arXiv subjects

Michael Weiner

Publications and source records attributed to Michael Weiner.

3 recordsLinked to original sources

arXiv2026

Points of maximal traffic on a grid with obstruction

For $n\in\mathbb{N}$, we consider the set of lattice paths from $(0,0)$ to $(n,n)$ using only unit north and east steps. Given a point $B$ to be avoided, we ask: at which point $A$ on the grid with corners $(0,0)$ and $(n,n)$, different from the endpoints, does the largest number of $B$-avoiding lattice paths pass through? We show that for $n\ge 9$, regardless of the location of $B$, the maximum is attained at one of ten specific points clustered near the two endpoints of the grid. This stability, however, conceals an interesting anomaly. When the obstruction $B$ lies on the antidiagonal $x+y=n$, the points of maximal traffic migrate from the near-corner points $(1,1)$ and $(n-1,n-1)$ to boundary points in the set of possible maximizers. The migration occurs for every $8\le n\le 375$, and intermittently up to $n=495$. We conjecture that the anomaly disappears for $n\ge 496$.

math.CO↗

arXiv2025

Agentic AI for Scaling Diagnosis and Care in Neurodegenerative Disease

United States healthcare systems are struggling to meet the growing demand for neurological care, particularly in Alzheimer's disease and related dementias (ADRD). Generative AI built on language models (LLMs) now enables agentic AI systems that can enhance clinician capabilities to approach specialist-level assessment and decision-making in ADRD care at scale. This article presents a comprehensive six-phase roadmap for responsible design and integration of such systems into ADRD care: (1) high-quality standardized data collection across modalities; (2) decision support; (3) clinical integration enhancing workflows; (4) rigorous validation and monitoring protocols; (5) continuous learning through clinical feedback; and (6) robust ethics and risk management frameworks. This human centered approach optimizes clinicians' capabilities in comprehensive data collection, interpretation of complex clinical information, and timely application of relevant medical knowledge while prioritizing patient safety, healthcare equity, and transparency. Though focused on ADRD, these principles offer broad applicability across medical specialties facing similar systemic challenges.

cs.CY↗

arXiv2023

Factorization of quadratic polynomials in the ring of formal power series over Z

We establish necessary and sufficient conditions for a quadratic polynomial to be irreducible in the ring $Z[[x]]$ of formal power series with integer coefficients. For $n,m\ge 1$ and $p$ prime, we show that $p^n+p^mβx+αx^2$ is reducible in $Z[[x]]$ if and only if it is reducible in $Z_p[x]$, the ring of polynomials over the $p$-adic integers.

math.AC↗