Rational Solutions of Riccati-like Partial Differential Equations
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: 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: Optimal skewed tiling for cache locality enhancement
abstract: Iterative stencil loops are used in scientific programs to implement relaxation methods for numerical simulation and signal processing. Such loops iteratively modify the same array elements over different time steps. Hence, exploitation of temporal data locality can lead to significantly improved cache performance. This paper shows that, to optimally tile iterative stencil loops, the imperfectly nested inner loops must be realigned such that they can be minimally skewed across different time steps. A memory-reference cost analysis proves that the number of cache misses is minimized when the skewing is minimum. A graph-theoretical algorithm, which takes polynomial time, is presented to determine the minimum skew factors for a given nesting of iterative stencil loops.

title: C-Miner: Mining Block Correlations in Storage Systems
abstract: Block correlations are common semantic patterns in storage systems. These correlations can be exploited for improving the effectiveness of storage caching, prefetching, data layout and disk scheduling. Unfortunately, information about block correlations is not available at the storage system level. Previous approaches for discovering file correlations in file systems do not scale well enough to be used for discovering block correlations in storage systems. 
 
In this paper, we propose C-Miner, an algorithm which uses a data mining technique called frequent sequence mining to discover block correlations in storage systems. C-Miner runs reasonably fast with feasible space requirement, indicating that it is a practical tool for dynamically inferring correlations in a storage system. Moreover, we have also evaluated the benefits of block correlation-directed prefetching and data layout through experiments. Our results using real system workloads show that correlation-directed prefetching and data layout can reduce average I/O response time by 12-25% compared to the base case, and 7-20% compared to the commonly used sequential prefetching scheme.

title: An Object-Oriented Approach Using a Top-Down and Bottom-Up Process for Manipulative Action Recognition
abstract: Different from many gesture-based human-robot interaction applications, which focused on the recognition of the interactional or the pointing gestures, this paper proposes a vision-based method for manipulative gesture recognition aiming to achieve natural, proactive, and non-intrusive interaction between humans and robots. The main contributions of the paper are an object-centered scheme for the segmentation and characterization of hand trajectory information, the use of particle filtering methods for an action primitive spotting, and the tight coupling of bottom-up and top-down processing that realizes a task-driven attention filter for low-level recognition steps. In contrast to purely trajectory based techniques, the presented approach is called object-oriented w.r.t. two different aspects: it is object-centered in terms of trajectory features that are defined relative to an object, and it uses object-specific models for action primitives. The system has a two-layer structure recognizing both the HMM-modeled manipulative primitives and the underlying task characterized by the manipulative primitive sequence. The proposed top-down and bottom-up mechanism between the two layers decreases the image processing load and improves the recognition rate.

title: Chromatic sums of 2-edge-connected maps on the plane
abstract: This paper provides the chromatic sum function equation of rooted 2-edge-connected maps on the plane. The enumerating function equations of rooted biloopless maps, rooted nonseparable maps, rooted 2-edge-connected bipartite maps and rooted loopless Eulerian maps on the plane are derived by the chromatic sum function equation of rooted 2-edge-connected maps on the plane. Moreover, some explicit expressions of enumerating functions are also derived.

title: A technique for reducing synchronization overhead in large scale multiprocessors
abstract: A b s t r a c t The effectiveness of multiprocessing a single subroutine in a tightly coupled muir!processor system is highly dependent (among other factors) on the amount of overhead incurred due to synchronized references to shared data items by active processes. In this paper we present a technique to reduce this overhead. This is achieved by reducing the number of synchronized references issued by different processes. We describe the criteria used to identify the variables whose synchronized accesses will eliminate the need to synchronize references to other variables. Our technique can be implemented in optimizing compilers for mnltiprocessor machines. It can also be used when designing parallel algorithms for multiproeessors. We implemented the technique as a pass in the Parafrase system of the University of Illinois. Relevant measurements on all the subroutines of the EISPACK package are reported (61 subroutines). The results show that our technique is quite effective. For subroutines with interprocess communication, it reduced the number of memory references requiring synchronization by 10% in two thirds of these subroutines and by more than 30% for one third of the subroutines.