Physical Sciences and Mathematics Commons^™

On Combinatorics Of Voronoi Polytopes For Perturbations Of The Dual Root Lattices, Alexey Garber

School of Mathematical & Statistical Sciences Faculty Publications

The Voronoi conjecture on parallelohedra claims that for every convex polytope P that tiles Euclidean d-dimensional space with translations there exists a d-dimensional lattice such that P and the Voronoi polytope of this lattice are affinely equivalent. The Voronoi conjecture is still open for the general case but it is known that some combinatorial restrictions for the face structure of P ensure that the Voronoi conjecture holds for P. In this article, we prove that if P is the Voronoi polytope of one of the dual root lattices Dd*, E6*, E7* or E8*=E8 or their small perturbations, then every parallelohedron …

Logarithmic Algorithms For Fair Division Problems, Alexandr Grebennikov, Xenia Isaeva, Andrei V. Malyutin, Mikhail Mikhailov, Oleg R. Musin

School of Mathematical & Statistical Sciences Faculty Publications

We study the algorithmic complexity of fair division problems with a focus on minimizing the number of queries needed to find an approximate solution with desired accuracy. We show for several classes of fair division problems that under certain natural conditions on sets of preferences, a logarithmic number of queries with respect to accuracy is sufficient.

Managing Inter-Organizational Trust And Risk Perceptions In Transboundary Fisheries Governance Networks, Evelyn Roozee, Dongkyu Kim, Antonia Sohns, Jasper R. De Vries, Owen Temby, Gordon M. Hickey

School of Earth, Environmental, & Marine Sciences Faculty Publications

Transboundary fishery management represents a significant governance challenge that requires ongoing inter-organizational communication, collaboration, and collective action to ensure sustainability. Previous research suggests that different dimensions of perceived risk, trust, and control interact in complex ways to affect inter-organizational collaborative performance, providing an administrative ‘architecture’ that enables partners to share resources, engage in teamwork, resolve conflict, and coordinate tasks and responsibilities while also allaying their concerns about the alliance. However, the extent to which different control mechanisms influence trust and mitigate the perceived risks of collaboration between the diverse organizations involved in transboundary fisheries management remains unclear. This paper presents …

Symmetries And Integrable Systems, Sen-Yue Lou, Bao-Feng Feng

School of Mathematical & Statistical Sciences Faculty Publications

Symmetry plays key roles in modern physics especially in the study of integrable systems because of the existence of infinitely many local and nonlocal generalized symmetries. In addition to the fundamental role to find exact group invariant solutions via Lie point symmetries, some important new developments on symmetries and conservation laws are reviewed. The recursion operator method is important to find infinitely many local and nonlocal symmetries of (1+1)-dimensional integrable systems. In this paper, it is pointed out that a recursion operator may be obtained from one key symmetry, say, a residual symmetry. For (2+1)-dimensional integrable systems, the master-symmetry approach …

Structure Of Fine Selmer Groups In Abelian P-Adic Lie Extensions, Debanjana Kundu, Filippo Alberto Edoardo Nuccio Mortarino Majno Di Capriglio, Sujatha Ramdorai

School of Mathematical & Statistical Sciences Faculty Publications

This paper studies fine Selmer groups of elliptic curves in abelian p -adic Lie extensions. A class of elliptic curves are provided where both the Selmer group and the fine Selmer group are trivial in the cyclotomic Z p -extension. The fine Selmer groups of elliptic curves with complex multiplication are shown to be pseudonull over the trivializing extension in some new cases. Finally, a relationship between the structure of the fine Selmer group for some CM elliptic curves and the Generalized Greenberg's Conjecture is clarified.

Optimizing Energy Consumption In Smart Homes Using Ga-Lstm, Akibor Junior Chukwuka, Bakare-Bolaji Moyosoreoluwa, Baboucarr Dibba

School of Mathematical & Statistical Sciences Faculty Publications

The need to optimize energy consumption arises from the inadequate energy supply many homes face. However, to optimize energy consumption in a home, one must be equipped with the knowledge of the energy consumption rate and energy supply rate in the home. This paper proposed the use of a Long Short-Term Memory (LSTM) model optimized by Genetic Algorithm (GA) to optimize the energy consumption in a smart home. The model was designed using 8 input variables, which were observed weather information of a given region over a span of 350 days. The data set was split into a training data …

Investigating Preservice Teachers’ Conceptualizations Of Mathematical Knowledge For Teaching Through Video Analysis, Bima Sapkota

School of Mathematical & Statistical Sciences Faculty Publications

Mathematics Preservice Teachers’ (M-PSTs) conceptions of Mathematical Knowledge for Teaching (MKT) enhance their reflective skills because they utilize such conceptions to reflect on how to contextualize content knowledge during secondary mathematics teaching. While previous studies suggested M-PSTs develop MKT, including pedagogical content knowledge by analyzing teaching in video lessons, how M-PSTs enhance their conceptions of MKT through such analysis is underexplored. I used a collective case study approach to investigate how four secondary M-PSTs conceptualized MKT when they analyzed and discussed teaching represented in a video lesson using the MKT framework. The findings indicated that the M-PSTs often described teacher …

Modeling The Effect Of Observational Social Learning On Parental Decision-Making For Childhood Vaccination And Diseases Spread Over Household Networks, Tamer Oraby, Andras Balogh

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we introduce a novel model for parental decision-making about vaccinations against a childhood disease that spreads through a contact network. This model considers a bilayer network comprising two overlapping networks, which are either Erdős–Rényi (random) networks or Barabási–Albert networks. The model also employs a Bayesian aggregation rule for observational social learning on a social network. This new model encompasses other decision models, such as voting and DeGroot models, as special cases. Using our model, we demonstrate how certain levels of social learning about vaccination preferences can converge opinions, influencing vaccine uptake and ultimately disease spread. In addition, …

Conditional Constrained And Unconstrained Quantization For Probability Distributions, Megha Pandey, Mrinal Kanti Roychowdhury

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we present the idea of conditional quantization for a Borel probability measure P on a normed space Rk. We introduce the concept of conditional quantization in both constrained and unconstrained scenarios, along with defining the conditional quantization errors, dimensions, and coefficients in each case. We then calculate these values for specific probability distributions. Additionally, we demonstrate that for a Borel probability measure, the lower and upper quantization dimensions and coefficients do not depend on the conditional set of the conditional quantization in both constrained and unconstrained quantization.

Flow And Stability Of Three-Dimensional Rotating Viscoelastic Jet, Daniel N. Riahi

School of Mathematical & Statistical Sciences Faculty Publications

We consider rotationally driven nonlinear viscoelastic jet. In contrast to previous unrealistic planar studies with no gravity effect, we investigate here realistic three-dimensional jet with gravity effect. Using theoretical and computational methods, we develop models for such jet and its stability and determine the solutions. We find three-dimensional jet with gravity effect leads to faster and thinner jet. For jet arc length higher than its exit diameter, our calculation with typical parameter values shows that jet radius is smaller by a factor of more than 1.4 and jet speed is higher by factor of more than 2 as are compared …

Assessing Concepts, Procedures, And Cognitive Demand Of Chatgpt-Generated Mathematical Tasks, Bima Sapkota, Liza Bondurant

School of Mathematical & Statistical Sciences Faculty Publications

In November 2022, ChatGPT, an Artificial Intelligence (AI) large language model (LLM) capable of generating human-like responses, was launched. ChatGPT has a variety of promising applications in education, such as using it as thought-partner in generating curricular resources. However, scholars also recognize that the use of ChatGPT raises concerns, such as outputs that are inaccurate, nonsensical, or vague. We, two mathematics teacher educators, engaged in a collaborative self-study using qualitative descriptive approaches to investigate the procedures, concepts, and cognitive demand of ChatGPT-generated mathematical tasks focused on fraction multiplication using the area model approach. We found that the ChatGPT-generated tasks were …

Exploring International Educators' Learning About Local And Global Social Justice In A Virtual Community Of Practice, Bima Sapkota, Xuwei Luo, Muna Sapkota, Murat Akarsu, Emmanuel Deogratias, Daphne Fauber, Rose Mbewe, Fidelis Mumba, Ram Krishna Panthi, Jill Newton

School of Mathematical & Statistical Sciences Faculty Publications

In this chapter, the authors report themes that emerged when a cross-cultural team of researchers involved in a virtual international community of practice (Global Social Justice in Education-GSJE) investigated reflections on activities focused on social justice in local and global contexts. The findings suggested that the activities elicited GSJE community members' understandings of the complexities of social justice associated with naming practices, privilege, and the arts within their own and across contexts. The authors discuss implications of the activities to advance diverse educators' understanding of social justice in global and local contexts. They also unpack the opportunities and challenges that …

Ivermectin, Colleen Aldous, Eleftherios Gkioulekas, Philip Oldfield

School of Mathematical & Statistical Sciences Faculty Publications

No abstract provided.

Brillouin Zones Of Integer Lattices And Their Perturbations, Herbert Edelsbrunner, Alexey Garber, Mohadese Ghafari, Teresa Heiss, Morteza Saghafian, Mathijs Wintraecken

School of Mathematical & Statistical Sciences Faculty Publications

For a locally finite set, 𝐴⊆ℝ𝑑 , the 𝑘 th Brillouin zone of 𝑎∈𝐴 is the region of points 𝑥∈ℝ𝑑 for which ‖𝑥−𝑎‖ is the 𝑘 th smallest among the Euclidean distances between 𝑥 and the points in 𝐴 . If 𝐴 is a lattice, the 𝑘 th Brillouin zones of the points in 𝐴 are translates of each other, and together they tile space. Depending on the value of 𝑘 , they express medium- or long-range order in the set. We study fundamental geometric and combinatorial properties of Brillouin zones, focusing on the integer lattice and its perturbations. Our …

Heuristics For Anti-Cyclotomic ℤp-Extensions, Debanjana Kundu, Lawrence C. Washington

School of Mathematical & Statistical Sciences Faculty Publications

This paper studies Iwasawa invariants in anti-cyclotomic towers. We do this by proposing two heuristics supported by computations. First we propose the Intersection Heuristics: these model “how often” the p-Hilbert class field of an imaginary quadratic field intersects the anti-cyclotomic tower and to what extent. Second we propose the Invariants Heuristics: these predict that the Iwasawa invariants 𝜆 and 𝜇 usually vanish for imaginary quadratic fields where p is non-split.

On The Center And The Antipode Of The Super-Yangian Of Q(1), Elena Poletaeva

School of Mathematical & Statistical Sciences Faculty Publications

For the queer Lie superalgebra Q(1), we explicitly describe the center of the super-Yangian Y Q(1) of Q(1) in terms of generators of Y Q(1). We also describe the square of the antipodal map on Y Q(1) and use the antipode to construct an involutive automorphism of Y Q(1).

Ultradeep Atca Imaging Of 47 Tucanae Reveals A Central Compact Radio Source, Alessandro Paduano, Arash Bahramian, James C. A. Miller-Jones, Adela Kawka, Tim J. Galvin, Liliana E. Rivera Sandoval, Sebastian Kamann, Jay Strader, Laura Chomiuk, Craig O. Heinke

Physics & Astronomy Faculty Publications

We present the results of an ultradeep radio continuum survey, containing ∼480 hr of observations, of the Galactic globular cluster 47 Tucanae with the Australia Telescope Compact Array. This comprehensive coverage of the cluster allows us to reach rms noise levels of 1.19 μJy beam−1 at 5.5 GHz, 940 nJy beam−1 at 9 GHz, and 790 nJy beam−1 in a stacked 7.25 GHz image. This is the deepest radio image of a globular cluster and the deepest image ever made with the Australia Telescope Compact Array. We identify ATCA J002405.702-720452.361, a faint (6.3 ± 1.2 μJy at 5.5 …

Advancements In Glitch Subtraction Systems For Enhancing Gravitational Wave Data Analysis: A Brief Review, Mohammad Abu Thaher Chowdhury

Physics & Astronomy Faculty Publications

Glitches are transitory noise artifacts that degrade the detection sensitivity and accuracy of interferometric observatories such as LIGO and Virgo in gravitational wave astronomy. Reliable glitch subtraction techniques are essential for separating genuine gravitational wave signals from background noise and improving the accuracy of astrophysical investigations. This review study summarizes the main glitch subtraction methods used in the industry. We talk about the efficacy of classic time-domain techniques in real-time applications, like matched filtering and regression methods. The robustness of frequency-domain approaches, such as wavelet transformations and spectral analysis, in detecting and mitigating non-stationary glitches is assessed. We also investigate …

Atomically Dispersed Zeolite-Supported Rhodium Complex: Selective And Stable Catalyst For Acetylene Semi-Hydrogenation, Yuxin Zhao, Özge D. Bozkurt, Samira F. Kurtoğlu-Öztulum, Melisa Su Yordanli, Adam S. Hoffman, Jiyun Hong, Jorge E. Perez-Aguilar, Aylin Saltuk, Deniz Akgül, Tülay Ateşin

School of Integrative Biological & Chemical Sciences (Formerly Dept. of Chemistry)

Highlights

• Rhodium has heretofore been known to be unselective for acetylene semi-hydrogenation.

• Electronic properties of rhodium are tuned by choice of support and metal nuclearity.

• Selectivity is maximized when Rh is atomically dispersed on a weak electron donor.

• Zeolite-supported Rh complex with C2H2 ligands offers a stable C2H4 selectivity > 90 %.

• Results demonstrate unprecedented catalytic properties of Rh for semi-hydrogenation.

Abstract

Supported rhodium catalysts are known to be unselective for semi-hydrogenation reactions. Here, by tuning the electronic structure of supported mononuclear rhodium sites determined by the metal nuclearity and the electron-donor properties of the support, we report that atomically dispersed …

Efficient Hierarchical Contrastive Self-Supervising Learning For Time Series Classification Via Importance-Aware Resolution Selection, Kevin Garcia, Juan M. Perez, Yifeng Gao

Computer Science Faculty Publications

Recently, there has been a significant advancement in designing Self-Supervised Learning (SSL) frameworks for time series data to reduce the dependency on data labels. Among these works, hierarchical contrastive learning-based SSL frameworks, which learn representations by contrasting data embeddings at multiple resolutions, have gained considerable attention. Due to their ability to gather more information, they exhibit better generalization in various downstream tasks. However, when the time series data length is significant long, the computational cost is often significantly higher than that of other SSL frameworks. In this paper, to address this challenge, we propose an efficient way to train hierarchical …

A Simple Proof That Ricochet Robots Is Pspace-Complete, Jose Balanza-Martinez, Angel A. Cantu, Robert Schweller, Tim Wylie

Computer Science Faculty Publications

In this paper, we seek to provide a simpler proof that the relocation problem in Ricochet Robots (Lunar Lockout with fixed geometry) is PSPACE-complete via a reduction from Finite Function Generation (FFG). Although this result was originally proven in 2003, we give a simpler reduction by utilizing the FFG problem, and put the result in context with recent publications showing that relocation is also PSPACE-complete in related models.

Efficient High-Resolution Time Series Classification Via Attention Kronecker Decomposition, Aosong Feng, Jialin Chen, Juan Garza, Brooklyn Berry, Francisco Salazar, Yifeng Gao, Rex Ying, Leandros Tassiulas

Computer Science Faculty Publications

The high-resolution time series classification problem is essential due to the increasing availability of detailed temporal data in various domains. To tackle this challenge effectively, it is imperative that the state-of-theart attention model is scalable to accommodate the growing sequence lengths typically encountered in highresolution time series data, while also demonstrating robustness in handling the inherent noise prevalent in such datasets. To address this, we propose to hierarchically encode the long time series into multiple levels based on the interaction ranges. By capturing relationships at different levels, we can build more robust, expressive, and efficient models that are capable of …

Self Pre-Training With Topology- And Spatiality-Aware Masked Autoencoders For 3d Medical Image Segmentation, Pengfei Gu, Yejia Zhang, Huimin Li, Chaoli Wang, Danny Z. Chen

Computer Science Faculty Publications

Masked Autoencoders (MAEs) have been shown to be effective in pre-training Vision Transformers (ViTs) for natural and medical image analysis problems. By reconstructing missing pixel/voxel information in visible patches, a ViT encoder can aggregate contextual information for downstream tasks. But, existing MAE pre-training methods, which were specifically developed with the ViT architecture, lack the ability to capture geometric shape and spatial information, which is critical for medical image segmentation tasks. In this paper, we propose a novel extension of known MAEs for self pre-training (i.e., models pre-trained on the same target dataset) for 3D medical image segmentation. (1) We propose …

Limit Distributions Of Products Of Independent And Identically Distributed Random 2 × 2 Stochastic Matrices: A Treatment With The Reciprocal Of The Golden Ratio, Santanu Chakraborty

School of Mathematical & Statistical Sciences Faculty Publications

Consider a sequence (Xn)n≥1 of i.i.d. 2×2 stochastic matrices with each Xn distributed as μ. This μ is described as follows. Let (Cn,Dn)T denote the first column of Xn and for a given real r with 012 is very challenging. Considering the extreme nontriviality of this case, we stick to a very special such r, namely, r=√5−12 (the reciprocal of the golden ratio), briefly mention the challenges in this nontrivial case, and completely identify λ for a very special situation.

Observed Impacts Of Large Wind Farms On Grassland Carbon Cycling, Donghai Wu, Steven M. Grodsky, Wenfang Xu, Naijing Liu, Rafael M. Almeida, Liming Zhou, Lee M. Miller, Somnath Baidya Roy, Geng Xia, Anurag A. Agrawal

School of Earth, Environmental, & Marine Sciences Faculty Publications

Download : Download high-res image (181KB)

Download : Download full-size image

The Tor Algebra Of Trimmings Of Gorenstein Ideals, Luigi Ferraro, Alexis Hardesty

School of Mathematical & Statistical Sciences Faculty Publications

Let (R,\mathfrak m,\Bbbk ) be a regular local ring of dimension 3. Let I be a Gorenstein ideal of R of grade 3. Buchsbaum and Eisenbud proved that there is a skew-symmetric matrix of odd size such that I is generated by the sub-maximal pfaffians of this matrix. Let J be the ideal obtained by multiplying some of the pfaffian generators of I by \mathfrak m; we say that J is a trimming of I. Building on a recent paper of Vandebogert, we construct an explicit free resolution of R/J and compute a partial DG algebra structure on this …

Gwtc-3: Compact Binary Coalescences Observed By Ligo And Virgo During The Second Part Of The Third Observing Run, R. Abbott, T. Abbott, F. Acernese, K. Ackley, Teviet Creighton, Mario C. Diaz, Soma Mukherjee, Volker Quetschke, Wenhui Wang, Francisco Llamas

Physics & Astronomy Faculty Publications

The third Gravitational-Wave Transient Catalog (GWTC-3) describes signals detected with Advanced LIGO and Advanced Virgo up to the end of their third observing run. Updating the previous GWTC-2.1, we present candidate gravitational waves from compact binary coalescences during the second half of the third observing run (O3b) between 1 November 2019, 15 ∶ 00 Coordinated Universal Time (UTC) and 27 March 2020, 17 ∶ 00 UTC. There are 35 compact binary coalescence candidates identified by at least one of our search algorithms with a probability of astrophysical origin p astro > 0.5 . Of these, 18 were previously reported as low-latency …

Gwtc-3: Compact Binary Coalescences Observed By Ligo And Virgo During The Second Part Of The Third Observing Run, R. Abbott, T. D. Abbott, F. Acernese, K. Ackley, Teviet Creighton, Mario C. Diaz, F. Llamas, Soma Mukherjee, Volker Quetschke, Wenhui Wang

Physics & Astronomy Faculty Publications

The third Gravitational-Wave Transient Catalog (GWTC-3) describes signals detected with Advanced LIGO and Advanced Virgo up to the end of their third observing run. Updating the previous GWTC-2.1, we present candidate gravitational waves from compact binary coalescences during the second half of the third observing run (O3b) between 1 November 2019, 15∶00 Coordinated Universal Time (UTC) and 27 March 2020, 17∶00 UTC. There are 35 compact binary coalescence candidates identified by at least one of our search algorithms with a probability of astrophysical origin ��astro>0.5. Of these, 18 were previously reported as low-latency public alerts, and 17 are reported …

Activity Patterns Of The Endangered Amargosa Vole (Microtus Californicus Scripensis), Austin N. Roy, Anna D. Rivera Roy, Deana L. Clifford, Janet E. Foley

School of Earth, Environmental, & Marine Sciences Faculty Publications

Examining the activity patterns of wildlife is an important aspect of understanding the ecology of a species and may be especially important for species of conservation concern. We used remotely triggered cameras to describe the daily and seasonal activity patterns and examine ecological factors that influence the activity of the Amargosa Vole (Microtus californicus scirpensis), a California endemic listed federally and by the state as Endangered, and is a marsh habitatspecialist in the Mojave Desert. We found that vole activity was greatest during crepuscular periods, followed by nocturnal and diurnal periods. We saw strong seasonal effects, with the highest activity …

Effects Of Elevated Temperature On 8-Ohdg Expression In The American Oyster (Crassostrea Virginica): Induction Of Oxidative Stress Biomarkers, Cellular Apoptosis, Dna Damage And Γh2ax Signaling Pathways, Md Faizur Rahman, Mohammad Maruf Billah, Richard Kline, Md Saydur Rahman

School of Earth, Environmental, & Marine Sciences Faculty Publications

Global temperature is increasing due to anthropogenic activities and the effects of elevated temperature on DNA lesions are not well documented in marine organisms. The American oyster (Crassostrea virginica, an edible and commercially important marine mollusk) is an ideal shellfish species to study oxidative DNA lesions during heat stress. In this study, we examined the effects of elevated temperatures (24, 28, and 32 °C for one-week exposure) on heat shock protein-70 (HSP70, a biomarker of heat stress), 8-hydroxy-2’-deoxyguanosine (8-OHdG, a biomarker of pro-mutagenic DNA lesion), double-stranded DNA (dsDNA), γ-histone family member X (γH2AX, a molecular biomarker of DNA damage), …