Digital Commons Network^™

Math 111: Introduction To Statistics And Probability, Yu Wang

Open Educational Resources

Introduce the different linear statistical models and develop critical thinking for statistical modeling in scientific and policy contexts; Apply statistical computer software tools to develop useful data analysis skills based on the use of linear regression models. Topics to be covered: simple linear regression, multiple regression, nonlinear regression and logistic regression models; Random and mixed effects models; The application of statistical software tools.

Cooperative Target Tracking In Concentric Formations, Lili Ma

Publications and Research

This paper considers the problem of coordinating multiple unmanned aerial vehicles (UAVs) in a circular formation around a moving target. The main contribution is allowing for versatile formation patterns on the basis of the following components. Firstly, new uniform spacing control laws are proposed that spread the agents not necessarily over a full circle, but over a circular arc. Uniform spacing formation controllers are proposed, regulating either the separation distances or the separation angles between agents. Secondly, the use of virtual agents is proposed to allow for different radii in agents’ orbits. Thirdly, a hierarchical combination of formation patterns is …

Three Imprimitive Character Sums, Brad Isaacson

Publications and Research

We express three imprimitive character sums in terms of generalized Bernoulli numbers. These sums are generalizations of sums introduced and studied by Arakawa, Berndt, Ibukiyama, Kaneko and Ramanujan in the context of modular forms and theta function identities. As a corollary, we obtain a formula for cotangent power sums considered by Apostol.

Elementary College Geometry (2021 Ed.), Henry Africk

Open Educational Resources

This text is intended for a brief introductory course in plane geometry. It covers the topics from elementary geometry that are most likely to be required for more advanced mathematics courses. The only prerequisite is a semester of algebra. The emphasis is on applying basic geometric principles to the numerical solution of problems. For this purpose the number of theorems and definitions is kept small. Proofs are short and intuitive, mostly in the style of those found in a typical trigonometry or precalculus text. There is little attempt to teach theorem proving or formal methods of reasoning. However the topics …

Public Interest Technology – Exploring Covid-19 Health Data, Sarah Zelikovitz

Open Educational Resources

This module is part of a Introduction to Data Science course that covers the different parts of the data science process: data acquisition, cleaning, exploratory data analysis, and modeling. The COVID-19 pandemic has created much interest in public health data, as well as interest in visualization of all types of data. Public health data has a set of challenges that is unique to health data, with HIPAA laws, and real time collection of data. With COVID-19, the challenges are particularly amplified, as data collection and statistics collected are constantly changing in response to feedback from labs, hospitals, drug companies, and …

Developmental Psychology Syllabus, Rodina Sadek

Open Educational Resources

No abstract provided.

All We Need Is One Mic: A Call For Anti-Racist Solidarity To Deconstruct Anti-Black Racism In Educational Leadership, Soribel Genao, Yaribel Mercedes

Publications and Research

In this article, we outline some of the vital measurements of racism and anti-blackness as a macro system in education. We contend that principal preparation programs have not explicitly prioritized anti-racist school leadership, while often resisting the possibilities of solidarity or one mic of knowledge to increase anti-racist dispositions. Considering the lexicon of whiteness as an assemblage, a racial discourse should be “supported by material practices and institutions,” that prepare educational leaders to examine anti-blackness curriculum that have been embedded as a standard method. We also posit that theoretical understanding of racism as global whiteness from a post-oppositional lens and …

Dynamics Of Transmission In Disordered Topological Insulators, Yuhao Kang, Yiming Huang, Azriel Genack

Publications and Research

Robust transmission in topological insulators makes it possible to steer waves without attenuation along bent paths within imperfectly fabricated photonic devices. But the absence of reflection does not guarantee the fidelity of pulsed transmission which is essential for core photonic functionalities. Pulse transmission is disrupted by localized modes in the bulk of topological insulators which coexist with the continuum edge mode and are pushed deeper into the band gap with increasing disorder. Here we show in simulations of the Haldane model that pulse propagation in disordered topological insulators is robust throughout the central portion of the band gap where localized …

Protocol For Safe, Affordable, And Reproducible 1 Isolation And Quantitation 2 Of Sars-Cov-2 Rna From Wastewater, Monica Trujillo, Kristen Cheung, Anna Gao, Irene Hoxie, Sherin Kannoly, Nanami Kubota, Kaung Myat San, Davida S. Smyth, John J. Dennehy

Publications and Research

The following protocol describes our workflow for processing wastewater with the goal of detecting the genetic signal of SARS-CoV-2. The steps include pasteurization, virus concentration, RNA extraction, and quantification by RT-qPCR. We include auxiliary steps that provide new users with tools and strategies that will help troubleshoot key steps in the process. This protocol is one of the safest, cheapest, and most reproducible approaches for the detection of SARS-CoV-2 RNA in wastewater. Furthermore, the RNA obtained using this protocol, minus the pasteurization step, can be sequenced both using a targeted approach sequencing specific regions or the whole genome. The protocol …

Computable Procedures For Fields, Russell Miller

Publications and Research

This tutorial will introduce listeners to many questions that can be asked about computable processes on fields, and will present the answers that are known, sometimes with proofs. This is not original work. The questions in greatest focus here include decision procedures for the existence of roots of polynomials in specific fields, for the irreducibility of polynomials over those fields, and for transcendence of specific elements over the prime subfield. Several of these questions are related to the construction of algebraic closures, making Rabin's Theorem prominent.

Toward Transformable Photonics: Reversible Deforming Soft Cavities, Controlling Their Resonance Split And Directional Emission, Mark Douvidzon, Shai Maayani, Harel Nagar, Tamir Admon, Vladimir Shuvayev, Lan Yang, Lev Deych, Yael Roichman, Tal Carmon

Publications and Research

We report on reversible and continuously deformable soft micro-resonators and the control of their resonance split and directional emission. Assisted by computerized holographic-tweezers, functioning as an optical deformer of our device, we gradually deform the shape and change the functionality of a droplet whispering-gallery cavity. For example, we continuously deform hexagonal cavities to rectangular ones and demonstrate switching to directionally emitting mode-of-operation, or splitting a resonant mode to a 10-GHz separated doublet. A continuous trend of improving spatial light modulators and tweezers suggests that our method is scalable and can control the shape and functionality of many individual devices. We …

Creating A Culturally Relevant Statistics Assignment On Z-Scores, Grace Pai

Publications and Research

Culturally relevant teaching or pedagogy has become increasingly popular both in practice and in research, but there are still few curricular resources for instructors to use, particularly for a college-level mathematics course. Departing from the question “relevant to whom,” this article illustrates how to design a statistics assignment on z-scores that is culturally relevant to students based on their prior experiences. Ultimately, the author shares design principles—which includes the importance of considering student trauma—that can be transferable to any statistics or quantitative analysis/reasoning class.

Dimers, Orientifolds And Stability Of Supersymmetry Breaking Vacua, Riccardo Argurio, Matteo Bertolini, Sebastían Franco, Eduardo García-Valdecasas, Shani Meynet, Antoine Pasternak, Valdo Tatitscheff

Publications and Research

We study (orientifolded) toric Calabi-Yau singularities in search for D-brane configurations which lead to dynamical supersymmetry breaking at low energy. By exploiting dimer techniques we are able to determine that while most realizations lead to a Coulomb branch instability, a rather specific construction admits a fully stable supersymmetry breaking vacuum. We describe the geometric structure that a singularity should have in order to host such a construction, and present its simplest example, the Octagon.

Topological Terms And Diffeomorphism Anomalies In Fluid Dynamics And Sigma Models, V. Parameswaran Nair

Publications and Research

The requirement of diffeomorphism symmetry for the target space can lead to anomalous commutators for the energy-momentum tensor for sigma models and for fluid dynamics, if certain topological terms are added to the action. We analyze several examples . A particular topological term is shown to lead to the known effective hydrodynamics of a dense collection of vortices, i.e. the vortex fluid theory in 2+1 dimensions. The possibility of a similar vortex fluid in 3+1 dimensions, as well as a fluid of knots and links, with possible extended diffeomorphism algebras is also discussed.

Lives In Musicology: My Life In Writings, Kofi Agawu

Publications and Research

Responding to an invitation from the editors of Acta Musicologica to tell the story of his life in musicology, Kofi Agawu describes his upbringing and early education in Ghana and his university studies in the UK and the US. In a career focused on teaching, research, and writing, he outlines a number of intellectual projects involving the analysis of African and European music. He ends by acknowledging renewed discussions of race and identity in the musical academy today, and hints at his own growing interest in African art music.

Dimers, Orientifolds And Anomalies, Riccardo Argurio, Matteo Bertolini, Sebastían Franco, Eduardo Garcia-Valdecasas, Shani Meynet, Antoine Pasternak, Valdo Tatitscheff

Publications and Research

We study 4d N = 1 gauge theories engineered via D-branes at orientifolds of toric singularities, where gauge anomalies are cancelled without the introduction of non-compact flavor branes. Using dimer model techniques, we derive geometric criteria for establishing whether a given singularity can admit anomaly-free D-brane configurations purely based on its toric data and the type of orientifold projection. Our results therefore extend the dictionary between geometric properties of singularities and physical properties of the corresponding gauge theories.

Light-Ray Moments As Endpoint Contributions To Modular Hamiltonians, Daniel Kabat, Gilad Lifschytz, Phuc Nguyen, Debajyoti Sarkar

Publications and Research

We consider excited states in a CFT, obtained by applying a weak unitary perturbation to the vacuum. The perturbation is generated by the integral of a local operator J⁽ⁿ⁾ of modular weight n over a spacelike surface passing through x = 0. For |n| ≥ 2 the modular Hamiltonian associated with a division of space at x = 0 picks up an endpoint contribution, sensitive to the details of the perturbation (including the shape of the spacelike surface) at x = 0. The endpoint contribution is a sum of light-ray moments of the perturbing operator …

Application Of The Revised Universal Soil Loss Equation To Develop A Management Plan In The Chittagong Hill Tracts Region Of Bangladesh, Nira Rahman

Theses and Dissertations

Land degradation from soil erosion is a major issue in hilly areas of tropical regions such as the Chittagong Hill Tracts (CHT) of Bangladesh. The combination of an elevated topography, high-intensity storms that are further exacerbated by the impacts of climate change, and farming practices increase the susceptibility of the region to soil erosion. The Revised Universal Soil Loss Equation (RUSLE) was developed in the mid-latitude dry climate zone of the United States during the 1990s to assist soil conservationists in implementing farming strategies that would address soil loss. Since then, researchers employed remote sensing and geographic information systems (GIS) …

Floor Plan Assignment In Elementary Mathematics Education, Tunde Jakab

Open Educational Resources

In this upper elementary mathematics education assignment, the prospective teachers gain hands-on experience in measuring distances in feet and inches, calculating areas, and converting distance and area measurements. Moreover, they solve a real-life situation by choosing the most economical tiles for their kitchen. This last part (3) of the assignment develops critical thinking and expressing one's thought processes. Part 3 can be used as an in-class discussion, which further promotes reasoning skills.

Create A New Login Authentication And User Authorization Using Ms Sql Server, Safet Jahaj

Open Educational Resources

The document describes the steps on creating a new login authentication using the mixed mode, and adding user authorizations.

Accessibility: Disabilities Treasure Hunt, Devorah Kletenik

Open Educational Resources

This is a treasure hunt game that simulates various disabilities and gives a sense of how frustrating non-accessible content can be for people with disabilities. Suitable for a general audience, no programming experience necessary.

An editable copy is also given, along with ideas about how to make it more accessible.

Ant-3700 - Introduction To Anthropology, Igor Pashkovskiy

Open Educational Resources

Movement away from the textbook model has potential to foster equitable access to course materials as well as reduce textbook costs for students. As such, transition to a zero cost/OER classroom included the curation of open access scholarly literature to cover the four-field approach presently taught in introductory anthropology courses.

Revealing Topology With Transformation Optics, Lizhen Lu, Kun Ding, Emanuele Galiffi, Xikui Ma, Tianyu Dong, J. B. Pendry

Advanced Science Research Center

Symmetry deepens our insight into a physical system and its interplay with topology enables the discovery of topological phases. Symmetry analysis is conventionally performed either in the physical space of interest, or in the corresponding reciprocal space. Here we borrow the concept of virtual space from transformation optics to demonstrate how a certain class of symmetries can be visualised in a transformed, spectrally related coordinate space, illuminating the underlying topological transitions. By projecting a plasmonic system in a higher-dimensional virtual space onto a lower-dimensional system in real space, we show how transformation optics allows us to construct a topologically non-trivial …

Transmission Zeros With Topological Symmetry In Complex Systems, Yuhao Kang, Azriel Genack

Publications and Research

Understanding vanishing transmission in Fano resonances in quantum systems and metamaterials and perfect and ultralow transmission in disordered media, has advanced the understanding and applications of wave interactions. Here we use analytic theory and numerical simulations to understand and control the transmission and transmission time in complex systems by deforming a medium and by adjusting the level of gain or loss. Unlike the zeros of the scattering matrix, the position and motion of the zeros of the determinant of the transmission matrix in the complex plane of frequency and field decay rate have robust topological properties. In systems without loss …

Elucidation Of The Structure Of Supramolecular Polymorphs In Peptide Nanofibres Using Raman Spectroscopy, Sian Sloan-Dennison, Ayala Lampel, Eileen Raßlenberg, Rein V. Ulijn, Ewen Smith, Karen Faulds, Duncan Graham

Advanced Science Research Center

Peptide fibre formation via molecular self-assembly is a key step in a range of cellular processes and increasingly considered as an approach to produce supramolecular biomaterials. We previously demonstrated the self-assembly of the tripeptide lysine-dityrosine (KYY) as a substrate for the formation of proton-conducting melanin-like materials. Point based Raman scattering is one of several techniques which were used to characterise the secondary structure of the KYY nanofibre but as is often the case with this type of fibre, the spectra are rather complex and in addition there were variations in intensity between samples making interpretation difficult. Using Raman mapping we …

Hyperbolic Surface Wave Propagation In Mid-Infrared Metasurfaces With Extreme Anisotropy, Ahmed Mekawy, Andrea Alù

Advanced Science Research Center

Hyperbolic metasurfaces are characterized by an extreme anisotropy of their effective conductivity tensor, which may be induced at visible frequencies by sculpting metals at the subwavelength scale. In this work, we explore practical implementations of hyperbolic metasurfaces at mid-infrared wavelengths, exploiting devices composed of metals and high-index semiconductor materials, which can support the required field confinement and extreme anisotropy required to realize low loss hyperbolic surface waves. In particular, we discuss the role of broken symmetries in these hybrid metasurfaces to enable large and broadband hyperbolic responses spanning the entire mid-infrared wavelength range (3–30 μm). Our findings pave the way …

Elevated Growth And Biomass Along Temperate Forest Edges, Luca L. Morreale, Jonathan R. Thompson, Xiaojing Tang, Andrew Reinmann, Lucy R. Hutyra

Advanced Science Research Center

Fragmentation transforms the environment along forest edges. The prevailing narrative, driven by research in tropical systems, suggests that edge environments increase tree mortality and structural degradation resulting in net decreases in ecosystem productivity. We show that, in contrast to tropical systems, temperate forest edges exhibit increased forest growth and biomass with no change in total mortality relative to the forest interior. We analyze >48,000 forest inventory plots across the north-eastern US using a quasi-experimental matching design. At forest edges adjacent to anthropogenic land covers, we report increases of 36.3% and 24.1% in forest growth and biomass, respectively. Inclusion of edge …

Observation Of Anti-Parity-Time-Symmetry, Phase Transitions And Exceptional Points In An Optical Fibre, Arik Bergman, Robert Duggan, Kavita Sharma, Moshe Tur, Avi Zadok, Andrea Alù

Advanced Science Research Center

The exotic physics emerging in non-Hermitian systems with balanced distributions of gain and loss has recently drawn a great deal of attention. These systems exhibit phase transitions and exceptional point singularities in their spectra, at which eigen-values and eigen-modes coalesce and the overall dimensionality is reduced. So far, these principles have been implemented at the expense of precise fabrication and tuning requirements, involving tailored nano-structured devices with controlled optical gain and loss. In this work, anti-parity-time symmetric phase transitions and exceptional point singularities are demonstrated in a single strand of single-mode telecommunication fibre, using a setup consisting of off-the-shelf components. …

Efficient Nonreciprocal Mode Transitions In Spatiotemporally Modulated Acoustic Metamaterials, Zhaoxian Chen, Yugui Peng, Haoxiang Li, Jingjing Liu, Yujiang Ding, Bin Liang, Xue-Feng Zhu, Yanqing Lu, Jianchun Cheng, Andrea Alù

Advanced Science Research Center

In linear, lossless, time-invariant, and nonbiased acoustic systems, mode transitions are time reversible, consistent with Lorentz reciprocity and implying a strict symmetry in space-time for sound manipulation. Here, we overcome this fundamental limitation by implementing spatiotemporally modulated acoustic metamaterials that support nonreciprocal sound steering. Our mechanism relies on the coupling between an ultrathin membrane and external biasing electromagnetic fields, realizing programmable dynamic control of the acoustic impedance over a motionless and noiseless platform. The fast and flexible impedance modulation of our metamaterial imparts an effective unidirectional momentum in space-time to realize nonreciprocal transitions in k-ω space between different diffraction …

Acoustic Spoof Surface Plasmon Polaritons For Filtering, Isolation And Sensing, Nikolina Jankovi´, Selena Ilić, Vesna Bengin, Slobodan Birgermajer, Vasa Radonić, Andrea Alù

Advanced Science Research Center

We study a waveguide structure supporting acoustic spoof plasmon polaritons (aSSPPs) perturbed by a defect, whose specifically tailored geometry enables controllable transmission characterized by a uniform phase distribution and very steep narrowband response. The structure is analyzed using transmission-line theory and numerical simulations, providing evidence for its use in advanced filters, isolators and sensor technology. In order to demonstrate the applicability of the aSSPP waveguide with defect, two selective narrowband filter designs are discussed and explored. Furthermore, we propose an acoustic isolator that exploits steady fluid flow to break reciprocity and provide large isolation in a narrowband region. We also …