Research
Research
Research
Research
1,121+ open-access research outputs.
This study aims to examine the historical air pollution data from major Indian cities using fractal analysis to measure environmental risk. The fractal dimension of the major air pollutants is compute…
In 2016, Viazovska famously solved the sphere packing problem in dimension $8$, using modular forms to construct a 'magic' function satisfying optimality conditions determined by Cohn and Elkies in 20…
In computational science workflows, it is often the case that 1) objective functions for optimization involve multiple simulation outputs, and 2) those simulations can be performed (at least partially…
The Onsager-Stefan-Maxwell (OSM) equations are an important model of mass transport in multicomponent flows with multiple chemical species. They describe the coupling of diffusive fluxes between speci…
Let $V$ be a grading-restricted vertex algebra and let $A^\infty(V)=U^\infty(V)/Q^\infty(V)$ be the associative algebra constructed by Huang, where $U^\infty(V)$ is the space of column-finite infinite…
We present a method to quantify a system's resilience capacity, i.e., the set of degradation magnitudes for which all functional requirements remain satisfied. These requirements come from human stake…
In AI-rich higher education, polished written mathematics has become easier to produce than trustworthy evidence of understanding. This article develops a human-scale methodology for service mathemati…
This tutorial contrasts probabilistic modeling and robust optimization to determine decisions in humanitarian logistics, specifically supply chains subject to adversarial (natural and human) disruptio…
Let $f(m)$ be the largest integer such that for every set $A = \{a_1 < \cdots < a_m\}$ of $m$ positive integers and every open interval $I$ of length $2a_m$, there exist at least $f(m)$ disjoint pairs…
Artificial intelligence (AI) is the name popularly given to a broad spectrum of computer tools designed to perform increasingly complex cognitive tasks, including many that used to solely be the provi…
Since the earliest stages of human civilization, advances in technology have been tightly linked to our ability to understand and predict the mechanical behavior of materials. In recent years, this ch…
We construct Igusa stacks for all Shimura varieties of abelian type and derive consequences for the cohomology of these Shimura varieties. As an application, we prove that the Fargues--Scholze local L…
Identifying causality is fundamental for human understanding of the world, where complex non-autonomous systems such as species population changes, brain activities, etc. are extensively existed. Sinc…
Conventional multi-objective optimisation approaches (e.g., MOO-CP or MIP) fail in group decision-making by aggregating heterogeneous objectives without a valid preference foundation, producing Pareto…
Graph colorings have been of interest to mathematicians for a long time, but relatively recently, social scientists have also found them to be interesting tools for studying group behavior. In the las…
This paper proposes and analyzes a malaria transmission model structured by the chronological age of the human host population. The model couples an age-structured SIRS system for humans, incorporatin…
Mathematics is changing. Computers are verifying proofs, checking calculations, and exploring complex structures that would overwhelm human effort. Yet curiosity-driven research is where tomorrow's br…
AI systems can generate outputs at scale, but most outputs require human approval before release. This creates a bottleneck: humans cannot keep pace with AI-generated volume. A natural response is to …
In an act of sabotage or terrorism, hazardous material might be released deliberately into the atmosphere to threaten individuals, e.g., those operating critical infrastructure. Hazardous materials in…
We approach the sorites paradox (SP) through an observer-based and time-dependent approach to truth of vague assertions. Formally the approach gives rise to a semantics, called fluxing-object semantic…
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