For each of the lattices A,(n 2 I), D,,(n 2 2), EC, E,, E,, and their duals a very fast algorithm is given for finding the closest lattice point to an arbitrary point. If these lattices are used for vector quantizing of uniformly distributed data, the algorithm finds the min imum distortion lattice point. If the lattices are used as codes for a Gaussian channel, the algorithm performs max imum ...

We present a method for performing transductive inference on very large datasets. Our algorithm is based on multiclass Gaussian processes and is effective whenever the multiplication of the kernel matrix or its inverse with a vector can be computed sufficiently fast. This holds, for instance, for certain graph and string kernels. Transduction is achieved by variational inference over the unlabe...

In this paper we discuss a possibility to extend unimodular transformations to non-perfectly nested loops. The main idea behind this extension is to convert a non-perfectly nested loop into a perfectly nested one by moving code into to innermost loop and properly guarding it to avoid multiple execution. This form of the loop can be viewed as an intermediate form for the transformation. Having o...

Partial differential equations (PDEs) are commonly used to model a wide variety of physical phenomena. A PDE model of a physical problem is typically described by conservation laws, constitutive laws, material properties, boundary conditions, boundary data, and geometry. In most practical applications, however, the PDE model is only an approximation to the real physical problem due to both (i) ...

0. Notations Throughout the paper we use the following notations: We write e(z) = e; C, R, Q, Z, N and N0, denote the set of complex numbers, real numbers, rational numbers, integers, positive integers, and positive integers including zero, respectively. Q(i) denotes the field of Gaussian numbers, and Z[i] the ring of Gaussian integers. We write tr(z) and N(z) for the trace and the norm of z ov...

BACKGROUND Present knowledge indicates a multilayered hierarchical gene regulatory network (ML-hGRN) often operates above a biological pathway. Although the ML-hGRN is very important for understanding how a pathway is regulated, there is almost no computational algorithm for directly constructing ML-hGRNs. RESULTS A backward elimination random forest (BWERF) algorithm was developed for constr...

In this article, we develop a new Rao-Blackwellized Monte Carlo smoothing algorithm for conditionally linear Gaussian models. The algorithm is based on the forwardfiltering backward-simulation Monte Carlo smoother concept and performs the backward simulation directly in the marginal space of the non-Gaussian state component while treating the linear part analytically. Unlike the previously prop...

This paper presents a new similarity measure for object recognition from large libraries of line-patterns. The measure draws its inspiration from both the Hausdor distance and a recently reported Bayesian consistency measure that has been sucessfully used for graphbased correspondence matching. The measure uses robust error-kernels to gauge the similarity of pairwise attribute relations de ned ...

Let s ≥ 1 be an integer. A Gaussian network is a function on R of the form g(x) = ∑N k=1 ak exp(−‖x − xk‖ ). The minimal separation among the centers, defined by min1≤j 6=k≤N ‖xj − xk‖, is an important characteristic of the network that determines the stability of interpolation by Gaussian networks, the degree of approximation by such networks, etc. We prove that if g(x) = ∑N k=1 ak exp(−‖x − x...

We prove that standard Gaussian random multipliers are expected to stabilize numerically both Gaussian elimination with no pivoting and block Gaussian elimination. Our tests show similar results where we applied circulant random multipliers instead of Gaussian ones.