相关论文: Complexity test modules
We provide explicit bounds on the difference of heights of isogenous Drinfeld modules. We derive a finiteness result in isogeny classes. In the rank 2 case, we also obtain an explicit upper bound on the size of the coefficients of modular…
Topological complexity is a numerical homotopy invariant that measures the instability of motion planning in a space. To study the topological complexity of non-simply connected spaces, Costa and Farber introduced a cohomology class whose…
Complexity analysis becomes a common task in supervisory control. However, many results of interest are spread across different topics. The aim of this paper is to bring several interesting results from complexity theory and to illustrate…
We provide an upper bound on the topological complexity of twisted products. We use it to give an estimate $$TC(X)\le TC(\pi_1(X))+\dim X$$ of the topological complexity of a space in terms of its dimension and the complexity of its…
We describe rings over which every right module is almost injective. We give a description of rings over which every simple module is a almost projective.
We define the notion of the canonical module of a complex. We then consider Serre's conditions for a complex and study their relationship to the local cohomology of the canonical module and its ring of endomorphisms.
We use algebraic geometry to study matrix rigidity, and more generally, the complexity of computing a matrix-vector product, continuing a study initiated by Kumar, et. al. We (i) exhibit many non-obvious equations testing for (border)…
Local cohomology modules, even over a Noetherian ring $R$, are typically unwieldly. As such, it is of interest whether or not they have finitely many associated primes. We prove the affirmative in the case where $R$ is a Stanley-Reisner…
We construct an explicit filtration of the ring of algebraic power series by finite dimensional constructible sets, measuring the complexity of these series. As an application, we give a bound on the dimension of the set of algebraic power…
We use topological methods to study complexity of deep computations and limit computations. We use topology of function spaces, specifically, the classification Rosenthal compacta, to identify new complexity classes. We use the language of…
Detecting community structure is fundamental to clarify the link between structure and function in complex networks and is used for practical applications in many disciplines. A successful method relies on the optimization of a quantity…
Based on cluster de-synchronization properties of phase oscillators, we introduce an efficient method for the detection and identification of modules in complex networks. The performance of the algorithm is tested on computer generated and…
We introduce the topological complexity of the work map associated to a robot system. In broad terms, this measures the complexity of any algorithm controlling, not just the motion of the configuration space of the given system, but the…
Measuring software complexity plays an important role to meet the demands of complex software. The cyclomatic complexity is one of most used and renowned metric among the other three proposed and researched metrics that are namely: Line of…
The cohomology ring of a finite group, with coefficients in a finite field, can be computed by a machine, as Carlson has showed. Here "compute" means to find a presentation in terms of generators and relations, and involves only the…
In this note, we provide a unifying framework to investigate the computational complexity of classical spin models and give the full classification on spin models in terms of system dimensions, randomness, external magnetic fields and types…
The complex software systems developed nowadays require assessing their quality and proneness to errors. Reducing code complexity is a never-ending problem, especially in today's fast pace of software systems development. Therefore, the…
Projecting fields between different meshes commonly arises in computational physics. This operation requires a supermesh construction and its computational cost is proportional to the number of cells of the supermesh $n$. Given any two…
Differential modules are natural generalizations of complexes. In this paper, we study differential modules with complete intersection homology, comparing and contrasting the theory of these differential modules with that of the Koszul…
Complexity is an interdisciplinary concept which, first of all, addresses the question of how order emerges out of randomness. For many reasons matrices provide a very practical and powerful tool in approaching and quantifying the related…