Mathematics Commons^™

Demystifying Hardware Formal Verification For Undergraduate Education: A Risc-V Processor Case Study With Coursework Implementation, Riley A. Peters

Master's Theses

Hardware verification engineers apply formal methods to prove that a digital device always behaves according to its specification. This differs from traditional functional verification, in which engineers establish correctness by repeatedly sending test inputs to the device and comparing the outputs against a reference model. With the growing complexity of integrated circuits, the demand for digital verification engineers with formal methods experience has continued to increase. However, California Polytechnic State University: San Luis Obispo's current curriculum lacks dedicated material to prepare students for these roles.

This thesis seeks to address the lack of formal methods material through two efforts. First, …

Identical Vanishing Of Coefficients In The Series Expansion Of Eta Quotients, Modulo 4, 9 And 25, Tim Huber, James Mclaughlin, Dongxi Ye

School of Mathematical & Statistical Sciences Faculty Publications

Let A(q)=:∑∞n=0anqn and B(q)=:∑∞n=0bnqn be two eta quotients. In some previous papers, the present authors considered the problem of when

an=0⟺bn=0.

In the present paper we consider the “mod m” version of this problem, i.e. for which eta quotients A(q) and B(q) and for which integers m>1 do we have (non-trivially) that

an≡0(modm)⟺bn≡0(modm)?

(We say “non-trivially” as there are trivial situations where an≡bn(modm) for all n≥0). The m for which we found non-trivial (in the sense just mentioned) results were m=p2, p=2,3 and 5. For m=4 and m=9, we found results which …

Mat1500 Calculus I Syllabus, Xinlong Dong

Open Educational Resources

No abstract provided.

Accessibility For Mathematical Documents, Xinlong Dong

Open Educational Resources

No abstract provided.

Reconstructing Soil Conductivity Profiles From Electromagnetic Induction Data, Tyler Philip Casas

Theses and Dissertations

Construction of infrastructure in cold regions poses a significant challenge, particularly due to permafrost degradation, which can lead to significant structural damage and deterioration to facilities and transportation systems. In recent years, the issue of geophysical hazard detection has been instrumental in minimizing ground subsidence risks when con- structing infrastructure in cold regions. As a commonly used technology for geophysical applications, electromagnetic induction (EMI) can be used for (i) detecting ground subsurface layers and (ii) characterizing soil types via electrical conductivities. However, EMI technology tends to struggle with lower resolution at lower frequencies and shallow depth of penetration at higher …

Minimal Supersolution Of Bsdes Driven By Continuous Martingales In A General Filtration, Badr Elmansouri, Mohamed El Otmani

Journal of Stochastic Analysis

In this paper, we study minimal supersolutions of backward stochastic differential equations (BSDEs) driven by a continuous local martingale in a general filtration. We establish existence, uniqueness, and stability results under various mild conditions on the terminal value and the generator. Additionally, we explore the connection between the concept of non-linear expectation and minimal supersolutions, emphasizing the specific properties that are relevant to our framework. We also prove a general monotonic limit theorem and apply this result to determine the smallest constrained supersolution of a BSDE with a possibly non-convex constraint.

Hybrid Vision Transformer–Cnn Framework For Alzheimer’S Disease Cell Type Classification: A Comparative Study With Vision–Language Models, Md Easin Hasan, Md Tahmid Hasan Fuad, Omar Sharif, Amy Wagler

School of Mathematical & Statistical Sciences Faculty Publications

Accurate identification of Alzheimer’s disease (AD)-related cellular characteristics from microscopy images is essential for understanding neurodegenerative mechanisms at the cellular level. While most computational approaches focus on macroscopic neuroimaging modalities, cell type classification from microscopy remains relatively underexplored. In this study, we propose a hybrid vision transformer–convolutional neural network (ViT–CNN) framework that integrates DeiT-Small and EfficientNet-B7 to classify three AD-related cell types—astrocytes, cortical neurons, and SH-SY5Y neuroblastoma cells—from phase-contrast microscopy images. We perform a comparative evaluation against conventional CNN architectures (DenseNet, ResNet, InceptionNet, and MobileNet) and prompt-based multimodal vision–language models (GPT-5, GPT-4o, and Gemini 2.5-Flash) using zero-shot, few-shot, and chain-of-thought …

Discrete Quantization On Spherical Geometries: Explicit Models, Computations, And Didactic Exposition, Mrinal Kanti Roychowdhury

School of Mathematical & Statistical Sciences Faculty Publications

This article presents a comprehensive and analytically explicit study of optimal discrete quantization on spherical geometries equipped with the geodesic metric. Focusing on highly symmetric configurations on the unit sphere 𝕊2, we investigate three explicit models of discrete uniform distributions and derive closed-form expressions for their optimal quantizers and corresponding mean square quantization errors. (I) For N equally spaced points on the equator, we obtain exact error formulas for both divisible and non-divisible cases 𝑛 ∤𝑁, demonstrating that optimal Voronoi cells form contiguous arcs with midpoint representatives. (II) For two antipodally symmetric small circles at latitudes ±𝜙0, each with M …

Assessing The Geomechanical Modelling Of Underground Reservoir For Co₂ Storage Trapping Mechanisms, Bonavian Hasiholan, Mohammed Ali Farea, Elhassan Mostafa Abdallah, Sami Abdelrahman M. Yagoub, Yasir Mukhtar

Mathematical Modelling and Numerical Simulation with Applications

Effective carbon dioxide (CO₂) storage is essential for mitigating climate change amid increasing global greenhouse gas emissions. This study investigates the influence of geomechanics on CO₂ storage performance within carbon capture and storage (CCS), focusing on structural, residual, and solubility trapping mechanisms using a fully coupled modeling framework. Two numerical models, with and without geomechanical effects, are developed to evaluate impacts on reservoir behavior, CO₂ migration, and trapping efficiency. Each mechanism is analyzed separately and within an integrated framework to assess their combined contributions. Results indicate that geomechanical coupling increases reservoir pressure, reduces CO₂ flow velocity, enhances migration control, and …

Limit Theorems For Andrews’ Restricted Overpartitions, Tapas Bhowmik, Alex Cao, Jack Frew, John Lehman, Wei-Lun Tsai

Faculty Publications

The study of overpartitions in recent years has been used to great effect in various fields, including hypergeometric series, q-series identities, and mathematical physics. We investigate the limiting distributions of the number of parts in a family of overpartitions of n,  introduced by Andrews, where parts are counted with two different weights. Using Andrews’ identities and the saddle-point method, we establish two central limit theorems (CLTs) for the number of parts as n → ∞, corresponding to these weightings. We also derive explicit formulas for the mean and variance in each case.

A Virtual Community Math Circle, Skona Brittain, Sayonita Ghosh Hajra, Steve Heller, Daniel Hodgins, Peter Petto, Gabriella Pinter, Lauren Rose, A. Gwinn Royal, Asmita Sodhi

Journal of Math Circles

The Julia Robinson Mathematics Festival (JRMF) Community Math Circle is free, volunteer-run, and online. We collaborate with JRMF and use their activities in our events. Started during the pandemic, the Community Math Circle continues to thrive. We have about 40 participants attending every month, typically kids aged 6 to 13, teachers, facilitators, and other adults. This article describes how our event is organized, planned, and executed, and how we train facilitators. We will also offer reflections on our successes and challenges.

On Cartan’S Examples Of Isoparametric Hypersurfaces And Their Focal Submanifolds, Thomas E. Cecil, Patrick J. Ryan

Mathematics and Computer Science Department Faculty Scholarship

This paper is a survey of Cartan’s examples of isoparametric hypersurfaces in spheres and their focal submanifolds that were described in his fundamental work on the subject, which appeared in four papers [2]–[5] published during the period 1938–1940.

The Butterfly Effect In Economics: Exploring Chaos With A Simple Financial Model, Sandy Hs Herho

CODEE Journal

Wild swings in financial markets need not result from external shocks like earthquakes or wars—they can emerge from deterministic chaos. This article introduces kalimusada, an open-source Python library that lets students and instructors explore this phenomenon through a simple three- equation model of financial dynamics. The model couples interest rates, investment, and prices through nonlinear feedback, generating bounded but unpredictable oscillations characteristic of chaos. Tiny differences in starting conditions—smaller than any measurement could detect—grow exponentially until two initially identical economies follow completely different paths. The library provides ready-to-use tools for visualizing this “butterfly effect” in economics, computing divergence metrics, and …

Effective Wordle Heuristics, Ronald I. Greenberg

Computer Science: Faculty Publications and Other Works

While previous researchers have performed an exhaustive search to determine an optimal Wordle strategy, that computation is very time consuming and produced a strategy using words that are unfamiliar to most people. With Wordle solutions being gradually eliminated (with a new puzzle each day and no reuse), an improved strategy could be generated each day, but the computation time makes a daily exhaustive search impractical. This paper shows that simple heuristics allow for fast generation of effective strategies and that little is lost by guessing only words that are possible solution words rather than more obscure words.

Systematic Synthesis Of Crispr/Cas Applications For Enhancing Salt Tolerance In Crops: A Decade Of Progress And Challenges, Xindi Sun, Fusheng Wu, Zhuanzhuan Ma, Guohao Liang, Shumei Chen, Xutong Hu, Shugao Fan, Ying Zhao

School of Mathematical & Statistical Sciences Faculty Publications

Soil salinity is a major constraint on global crop productivity, driving the need for salt-tolerant varieties. While CRISPR-Cas genome editing offers targeted solutions for trait improvement, significant biological and technical bottlenecks limit its application in conferring salt stress resilience. This systematic summarizes findings from 83 peer-reviewed studies (2015–2024) employing CRISPR/Cas technologies to improve salt tolerance in five major crops (rice, wheat, maize, sorghum, barley). Our systematic review reveals that early single-gene edits achieved modest gains (30–50% Na⁺ exclusion) but often showed limited yield gains in field settings, potentially due to compensatory regulation and environmental variation. The literature suggests that multiplex …

Unitary Rational Functions: The Scaled Quaternion Case, Daniel Alpay, Ilwoo Choo, Mihaela Vajiac

Mathematics, Physics, and Computer Science Faculty Articles and Research

We develop the theory of minimal realizations and factorizations of rational functions where the coefficient space is a ring of the type introduced in our previous work, the scaled quaternions, which includes as special cases the quaternions and the split quaternions. The methods involved are not a direct generalization of the complex or quaternionic settings, and in particular, the adjoint is not the classical adjoint and we use properties of real Hilbert spaces. This adjoint allows to define the counterpart of unitarity for matrix-rational functions, and we develop the corresponding theories of realizations and unitary factorizations. We also begin a …

Positive Solutions Of Semipositone Singular Three-Points Boundary Value Problems For Nonlinear Fractional Differential Equations, Xueyan Zhang, Zhaocai Hao, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

This study introduces the existence of one positive solution for a specific category of semipositive singular three-point boundary value problems associated with Caputo fractional differential equations. The proof relies on the application of the Guo–Krasnosel'skii fixed point theorem. In the end, we provide an illustrative example.

Corrigendum To “Interim Rationalizable Implementation Of Functions” (Kunimoto T, Saran R, Serrano R (2024) Mathematics Of Operations Research 49(3):1791–1824), Takashi Kunimoto, Rene Saran, Roberto Serrano

Research Collection School Of Economics

This is the brief corrigendum to “Interim rationalizable implementation of functions” [Kunimoto T, Saran R, Serrano R (2024) Interim rationalizable implementation of functions. Math. Oper Res. 49(3):1791–1824].

One-Step Purification Of A Bioactive Pak1-Derived Peptide, Djamali Muhoza, Emily P. Esquivel, Stacy R. Hunter, Pateince S. Okoto, Thallapuranam K.S. Kumar, Paul D. Adams

Chemistry & Biochemistry Faculty Publications and Presentations

The serine/threonine kinase PAK1 serves as a mediator of cytoskeletal reorganization and cancer-related signaling downstream of the small GTPases. Due to the challenges in purifying PAK1 complexes, a 46-residue peptide from PAK1, is widely used to study PAK1-Cdc42 signaling. Traditionally, this purification involved multi-step chromatography of recombinant GST-PBD46 complexes, yielding approximately 1 mg per 1.5 L culture. In this study, a 30 min heat treatment step after thrombin cleavage was used to precipitate GST while leaving pure PBD46 in solution. This step eliminated the need for further affinity and size-exclusion chromatography steps. This improved protocol produces proteins with a 6.5-fold …

Flips In Two-Dimensional Hypertriangulations, Herbert Edelsbrunner, Alexey Garber, Mohadese Ghafari, Teresa Heiss, Morteza Saghafian

School of Mathematical & Statistical Sciences Faculty Publications

We study flips in hypertriangulations of planar points sets. Here a level-k hypertriangulation of n points in the plane is a subdivision induced by the projection of a k-hypersimplex, which is the convex hull of the barycenters of the (k−1)-dimensional faces of the standard (n−1)-simplex. In particular, we introduce four types of flips and prove that the level-2 hypertriangulations are connected by these flips.