This paper provides a solution to the open problem of automatic rewriting loop nests for non-unimodular transformations. We present an algorithm that rewrites a loop nest under any non-singular (unimod-ular or non-unimodular) transformation. The algorithm works nicely with unimodular transformations being treated as a special case. The rst step of the algorithm calculates the loop bounds using ...

This paper focuses on covariant point-shifts of point processes on topological groups, which map points of a point process to other points of the point process in a translation invariant way. Foliations and connected components generated by point-shifts are studied, and the cardinality classification of connected components, previously known on Euclidean space, is generalized to unimodular grou...

In this article we characterize the ideal unimodular singularities in terms of their invariants. On the basis of this characterization we give an implementation of a classifier for ideal unimodular singularities in the computer algebra system SINGULAR.

Unimodular gravity is classically equivalent to General Relativity. This equivalence extends to actions which are functions of the curvature scalar. At the quantum level, the dynamics could differ. Most importantly, the cosmological constant is not a coupling in the unimodular action, providing a new vantage point from which to address the cosmological constant fine-tuning problem. Here, a quan...

Unimodular transformation has been proposed as a powerful techniques for loop parallelization in imperative language programs. In this paper, we propose to apply unimodular transformation to functional language programs. In particular, we propose a method of applying unimodular transformation to monolithic arrays such as Haskell array comprehensions. Using our method, a compiler can deduce a sa...

We consider totally unimodular multistage stochastic programs, that is, multistage stochastic programs whose extensive-form constraint matrices are totally unimodular. We establish several sufficient conditions and identify examples that have arisen in the literature.

The Lapped Orthogonal Transform (LOT) [ I ] is a popular transform and has found many applications in signal processing. Its extension, BiOrthogonal Lapped Transform (BOLT), has been investigated in detail in [2]. In this paper, we will study Lapped Unimodular Transform (LUT). All of these three transforms are first-order matrices with FIR inverses. We will show that like LOT and BOLT, all LUTs...

We characterize the class of integral square matrices M having the property that for every integral vector q the linear complementarity problem with data M; q has only integral basic solutions. These matrices, called principally unimodular matrices, are those for which every principal nonsingular submatrix is unimodular. As a consequence , we show that if M is rank-symmetric and principally uni...

In this paper, binary extremal self-dual codes of length 48 and extremal unimodular lattices in dimension 48 are studied through their shadows and neighbors. We relate an extremal singly even self-dual [48, 24, 10] code whose shadow has minimum weight 4 to an extremal doubly even selfdual [48, 24, 12] code. It is also shown that an extremal odd unimodular lattice in dimension 48 whose shadow ha...