Here, μ represents the overall mean, βi is the deviation of respondent i from the overall mean, and εij is the deviation of i-th respondent’s reported value from his true value, μ+ βi, on occasion j. βi and εij are independent normal with mean 0 and variance σ β and σ , respectively. The intraclass correlation coefficient (ICC) ρ is calculated as share of between-class variability σ β in total ...

For Σ a compact subset of C symmetric with respect to conjugation and f : Σ → C a continuous function, we obtain sharp conditions on f and Σ that insure that f can be approximated uniformly on Σ by polynomials with nonnegative coefficients. For X a real Banach space, K ⊆ X a closed but not necessarily normal cone with K −K = X, and A : X → X a bounded linear operator with A[K] ⊆ K, we use these...

Let N = H/Γ be a hyperbolic 3-manifold with free fundamental group π1(N) ∼= Γ ∼= 〈A,B〉, such that [A,B] is parabolic. We show that the limit set Λ of N is always locally connected. More precisely, let Σ be a compact surface of genus 1 with a single boundary component, equipped with the Fuchsian action of π1(Σ) on the circle S ∞ . We show that for any homotopy equivalence f : Σ → N , there is a ...

A methodology for the design of Continuous-Time (CT) Sigma-Delta (Σ∆) modulators with VCO-based quantizer is proposed. The coefficients of the CT Σ∆ modulator are accurately calculated such that the noise transfer function of the modulator is exactly the same as a Discrete-Time (DT) Σ∆ modulator of the same order. Several design examples for different modulator orders and feedback DAC signal sh...

Suppose that Q is a positive defined n×n matrix, and Q[x̲]=x̲TQx̲ with x̲∈Zn. The Epstein zeta-function ζ(s;Q), s=σ+it, defined, for σ>n2, by the series ζ(s;Q)=∑x̲∈Zn∖{0̲}(Q[x̲])−s, it has meromorphic continuation to whole complex plane. Let n⩾4 be even, while φ(t) an increasing differentiable function continuous monotonic bounded derivative φ′(t) such φ(2t)(φ′(t))−1≪t, sequence {aφ(k)} uniformly d...

This paper presents a mixed equation-based and simulation-based design methodology for continuous-time Sigma-Delta modulators from high level specifications down to Layout. The calculation and scaling of the SigmaDelta coefficients as well as circuit sizing and layout generation are implemented in the same analog design environment CAIRO+. The design of a complete third order current-mode conti...

The design of Continuous-Time (CT) Sigma-Delta modulator obtained by a discrete-time prototype is discussed. A proper heuristic transformation of the prototype enables an exact equivalence of CT and DT. This permits the trimming by computer simulations of the coefficients of the CT to account for the effect of real analog blocks. Simulation results for a second and third order scheme with real ...

A methodology for the simulation of continuous time sigma-delta (Σ∆) converters is presented in this paper. This method permits the simulation of Σ∆ modulators employing continuous-time filters using a fixed-step algorithm. The analysis method is based on the discretization of a continuous-time model and using a discrete simulator, which is more efficient than an analog simulator. In our analys...

In this article we consider Wigner matrices (XN)N∈N with variance profiles which are of the form XN(i,j)=σ(i∕N,j∕N)ai,j∕ N where σ is a symmetric real positive function [0,1]2, either continuous or piecewise constant and ai,j independent, centered one above diagonal. We prove large deviation principle for largest eigenvalue those under condition that they have sharp sub-Gaussian tails some addi...