117639554
Multidimensional two-scale dilation equations
Abstract . This work involves the study of multidimensional scaling functions. These functions satisfy a two-scale dilation equation, just as the 1-D scaling functions which are used to construct 1-D wavelets. Two frameworks are presented for studying these dilation equations. Fourier methods are used to analyze existence, uniqueness and regularity of solutions. Expansions with infinite matrix products are used to derive an iterated function system (IFS) algorithm for generating the scaling function. Application to subdivision schemes for surface generation is presented, as a genuine multidimensional example where scaling functions arise and the IFS algorithm can be applied.
121024775
Arbitrarily smooth orthogonal nonseparable wavelets in R 2
For each $r\in\N$, we construct a family of bivariate orthogonal wavelets with compact support that are nonseparable and have vanishing moments of order r or less. The starting point of the construction is a scaling function that satisfies a dilation equation with special coefficients and a special dilation matrix M: the coefficients are aligned along two adjacent rows, and $\detwo$. We prove that if $\M^2=\pm 2I$, e.\,g., %%$\M=\ourmtx$ or $\M=\qsymtx$, $M=({0\,\,2 \atop 1\,\,0})$ or $M=({1\,\,\phantom{-}1 \atop 1\,\,-1})$, then the smoothness of the wavelets improves asymptotically by $1-\frac{1}{2}\log_23 \approx 0.2075$ when r is incremented by 1. Hence they can be made arbitrarily smooth by choosing r large enough.
1536242
Substitution Delone Sets 

Abstract. Substitution Delone set families are families of Delone sets X =(X1, . . ., Xn) which satisfy the inflation functional equation
 X_i = \bigvee_{j=1}^m ( \mbox{\phvr A} (X_j) + {\cal D}_$ij$ ) , \qquad 1 \le i \le m, 
 in which A is an expanding matrix, i.e., all of the eigenvalues of A fall outside the unit circle. Here the Dij are finite sets of vectors in Rd and V denotes union that counts multiplicity. This paper characterizes families X=(X1, . . ., Xn) that satisfy an inflation functional equation, in which each Xi is a multiset (set with multiplicity) whose underlying set is discrete. It then studies the subclass of Delone set solutions, and gives necessary conditions on the coefficients of the inflation functional equation for such solutions X to exist. It relates Delone set solutions to a narrower subclass of solutions, called self-replicating multi-tiling sets, which arise as tiling sets for self-replicating multi-tilings.

18765129
Security Analysis of Enterprise Network Based on Stochastic Game Nets Model
In this paper, we propose a novel modeling method, Stochastic Game Nets (SGN), and use it to model and analyze the security issues in enterprise networks. Firstly, the definition and modeling algorithm of Stochastic Game Nets are given. And then we apply the Stochastic Game Nets method to describe the attack and defense course in the enterprise networks successfully, and find a Nash equilibrium. Finally we analyze the confidentiality and integrity of the enterprise network quantificationally based on the model. The method can also be applied to other areas with respect to a game.
12547630
Performance Evaluation of a Privacy-Enhancing Framework for Personalized Websites
Reconciling personalization with privacy has been a continuing interest in the user modeling community. In prior work, we proposed a dynamic privacy-enhancing user modeling framework based on a software product line architecture (PLA). Our system dynamically selects personalization methods during runtime that respect users' current privacy preferences as well as the prevailing privacy laws and regulations. One major concern about our approach is its performance since dynamic architectural reconfiguration during runtime is usually resource-intensive. In this paper, we describe four implementations of our system that vary two factors, and an in-depth performance evaluation thereof under realistic workload conditions. Our study shows that a customized version performs better than the original PLA implementation, that a multi-level caching mechanism improves both versions, and that the customized version with caching performs best. The average handling time per user session is less than 0.2 seconds for all versions except the original PLA implementation. Overall, our results demonstrate that with a reasonable number of networked hosts in a cloud computing environment, an internationally operating website can use our dynamic PLA-based user modeling approach to personalize their user services, and at the same time respect the individual privacy desires of their users as well as the privacy norms that may apply.
452800
Rough Derivatives in Rough Function Model and Their Application
On the theory and application of rough derivatives in rough function model, the notion of generalized rough functions is defined to improve the definition of higher order rough derivatives Pawlak proposed, and analyze the functional features of roughly derived functions and higher order roughly derived functions. The rough extremum definition of discrete functions is given, Fermat theorem and Rolle theorem of roughly smooth discrete functions are proposed and proved, which complete and perfect the theoretical foundation of rough derivatives application in rough function model. The concepts that are rough monotone and rough convexity of discrete functions are defined. By comparing with the derivative application of real continuous function, a series of theorems are put forward which are the relation theorem of rough derivatives and rough monotone, the two sufficient conditions of rough extrema, the two relation theorems of rough derivatives and rough convexity. Moreover, some new results are achieved such as the sufficient condition of rough smoothing of discrete functions, etc.
16300996
Research on Optimization Algorithm for Attribute Reduction of Decision System
Attribute reduction is one of the central issue in the theoretical research of rough set, aiming at the NP-hard problem of acquiring minimal reduction and all reduction, an optimization algorithm is proposed to construct reduction tree based on discernibility matrix for acquiring attribute reduction. The discernibility set is acquired by improving discernibility matrix first, then the core and reduction candidate information are obtained, finally the minimal reduction and all reduction are sought fast and effectively by considering attribute frequency as heuristic information, and time cost of the algorithm is analyzed. The time complexity of the algorithm is lower than other presented algorithms.
206733202
Foreground and Shadow Detection Based on Conditional Random Field
This paper presents a conditional random field (CRF) approach to integrate spatial and temporal constraints for moving object detection and cast shadow removal in image sequences. Interactions among both detection (foreground/background/shadow) labels and observed data are unified by a probabilistic framework based on the conditional random field, where the interaction strength can be adaptively adjusted in terms of data similarity of neighboring sites. Experimental results show that the proposed approach effectively fuses contextual dependencies in video sequences and significantly improves the accuracy of object detection.