arXiv preprints from January 1, 2026 through September 22, 2026 — 06:39:51 EST
This work studies constrained blackbox optimization problems that cannot be solved in reasonable time due to prohibitive computational costs. This challenge is especially prevalent in industrial applications, where blackbox evaluations are costly. However, constraints can be evaluated at various fidelities at a lower computational...
We study estimation of the intercept parameter in an integrated Galton-Watson process, a basic building-block for many count-valued time series models. In this unit root setting, the ordinary least squares estimator is inconsistent, whereas an existing weighted least squares (WLS) estimator is consistent only in the case where the...
We investigate the existence of compact Hausdorff spaces $X$ that are minimum with respect to $cX=K$ for some fixed covering operator $c$ and compact Hausdorff space $K$ with $cK=K$. Then, using the Yosida representation theorem, we show how that situation relates to the existence of Archimedean vector lattices $A$ with distinguished...
We describe an explicit basis for the $\operatorname{SU}(2)$-invariant space of the exterior power $\wedge_{2k} \mathbb{C}^{2m}$ via the combinatorics of plane partitions. In quantum chemistry, this is the space of spin adapted quantum states of an electronic system with $m$ spin orbitals and $k$ electron pairs. We construct our basis...
We develop a structure-preserving computational framework for optimal mixing control in incompressible flows. Our approach exactly conserves the continuous system's key invariants (mass and $L^2$-energy), while also maintaining discrete state-adjoint duality at every time step. These properties are achieved by integrating a centered...
We establish the full asymptotic for the discrete second moment of the Riemann zeta function of mixed derivatives evaluated at the zeta zeros, providing both unconditional and conditional error terms. This was first studied by Gonek, where only the leading order asymptotic was given, later extended by Conrey--Snaith and Milinovich to...
We develop the basic theory of eigenvalues of $p$-adic random matrices, analogous to the classical theory for random matrices over $\mathbb{R}$ and $\mathbb{C}$. Such eigenvalue statistics were proposed as a model for the zeroes of $p$-adic $L$-functions by Ellenberg-Jain-Venkatesh, who computed the limiting distribution of the number...
Characterisations of metrizable topological spaces or metrizable uniform spaces are well known. A natural counterpart to being metrizable for topological spaces can be expressed in terms of probabilistic metrizability for approach spaces. The notion of a probabilistic metrizable approach space is based on a well known concrete functor...
This work models brittle fracture using a linearized surface-substrate theory in which the crack faces possess surface stresses derived from a surface strain-gradient elastic energy. The model incorporates surface stretching, curvature, and surface gradients of stretching into the surface energy, thereby capturing small-length-scale...
Seidel switching is a classical operation on graphs which plays a central role in the theory of two-graphs, signed graphs, and switching classes. In this paper we focus on those switches which leave a given graph invariant up to isomorphism. We call such subsets of the vertex set \emph{identity Seidel switches}. After recalling basic...
The Clifford algebra language allows us to rewrite the Lamé-Navier system in terms of the Euclidean Dirac operator. In this paper, the main question we shall be concerned with is whether or not a higher order Lipschitz function on the boundary $Γ$ of a Jordan domain $Ω\subset\mathbb{R}^m$ can be decomposed into a sum of the two...
We provide two representations of the Segal category $\mathcal{X}$ modeling natural phenomena, the first one being based on the concept of micro-reversibility, producing a long sequence $Σ$ of categories as a resolution of $\mathcal{X}$, the second one providing graded categories cofibered in groupoids over the categories of $Σ$,...
The aim of this text is to provide a linguistically accessible, but comprehensive introduction into a variety of topics in dynamical systems and its applications. Whilst preliminary knowledge of dynamical systems is useful, it is not essential and readers are only assumed to have familiarity with foundational undergraduate mathematics...
Let $\mathcal{A}$ be a $k$-th order $n$-dimensional tensor, and we denote by ${\rm am}(λ, \mathcal{A})$ the algebraic multiplicity of the eigenvalue $λ$ of $\mathcal{A}$. The projective eigenvariety $\mathbb{V}_λ(\mathcal{A})$ is defined as the set of eigenvectors of $\mathcal{A}$ associated with $λ$, considered in the complex...
We present a Neumann series of spherical Bessel functions representation for solutions of the Sturm--Liouville equation in impedance form \[ (κ(x)u')' + λκ(x)u = 0,\quad 0 < x < L, \] in the case where $κ\in W^{1,2}(0,L)$ and has no zeros on the interval of interest. The $x$-dependent coefficients of this representation can be...
We study the distribution of $2$-torsion in class groups and narrow class groups of cubic fields and cubic orders subject to prescribed shape conditions. The \emph{shape} of a cubic order in a number field is a natural geometric invariant taking values in the modular surface $\mathbb{H}/\operatorname{GL}_2(\mathbb{Z})$. Fix a subset...
We introduce Minary, a computational framework designed as a candidate for the first formally provable autopoietic primitive. Minary represents interacting probabilistic events as multi-dimensional vectors and combines them via linear superposition rather than multiplicative scalar operations, thereby preserving uncertainty and...
This paper studies the use of Multi-Grade Deep Learning (MGDL) for solving highly oscillatory Fredholm integral equations of the second kind. We provide rigorous error analyses of continuous and discrete MGDL models, showing that the discrete model retains the convergence and stability of its continuous counterpart under sufficiently...
Let $F: T^{1,0}M\rightarrow[0,+\infty)$ be a strongly convex complex Finsler metric on a complex manifold $M$ and $\pmb{J}$ the canonical complex structure on the complex manifold $T^{1,0}M$. We give a geometric characterization of strongly convex Kähler-Berwald metrics. In particular, we prove that $\pmb{J}$ is horizontally parallel...
Standard risk metrics used in model validation, such as the Kolmogorov-Smirnov distance, fail to converge at practical rates when applied to high-frequency financial data characterized by heavy tails (infinite skewness). This creates a "noise barrier" where valid risk models are rejected due to tail events irrelevant to central...
We consider classical/quantum correspondence in Lindblad evolution with jump operators for which the corresponding Fokker--Planck equation is subelliptic. This allows us to consider the physical model proposed by Zurek and Paz, and to extend some of the recent mathematical results of Hernandez, Ranard and Riedel, Galkowski and...
Fractional Burgers equations pose substantial challenges for classical numerical methods due to the combined effects of nonlocality and shock-forming nonlinear dynamics. In particular, linear approximation frameworks-such as spectral, finite-difference, or discontinuous Galerkin methods-often suffer from Gibbs-type oscillations or...
This paper is concerned with two extremal problems from matrix analysis. One is about approximating the top eigenspaces of a Hermitian matrix and the other one about approximating the orthonormal polar factor of a general matrix. Tight error bounds on the quality of the approximations are obtained.
It is well-known that an associative algebra shares the same growth and Gelfand-Kirillov dimension (GK-dimension) as its associated monomial algebra with respect to a degree-lexicographic order. This article mainly investigates the relationship between the GK-dimension of an algebra and that of its associated monomial algebra with...
We develop the specification and orbit-decomposition approach to equilibrium states for parabolic rational maps of the Riemann Sphere. Our result extends the well-known results on uniqueness of equilibrium states in this setting, notably the results of Denker, Przytycki and Urbański. We extend the class of potentials from Hölder to...