Papers

Let $r,s,t\geq2$ be integers. For $r$-graphs $G$ and $F_1,\dots,F_s$, we write $G\to(F_1,\dots,F_s)$ if every $s$-edge-coloring of $G$ yields a monochromatic copy of $F_i$ in the $i$-th color for some $1\leq i\leq s$. Let $\mathcal{R}(F_1,\dots,F_s)$ denote the family of all $r$-graphs $G$ with $G\to(F_1,\dots,F_s)$. When $F_1=\dots=F_s=F$, we write $\mathcal{R}(F;s)=\mathcal{R}(F_1,\dots,F_s)$. In this paper, we investigate when $\mathcal{R}(H;s)\subseteq\mathcal{R}(Q_1,\dots,Q_t)$ holds, where $H=H^{(r)}(n,p)$ is a random $r$-graph and $Q_1,\dots,Q_t$ are fixed $r$-graphs. Our main result determines the threshold for a large class of such $Q_1,\dots,Q_t$, including complete $r$-graphs. The key ingredient in our proof is a generalization of a result of Graham, Łuczak, Rödl, and Ruciński, which provides a necessary and sufficient condition for $\mathcal{R}(F_1,\dots,F_s)\subseteq\mathcal{R}(Q_1,\dots,Q_t)$, where $Q_1,\dots,Q_t$ are highly connected. As a byproduct, we characterize when two tuples of highly connected $r$-graphs are Ramsey equivalent.

Dobbs proved that the second iterate of almost every line in the complex plane under the exponential function is dense in the plane. In this paper, we prove an analogous result for the second iterate of the Zorich map in $\mathbb{R}^3$.

In 1979, Johnson and Wolfe proved that norm-attaining operators are dense in $L(C(K),C(S))$ when $K$ and $S$ are compact Hausdorff spaces in the real setting. The corresponding complex case has remained open since then, mainly because the real proof relies on order and sign-decomposition arguments that are no longer available for complex measures. In this paper, we settle the complex case. We prove that, for arbitrary compact Hausdorff spaces $K$ and $S$, the set of norm-attaining operators from the complex space $C(K)$ into the complex space $C(S)$ endowed with the supremum norm is dense in $L(C(K),C(S))$. The proof replaces the real order-theoretic mechanism by a measure-theoretic phase-correction argument, based on polar decompositions, unimodular approximation, and a semicontinuity principle for weighted total variation. This yields a complex defect-reduction procedure which recovers the Johnson-Wolfe density theorem in full generality for complex $C(K)$-spaces.

In Grayson's combinatorial description of higher K-groups, the generators are bounded acyclic binary multi-complexes of arbitrary size. Generalising work by Kasprowski, Winges and the author, we show in this paper that multi-complexes of bounded size suffice and we provide the corresponding relations. Furthermore, we report on the progress in our attempt to algebraically prove the surjectivity of Quillen's dévissage isomorphism for K_1 and we give an elementary and fairly simple example in the codomain which appears to require a more sophisticated approach.

In this paper, we propose several constructions of Locally Recoverable Codes from elliptic surfaces. In particular, we are able to obtain codes with availability $t>2$, codes with hierarchical locality and, finally, codes which combine availability and hierarchical locality. Our constructions rely on the properties of the torsion groups of elliptic curves and on the fibered structure of elliptic surfaces. In particular, the geometry of the surface is used to introduce a multi-dimensional setting, allowing for more recovery sets, eventually nested one within another.

We give almost sure convergence rate bounds of ratio consensus algorithms when the protocol can be reformulated to be linear updates of vector values on a possibly larger, augmented network. This is an improvement of the results of Gerencsér and Gerencsér from 2021 by allowing zero values on auxiliary nodes infinitely often which makes the technique applicable to a much larger family of algorithms.

Reconstructing a thermal model capable of efficiently simulating the behavior of a spacecraft from sparse and localized temperature measurements remains a challenging task. To address this, we introduce a physically-constrained calibration framework for Lumped Parameter Thermal Models (LPTMs), formulated as a trajectory-based inverse problem for graph dynamical systems. The model reconstructs thermal dynamics directly from temperature measurements and known inputs, without relying on a priori parameter values derived from material properties or geometric assumptions. Physical admissibility is enforced at the parameterization level: positivity of nodal coefficients and symmetry of conductive interactions are imposed by construction. This guarantees stable dynamics and restricts the identification problem to a physically meaningful parameter space, improving conditioning without the need of additional regularization. The identification problem is addressed through trajectory matching, ensuring stable rollout over extended time horizons. The methodology is validated on synthetic datasets generated from high-fidelity finite element simulations under progressively complex forcing conditions. The calibrated LPTMs accurately reproduce long-term temperature evolution and exhibit robustness to measurement noise. The proposed framework provides a systematic approach to the calibration of reduced-order thermal models by combining physical structure with data-driven identification. The numerical results show a favorable balance between accuracy and computational efficiency, making the models suitable for integration in spacecraft thermal Digital Twin applications.

Let $C_n=n2^n+1$ denote the $n$th Cullen number. There has been recent interest in finding all Cullen numbers having a given Diophantine property. We prove that, for a fixed integer $k$ and bounded integers $a_1,\ldots,a_k$, the greatest prime divisor of $C_n-a_1m_1!-\cdots-a_km_k!$ tends to infinity, in an effective way. We prove this for some more general families of ternary recurrence sequences as well. We also solve the Diophantine equation $$C_n = m_1! + m_2! + s,$$ where $s$ is a positive integer composed of primes $2,3,5,7$.

We prove a weak fundamental principle for $\lambda$-homogeneous solutions of homogeneous constant-coefficient systems on open pointed convex cones. Starting with the solution family $S_{\mathcal B}$ arising in the Ehrenpreis–Palamodov theory, we construct a corresponding family $S_{\mathcal B,\lambda}$ by replacing the exponential kernels $e^{\langle x,z\rangle}$ with homogeneous kernels $(-\langle x,z\rangle)^\lambda$. The key tool is a Mellin-type operator on Paley–Wiener spaces, which links the classical theory to the Euler-constrained setting. For $\lambda\in \mathbb{C}\setminus \mathbb{N}_0$ and under a visibility assumption, we show that the span of $S_{\mathcal B,\lambda}$ is dense in the space of $\lambda$-homogeneous solutions.

This paper gives a complete description of the solutions of the global positioning problem, emphasizing the under-determined case. We show that the solutions form a quadric, which may degenerate in various ways. Perhaps more surprisingly, the satellite positions also lie on a quadric, and these two quadrics exhibit a remarkable duality: They live on perpendicular affine spaces but share the same axis of symmetry. Moreover, the vertices of one quadric are the foci of the other and vice versa. The results of this paper are not only applicable to the global positioning problem, but to a wider class of problems known as pseudorange-multilateration. This includes a range of real-world localization problems where a signal is emitted at an unknown emission time, and received by sensors at known positions. In particular, the paper can be useful for solving an under-determined multilateration problem in the presence of additional constraints. We illustrate this with two examples: locating a cleaning robot on the ground and locating a raft on the ocean.

This article presents an overview of quasineutral limits in plasma models. Starting from the Vlasov-Poisson system, it explains the role of the Debye length, the emergence of a kinetic incompressibility constraint, and the stability issues caused by fast oscillations and singular electric fields. A central theme is that the geometry of the kinetic flow should be reflected in the way perturbations are measured. This leads to kinetic Wasserstein distances adapted to phase-space dynamics, which provide refined stability estimates for quasineutral limits. The article also discusses related models with thermalized electrons and the additional challenges of the electromagnetic Vlasov-Maxwell setting.

We study sums of locally dependent scores associated with general marked (i.e., labeled) Euclidean point processes. We introduce geometric mixing conditions on the underlying point process and a Lipschitz-"localization" condition on the scores, which jointly ensure a central limit theorem for the sums of the scores as well as expectation and variance asymptotics. Our localization condition is formulated using the bounded Lipschitz metric, providing a distributional criterion. This stands in contrast to the classical stabilization conditions in stochastic geometry, which are typically based on stopping-set constructions. To demonstrate the applicability of our general framework, we consider several stochastic processes indexed by spatial random graphs. These include spin systems, interacting diffusions, and interacting particle systems. In particular, spin systems highlight the importance of our localization condition. Additional applications include empirical random fields and geostatistical Boolean models.

The emerging literature on hypothesis testing with data-dependent significance levels relies on a particular extension of the Type-I error. Existing arguments for this extension are heuristic. We show it is uniquely characterized by three axioms: law-invariance, agreement with classical testing on constant levels, and the preservation of (in)validity under independent selection of the level. We find that three analogous axioms characterize the e-value as a multi-decision generalization of a test in a decision-theoretic framework. We recover the p-value by dropping the invalidity half of the independent selection axiom, showing that e-values correspond to those p-values for which a data-independent choice between two invalid p-values cannot produce a valid p-value. Our main technical contribution is to show how e-values emerge in every decision problem with a notion of validity that satisfies law invariance, the independent selection axiom, and an axiom stating that a procedure that selects an invalid procedure with arbitrarily high probability must itself be invalid. In an application to post-hoc decision-making, we justify expectation-based error rates in multiple testing and recover the 'e-closure principle' as a special case.

Asynchronous iterative methods tolerate straggling processors by allowing workers to proceed with stale data, but at a cost: the iterates become inconsistent, potentially degrading convergence. We investigate whether convergence accelerators such as Anderson acceleration compensate for this degradation. We experimentally study three fixed-point iterations: the Jacobi method for sparse linear systems, value iteration for the Bellman equation, and the Hartree–Fock self-consistent field (SCF) iteration. The experiments are conducted using a high-performance execution framework Ray, which abstracts the complexity of distributed systems and enables code parallelization and fault injection with minimal changes. We establish two main results. First, straggler tolerance is universal: asynchronous execution provides wall-clock speedups of $2.9\times$ (Jacobi), $7.7\times$ (VI), and $16.9\times$ (SCF) over synchronous execution with a 100\,ms-delayed worker, independent of whether acceleration is used. Second, Anderson acceleration's effectiveness under asynchrony depends on where staleness enters the computation. We identify two staleness mechanisms: iterate-level corruption, where stale worker returns directly overwrite portions of the accelerated iterate (as in block Jacobi), and evaluation-level perturbation, where staleness acts as a bounded perturbation to the fixed-point map evaluation (as in VI and SCF). Anderson acceleration fails categorically under the first mechanism but retains its benefits under the second, consistent with the perturbation analysis of Toth et al.\ (2017). This distinction, rather than the contraction norm or smoothness of the map, is the primary determinant of whether acceleration survives asynchronous execution.

We introduce the intersection orbital graph $\Gamma(G_1, G_2; \Omega)$ associated with two permutation groups $G_1, G_2 \leq \mathrm{Sym}(\Omega)$ on a finite set $\Omega$.

In a previous paper we introduced a version of associativity for a partial infinitary operation. We prove here that if $\gamma$ is an infinite ordinal and some associative infinitary operation is defined for all sequences indexed by ordinals $ \leq \gamma$, then such an operation can be uniquely expanded to apply to every sequence indexed by any ordinal of cardinality $ |\gamma |$. In particular, if some associative operation is defined for all finite sequences as well as for all $ \omega$-indexed sequences, then the operation can be uniquely expanded to apply to every sequence indexed by a countable ordinal.

This paper presents a unified multi-asset, multi-group asset-flow model that integrates three foundational frameworks from the behavioral finance literature. The model captures the dynamics of financial markets where multiple assets are traded by multiple investor groups, each with distinct trend-following (momentum) and value-based (fundamental) strategies. Unlike classical efficient market models, our framework explicitly incorporates the finiteness of cash and shares, asymmetric cross-asset coupling in buying decisions, and endogenous wealth redistribution across groups. We derive the complete system of ordinary differential equations governing price, cash, share, and sentiment dynamics, and establish the fundamental properties of positivity and boundedness for all physically relevant variables. The equilibrium set is characterized as a manifold parameterized by cash distribution, with the fundamental equilibrium as a special point. Through linear stability analysis, we identify conditions under which the fundamental equilibrium loses stability via a supercritical Hopf bifurcation, giving rise to persistent limit cycles. The model is validated against three benchmark papers: the single-asset multi-group model of DeSantis, Swigon, and Caginalp (2012); the two-asset single-group model of Bulut, Merdan, and Swigon (2019); and the two-asset two-group Nigeria-Libya oil market model of Cavani (2026). Our numerical simulations reproduce all key theoretical predictions, including equilibrium manifolds, Hopf bifurcation thresholds, limit cycle periods, and asymmetric contagion patterns.

In a former paper we introduced partial infinitary noncommutative semigroups and showed, among other, that significant differences arise in comparison with the commutative case, previously studied in the literature. For example, in the commutative case we cannot have an infinitary identity $e$ together with two elements $a \not= e$, $b \not= e$ such that $ab= e$, just under the assumption that the countable product $abababa\dots$ is defined. Here we show that this is possible in the noncommutative case, actually, we can have an infinitary semigroup on a countable set with a complete identity and such that the operation is defined for every indexed linearly ordered set.

Several numerical reconstruction algorithms for the inverse boundary value problem of the 1-dimensional wave equation exist. In this paper we revisit two of them, the Sondhi-Gopinath (SG) method from 1971 and the Korpela-Lassas-Oksanen (KLO) method from 2016. Our main contribution is a systematic and statistical comparison of the performance of these two well established methods. The stability of the SG algorithm, even in practical applications, is well known. KLO has a regularisation scheme with a theoretical proof, and is an evolution of the boundary control method. Both are based on the idea of constructing solutions that are characteristic functions of a set at a given time. This similarity has been pointed out before, but no systematic comparison has been published. We compare the performance of the two algorithms with noisy simulated data. The application in our mind is the reconstruction of the internal cross-sectional area of a pressurised fluid pipe. The area corresponds to the first order $\partial_x$-term of the wave equation. Instead of just observing the performance on a few test cases, we generate $n=1000$ random area profiles of various smoothness levels and measurement noise up to $10\%$ of the signal energy and perform statistical tests. SG and KLO have a difference of one time-derivative in their standard boundary data, which complicates the analysis. Our results show that SG performs better in the low noise regime, and KLO with high noise. SG is easier to implement and runs faster.

Various kinds of infinitary operations satisfying forms of associativity have been considered in the literature by various authors, including A. Tarski, C. Karp, J. H. Conway, D. Krob, N. Bedon, and C. Rispal. Applications include the arithmetics of binary relations, quasigroups, and automata theory, We present a general definition for an infinitary noncommutative partial semigroup; the definition extends and encompasses all the previous notions. In particular, we show that new phenomena occur in the noncommutative case, giving rise to a somewhat richer (and, by the way, more difficult) theory.

We investigate Büchi Arithmetic $\mathsf{BA}_k$ – the elementary theory of the natural numbers equipped with addition and the function mapping a number $x$ to the greatest power of $k$ dividing $x$. $\mathsf{BA}_k$ is known to be decidable and to enjoy a few important properties, in particular, a first-order structure is automatic iff it is interpretable in $\mathsf{BA}_k$. We propose a natural axiomatization of this theory based on a comprehension schema restricted to bounded formulas, interpreting natural numbers as finite (multi)sets of powers of $k$ via their base-$k$ expansions. The completeness proof for this axiomatization proceeds through a formalization of the Büchi-Bruyère Theorem on the equivalence of definability in Büchi Arithmetic and recognizability by finite automata.

For models evaluated at a random set of independent variables, the variance-based Shapley effects range between Sobol' indices, and the corresponding total indices admit derivative-based upper-bounds. Such relationships fail when the inputs are non-independent. This study investigates a general inequality link between the variance-based dependent sensitivity indices, recently introduced by us, and the variance-based Shapley effects for models with dependent inpus. It turns out that Shapley effects range between the main and total dependent sensitivity indices, and such indices are computationally more attractive. Moreover, different upper-bounds of such indices are provided so as to ease the identification of non-relevant inputs in higher dimensions as well as to obtain sometimes practical estimates of total dependent indices. Some of such bounds rely on the traditional gradients, while others rely on generalized sensitivity indices using dependency models.

The smallest eigenvalues of (distance-j) Hamming graphs with distance parameter j at least half the length were completely determined by Brouwer et al. (2018). In the present work, we address the complementary regime, namely distances j strictly less than half the length, and derive asymptotic lower bounds on the smallest eigenvalue of binary Hamming graphs. For certain natural generalizations, specifically Cayley graphs defined over quaternary vector spaces, we asymptotically determine the smallest eigenvalue as well. As an application, we obtain lower bounds on the quantum chromatic number of these graphs. In particular, for the aforementioned Cayley graphs over quaternary vectors, our lower bounds for the quantum chromatic number coincide with known upper bounds.

We investigate the trade-off between controllability, channel access, and age-related performance in a wireless network of control systems. Controllers share a random-access channel to transmit control inputs to actuators over slotted blocks. We measure reliable control via block controllability, where a block is controllable if it contains a required number of consecutive successful transmissions. In parallel, we capture information freshness via the age of information. To enable efficient allocation of channel resources over time, we introduce adaptive access probabilities at the block level, prioritizing controllers that have not yet achieved controllability. We then derive closed-form expressions for block controllability probability, the peak latency between inter-block consecutive successes, and peak age of information. We further characterize the peak control latency, defined as the time between consecutive controllable blocks. Finally, we optimize access probabilities to jointly balance controllability and age-related metrics. Numerical results illustrate the effectiveness of the proposed adaptive access policies in managing this trade-off in interference-limited wireless control networks.

In this paper, we study a class of double Lambert series and establish several identities and transformation relations for them. These formulae provide useful tools for reducing certain double Lambert series to single Lambert series. As applications, we derive identities related to recent conjectures of Andrews, Dixit, Schultz, and Yee, and of Amdeberhan, Andrews, and Ballantine. We also propose a new proof of a result of Amdeberhan, Andrews, and Ballantine.

We develop operator-theoretic and cohomological tools for quaternionic quasi-Lie structures, with sliding mode control as a motivating application. Three main results are established. First, an exact operator-norm transfer under the quaternionic anti-isomorphism $a \mapsto \bar{a}$, which enables quantitative bounds from~\cite{Athmouni2026} to transfer between left- and right-module conventions with no constant factor. Second, a transcription of the cohomological rigidity result of~\cite{Athmouni2026} into a form usable here: in the homogeneous case, under a local cohomological non-obstruction hypothesis, an explicit bilinear correction $\Omega$ produces a bracket satisfying the Jacobi identity exactly on a ball of admissible radius, with all quantitative constants expressed through $C_{2}$ and the admissible radius. Third, the projected Jacobi defect is shown to satisfy a generalized one-sided Lipschitz condition with computable constants, obtained via a uniform-selection argument handling state-dependence of the measurable selection. As an application, we develop a robust control framework with a cohomological matching condition replacing pointwise verification: an integral sliding surface yields $\beta$-exponential stability via an iterative linear matrix inequality (LMI) scheme. The work is purely analytical; closed-loop numerical simulations for multidimensional systems are deferred to a companion paper. The framework is restricted to the homogeneous quasi-Lie case; the Sobolev extension is conjectural, and algorithm termination is established conditionally on sufficient continuity assumptions on the LMI solution map.

In this paper, we develop an efficient preconditioned unfitted finite element method for the elliptic interface problem, based on the reconstructed discontinuous approximation. The key idea is to impose suitable constraints on the local least squares reconstruction. These constraints ensure the stability near cut interface elements and, more importantly, establish a norm equivalence between the high-order space and the lowest-order piecewise constant space. This result allows us to construct an optimal preconditioner directly from the lowest-order system on the same unfitted mesh for any high-order scheme. The resulting method combines a cut discontinuous Galerkin formulation with Nitsche's penalty technique. The approximation space achieves arbitrarily high order accuracy with only one degree of freedom per element. We prove optimal error estimates and show that the condition number of the preconditioned system is uniformly bounded independently of the mesh size, coefficient contrast, and the location of the interface relative to the mesh. Multigrid algorithms are further designed to efficiently approximate the inverse of the lowest-order system matrix. Numerical experiments in two and three dimensions confirm the optimal convergence rates and demonstrate the robustness and efficiency of the proposed preconditioning method.

In this short note, we establish an upper bound for the conjugate radius of an open $n$-dimensional Riemannian manifold under a scalar curvature lower bound and a bottom-of-spectrum upper bound. As a consequence, if $\lambda_{0}(M)=0$ and scalar curvature $\ge n(n-1)$, then the conjugate radius $\le \pi$.

We study Brownian motion on Hermitian symmetric spaces of non-compact type in their bounded-domain realization. Using Jordan triple systems, we identify the spectral values after an appropriate change of variables as a Heckman-Opdam diffusion of type $BC_r$. We then analyze two Brownian functionals: the symplectic area associated with the canonical Kähler form, and, in the tube-type case, the winding defined by the Jordan determinant. For the area process we prove a martingale representation, a central limit theorem, and an exact conditional characteristic function expressed as a ratio of Heckman-Opdam heat kernels. For the determinant winding process we obtain analogous heat kernel formulas and prove convergence to a Cauchy law with scale determined by the initial determinant. These results extend classical formulas of Paul Lévy and Marc Yor from the Euclidean setting to the full class of Hermitian symmetric spaces of non-compact type.

We consider a question of Edjvet and Vdovina concerning which groups defined by special presentations are large. For each integer $n \ge 3$, we construct an $n$-generator one-relator presentation whose star graph is the complete bipartite graph $K_{n,n}$; the resulting groups are large and hyperbolic. We also classify concise special presentations with star graph $K_{3,3}$, showing that they are one-relator presentations and that, up to Tietze equivalence, there are exactly twelve that define torsion-free groups. The torsion cases arise precisely as positive powers of the relators in the torsion-free cases, and define pairwise non-isomorphic groups that remain large and hyperbolic.