arXiv subjects

David Zeng

Publications and source records attributed to David Zeng.

7 recordsLinked to original sources

arXiv2025

VC-dimension of generalized progressions in some nonabelian groups

We analyze generalized progressions in some nonabelian groups using a measure of complexity called VC-dimension, which was originally introduced in statistical learning theory by Vapnik and Chervonenkis. Here by a "generalized progression" in a group $G$, we mean a finite subset of $G$ built from a fixed set of generators in analogy to a (multidimensional) arithmetic progression of integers. These sets play an important role in additive combinatorics and, in particular, the study of approximate groups. Our two main results establish finite upper bounds on the VC-dimension of certain set systems of generalized progressions in finitely generated free groups and also the Heisenberg group over $\mathbb{Z}$.

math.GR↗

arXiv2024

Development of CNN Architectures using Transfer Learning Methods for Medical Image Classification

The application of deep learning-based architecture has seen a tremendous rise in recent years. For example, medical image classification using deep learning achieved breakthrough results. Convolutional Neural Networks (CNNs) are implemented predominantly in medical image classification and segmentation. On the other hand, transfer learning has emerged as a prominent supporting tool for enhancing the efficiency and accuracy of deep learning models. This paper investigates the development of CNN architectures using transfer learning techniques in the field of medical image classification using a timeline mapping model for key image classification challenges. Our findings help make an informed decision while selecting the optimum and state-of-the-art CNN architectures.

cs.CV↗

arXiv2022

Box-ball systems and RSK recording tableaux

A box-ball system (BBS) is a discrete dynamical system consisting of n balls in an infinite strip of boxes. During each BBS move, the balls take turns jumping to the first empty box, beginning with the smallest-numbered ball. The one-line notation of a permutation can be used to define a BBS state. This paper proves that the Robinson--Schensted (RS) recording tableau of a permutation completely determines the dynamics of the box-ball system containing the permutation. Every box-ball system eventually reaches steady state, decomposing into solitons. We prove that the rightmost soliton is equal to the first row of the RS insertion tableau and it is formed after at most one BBS move. This fact helps us compute the number of BBS moves required to form the rest of the solitons. First, we prove that if a permutation has an L-shaped soliton decomposition then it reaches steady state after at most one BBS move. Permutations with L-shaped soliton decompositions include noncrossing involutions and column reading words. Second, we make partial progress on the conjecture that every permutation on n objects reaches steady state after at most n-3 BBS moves. Furthermore, we study the permutations whose soliton decompositions coincide with standard tableaux; we conjecture that they are closed under consecutive pattern containment and that the RS recording tableaux belonging to such permutations are counted by the Motzkin numbers.

math.CO↗

arXiv2020

A Systematic Review of Natural Language Processing for Knowledge Management in Healthcare

Driven by the visions of Data Science, recent years have seen a paradigm shift in Natural Language Processing (NLP). NLP has set the milestone in text processing and proved to be the preferred choice for researchers in the healthcare domain. The objective of this paper is to identify the potential of NLP, especially, how NLP is used to support the knowledge management process in the healthcare domain, making data a critical and trusted component in improving the health outcomes. This paper provides a comprehensive survey of the state-of-the-art NLP research with a particular focus on how knowledge is created, captured, shared, and applied in the healthcare domain. Our findings suggest, first, the techniques of NLP those supporting knowledge management extraction and knowledge capture processes in healthcare. Second, we propose a conceptual model for the knowledge extraction process through NLP. Finally, we discuss a set of issues, challenges, and proposed future research areas.

cs.CY↗

arXiv2020

Green Security Game with Community Engagement

While game-theoretic models and algorithms have been developed to combat illegal activities, such as poaching and over-fishing, in green security domains, none of the existing work considers the crucial aspect of community engagement: community members are recruited by law enforcement as informants and can provide valuable tips, e.g., the location of ongoing illegal activities, to assist patrols. We fill this gap and (i) introduce a novel two-stage security game model for community engagement, with a bipartite graph representing the informant-attacker social network and a level-$\kappa$ response model for attackers inspired by cognitive hierarchy; (ii) provide complexity results and exact, approximate, and heuristic algorithms for selecting informants and allocating patrollers against level-$\kappa$ ($\kappa<\infty$) attackers; (iii) provide a novel algorithm to find the optimal defender strategy against level-$\infty$ attackers, which converts the problem of optimizing a parameterized fixed-point to a bi-level optimization problem, where the inner level is just a linear program, and the outer level has only a linear number of variables and a single linear constraint. We also evaluate the algorithms through extensive experiments.

cs.GT↗

arXiv2019

Fairness-Efficiency Tradeoffs in Dynamic Fair Division

We investigate the tradeoffs between fairness and efficiency when allocating indivisible items over time. Suppose T items arrive over time and must be allocated upon arrival, immediately and irrevocably, to one of n agents. Agent i assigns a value v_{it} in [0,1] to the t-th item to arrive and has an additive valuation function. If the values are chosen by an adaptive adversary it is known that the algorithm that minimizes maximum pairwise envy simply allocates each item uniformly at random; the maximum pairwise envy is then sublinear in T. If the values are independently and identically drawn from an adversarially chosen distribution D, it is also known that, under some mild conditions on D, allocating to the agent with the highest value -- a Pareto efficient allocation -- is envy-free with high probability. In this paper we study fairness-efficiency tradeoffs in this setting and provide matching upper and lower bounds under a spectrum of progressively stronger adversaries. On one hand we show that, even against a non-adaptive adversary, there is no algorithm with sublinear maximum pairwise envy that Pareto dominates the simple algorithm that allocates each item uniformly at random. On the other hand, under a slightly weaker adversary regime where item values are drawn from a known distribution and are independent with respect to time, i.e. v_{it} is independent of v_{it'} but possibly correlated with v_{i't}, optimal (in isolation) efficiency is compatible with optimal (in isolation) fairness. That is, we give an algorithm that is Pareto efficient ex-post and is simultaneously optimal with respect to fairness: for each pair of agents i and j, either i envies j by at most one item (a prominent fairness notion), or $i$ does not envy j with high probability. En route, we prove a structural result about allocations of divisible items that might be of independent interest.

cs.GT↗

arXiv2014

Convex Optimization in Julia

This paper describes Convex, a convex optimization modeling framework in Julia. Convex translates problems from a user-friendly functional language into an abstract syntax tree describing the problem. This concise representation of the global structure of the problem allows Convex to infer whether the problem complies with the rules of disciplined convex programming (DCP), and to pass the problem to a suitable solver. These operations are carried out in Julia using multiple dispatch, which dramatically reduces the time required to verify DCP compliance and to parse a problem into conic form. Convex then automatically chooses an appropriate backend solver to solve the conic form problem.

math.OC↗