Since Beck, Katz, and Tucker (1998), the standard method for modeling time dependence in binary data has been to incorporate time dummies or splined time in logistic regressions. Although we agree with the need for modeling time dependence, we demonstrate that time dummies can induce estimation problems due to separation. Splines do not suffer from these problems. However, the complexity of spl...

In this paper, we study the Empirical Risk Minimization problem in the non-interactive local model of differential privacy. We first show that if the ERM loss function is (∞, T )-smooth, then we can avoid a dependence of the sample complexity, to achieve error α, on the exponential of the dimensionality p with base 1/α (i.e., α−p), which answers a question in (Smith et al., 2017). Our approach ...

In this paper, we discuss the sensitivity analysis of model response when uncertain inputs are not independent one other. case, two different kinds indices can be evaluated: (i) that account for dependence/correlation an input or group with remainder and (ii) do dependence. We argue distinction applies to any global measure. present work, focus on estimation variance-based which based second-or...

We consider the linear elliptic equation −div(a∇u) = f on some bounded domain D, where a has the form a = exp(b) with b a random function defined as b(y) = ∑ j≥1 yjψj where y = (yj) ∈ RN are i.i.d. standard scalar Gaussian variables and (ψj)j≥1 is a given sequence of functions in L∞(D). We study the summability properties of Hermite-type expansions of the solution map y 7→ u(y) ∈ V := H 0 (D), ...

the wiener index is a graph invariant that has found extensive application in chemistry. inaddition to that a generating function, which was called the wiener polynomial, who’sderivate is a q-analog of the wiener index was defined. in an article, sagan, yeh and zhang in[the wiener polynomial of a graph, int. j. quantun chem., 60 (1996), 959969] attainedwhat graph operations do to the wiener po...

We introduce and compute a 2-parameter family deformation of the Apolynomial that encodes the color dependence of the superpolynomial and that, in suitable limits, reduces to various deformations of the A-polynomial studied in the literature. These special limits include the t-deformation which leads to the “refined A-polynomial” introduced in the previous work of the authors and the Q-deformat...

Ionic polymer-metal composites (IPMCs) exhibit humidity-dependent sensing behavior when operating in air, which weakens the reliability of the IPMC sensors. To better understand the underlying physics of this behavior and capture the humiditydependence analytically, in this paper the influence of the ambient humidity on IPMC sensors is characterized and modeled from a physical perspective. In p...

Using the Sigma Plot program, using available experimental data on heat capacity of scandium, yttrium, praseodymium, cerium, neodymium, lanthanum, and europium, equations temperature dependence specific molar were established. The optimal degrees for in these determined Fisher statistical criterion. It is revealed that general form metals a four-term polynomial C (T) = + b T c T2 d T3.

Motivated by the application of Lyapunov methods to partial differential equations (PDEs), we study functional inequalities form f(I1(u), . ., Ik(u)) ? 0 where f is a polynomial, u any function satisfying prescribed constraints, and I1(u), .,Ik(u) are integral functionals whose integrands polynomial in u, its derivatives, integration variable. We show that such can be strengthened into sufficie...