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### Computing generalized Frobenius powers of monomial ideals

Provost and Senior Vice PresidentMathematicsMathematic

### Carbon Emission Underreporting: Evidence from Satellite Emission Data

I compare satellite emissions data to company reports filed with the U.S. Environmental Protection Agency (EPA) to identify firms that underreport their carbon emissions. I find that firms are more likely to underreport their emissions to the EPA when they are more publicly visible, face greater shareholder pressure for corporate greening, and are subject to cap-and-trade programs. Firms are less likely to underreport their emissions when they have greater monitoring from the board of directors and are more likely to be affected by environmental disclosure mandates. Next, I examine the relation between firms’ emission intensity and characteristics of their environmental disclosures in 10-Ks. As expected, I find that firms’ emission intensity relates positively to both the number of environmental keywords and optimistic tone used in disclosures. However, these relations weaken for firms that underreport their emissions. The results are consistent with firms attempting to hide their underreporting of emissions and avoid litigation risks. Overall, the results suggest that investors and other stakeholders should be cautious when using self-reported environmental information, and that regulators’ concern about existing climate disclosures in annual reports (10-Ks) not adequately reflecting actual operations is warranted

### Compactifying sufficiently regular covering spaces of compact 3-manifolds

In this paper it is proven that if the group of covering translations of the covering space of a compact, connected, P²-irreducible 3-manifold corresponding to a non-trivial, finitely-generated subgroup of its fundamental group is infinite, then either the covering space is almost compact or the subgroup is infinite cyclic and has normalizcr a non-finitely-generated subgroup of the rational numbers. In the first case additional information is obtained which is then used to relate Thurston's hyperbolization and virtual bundle conjectures to some algebraic conjectures about certain 3-manifold groups.Mathematic

### Expected number of real zeros for random orthogonal polynomials

We study the expected number of real zeros for random linear combinations of orthogonal polynomials. It is well known that Kac polynomials, spanned by monomials with i.i.d. Gaussian coefficients, have only (2/π + o(1))logn expected real zeros in terms of the degree n. If the basis is given by the orthonormal polynomials associated with a compactly supported Borel measure on the real line, or associated with a Freud weight defined on the whole real line, then random linear combinations have expected real zeros. We prove that the same asymptotic relation holds for all random orthogonal polynomials on the real line associated with a large class of weights, and give local results on the expected number of real zeros. We also show that the counting measures of properly scaled zeros of these random polynomials converge weakly to either the Ullman distribution or the arcsine distribution.Mathematic

### Double burden of COVID-19 knowledge deficit: low health literacy and high information avoidance

Objective: People with lower levels of health literacy are likely to report engaging in information avoidance. However, health information avoidance has been overlooked in previous research on responses to viral outbreaks. The purpose of this cross-sectional survey study was to assess the relationship between health literacy and COVID-19 information avoidance. Students (n = 561) at a university in the south central region of the U.S. completed our online survey conducted from April to June 2020 using simple random sampling. We measured information avoidance and the degree to which people opt not to learn about COVID-19 when given the choice. We assessed participants’ health literacy level using the Newest Vital Sign (NVS), eHealth Literacy Scale (eHEALS), and All Aspect of Health Literacy Scale (AAHLS). Results: Those with lower health literacy were more likely to avoid information about COVID-19. This negative association between health literacy and information avoidance was consistent across all types of health literacy measures: NVS scores (b = − 0.47, p = 0.033), eHEALS scores (b = − 0.12, p = 0.003), functional health literacy (b = − 0.66, p = 0.001), communicative health literacy (b = − 0.94, p < 0.001), information appraisal (b = − 0.36, p = 0.004), and empowerment (b = − 0.62, p = 0.027). The double burden of low health literacy and high information avoidance is likely to lead to a lack of knowledge about COVID-19.Hlth Sci, Couns & Couns Psyc (HCCP

### Real roots of random orthogonal polynomials with exponential weights

We consider random orthonormal polynomialsPₙ(x) = ₙ∑ᵢ=₀ ξᵢpᵢ(x),where ξ₀, . . . , ξ₀ are independent random variables with zero mean, unit variance and uniformly bounded (2+ε₀)-moments, and {pn}∞ₙ=₀ is the system of orthonormal polynomials with respect to a general exponential weight W on the real line. This class of orthogonal polynomials includes the popular Hermite and Freud polynomials. We establish universality for the leading asymptotics of the expected number of real roots of Pₙ, both globally and locally. In addition, we find an almost sure limit of the measures counting all roots of Pₙ. This is accomplished by introducing new ideas on applications of the inverse Littlewood-Offord theory in the context of the classical three term recurrence relation for orthogonal polynomials to establish anti-concentration properties, and by adapting the universality methods to the weighted random orthogonal polynomials of the form WPₙ.Mathematic

### Approximation of conformal mapping via the Szegő kernel method

We study the uniform approximation of the canonical conformal mapping, for a Jordan domain onto the unit disk, by polynomials generated from the partial sums of the Szegő kernel expansion. These polynomials converge to the conformal mapping uniformly on the closure of any Smirnov domain. We prove estimates for the rate of such convergence on domains with piecewise analytic boundaries, expressed through the smallest exterior angle at the boundary. Furthermore, we show that the rate of approximation on compact subsets inside the domain is essentially the square of that on the closure. Two standard applications to the rate of decay for the contour orthogonal polynomials inside the domain, and to the rate of locally uniform convergence of Fourier series are also given.Mathematic

### The best keying protocol for sensor networks

Many sensor networks, especially mobile networks or those networks that are deployed to monitor crisis situations, are deployed in an arbitrary and unplanned fashion. Thus, any sensor in such a network may end up being adjacent to any other sensor in the network. To secure the communications between every two adjacent sensors in such a network, each sensor x in the network needs to store n − 1 symmetric keys that x shares with the other sensors, where n is the number of sensors in the network. This storage requirement of the keying protocol is rather severe, especially when n is large and the available storage in each sensor is modest. Earlier efforts to redesign this keying protocol and reduce the number of keys to be stored in each sensor have produced protocols that are vulnerable to collusion. In this paper, we present a collusion-proof keying protocol where each sensor needs to store (n+1)/2 keys, which is much less than the n−1 keys in the original keying protocol. We also show that in any collusion-proof keying protocol, each sensor needs to store at least (n−1)/2 keys.Computer Science

### Heights of polynomials over lemniscates

We consider a family of heights defined by the Lₚ norms of polynomials with respect to the equilibrium measure of a lemniscate for 0 ≤ p ≤ ∞, where p = 0 corresponds to the geometric mean (the generalized Mahler measure) and p = ∞ corresponds to the standard supremum norm. This special choice of the measure allows to find an explicit form for the geometric mean of a polynomial, and estimate it via certain resultant. For lemniscates satisfying appropriate hypotheses, we establish explicit polynomials of lowest height, and also show their uniqueness. We discuss relations between the standard results on the Mahler measure and their analogues for lemniscates that include generalizations of Kronecker’s theorem on algebraic integers in the unit disk, as well as of Lehmer’s conjecture.Mathematic

### Central Limit Theorem for the number of real roots of random orthogonal polynomials

In this note we study the number of real roots of a wide class of random orthogonal polynomials with gaussian coefficients. Using the method of Wiener Chaos we show that the fluctuation in the bulk is asymptotically gaussian, even when the local correlations are different.Mathematic