Extended endocrine therapy beyond 5 years is of major concern to ER + breast cancer survivors. However, it might be unsuitable to apply routinely used genomic tests designed for early recurrence risks to distant recurrence within 10 years in extended treatment context. These tests initially aim at high sensitivities with Type I errors much higher than Type II. Having lower positive predictive values (PPVs), these tests can bring many false positives who might not need further treatment options to avoid adversely affecting quality of life. Alternatively, we proposed a top-down approach to the raised issues. We built 149 targeted genes from four genomic tests upon 381 ER-positive node-negative patients with either metastasis free beyond 10 years (n = 202) or metastasis within 10 years (n = 179). By a basket of SVM-wrapped length-constraint feature selection (LCFS), we discovered four genomic SVMs that traded off Type I against Type II errors. Two independent cohorts were used to validate disease outcome predictions. A 36-gene SVM balanced sensitivities with PPVs at good levels: 74% vs 76% on 10-fold cross validation (n = 347) and 75% vs 71% on a test set (n = 34). Neither Oncotype DX RS (cutoff = 18, 31, 60.97) nor PAM50 ROR-S (cutoff = 29, 53, 61.18) could. Independent cohorts showed the 36-gene SVM predicted disease free survival (n = 136, HR = 2.59; 95% CI, 1.4-4.8) and disease specific survival (n = 127, HR = 4.06; 95% CI, 1.63-10.11) better than RS (DFS, HR = 2.15; DSS, HR = 3.86) and ROR-S (DFS, HR = 2.29; DSS, HR = 2.76). The case study demonstrated how we identified a genomic test to balance Type I against Type II errors for risk stratification. The top-down approach centered around the LCFS-metaheuristics basket is a generic methodology for clinical decision-making and quality of life using targeted profiling data where the number of dimensions (p) is smaller than the number of samples (n).

Energy-efficient multicast routing algorithms have predominantly focused on wireless or ad-hoc mobile networks. However, since the turn of the century the need for energy efficient approaches to routing in wired networks has been steadily rising. In this paper, we introduce an objective function for multicast routing in wired networks taking energy consumption into consideration. A number of hybrid Genetic and Simulated Annealing based algorithms have been shown to be able to find solutions to the multicast routing problem superior to solely Genetic or Simulated Annealing based algorithms. Our approach adapts a population-based hybrid algorithm for routing multiple simultaneous multicast requests. We examine the performance in terms of energy efficiency against solutions found by Logarithmic Simulated Annealing and Genetic based algorithms. We find that the hybrid approach, in 87% of instances, was able to find superior solutions, and in 96% of instances, solutions superior or equal to the best solution given by either Simulated Annealing or Genetic approaches. The extent of the improvement however varied greatly from a few hundred to within ten Joules, with the improvement on the best solution ranging from 5.6 to 531.5 Joules.

Cancer classification through high-throughput gene expression profiles has been widely used in biomedical research. Most recently, we portrayed a multivariate method for large scale gene selection based on information theorem with a central issue of feature interdependence and validated its effectiveness using a colon cancer benchmark. The completed research work now contributes to this article. Firstly, we have refined the method and proposed a complete framework to select a gene signature for a certain disease phenotype prediction under high-throughput technologies. The framework has then been applied to a brain cancer gene expression profiles derived from Affymetrix Human Genome U95Av2 Array, where the interrogated genes are six times more than that in the previous studied colon cancer data set. Three information theorem based filters were used for comparison. Our experimental result shows that the framework outperformed them in terms of classification performance with three performance measures. Additionally, to demonstrate how effectively feature interdependence has been tackled in the framework, two sets of enrichment analysis have also been performed. The results also show that more statistically significant gene sets and regulatory interactions could be found in our gene signature. Therefore, this framework could be promising for high-throughput gene selection around gene synergy.

MOTIVATION: We study microRNA (miRNA) bindings to metastable RNA secondary structures close to minimum free energy conformations in the context of single nucleotide polymorphisms (SNPs) and messenger RNA (mRNA) concentration levels, i.e. whether features of miRNA bindings to metastable conformations could provide additional information supporting the differences in expression levels of the two sequences defined by a SNP. In our study, the instances [mRNA/3'UTR; SNP; miRNA] were selected based on strong expression level analyses, SNP locations within binding regions and the computationally feasible identification of metastable conformations. RESULTS: We identified 14 basic cases [mRNA; SNP; miRNA] of 3' UTR-lengths ranging from 124 up to 1078 nt reported in recent literature, and we analyzed the number, structure and miRNA binding to metastable conformations within an energy offset above mfe conformations. For each of the 14 instances, the miRNA binding characteristics are determined by the corresponding STarMir output. Among the different parameters we introduced and analyzed, we found that three of them, related to the average depth and average opening energy of metastable conformations, may provide supporting information for a stronger separation between miRNA bindings to the two alleles defined by a given SNP. AVAILABILITY AND IMPLEMENTATION: At http://kks.inf.kcl.ac.uk/MSbind.html the MSbind tool is available for calculating features of metastable conformations determined by putative miRNA binding sites.

MOTIVATION: We study a stochastic method for approximating the set of local minima in partial RNA folding landscapes associated with a bounded-distance neighbourhood of folding conformations. The conformations are limited to RNA secondary structures without pseudoknots. The method aims at exploring partial energy landscapes pL induced by folding simulations and their underlying neighbourhood relations. It combines an approximation of the number of local optima devised by Garnier and Kallel (2002) with a run-time estimation for identifying sets of local optima established by Reeves and Eremeev (2004). RESULTS: The method is tested on nine sequences of length between 50 nt and 400 nt, which allows us to compare the results with data generated by RNAsubopt and subsequent barrier tree calculations. On the nine sequences, the method captures on average 92% of local minima with settings designed for a target of 95%. The run-time of the heuristic can be estimated by O(n(2)Dνlnν), where n is the sequence length, ν is the number of local minima in the partial landscape pL under consideration and D is the maximum number of steepest descent steps in attraction basins associated with pL.

The paper aims at tight upper bounds on the size of pattern classification circuits that can be used for a priori parameter settings in a machine learning context. The upper bounds relate the circuit size S(C) to n L := [log 2 m L ], where m L is the number of training samples. In particular, we show that there exist unbounded fan-in threshold circuits with less than (a) S R cc := 2·√2 n L + 3 gates for unbounded depth, (b) S L cc := 34.8 · √2 n L + 14 · n L − 11 · log 2 n L + 2 gates for small bounded depth, where in both cases all m L samples are classified correctly. We note that the upper bounds do not depend on the length n of input (sample) vectors. Since n L << n in real-world problem settings, the upper bounds return values that are suitable for practical applications. We provide experimental evidence that the circuit size estimations work well on a number of pattern classification tasks. As a result, we formulate the conjecture that [1.25 · S R cc or [0.07 · S L cc ] gates are sufficient to achieve a high generalization rate of bounded-depth classification circuits.

Abstract—Over the past ten years, methods from statisti-cal physics have provided a deeper inside into the average complexity of hard combinatorial problems, culminating in a rigorous proof for the asymptotic behaviour of the k-SAT phase transition threshold by Achlioptas and Peres in 2004. On the other hand, when dealing with individual instances of hard problems, gathering information about specific properties of instances in a pre-processing phase might be helpful for an appropriate adjustment of local search-based procedures. In the present paper, we address both issues in the context of landscapes induced by k-SAT instances: Firstly, we utilize a sampling method devised by Garnier and Kallel in 2002 for approximations of the number of local maxima in land-scapes generated by individual k-SAT instances and a simple neighbourhood relation. The objective function is given by the number of satisfied clauses. Secondly, we outline a method for obtaining upper bounds for the average number of local maxima in k-SAT instances which indicates some kind of phase transition for the neighbourhood-specific ratio m/n = Θ(2k/k). I.

Over the past few years, the importance of axonal conduction delays has been emphasized by a number of authors. Different models are proposed for the approximation of signal delays, where some of them have been evaluated in the context of the optimal neuronal layout problem. Our paper presents computational experiments on the impact of two wiring cost functions, proposed by D. Chklovskii and O. Shefi et al., when applied to interneuronal connections in small ML neuronal networks.

We describe a population-based search algorithm for cost minimization of multicast routing. The algorithm utilizes the partially mixed crossover operation (PMX) and a landscape analysis in a pre-processing step. The aim of the landscape analysis is to estimate the depth Γ of the deepest local minima in the landscape generated by the routing tasks and the objective function. The analysis employs simulated annealing with a logarithmic cooling schedule (LSA). The local search performs alternating sequences of descending and ascending steps for each individual of the population, where the length of a sequence with uniform direction is controlled by the estimated value of Γ. We present results from computational experiments on a synthetic routing tasks, and we provide experimental evidence that our genetic local search procedure, that combines LSA and PMX, performs better than algorithms using either LSA or PMX only.

We present a pattern classification method that combines the classical Perceptron algorithm with simulated annealing. For a sample set S of n-dimensional patterns labeled as positive and negative, our algorithm computes threshold circuits of small depth where the linear threshold functions of the first layer are calculated by simulated annealing with the logarithmic cooling schedule c(k) = Γ(k)/ ln (k + 2). The parameter Γ depends on the sample set and changes in time, and the neighborhood relation is determined by the Perceptron algorithm. We apply the approach to the recognition of focal liver tumours. From 400 positive (focal liver tumour) and 400 negative (normal liver tissue) examples a depth-six threshold circuit is calculated. The examples are of size n = 14161 = 119 × 119 and they are presented in the DICOM format. On test sets of 100 + 100 examples (disjoint from the learning set) we obtain a correct classification of more than 98%.

The authors consider optimal placements of two-dimensional flexible (elastic, deformable) objects. The objects are discs of equal size placed within a rigid boundary. The paper is divided into two parts. In the first part, analytical results for three types of regular, periodic arrangements-the hexagonal, square, and triangular placements-are presented. The regular arrangements are analyzed for rectangular boundaries and radii of discs that are small compared to the area of the placement region, because, in this case, the influence of boundary conditions can be neglected. This situation is called the unbounded case. They show that, for the unbounded case among the three regular placements, the type of hexagonal arrangements provides the largest number of placed units for the same deformation depth. Furthermore, it can be proved that these regular placements are not too far from the truly optimal arrangements. For example, hexagonal placements differ at most by the factor of 1.1 from the largest possible number of generally shaped units in arbitrary arrangements. These analytical results are used as guidances for testing stochastic algorithms optimizing placements of flexible objects. In the second part, mainly two problems are considered: the underlying physical model and a simulated annealing algorithm maximizing the number of flexible discs in equilibrium placements. Along with the physical model, an approximate formula is derived, reflecting the deformation/force relationship for a large range of deformations.

For pt.I see ibid., p.890-904. The paper is a continuation of the first part, where the authors considered regular arrangements of flexible objects for the unbounded case. The present part deals with a simulated annealing algorithm maximizing the number of flexible objects in equilibrium placements within rigid boundaries. The forces caused by the boundary are taken into account, i.e., the bounded case of placements is considered. The simulated annealing procedure makes use of the special structure of the underlying configuration space and relationships between deformations of flexible objects and resulting forces. This allows one to obtain tight bounds for the annealing parameters which result in n/sup 3/2//spl middot/In/sup 5/2/ and n/spl middot/In/sup 2/n time bounds, respectively, for the computation of equilibrium states by two different cooling schedules. The deformation/force formula is derived from a physical model of flexible discs and is based on numerical experiments which were performed for different materials and different sizes of objects. The algorithm was first implemented and tested for the unbounded case. The run-time is relatively short, even for large numbers of placed discs. These results are compared to the analytical ones obtained for regular placements in the first part of the paper, and agreement between these two sets of results are observed. Furthermore, several experiments for placements with boundary conditions were carried out and the resulting placements clearly show the effect of the forces from the rigid boundary.