arXiv preprints from January 1, 2026 through September 26, 2026 — 05:18:51 EST
This paper develops a bridge between bi-Hamiltonian structures of Poisson-Lie type, contact Hamiltonian dynamics, and the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) formalism for quantum open systems. On the classical side, we consider bi-Hamiltonian systems defined by a Poisson pencil with non-trivial invariants. Using an exact...
A fundamental requirement for full autonomy is the ability to sustain accurate navigation in the absence of external data, such as GNSS signals or visual information. In these challenging environments, the platform must rely exclusively on inertial sensors, leading to pure inertial navigation. However, the inherent noise and other...
Multimodal Large Language Models (MLLMs) have shown strong potential for radiology report generation, yet their clinical translation is hindered by architectural heterogeneity and the prevalence of factual hallucinations. Standard supervised fine-tuning often fails to strictly align linguistic outputs with visual evidence, while...
This paper establishes sharp bounds for the second and third-order Toeplitz determinants associated with starlike functions $f$ in the unit disk such that $f(z)-z$ has a zero of order $k+1$ at $z=0$. These bounds are further extended to starlike mappings defined on the unit ball in a complex Banach space and on bounded starlike...
Generalist robots are becoming a reality, capable of interpreting natural language instructions and executing diverse operations. However, their validation remains challenging because each task induces its own operational context and correctness specification, exceeding the assumptions of traditional validation methods. We propose a...
Autonomous landing on mobile platforms is crucial for extending quadcopter operational flexibility, yet conventional methods are often too inefficient for highly dynamic scenarios. The core limitation lies in the prevalent ``track-then-descend'' paradigm, which treats the platform as a passive target and forces the quadcopter to...
We prove the Hilbert-Chow crepant resolution conjecture in the exceptional curve classes for all projective surfaces and all genera. In particular, this confirms Ruan's cohomological Hilbert-Chow crepant resolution conjecture. The proof exploits Fulton-MacPherson compactifications, reducing the conjecture to the case of the affine...
This is a set of lectures on tensor networks with a strong emphasis on the core algorithms involving Matrix Product States (MPS) and Matrix Product Operators (MPO). Compared to other presentations, particular care has been given to disentangle aspects of tensor networks from the quantum many-body problem: MPO/MPS algorithms are...
Norwegian, spoken by approximately five million people, remains underrepresented in many of the most significant breakthroughs in Natural Language Processing (NLP). To address this gap, the NorLLM team at NorwAI has developed a family of models specifically tailored to Norwegian and other Scandinavian languages, building on diverse...
Streamwise roll and streak structures (RSS) are prominent features observed in both atmospheric and oceanic planetary boundary layers (PBL) as well as in laboratory scale Wall bounded shear flows. Despite their structural similarity across these systems, the mechanisms responsible for forming and sustaining the RSS remain debated....
Fairness in machine learning is increasingly critical, yet standard approaches often treat data as static points in a high-dimensional space, ignoring the underlying generative structure. We posit that sensitive attributes (e.g., race, gender) do not merely shift data distributions but causally warp the geometry of the data manifold...
In this paper, we introduce FlexProofs, a new vector commitment (VC) scheme that achieves two key properties: (1) the prover can generate all individual opening proofs for a vector of size $N$ in optimal time ${\cal O}(N)$, and there is a flexible batch size parameter $b$ that can be increased to further reduce the time to generate...
We consider the problem of covering $\mathbb{Z}^2$ with a finite number of sublattices of finite index, satisfying a simple minimality or non-degeneracy condition. We show how this problem may be viewed as a projective (or homogeneous) version of the well-known problem of covering systems of congruences. We give a construction of...
In enterprise search, building high-quality datasets at scale remains a central challenge due to the difficulty of acquiring labeled data. To resolve this challenge, we propose an efficient approach to fine-tune small language models (SLMs) for accurate relevance labeling, enabling high-throughput, domain-specific labeling comparable...
Recent advances in Vision-Language Models (VLMs) have improved performance in multi-modal learning, raising the question of whether these models truly understand the content they process. Crucially, can VLMs detect when a reasoning process is wrong and identify its error type? To answer this, we present MMErroR, a multi-modal...
Spin waves (magnons) in 2D materials have received increasing interest due to their unique states and potential for tunability. However, many interesting features of these systems, including Dirac points and topological states, occur at high frequencies, where experimental probes are limited. Here, we study a crystal formed by...
Berry and Tabor conjectured in 1977 that spectra of generic integrable quantum systems have the same local statistics as a Poisson point process. We verify their conjecture in the case of the two-point spectral density for a quantum particle in a three-dimensional box, subject to a Diophantine condition on the domain's proportions. A...
Let $I$ be a monomial ideal of a polynomial ring $R=K[x_1,\ldots,x_n]$ over a field $K$ and let ${\rm sgn}(I)$ be its signature ideal. If $I$ is not a principal ideal, we show that the depth of $R/I$ is the depth of $R/{\rm sgn}(I)$, and the regularity of $R/{\rm sgn}(I)$ is at most the regularity of $R/I$. For ideals of height at...
Ion exchange kinetic flux equations have been extensively investigated since the mid-twentieth century and continue to provide a fundamental framework for describing mass transport phenomena in solid materials. Despite the maturity of this field, inconsistencies remain in the literature concerning the definition, dimensional...
I give a short proof of a recent result due to Kiefer and Ryzhikov showing that a finite irreducible semigroup of $n\times n$ matrices has cardinality at most $3^{n^2}$.
While Large Language Models (LLMs) have demonstrated significant potential in natural language processing , complex general-purpose reasoning requiring multi-step logic, planning, and verification remains a critical bottleneck. Although Reinforcement Learning with Verifiable Rewards (RLVR) has succeeded in specific domains , the field...
We formalize a minimal setting in which a chronology (a strict partial order on events) is forced by consistency of distributed information under local composability. The system maintains distributed records interpreted as constraints over a global possibility space (Omega, Sigma), optionally with a measure mu. Events act locally by...
LLM agents can reason and use tools, but they often break down on long-horizon tasks due to unbounded context growth and accumulated errors. Common remedies such as context compression or retrieval-augmented prompting introduce trade-offs between information fidelity and reasoning stability. We present InfiAgent, a general-purpose...
Evaluating machine learning (ML) model bias is key to building trustworthy and robust ML systems. Counterfactual Fairness (CF) audits allow the measurement of bias of ML models with a causal framework, yet their conclusions rely on a single causal graph that is rarely known with certainty in real-world scenarios. We propose CF with...
The identification of fractionalized excitations in quantum spin liquids (QSLs) remains a central challenge in condensed matter physics. In dipolar-octupolar (DO) pyrochlores, such as $\text{Ce}_2\text{Zr}_2\text{O}_7$, the candidate $π$-flux quantum spin ice (QSI) state is predicted to host both gapless emergent photons and a...