Weighing matrices and spherical codes

Mutually unbiased weighing matrices (MUWM) are closely related to an antipodal spherical code with 4 angles. In the present paper, we clarify the relationship between MUWM and the spherical sets, and give the complete solution about the maximum size of a set of MUWM of weight 4 for any order. Moreover we describe some natural generalization of a set of MUWM from the viewpoint of spherical codes, and determine several maximum sizes of the generalized sets. They include an affirmative answer of the problem of Best, Kharaghani, and Ramp.Comment: Title is changed from "Association schemes related to weighing matrices

A feasibility approach for constructing combinatorial designs of circulant type

In this work, we propose an optimization approach for constructing various classes of circulant combinatorial designs that can be defined in terms of autocorrelations. The problem is formulated as a so-called feasibility problem having three sets, to which the Douglas-Rachford projection algorithm is applied. The approach is illustrated on three different classes of circulant combinatorial designs: circulant weighing matrices, D-optimal matrices, and Hadamard matrices with two circulant cores. Furthermore, we explicitly construct two new circulant weighing matrices, a $CW(126,64)$ and a $CW(198,100)$, whose existence was previously marked as unresolved in the most recent version of Strassler's table

Edge Label Inference in Generalized Stochastic Block Models: from Spectral Theory to Impossibility Results

The classical setting of community detection consists of networks exhibiting a clustered structure. To more accurately model real systems we consider a class of networks (i) whose edges may carry labels and (ii) which may lack a clustered structure. Specifically we assume that nodes possess latent attributes drawn from a general compact space and edges between two nodes are randomly generated and labeled according to some unknown distribution as a function of their latent attributes. Our goal is then to infer the edge label distributions from a partially observed network. We propose a computationally efficient spectral algorithm and show it allows for asymptotically correct inference when the average node degree could be as low as logarithmic in the total number of nodes. Conversely, if the average node degree is below a specific constant threshold, we show that no algorithm can achieve better inference than guessing without using the observations. As a byproduct of our analysis, we show that our model provides a general procedure to construct random graph models with a spectrum asymptotic to a pre-specified eigenvalue distribution such as a power-law distribution.Comment: 17 page

WeighstEd

The purpose of this design thesis is to outline and describe the design project; WeighstEd. WeighstEd, is a data collection, storage, and analysis system for food waste to help Santa Clara University’s Sustainability Center reach a quantifiable food waste reduction goal of 10% by 2020 by using data to make informed cafeteria changes. The report will outline the entire engineering design process from ideation to manufacture including analysis techniques and benchmark testing. This report will serve as a written documentation of three mechanical engineers Senior Design Project completed at Santa Clara University. WeighstEd will be implemented at on campus events and in the university cafeteria beginning in the 2019-2020 school year

Effect of body composition methodology on heritability estimation of body fatness

Heritability estimates of human body fatness vary widely and the contribution of body composition methodology to this variability is unknown. The effect of body composition methodology on estimations of genetic and environmental contributions to body fatness variation was examined in 78 adult male and female monozygotic twin pairs reared apart or together. Body composition was assessed by six methods - body mass index (BMI), dual energy x-ray absorptiometry (DXA), underwater weighing (UWW), total body water (TBW), bioelectric impedance (BIA), and skinfold thickness. Body fatness was expressed as percent body fat, fat mass, and fat mass/height2 to assess the effect of body fatness expression on heritability estimates. Model-fitting multivariate analyses were used to assess the genetic and environmental components of variance. Mean BMI was 24.5 kg/m2 (range of 17.8-43.4 kg/m2). There was a significant effect of body composition methodology (p<0.001) on heritability estimates, with UWW giving the highest estimate (69%) and BIA giving the lowest estimate (47%) for fat mass/height2. Expression of body fatness as percent body fat resulted in significantly higher heritability estimates (on average 10.3% higher) compared to expression as fat mass/height2 (p=0.015). DXA and TBW methods expressing body fatness as fat mass/height2 gave the least biased heritability assessments, based on the small contribution of specific genetic factors to their genetic variance. A model combining DXA and TBW methods resulted in a relatively low FM/ht2 heritability estimate of 60%, and significant contributions of common and unique environmental factors (22% and 18%, respectively). The body fatness heritability estimate of 60% indicates a smaller contribution of genetic variance to total variance than many previous studies using less powerful research designs have indicated. The results also highlight the importance of environmental factors and possibly genotype by environmental interactions in the etiology of weight gain and the obesity epidemic.R01 AR046124 - NIAMS NIH HHS; R01 MH065322 - NIMH NIH HHS; T32 HL069772 - NHLBI NIH HHS; R21 DK078867 - NIDDK NIH HHS; R37 DA018673 - NIDA NIH HHS; R01 DK076092 - NIDDK NIH HHS; R01 DK079003 - NIDDK NIH HHS; F32 DK009747 - NIDDK NIH HHS; R01 DA018673 - NIDA NIH HH

Eigenmode-based capacitance calculations with applications in passivation layer design

The design of high-speed metallic interconnects such as microstrips requires the correct characterization of both the conductors and the surrounding dielectric environment, in order to accurately predict their propagation characteristics. A fast boundary integral equation approach is obtained by modeling all materials as equivalent surface charge densities in free space. The capacitive behavior of a finite dielectric environment can then be determined by means of a transformation matrix, relating these charge densities to the boundary value of the electric potential. In this paper, a new calculation method is presented for the important case that the dielectric environment is composed of homogeneous rectangles. The method, based on a surface charge expansion in terms of the Robin eigenfunctions of the considered rectangles, is not only more efficient than traditional methods, but is also more accurate, as shown in some numerical experiments. As an application, the design and behavior of a microstrip passivation layer is treated in some detail