Vector bundles on the projective line and finite domination of chain complexes

Finitely dominated chain complexes over a Laurent polynomial ring in one indeterminate are characterised by vanishing of their Novikov homology. We present an algebro-geometric approach to this result, based on extension of chain complexes to sheaves on the projective line. We also discuss the K-theoretical obstruction to extension.Comment: v1: 11 page

Paradigms for Parameterized Enumeration

The aim of the paper is to examine the computational complexity and algorithmics of enumeration, the task to output all solutions of a given problem, from the point of view of parameterized complexity. First we define formally different notions of efficient enumeration in the context of parameterized complexity. Second we show how different algorithmic paradigms can be used in order to get parameter-efficient enumeration algorithms in a number of examples. These paradigms use well-known principles from the design of parameterized decision as well as enumeration techniques, like for instance kernelization and self-reducibility. The concept of kernelization, in particular, leads to a characterization of fixed-parameter tractable enumeration problems.Comment: Accepted for MFCS 2013; long version of the pape

Fast algorithms for min independent dominating set

We first devise a branching algorithm that computes a minimum independent dominating set on any graph with running time O*(2^0.424n) and polynomial space. This improves the O*(2^0.441n) result by (S. Gaspers and M. Liedloff, A branch-and-reduce algorithm for finding a minimum independent dominating set in graphs, Proc. WG'06). We then show that, for every r>3, it is possible to compute an r-((r-1)/r)log_2(r)-approximate solution for min independent dominating set within time O*(2^(nlog_2(r)/r))

Direct and indirect orthotic management of medial compartment osteoarthritis of the knee

Osteoarthritis (OA) is a painful condition and affects approximately 80% of individuals by the age of 55 [1], with knee OA occurring two times more frequently than OA of the hand or hip [2].The condition is more prevalent in the medial compartment and restricts the daily lives of individuals due to pain and a lack of functional independence. Patients with medial compartment osteoarthritis often have a varus alignment, with the mechanical axis and load bearing passing through this compartment with a greater adduction moment leading to greater pain and progression of osteoarthritis [3]. Surgery for the condition is possible although in some cases, particularly younger patients or those not yet requiring surgery, clinical management remains a challenge. Before surgery is considered, however, conservative management is advocated, though no one treatment has been shown to be most effective, and there are few quality biomechanical or clinical studies. Of the conservative approaches the principal orthotic treatments are valgus knee braces and laterally wedged foot inlays. Studies of knee valgus bracing have consistently demonstrated an associated decreased pain and improved function [4], and greater confidence [5]. A laterally wedged foot inlay has a thicker lateral border and applies a valgus moment to the heel. It is theorised that by changing the position of the ankle and subtalar joints during weight-bearing [6] the lateral wedges may apply a valgus moment across the knee as well as the rearfoot, with the assumed reduction on load in the medial knee compartment [7]. However, there has been no study to directly compare these orthotic treatments in the same study. The aim of this research is to investigate the efficacy of valgus knee braces and laterally wedged foot inlays in reducing the varus knee moment

Connecting Terminals and 2-Disjoint Connected Subgraphs

Given a graph $G=(V,E)$ and a set of terminal vertices $T$ we say that a superset $S$ of $T$ is $T$-connecting if $S$ induces a connected graph, and $S$ is minimal if no strict subset of $S$ is $T$-connecting. In this paper we prove that there are at most ${|V \setminus T| \choose |T|-2} \cdot 3^{\frac{|V \setminus T|}{3}}$ minimal $T$-connecting sets when $|T| \leq n/3$ and that these can be enumerated within a polynomial factor of this bound. This generalizes the algorithm for enumerating all induced paths between a pair of vertices, corresponding to the case $|T|=2$. We apply our enumeration algorithm to solve the {\sc 2-Disjoint Connected Subgraphs} problem in time $O^*(1.7804^n)$, improving on the recent $O^*(1.933^n)$ algorithm of Cygan et al. 2012 LATIN paper.Comment: 13 pages, 1 figur

Approximation Algorithms for the Capacitated Domination Problem

We consider the {\em Capacitated Domination} problem, which models a service-requirement assignment scenario and is also a generalization of the well-known {\em Dominating Set} problem. In this problem, given a graph with three parameters defined on each vertex, namely cost, capacity, and demand, we want to find an assignment of demands to vertices of least cost such that the demand of each vertex is satisfied subject to the capacity constraint of each vertex providing the service. In terms of polynomial time approximations, we present logarithmic approximation algorithms with respect to different demand assignment models for this problem on general graphs, which also establishes the corresponding approximation results to the well-known approximations of the traditional {\em Dominating Set} problem. Together with our previous work, this closes the problem of generally approximating the optimal solution. On the other hand, from the perspective of parameterization, we prove that this problem is {\it W[1]}-hard when parameterized by a structure of the graph called treewidth. Based on this hardness result, we present exact fixed-parameter tractable algorithms when parameterized by treewidth and maximum capacity of the vertices. This algorithm is further extended to obtain pseudo-polynomial time approximation schemes for planar graphs

A rigorous evaluation of crossover and mutation in genetic programming

The role of crossover and mutation in Genetic Programming (GP) has been the subject of much debate since the emergence of the field. In this paper, we contribute new empirical evidence to this argument using a rigorous and principled experimental method applied to six problems common in the GP literature. The approach tunes the algorithm parameters to enable a fair and objective comparison of two different GP algorithms, the first using a combination of crossover and reproduction, and secondly using a combination of mutation and reproduction. We find that crossover does not significantly outperform mutation on most of the problems examined. In addition, we demonstrate that the use of a straightforward Design of Experiments methodology is effective at tuning GP algorithm parameters

MaxEnt power spectrum estimation using the Fourier transform for irregularly sampled data applied to a record of stellar luminosity

The principle of maximum entropy is applied to the spectral analysis of a data signal with general variance matrix and containing gaps in the record. The role of the entropic regularizer is to prevent one from overestimating structure in the spectrum when faced with imperfect data. Several arguments are presented suggesting that the arbitrary prefactor should not be introduced to the entropy term. The introduction of that factor is not required when a continuous Poisson distribution is used for the amplitude coefficients. We compare the formalism for when the variance of the data is known explicitly to that for when the variance is known only to lie in some finite range. The result of including the entropic measure factor is to suggest a spectrum consistent with the variance of the data which has less structure than that given by the forward transform. An application of the methodology to example data is demonstrated.Comment: 15 pages, 13 figures, 1 table, major revision, final version, Accepted for publication in Astrophysics & Space Scienc

Fitting a sum of exponentials to lattice correlation functions using a non-uniform prior

Excited states are extracted from lattice correlation functions using a non-uniform prior on the model parameters. Models for both a single exponential and a sum of exponentials are considered, as well as an alternate model for the orthogonalization of the correlation functions. Results from an analysis of torelon and glueball operators indicate the Bayesian methodology compares well with the usual interpretation of effective mass tables produced by a variational procedure. Applications of the methodology are discussed.Comment: 12 pages, 8 figures, 8 tables, major revision, final versio