On a Class of Fractional Type Integral Equations in Variable Exponent Spaces

2000 Mathematics Subject Classification: 45A05, 45B05, 45E05,45P05, 46E30

An Analog of the Tricomi Problem for a Mixed Type Equation with a Partial Fractional Derivative

Mathematics Subject Classification 2010: 35M10, 35R11, 26A33, 33C05, 33E12, 33C20.

Fractional Calculus of P-transforms

MSC 2010: 44A20, 33C60, 44A10, 26A33, 33C20, 85A99

On a 3D-Hypersingular Equation of a Problem for a Crack

MSC 2010: 45DB05, 45E05, 78A45

Viability Kernels of Higher Order

AMS subject classification: Primary 34A60, Secondary 49K24.

Viability, Optimality and Stability of Dynamical Systems and Estimation of Convergence of Numerical Schemes

AMS subject classification: 49N35,49N55,65Lxx.

Attributed graph kernels using the Jensen-Tsallis q-differences

We propose a family of attributed graph kernels based on mutual information measures, i.e., the Jensen-Tsallis (JT) q-differences (for q  ∈ [1,2]) between probability distributions over the graphs. To this end, we first assign a probability to each vertex of the graph through a continuous-time quantum walk (CTQW). We then adopt the tree-index approach [1] to strengthen the original vertex labels, and we show how the CTQW can induce a probability distribution over these strengthened labels. We show that our JT kernel (for q  = 1) overcomes the shortcoming of discarding non-isomorphic substructures arising in the R-convolution kernels. Moreover, we prove that the proposed JT kernels generalize the Jensen-Shannon graph kernel [2] (for q = 1) and the classical subtree kernel [3] (for q = 2), respectively. Experimental evaluations demonstrate the effectiveness and efficiency of the JT kernels.

Attributed graph similarity from the quantum Jensen-Shannon divergence

One of the most fundamental problem that we face in the graph domain is that of establishing the similarity, or alternatively the distance, between graphs. In this paper, we address the problem of measuring the similarity between attributed graphs. In particular, we propose a novel way to measure the similarity through the evolution of a continuous-time quantum walk. Given a pair of graphs, we create a derived structure whose degree of symmetry is maximum when the original graphs are isomorphic, and where a subset of the edges is labeled with the similarity between the respective nodes. With this compositional structure to hand, we compute the density operators of the quantum systems representing the evolution of two suitably defined quantum walks. We define the similarity between the two original graphs as the quantum Jensen-Shannon divergence between these two density operators, and then we show how to build a novel kernel on attributed graphs based on the proposed similarity measure. We perform an extensive experimental evaluation both on synthetic and real-world data, which shows the effectiveness the proposed approach. © 2013 Springer-Verlag.

A New Class of Processes for Formalizing and Generalizing Individual-Based Models: The Semi-Semi-Markov Processes

2000 Mathematics Subject Classification: 60K15, 60K20, 60G20,60J75, 60J80, 60J85, 60-08, 90B15.

Monte Carlo Method for Reconstruction of Densities

2000 Mathematics Subject Classification: 65C05

Comparing Several Methods of Discriminant Analysis on the Case of Wine Data

2000 Mathematics Subject Classification: 62H30, 62J20, 62P12, 68T99

A Comparative Analysis of Predictive Learning Algorithms on High-Dimensional Microarray Cancer Data

This research evaluates pattern recognition techniques on a subclass of big data where the dimensionality of the input space (p) is much larger than the number of observations (n). Specifically, we evaluate massive gene expression microarray cancer data where the ratio κ is less than one. We explore the statistical and computational challenges inherent in these high dimensional low sample size (HDLSS) problems and present statistical machine learning methods used to tackle and circumvent these difficulties. Regularization and kernel algorithms were explored in this research using seven datasets where κ < 1. These techniques require special attention to tuning necessitating several extensions of cross-validation to be investigated to support better predictive performance. While no single algorithm was universally the best predictor, the regularization technique produced lower test errors in five of the seven datasets studied.

Averaging operators and set-valued maps

MSC 2010: 54C35, 54C60.

Existence of Solutions for a Class of Quasi-Linear Singular Integro-Differential Equations

2000 Mathematics Subject Classification: 45F15, 45G10, 46B38.

Bi-directional double auction for financial market simulation

Typical Double Auction (DA) models assume that trading agents are one-way traders. With this limitation, they cannot directly reflect the fact individual traders in financial markets (the most popular application of double auction) choose their trading directions dynamically. To address this issue, we introduce the Bi-directional Double Auction (BDA) market which is populated by two-way traders. Based on experiments under both static and dynamic settings, we find that the allocative efficiency of a static continuous BDA market comes from rational selection of trading directions and is negatively related to the intelligence of trading strategies. Moreover, we introduce Kernel trading strategy designed based on probability density estimation for general DA market. Our experiments show it outperforms some intelligent DA market trading strategies. Copyright © 2013, International Foundation for Autonomous Agents and Multiagent Systems (www.ifaamas.org). All rights reserved.