On some extremal problems for mutual information and entropy

The problem of determining the maximum mutual information I(X; Y) and minimum entropy H(X, Y) of a pair of discrete random variables X and Y is considered under the condition that the probability distribution of X is fixed and the error probability Pr{Y ≠ X} takes a given value ε, 0 ≤ ε ≤ 1. Precise values for these quantities are found, which in several cases allows us to obtain explicit formulas for both the maximum information and minimum entropy in terms of the probability distribution of X and the parameter ε.     

On Some Optimization Problems for the Rényi Divergence

We consider the problem of determining the maximum and minimum of the Rényi divergence D_λ(P||Q) and D_λ(Q||P) for two probability distribution P and Q of discrete random variables X and Y provided that the probability distribution P and the parameter α of α-coupling between X and Y are fixed, i.e., provided that Pr{X = Y } = α.     

Combinatorial methods for constructing bipartite uniform minimal quasicomplete graphs (symmetrical block designs)

Consideration was given to a specific family of bipartite graphs consisting of two disjoint subsets X and Y of vertices and characterized by that each vertex in X (Y) is connected to each of the remaining vertices in X (Y) by a unique path of length two passing through some vertex in Y (X). The prefix “quasi” reflects the fact that complete connection of the vertices is realized by paths of length two rather than by edges. The problem of constructing uniform minimal graphs with identical cardinalities of the subsets X and Y which is of practical interest for complex communication networks was discussed. It belongs to the class of combinatorial problems of construction of the so-called symmetrical block designs.     

On risk concentration for convex combinations of linear estimators

We consider the estimation problem for an unknown vector β ∈ Rp in a linear model Y = Xβ + σξ, where ξ ∈ Rⁿ is a standard discrete white Gaussian noise and X is a known n × p matrix with n ≥ p. It is assumed that p is large and X is an ill-conditioned matrix. To estimate β in this situation, we use a family of spectral regularizations of the maximum likelihood method β^α(Y) = H ^α(X ^T X) β ^?(Y), α ∈ R⁺, where β ^?(Y) is the maximum likelihood estimate for β and {H ^α(·): R⁺ → [0, 1], α ∈ R⁺} is a given ordered family of functions indexed by a regularization parameter α. The final estimate for β is constructed as a convex combination (in α) of the estimates β^α(Y) with weights chosen based on the observations Y. We present inequalities for large deviations of the norm of the prediction error of this method.     

Abstract Interpolation by Continued Thiele-Type Fractions

We have constructed and substantiated a generalization of continued Thiele-type fractions to the case of interpolation of nonlinear operators acting from a linear topological space X into an algebra Y with unit element I. It is shown that important particular cases of this generalization are interpolation continued Thiele-type fractions for vector-valued and matrix-valued functions and also for functionals of several variables.     

Integrating tourist packages and tourist attractions for personalized trip planning based on travel constraints

In recent years, with the upgrading of mobile positioning and the popularity of smart devices, location related research gets a lot of attentions. One of popular issues is the trip planning problem. Although many related scientific or technical literature have been proposed, most of them focused only on tourist attraction recommendation or arrangement meeting some user demands. In fact, to grasp the huge tourism opportunities, more and more tour operators design tourist packages and provide to users. Generally, tourist packages have many advantages such as cheaper ticket price and higher transportation convenience. However, researches on trip planning combining tourist packages have not been mentioned in the past studies. In this research, we present a new approach named Package-Attraction-based Trip Planner (PAT-Planner) to simultaneously combine tourist packages and tourist attractions for personalized trip planning satisfying users’ travel constraints. In PAT-Planner, we first based on user preferences and temporal characteristics to design a Score Inference Model for respectively measuring the score of a tourist package or tourist attraction. Then, we develop the Hybrid Trip-Mine algorithm meeting user travel constraints for personalized trip planning. Besides, we further propose two improvement strategies, namely Score Estimation and Score Bound Tightening, based on Hybrid Trip-Mine to speed up the trip planning efficiency. As far as we know, our study is the first attempt to simultaneously combine tourist packages and tourist attractions on trip planning problem. Through a series of experimental evaluations and case studies using the collected Gowalla datasets, PAT-Planner demonstrates excellent planning effects.     

Noise Level Estimation in High-Dimensional Linear Models

We consider the problem of estimating the noise level σ² in a Gaussian linear model Y = Xβ+σξ, where ξ ∈ ?ⁿ is a standard discrete white Gaussian noise and β ∈ ?^p an unknown nuisance vector. It is assumed that X is a known ill-conditioned n × p matrix with n ≥ p and with large dimension p. In this situation the vector β is estimated with the help of spectral regularization of the maximum likelihood estimate, and the noise level estimate is computed with the help of adaptive (i.e., data-driven) normalization of the quadratic prediction error. For this estimate, we compute its concentration rate around the pseudo-estimate ||Y ? Xβ||²/n.     

Robust formulation for Reliability-based design optimization of structures

The reliability-based design optimization (RBDO) has been widely recognized as a powerful optimization tool under probabilistic constraints, through appropriate modeling of uncertainties. However, the drawback of RBDO is that it does not reflect the ability of the structure to comply with large data variations, unforeseen actions or deterioration mechanisms. On the other hand, the robust design optimization (RDO) reduces the variability of the structural performance, in addition to its mean level. However, RDO does not take direct advantage of the interaction between controllable (product design values) and noise variables (environmental random values), and the obtained results do not accurately indicate what parameter has the highest effect on the performance characteristics. The purpose of this paper is to propose a robust formulation for reliability-based design optimization (RRBDO) that combines the advantages of both optimization procedures and overcomes their weaknesses. The optimization model proposed overcomes the limitations of the existing models without compromising the reliability level, by considering a robust convex objective function and a performance variation constraint. The proposed formulation can consider the total cost of structures and can control structural parameter variations. It takes into account uncertainty and variability in the same mathematical formulation. A numerical solution procedure is also developed, for which results are analyzed and compared with RBDO for several examples of concrete and steel structures.     

Virtual reality software package for implementing motor learning and rehabilitation experiments

Virtual reality games for rehabilitation are attracting increasing growth. In particular, there is a demand for games that allow therapists to identify an individual’s difficulties and customize the control of variables, such as speed, size, distance, as well as visual and auditory feedback. This study presents and describes a virtual reality software package (Bridge Games) to promote rehabilitation of individuals living with disabilities and highlights preliminary researches of its use for implementing motor learning and rehabilitation. First, the study presents seven games in the software package that can be chosen by the rehabilitation team, considering the patient’s needs. All game characteristics are described including name, function presentation, objective and valuable measurements for rehabilitation. Second, preliminary results illustrate some applications of two games, considering 343 people with various disabilities and health status. Based on the results, in the Coincident Timing game, there was a main effect of movement sensor type (in this instance the most functional device was the keyboard when compared with Kinect and touch screen) on average time reached by sample analyzed, F(2, 225) = 4.42, p < 0.05. Similarly, in the Challenge! game, a main effect was found for movement sensor type. However, in this case, touch screen provided better performance than Kinect and Leap Motion, F(2, 709) = 5.90, p < 0.01. Thus, Bridge Games is a possible software game to quantify motor learning. Moreover, the findings suggest that motor skills might be practiced differently depending on the environmental interface in which the game may be used.     

Advanced methods for the estimation of an unknown projection from a map

This article presents three new methods (M5, M6, M7) for the estimation of an unknown map projection and its parameters. Such an analysis is beneficial and interesting for historic, old, or current maps without information about the map projection; it could improve their georeference. The location similarity approach takes into account the residuals on the corresponding features; the minimum is found using the non-linear least squares. For the shape similarity approach, the minimized objective function ? takes into account the spatial distribution of the features, together with the shapes of the meridians, parallels and other 0D-2D elements. Due to the non-convexity and discontinuity, its global minimum is determined using the global optimization, represented by the differential evolution. The constant values of projection φ _k , λ _k , φ ₁, λ ₀, and map constants R,ΔX,ΔY, α (in relation to which the methods are invariant) are estimated. All methods are compared and the results are presented for the synthetic data as well as for 8 early maps from the Map Collection of the Charles University and the David Rumsay Map Collection. The proposed algorithms have been implemented in the new version of the detectproj software.     

Almost cover-free codes

We say that an s-subset of codewords of a code X is (s, l)-bad if X contains l other codewords such that the conjunction of these l words is covered by the disjunction of the words of the s-subset. Otherwise, an s-subset of codewords of X is said to be (s, l)-bad. A binary code X is called a disjunctive (s, l) cover-free (CF) code if X does not contain (s, l)-bad subsets. We consider a probabilistic generalization of (s, l) CF codes: we say that a binary code is an (s, l) almost cover-free (ACF) code if almost all s-subsets of its codewords are (s, l)-good. The most interesting result is the proof of a lower and an upper bound for the capacity of (s, l) ACF codes; the ratio of these bounds tends as s→∞ to the limit value log₂ e/(le).     

On horizons and wormholes in k-essence theories

We study the properties of possible static, spherically symmetric configurations in k-essence theories with the Lagrangian functions of the form F(X), X ≡ ?,_α ?,^α. A no-go theorem has been proved, claiming that a possible black-hole-like Killing horizon of finite radius cannot exist if the function F(X) is required to have a finite derivative dF/dX. Two exact solutions are obtained for special cases of kessence: one for F(X) = F ₀ X ^1/3, another for F(X) = F ₀|X|^1/2 ? 2Λ, where F ₀ and Λ are constants. Both solutions contain horizons, are not asymptotically flat, and provide illustrations for the obtained nogo theorem. The first solution may be interpreted as describing a black hole in an asymptotically singular space-time, while in the second solution two horizons of infinite area are connected by a wormhole.     

One-Nonterminal Conjunctive Grammars over a Unary Alphabet

Systems of equations of the form X _i =φ _i (X ₁,…,X _n ) (1≤ i ≤ n) are considered, in which the unknowns are sets of natural numbers. Expressions φ _i may contain the operations of union, intersection and elementwise addition \(S+T=\{m+n\mid m\in S\), n∈T}. A system with an EXPTIME-complete least solution is constructed in the paper through a complete arithmetization of EXPTIME-completeness. At the same time, it is established that least solutions of all such systems are in EXPTIME. The general membership problem for these equations is proved to be EXPTIME-complete. Among the consequences of the result is EXPTIME-completeness of the compressed membership problem for conjunctive grammars.     

On conditional diagnosability and reliability of the BC networks

An n-dimensional bijective connection network (in brief, BC network), denoted by X _n , is an n-regular graph with 2 ⁿ nodes and n2 ^n?1 edges. Hypercubes, crossed cubes, twisted cubes, and Möbius cubes all belong to the class of BC networks (Fan and He in Chin. J. Comput. 26(1):84–90, [2003]). We prove that the super connectivity of X _n is 2n?2 for n≥3 and the conditional diagnosability of X _n is 4n?7 for n≥5. As a corollary of this result, we obtain the super connectivity and conditional diagnosability of the hypercubes, twisted cubes, crossed cubes, and Möbius cubes.     

Tracking frequent items over distributed probabilistic data

Tracking frequent items (also called heavy hitters) is one of the most fundamental queries in real-time data due to its wide applications, such as logistics monitoring, association rule based analysis, etc. Recently, with the growing popularity of Internet of Things (IoT) and pervasive computing, a large amount of real-time data is usually collected from multiple sources in a distributed environment. Unfortunately, data collected from each source is often uncertain due to various factors: imprecise reading, data integration from multiple sources (or versions), transmission errors, etc. In addition, due to network delay and limited by the economic budget associated with large-scale data communication over a distributed network, an essential problem is to track the global frequent items from all distributed uncertain data sites with the minimum communication cost. In this paper, we focus on the problem of tracking distributed probabilistic frequent items (TDPF). Specifically, given k distributed sites S = {S ₁, … , S _k }, each of which is associated with an uncertain database \(\mathcal {D}_{i}\) of size n _i , a centralized server (or called a coordinator) H, a minimum support ratio r, and a probabilistic threshold t, we are required to find a set of items with minimum communication cost, each item X of which satisfies P r(s u p(X) ≥ r × N) > t, where s u p(X) is a random variable to describe the support of X and \(N={\sum }_{i=1}^{k}n_{i}\). In order to reduce the communication cost, we propose a local threshold-based deterministic algorithm and a sketch-based sampling approximate algorithm, respectively. The effectiveness and efficiency of the proposed algorithms are verified with extensive experiments on both real and synthetic uncertain datasets.     

Energy Efficient Sleep Schedule with Service Coverage Guarantee in Wireless Sensor Networks

Service oriented architecture has been proposed to support collaborations among distributed wireless sensor network (WSN) applications in an open dynamic environment. However, WSNs are resource constraint, and have limited computation abilities, limited communication bandwidth and especially limited energy. Fortunately, sensor nodes in WSNs are usually deployed redundantly, which brings the opportunity to adopt a sleep schedule for balanced energy consumption to extend the network lifetime. Due to miniaturization and energy efficiency, one sensor node can integrate several sense units and support a variety of services. Traditional sleep schedule considers only the constraints from the sensor nodes, can be categorized to a one-layer (i.e., node layer) issue. The service oriented WSNs should resolve the energy optimization issue considering the two-layer constraints, i.e., the sensor nodes layer and service layer. Then, the one-layer energy optimization scheme in previous work is not applicable for service oriented WSNs. Hence, in this paper we propose a sleep schedule with a service coverage guarantee in WSNs. Firstly, by considering the redundancy degree on both the service level and the node level, we can get an accurate redundancy degree of one sensor node. Then, we can adopt fuzzy logic to integrate the redundancy degree, reliability and energy to get a sleep factor. Based on the sleep factor, we furthermore propose the sleep mechanism. The case study and simulation evaluations illustrate the capability of our proposed approach.     

Position-based coding and convex splitting for private communication over quantum channels

The classical-input quantum-output (cq) wiretap channel is a communication model involving a classical sender X, a legitimate quantum receiver B, and a quantum eavesdropper E. The goal of a private communication protocol that uses such a channel is for the sender X to transmit a message in such a way that the legitimate receiver B can decode it reliably, while the eavesdropper E learns essentially nothing about which message was transmitted. The \(\varepsilon \)-one-shot private capacity of a cq wiretap channel is equal to the maximum number of bits that can be transmitted over the channel, such that the privacy error is no larger than \(\varepsilon \in (0,1)\). The present paper provides a lower bound on the \(\varepsilon \)-one-shot private classical capacity, by exploiting the recently developed techniques of Anshu, Devabathini, Jain, and Warsi, called position-based coding and convex splitting. The lower bound is equal to a difference of the hypothesis testing mutual information between X and B and the “alternate” smooth max-information between X and E. The one-shot lower bound then leads to a non-trivial lower bound on the second-order coding rate for private classical communication over a memoryless cq wiretap channel.     

A new strategy for generating shortest addition sequences

An addition sequence problem is given a set of numbers X = {n ₁, n ₂, . . . , n _m }, what is the minimal number of additions needed to compute all m numbers starting from 1? This problem is NP-complete. In this paper, we present a branch and bound algorithm to generate an addition sequence with a minimal number of elements for a set X by using a new strategy. Then we improve the generation by generalizing some results on addition chains (m = 1) to addition sequences and finding what we will call a presumed upper bound for each n _j , 1 ≤ j ≤ m, in the search tree.     

FIU-Miner (a fast,integrated, and user-friendly system for data mining) and its applications

The advent of Big Data era drives data analysts from different domains to use data mining techniques for data analysis. However, performing data analysis in a specific domain is not trivial; it often requires complex task configuration, onerous integration of algorithms, and efficient execution in distributed environments. Few efforts have been paid on developing effective tools to facilitate data analysts in conducting complex data analysis tasks. In this paper, we design and implement FIU-Miner, a Fast, Integrated, and User-friendly system to ease data analysis. FIU-Miner allows users to rapidly configure a complex data analysis task without writing a single line of code. It also helps users conveniently import and integrate different analysis programs. Further, it significantly balances resource utilization and task execution in heterogeneous environments. Case studies of real-world applications demonstrate the efficacy and effectiveness of our proposed system.