arXiv preprints from January 1, 2026 through September 23, 2026 — 00:18:42 EST
Rapid data assimilation is required for real-time prediction and control in digital twins. For many physical systems, the data assimilation task requires the solution of a physics-constrained inverse problem, which is often computationally intractable in real time using traditional physics solvers. This work presents a reduced-basis...
We study pointwise convergence of polynomial ergodic averages over short intervals whose left endpoints tend to infinity. For a polynomial orbit of degree $d\geq2$ and doubly lacunary starting times, we prove $L^p$ variational estimates, and hence almost-everywhere convergence, for $1<p<\infty$ in the range $c>(d-1)/d$. This gives the...
We consider the SIS contact process on a Poisson system of independent Brownian motions in $\mathbb{R}^d$ of intensity $η$. Two particles are in contact when their distance is at most $2r$. An infected particle transmits the infection to a susceptible particle in contact with it at rate $λ\in(0,\infty]$, and recovers at rate...
Let $\mathbb{H}=\{z\in\mathbb{C}:\operatorname{Im}z>0\}$, and let $N(\mathbb{H})$ denote the Nevanlinna class in $\mathbb{H}$, consisting of meromorphic functions representable as quotients of two bounded analytic functions in $\mathbb{H}$. We construct a nonconstant meromorphic function $F$ on $\mathbb{C}$ such that...
Weil's criterion equates the Riemann Hypothesis with the positivity of an explicit quadratic form $Q(f)$. For test functions supported in a window $[-L,L]$ we study the profile $λ^*(L)=\inf Q(f)/\|f\|_2^2$ from both sides. A one-stroke reduction converts window positivity into positive semidefiniteness of a finite matrix; executing it...
We show that the operadic structure on the cohomology of the poset of noncrossing 2-partitions is isomorphic to the Brace operad.
Jungin Lee in 2018 proved a necessary and sufficient condition that an integral quadratic form $\sum_{i=1}^{m} a_iX_i^2$ is universal over $M_2(\mathbb{Z})$. For a positive integer $n \geq 2$, Lee defined $f(n)$ to be the smallest positive integer $m$ such that for every pairwise coprime $a_1, a_2, \ldots a_m \in \mathbb{Z}$,...
This paper develops the first end-to-end application of cross-sectional learning-to-rank to the S&P 500 weekly options (SPXW) zero-day-to-expiration surface, integrated with margin-aware position sizing, an abstention rule driven by model uncertainty, and a strict out-of-time integrity check. A LightGBM LambdaRank ranker scores a...
Lead-lag relationships are widely used in financial time series, and many clustering algorithms based on them have been developed. The traditional DTW-KMedoids algorithm performs well both on the synthetic dataset and the real financial dataset. However, there are still several limitations to these algorithms: low efficiency caused by...
Credit risk models increasingly need to combine predictive accuracy with transparent explanations and auditable fairness constraints. Logistic regression remains attractive because its coefficients are easy to interpret, but it can miss nonlinear structure. Flexible models can improve prediction, but their explanations are often...
We show that the key optimization results of the classical Markowitz portfolio selection theory, originally formulated for variance as the risk measure, remain available in explicit closed form under a broader class of strictly convex quadratic risk measures. The proposed framework replaces the covariance matrix with an arbitrary...
This work complements our previous paper, which studies borrower-side strategies in decentralized lending markets, by focusing on lender-side capital allocation. We consider a lender who seeks to allocate a fixed budget across multiple markets sharing the same supplied asset. Accounting for the impact of supplied capital on lending...
We study long-range correlated Wigner-type matrices built from row-independent stationary Gaussian sequences. For exponentially decaying (AR(1)) correlations, the bulk spectral density deforms from the semicircle law via an explicit combinatorial "hub" mechanism, yet we verify the flatness and decay hypotheses of the...
We study equilibria in a closed, fee-free constant-function market maker (CFMM) economy with two assets and two traders. An interior state is a unilateral no-trade equilibrium exactly when the CFMM marginal price equals both traders' marginal rates of substitution. For an interior initial state, individually rational unilateral...
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...
Action-conditioned world models are increasingly used as learned simulators for policy evaluation and improvement, yet their effectiveness rests on an unverified assumption: generated futures faithfully reflect arbitrary valid actions. Existing benchmarks are typically confined to expert demonstrations, leaving off-expert action...
We show Lagrange and Hermite interpolation are possible using Stieltjes polynomials, linear combinations of iterated Stieltjes integrals of a constant function. We introduce divided differences via Newton interpolation and provide an explicit error formula of Peano kernel type via a new Taylor formula. Finally, we use the properties...
Scalar-induced gravitational waves (SIGWs) probe primordial curvature perturbations beyond cosmic microwave background scales, while primordial black holes (PBHs) probe the rare tail of the same statistics. We ask whether SIGW morphology can reveal scale-dependent primordial non-Gaussianity. We adopt the internal-leg separable kernel,...
World action models (WAMs) improve robot control by modeling how observations evolve, but generating future observations at test time incurs substantial latency. Fast-WAM removes this process for efficiency; however, our matched implementations show lower generalization for Fast-WAM than for future-aware alternatives, especially with...
Generative models are commonly ranked by Fréchet Inception Distance (FID) and Kernel Inception Distance (KID), yet FID's first-two-moment summary can miss distributional differences, and a reported scalar gap alone is not a calibrated test against sampling variation. FID's moment restriction has concrete consequences: on ImageNet,...
Distributed multiple-input multiple-output (D-MIMO) is envisioned as a key deployment architecture for future wireless systems, offering improved coverage and robustness through spatial separation, and favorable geometry for localization and sensing. Its greatest potential for localization lies in joint coherent processing across...
For $N$ lattices in $\R^d$ with volume $1$ and pairwise trivial intersections, every nonzero common tiling function has support diameter $Ω(N^{1/d})$, while for lattice families whose fundamental domains have uniformly bounded diameters, the standard convolution construction gives an $O(N)$ upper bound, leaving a gap that has remained...
The oscillation of M(x), the partial sum of the Möbius function has been in the focus of researchers in the theory of primes since the famous conjecture of Mertens in 1905 (formulated in a weaker form by Stieltjes in 1885 in a letter to Hermite). The average order of the modulus of M(x) in an interval of type [0,Y] is clearly in...
Smart glasses are evolving from capture and display accessories into first-person intelligence platforms that connect human perception, persistent context, and digital or physical action. Their on-body viewpoint aligns with the wearer's vision, audition, motion, and hand-object interaction, but must operate under tight energy,...
Recursive self-improvement (RSI) remains hard in long-horizon tasks, where growing histories obscure the task state and misalign skill invocation. We introduce Recuris, a recursive Experiential-Working Memory architecture for long-horizon agent harnesses, in which Working Memory tracks task progress and guides skill selection from...