Related papers: Decline and Fall of the ICALP 2008 Modular Decompo…
This paper proposes a geometric solution to the problem of prime decomposability of concurrent processes first explored by R. Milner and F. Moller in [MM93]. Concurrent programs are given a geometric semantics using cubical areas, for which…
We obtain two new algorithms for partial fraction decompositions; the first is over algebraically closed fields, and the second is over general fields. These algorithms takes $O(M^2)$ time, where $M$ is the degree of the denominator of the…
Consider a finite-dimensional algebra $A$ and any of its moduli spaces $\mathcal{M}(A,\mathbf{d})^{ss}_{\theta}$ of representations. We prove a decomposition theorem which relates any irreducible component of…
We respond to the criticism raised in the paper arXiv:1704.07831.
In this paper, we get an elementary and important lemma(See Lemma 3.2) which is about pushout and pullback of modules. And we prove a weak form of a long open conjecture on vanishing of group cohomology for blocks.
Under successive cancellation (SC) decoding, polar codes are inferior to other codes of similar blocklength in terms of frame error rate. While more sophisticated decoding algorithms such as list- or stack-decoding partially mitigate this…
Let $A$ be a finite-dimensional algebra over an algebraically closed field $\Bbbk$. For any finite-dimensional $A$-module $M$ we give a general formula that computes the indecomposable decomposition of $M$ without decomposing it, for which…
A constructive method for decomposing finite dimensional representations of semisimple real Lie algebras is developed. The method is illustrated by an example. We also discuss an implementation of the algorithm in the language of the…
For any unitary matrix there exists a ZXZ decomposition, according to a theorem by Idel and Wolf. For any even-dimensional unitary matrix there exists a block-ZXZ decomposition, according to a theorem by F\"uhr and Rzeszotnik. We conjecture…
We prove that a large family of graphs which are decomposable with respect to the modular decomposition can be reconstructed from their collection of vertex-deleted subgraphs.
We investigate a general matrix factorization for deviance-based data losses, extending the ubiquitous singular value decomposition beyond squared error loss. While similar approaches have been explored before, our method leverages…
We develop the symplectic elimnation algorithm. This algorithm using simple row operations reduce a symplectic matrix to a diagonal matrix. This algorithm gives rise to a decomposition of an arbitrary matrix into a product of a symplectic…
A (fragment of a) process algebra satisfies unique parallel decomposition if the definable behaviours admit a unique decomposition into indecomposable parallel components. In this paper we prove that finite processes of the pi-calculus,…
We study certain linear algebra algorithms for recursive block matrices. This representation has useful practical and theoretical properties. We summarize some previous results for block matrix inversion and present some results on…
Linear bilevel programs (linear BLPs) have been widely used in computational mathematics and optimization in several applications. Single-level reformulation for linear BLPs replaces the lower-level linear program with its…
Lagrangian duality in mixed integer optimization is a useful framework for problems decomposition and for producing tight lower bounds to the optimal objective, but in contrast to the convex counterpart, it is generally unable to produce…
Many applications in scientific computing and data science require the computation of a rank-revealing factorization of a large matrix. In many of these instances the classical algorithms for computing the singular value decomposition are…
The special theme of DCM 2009, co-located with ICALP 2009, concerned Computational Models From Nature, with a particular emphasis on computational models derived from physics and biology. The intention was to bring together different…
Computing modular coincidences can show whether a given substitution system, which is supported on a point lattice in R^d, consists of model sets or not. We prove the computatibility of this problem and determine an upper bound for the…
We exploit the truncated singular value decomposition and the recently proposed circulant decomposition for an efficient first-order approximation of the multiplication of large dense matrices. A decomposition of each matrix into a sum of a…