Semidefinite programming bounds for Lee codes

For $q,n,d \in \mathbb{N}$, let $A_q^L(n,d)$ denote the maximum cardinality of a code $C \subseteq \mathbb{Z}_q^n$ with minimum Lee distance at least $d$, where $\mathbb{Z}_q$ denotes the cyclic group of order $q$. We consider a semidefinite programming bound based on triples of codewords, which bound can be computed efficiently using symmetry reductions, resulting in several new upper bounds on $A_q^L(n,d)$. The technique also yields an upper bound on the independent set number of the $n$-th strong product power of the circular graph $C_{d,q}$, which number is related to the Shannon capacity of $C_{d,q}$. Here $C_{d,q}$ is the graph with vertex set $\mathbb{Z}_q$, in which two vertices are adjacent if and only if their distance (mod $q$) is strictly less than $d$. The new bound does not seem to improve significantly over the bound obtained from Lov\'asz theta-function, except for very small $n$.Comment: 14 pages. arXiv admin note: text overlap with arXiv:1703.0517

Why is it hard to beat O(n2)O(n^2) for Longest Common Weakly Increasing Subsequence?

The Longest Common Weakly Increasing Subsequence problem (LCWIS) is a variant of the classic Longest Common Subsequence problem (LCS). Both problems can be solved with simple quadratic time algorithms. A recent line of research led to a number of matching conditional lower bounds for LCS and other related problems. However, the status of LCWIS remained open. In this paper we show that LCWIS cannot be solved in strongly subquadratic time unless the Strong Exponential Time Hypothesis (SETH) is false. The ideas which we developed can also be used to obtain a lower bound based on a safer assumption of NC-SETH, i.e. a version of SETH which talks about NC circuits instead of less expressive CNF formulas

Counting Triangles in Large Graphs on GPU

The clustering coefficient and the transitivity ratio are concepts often used in network analysis, which creates a need for fast practical algorithms for counting triangles in large graphs. Previous research in this area focused on sequential algorithms, MapReduce parallelization, and fast approximations. In this paper we propose a parallel triangle counting algorithm for CUDA GPU. We describe the implementation details necessary to achieve high performance and present the experimental evaluation of our approach. Our algorithm achieves 8 to 15 times speedup over the CPU implementation and is capable of finding 3.8 billion triangles in an 89 million edges graph in less than 10 seconds on the Nvidia Tesla C2050 GPU.Comment: 2016 IEEE International Parallel and Distributed Processing Symposium Workshops (IPDPSW

A survey of methods of feasible directions for the solution of optimal control problems

Three methods of feasible directions for optimal control are reviewed. These methods are an extension of the Frank-Wolfe method, a dual method devised by Pironneau and Polack, and a Zontendijk method. The categories of continuous optimal control problems are shown as: (1) fixed time problems with fixed initial state, free terminal state, and simple constraints on the control; (2) fixed time problems with inequality constraints on both the initial and the terminal state and no control constraints; (3) free time problems with inequality constraints on the initial and terminal states and simple constraints on the control; and (4) fixed time problems with inequality state space contraints and constraints on the control. The nonlinear programming algorithms are derived for each of the methods in its associated category

A modified secant method for unconstrained minimization

A gradient-secant algorithm for unconstrained optimization problems is presented. The algorithm uses Armijo gradient method iterations until it reaches a region where the Newton method is more efficient, and then switches over to a secant form of operation. It is concluded that an efficient method for unconstrained minimization has been developed, and that any convergent minimization method can be substituted for the Armijo gradient method

Mixed logit modelling of airport choice in multi-airport regions

This paper presents an analysis of the choice of airport by air travellers departing from the San Francisco Bay (SF-B) area. The analysis uses the mixed multinomial logit model, which allows for a random distribution of tastes across decision makers. To our knowledge, this is the first application using this model form in the analysis of airport choice. The results indicate that there is significant heterogeneity in tastes, especially with respect to the sensitivity to access time, characterised by deterministic variations between groups of travellers (business/leisure, residents/visitors) as well as random variations within groups of travellers. The analysis reinforces earlier findings showing that business travellers are far less sensitive to fare increases than leisure travellers, and are willing to pay a higher price for decreases in access time (and generally also increases in frequency) than is the case for leisure travellers. Finally, the results show that the random variation between business travellers in terms of sensitivity to access time is more pronounced than that between leisure travellers, as is the case for visitors when compared to residents

Comitology between Political Decision-Making and Technocratic Governance: Regulating GMOs in the European Union

The EU’s comitology system is generally considered to be an effective mechanism for facilitating efficient policy implementation while at the same time ensuring a degree of Member State control over the process. However, if this assessment is applicable to most areas of routine decision-making, the regulation of GMO authorizations by the European Commission, which also falls under comitology, presents a markedly different picture. The article shows the particular problems that occur in this field, outlining the involvement of a number of different actors (comitology committees, Council, European Commission and the European Food Safety Authority (EFSA) and their interaction in what has become a complex and protracted policy process. The articles identifies a number of key issues – the reliance of the Commission on EFSA’s scientific expertise, the weakness of political accountability due to divisions among the Member States, the difficulties of the European Commission to achieve compliance with European and international rules – and discusses the impact that these have on the legitimacy, efficiency and effectiveness of policy-making in this area. The article concludes that, due to the problems arising from the particular arrangement of interests and procedures in this area, the operation of comitology in the regulation of GMOs is highly problematic

On the removal of ill conditioning effects in the computation of optimal controls

Ill conditioning effects eliminated in nonlinear programming algorithms for optimal control