition excluding very low-level Cantor endpoints, and assuming a counting/input hypothesis for the contribution of non-deep orbit indices, we show that for the quadratic field $K=\mathbb{Q}(α)$ there exist constants $A_K,B_K>0$ such that \[ \mathrm{exit}(α)\ \le\ A_K\,(\log_3 H)^2 + B_K. \]...
Two algorithms are proposed, analyzed, and tested for solving continuous optimization problems with nonlinear equality constraints. Each is an extension of a stochastic momentum-based method from the unconstrained setting to the setting of a stochastic Newton-SQP-type algorithm for solving equality-constrained problems. One is an...
Generalized Disjunctive Programming (GDP) provides a powerful framework for combining algebraic constraints with logical disjunctions. To solve these problems, mixed-integer reformulations are required, but traditional reformulation schemes, such as Big-M and Hull, either yield a weak continuous relaxation or result in a bloated model...
In this article we continue the investigation of the length of the narrow $2$-class field tower of real quadratic number fields $\mathrm{k}$ whose discriminants are not a sum of two squares and for which their $2$-class groups are elementary of order $4$. Letting $\mathrm{G}$ equal the Galois group of the second Hilbert narrow...
Linearized shallow neural networks that are constructed by fixing the hidden-layer parameters have recently shown strong performance in solving partial differential equations (PDEs). Such models, widely used in the random feature method (RFM) and extreme learning machines (ELM), transform network training into a linear least-squares...
The first purpose of this work is to provide a friendly introduction to the theory of nonautonomous linear systems of ordinary differential equations, the property of exponential dichotomy and its corresponding spectral theory. The second purpose of this work is disseminate the linearization results carried out by the authors in a...
A ball polyhedron is a finite intersection of congruent balls in $\mathbb{R}^3$. These shapes arise in various contexts in discrete and convex geometry. We focus on Reuleaux polyhedra, the subclass of ball polyhedra whose centers and vertices coincide. Building on Bogosel's recent work on the volume of Meissner polyhedra, we derive a...
Studying Nambu solutions of the rainbow-ladder gap equation in QCD at zero temperature and chemical potential, we prove that the mass function emerges continuously from zero as the interaction strength is increased past the critical point for all positive, asymptotically perturbative kernels almost everywhere continuous in $L^1$ using...
The transition of transit fleets to alternative powertrains offers a potential pathway to reducing the cost of mobility. However, the limited range and long charging durations of battery electric buses (BEBs) introduce significant operational complexities, necessitating innovative scheduling and charging strategies. This study...
In this paper we study directional second-order tangent sets of real and complex analytic sets. For an analytic set $X\subseteq \mathbb K^n$ and a nonzero tangent direction $u\in T_0X$, we compare the geometric directional second-order tangent set $T^2_{0,u}X$, defined through second-order expansions of analytic curves in $X$, with...
Singular stochastic partial differential equations informally refer to the partial differential equations with rough random force that leads to the products in the nonlinear terms becoming ill-defined. Besides the theories of regularity structures and paracontrolled distributions, the technique of convex integration has emerged as a...
We sketch the proof of an effective equidistribution theorem for one-parameter unipotent subgroups in $S$-arithmetic quotients arising from $\mathbf K$-forms of $\mathrm{SL}_2^{\mathsf n}$ where $\mathbf K$ is a number field. This gives an effective version of equidistribution results of Ratner and Shah with a polynomial rate. The...
We present a unified operator-theoretic framework for stochastic calculus based on the factorization (Id - E)F = δ_X Π_X D_X F, valid for F_T^X-measurable F in L^2(Ω) when the driving process X has the representation property. For a square-integrable process X with stochastic integral δ_X, we define the operator-covariant derivative...