The role of entropy in word ranking

Entropy as a measure of complexity in the systems has been applied for ranking the words in the human written texts. We introduce a novel approach to evaluate accuracy for retrieved indices. We also have an illustrative comparison between proposed entropic metrics and some other methods in extracting the keywords. It seems that, some of the discussed metrics apply similar features for word ranking in the text. This work recommend the entropy as a systematic measure in text mining.     

Local and 2-local derivations on noncommutative Arens algebras

The paper is devoted to so-called local and 2-local derivations on the noncommutative Arens algebra L ^ω(M,τ) associated with a von Neumann algebra M and a faithful normal semi-finite trace τ. We prove that every 2-local derivation on L ^ω(M,τ) is a spatial derivation, and if M is a finite von Neumann algebra, then each local derivation on L ^ω(M,τ) is also a spatial derivation and every 2-local derivation on M is in fact an inner derivation.     

A fast dual proximal gradient algorithm for convex minimization and applications

We consider the convex composite problem of minimizing the sum of a strongly convex function and a general extended valued convex function. We present a dual-based proximal gradient scheme for solving this problem. We show that although the rate of convergence of the dual objective function sequence converges to the optimal value with the rate O(1/k²)$O(1/k^2)$, the rate of convergence of the primal sequence is of the order O(1/k)$O(1/k)$.     

Estimation of mutual information by the fuzzy histogram

Mutual Information (MI) is an important dependency measure between random variables, due to its tight connection with information theory. It has numerous applications, both in theory and practice. However, when employed in practice, it is often necessary to estimate the MI from available data. There are several methods to approximate the MI, but arguably one of the simplest and most widespread techniques is the histogram-based approach. This paper suggests the use of fuzzy partitioning for the histogram-based MI estimation. It uses a general form of fuzzy membership functions, which includes the class of crisp membership functions as a special case. It is accordingly shown that the average absolute error of the fuzzy-histogram method is less than that of the naïve histogram method. Moreover, the accuracy of our technique is comparable, and in some cases superior to the accuracy of the Kernel density estimation (KDE) method, which is one of the best MI estimation methods. Furthermore, the computational cost of our technique is significantly less than that of the KDE. The new estimation method is investigated from different aspects, such as average error, bias and variance. Moreover, we explore the usefulness of the fuzzy-histogram MI estimator in a real-world bioinformatics application. Our experiments show that, in contrast to the naïve histogram MI estimator, the fuzzy-histogram MI estimator is able to reveal all dependencies between the gene-expression data.     

A joinings classification and a special case of Raghunathan’s conjecture in positive characteristic (with an appendix by Kevin Wortman)

We prove the classification of joinings for maximal horospherical subgroups acting on homogeneous spaces without any restriction on the characteristic. Using the linearization technique, we deduce a special case of Raghunathan’s orbit closure conjecture. In the appendix, quasi-isometries of higher rank lattices in semisimple algebraic groups over fields of positive characteristic are characterized.     

Some exact solutions of the oscillatory motion of a generalized second grade fluid in an annular region of two cylinders

The velocity field and the associated shear stress corresponding to the longitudinal oscillatory flow of a generalized second grade fluid, between two infinite coaxial circular cylinders, are determined by means of the Laplace and Hankel transforms. Initially, the fluid and cylinders are at rest and at t = 0＋ both cylinders suddenly begin to oscillate along their common axis with simple harmonic motions having angular frequencies Ω1 and Ω2. The solutions that have been obtained are presented under integral and series forms in terms of the generalized G and R functions and satisfy the governing differential equation and all imposed initial and boundary conditions. The respective solutions for the motion between the cylinders, when one of them is at rest, can be obtained from our general solutions. Furthermore, the corresponding solutions for the similar flow of ordinary second grade fluid and Newtonian fluid are also obtained as limiting cases of our general solutions. At the end, the effect of different parameters on the flow of ordinary second grade and generalized second grade fluid are investigated graphically by plotting velocity profiles.     

On presentations of integer polynomial points of simple groups over number fields

Let K be a number field and let A be its ring of integers. Let G be a connected, noncommutative, absolutely almost simple algebraic K-group. If the K-rank of G equals 2, then G(A[t]) is not finitely presented.     

Neural network prediction of load from the morphology of trabecular bone

Bone adaptation models are often solved in the forward direction, meaning that the response of bone to a given set of loads is determined by running a bone tissue adaptation model. The model is generally solved using a numerical technique such as the finite element model. Conversely, one may be interested in the loads that have resulted in a given state of bone. This is the inverse of the former problem. Even though the inverse problem has several applications, it has not received as much attention as the forward problem, partly because solving the inverse problem is more difficult. A nonlinear system identification technique is needed for solving the inverse problem. In this study, we use artificial neural networks for prediction of tissue adaptation loads from a given density distribution of trabecular bone. It is shown that the proposed method can successfully identify the loading parameters from the density distribution of the tissue. Two important challenges for all load prediction algorithms are the non-uniqueness of the solution of the inverse problem and the inaccuracies in the measurement of the morphology of the tissue. Both challenges are studied, and it is shown that the load prediction technique proposed in this paper can overcome both.     

Chaos-enhanced accelerated particle swarm optimization

There are more than two dozen variants of particle swarm optimization (PSO) algorithms in the literature. Recently, a new variant, called accelerated PSO (APSO), shows some extra advantages in convergence for global search. In the present study, we will introduce chaos into the APSO in order to further enhance its global search ability. Firstly, detailed studies are carried out on benchmark problems with twelve different chaotic maps to find out the most efficient one. Then the chaotic APSO (CAPSO) will be compared with some other chaotic PSO algorithms presented in the literature. The performance of the CAPSO algorithm is also validated using three engineering problems. The results show that the CAPSO with an appropriate chaotic map can clearly outperform standard APSO, with very good performance in comparison with other algorithms and in application to a complex problem.     

Lattice Boltzmann simulation of non-Newtonian flows past confined cylinders

A second-order lattice Boltzmann algorithm is used for Power-Law non-Newtonian flow simulation. The shear dependent behavior of the fluid is implemented through calculating the shear locally from the lattice distribution functions. A step by step verification procedure is taken to ensure the accuracy and the physical correctness of the numerical simulation. The flow past a series of tandem arrangement of two cylinders is computed in a confined domain. The effects of Reynolds number, the Power-Law index, and the distance between two cylinders on both the flow field and the drag coefficients of the cylinders are examined in detail.