A subresultant theory for Ore polynomials with applications
The subresultant theory for univariate commutative polynomials is generalized to Ore polynomials. The generalization includes: the subresultant theorem, gap structure, and subresultant algorithm. Using this generalization, we de ne Sylvester's resultant of two Ore polynomials, derive the respective determinantal formulas for the greatest common right divisor and least common left multiple of two Ore polynomials, and present a fraction-free version of the noncommutative extended Euclidean algorithm.

title: Factoring zero-dimensional ideals of linear partial differential operators
abstract: We present an algorithm for factoring a zero-dimensional left ideal in the ring <b>Q</b>(<i>x, y</i>) [∂<inf><i>x</i></inf>, ∂<inf><i>y</i></inf>], i.e. factoring a linear homogeneous partial differential system whose coefficients belong to <b>Q</b>(<i>x, y</i>), and whose solution space is finite-dimensional over <b>Q.</b> The algorithm computes all the zero-dimensional left ideals containing the given ideal. It generalizes the Beke-Schlesinger algorithm for factoring linear ordinary differential operators, and uses an algorithm for finding hyperexponential solutions of such ideals.

title: Factoring systems of linear PDEs with finite-dimensional solution spaces
abstract: A D-finite system is a finite set of linear homogeneous partial differential equations in several independent and dependent variables, whose solution space is of finite dimension. Let L be a D-finite system with rational function coefficients. We present an algorithm for computing all hyperexponential solutions of L, and an algorithm for computing all D-finite systems whose coefficients are also rational functions, and whose solutions are contained in the solution space of L.

title: Rational Solutions of Riccati-like Partial Differential Equations
abstract: When factoring linear partial differential systems with a finite-dimensional solution space or analysing symmetries of nonlinear ODEs, we need to look for rational solutions of certain nonlinear PDEs. The nonlinear PDEs are called Riccati-like because they arise in a similar way as Riccati ODEs. In this paper we describe the structure of rational solutions of a Riccati-like system, and an algorithm for computing them. The algorithm is also applicable to finding all rational solutions of Lie?s system { ?xu+u2+a1u+a2v+a3, ?yu+uv+b1u+b2v+b3, ?xv+uv+c1u+c2v+c3, ?yv+v2+d1u+d2v+d3},where a1, . . . , d3are rational functions of x and y.

title: Finding roots of unity among quotients of the roots of an integral polynomial
abstract: We present an efficient algorithm for testing whether a given integral polynomial has two distinct roots a, B such that fflp is a root of unity. The test is based on results obtained by investigation of the structure of the splitting field of the polynomial. By this investigate ion, we found also an improved bound for the least common multiple of the orders of roots of unity appearing as quotients of distinct roots.

title: A Parallel Implementation of Non-rigid Registration Using a Volumetric Biomechanical Model
abstract: Because of the accuracy required in a neurosurgical procedure, tracking intra-operative deformations is a challenging task. Furthermore, the clinical demand for fast non rigid registration will have to be met in a very near future. In this paper, we propose a patient-specific biomechanical model based on block-matching in order to register two MR images of the same patient with a parallel implementation. Compared to other intra-operative registration techniques, this method combines a viscoelastic mechanical regularization with a correlation-based iconic energy term. We first shortly present the theoretical aspects of our method (more detailed in ). Then we describe in more details the parallel implementation of the algorithm. Finally we present a retrospective registration study made of four pre/post operative MRI pairs.

title: iFlow: Middleware-assisted Rendezvous-based Information Access for Mobile Ad Hoc Applications
abstract: Due to node mobility and limitations on bandwidth availability in wireless channels, there exist unique challenges towards achieving efficient and effective information access in wireless ad hoc networks with mobile nodes. In this paper, we address two critical questions: (1) How may information be accessed with the highest degree of bandwidth efficiency? and (2) How should algorithms be designed so that node mobility contributes positively towards high performance and efficiency? We present iFlow, a middleware-based framework for bandwidth-efficient and delay-aware information access for mobile ad hoc applications. We present the case of information rendezvous, where the demands for information are satisfied by the supplies in a fully distributed fashion, across third-party nodes beyond information suppliers and consumers. Such rendezvous is achieved via controlled diffusion of information from the suppliers, matched by the gleaning process on the consumers. We validate our claims using simulation and experimental results.

title: Buffer insertion in large circuits with constructive solution search techniques
abstract: Most existing buffer insertion algorithms, such as van Ginneken's algorithm, consider only individual nets. As a result, these algorithms tend to over buffer when applied to combinational circuits, since it is difficult to decide how many buffers to insert in each net. Recently, Sze, et al.  proposed a path-based algorithm for buffer insertion in combinational circuits. However their algorithm is inefficient for large circuits when there are many critical paths. In this paper, we present a new buffer insertion algorithm for combinational circuits such that the timing requirements are met and the buffer cost is minimized. Our algorithm iteratively inserts buffers in the circuit to improve the circuit delay. The core of this algorithm is simple but effective technique that guides the search for a good buffering solution. Experimental results on ISCAS85 circuits show that our new algorithm on average uses 36% less buffers and runs 3 times faster than Sze's algorithm

title: Rate-distortion optimal video summary generation
abstract: The need for video summarization originates primarily from a viewing time constraint. A shorter version of the original video sequence is desirable in a number of applications. Clearly, a shorter version is also necessary in applications where storage, communication bandwidth, and/or power are limited. The summarization process inevitably introduces distortion. The amount of summarization distortion is related to its "conciseness", or the number of frames available in the summary. If there are m frames in the original sequence and n frames in the summary, we define the summarization rate as m/n, to characterize this "conciseness". We also develop a new summarization distortion metric and formulate the summarization problem as a rate-distortion optimization problem. Optimal algorithms based on dynamic programming are presented and compared experimentally with heuristic algorithms. Practical constraints, like the maximum number of frames that can be skipped, are also considered in the formulation and solution of the problem.

title: A circuit level fault model for resistive opens and bridges
abstract: Delay faults are an increasingly important test challenge. Traditional open and bridge fault models are incomplete because only the functional fault or a subset of delay fault are modeled. In this paper, we propose a circuit level model for resistive open and bridge faults. All possible fault behaviors are illustrated and a general resistive bridge delay calculation method is proposed. The new models are practical and easy to use. Fault simulation results show that the new models help the delay test to catch more bridge faults.