Parameter estimation by implicit sampling

Implicit sampling is a weighted sampling method that is used in data assimilation, where one sequentially updates estimates of the state of a stochastic model based on a stream of noisy or incomplete data. Here we describe how to use implicit sampling in parameter estimation problems, where the goal is to find parameters of a numerical model, e.g.~a partial differential equation (PDE), such that the output of the numerical model is compatible with (noisy) data. We use the Bayesian approach to parameter estimation, in which a posterior probability density describes the probability of the parameter conditioned on data and compute an empirical estimate of this posterior with implicit sampling. Our approach generates independent samples, so that some of the practical difficulties one encounters with Markov Chain Monte Carlo methods, e.g.~burn-in time or correlations among dependent samples, are avoided. We describe a new implementation of implicit sampling for parameter estimation problems that makes use of multiple grids (coarse to fine) and BFGS optimization coupled to adjoint equations for the required gradient calculations. The implementation is "dimension independent", in the sense that a well-defined finite dimensional subspace is sampled as the mesh used for discretization of the PDE is refined. We illustrate the algorithm with an example where we estimate a diffusion coefficient in an elliptic equation from sparse and noisy pressure measurements. In the example, dimension\slash mesh-independence is achieved via Karhunen-Lo\`{e}ve expansions

Weighted ancestors in suffix trees

The classical, ubiquitous, predecessor problem is to construct a data structure for a set of integers that supports fast predecessor queries. Its generalization to weighted trees, a.k.a. the weighted ancestor problem, has been extensively explored and successfully reduced to the predecessor problem. It is known that any solution for both problems with an input set from a polynomially bounded universe that preprocesses a weighted tree in O(n polylog(n)) space requires \Omega(loglogn) query time. Perhaps the most important and frequent application of the weighted ancestors problem is for suffix trees. It has been a long-standing open question whether the weighted ancestors problem has better bounds for suffix trees. We answer this question positively: we show that a suffix tree built for a text w[1..n] can be preprocessed using O(n) extra space, so that queries can be answered in O(1) time. Thus we improve the running times of several applications. Our improvement is based on a number of data structure tools and a periodicity-based insight into the combinatorial structure of a suffix tree.Comment: 27 pages, LNCS format. A condensed version will appear in ESA 201

Transient Analysis for Music and Moving Images: Consideration for Television Advertising

In audiovisual composition, coupling montage moving images with music is common practice. Interpretation of the effect on an audioviewer's consequent interpretation of the composition is discursive and unquantified. Meth-odology for evaluating the audiovisual multimodal inter-activity is proposed, developing an analysis procedure via the study of modality interdependent transient structures, explained as forming the foundation of perception via the concept of Basic Exposure response to the stimulus. The research has implications for analysis of all audiovisual media, with practical implications in television advertis-ing as a discrete typology of target driven audiovisual presentation. Examples from contemporary advertising are used to explore typical transient interaction patterns and the consequences of which are discussed from the practical viewpoint of the audiovisual composer

An implicit tax rate for non-financial corporations: Definition and comparison with other tax indicators

This paper develops a macroeconomic implicit tax rate for non-financial corporations based on national accounts data. This indicator is compared with a more micro-oriented implicit tax rate based on accounting data collected in the BACH database (Bank for the Accounts of Companies Harmonised) of the European Commission and the all-in top statutory corporate tax rate.European Union, Implicit tax rates, Backward-looking tax indicators, International comparative analysis, Corporate Taxation

Planning Curricular Proposals on Sound and Music with Prospective Secondary-School Teachers

Sound is a preferred context to build foundations on wave phenomena, one of the most important disciplinary referents in physics. It is also one of the best-set frameworks to achieve transversality, overcoming scholastic level and activating emotional aspects which are naturally connected with every day life, as well as with music and perception. Looking at sound and music by a transversal perspective - a border-line approach between science and art, is the adopted statement for a teaching proposal using meta-cognition as a strategy in scientific education. This work analyzes curricular proposals on musical acoustics, planned by prospective secondary-school teachers in the framework of a Formative Intervention Module answering the expectation of making more effective teaching scientific subjects by improving creative capabilities, as well as leading to build logical and scientific categorizations able to consciously discipline artistic activity in music students. With this aim, a particular emphasis is given to those concepts - like sound parameters and structural elements of a musical piece, which are best fitted to be addressed on a transversal perspective, involving simultaneously physics, psychophysics and music.Comment: 12 pages with 5 figures. Submitted for publication in Physics Curriculum Design, Development and Validation - GIREP 2008 book of selected papers, 200

Optimal Hierarchical Layouts for Cache-Oblivious Search Trees

This paper proposes a general framework for generating cache-oblivious layouts for binary search trees. A cache-oblivious layout attempts to minimize cache misses on any hierarchical memory, independent of the number of memory levels and attributes at each level such as cache size, line size, and replacement policy. Recursively partitioning a tree into contiguous subtrees and prescribing an ordering amongst the subtrees, Hierarchical Layouts generalize many commonly used layouts for trees such as in-order, pre-order and breadth-first. They also generalize the various flavors of the van Emde Boas layout, which have previously been used as cache-oblivious layouts. Hierarchical Layouts thus unify all previous attempts at deriving layouts for search trees. The paper then derives a new locality measure (the Weighted Edge Product) that mimics the probability of cache misses at multiple levels, and shows that layouts that reduce this measure perform better. We analyze the various degrees of freedom in the construction of Hierarchical Layouts, and investigate the relative effect of each of these decisions in the construction of cache-oblivious layouts. Optimizing the Weighted Edge Product for complete binary search trees, we introduce the MinWEP layout, and show that it outperforms previously used cache-oblivious layouts by almost 20%.Comment: Extended version with proofs added to the appendi