1 Supplemental Material 1: Fitting Algorithm The estimation algorithm for the general model is a two-step (EM) iterative procedure to find the maximum of the likelihood of the observed data. The estimation algorithm iteratively computes (E-step) and maximizes (M-step) the expected likelihood of the complete data conditional on the observed data. The joint log-likelihood is l(α,β, σ ε , σ 2 s , ...

This paper develops two new algorithms for solving a finite constraint satisfaction problem (FCSP) in parallel. In particular, we give a parallel algorithm for the EREW PRAM model and a distributed algorithm for networks of interconnected processors. I f an FCSP can be represented b y an acyclic constraint network of sire n with width bounded b y a constant then (1) the parallel algorithm takes...

Let Y be a convex set inRk defined by polynomial inequalities and equations of degree at most d ≥ 2 with integer coefficients of binary length at most l. We show that if the set of optimal solutions of the integer programming problem min{yk | y = (y1, . . . , yk) ∈ Y ∩Zk} is not empty, then the problem has an optimal solution y∗ ∈ Y ∩Zk of binary length ld O(k ). For fixed k, our bound implies ...

The focus of this paper is on a parallel algorithm for solving the transport equations in a slab geometry using multigrid. The spatial discretization scheme used is a nite element method called Modiied Linear Discontinuous scheme (MLD). The MLD scheme represents a lumped version of the standard Linear Discontinuous scheme (LD). The parallel algorithm was implemented on the Connection Machine 2 ...

Neuropeptide Y (NPY) is an inhibitory neuromodulator expressed abundantly in the central nervous system that is suspected of being an endogenous antiepileptic agent that can control propagation of limbic seizures. Electrophysiological and pharmacological data suggest that these actions of NPY are mediated by G protein-coupled NPY Y2 and NPY Y5 receptors. To determine whether the NPY Y5 receptor...

Variable selection for sparse linear regression is the problem of finding, given anm×pmatrixB and a target vector y, a sparse vector x such thatBx approximately equals y. Assuming a standard complexity hypothesis, we show that no polynomial-time algorithm can find a k′-sparse x with ||Bx − y|| ≤ h(m, p), where k′ = k ·2log p and h(m, p) ≤ pC1m1−C2 , where δ > 0, C1 > 0, C2 > 0 are arbitrary. Th...

An integer-valued function f on the set 2V of all subsets of a finite set V is a connectivity function if it satisfies the following conditions: (1) f(X) + f(Y ) ≥ f(X ∩Y )+ f(X ∪Y ) for all subsets X, Y of V , (2) f(X) = f(V \X) for all X ⊆ V , and (3) f(∅) = 0. Branch-width is defined for graphs, matroids, and more generally, connectivity functions. We show that for each constant k, there is ...

In this paper, we analyze the statistical properties of a randomized binary search algorithm and its variants. The basic discrete version of the problem is as follows. Suppose there are total m items, numbered 1, 2, ..., m, out of which the first k items are marked, where k is unknown. The objective is to choose one of the marked items uniformly at random. In each step of the basic algorithm, a...

Approximating the length of the longest increasing sequence (LIS) of an array is a well-studied problem. We study this problem in the data stream model, where the algorithm is allowed to make a single left-to-right pass through the array and the key resource to be minimized is the amount of additional memory used. We present an algorithm which, for any δ > 0, given streaming access to an array ...