Rectilinear crossing number of the double circular complete bipartite graph

In this work, we study a mathematically rigorous metric of a graph visualization quality under conditions that relate to visualizing a bipartite graph. Namely we study rectilinear crossing number in a special arrangement of the complete bipartite graph where the two parts are placed on two concentric circles. For this purpose, we introduce a combinatorial formulation to count the number of crossings. We prove a proposition about the rectilinear crossing number of the complete bipartite graph. Then, we introduce a geometric optimization problem whose solution gives the optimum radii ratio in the case that the number of crossings for them is minimized. Later on, we study the magnitude of change in the number of crossings upon change in the radii of the circles. In this part, we present and prove a lemma on bounding the changes in the number of crossings of that is followed by a theorem on asymptotics of the bounds.Comment: 15 pages, 11 figure

Visible Optical Coherence Tomography based Multimodal Imaging for Quantification of Retinal Lipofuscin

Retinal degeneration is the leading cause of irreversible low vision and blindness in the world, that describes conditions characterized by progressive loss of photoreceptors. Retinal Pigment Epithelium (RPE) is located under photoreceptors’ outer segments and plays an important role in the maintenance of photoreceptors by completing the visual cycle and phagocytosis of shed photoreceptor outer segments. Lipofuscin, a byproduct of the visual cycle, is a nondegradable compound that accumulates in the RPE cells and eventually damages the RPE cells and inevitably causes photoreceptor degeneration. Lipofuscin is the major cause of fundus fluorescence that can be detected by Fundus Autofluorescent (FAF) imaging systems. Reliable and quantified FAF values are necessary for lipofuscin quantification which can be a significant tool in the diagnosis of retinal degenerative disease in early stages and provide a better opportunity for treatment before the loss of vision stage. However, FAF is attenuated by the ocular media prior to the RPE, including cornea, lens, vitreous body, retinal layers in front of the RPE, and the melanin granules within the RPE cells that migrate to the apical region upon light exposure. This attenuation varies among people and for an individual over time and cannot be measured directly, thus hurdles measurement of the true FAF values. Further, differences in acquisition systems such as illumination power and detector sensitivity, directly affect the measured FAF. This issue has been addressed by implementing a reference target in the FAF imaging system. Normalizing the FAF signal to that of the target eliminates the dependency on the acquisition parameters. However, the issue of pre-RPE and RPE melanin attenuation remains unresolved. Further, the fluorescence characteristics of the commercially available fluorescent reference are quite different than retinal lipofuscin that challenges the quantification of the absolute amount of lipofuscin in the RPE. In this dissertation, we propose a new multimodal imaging system based on visible-light optical coherence tomography (VIS-OCT) that provides a three-dimensional image. The technology simultaneously acquires VIS-OCT and FAF with a single broadband visible light source. Since both images are originated from the same group of photons and travel through the same ocular media at the same time, the attenuation factor is similar in both modalities. Therefore, by normalizing FAF by VIS-OCT of the RPE layer, the attenuation of the pre_RPE media can be eliminated. Further, we implemented two reference targets to quantify VIS-OCT and FAF and eliminate the dependency on acquisition parameters. These references were later substituted by a single customized reference that consists of the major lipofuscin fluorophore, called A2E. The quantitative imaging independent of system fluctuation, and attenuation of pre-RPE and RPE melanin was successfully tested on retinal simulating phantoms, in vivo on the animal retina, and human subjects. The in vivo quantification in small animals linearly correlates with A2E content measured by mass spectrometry. Quantitative imaging of human retinas is consistent with the linear accumulation of lipofuscin with age. The VIS-OCT-FAF has the potential for clinical diagnosis

Two Essays on Investor Attention and Asset Pricing

This dissertation explores the effect of investor attention, as measured by Google Search Volume Index, on security prices. It seeks to answer the following research questions: 1) what is the effect of investor attention on the expected returns of EREITs? And 2) what is the impact of investor attention on the open market repurchases post announcement returns? Classic theory suggests that information is immediately incorporated into stock prices. However, existing empirical evidence shows that investors are limited in terms of the amount of information they can process. Kahneman (1973) advances that attention is a scarce cognitive resource. Individuals suffer from bounded rationality. When faced with large amounts of information, they are limited in terms of how much they can process. This implies that prices may not reflect all available information due to limited investor attention. Essay 1 investigates the effect of investor attention on the expected returns of EREITs. The attention hypothesis of Barber and Odean (2008) suggests that increased attention leads to increased buying, which pushes prices and returns higher temporarily, but is followed by a reversal. We test the attention hypothesis on EREITs from 2004 to 2012 using Search Volume Index (SVI) data in Google Trends. We find that EREITs that generate high investor attention, as measured by SVI, earn higher returns compared to EREITs that generate no investor attention. The results are driven by small stocks and stocks with high book to market ratio. We report that the SVI effect is not due to impediments to trade and conjecture that SVI increases investor recognition among EREITs that are characterized by information incompleteness, leading to higher returns. Over time, this increase in returns is followed by a reversal. Essay 2 uses the attention hypothesis to generate insights into stock repurchases price drift. Using a sample of 318 firms that made repurchase announcements between 2004 and 2008 and which have weekly search volume data in Google Trends, we find that investor attention has an effect on the repurchase drift for stocks during the first year following the announcement. More specifically, high abnormal search volume leads to a positive effect on cumulative returns during the first year following the announcement for small stocks, stocks with high idiosyncratic risk, low market to book ratio, and low past return. Prior research has shown that for such stocks, the repurchase drift lasts for three years due to limits to arbitrage. As these stocks are dominated by retail investors, an increase in retail investors\u27 attention results in increased buying, which pushes prices and cumulative returns higher. Low abnormal search volume signals a decrease in investor attention and results in negative returns among all stocks. The results provide further support to the attention hypothesis. Both essays find evidence that the level of investor attention has an effect on security prices. This is contrary to the predictions of the classical theory that postulates that information is immediately incorporated into stock prices

NONEQUILIBRIUM DYNAMICS OF ENTANGLED POLYMERIC FLUIDS

Individual molecule dynamics have been shown to influence significantly the bulk rheological and microstructural properties of polymeric liquids undergoing high strain-rate flows. The objective of this study was to perform equilibrium and Nonequilibrium Molecular Dynamics (NEMD) simulations for monodisperse polyethylene liquids over a wide range of deformation rates under steady shear and planar elongational flows in an attempt to understand the underlying physical processes that shape the dynamical responses of these complex liquids.Under steady shear conditions, the rheological and dynamical responses exhibited different behavior as functions of shear rate, which could be categorized within four shear rate regions. For shear rates smaller than the inverse disengagement time, the topological properties of the liquid remained relatively unperturbed from quiescent conditions and the rheological characteristic functions remained constant throughout. For shear rates between the inverse disengagement and inverse Rouse times, chain orientation became the dominant dynamical system response with only a mild degree of chain stretching and disentanglement being evident. Rheological characteristic functions displayed shear-thinning behavior, and a plateau in the shear stress profile was observed. For shear rates between the inverse Rouse and inverse entanglement times, significant chain stretching became apparent which led to a reduction in the number of entanglements, thereby enabling a rotational motion of the individual molecules in response to the vorticity of the shear field. At higher shear rates, the rotational motion of the chains became the sole relaxation mode of the system as the number of entanglements was gradually reduced to a low level. The analysis of the transient responses revealed that the stress overshoot and undershoot commonly observed at high shear rate can likely be attributed to tube orientation rather than tube stretching.Under planar elongational flow, a coil-stretch transition, with an associated hysteresis in the configurational flow profile, was observed over a specific range of strain rates. Steady state results revealed bimodal distribution functions in which configurational states were simultaneously populated by relatively coiled and stretched molecules. The realization of this bi-phasic coil-stretch transition was an unanticipated microphase separation into a heterogeneous liquid composed of regions of either highly stretched or tightly coiled macromolecules

Strengthening Relaxed Decision Diagrams for Maximum Independent Set Problem: Novel Variable Ordering and Merge Heuristics

Finding high-quality bounds is key to devising efficient exact solution approaches for Discrete Optimization (DO) problems. To this end, Decision Diagrams (DDs) provide strong and generic bounding mechanisms. This paper focuses on so-called relaxed DDs which, by merging nodes, over-approximate the solution space of DO problems and provide dual bounds the quality of which hinges upon the ordering of the variables in the DD compilation and on the selection of the nodes to merge. Addressing the Maximum Independent Set Problem, we present a novel dynamic variable ordering strategy relying on induced subgraphs of the original graph, and a new tie-based merge heuristic. In a set of computational experiments, we show that our strategies yield much stronger bounds than the standard state-of-the-art approaches. Furthermore, implementing our heuristics in a DD-based branch-and-bound, we reduce the solution times by around 33 % on average and by more than 50 % on hard instances

Mixed coordinate Node link Visualization for Co_authorship Hypergraph Networks

We present an algorithmic technique for visualizing the co-authorship networks and other networks modeled with hypergraphs (set systems). As more than two researchers can co-author a paper, a direct representation of the interaction of researchers through their joint works cannot be adequately modeled with direct links between the author-nodes. A hypergraph representation of a co-authorship network treats researchers/authors as nodes and papers as hyperedges (sets of authors). The visualization algorithm that we propose is based on one of the well-studied approaches representing both authors and papers as nodes of different classes. Our approach resembles some known ones like anchored maps but introduces some special techniques for optimizing the vertex positioning. The algorithm involves both continuous (force-directed) optimization and discrete optimization for determining the node coordinates. Moreover, one of the novelties of this work is classifying nodes and links using different colors. This usage has a meaningful purpose that helps the viewer to obtain valuable information from the visualization and increases the readability of the layout. The algorithm is tuned to enable the viewer to answer questions specific to co-authorship network studies.Comment: 10 pages, 3 figures, 1 tabl

Precise Analysis of Polymer Rotational Dynamics

Through the analysis of individual chain dynamics alongside the corresponding molecular structures under shear via nonequilibrium molecular dynamics simulations of C178H358 linear and short-chain branched polyethylene melts under shear flow, we observed that the conventional method based on the chain end-to-end vector (and/or the gyration tensor of chain) is susceptible to quantitatively inaccurate measurements and often misleading information in describing the rotational dynamics of polymers. Identifying the flaw as attributed to strong irregular Brownian fluctuations inherent to the chain ends associated with their large free volume and strong molecular collisions, we propose a simple, robust way based on the chain center-to-center vector connecting the two centers of mass of the bisected chain, which is shown to adequately describe polymer rotational dynamics without such shortcomings. We present further consideration that the proposed method can be useful in accurately measuring the overall chain structure and dynamics of polymeric materials with various molecular architectures, including branched and ring polymers.open

Providing a control method of BTB-VSC Converters under unbalanced faults

Microgrids need control strategies to achieve maximum performance. An appropriate control strategy should have high performance in unbalanced conditions in addition to normal conditions. Today, the use of microgrids, with a variety of power sources, including solar, wind, diesel, energy storage sources to increase the capability of distribution grid has made significant progress. However, controlling and managing their energy in the event of a fault is a challenge that researchers are faced. In this article, two microgrids connected to the grid are studied using a back-to-back (BTB)-voltage source converters (VSC) converter. The results of this research showed that by the usage of above-mentioned convertor first, with power management between microgrids the frequency remains constant in island mode second, they are isolated from each other in terms of faults. The results showed that the use of the proposed method controlled the frequency of two microgrids simultaneously

Probabilistic Reasoning in Generative Large Language Models

This paper considers the challenges Large Language Models (LLMs) face when reasoning over text that includes information involving uncertainty explicitly quantified via probability values. This type of reasoning is relevant to a variety of contexts ranging from everyday conversations to medical decision-making. Despite improvements in the mathematical reasoning capabilities of LLMs, they still exhibit significant difficulties when it comes to probabilistic reasoning. To deal with this problem, we introduce the Bayesian Linguistic Inference Dataset (BLInD), a new dataset specifically designed to test the probabilistic reasoning capabilities of LLMs. We use BLInD to find out the limitations of LLMs for tasks involving probabilistic reasoning. In addition, we present several prompting strategies that map the problem to different formal representations, including Python code, probabilistic algorithms, and probabilistic logical programming. We conclude by providing an evaluation of our methods on BLInD and an adaptation of a causal reasoning question-answering dataset. Our empirical results highlight the effectiveness of our proposed strategies for multiple LLMs