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Biomass Budget And Energy Flow In Alluvial Meadow Ecosystem, Milena Rychnovska, Blanka Ulehlova, Jana Jakrlova, Marta Tesrova Jul 2026

Biomass Budget And Energy Flow In Alluvial Meadow Ecosystem, Milena Rychnovska, Blanka Ulehlova, Jana Jakrlova, Marta Tesrova

IGC Proceedings (1977-2023)

Primary production, production processes, and decomposition have been studied in alluvial meadow ecosystems for 6 years. Water has been found to be the decisive factor in the energy flow and mineral elements turnover. The quality and quantity of production and decomposition processes depend on the oc­currence and duration o( floods. Permanent pool of underground biomass in Alopecurus pratensis stand makes 45.3 %, permanent pool of shoot biomass makes 54.7 % of the total biomass. 19.4 % of the total biomass is taken off as forage. 11. 7 % of shoot biomass is de­composed during the summer season, and 3 .1 …


Current Aspects Of Eco-Physiological Studies Of Meadow Plants, Momcilo Konic Jul 2026

Current Aspects Of Eco-Physiological Studies Of Meadow Plants, Momcilo Konic

IGC Proceedings (1977-2023)

Basic parameters applied in eco-physiological studies of meadow plants are: water balance (hydration, transpiration intensity, amounts and forms of water, water deficit, etc.), assim­ilation balance (CO2 balance, assimilation performance, compensation effect), matter pro­duction. Eco-physiological studies should be followed by microclimatic measurements and the anatomical analysis of the meadow plants under study. Eco-physiological studies of meadow plants, if performed in a complex and systematic way, constitute the safest basis for detennining the characters of the entire meadow plant com­munity under the concrete conditions of natural factors prevailing in terms of natural condi­tions and human influence.


Landscape Management Problems Of Grassland Utilization In Mountainous Regions Of The Gdr, Peter Hentschel Jul 2026

Landscape Management Problems Of Grassland Utilization In Mountainous Regions Of The Gdr, Peter Hentschel

IGC Proceedings (1977-2023)

In the medium-altitude mountains of the GDR, many meadows cannot be utilized for intensive forage production. Because of their importance for recreation, game feeding and nature con­servation, general afforestation is not possible. A model is presented that allows for every meadow to choose between intensive utili­zation, afforestation, and reservation for other social needs. Management methods for mead­ows not suitable for intensive utilization, espe­cially the employment of herbicides, are dis­cussed.


On Universal C∗ Algebras Associated To Operator Spaces And Generalized Crossed Products, Sayan Kansa Banik Jul 2026

On Universal C∗ Algebras Associated To Operator Spaces And Generalized Crossed Products, Sayan Kansa Banik

Doctoral Theses

In my thesis, we study generalized crossed product constructions of the group \( C^* \)-algebra \( C^*(G) \) with respect to certain completely positive maps, where \( G \) is assumed to be a discrete amenable group. We also investigate the universal \( C^* \)-algebra \( \mathcal{E}_\alpha \) introduced by Hirshberg, which is constructed from \( C^*(G) \) and a pure injective homomorphism \( \alpha \colon G \to G \). In particular, we analyze its relationship with Exel's construction of generalized crossed products associated with the endomorphism of \( C^*(G) \) induced by \( \alpha \), together with an appropriate …


Oregon State Rank Assessment For Oregon Daisy (Erigeron Oreganus), Nora Dunkirk, Sue Vrilakas Jul 2026

Oregon State Rank Assessment For Oregon Daisy (Erigeron Oreganus), Nora Dunkirk, Sue Vrilakas

Institute for Natural Resources Publications

Oregon state conservation status assessment for Oregon Daisy (Erigeron oreganus) using NatureServe methodology, 2026.


Oregon State Rank Assessment For Bensonia (Bensoniella Oregana), Nora Dunkirk, Sue Vrilakas, Gabriel Campbell Jul 2026

Oregon State Rank Assessment For Bensonia (Bensoniella Oregana), Nora Dunkirk, Sue Vrilakas, Gabriel Campbell

Institute for Natural Resources Publications

Oregon state conservation status assessment for Bensonia (Bensoniella oregana) using NatureServe methodology, 2026.


The Sigma Ring And Other Distinctive Features Of Surface Potentials Of Group 1 Systems, Kelling J. Donald, Victoria Rankin, Brice Di Carlo, Jonathan E. Findley, Ethan B. Leonard Jul 2026

The Sigma Ring And Other Distinctive Features Of Surface Potentials Of Group 1 Systems, Kelling J. Donald, Victoria Rankin, Brice Di Carlo, Jonathan E. Findley, Ethan B. Leonard

Chemistry Faculty Publications

For a sigma hole induced on a terminal atom, such as a halogen atom (X) in a molecule R-X, it is commonly expected that the maximum potential in that sigma hole will arise along the extension of the R-X bond, opposite the overlap region. We find, however, that for the majority of group 1 halides (MX) that expectation fails. Conventional sigma holes appear on Na in its halides and hydrides, but not so for M = K, Rb, or Cs. Instead, a sigma ring─a latitudinal ring maximum─is observed in the surface potentials of those molecules. That anomaly is examined, and …


Detecting And Correcting Systematic Image Distortion In Digital Atomic-Resolution Images From Crystals: Projected Symmetry Of Graphite Calibration Samples For Scanning Prove Microscopy And Subperiodic Crystals For Aberration-Corrected Transmission Electron Microscopy, Tyler Michael Bortel Jul 2026

Detecting And Correcting Systematic Image Distortion In Digital Atomic-Resolution Images From Crystals: Projected Symmetry Of Graphite Calibration Samples For Scanning Prove Microscopy And Subperiodic Crystals For Aberration-Corrected Transmission Electron Microscopy, Tyler Michael Bortel

Dissertations and Theses

Though it is an impressive technology, Scanning Tunneling Microscopy (STM) produces images commonly plagued by small systematic errors, often called "drift". These effects have a variety of causes, most notably nonlinear behavior of piezoelectric actuator tubes responsible for the positioning of the scanning probe or sample. One result of these distortions is a potential incorrect classification of the symmetry groups and projected Laue classes of recorded images from crystals—made possible by using recently developed objective methods. An implementation of a known method for detecting and correcting these errors is presented. This method operates strictly in Fourier space so as to …


Religious Bias In Llms Is Significantly Understudied, Sheryl Carty, Nancy Fulda, Walter Reade Jul 2026

Religious Bias In Llms Is Significantly Understudied, Sheryl Carty, Nancy Fulda, Walter Reade

Faculty Publications

In the earlier years of development of LLMs, it was relatively easy to prompt an LLM to respond with toxic or biased statements about religion. Subsequent improvements in frontier models addressed many of the issues of bias and toxicity in general, including against religion. At the same time, the adoption and usage of these models has grown exponentially. Small and implicit biases, therefore, have a magnified overall impact. In this paper, we (1) briefly review previous efforts to measure religious bias in LLMs, (2) show, by reviewing over 12,000 papers dealing with bias in LLMs, that religious bias has been …


Security Architecture Decision Framework For Endpoint Protection In Resource-Constrained K-12 Environments, Jason Folker Jul 2026

Security Architecture Decision Framework For Endpoint Protection In Resource-Constrained K-12 Environments, Jason Folker

Journal of Cybersecurity Education, Research and Practice

K-12 educational institutions face an ongoing challenge in protecting endpoints when budgets and staffing prevent the implementation of standard security best practices. Technology directors routinely make difficult decisions about administrative rights, software controls, and security tooling, but they lack frameworks designed for the constraints and priorities specific to educational environments. This paper develops a security architecture decision framework tailored for K-12 endpoint protection. The framework integrates five weighting dimensions to help technology directors evaluate competing architectural choices. These dimensions include educational impact, security risk reduction, resource requirements, compliance obligations, and operational feasibility. The framework creates structured documentation that helps decision-makers …


Pseudodifferential Absorbing Boundary Conditions For Waves, Lauren Taylor Jul 2026

Pseudodifferential Absorbing Boundary Conditions For Waves, Lauren Taylor

Mechanical Engineering Theses

Absorbing boundary conditions (ABCs) are required to truncate the computational domain when performing Finite Element Analyses of exterior acoustic problems where physical domain is unbounded. ABC is applied on a fictitious boundary containing the scatterer and ideally allows outgoing waves to leave without non-physical reflections. Preventing artificial reflections is essential to benefit from the accuracy of the numerical method used. Otherwise, ABC acts as a reflective surface, and artificial reflections distort the solution in the entire domain which is not recoverable by any type of refinement. Pseudodifferential ABCs were used to describe the Dirichlet-to-Neumann map which maps known boundary values …


Narrowband Searches For Continuous Gravitational Waves From Known Pulsars In The First Two Parts Of The Fourth Ligo–Virgo–Kagra Observing Run, The Ligo Scientific Collaboration, The Virgo Collaboration, The Kagra Collaboration, Marc Favata, Shoan Ghosh, Rodica M. Martin Jul 2026

Narrowband Searches For Continuous Gravitational Waves From Known Pulsars In The First Two Parts Of The Fourth Ligo–Virgo–Kagra Observing Run, The Ligo Scientific Collaboration, The Virgo Collaboration, The Kagra Collaboration, Marc Favata, Shoan Ghosh, Rodica M. Martin

Department of Physics and Astronomy Faculty Scholarship and Creative Works

Rotating nonaxisymmetric neutron stars (NSs) are promising sources for continuous gravitational waves (CWs). CWs may, if detected, inform us about the internal structure and equation of state of NSs. Here, we present a narrowband search for CWs from known pulsars, for which a matched-filter search can be applied. Narrowband searches are robust to mismatches between electromagnetic (EM) and gravitational emissions, in contrast to fully targeted searches where they are assumed to be phase-locked. In this work, we search for the CW counterparts emitted by 34 pulsars using data from the first and second parts of the fourth LIGO–Virgo–KAGRA observing run. …


Coherent Two-Photon Backscattering And Induced Angular Quantum Correlations In Multiple-Scattered Two-Photon States Of The Light, Nooshin M. Estakhri, Theodore B. Norris Jul 2026

Coherent Two-Photon Backscattering And Induced Angular Quantum Correlations In Multiple-Scattered Two-Photon States Of The Light, Nooshin M. Estakhri, Theodore B. Norris

Engineering Faculty Articles and Research

We present the emergence of coherent two-photon backscattering, a manifestation of weak localization, in multiple scattering of maximally entangled pure and fully mixed two-photon states and examine the effect of entanglement and classical correlations. Quantum correlations in backscattering are investigated for finite three-dimensional disordered structures in the weak localization regime, as well as systems of a small number of scatterers with specified spatial arrangements. No assumptions are made about the statistical behavior of the scattering matrix elements. Furthermore, we study the interplay between quantum correlations induced by multiple scattering and the correlations that may be present in the illumination fields, …


The Exergy Of Materials With Application To Socio-Economic Metabolisms And Industrial Ecology, Matthew Kuperus Heun, Erin Schuman, Sofie Schumerth, Tânia Sousa Jul 2026

The Exergy Of Materials With Application To Socio-Economic Metabolisms And Industrial Ecology, Matthew Kuperus Heun, Erin Schuman, Sofie Schumerth, Tânia Sousa

University Faculty Publications and Creative Works

2026 International Society for Industrial Ecology Socio-Economic Metabolism (ISIE-SEM) Conference Cabridge University, Cambridge, England


Open Neighbourhood Edge Degree And Metric Descriptors Qspr And Multi Criteria Analysis Of Chemicals And Antiviral Drugs, Gayathri A Ms Jul 2026

Open Neighbourhood Edge Degree And Metric Descriptors Qspr And Multi Criteria Analysis Of Chemicals And Antiviral Drugs, Gayathri A Ms

Theses and Dissertations

Chemical Graph theory offers powerful computational methods for evaluating chemical structures, significantly impacting cheminformatics and drug analysis. It provides a robust mathematical framework to represent, model, and analyse molecular systems through topological indices and graph invariants. These indices serve as effective numerical descriptors, encapsulating significant structural information that enhances the prediction of physicochemical and biological properties. This thesis utilizes mathematical modeling, algorithmic computation, and decision making process to derive extensive insights to drug discovery and molecular analysis.

The thesis introduces a new class of topological indices ONE1, ONE2, ONE3, ONE4, ONE5,ONE6 and ONE7 based on open-neighbourhood-edge-degree and it evaluates the …


Ecorxchoice.Com— An Sidp-Funded Calculator Integrating Environmental Metrics With Antimicrobial Stewardship, Pamela S. Lee, Hugh Gordon, Theresa Ferguson, Tien Dinh, Misty Vu, Marina Nguyen, Chaynor Hsiao, Gary Fong Jul 2026

Ecorxchoice.Com— An Sidp-Funded Calculator Integrating Environmental Metrics With Antimicrobial Stewardship, Pamela S. Lee, Hugh Gordon, Theresa Ferguson, Tien Dinh, Misty Vu, Marina Nguyen, Chaynor Hsiao, Gary Fong

Pharmacy Faculty Articles and Research

Healthcare sustainability is a multidisciplinary field that seeks to mitigate healthcare’s environmental consequences. Antimicrobial stewardship and healthcare sustainability both aim to reduce wasteful resource use while maximizing patient safety. However, a strong partnership between antimicrobial stewardship and healthcare sustainability has yet to develop. To facilitate environmentally sustainable decision-making in antimicrobial prescribing, we developed a web-based calculator (EcoRxChoice (www.ecorxchoice.com)) where users can enter different antimicrobial regimens and compare how much plastic waste each regimen creates. This work was supported in part by the Society of Infectious Diseases Pharmacists (SIDP), reflecting SIDP’s commitment to strengthening sustainability as a practical extension of antimicrobial …


Cooperative Evolution For Discovering Scalable Spiking Neural Network Architectures, Catherine C. Rodriquez Jul 2026

Cooperative Evolution For Discovering Scalable Spiking Neural Network Architectures, Catherine C. Rodriquez

LSU Master's Theses

SNNs are a foundational model in neuromorphic computing, where efficient architectures must be discovered for a wide range of applications. Evolutionary methods, such as EONS, offer a flexible approach to this search but become increasingly difficult to scale as task complexity grows due to the rapidly expanding combined topology–parameter search space and associated memory demands. To address this challenge, we propose a co-evolutionary ensemble framework in which a population of candidate SNNs is evolved with fitness defined by each network’s marginal contribution to group performance. Grounded in cooperative game theory and difference evaluation functions from multiagent systems, this formulation provides …


Mental Health Self-Perceptions And Resource Utilization In Undergraduate Students At Binghamton University, Nicole J. Dreznin, Sarah Marcus Jul 2026

Mental Health Self-Perceptions And Resource Utilization In Undergraduate Students At Binghamton University, Nicole J. Dreznin, Sarah Marcus

Binghamton University Undergraduate Journal

Undergraduate students face increasing rates of mental health challenges, however discrepancies in mental health literacy and utilization of resources may exist across student populations. This study examined the perceptions of mental health in undergraduate students at Binghamton University and if they differed among STEM vs non-STEM, man vs. women, and first-generation vs. continuing generation undergraduate students. A 20-question survey, containing 5 demographic questions and 15 mental health related questions was distributed through Qualtrics to 9 undergraduate classes. The available response choices were based on the Likert scale. A total of 1266 students participated.  Chi square tests of independence were done …


Analytic Solutions To Oceanographic Kinematic Property Equations, James Turbett Jul 2026

Analytic Solutions To Oceanographic Kinematic Property Equations, James Turbett

Theses and Dissertations

With the recent advent of large submesoscale drifter deployments, interpreting the timeseries of kinematic properties (KP) - divergence, vorticity, shear, and normal strain rates observed therein is a pressing issue. The evolution equations for the four KP are derived from the two-dimensional momentum conservation equations. The resulting equations, a nonlinear coupled system of ordinary differential equations, capture the submesoscale motion of drifters along fixed ocean surfaces, with time and space scales on the order of days and kilometers. This thesis builds theory around KP timeseries behavior by solving for the analytic solutions in the particular cases that one KP is …


Dynlp: Parallel Dynamic Batch Update For Label Propagation In Graph-Based Semi-Supervised Learning, S. M. Shovan, Arindam Khanda, S. M. Ferdous, Sajal K. Das, Mahantesh Halappanavar Jul 2026

Dynlp: Parallel Dynamic Batch Update For Label Propagation In Graph-Based Semi-Supervised Learning, S. M. Shovan, Arindam Khanda, S. M. Ferdous, Sajal K. Das, Mahantesh Halappanavar

Computer Science Faculty Research & Creative Works

Semi-supervised learning aims to infer class labels using only a small fraction of labeled data. In graph-based semi-supervised learning, this is typically achieved through label propagation to predict labels of unlabeled nodes. However, in real-world applications, new data often arrives in batches, and stale data often becomes irrelevant. Each time a new batch appears, reapplying the traditional label propagation algorithm to recompute all labels is redundant, computationally intensive, and inefficient. To address the absence of an efficient label propagation update method, we propose DynLP, a novel GPU-centric Dynamic Batched Parallel Label Propagation algorithm that performs only the necessary updates, propagating …


Real-Time Image Denoising And Reconstruction Using Generative Adversarial Networks (Gans), Roa'a M. Al-Airaji, Haider Th. Salim Alrikabi, Rula Kamil, Svyd Iryna Jul 2026

Real-Time Image Denoising And Reconstruction Using Generative Adversarial Networks (Gans), Roa'a M. Al-Airaji, Haider Th. Salim Alrikabi, Rula Kamil, Svyd Iryna

Karbala International Journal of Modern Science

This paper presents a real-time image denoising and reconstruction system based on a compact Generative Adversarial Network (GAN) designed for embedded systems and edge computing. The proposed model employs a [ generator and a PatchGAN discriminator, trained using hybrid loss function that combines L1, perceptual, and adversarial terms to balance pixel and perceptual realism. Evaluations were conducted on multiple datasets, including DIV2K, BSD68, SIDD, DND, RENOIR, and PolyU at noise levels (σ = 15, 25, 50). Quantitatively, the proposed model achieves an average PSNR of 32.8 dB and an SSIM of 0.88, which is higher by more than 3 dB …


Synergistic Effects Of Arbuscular Mycorrhizal Fungi And Foliar Nitrogen–Phosphorus Application On Maize Productivity Under Irrigated And Rainfed Conditions, Mst. Lailatul Ferdows, Saima Biswas, Mizanur Rahman, F. M.Jamil Uddin, Md. Nayan, Aporna Tabassum Api, Mohaiminul Islam, Nadia Islam, Swapan Kumar Paul, Md. Harun Rashid Jul 2026

Synergistic Effects Of Arbuscular Mycorrhizal Fungi And Foliar Nitrogen–Phosphorus Application On Maize Productivity Under Irrigated And Rainfed Conditions, Mst. Lailatul Ferdows, Saima Biswas, Mizanur Rahman, F. M.Jamil Uddin, Md. Nayan, Aporna Tabassum Api, Mohaiminul Islam, Nadia Islam, Swapan Kumar Paul, Md. Harun Rashid

School of Earth, Environmental, & Marine Sciences Faculty Publications

A field experiment was conducted at the Agronomy Field Laboratory of Bangladesh Agricultural University to evaluate the effects of arbuscular mycorrhizal fungi (AMF) inoculation and foliar supplementation of nitrogen (N) and phosphorus (P) on the performance of maize (Zea mays L.) under irrigated and rainfed conditions. The experiment followed a randomised complete block design with two levels of AMF (inoculated and non-inoculated) and four foliar treatments (no N and P, N only, P only, and combined N + P). The recommended dose of fertiliser (RDF) was applied as a soil application to all treatments. AMF inoculation significantly increased grain yield …


Mapping And Diagnosing Local Climate Zones For Urban Heat Assessment And Planning In Tropical Cities, Inuwa Sani Sani, Adi Wibowo Jul 2026

Mapping And Diagnosing Local Climate Zones For Urban Heat Assessment And Planning In Tropical Cities, Inuwa Sani Sani, Adi Wibowo

Journal of Environmental Science and Sustainable Development

Rapid urbanization and rising heat risk are intensifying thermal stress and environmental degradation in tropical cities. This study applies the Local Climate Zone (LCZ) framework to examine how urban morphology influences land surface temperature (LST) and to support evidence-based urban planning and climate adaptation in Makassar, Indonesia. We hypothesized that compact built LCZs (1–3) exhibit significantly higher LST than vegetated LCZs (A–G). Landsat 8 OLI and MODIS LST datasets (2013–2023) were processed in Google Earth Engine to evaluate decade-long urban development and thermal dynamics. LCZs were classified using a Random Forest (RF) model trained with approximately 100 manually digitized polygons …


Coupled-Pendulum Modeling In An Ode Class: An Assignment On Fourier-Initialized Gradient Descent In Machine Learning, Huy Truong, Andrew Bennett Jul 2026

Coupled-Pendulum Modeling In An Ode Class: An Assignment On Fourier-Initialized Gradient Descent In Machine Learning, Huy Truong, Andrew Bennett

CODEE Journal

As data-driven methods are increasingly used in science and engineering, students benefit from learning to integrate machine learning techniques with traditional mathematical modeling. We present a hands-on extra-credit assignment for an undergraduate ordinary differential equations (ODE) course that enables students to compare classical analytical methods with data-driven approaches on the same physical system. Using a coupled-pendulum system---two pendulums connected by a spring---with real experimental data acquired via video tracking of a real physical setup, students work through three models in a guided Jupyter notebook with all code provided. First, they fit a neural network with Fourier features as a purely …


Development And Evaluation Of A Community-Based Water Quality Monitoring Program In Mississippi, Beth H. Baker, Lily Langstaff, Mona Dominguez, Sergio Ruiz-Cordova, Eric Sparks, Madison Gnoose Jul 2026

Development And Evaluation Of A Community-Based Water Quality Monitoring Program In Mississippi, Beth H. Baker, Lily Langstaff, Mona Dominguez, Sergio Ruiz-Cordova, Eric Sparks, Madison Gnoose

Journal of Extension

Community-based water monitoring (CBWM) programs provide mechanisms for education and water quality data collection. In this pilot program, we adapted a long-standing CBWM program from Alabama to Mississippi. We assessed the efficacy of the initial program implementation in promoting changes in knowledge, skills, and behavior of participants. Results indicated that 94% of survey respondents reported increased knowledge, 96% reported learning a new skill, and 99% reported an intention to start monitoring, but only 33% engaged in active monitoring. This evaluation summary offers data-driven strategies to expand and adopt CBWM into Extension curricula that build knowledge, skills, and capacity for community …


Energy Efficiency Limits And Future Electricity Demand Of Computing Devices, Ricardo Pinto, Tiago Domingos, Paul E. Brockway, Matthew Kuperus Heun, Tânia Sousa Jul 2026

Energy Efficiency Limits And Future Electricity Demand Of Computing Devices, Ricardo Pinto, Tiago Domingos, Paul E. Brockway, Matthew Kuperus Heun, Tânia Sousa

University Faculty Publications and Creative Works

  • ICT (information and communication technologies) represented 4% of the world electricity consumption in 2020; 
  • Computing devices represented 2% of the world electricity consumption in 2020; 
  • In recent scenarios datacentre electricity demand reaches 3% of world electricity in 2030, and more than 4% in 2035


Toward Intelligent Machines: Conscious Learning And Hardware-Accelerated Ai, Pavia Bera Jul 2026

Toward Intelligent Machines: Conscious Learning And Hardware-Accelerated Ai, Pavia Bera

USF Tampa Graduate Theses and Dissertations

Artificial intelligence systems excel at narrow, well-defined tasks but remain brittle at theboundaries of their training distributions: they cannot quantify uncertainty, adapt continuously to non-stationary data, or operate efficiently on energy-constrained hardware. This dissertation addresses these limitations through four coordinated contributions spanning probabilistic learning algorithms, biologically inspired temporal memory, cross-entity warning propagation via distributed associative memory, and spintronic processing-in-memory.

The first contribution introduces Boosted Bayesian Neural Networks (BBNNs), which extend standard mean-field variational inference by iteratively constructing a mixture posterior through Boosting Variational Inference. On five clinical medical classification datasets, BBNNs achieve superior uncertainty calibration—lower Negative Log-Likelihood and Expected Calibration …


Heterogeneous Graph-Augmented Contrastive Learning For Extreme Multi-Class Fiqh Classification, Ali A. Jalil Jul 2026

Heterogeneous Graph-Augmented Contrastive Learning For Extreme Multi-Class Fiqh Classification, Ali A. Jalil

Al-Bahir

  • Background/Introduction: Fine-grained text classification in the field of Islamic Jurisprudence (Fiqh) is difficult because of the structural interdependence of the legal concepts and the extremely multi-class long-tail data distribution (667 classes with 5,979 samples, 52.2% of which contain less than 5 samples). The main problem with traditional flat classifiers is that they assume that target classes are independent and orthogonal output neurons which discards very important relational semantics.
  • Objectives: This paper seeks to remediate this extreme imbalance and maintain structural taxonomy by modeling the structural space of classification label space itself as an object to be learned, while giving a …


Differential Topology And The Poincaré-Hopf Theorem, Tara Saini Jul 2026

Differential Topology And The Poincaré-Hopf Theorem, Tara Saini

Rose-Hulman Undergraduate Mathematics Journal

In this paper, we will develop the ideas needed to understand and prove the Poincaré–Hopf Theorem, which connects the local behavior of smooth vector fields to global topological properties. We will begin by introducing smooth manifolds and smooth maps, which are the basis of differential topology. We will then define derivatives of smooth maps through tangent spaces and use these to classify points. To build toward the theorem, we will introduce orientation, degree, and smooth vector fields. These concepts will culminate in a proof of the Poincaré–Hopf Theorem, aided by Brouwer’s Fixed Point Theorem. Finally, we will apply the result …


A Closed Form For The Pulsar Sequence, Ryan Z. Liu Jul 2026

A Closed Form For The Pulsar Sequence, Ryan Z. Liu

Rose-Hulman Undergraduate Mathematics Journal

In this paper, we study the Pulsar Sequence, an integer sequence derived from Latin-square-based “Pulsar puzzles” introduced by the Cracking the Cryptic YouTube channel. A Pulsar puzzle consists of two interlocked spirals of circled and uncircled squares, generating the Dual and Pulsar sequences, respectively. We investigate the properties of the Pulsar puzzle and focus our work on constructing the Pulsar Sequence, allowing us to solve a Pulsar puzzle of any size. A general formula to calculate any term of the Pulsar Sequence is proposed at the end of the paper.