The problem of determining power integral bases in algebraic number fields is equivalent to solving the corresponding index form equations. As is known (cf. Győry [25]), every index form equation can be reduced to an equation system consisting of unit equations in two variables over the normal closure of the original field. However, the unit rank of the normal closure is usually too large for p...

Nearest-neighbor collaborative filtering (CF) algorithms are gaining widespread acceptance in recommender systems and e-commerce applications. User ratings are not expected to be independent, as users follow trends of similar rating behavior. In terms of Text Mining, this is analogous to the formation of higher-level concepts from plain terms. In this paper, we propose a novel CF algorithm whic...

In this paper, we present a framework for fitting multivariate Hawkes processes for large-scale problems, both in the number of events in the observed history n and the number of event types d (i.e. dimensions). The proposed Scalable LowRank Hawkes Process (SLRHP) framework introduces a lowrank approximation of the kernel matrix that allows to perform the nonparametric learning of the d trigger...

Dynamical low-rank approximation, as has been demonstrated recently, can be extremely efficient in solving kinetic equations. However, a major deficiency is that they do not preserve the structure of underlying physical problem. For example, classic dynamical methods violate mass, momentum, and energy conservation. In [L. Einkemmer, I. Joseph, J. Comput. Phys. 443:110495, 2021] conservative app...

Adaptive penalty function methods (APFMs) are promising constraints handling techniques. In an APFM, a parameter which balances constrains’ violations and objective values is adaptively adjusted. This work modifies APFM that uses near feasibility threshold (NFT), portion around the feasible region where infeasible solutions considered as good ones, for constrained multiobjective optimization. T...

Peer-to-peer (P2P) network systems gain a huge popularity due to their scalability and reliability in architectures and search facilities. Basically, most of the real world P2P network is unstructured. Due to their unstructured nature it is often impossible to pre-define the searching criteria. As a solution, flooding scheme is used in most cases. But one major limitation of flooding is its que...