New entropy estimates for the Oldroyd-B model, and related models

This short note presents the derivation of a new {\it a priori} estimate for the Oldroyd-B model. Such an estimate may provide useful information when investigating the long-time behaviour of macro-macro models, and the stability of numerical schemes. We show how this estimate can be used as a guideline to derive new estimates for other macroscopic models, like the FENE-P model

Uniform Asymptotics of Orthogonal Polynomials Arising from Coherent States

In this paper, we study a family of orthogonal polynomials $\{\phi_n(z)\}$ arising from nonlinear coherent states in quantum optics. Based on the three-term recurrence relation only, we obtain a uniform asymptotic expansion of $\phi_n(z)$ as the polynomial degree $n$ tends to infinity. Our asymptotic results suggest that the weight function associated with the polynomials has an unusual singularity, which has never appeared for orthogonal polynomials in the Askey scheme. Our main technique is the Wang and Wong's difference equation method. In addition, the limiting zero distribution of the polynomials $\phi_n(z)$ is provided

Impacts of Covid-19 mode shift on road traffic

This article is driven by the following question: as the communities reopen after the COVID-19 pandemic, will changing transportation mode share lead to worse traffic than before? This question could be critical especially if many people rush to single occupancy vehicles. To this end, we estimate how congestion will increases as the number of cars increase on the road, and identify the most sensitive cites to drop in transit usage. Travel time and mode share data from the American Community Survey of the US Census Bureau, for metro areas across the US. A BPR model is used to relate average travel times to the estimated number of commuters traveling by car. We then evaluate increased vehicle volumes on the road if different portions of transit and car pool users switch to single-occupancy vehicles, and report the resulting travel time from the BPR model. The scenarios predict that cities with large transit ridership are at risk for extreme traffic unless transit systems can resume safe, high throughput operations quickly.Comment: 14 pages, 11 figure

Off-Policy Evaluation of Probabilistic Identity Data in Lookalike Modeling

We evaluate the impact of probabilistically-constructed digital identity data collected from Sep. to Dec. 2017 (approx.), in the context of Lookalike-targeted campaigns. The backbone of this study is a large set of probabilistically-constructed "identities", represented as small bags of cookies and mobile ad identifiers with associated metadata, that are likely all owned by the same underlying user. The identity data allows to generate "identity-based", rather than "identifier-based", user models, giving a fuller picture of the interests of the users underlying the identifiers. We employ off-policy techniques to evaluate the potential of identity-powered lookalike models without incurring the risk of allowing untested models to direct large amounts of ad spend or the large cost of performing A/B tests. We add to historical work on off-policy evaluation by noting a significant type of "finite-sample bias" that occurs for studies combining modestly-sized datasets and evaluation metrics involving rare events (e.g., conversions). We illustrate this bias using a simulation study that later informs the handling of inverse propensity weights in our analyses on real data. We demonstrate significant lift in identity-powered lookalikes versus an identity-ignorant baseline: on average ~70% lift in conversion rate. This rises to factors of ~(4-32)x for identifiers having little data themselves, but that can be inferred to belong to users with substantial data to aggregate across identifiers. This implies that identity-powered user modeling is especially important in the context of identifiers having very short lifespans (i.e., frequently churned cookies). Our work motivates and informs the use of probabilistically-constructed identities in marketing. It also deepens the canon of examples in which off-policy learning has been employed to evaluate the complex systems of the internet economy.Comment: Accepted by WSDM 201

Efficient finite element modeling of reinforced concrete columns confined with fiber reinforced polymers

Fiber reinforced polymer (FRP) composites have found extensive applications in the field of Civil Engineering due to their advantageous properties such as high strength-to-weight ratio and high corrosion resistance. This study presents a simple and efficient frame finite element (FE) able to accurately estimate the load-carrying capacity and ductility of reinforced concrete (RC) circular columns confined with externally bonded fiber reinforced polymer (FRP) plates and/or sheets. The proposed FE considers distributed plasticity with fiber-discretization of the cross-sections in the context of a force-based (FB) formulation. The element is able to model collapse due to concrete crushing, reinforcement steel yielding, and FRP rupture. The frame FE developed in this study is used to predict the load-carrying capacity of FRP-confined RC columns subjected to both concentric and eccentric axial loading. Numerical simulations and experimental results are compared based on experimental tests available in the literature and published by different authors. The numerically simulated responses agree well with the corresponding experiment results. The outstanding features of this FE include computational efficiency, accuracy and ease of use. Therefore, the proposed FE is suitable for efficient and accurate modeling and analysis of RC columns confined with externally retrofitted FRP plates/sheets as for parametric studies requiring numerous FE analyses

The spectral analysis of random graph matrices

A random graph model is a set of graphs together with a probability distribution on that set. A random matrix is a matrix with entries consisting of random values from some specified distribution. Many different random matrices can be associated with a random graph. The spectra of these corresponding matrices are called the spectra of the random graph. The spectra of random graphs are critical to understanding the properties of random graphs. This thesis contains a number of results on the spectra and related spectral properties of several random graph models. In Chapter 1, we briefly present the background, some history as well as the main ideas behind our work. Apart from the introduction in Chapter 1, the first part of the main body of the thesis is Chapter 2. In this part we estimate the eigenvalues of the Laplacian matrix of random multipartite graphs. We also investigate some spectral properties of random multipartite graphs, such as the Laplacian energy, the Laplacian Estrada index, and the von Neumann entropy. The second part consists of Chapters 3, 4, 5 and 6. Guo and Mohar showed that mixed graphs are equivalent to digraphs if we regard (replace) each undirected edge as (by) two oppositely directed arcs. Motivated by the work of Guo and Mohar, we initially propose a new random graph model – the random mixed graph. Each arc is determined by an in-dependent random variable. The main themes of the second part are the spectra and related spectral properties of random mixed graphs. In Chapter 3, we prove that the empirical distribution of the eigenvalues of the Hermitian adjacency matrix converges to Wigner’s semicircle law. As an application of the LSD of Hermitian adjacency matrices, we estimate the Hermitian energy of a random mixed graph. In Chapter 4, we deal with the asymptotic behavior of the spectrum of the Hermitian adjacency matrix of random mixed graphs. We derive a separation result between the first and the remaining eigenvalues of the Hermitian adjacency matrix. As an application of the asymptotic behavior of the spectrum of the Hermitian adjacency matrix, we estimate the spectral moments of random mixed graphs. In Chapter 5, we prove that the empirical distribution of the eigenvalues of the normalized Hermitian Laplacian matrix converges to Wigner’s semicircle law. Moreover, in Chapter 6, we provide several results on the spectra of general random mixed graphs. In particular, we present a new probability inequality for sums of independent, random, self-adjoint matrices, and then apply this probability inequality to matrices arising from the study of random mixed graphs. We prove a concentration result involving the spectral norm of a random matrix and that of its expectation. Assuming that the probabilities of all the arcs of the mixed graph are mutually independent, we write the Hermitian adjacency matrix as a sum of random self-adjoint matrices. Using this, we estimate the spectrum of the Hermitian adjacency matrix, and prove a concentration result involving the spectrum of the normalized Hermitian Laplacian matrix and its expectation. Finally, in Chapter 7, we estimate upper bounds for the spectral radii of the skew adjacency matrix and skew Randić matrix of random oriented graphs