arXiv preprints from January 1, 2026 through September 8, 2026 — 02:04:42 EST
Reliable beam management is a central challenge for 6G millimeter-wave (mmWave) vehicle-to-infrastructure (V2I) links, where narrow beams provide high array gain but are vulnerable to mobility-induced misalignment, blockage, and domain variation. BeamGuard is a multimodal sensing-aided beam-management framework that combines...
This paper proposes acoustic echo control based on sound object identification for suppressing acoustic echo and howling in conferencing environments with complicated acoustic paths, where multiple hands-free terminals coexist in the same room. Conventional acoustic echo cancellers target fixed intra-device echo paths; however,...
Coupled feedback networks are often monitored channel by channel even though cross-channel paths alter both stability margins and transmitted disturbances. We study identification of a structured feedback matrix L_t = Phi diag(gamma_t) in an output-only setting: no commanded, probing, or reference input exists -- only temporally...
We develop a PDE-based methodology for pricing and hedging European contingent claims in general one-dimensional diffusion markets characterized solely by their scale function and speed measure, possibly without a classical SDE representation, and with constant interest rate. We derive a hedging equation whose solution generates a...
Backtests of trading strategies are often selected after many parameter trials. A strong historical result can therefore reflect search luck rather than a persistent signal. Standard summaries such as return, Sharpe ratio, and drawdown do not record how many candidates were tried, whether the selected rule survives out-of-sample...
In this study, we construct the first orthogonal basis for additively consistent subspace in pairwise comparisons theory. This construction is based on our representation of additively consistent best approximations of skew-symmetric matrices with respect to a tensor basis having minimal support. The orthogonal basis establishes the...
Let $X$ be an $n$-dimensional generalized Grassmannian not isomorphic to $\mathbb{P}^n$. We prove that $k(X)\le n-1$, where $k(X)$ denotes the maximal integer such that every uniform bundle on $X$ of rank at most $k(X)$ is homogeneous. In particular, for smooth quadrics $\mathbb{Q}^n$, we have $k(\mathbb{Q}^n)=n-1$ for odd $n$, and...
We investigate the statistics of the time-integrated current in an infinite one-dimensional gas of independent active Ornstein--Uhlenbeck particles, as a model system for studying an active generalisation of the corresponding passive (diffusive) phenomenology. Unlike the latter, where current fluctuations exhibit universal...
The defining feature of one-sided device-independent quantum key distribution is its asymmetric trust model in which only one party is characterized. This scenario sets an interesting middle ground between high key rates achievable by characterizing devices and the security of full device-independence. Here, we provide new tools,...
In this paper, we investigate the neighbourhood convexity ($n$-convexity) on graphs, a new finite convexity space grounded in the common closed neighbourhood closure operator. Unlike standard path-based graph convexities, $n$-convexity shows a non-canonical behaviour, giving rise to compelling structural properties and being almost...
This note supplies examples for the manuscript: Rigidity on the Two-Torus and Sarnak's Conjecture. For every $0<δ<\tfrac12$, we give two constructions of semi-irrational $C^\infty$ diffeomorphisms of $\mathbb{T}^2$ that satisfy the hypotheses of both Theorems 1 and 2 of that manuscript but do not have bounded mean motion, together...
Thousands of sangaku tablets, inscribed with colorful geometry problems, were posted in shrines and temples across the Japanese archipelago starting in the Edo period (1603--1868), representing an intersection of artistic, religious, and mathematical traditions. The Sangaku Archive is an attempt to carefully document these objects...
Let $s_2(n)$ be the binary sum-of-digits function and let $c_t$ be the natural density of the integers $n\ge0$ for which $s_2(n+t)\ge s_2(n)$. Earlier work of the author proved the universal exponential bound $$c_t-\frac12\ge 2^{-2s_2(t)-1},$$ thereby resolving Cusick's conjecture for every $t$. This estimate, however, does not...
Lacey used sparse domination to study the sharp weighted norm estimate of the maximal function of predictable multipliers in discrete time filtration spaces. Domelevo, Petermichl, and Škreb developed the self similarity argument known as sparse domination in an abstract martingale setting with a continuous time parameter. In our...
A celebrated result of Bayer and Stillman from 1987 states that for a homogeneous ideal $I$ of a polynomial ring $S$, the regularities of $S/I$ and $S/\textrm{GIN}(I)$ are the same under the reverse lexicographic monomial ordering, where $\textrm{GIN}(I)$ is the generic initial ideal. If $R$ is a polynomial ring whose variables are...
Detailed multicellular growth simulations based on subcellular element models (SEMs) can capture complex tissue development, but their element-level interactions impose substantial computational cost. This work presents a scalable multi-GPU framework for 3D multicellular growth simulation that combines GPU acceleration, spatial...
We construct infinitely many new pairwise nondiffeomorphic smooth structures on infinitely many closed simply connected spin 4-manifolds with positive signature. Our construction builds on an infinite family of simply connected complex surfaces of general type due to Roulleau and Urzúa that populate points arbitrarily near the...
We determine, up to absolute constants, the worst-case number of point evaluations required for a weighted $L_2$ Marcinkiewicz-Zygmund inequality for an $m$-dimensional complex function space. If $0<\varepsilon<1$ is the relative distortion, this number is $$Θ\Big(\min\Big\{m^2,\frac{m}{\varepsilon^2}\Big\}\Big),$$ and exact...
The Serre problem asked if a locally trivial holomorphic fibration with Stein base and Stein fiber is itself Stein. \v Skoda constructed the first counterexample for this problem. Later, Cœuré and Loeb constructed another remarkable counterexample, with bounded domain of holomorphy as fiber. The total space of their fibration has...
In this paper, we establish the boundedness of the bilinear Bochner-Riesz means $\mathcal{B}^α_R$ on the complex sphere $\mathbb{S}$. More precisely, we prove that $\mathcal{B}^α_R$ is bounded from $L^{p_1}(\mathbb{S}) \times L^{p_2}(\mathbb{S}) \to L^p(\mathbb{S})$ where $1/p_1+1/p_2=1/p$ and $1\leq p_1, p_2 \leq \infty$, for an...
We prove mode stability for the massless scalar wave equation on Kerr-de Sitter black hole spacetimes in the full subextremal range. In combination with recent work by Petersen-Vasy, this proves, unconditionally, that sufficiently regular solutions of the scalar wave equation decay exponentially fast to constants.
Böhm metrics on $S^{k+1}\times S^l$ and $S^{k+l+1}$ ($k,l\geqslant 2$, $k+l\leqslant 8$) occur in sequences of Einstein metrics that converge to a cone. We prove that, along such a sequence, the number of negative eigenvalues of the Lichnerowicz Laplacian acting on transverse-traceless tensors tends to infinity: these metrics become...
The huge amount of literature about the divergence equation in bounded Lipschitz domains of $\R^n$ ($n\ge2$) is fairly disconnected and even apparently simple problems remain unsolved. We go several steps further in the knowledge of this equation and of some related inequalities. We prove that among its infinitely many solutions there...
We study steady solutions to the two-dimensional incompressible Euler equations in an infinite channel, whose far-field limits are uniformly non-stagnant shear flows. In the smooth category,for a broad class of prescribed far-field shear profiles, non-shear steady states exist via the construction of two-dimensional solutions of the...
For a finite associative unital ring $R$, the null ideal of $R$ is the collection of polynomials with coefficients from $R$ that send each element of $R$ to zero under evaluation. It was conjectured that the null ideal of $R$ is always a two-sided ideal of its overlying polynomial ring. The conjecture was proved to be false with the...