Diversifying Top-K Results

Top-k query processing finds a list of k results that have largest scores w.r.t the user given query, with the assumption that all the k results are independent to each other. In practice, some of the top-k results returned can be very similar to each other. As a result some of the top-k results returned are redundant. In the literature, diversified top-k search has been studied to return k results that take both score and diversity into consideration. Most existing solutions on diversified top-k search assume that scores of all the search results are given, and some works solve the diversity problem on a specific problem and can hardly be extended to general cases. In this paper, we study the diversified top-k search problem. We define a general diversified top-k search problem that only considers the similarity of the search results themselves. We propose a framework, such that most existing solutions for top-k query processing can be extended easily to handle diversified top-k search, by simply applying three new functions, a sufficient stop condition sufficient(), a necessary stop condition necessary(), and an algorithm for diversified top-k search on the current set of generated results, div-search-current(). We propose three new algorithms, namely, div-astar, div-dp, and div-cut to solve the div-search-current() problem. div-astar is an A* based algorithm, div-dp is an algorithm that decomposes the results into components which are searched using div-astar independently and combined using dynamic programming. div-cut further decomposes the current set of generated results using cut points and combines the results using sophisticated operations. We conducted extensive performance studies using two real datasets, enwiki and reuters. Our div-cut algorithm finds the optimal solution for diversified top-k search problem in seconds even for k as large as 2,000.Comment: VLDB201

Low Density Nuclear Matter in Heavy Ion Collisions

The symmetry energy is the energy difference between symmetric nuclear matter and pure neutron matter at a given density. Around normal nuclear density, i.e. p/p0 =1, and temperature, i.e. T = 0, the symmetry energy is approximately 23.5 MeV/nucleon for finite nuclear matter and 30 MeV/nucleon for infinite nuclear matter, but at other densities, the symmetry energies are very poorly understood. Since the symmetry energy is very important in understanding many aspects of heavy ion reactions, structure, and nuclear astrophysics, many different models have been developed and some predications of the density dependence of symmetry energy have been made. Intermediate energy heavy ion collisions provide a unique tool to probe the nuclear equation of state. The initial compression and the thermal shock in Fermi- Energy heavy ion collisions lead naturally to the production of nucleonic matter at varying temperatures and densities which are interesting in this context. Since the light particle emission during this stage witnesses each stage of the reaction, it carries essential information on the early dynamics and on the degree of equilibration at each stage of the reaction. The kinematic features and yields of emitted light particles and clusters in the invairant velocity frame have been exploited to probe the nature of the intermediate system and information on the Equation Of State (EOS) with emphasis on the properties of the low density participant matter produced in such collisions. In order to pursue this effort and broaden the density range over which the symmetry energies are experimentally determined we have now carried out a series of experiments in which the reactions of 112Sn and 124Sn with projectiles, ranging from 4He,10B, 20Ne, 40Ar to 64Zn, all at the same energy per nucleon, 47 Mev/u, were performed. In this series of experiments different collision systems should lead to different average densities. By careful comparisons of the yields, spectra and angular distributions observed for particle emission from these different systems we attempted to cleanly separate early emission resulting from nucleon-nucleon collisions from that resulting from evaporation from the thermalized system and obtain a much cleaner picture of the dynamic evolution of the hotter systems. The Albergo Model has been used to calculate the density and temperature, symmetry free energies with the isoscaling technique for systems with different N/Z ratios. Those are compared with Roepke Model results. Also other models like VEOS, Lattimer, and Shen-Toki have been added to calculate the alpha mass fraction in order to understand the properties of low density matter further

A Validation Approach to Over-parameterized Matrix and Image Recovery

In this paper, we study the problem of recovering a low-rank matrix from a number of noisy random linear measurements. We consider the setting where the rank of the ground-truth matrix is unknown a prior and use an overspecified factored representation of the matrix variable, where the global optimal solutions overfit and do not correspond to the underlying ground-truth. We then solve the associated nonconvex problem using gradient descent with small random initialization. We show that as long as the measurement operators satisfy the restricted isometry property (RIP) with its rank parameter scaling with the rank of ground-truth matrix rather than scaling with the overspecified matrix variable, gradient descent iterations are on a particular trajectory towards the ground-truth matrix and achieve nearly information-theoretically optimal recovery when stop appropriately. We then propose an efficient early stopping strategy based on the common hold-out method and show that it detects nearly optimal estimator provably. Moreover, experiments show that the proposed validation approach can also be efficiently used for image restoration with deep image prior which over-parameterizes an image with a deep network.Comment: 29 pages and 9 figure