In today’s lecture, we mainly talked about random walk on graphs and introduce the concept of graph expander, as well as an application of random walk to show its effectiveness. 1 Cheerger’s Inequality Recap Given a d-regular graph with its adjacent matrix A, we define the Laplacian of this graph with adjacent matrix N = I − 1

1. Wave-convection coupling is a well observed, very important, yet relatively simple form of large-scale organization of convection 2. This coupling cannot be studied under the traditional single column framework Results with a CSRM Spontaneous development of coupled waves Precipitation v.s. time for a range of horizontal wavelengths Coupling to wave starts here. Without coupling, the standard deviation is 0.6mm/day Results with parameterizations As in the CSRM experiments, runs below are with fixed radiation and simple bulk formula for surface fluxes (no enhancement from downdrafts induced gustiness). A mean vertical advection however is not imposed.

Morning Session: Introductory Material The morning section will focus on the foundations of subdivision, starting with subdivision curves and moving on to surfaces. We will review and compare a number of different schemes and discuss the relation between subdivision and splines. The emphasis will be on properties of subdivsion most relevant for applications.

A heuristic for improving the regularity of accesses by global loop transformations in the polyhedral model

F8.04> n ; we get the equation 8 < : div (a (x; Du)) = f on #; u 2 W 1;p 0 (#) : (2) Equations of this type model many physical phenomena where the underlying material is heterogeneous, i.e., # consists of a material with dierent properties for dierent positions in #. Because of the dependence of x; the equation (2) is much more dicult to handle than equation (1). In mathematical models of microscopically heterogeneous materials, various local characteristics are usually described by maps of the form a h (x; )=a x " h ; ,wherea (;) is assumed to be periodic and " h is a small parameter. This means that " h is a parameter which varies the frequency of a<

• Believing is not an all-or-nothing matter. Opinions come in varying gradations of strength ranging from full certainty of truth to complete certainty of falsehood. • Gradational belief is governed by the laws of probability, which codify the minimum standards of consistency (or “coherence”) to which rational opinions must confirm. • Learning involves Bayesian conditioning: a person who acquires data D should modify her opinions in such a way that her “posterior ” views about the relative odds of propositions consistent with D agree with her “prior ” views about these relative odds. 2 | • Gradational beliefs are often revealed in decisions. Rational agents choose options they estimate will produce desirable outcomes, and these estimates are a function of their beliefs. You should (determinately) prefer OX to OY if and only if you are more confident of X than of Y. PROBLEMS WITH PRECISE DEGREES OF BELIEF • It is psychologically unrealistic to suppose that people have attitudes that are precise enough to be represented by real numbers. What could c(X) = 1/π mean? • Since evidence is often incomplete, imprecise or equivocal, the right response is often to have beliefs that are incomplete, imprecise or equivocal. A black/white coin is chosen randomly from an urn containing coins of every possible bias < β < . You have no information about the proportions with which coins of various biases appear in the urn. How confident should you be that the coin comes up black when next tossed?

explicit recommendations on the way forward. Laurel Allender, Ph.D., is a research psy-chologist with the U.S. Army Research Lab-oratory (ARL), with interests that include cognitive modeling and temporal cognition, human-robot interaction, and performance on the move. Rene de Pontbriand, Ph.D., serves as associate director for research at the ARL’s Human Research and Engineer-ing Department and chairs the ARL Strate-gic Technology Initiative on Neuroscience.

”The term pack rat is [..] used in English as slang to refer to a person who collects miscellaneous items and has trouble getting rid of them (a compulsive hoarder) [...] ” 1

Abstract. A new approach to query optimization, truly adaptive optimization (TAO), is presented. TAO is a general optimization strategy and is composed of three elements: 1. a fast solution space search algorithm, derived from A*, which uses an informed heuristic lookahead; 2. a relaxation technique which allows to specify a tolerance on the quality of the resulting query execution plan; 3. a paradigm to prove the suboptimality of search subspaces. Non-procedural pruning rules can be used to describe specific problem knowledge, and can be easily added to the optimizer, as the specific problem becomes better understood. The main contribution over previous research is the use of relaxation techniques and that TAO provides a unifying framework for query optimization problems, which models a complexity continuum going from fast heuristic searches to exponential optimal searches while guaranteeing a selected plan quality. In addition, problem knowledge can be exploited to speed the search up. As a preliminary example, the method is applied to query optimization for databases distributed over a broadcast network. Simulation results are reported. 1

We derive a predictor of a random variable in a given position under simple random sampling. The predictor corresponds to the value of the realized subject if the