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Based on the notion of maximal correlation, we introduce a new measure of correlation between two different rankings of the same group of items. Our measure captures various types of correlation detected in previous measures of rank correlation like the Spearman correlation and the Kendall tau correlation. We show that the maximal rank correlation satisfies the data processing and tensorization properties (that make ordinary maximal correlation applicable to problems in information theory). Furthermore, MRC is shown to be intimately related to the FKG inequality. Finally, we pose the problem of the complexity of the computation of this new measure. We make partial progress by giving a simple... 

It is shown that in a controlled adiabatic homotopy between two Hamiltonians, H0 and H1, the gap or "anti- crossing" phenomenon can be viewed as the development of cusps and swallow tails in the region of the complex plane where two critical value curves of the quadratic map associated with the numerical range of H0 + i H 1 come close. The "near crossing" in the energy level plots happens to be a generic situation, in the sense that a crossing is a manifestation of the quadratic numerical range map being unstable in the sense of differential topology. The stable singularities that can develop are identified and it is shown that they could occur near the gap, making those singularities of... 

A social network is a set of people (or organizations or other social entities) connected by a set of social relationships, such as friendship, co-working or information exchange. Social network analysis focuses on the analysis of patterns of relationships among people, organizations, states and such social entities. Social network analysis provides both a visual and a mathematical analysis of human relationships. Web can also be considered as a social network. Social networks are formed between Web pages by hyperlinking to other Web pages. In this paper a state of the art survey of the works done on social network analysis ranging from pure mathematical analyses in graphs to analyzing the... 

This paper considers an imperfect production system in which defective items are produced in. each cycle of production. We assume that the defectives produced within each cycle will be reworked immediately after each production run is completed. We also assume some scrap is produced and detected during the rework period. Further, we assume that the number of scrapped items produced during the rework period is a random variable. For this system, using some theorem from the renewal theory, the expected total cost function per unit time is derived and the optimal batch quantity is obtained  

We study the collision detection of n moving balls of arbitrary sizes in 3-dimensional space. We improve both the storage and the event-handling time of the best existing KDS [1] by several logarithmic factors. Precisely, our KDS maintains O(n) certificates at the current time, uses O(nlog2⁡n) storage, handles each event in O(log3⁡n) time, and processes O(n2) events in the worst case, assuming that the balls follow constant-degree algebraic trajectories. © 2021 Elsevier B.V  

We study the collision detection of n moving balls of arbitrary sizes in 3-dimensional space. We improve both the storage and the event-handling time of the best existing KDS [1] by several logarithmic factors. Precisely, our KDS maintains O(n) certificates at the current time, uses O(nlog2⁡n) storage, handles each event in O(log3⁡n) time, and processes O(n2) events in the worst case, assuming that the balls follow constant-degree algebraic trajectories. © 2021 Elsevier B.V  

Since Di Gianantonio introduced his semantics for exact real number computation, there has always been a struggle to maintain data abstraction and efficiency as much as possible. The interval domain model - or its variations - can be regarded as the standard setting to obtain maximum data abstraction. As for efficiency there has been much focus on sequentially to the extent that these two terms have become almost synonymous. [2, 3] demonstrated that there is not much one can get by sequential computation in the interval domain model. In [4, 5] we reinforced this result by exposing the limited power of (some extensions of) the sequential fragment of Real-PCF. The previous argument suggests... 

There have been significant developments in the design and application of algorithms for both one-dimensional signal processing and multidimensional signal processing, namely image and video processing, with the recent focus changing from a step-by-step procedure of designing the algorithm first and following up with in-depth analysis and performance improvement to instead applying heuristic-based methods to solve signal-processing problems. In this book the contributing authors demonstrate both general-purpose algorithms and those aimed at solving specialized application problems, with a special emphasis on heuristic iterative optimization methods employing modern evolutionary and swarm... 

Endothelial dysfunction, which can be noninvasively assessed by flow mediated vasodilation (FMD), predicts an increased rate of adverse cardiovascular events. The endothelial dysfunction is considered as a leading cause of development and progression of the atherosclerotic process. The main aim of this study is to review different non-invasive methods to assess the endothelial dysfunction and to propose enhancements to a new method based on photoplethysmography (PPG). First, non-invasive techniques developed for the evaluation of peripheral endothelial function (including the Doppler ultrasound (US)) will be reviewed. Although noninvasive, US -based techniques present a few disadvantages. To... 

A measure of correlation is said to have the tensorization property if it does not change when computed for i.i.d. copies. More precisely, a measure of correlation between two random variables X, Y denoted by rho (X, Y), has the tensorization property if ρ(Xn, Yn)=ρ (X, Y) where (Xn, Yn) denotes n i.i.d. copies of (X, Y). Two well-known examples of such measures are the maximal correlation and the hypercontractivity ribbon (HC ribbon). We show that the maximal correlation and the HC ribbon are special cases of the new notion of Φ-ribbons, defined in this paper for a class of convex functions Φ. Φ-ribbon reduces to the HC ribbon and the maximal correlation for special choices of Φ, and is a... 

This paper introduces a novel, cost effective visual cryptography scheme suitable for color image transmission over bandwidth constraint channels. Unlike previously proposed schemes, the solution offers perfect reconstruction while producing shares with size smaller than that of the input image. The maximum distance separable (MDS) code principle used in the design allows for the introduction of a flexible framework that compares favorably to competing solutions as it can be seen by examining the experimental results included in this paper. ©2008 IEEE  

We propose a method for analyzing the data for the rates of exchange of various currencies versus the U.S. dollar. The method analyzes the return time series of the data as a Markov process, and develops an effective equation which reconstructs it. We find that the Markov time scale, i.e., the time scale over which the data are Markov-correlated, is one day for the majority of the daily exchange rates that we analyze. We derive an effective Langevin equation to describe the fluctuations in the rates. The equation contains two quantities, D(1) and D(2), representing the drift and diffusion coefficients, respectively. We demonstrate how the two coefficients are estimated directly from the... 

This paper introduces adaptive consensus, a spatio-temporal adaptive method to improve convergence behavior of the current consensus fusion schemes. This is achieved by introducing a time adaptive weighting method for updating each sensor data in each iteration. Adaptive consensus method will improve node convergence rate, average convergence rate and the variance of error over the network. A mathematical formulation of the method according to the adaptive filter theory as well as derivation of the time adaptive weights and convergence conditions are presented. The analytical results are verified by simulation as well. ©2006 IEEE  

We propose a novel inverse method that utilizes a set of data to construct a simple equation that governs the stochastic process for which the data have been measured, hence enabling us to reconstruct the stochastic process. As an example, we analyze the stochasticity in the beat-to-beat fluctuations in the heart rates of healthy subjects as well as those with congestive heart failure. The inverse method provides a novel technique for distinguishing the two classes of subjects in terms of a drift and a diffusion coefficients which behave completely differently for the two classes of subjects, hence potentially providing a novel diagnostic tool for distinguishing healthy subjects from those... 

The problem of the characterization of perfect entanglers was investigated. Perfect entanglers have been defined as unitary operators that can generate maximally entangled states from some suitably chosen separable states. Some well defined tools have also been used to measure the entangling properties of quantum operators and two-qubit states. It was found that such tools help to analyze perfect entanglers and also have the unique property of maximally entangling a complete set of orthonormal product vectors. The results show that the qubit gates provided minimum universal gate construction and two of them were necessary and sufficient in implementation of a generic two-qubit gate