Knowledge Structures and Evidential Reasoning in Decision Analysis

The roles played by decision factors in making complex subject are decisions are characterized by how these factors affect the overall decision. Evidence that partially matches a factor is evaluated, and then effective computational rules are applied to these roles to form an appropriate aggregation of the evidence. The use of this technique supports the expression of deeper levels of causality, and may also preserve the cognitive structure of the decision maker better than the usual weighting methods, certainty-factor or other probabilistic models can.Comment: Appears in Proceedings of the First Conference on Uncertainty in Artificial Intelligence (UAI1985

Cram\'{e}r Type Moderate Deviation for the Maximum of the Periodogram with Application to Simultaneous Tests in Gene Expression Time Series

In this paper, Cram\'{e}r type moderate deviations for the maximum of the periodogram and its studentized version are derived. The results are then applied to a simultaneous testing problem in gene expression time series. It is shown that the level of the simultaneous tests is accurate provided that the number of genes $G$ and the sample size $n$ satisfy $G=\exp(o(n^{1/3}))$.Comment: Some constants in Lemma 4.1 are specified. Other context remains the sam

Localization Guided Learning for Pedestrian Attribute Recognition

Pedestrian attribute recognition has attracted many attentions due to its wide applications in scene understanding and person analysis from surveillance videos. Existing methods try to use additional pose, part or viewpoint information to complement the global feature representation for attribute classification. However, these methods face difficulties in localizing the areas corresponding to different attributes. To address this problem, we propose a novel Localization Guided Network which assigns attribute-specific weights to local features based on the affinity between proposals pre-extracted proposals and attribute locations. The advantage of our model is that our local features are learned automatically for each attribute and emphasized by the interaction with global features. We demonstrate the effectiveness of our Localization Guided Network on two pedestrian attribute benchmarks (PA-100K and RAP). Our result surpasses the previous state-of-the-art in all five metrics on both datasets.Comment: Accepted by BMVC 201

HCLAE: High Capacity Locally Aggregating Encodings for Approximate Nearest Neighbor Search

Vector quantization-based approaches are successful to solve Approximate Nearest Neighbor (ANN) problems which are critical to many applications. The idea is to generate effective encodings to allow fast distance approximation. We propose quantization-based methods should partition the data space finely and exhibit locality of the dataset to allow efficient non-exhaustive search. In this paper, we introduce the concept of High Capacity Locality Aggregating Encodings (HCLAE) to this end, and propose Dictionary Annealing (DA) to learn HCLAE by a simulated annealing procedure. The quantization error is lower than other state-of-the-art. The algorithms of DA can be easily extended to an online learning scheme, allowing effective handle of large scale data. Further, we propose Aggregating-Tree (A-Tree), a non-exhaustive search method using HCLAE to perform efficient ANN-Search. A-Tree achieves magnitudes of speed-up on ANN-Search tasks, compared to the state-of-the-art

Classifications and canonical forms of tensor product expressions in the presence of permutation symmetries

Complicated mathematical equations involving products of tensors with permutation symmetries, frequently encountered in fields such as general relativity and quantum chemistry (e.g., equations in high-order coupled cluster theories), require computer-based automatic derivations and manipulations. In these processes, a key step is the collection of tensor product terms that can be found identical by utilizing permutation symmetries of tensors or relabeling dummy indices, which is usually achieved by defining a canonical form for tensor product expressions. However, the problem of finding a canonical form is nontrivial, and can be potentially of exponential cost in the number of indices. In this work, we provided a general solution to this tensor canonicalization problem.Comment: 17 pages, 7 figure

Extended thermodynamics and microstructures of four-dimensional charged Gauss-Bonnet black hole in AdS space

The discovery of new four-dimensional black hole solutions presents a new approach to understand the Gauss-Bonnet gravity in low dimensions. In this paper, we test the Gauss-Bonnet gravity by studying the phase transition and microstructures for the four-dimensional charged AdS black hole. In the extended phase space, where the cosmological constant and the Gauss-Bonnet coupling parameter are treated as thermodynamic variables, we find that the thermodynamic first law and the corresponding Smarr formula are satisfied. Both in the canonical ensemble and grand canonical ensemble, we observe the small-large black hole phase transition, which is similar to the case of the van der Walls fluid. This phase transition can also appear in the neutral black hole system. Furthermore, we construct the Ruppeiner geometry, and find that besides the attractive interaction, the repulsive interaction can also dominate among the microstructures for the small black hole with high temperature in a charged or neutral black hole system. This is quite different from the five-dimensional neutral black hole, for which only dominant attractive interaction can be found. The critical behaviors of the normalized scalar curvature are also examined. These results will shed new light into the characteristic property of four-dimensional Gauss-Bonnet gravity.Comment: 17 pages, 9 figures, and 2 tables, references added. Accepted for publication in PR

Equatorial and quasi-equatorial gravitational lensing by Kerr black hole pierced by a cosmic string

In the present paper, we study numerically the equatorial lensing and quasiequatorial lensing by Kerr black hole pierced by a cosmic string in the strong deflection limit. We calculate the strong deflection limit coefficients and the deflection angle, which are found to depend closely on the cosmic string parameter $\beta$ and dimensionless spin $a_{*}$. The magnification and positions of relativistic images are also computed in the strong deflection limit and a two-dimensional lens equation is derived. The most important and outstanding effect is that the caustics drift away from the optical axis and shift in the clockwise direction with respect to the Kerr black hole. For fixed $a_{*}$ of the black hole, the caustics drift farther away from the optical axis for a large value of $\beta$. And for fixed $\beta$, they drift farther for high $a_{*}$. We also obtain the intersections of the critical curves with the equatorial plane, which decrease with $a_{*}$ and $\beta$. In particular, we obtain a quantity $\bar{\mu}_{k+1}/\bar{\mu}_{k}$, which is independent of the black hole spin and mass. Thus, through measuring it, one is allowed to determine the value of $\beta$ from astronomical observations.Comment: 29 pages, 9 figure

Clapeyron equations and fitting formula of the coexistence curve in the extended phase space of charged AdS black holes

In this paper, we first review the equal area laws and Clapeyron equations in the extended phase space of the charged anti-de Sitter black holes. With different fixed parameters, the Maxwell's equal area law holds not only in the pressure-thermodynamic volume oscillatory line, but also in the charge-electric potential and temperature-entropy oscillatory lines. The conventional Clapeyron equation is generalized and two extra equations are found. Moreover, we show that the coexistence curve of the small and large charged black holes is charge independent in the reduced parameter space for any dimension of spacetime. The highly accurate fitting formula for the coexistence curve is also presented. Using this fitting formula of the coexistence curve, we find that the Clapeyron equations are highly consistent with the calculated values. The fitting formula is also very useful for further study on the thermodynamic property of the system varying along the coexistence curve.Comment: 13 pages, 7 figures, 2 tables. The coexistence curves are refitted, and the figures and tables are changed accordingly. Accepted for publication in PR

Implementing black hole as efficient power plant

Treating the black hole molecules as working substance and considering its phase structure, we study the black hole heat engine by a charged anti-de Sitter black hole. In the reduced temperature-entropy chart, it is found that the work, heat, and efficiency of the engine are free of the black hole charge. Applying the Rankine cycle with or without a back pressure mechanism to the black hole heat engine, the compact formula for the efficiency is obtained. And the heat, work and efficiency are worked out. The result shows that the black hole engine working along the Rankine cycle with a back pressure mechanism has a higher efficiency. This provides a novel and efficient mechanism to produce the useful mechanical work, and such black hole heat engine may act as a possible energy source for the high energy astrophysical phenomena near the black hole.Comment: 17 pages, 6 figures, and 2 table

Area Spectrum of the Large AdS Black Hole from Quasinormal Modes

Using the new physical interpretation of quasinormal modes proposed by Maggiore, we calculate the area and entropy spectra for the 3-dimensioal and 5-dimensional large AdS black holes. The spectra are obtained by imposing the Bohr-Sommerfeld quantization condition to the adiabatic invariant quantity. With this semiclassical method, we find that the spacings of the area and entropy spectra are equidistant and independent of the AdS radius of the black hole for both the cases. However, the spacings of the spectra are not the same for different dimension of space-time. The equidistant area spectra will be broken when the black hole has other parameters (i.e., charge and angular momentum) or in a non-Einstein's gravity theory.Comment: 10 pages, no figure