A hypergraph H = (V, ε) is a pair consisting of a vertex set V, and a set ε of subsets (the hyperedges of H) of V. A hypergraph H is r-uniform if all the hyperedges of H have the same cardinality r. Let H be an r-uniform hypergraph, we generalize the concept of trees for r-uniform hypergraphs. We say that an r-uniform hypergraph H is a generalized hypertree (GHT) if H is disconnected after removing any hyperedge E, and the number of components of GHT − E is a fixed value k (2 ≤ k ≤ r). We focus on the case that GHT − E has exactly two components. An edge-minimal GHT is a GHT whose edge set is minimal with respect to inclusion. After considering these definitions, we show that an r-uniform GHT on n vertices has at least 2n/(r + 1) edges and it has at most n − r + 1 edges if r ≥ 3 and n ≥ 3, and the lower and upper bounds on the edge number are sharp. We then discuss the case that GHT − E has exactly k (2 ≤ k ≤ r − 1) components.
In the past decades, due to the low design cost and easy maintenance, text-based CAPTCHAs have been extensively used in constructing security mechanisms for user authentications. With the recent advances in machine/deep learning in recognizing CAPTCHA images, growing attack methods are presented to break text-based CAPTCHAs. These machine learning/deep learning-based attacks often rely on training models on massive volumes of training data. The poorly constructed CAPTCHA data also leads to low accuracy of attacks. To investigate this issue, we propose a simple, generic, and effective preprocessing approach to filter and enhance the original CAPTCHA data set so as to improve the accuracy of the previous attack methods. In particular, the proposed preprocessing approach consists of a data selector and a data augmentor. The data selector can automatically filter out a training data set with training significance. Meanwhile, the data augmentor uses four different image noises to generate different CAPTCHA images. The well-constructed CAPTCHA data set can better train deep learning models to further improve the accuracy rate. Extensive experiments demonstrate that the accuracy rates of five commonly used attack methods after combining our preprocessing approach are 2.62% to 8.31% higher than those without preprocessing approach. Moreover, we also discuss potential research directions for future work.
A method of operational effectiveness analysis for aerocraft is proposed based on L1 regularized logistic model, for the problem of the operational effectiveness index is not easy to quantify analysis .The operational effectiveness of aerocraft is affected by many factors which relationship are complex, and index is difficult to quantitative analysis, when the aerocraft is in a complex battlefield environment. A set of analysis method and the analysis process for the study of the aerocraft operational effectiveness is provided. It uses machine learning methods to solve the problem of multi factors and complex relationship of operational effectiveness, by converted operational effectiveness sensitivity analysis to feature effectiveness judgment based on category. This method provides an effective method of tactical application for aerocraft penetration to seek the main influence factors from the whole.
Array comparative genomic hybridization (aCGH) and single nucleotide polymorphism (SNP) array data are becoming commonly available for scientists to study genetic mechanisms involved in complex biological processes. Such data typically contain a large number of probes observed repeatedly over time. Due to cost concerns, the number of replicates is often very limited. Effective hypothesis testing tools need to take into account the high dimensionality and small sample sizes. In this paper, we present a set of nonparametric hypothesis testing theory to test for main and interaction effects related to a large number of probes for longitudinal DNA copy number data from aCGH or SNP arrays. The asymptotic distributions of the test statistics are obtained under a realistic model setup that allows distribution-free robust inference in presence of temporal correlations for heteroscedastic high dimensional low sample size data. They provide a flexible tool for a wide range of scientists to accelerate novel gene discovery such as identification of genome regions of aberration to control tumor progression. Simulations and applications of the new methods to DNA copy number aberration from Wilm's tumor relapse study are presented.
This paper describes a problem arising in sea exploration, where the aim is to schedule the expedition of a ship for collecting information about the resources on the seafloor. The aim is to collect data by probing on a set of carefully chosen locations, so that the information available is optimally enriched. This problem has similarities with the orienteering problem, where the aim is to plan a time-limited trip for visiting a set of vertices, collecting a prize at each of them, in such a way that the total value collected is maximum. In our problem, the score at each vertex is associated with an estimation of the level of the resource on the given surface, which is done by regression using Gaussian processes. Hence, there is a correlation among scores on the selected vertices; this is a first difference with respect to the standard orienteering problem. The second difference is the location of each vertex, which in our problem is a freely chosen point on a given surface.
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