Related papers: Decline and Fall of the ICALP 2008 Modular Decompo…
By suitable examples we illustrate an algorithm for composition of inverse problems.
This article presents a class of modified new modulus-based iterative methods to process the large and sparse implicit complementarity problem (ICP). By using two positive diagonal matrices, we formulate a fixed-point equation which is…
This paper studies the problem of decomposing a low-rank positive-semidefinite matrix into symmetric factors with binary entries, either $\{\pm 1\}$ or $\{0,1\}$. This research answers fundamental questions about the existence and…
Prolog's ability to return multiple answers on backtracking provides an elegant mechanism to derive reversible encodings of combinatorial objects as Natural Numbers i.e. {\em ranking} and {\em unranking} functions. Starting from a…
This is an erratum to math.AG/9803126, Tohoku 51 (1999) 489-537. This erratum describes: 1. the failure of the algorithm in [AMR] and [Morelli1] for the strong factorization pointed out by Kalle Karu, 2. the statement of a refined weak…
We prove a conjecture of Denef on parameterized $p$-adic analytic integrals using an analytic cell decomposition theorem, which we also prove in this paper. This cell decomposition theorem describes piecewise the valuation of analytic…
We present a novel algorithm for overcomplete independent components analysis (ICA), where the number of latent sources k exceeds the dimension p of observed variables. Previous algorithms either suffer from high computational complexity or…
In this note we aim at putting more emphasis on the fact that trying to solve non-convex optimization problems with coordinate-descent iterative linear matrix inequality algorithms leads to suboptimal solutions, and put forward other…
Primary decomposition is a very important tool of commutative algebra and geometry. In this paper we generalized some of the existing algorithms of primary decomposition developed by Eisenbud et al. (cf. [EHV]) for free modules and also…
A polynomial-time algorithm is produced which, given generators for a group of permutations on a finite set, returns a direct product decomposition of the group into directly indecomposable subgroups. The process uses bilinear maps and…
This paper introduces a novel general-purpose algorithm for Pauli decomposition that employs matrix slicing and addition rather than expensive matrix multiplication, significantly accelerating the decomposition of multi-qubit matrices. In a…
Recent transformer language models achieve outstanding results in many natural language processing (NLP) tasks. However, their enormous size often makes them impractical on memory-constrained devices, requiring practitioners to compress…
In this survey, we first review some known results on the representation theory of algebras with triangular decomposition, including the classification of the simple modules. We then discuss a recipe to construct Hopf algebras with…
We present LinApart2, a major update to the LinApart algorithm for univariate partial fraction decomposition. Unlike its predecessor, LinApart2 can handle denominators of arbitrary polynomial degree without explicit factorization, while…
The recently-discovered polar codes are widely seen as a major breakthrough in coding theory. These codes achieve the capacity of many important channels under successive cancellation decoding. Motivated by the rapid progress in the theory…
Withdrawn because of non-correctness. Would have implied too much to be true :-|
This diploma thesis is concerned with functional decomposition $f = g \circ h$ of polynomials. First an algorithm is described which computes decompositions in polynomial time. This algorithm was originally proposed by Zippel (1991). A…
This paper has been withdrawn as it has been superseded by 0808.2697
Axion-like particles (ALPs) that decay into photon pairs pose a challenge for experiments that rely on the construction of a decay vertex in order to search for long-lived particles. This is particularly true for beam-dump experiments,…
We combine several folklore observations to provide a working framework for iterating constructions which contradict the axiom of choice. We use this to define a model in which any kind of structural failure must fail with a proper class of…