<Emphasis Type="Italic">K</Emphasis>-Optimal Rule Discovery

K-optimal rule discovery finds the K rules that optimize a user-specified measure of rule value with respect to a set of sample data and user-specified constraints. This approach avoids many limitations of the frequent itemset approach of association rule discovery. This paper presents a scalable algorithm applicable to a wide range of K-optimal rule discovery tasks and demonstrates its efficiency.     

Sparse Support Vector Machine with <Emphasis Type="Italic">L</Emphasis><Subscript><Emphasis Type="Italic">p</Emphasis></Subscript> Penalty for Feature Selection

We study the strategies in feature selection with sparse support vector machine (SVM). Recently, the socalled L _p -SVM (0 < p < 1) has attracted much attention because it can encourage better sparsity than the widely used L ₁-SVM. However, L _p -SVM is a non-convex and non-Lipschitz optimization problem. Solving this problem numerically is challenging. In this paper, we reformulate the L _p -SVM into an optimization model with linear objective function and smooth constraints (LOSC-SVM) so that it can be solved by numerical methods for smooth constrained optimization. Our numerical experiments on artificial datasets show that LOSC-SVM (0 < p < 1) can improve the classification performance in both feature selection and classification by choosing a suitable parameter p. We also apply it to some real-life datasets and experimental results show that it is superior to L ₁-SVM.     

On <Emphasis Type="Italic">L</Emphasis>-soft merotopies

The goal of this paper is to focus on the notions of merotopy and also merotopology in the soft universe. First of all, we propose L-soft merotopic (nearness) spaces and L-soft guild. Then, we study binary, contigual, regular merotopic spaces and also relations between them. We show that the category of binary L-soft nearness spaces is bireflective in the category of L-soft nearness spaces. Later, we define L-approach soft merotopological (nearness) spaces by giving several examples. Finally, we define a simpler characterization of L-approach soft grill merotopological space called grill-determined L-approach soft merotopological space. We investigate the categorical structures of these notions such as we prove that the category of grill-determined L-approach soft merotopological spaces is a topological category over the category of L-soft topological spaces. At the end, we define a partial order on the family of all L-approach soft grill merotopologies and show that this family is a completely distributive complete lattice with respect to the defined partial order.     

Adaptive (<Emphasis Type="Italic">k</Emphasis>, <Emphasis Type="Italic">F</Emphasis><Subscript>1</Subscript>) interpolation-based hiding scheme

In 2012, Lee et al. proposed an interpolation technique with neighboring pixels (INP) as the base to conceal secret information in predicted pixels. Their method can effectively predict the pixel between two neighboring pixels. However, the different lengths of secret messages caused great distortion when a large secret message was concealed in the predicted value. Therefore, the proposed scheme applies the center folding strategy to fold the secret message for reducing image distortion. Furthermore, the proposed scheme references the variance of the neighboring pixel to determine the length of the secret message for controlling image quality. The parameter pair (k, F ₁) is used to categorize the variance and determine the size of the secret message hidden in each category. k is the total number of thresholds which computed based on the characteristics of each image for balancing hiding payload and image quality. F ₁ is the length of the secret message for the smoothest area. The experimental results show that the embedding capacity of the proposed method is 1.5 bpp higher than that of existing methods. For the same hiding payload, the image quality of the proposed method is 1.6 dB higher than that of existing methods.     

Corepresentation of a sylow <Emphasis Type="Italic">p</Emphasis>-subgroup of a group <Emphasis Type="Italic">S</Emphasis><Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>

The corepresentation of a Sylow p-subgroup of a symmetric group in the form of generating relations is investigated, and a Sylow subgroup of a group , i.e., an n-fold wreath product of regular cyclic groups of prime order, that is isomorphic to the group of automorphisms of a spherically homogeneous root tree is also studied. Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 27–41, January–February 2009.     

Maximizing bichromatic reverse nearest neighbor for <Emphasis Type="Italic">L</Emphasis><Subscript><Emphasis Type="Italic">p</Emphasis></Subscript>-norm in two- and three-dimensional spaces

Bichromatic reverse nearest neighbor (BRNN) has been extensively studied in spatial database literature. In this paper, we study a related problem called MaxBRNN: find an optimal region that maximizes the size of BRNNs for L _p -norm in two- and three- dimensional spaces. Such a problem has many real-life applications, including the problem of finding a new server point that attracts as many customers as possible by proximity. A straightforward approach is to determine the BRNNs for all possible points that are not feasible since there are a large (or infinite) number of possible points. To the best of our knowledge, there are no existing algorithms which solve MaxBRNN for any L _p -norm space of two- and three-dimensionality. Based on some interesting properties of the problem, we come up with an efficient algorithm called MaxOverlap for to solve this problem. Extensive experiments are conducted to show that our algorithm is efficient.     

Efficient <Emphasis Type="Italic">l</Emphasis><Subscript><Emphasis Type="Italic">q</Emphasis></Subscript> norm based sparse subspace clustering via smooth IRLS and ADMM

Recently, sparse subspace clustering, as a subspace learning technique, has been successfully applied to several computer vision applications, e.g. face clustering and motion segmentation. The main idea of sparse subspace clustering is to learn an effective sparse representation that are used to construct an affinity matrix for spectral clustering. While most of existing sparse subspace clustering algorithms and its extensions seek the forms of convex relaxation, the use of non-convex and non-smooth l _q (0 < q < 1) norm has demonstrated better recovery performance. In this paper we propose an l _q norm based Sparse Subspace Clustering method (lqSSC), which is motivated by the recent work that l _q norm can enhance the sparsity and make better approximation to l ₀ than l ₁. However, the optimization of l _q norm with multiple constraints is much difficult. To solve this non-convex problem, we make use of the Alternating Direction Method of Multipliers (ADMM) for solving the l _q norm optimization, updating the variables in an alternating minimization way. ADMM splits the unconstrained optimization into multiple terms, such that the l _q norm term can be solved via Smooth Iterative Reweighted Least Square (SIRLS), which converges with guarantee. Different from traditional IRLS algorithms, the proposed algorithm is based on gradient descent with adaptive weight, making it well suit for general sparse subspace clustering problem. Experiments on computer vision tasks (synthetic data, face clustering and motion segmentation) demonstrate that the proposed approach achieves considerable improvement of clustering accuracy than the convex based subspace clustering methods.     

An <Emphasis Type="Italic">R</Emphasis> || <Emphasis Type="Italic">C</Emphasis><Subscript>max</Subscript> Quantum Scheduling Algorithm

Grover’s search algorithm can be applied to a wide range of problems; even problems not generally regarded as searching problems, can be reformulated to take advantage of quantum parallelism and entanglement, and lead to algorithms which show a square root speedup over their classical counterparts. In this paper, we discuss a systematic way to formulate such problems and give as an example a quantum scheduling algorithm for an R||C_max problem. R||C_max is representative for a class of scheduling problems whose goal is to find a schedule with the shortest completion time in an unrelated parallel machine environment. Given a deadline, or a range of deadlines, the algorithm presented in this paper allows us to determine if a solution to an R||C_max problem with N jobs and M machines exists, and if so, it provides the schedule. The time complexity of the quantum scheduling algorithm is while the complexity of its classical counterpart is .     

Maximum <Emphasis Type="Italic">k</Emphasis>-Splittable <Emphasis Type="Italic">s</Emphasis>,<Emphasis Type="Italic">t</Emphasis>-Flows

Given a graph with a source and a sink node, the NP-hard maximum k-splittable s,t-flow (M k SF) problem is to find a flow of maximum value from s to t with a flow decomposition using at most k paths. The multicommodity variant of this problem is a natural generalization of disjoint paths and unsplittable flow problems. Constructing a k-splittable flow requires two interdepending decisions. One has to decide on k paths (routing) and on the flow values for the paths (packing). We give efficient algorithms for computing exact and approximate solutions by decoupling the two decisions into a first packing step and a second routing step. Usually the routing is considered before the packing. Our main contributions are as follows: (i) We show that for constant k a polynomial number of packing alternatives containing at least one packing used by an optimal M k SF solution can be constructed in polynomial time. If k is part of the input, we obtain a slightly weaker result. In this case we can guarantee that, for any fixed ε>0, the computed set of alternatives contains a packing used by a (1−ε)-approximate solution. The latter result is based on the observation that (1−ε)-approximate flows only require constantly many different flow values. We believe that this observation is of interest in its own right. (ii) Based on (i), we prove that, for constant k, the M k SF problem can be solved in polynomial time on graphs of bounded treewidth. If k is part of the input, this problem is still NP-hard and we present a polynomial time approximation scheme for it.     

Robust polynomial classifier using <Emphasis Type="Italic">L</Emphasis><Superscript>1</Superscript>-<Emphasis Type="Italic">norm</Emphasis> minimization

In this paper we present a robust polynomial classifier based on L ¹-norm minimization. We do so by reformulating the classifier training process as a linear programming problem. Due to the inherent insensitivity of the L ¹-norm to influential observations, class models obtained via L ¹-norm minimization are much more robust than their counterparts obtained by the classical least squares minimization (L ²-norm). For validation purposes, we apply this method to two recognition problems: character recognition and sign language recognition. Both are examined under different signal to noise ratio (SNR) values of the test data. Results show that L ¹-norm minimization provides superior recognition rates over L ²-norm minimization when the training data contains influential observations especially if the test dataset is noisy.     

Emergence of anti-<Emphasis Type="Italic">F</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) gravity in type-IV bouncing cosmology as due to <Emphasis Type="Italic">M</Emphasis><Subscript>0</Subscript>-brane

Recently, some authors considered the origin of a type-IV singular bounce in modified gravity and obtained the explicit form of F(R) which can produce this type of cosmology. In this paper, we show that during the contracting branch of type-IV bouncing cosmology, the sign of gravity changes, and antigravity emerges. In our model, M0 branes get together and shape a universe, an anti-universe, and a wormhole which connects them. As time passes, this wormhole is dissolved in the universes, F(R) gravity emerges, and the universe expands. When the brane universes become close to each other, the squared energy of their system becomes negative, and some tachyonic states are produced. To remove these states, universes are assumed to be compact, the sign of compacted gravity changes, and anti-F(R) gravity arises, which causes getting away of the universes from each other. In this theory, a Type-IV singularity occurs at t = t _s , which is the time of producing tachyons between expansion and contraction branches.     

Heidegger on technology and <Emphasis Type="Italic">Gelassenheit</Emphasis>: <Emphasis Type="Italic">wabi</Emphasis>-<Emphasis Type="Italic">sabi</Emphasis> and the art of <Emphasis Type="Italic">Verfallenheit</Emphasis>

The question of the contemporary relevance of Heidegger’s reflections on technology to today’s advanced technology is here explored with reference to the notion of “entanglement” towards a review of Heidegger’s understanding of technology and media, including the entertainment industry and modern digital life. Heidegger’s reflections on Gelassenheit have been connected with the aesthetics of the tea ceremony, disputing the material aesthetics of porcelain versus plastic. Here by approaching the art of wabi-sabi as the art of Verfallenheit, I argue that Gelassenheit may be understood in these terms.     

<Emphasis Type="Italic">t</Emphasis>-Private and <Emphasis Type="Italic">t</Emphasis>-Secure Auctions

In most of the auction systems the values of bids are known to the auctioneer. This allows him to manipulate the outcome of the auction. Hence, one might be interested in hiding these values. Some cryptographically secure protocols for electronic auctions have been presented in the last decade. Our work extends these protocols in several ways. On the basis of garbled circuits, i.e., encrypted circuits, we present protocols for sealed-bid auctions that fulfill the following requirements： 1） protocols are information-theoretically t-private for honest but curious parties; 2） the number of bits that can be learned by malicious adversaries is bounded by the output length of the auction; 3） the computational requirements for participating parties are very low： only random bit choices and bitwise computation of the XOR-function are necessary. Note that one can distinguish between the protocol that generates a garbled circuit for an auction and the protocol to evaluate the auction. In this paper we address both problems. We will present a t-private protocol for the construction of a garbled circuit that reaches the lower bound of 2t ＋ 1 parties, and Finally, we address the problem of bid changes in an auction. a more randomness efficient protocol for （t ＋ 1）^2 parties     

Stability Analysis of Networked Control Systems based on <Emphasis Type="Italic">L</Emphasis><Subscript>p</Subscript> Properties

To handle the communication constraint imposed by the serial communication channel in networked control systems (NCSs), we discuss a popular dynamic scheduling protocol called Maximum-Error-First (MEF) protocol. An important parameter in this protocol is the maximum allowable transmission interval (MATI), which indicates the communication cost for the task of control. To take as large MATI as possible under the constraint of guaranteeing stability is one formalization of the design requirement to consume as little communication resources as possible with the control performances ensured. A method to estimate this parameter based on the ? _p norm is suggested in this paper, which gives larger estimation than some methods do in the literature through simulation examples.     

EP<Emphasis Type="Italic">n</Emphasis>P: An Accurate <Emphasis Type="Italic">O</Emphasis>(<Emphasis Type="Italic">n</Emphasis>) Solution to the P<Emphasis Type="Italic">n</Emphasis>P Problem

We propose a non-iterative solution to the PnP problem—the estimation of the pose of a calibrated camera from n 3D-to-2D point correspondences—whose computational complexity grows linearly with n. This is in contrast to state-of-the-art methods that are O(n ⁵) or even O(n ⁸), without being more accurate. Our method is applicable for all n≥4 and handles properly both planar and non-planar configurations. Our central idea is to express the n 3D points as a weighted sum of four virtual control points. The problem then reduces to estimating the coordinates of these control points in the camera referential, which can be done in O(n) time by expressing these coordinates as weighted sum of the eigenvectors of a 12×12 matrix and solving a small constant number of quadratic equations to pick the right weights. Furthermore, if maximal precision is required, the output of the closed-form solution can be used to initialize a Gauss-Newton scheme, which improves accuracy with negligible amount of additional time. The advantages of our method are demonstrated by thorough testing on both synthetic and real-data.     

On the application of the <Emphasis Type="Italic">P</Emphasis><Subscript>1</Subscript><Superscript><Emphasis Type="Italic">mod</Emphasis></Superscript> element to incompressible flow problems

We consider the application of the nonconforming P₁^mod element to the approximation of the velocity in the incompressible Stokes and Navier–Stokes equations. We prove the uniform validity of an inf–sup condition if the pressure is approximated by piecewise constant functions. Under additional assumptions, we also prove the inf–sup condition for discontinuous piecewise linear approximations of the pressure. Numerical results show that the P₁^mod element allows to obtain significantly better approximations of the velocity than the Crouzeix–Raviart element.     

States on <Emphasis Type="Italic">R</Emphasis><Subscript>0</Subscript> algebras

The aim of this paper is to introduce the notion of states on R ₀ algebras and investigate some of their properties. We prove that every R ₀ algebra possesses at least one state. Moreover, we investigate states on weak R ₀ algebras and give some examples to show that, in contrast to R ₀ algebras, there exist weak R ₀ algebras which have no states. We also derive the condition under which finite linearly ordered weak R ₀ algebras have a state. This work is supported by NSFC (No.60605017).     

Intuitionistic (<Emphasis Type="Italic">S</Emphasis>, <Emphasis Type="Italic">T</Emphasis>)-fuzzy hyperquasigroups

The concept of intuitionistic fuzzy subhyperquasigroups in a hyperquasigroup with respect to an s-norm and a t-norm on intuitionistic fuzzy sets is introduced and their properties of such hyperquasigroups are studied. Intuitionistic (S, T)-fuzzy relations on a hyperquasigroup G are discussed. In particular, we investigate connections hyperquasigroups with binary quasigroups.     

On a topological universe of <Emphasis Type="Italic">L</Emphasis>-bornological spaces

This paper shows that given a certain frame L, the construct of strict L-bornological spaces, introduced by Abel and ?ostak, is a topological universe.     

The <Emphasis Type="Italic">MAP</Emphasis> + <Emphasis Type="Italic">MAP/PH</Emphasis>/1/<Emphasis Type="Italic">N</Emphasis> queuing system with single and batch arrivals of customers

The single-server queuing system with finite buffer was considered. The customers may arrive one-by-one or in batches. Arrivals of single customers and their batches obey the Markov input processes. The customers from a batch taken for servicing come one at a time at the exponentially distributed time intervals. The numbers of customers in batches are distributed geometrically. The time of customer servicing has a phase-type distribution. The numbers of batches and single customers that may be simultaneously accepted by the system are controllable parameters. The joint distribution of the number of batches and the number of customers in system, loss probabilities, distribution of the time of batch sojourn, and problems of optimization were analyzed.