Efficient management of backtracking in and-parallelism

A backtracking algorithm for AND-Parallelism and its implementation at the Abstract Machine level are presented: first, a class of AND-Parallelism models based on goal independence is defined, and a generalized version of Restricted AND-Parallelism (RAP) introduced as characteristic of this class. A simple and efficient backtracking algorithm for R A P is then discussed. An implementation scheme is presented for this algorithm which offers minimum overhead, while retaining the performance and storage economy of sequent ial implementations and taking advantage of goal independence to avoid unnecessary backtracking ("restricted intelligent backtracking"). Finally, the implementation of backtracking in sequential and AND-Parallcl systems is explained through a number of examples

Generalized Markov stability of network communities

We address the problem of community detection in networks by introducing a general definition of Markov stability, based on the difference between the probability fluxes of a Markov chain on the network at different time scales. The specific implementation of the quality function and the resulting optimal community structure thus become dependent both on the type of Markov process and on the specific Markov times considered. For instance, if we use a natural Markov chain dynamics and discount its stationary distribution -- that is, we take as reference process the dynamics at infinite time -- we obtain the standard formulation of the Markov stability. Notably, the possibility to use finite-time transition probabilities to define the reference process naturally allows detecting communities at different resolutions, without the need to consider a continuous-time Markov chain in the small time limit. The main advantage of our general formulation of Markov stability based on dynamical flows is that we work with lumped Markov chains on network partitions, having the same stationary distribution of the original process. In this way the form of the quality function becomes invariant under partitioning, leading to a self-consistent definition of community structures at different aggregation scales

Skew Calabi-Yau triangulated categories and Frobenius Ext-algebras

We investigate the conditions that are sufficient to make the Ext-algebra of an object in a (triangulated) category into a Frobenius algebra and compute the corresponding Nakayama automorphism. As an application, we prove the conjecture that hdet($\mu_A$) = 1 for any noetherian Artin-Schelter regular (hence skew Calabi-Yau) algebra A.Comment: 31 page

LTE-advanced self-organizing network conflicts and coordination algorithms

Self-organizing network (SON) functions have been introduced in the LTE and LTEAdvanced standards by the Third Generation Partnership Project as an excellent solution that promises enormous improvements in network performance. However, the most challenging issue in implementing SON functions in reality is the identification of the best possible interactions among simultaneously operating and even conflicting SON functions in order to guarantee robust, stable, and desired network operation. In this direction, the first step is the comprehensive modeling of various types of conflicts among SON functions, not only to acquire a detailed view of the problem, but also to pave the way for designing appropriate Self-Coordination mechanisms among SON functions. In this article we present a comprehensive classification of SON function conflicts, which leads the way for designing suitable conflict resolution solutions among SON functions and implementing SON in reality. Identifying conflicting and interfering relations among autonomous network management functionalities is a tremendously complex task. We demonstrate how analysis of fundamental trade-offs among performance metrics can us to the identification of potential conflicts. Moreover, we present analytical models of these conflicts using reference signal received power plots in multi-cell environments, which help to dig into the complex relations among SON functions. We identify potential chain reactions among SON function conflicts that can affect the concurrent operation of multiple SON functions in reality. Finally, we propose a selfcoordination framework for conflict resolution among multiple SON functions in LTE/LTEAdvanced networks, while highlighting a number of future research challenges for conflict-free operation of SON

Subsumption Algorithms for Three-Valued Geometric Resolution

In our implementation of geometric resolution, the most costly operation is subsumption testing (or matching): One has to decide for a three-valued, geometric formula, if this formula is false in a given interpretation. The formula contains only atoms with variables, equality, and existential quantifiers. The interpretation contains only atoms with constants. Because the atoms have no term structure, matching for geometric resolution is hard. We translate the matching problem into a generalized constraint satisfaction problem, and discuss several approaches for solving it efficiently, one direct algorithm and two translations to propositional SAT. After that, we study filtering techniques based on local consistency checking. Such filtering techniques can a priori refute a large percentage of generalized constraint satisfaction problems. Finally, we adapt the matching algorithms in such a way that they find solutions that use a minimal subset of the interpretation. The adaptation can be combined with every matching algorithm. The techniques presented in this paper may have applications in constraint solving independent of geometric resolution.Comment: This version was revised on 18.05.201