arXiv preprints from January 1, 2026 through September 28, 2026 — 19:23:47 EST
Fix two integers $1\leq d<e$. We study the birational geometry of a parameter space for pairs of homogeneous polynomials of degrees $d$ and $e$ in two variables (in which the higher degree polynomial is well defined only up to a multiple of the lower degree polynomial). We show that one can run the MMP on this space, and that it...
We present a novel probabilistic approach for optimal experimental path design. In this approach a discrete path optimization problem is defined on a static navigation mesh, and trajectories are modeled as random variables governed by a parametric Markov policy. The discrete path optimization problem is then replaced with an...
We present a comonadic approach to pretorsion theories on semiexact categories, i.e. categories equipped with a closed ideal of null morphisms that admits all kernels and all cokernels. We first prove that bihereditary pretorsion theories are comonadic in a 2-dimensional sense over the 2-category of semiexact categories with naturally...
The key-value (KV) cache is a primary memory bottleneck in Transformers. We propose Low-Rank Key-Value (LRKV) attention, which reduces KV cache memory by exploiting redundancy across attention heads, while being compute efficient. Each layer uses a shared full-rank KV projection augmented with low-rank, head-specific residuals,...
We study the Dvoretzky covering problem for random covering sets driven by general Borel probability measures. As our main result, we solve the problem of covering analytic sets by random covering sets generated by arbitrary Borel probability measures on the real line. Prior to this work, a complete solution was not known for any...
We present observations and analysis of the bound planetary microlensing event KMT-2025-BLG-1616. The planetary signal was captured by the Korea Microlensing Telescope Network (KMTNet) and the DECam Rogue Earths and Mars Survey (DREAMS). DREAMS's minute-cadence observations break the central/resonant degeneracy in the binary-lens...
Predictive Process Monitoring is a branch of process mining that aims to predict the outcome of an ongoing process. Recently, it leveraged machine-and-deep learning architectures. In this paper, we extend our prior LLM-based Predictive Process Monitoring framework, which was initially focused on total time prediction via prompting....
This paper introduces the XL set, a new collection of large-scale benchmark instances for the capacitated vehicle routing problem (CVRP). The set extends previous benchmarks by covering instances with 1,000 to 10,000 customers and a wide range of structural characteristics, following established generation principles from prior CVRP...
We present a study of Pseudo-LRD-NOM (Pseudo little red dot with no metal lines), a highly magnified low-mass galaxy behind the lensing cluster Abell 370 at z=5.96. We classify this object as a pseudo-LRD because its red rest-frame optical colour is contaminated by a prominent Halpha line (with EW0 >~ 800 Angstroms) present in its...
Direct observations of exoplanets probe the demographics and atmospheric composition of young self-luminous companions, yielding insight into their formation and early evolution history. In the near future, Gaia will reveal hundreds of nearby young exoplanets amenable to direct follow-up observations. Long-baseline interferometry with...
This article is an exposition on some recent theoretical advances in learning latent structured models, with a primary focus on the fundamental roles that optimal transport distances play in the statistical theory. We aim at what may be the most critical and novel ingredient in this theory: the motivation, formulation, derivation and...
As vision-language models (VLMs) tackle increasingly complex and multimodal tasks, the rapid growth of Key-Value (KV) cache imposes significant memory and computational bottlenecks during inference. While Multi-Head Latent Attention (MLA) offers an effective means to compress the KV cache and accelerate inference, adapting existing...
We study the classification of spaces of continuous functions $C(K)$ under positive linear maps. For infinite countable compacta, we show that whenever $C(K)$ and $C(L)$ are isomorphic, there exists an isomorphism $T:C(K)\to C(L)$ satisfying either $T\geq 0$ or $T^{-1}\geq 0$. We also prove that for any compact spaces $K$ and $L$, the...
This paper investigates the asymptotic behavior of stochastic recursive inclusions in the presence of non-zero, non-diminishing bias, a setting that frequently arises in zeroth-order optimization, stochastic approximation with iterate-dependent noise, and distributed learning with adversarial agents. The analysis is conducted through...
We introduce a smooth variant of the SCAD thresholding rule for wavelet denoising by replacing its piecewise linear transition with a raised cosine. The resulting shrinkage function is odd, continuous on R, and continuously differentiable away from the main threshold, yet retains the hallmark SCAD properties of sparsity for small...
Learning structured task representations from human demonstrations is essential for bimanual manipulation, where action ordering, object involvement, and interaction geometry vary significantly across executions. A key challenge lies in jointly capturing the discrete semantic task structure and the temporal evolution of object-centric...
Information overload and misinformation create significant challenges in extracting meaningful narratives from large news collections. This paper defines the nascent field of Interactive Narrative Analytics (INA), which combines computational narrative extraction with interactive visual analytics to support sensemaking. INA approaches...
Mini-EUSO is the first space-borne detector of the JEM-EUSO (Joint Exploratory Missions for Extreme Universe Space Observatory) program, operating on the International Space Station (ISS) since October 2019. Designed to search for Ultra-High Energy Cosmic Rays (UHECRs) above 10$^{21}~$eV and capable of placing a stringent upper limit...
Indoor high-capacity connectivity is frequently constrained by significant building penetration loss and the inherent uplink power limitations of a typical outdoor macro-cell deployment. While Mobile Network Operators (MNOs) must optimize spectrum across low-band (<1 GHz) and mid-band (1-7 GHz) frequencies, uplink performance remains...
Among hardware accelerators for deep-learning inference, data flow implementations offer low latency and high throughput capabilities. In these architectures, each neuron is mapped to a dedicated hardware unit, making them well-suited for field-programmable gate array (FPGA) implementation. Previous unrolled implementations mostly...
We prove that any finite $δ$-index hypersurface $M$ in ${\mathbb R}^{n+1}$ with constant mean curvature must be minimal, provided either of the following conditions holds: - the volume growth of $M$ is sub-exponential; - the Ricci curvature of $M$ satisfies $\operatorname{Ric}_M\geq -\frac{3(1-δ)}{n-1}|A|^2g,$ where $A$ is the...
We prove rigidity results describing contextually-constrained maps defined on Grassmannians and manifolds of ordered independent line tuples in finite-dimensional vector or Hilbert spaces. One statement in the spirit of the Fundamental Theorem of Projective Geometry classifies maps between full Grassmannians of two $n$-dimensional...
Incorporating self-interaction corrections (SIC) significantly improves chemical reaction barrier height predictions made using density functional theory methods. We present a detailed, orbital-by-orbital analysis of these corrections for three semi-local density functional approximations (DFAs) situated on the three lowest rungs of...
The shift from traditional synchronous generator (SG) based power generation to generation driven by power electronic devices introduces new dynamic phenomena and considerations for the control of large-scale power systems. In this paper, two aspects of all-inverter power systems are investigated: greater localization of system...
We have used Auriga --a set of state-of-the-art cosmological hydrodynamical simulations of Milky Way-size systems-- to study the impact of baryons on the Galactic subhalo population. A DM-only run counterpart of Auriga allows us to compare results with and without baryons. We repopulate the original suites with low-mass subhalos...