Disassociated indiscernibles

This work addresses a basic question by Kunen: how many normal measures can there be on the least measurable cardinal? Starting with a measurable cardinal κ of Mitchell order less than two () we define a Prikry type forcing which turns the number of normal measures over κ to any while making κ the first measurable.     

Vertices of given degree in series‐parallel graphs

We show that the numbers of vertices of a given degree k ≥ 1 in several kinds of series‐parallel labeled graphs of size n satisfy a central limit theorem with mean and variance proportional to n, and quadratic exponential tail estimates. We further prove a corresponding theorem for the number of nodes of degree two in labeled planar graphs. The proof method is based on generating functions and singularity analysis. In particular, we need systems of equations for multivariate generating functions and transfer results for singular representations of analytic functions. © 2009 Wiley Periodicals, Inc. Random Struct. Alg., 2010     

A search method for optimal control of a flow shop system of traditional machines

We consider a convex and nondifferentiable optimization problem for deterministic flow shop systems in which the arrival times of the jobs are known and jobs are processed in the order they arrive. The decision variables are the service times that are to be set only once before processing the first job, and cannot be altered between processes. The cost objective is the sum of regular costs on job completion times and service costs inversely proportional to the controllable service times. A finite set of subproblems, which can be solved by trust-region methods, are defined and their solutions are related to the optimal solution of the optimization problem under consideration. Exploiting these relationships, we introduce a two-phase search method which converges in a finite number of iterations. A numerical study is held to demonstrate the solution performance of the search method compared to a subgradient method proposed in earlier work.     

Polynomial bounds for Large Bernoulli sections of ℓ 1 N

We present a quantitative form of the result of Bai and Yin from [2], and use to show that the section of ℓ ₁ ^(1+δ)n spanned byn random independent sign vectors is with high probability isomorphic to euclidean with isomorphism constant polynomial in δ⁻¹. Partially supported by BSF grant 2002-006. Supported by the National Science Foundation under agreement No. DMS-0111298. Supported in part by the Israel Science Academy.     

On representations distinguished by unitary groups

Let E/F be a quadratic extension of number fields. We study periods and regularized periods of cusp forms and Eisenstein series on $\operatorname {GL}_{n}( \mathbf {A}_{E})$ over a unitary group of a Hermitian form with respect to E/F. We provide factorization for these periods into locally defined functionals, express these factors in terms of suitably defined local periods and characterize global distinction. We also study in detail the analogous local question and analyze the space of invariant linear forms under a unitary group.     

Global divergence of spatial coalescents

We study several fundamental properties of a class of stochastic processes called spatial Λ-coalescents. In these models, a number of particles perform independent random walks on some underlying graph G. In addition, particles on the same vertex merge randomly according to a given coalescing mechanism. A remarkable property of mean-field coalescent processes is that they may come down from infinity, meaning that, starting with an infinite number of particles, only a finite number remains after any positive amount of time, almost surely. We show here however that, in the spatial setting, on any infinite and bounded-degree graph, the total number of particles will always remain infinite at all times, almost surely. Moreover, if ${G\,=\,\mathbb{Z}^d}$ , and the coalescing mechanism is Kingman’s coalescent, then starting with N particles at the origin, the total number of particles remaining is of order (log* N) ^d at any fixed positive time (where log* is the inverse tower function). At sufficiently large times the total number of particles is of order (log* N) ^d-2, when d?>?2. We provide parallel results in the recurrent case d?=?2. The spatial Beta-coalescents behave similarly, where log log N is replacing log* N.     

Assessing the Impact of Bridging Analogies in Mechanics

The effects of bridging analogies teaching strategy and gender on Turkish high school students' misconceptions in mechanics were investigated. After a pilot study with 67 students in a nearby high school, the researchers administered the revised Mechanics Misconception Test to 119 high school students as a pretest. Students in the experimental group were instructed by using bridging analogies teaching strategy. At the end of a 3‐week treatment period, the same test was administered to all students as a posttest. The data were analyzed by using analysis of covariance (ANCOVA). The statistical results showed that bridging analogies teaching strategy was an effective means of reducing the number of misconceptions students held about normal forces, frictional forces, tension, gravity, inertia, and Newton's third law.     

Random walks on stochastic hyperbolic half planar triangulations

We study the simple random walk on stochastic hyperbolic half planar triangulations constructed in (Angel and Ray, Ann Probab, in press). We show that almost surely the walker escapes the boundary of the map in positive speed and that the return probability to the starting point after n steps scales like © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 49, 213–234, 2016     

Order restricted randomized designs for control versus treatment comparison

We develop a method of randomizing units to treatments that relies on subjective judgement or on possible coarse modeling to produce restrictions on the randomization. The procedure thus fits within the general framework of ranked set sampling. However, instead of selecting a single unit from each set for full measurement, all units within a set are used. The units within a set are assigned to different treatments. Such an assignment translates the positive dependence among units within a set into a reduction in variation of contrasting features of the treatments. A test for treatment versus control comparison, with controlled familywise error rate, is developed along with the associated confidence intervals. The new procedure is shown to be superior to corresponding procedures based on completely randomized or ranked set sample designs. The superiority appears both in asymptotic relative efficiency and in power for finite sample sizes. Importantly, this test does not rely on perfect rankings; rather, the information in the data on the quality of rankings is exploited to maintain the level of the test when rankings are imperfect. The asymptotic relative efficiency of the test is not affected by estimation of the quality of rankings, and the finite sample performance is only mildly affected.