8953485
Early termination in sparse interpolation algorithms
A probabilistic strategy, early termination, enables different interpolation algorithms to adapt to the degree or the number of terms in the target polynomial when neither is supplied in the input. In addition to dense algorithms, we implement this strategy in sparse interpolation algorithms. Based on early termination, racing algorithms execute simultaneously dense and sparse algorithms. The racing algorithms can be embedded as the univariate interpolation substep within Zippel's multivariate method. In addition, we experimentally verify some heuristics of early termination, which make use of thresholds and post-verification.
2559830
Algorithms for computing the sparsest shifts of polynomials via the Berlekamp/Massey algorithm
As a sub-procedure our algorithm executes the Berlekamp/Massey algorithm on a sequence of large integers or polynomials. We give a fraction-free version of the Berlekamp/Massey algorithm, which does not require rational numbers or functions and GCD operations on the arising numerators and denominators. The relationship between the solution of Toeplitz systems, Padé approximations, and the Euclidean algorithm is classical. Fraction-free versions [3] can be obtained from the subresultant PRS algorithm [2]. Dornstetter [6] gives an interpretation of the Berlekamp/Massey algorithm as a partial extended Euclidean algorithm. We map the subresultant PRS algorithm onto Dornstetter's formulation. We note that the Berlekamp/Massey algorithm is more efficient than the classical extended Euclidean algorithm.
7994736
Algorithms for computing sparsest shifts of polynomials in power, Chebyshev, and Pochhammer bases
We give a new class of algorithms for computing sparsest shifts of a given polynomial. Our algorithms are based on the early termination version of sparse interpolation algorithms: for a symbolic set of interpolation points, a sparsest shift must be a root of the first possible zero discrepancy that can be used as the early termination test. Through reformulating as multivariate shifts in a designated set, our algorithms can compute the sparsest shifts that simultaneously minimize the terms of a given set of polynomials. Our algorithms can also be applied to the Pochhammer and Chebyshev bases for the polynomials, and potentially to other bases as well. For a given univariate polynomial, we give a lower bound for the optimal sparsity. The efficiency of our algorithms can be further improved by imposing such a bound and pruning the highest degree terms.
86127
Symbolic-numeric sparse interpolation of multivariate polynomials
We consider the problem of sparse interpolation of an approximate multivariate black-box polynomial in floating-point arithmetic. That is, both the inputs and outputs of the black-box polynomial have some error, and all numbers are represented in standard, fixed-precision, floating point arithmetic. By interpolating the black box evaluated at random primitive roots of unity, we give efficient and numerically robust solutions. We note the similarity between the exact Ben-Or/Tiwari sparse interpolation algorithm and the classical Prony's method for interpolating a sum of exponential functions, and exploit the generalized eigenvalue reformulation of Prony's method. We analyze the numerical stability of our algorithms and the sensitivity of the solutions, as well as the expected conditioning achieved through randomization. Finally, we demonstrate the effectiveness of our techniques in practice through numerical experiments and applications.
15546337
On processing nested queries in distributed object-oriented database systems
In this paper, we discuss nested query processing in a distributed object-oriented database system. We present three query processing strategies to exploit parallelism in a distributed environment. Then, we review three access methods designed for centralized systems and discuss how they can be applied to the distributed environment. Heuristics for selecting attributes for indexing and determining where to store the indexes are also presented. Finally, a replication strategy is proposed for the path dictionary method.<<ETX>>
15087039
A data mining framework for building intrusion detection models
There is often the need to update an installed intrusion detection system (IDS) due to new attack methods or upgraded computing environments. Since many current IDSs are constructed by manual encoding of expert knowledge, changes to IDSs are expensive and slow. We describe a data mining framework for adaptively building Intrusion Detection (ID) models. The central idea is to utilize auditing programs to extract an extensive set of features that describe each network connection or host session, and apply data mining programs to learn rules that accurately capture the behavior of intrusions and normal activities. These rules can then be used for misuse detection and anomaly detection. New detection models are incorporated into an existing IDS through a meta-learning (or co-operative learning) process, which produces a meta detection model that combines evidence from multiple models. We discuss the strengths of our data mining programs, namely, classification, meta-learning, association rules, and frequent episodes. We report on the results of applying these programs to the extensively gathered network audit data for the 1998 DARPA Intrusion Detection Evaluation Program.
2400440
Protecting Secret Data from Insider Attacks
We consider defenses against confidentiality and integrity attacks on data following break-ins, or so-called intrusion resistant storage technologies. We investigate the problem of protecting secret data, assuming an attacker is inside a target network or has compromised a system. 
 
We give a definition of the problem area, and propose a solution, VAST, that uses large, structured files to improve the secure storage of valuable or secret data. Each secret has its multiple shares randomly distributed in an extremely large file. Random decoy shares and the lack of usable identification information prevent selective copying or analysis of the file. No single part of the file yields useful information in isolation from the rest. The file’s size and structure therefore present an enormous additional hurdle to attackers attempting to transfer, steal or analyze the data. The system also has the remarkable property of healing itself after malicious corruption, thereby preserving both the confidentiality and integrity of the data.
14065746
Cloning and aging in a VR family
Face cloning and animation considering wrinkle formation and aging are an aspiring goal and a challenging task. This paper describes a cloning method and an aging simulation in a family. We reconstruct a father, mother, son and daughter of one family and mix their shapes and textures in 3D to get virtual persons with some variation. The idea of reconstruction of a head is to detect features from two orthogonal pictures, modify a generic model with an animation structure and use an automatic texture mapping method. It is followed by a simple method to do 3D-shape interpolation and 2D morphing based on triangulation for experiments of mixing 3D heads between family members. Finally, wrinkles within facial animation and aging are generated based on detected feature points. Experiments are made to generate aging wrinkles on the faces of the son and the daughter.
14613627
Spatial Index on Air
With the advent of wireless networking and personal digital devices, the population of mobile users will increase significantly. Broadcasting is particularly suitable for environments having a large number of clients. In this paper, we study the query processing of some typical location-dependent queries, such as window queries and kNN queries, in a broadcast system. To reduce clients' power consumption and provide efficient services, a transformation of the objects is applied based on Hilbert curve. Furthermore, a linear index structure is constructed and several algorithms are devised to answer spatial queries. Experiments are conducted to evaluate the performance of the proposed transformation and related algorithms. Results show that the proposed schemes outperform existing algorithms significantly.