Digital Commons Network^™

Multi-Tasking Memcapacitive Networks, Dat Tran, Christof Teuscher

Electrical and Computer Engineering Faculty Publications and Presentations

Recent studies have shown that networks of memcapacitive devices provide an ideal computing platform of low power consumption for reservoir computing systems. Random, crossbar, or small-world power-law (SWPL) structures are common topologies for reservoir substrates to compute single tasks. However, neurological studies have shown that the interconnections of cortical brain regions associated with different functions form a rich-club structure. This structure allows human brains to perform multiple activities simultaneously. So far, memcapacitive reservoirs can perform only single tasks. Here, we propose, for the first time, cluster networks functioning as memcapacitive reservoirs to perform multiple tasks simultaneously. Our results illustrate that …

Polarization Topology At The Nominally Charged Domain Walls In Uniaxial Ferroelectrics, Yurii Tikhonov, Jesi R. Maguire, Conor J. Mccluskey, James P. V. Mcconville, Amit Kumar, Haidong Lu, Dennis Meier, Anna Razumnaya, John Martin Gregg, Alexei Gruverman, Valerii M. Vinokur, Igor Luk’Yanchuk

Department of Physics and Astronomy: Faculty Publications

Ferroelectric domain walls provide a fertile environment for novel materials physics. If a polarization discontinuity arises, it can drive a redistribution of electronic carriers and changes in band structure, which often result in emergent 2D conductivity. If such a discontinuity is not tolerated, then its amelioration usually involves the formation of complex topological patterns, such as flux-closure domains, dipolar vortices, skyrmions, merons, or Hopfions. The degrees of freedom required for the development of such patterns, in which dipolar rotation is a hallmark, are readily found in multiaxial ferroelectrics. In uniaxial ferroelectrics, where only two opposite polar orientations are possible, it …

Geometric Algorithms For Modeling Plant Roots From Images, Dan Zeng

McKelvey School of Engineering Theses & Dissertations

Roots, considered as the ”hidden half of the plant”, are essential to a plant’s health and pro- ductivity. Understanding root architecture has the potential to enhance efforts towards im- proving crop yield. In this dissertation we develop geometric approaches to non-destructively characterize the full architecture of the root system from 3D imaging while making com- putational advances in topological optimization. First, we develop a global optimization algorithm to remove topological noise, with applications in both root imaging and com- puter graphics. Second, we use our topology simplification algorithm, other methods from computer graphics, and customized algorithms to develop a high-throughput …

A Topologist’S Broken Heart, Josh Hiller

Journal of Humanistic Mathematics

A poem about a topologist's broken heart.

Mining The Soma Cube For Gems: Isomorphic Subgraphs Reveal Equivalence Classes, Edward Vogel, My Tram

Journal of Humanistic Mathematics

Soma cubes are an example of a dissection puzzle, where an object is broken down into pieces, which must then be reassembled to form either the original shape or some new design. In this paper, we present some interesting discoveries regarding the Soma Cube. Equivalence classes form aesthetically pleasing shapes in the solution set of the puzzle. These gems are identified by subgraph isomorphisms using SNAP!/Edgy, a simple block-based computer programming language. Our preliminary findings offer several opportunities for researchers from middle school to undergraduate to utilize graphs, group theory, topology, and computer science to discover connections between computation and …

Thickened Surfaces, Checkerboard Surfaces, And Quantum Link Invariants, Joseph W. Boninger

Dissertations, Theses, and Capstone Projects

This dissertation has two parts, each motivated by an open problem related to the Jones polynomial. The first part addresses the Volume Conjecture of Kashaev, Murakami, and Murakami. We define a polynomial invariant, J^T_n, of links in the thickened torus, which we call the nth toroidal colored Jones polynomial, and we show J^T_n satisfies many properties of the original colored Jones polynomial. Most significantly, J^T_n exhibits volume conjecture behavior. We prove a volume conjecture for the 2-by-2 square weave, and provide computational evidence for other links. We also give two equivalent constructions …

Topological Analysis Of Microtubules During Cell Division, Hemanth Kumar Mandya Nagaiah

Masters Theses and Doctoral Dissertations

Cells are complex biological systems, composed by many biopolymers, which undergo morphological changes during cell division. Microtubules are biopolymers essential for functions in the cell. Understanding the role of microtubules in cell division requires characterizing their conformations during this process. In this thesis, we model the microtubules by mathematical curves in space and use methods from Knot Theory to characterize the single and multi-chain topological complexity of such systems. We create computational methods for analyzing the topology of microtubules obtained through large electron tomography data. Our results show that the geometry/topology and entanglement of microtubules changes throughout cell division and …

The Examination Of The Arithmetic Surface (3, 5) Over Q, Rachel J. Arguelles

Electronic Theses, Projects, and Dissertations

This thesis is centered around the construction and analysis of the principal arithmetic surface (3, 5) over Q. By adjoining the two symbols i,j, where i² = 3, j² = 5, such that ij = -ji, I can produce a quaternion algebra over Q. I use this quaternion algebra to find a discrete subgroup of SL₂(R), which I identify with isometries of the hyperbolic plane. From this quaternion algebra, I produce a large list of matrices and apply them via Mobius transformations to the point (0, 2), which is the center of my Dirichlet domain. This …

Finite N-Quandles Of Twisted Double Handcuff And Complete Graph, Veronica Backer-Peral

Honors Thesis

The Double Handcuff and K4 graphs can be generalized to a single family of spatial graphs by adding a variable number of twists between two edges. We can identify spatial graphs by calculating a quotient of the fundamental quandle, known as an N-quandle, which is a spatial graph invariant. In this paper, we prove that the N-quandle associated with this family of spatial graphs is finite when all but two edges are given a label of 2, and the remaining two edges are assigned labels from the natural numbers. To prove that the N-quandle is finite, we produce Cayley graphs …

Cross-Temporal Snapshot Alignment For Dynamic Multi-Relational Networks, Lvjia Chen, Shangsong Liang

Machine Learning Faculty Publications

A dynamic network is often represented as a sequence of snapshots evolving over time. In certain real-world scenarios, the identities of nodes in snapshots of a dynamic network are unknown and need to be figured out. To deal with such a challenge, recently, the task of cross-temporal snapshot alignment for dynamic networks is proposed, which aims to match equivalent nodes across temporal snapshots of a dynamic network given a small set of identified nodes. However, in many dynamic multi-relational networks like temporal knowledge graphs, the relation type information of edges, which can be useful for the alignment task, is neglected …

Adaptive Protection Method For Distribution Networks Based On The Dynamic Topology, Gang Liu, Lin Zhu, Shenglong Qi, Haitao Liu, Xutao Li

Journal of Electric Power Science and Technology

The topology of distribution networks can be instantly modified to handle faults, but the operation ranges of the protection devices will be affected. In this paper, an adaptive protection method for distribution networks based on the dynamic topology is proposed to realize the optimal configuration of protection devices under different topologies. A dynamic topology tracking technology of node switch is built based on the traditional adaptive protection method. According to the system structure changes, this technology also amends the topology adaptively. During this step, the topology matrix is modified, and the system protection parameters are updated adaptively. Finally, the proposed …

Performance Of Xor Rule For Decentralized Detection Of Deterministic Signals In Bivariate Gaussian Noise, Xingjian Sun, Shailee Yagnik, Ramanarayanan Viswanathan, Lei Cao

Faculty and Student Publications

In this paper, we consider the performance of exclusive-OR (XOR) rule in detecting the presence or absence of a deterministic signal in bivariate Gaussian noise. Signals, when present at the two sensors, are assumed unequal, whereas the noise components have identical marginal distribution but are correlated. The sensors send their one-bit quantized data to a fusion center, which then employs the XOR rule to arrive at the final decision. Here we prove that, in the limit as the correlation coefficient r approaches 1, the optimum fusion rule for both parallel and tandem topologies is XOR with identical, alternating partitions (XORAP) …

Toward Feature-Preserving Vector Field Compression, Xin Liang, Sheng Di, Franck Cappello, Mukund Raj, Chunhui Liu, Kenji Ono, Zizhong Chen, Tom Peterka, Hanqi Guo

Computer Science Faculty Research & Creative Works

The objective of this work is to develop error-bounded lossy compression methods to preserve topological features in 2D and 3D vector fields. Specifically, we explore the preservation of critical points in piecewise linear and bilinear vector fields. We define the preservation of critical points as, without any false positive, false negative, or false type in the decompressed data, (1) keeping each critical point in its original cell and (2) retaining the type of each critical point (e.g., saddle and attracting node). The key to our method is to adapt a vertex-wise error bound for each grid point and to compress …

Does Bias Have Shape? An Examination Of The Feasibility Of Algorithmic Detection Of Unfair Bias Using Topological Data Analysis, Ansel Steven Tessier

Senior Projects Spring 2022

Artificial intelligence and machine learning systems are becoming ever more prevalent; at every turn these systems are asked to make decisions that have lasting impacts on peoples’ lives. It is becoming increasingly important that we ensure these systems are making fair and equitable decisions. For decades we have been aware of biased and unfair decision making in many sectors of society. In recent years a growing body of evidence suggests these biases are being captured in data that are then used to build artificial intelligence and machine learning systems, which themselves perpetuate these biases. The question is then, can we …

Trapped Surfaces, Topology Of Black Holes, And The Positive Mass Theorem, Lan-Hsuan Huang, Dan A. Lee

Publications and Research

No abstract provided.

Topological Hierarchies And Decomposition: From Clustering To Persistence, Kyle A. Brown

Browse all Theses and Dissertations

Hierarchical clustering is a class of algorithms commonly used in exploratory data analysis (EDA) and supervised learning. However, they suffer from some drawbacks, including the difficulty of interpreting the resulting dendrogram, arbitrariness in the choice of cut to obtain a flat clustering, and the lack of an obvious way of comparing individual clusters. In this dissertation, we develop the notion of a topological hierarchy on recursively-defined subsets of a metric space. We look to the field of topological data analysis (TDA) for the mathematical background to associate topological structures such as simplicial complexes and maps of covers to clusters in …

Algebraic Invariants Of Knot Diagrams On Surfaces, Ryan Martinez

HMC Senior Theses

In this thesis we first give an introduction to knots, knot diagrams, and algebraic structures defined on them accessible to anyone with knowledge of very basic abstract algebra and topology. Of particular interest in this thesis is the quandle which "colors" knot diagrams. Usually, quandles are only used to color knot diagrams in the plane or on a sphere, so this thesis extends quandles to knot diagrams on any surface and begins to classify the fundamental quandles of knot diagrams on the torus.

This thesis also breifly looks into Niebrzydowski Tribrackets which are a different algebraic structure which, in future …

Toward A Topology-Based Therapeutic Design Of Membrane Proteins: Validation Of Napi2b Topology In Live Ovarian Cancer Cells, Leisan Bulatova, Daria Savenkova, Alsina Nurgalieva, Daria Reshetnikova, Arina Timonina, Vera Skripova, Mikhail Bogdanov, Ramziya Kiyamova

Faculty and Staff Publications

NaPi2b is a sodium-dependent phosphate transporter that belongs to the SLC34 family of transporters which is mainly responsible for phosphate homeostasis in humans. Although NaPi2b is widely expressed in normal tissues, its overexpression has been demonstrated in ovarian, lung, and other cancers. A valuable set of antibodies, including L2 (20/3) and MX35, and its humanized versions react strongly with an antigen on the surface of ovarian and other carcinoma cells. Although the topology of NaPi2b was predicted

The Changing, Sabrina B. Black

Graduate Student Theses, Dissertations, & Professional Papers

In poems that center on experiences of childhood, adolescence, and young adulthood, The Changing explores the formation of identity and the malleability of the self. Sabrina Black writes into the spaces between people—at times finding connection there and at times isolation. Throughout the collection, the speaker reflects on complicated relationships with family members, classmates, and friends; on the ways those relationships have shaped her; and, most of all, on her relationship with that elusive thing called the self.

In a series of “Dear Advice Columnist” poems scattered throughout the manuscript, Black shifts focus away from personal experience, adopting the persona …