Lattic path proofs of extended Bressoud-Wei and Koike skew Schur function identities

Our recent paper provides extensions to two classical determinantal results of Bressoud and Wei, and of Koike. The proofs in that paper were algebraic. The present paper contains combinatorial lattice path proofs

Multiparty Quantum Communication Using Multiqubit Entanglement and Teleportation

We propose a 2N qubit entangled channel that can be used to teleport N qubits in a network to a single receiver. We describe the structure of this channel and explicitly demonstrate how the protocol works. The channel can be used to implement a scheme in which all parties have to participate in order for the teleportation to be successful. This can be advantageous in various scenarios and we discuss the potential application of this protocol to voting

AN ANALYSIS OF UNPLANNED LOSSES ON ARLEIGH BURKE CLASS DESTROYERS

The United States Navy (USN) faces challenges with crew manning levels on its afloat units, impacting operational readiness. Despite various efforts to address crew shortages, including workload studies and the optimal manning initiative, unplanned losses (UPLs) continue to disrupt naval operations. This thesis explores unplanned losses on USN Arleigh Burke Class guided-missile destroyers (DDGs) using a dataset derived from Fleet Training Management and Planning System (FLTMPS) data and machine learning techniques including logistic regression, random forest, and survival analysis, to identify factors that suggest a sailor's risk of becoming a UPL and to predict these events. Analyzing data from sailors assigned to DDGs over the course of a year, this study enhances understanding and prediction of UPLs, contributing to improved crew effectiveness and operational readiness. We found that 7% of the nearly 22,000 sailors assigned to DDGs left their command greater than six months prior to their projected rotation date (PRD). The random forest model performed best on our test set and identified variables related to tour completion, rank, and phase as particularly important in predicting UPLs. A Navy-wide definition of unplanned loss along with centralized data-collection of important features, reason for loss, and the specific date a sailor became unavailable to their ship would facilitate better understanding of causes and impacts of UPLs on surface ship manning.Distribution Statement A. Approved for public release: Distribution is unlimited.Lieutenant Commander, United States Nav

Math, ChatGPT, and You: The Problem with Mathematical Accuracy in Large Language Models

ChatGPT and other Large Language Models (LLMs) currently do a good job at generating novel text across many domains, but math remains a consistent issue when it comes to the accuracy of answers generated by these models. My research into various ways to manipulate the model have led me to the conclusion that a general closed form solution to help LLMs with math is both unrealistic and likely impossible. LLMs can be trained more successfully as you narrow the problem space, but consideration must be taken on the part of human user to recognize when an LLM is detrimental to your solution and a traditional programming solution should be taken instead