Local optima networks of hard combinatorial landscapes

Combinatorial optimization involves finding an optimal solution in a finite set of options; many everyday life problems are of this kind. However, the number of options grows exponentially with the size of the problem, such that an exhaustive search for the best solution is practically infeasible beyond a certain problem size. When efficient algorithms are not available, a practical approach to obtain an approximate solution to the problem at hand, is to start with an educated guess and gradually refine it until we have a good-enough solution. Roughly speaking, this is how local search heuristics work. These stochastic algorithms navigate the problem search space by iteratively turning the current solution into new candidate solutions, guiding the search towards better solutions. The search performance, therefore, depends on structural aspects of the search space, which in turn depend on the move operator being used to modify solutions. A common way to characterize the search space of a problem is through the study of its fitness landscape, a mathematical object comprising the space of all possible solutions, their value with respect to the optimization objective, and a relationship of neighborhood defined by the move operator. The landscape metaphor is used to explain the search dynamics as a sort of potential function. The concept is indeed similar to that of potential energy surfaces in physical chemistry. Borrowing ideas from that field, we propose to extend to combinatorial landscapes the notion of the inherent network formed by energy minima in energy landscapes. In our case, energy minima are the local optima of the combinatorial problem, and we explore several definitions for the network edges. At first, we perform an exhaustive sampling of local optima basins of attraction, and define weighted transitions between basins by accounting for all the possible ways of crossing the basins frontier via one random move. Then, we reduce the computational burden by only counting the chances of escaping a given basin via random kick moves that start at the local optimum. Finally, we approximate network edges from the search trajectory of simple search heuristics, mining the frequency and inter-arrival time with which the heuristic visits local optima. Through these methodologies, we build a weighted directed graph that provides a synthetic view of the whole landscape, and that we can characterize using the tools of complex networks science. We argue that the network characterization can advance our understanding of the structural and dynamical properties of hard combinatorial landscapes. We apply our approach to prototypical problems such as the Quadratic Assignment Problem, the NK model of rugged landscapes, and the Permutation Flow-shop Scheduling Problem. We show that some network metrics can differentiate problem classes, correlate with problem non-linearity, and predict problem hardness as measured from the performances of trajectory-based local search heuristics.

A random linear functional approach to efficiency bounds

This paper suggests a method for obtaining efficiency bounds in models containing either only infinite-dimensional parameters or both finite- and infinite-dimensional parameters (semiparametric models). The method is based on a theory of random linear functionals applied to the gradient of the log-likelihood functional and is illustrated by computing the lower bound for Cox's regression model

Self-avoiding random walks and Olbers' paradox

In this paper, we prove that a self-avoiding walk of infinite length provides a structure that would resolve Olbers' paradox. That is, if the stars of a universe were distributed like the vertices of an infinite random walk with each segment length of about a parsec, then the night sky could be as dark as actually observed on the Earth. Self-avoiding random walk structure can therefore resolve the Olbers' paradox even in a static universe.

Scaling behavior of random knots.

Using numerical simulations we investigate how overall dimensions of random knots scale with their length. We demonstrate that when closed non-self-avoiding random trajectories are divided into groups consisting of individual knot types, then each such group shows the scaling exponent of approximately 0.588 that is typical for self-avoiding walks. However, when all generated knots are grouped together, their scaling exponent becomes equal to 0.5 (as in non-self-avoiding random walks). We explain here this apparent paradox. We introduce the notion of the equilibrium length of individual types of knots and show its correlation with the length of ideal geometric representations of knots. We also demonstrate that overall dimensions of random knots with a given chain length follow the same order as dimensions of ideal geometric representations of knots.

Rapid optimization of drug combinations for the optimal angiostatic treatment of cancer.

Drug combinations can improve angiostatic cancer treatment efficacy and enable the reduction of side effects and drug resistance. Combining drugs is non-trivial due to the high number of possibilities. We applied a feedback system control (FSC) technique with a population-based stochastic search algorithm to navigate through the large parametric space of nine angiostatic drugs at four concentrations to identify optimal low-dose drug combinations. This implied an iterative approach of in vitro testing of endothelial cell viability and algorithm-based analysis. The optimal synergistic drug combination, containing erlotinib, BEZ-235 and RAPTA-C, was reached in a small number of iterations. Final drug combinations showed enhanced endothelial cell specificity and synergistically inhibited proliferation (p < 0.001), but not migration of endothelial cells, and forced enhanced numbers of endothelial cells to undergo apoptosis (p < 0.01). Successful translation of this drug combination was achieved in two preclinical in vivo tumor models. Tumor growth was inhibited synergistically and significantly (p < 0.05 and p < 0.01, respectively) using reduced drug doses as compared to optimal single-drug concentrations. At the applied conditions, single-drug monotherapies had no or negligible activity in these models. We suggest that FSC can be used for rapid identification of effective, reduced dose, multi-drug combinations for the treatment of cancer and other diseases.

Geometric stopping of a random walk and its applications to valuing equity-linked death benefits

We study discrete-time models in which death benefits can depend on a stock price index, the logarithm of which is modeled as a random walk. Examples of such benefit payments include put and call options, barrier options, and lookback options. Because the distribution of the curtate-future-lifetime can be approximated by a linear combination of geometric distributions, it suffices to consider curtate-future-lifetimes with a geometric distribution. In binomial and trinomial tree models, closed-form expressions for the expectations of the discounted benefit payment are obtained for a series of options. They are based on results concerning geometric stopping of a random walk, in particular also on a version of the Wiener-Hopf factorization.

L'exploitation des peintures en spray en criminalistique: mise en place d'une procédure de gestion et de comparaison des spectres infrarouges à l'aide des statistiques multivariées

La spectroscopie infrarouge (FTIR) est une technique de choix dans l'analyse des peintures en spray (traces ou bonbonnes de référence), grâce à son fort pouvoir discriminant, sa sensibilité, et ses nombreuses possibilités d'échantillonnage. La comparaison des spectres obtenus est aujourd'hui principalement faite visuellement, mais cette procédure présente des limitations telles que la subjectivité de la prise de décision car celle-ci dépend de l'expérience et de la formation suivie par l'expert. De ce fait, de faibles différences d'intensités relatives entre deux pics peuvent être perçues différemment par des experts, même au sein d'un même laboratoire. Lorsqu'il s'agit de justifier ces différences, certains les expliqueront par la méthode analytique utilisée, alors que d'autres estimeront plutôt qu'il s'agit d'une variabilité intrinsèque à la peinture et/ou à son vécu (par exemple homogénéité, sprayage, ou dégradation). Ce travail propose d'étudier statistiquement les différentes sources de variabilité observables dans les spectres infrarouges, de les identifier, de les comprendre et tenter de les minimiser. Le deuxième objectif principal est de proposer une procédure de comparaison des spectres qui soit davantage transparente et permette d'obtenir des réponses reproductibles indépendamment des experts interrogés. La première partie du travail traite de l'optimisation de la mesure infrarouge et des principaux paramètres analytiques. Les conditions nécessaires afin d'obtenir des spectres reproductibles et minimisant la variation au sein d'un même échantillon (intra-variabilité) sont présentées. Par la suite une procédure de correction des spectres est proposée au moyen de prétraitements et de sélections de variables, afin de minimiser les erreurs systématiques et aléatoires restantes, et de maximiser l'information chimique pertinente. La seconde partie présente une étude de marché effectuée sur 74 bonbonnes de peintures en spray représentatives du marché suisse. Les capacités de discrimination de la méthode FTIR au niveau de la marque et du modèle sont évaluées au moyen d'une procédure visuelle, et comparées à diverses procédures statistiques. Les limites inférieures de discrimination sont testées sur des peintures de marques et modèles identiques mais provenant de différents lots de production. Les résultats ont montré que la composition en pigments était particulièrement discriminante, à cause des étapes de corrections et d'ajustement de la couleur subies lors de la production. Les particularités associées aux peintures en spray présentes sous forme de traces (graffitis, gouttelettes) ont également été testées. Trois éléments sont mis en évidence et leur influence sur le spectre infrarouge résultant testée : 1) le temps minimum de secouage nécessaire afin d'obtenir une homogénéité suffisante de la peinture et, en conséquence, de la surface peinte, 2) la dégradation initiée par le rayonnement ultra- violet en extérieur, et 3) la contamination provenant du support lors du prélèvement. Finalement une étude de population a été réalisée sur 35 graffitis de la région lausannoise et les résultats comparés à l'étude de marché des bonbonnes en spray. La dernière partie de ce travail s'est concentrée sur l'étape de prise de décision lors de la comparaison de spectres deux-à-deux, en essayant premièrement de comprendre la pratique actuelle au sein des laboratoires au moyen d'un questionnaire, puis de proposer une méthode statistique de comparaison permettant d'améliorer l'objectivité et la transparence lors de la prise de décision. Une méthode de comparaison basée sur la corrélation entre les spectres est proposée, et ensuite combinée à une évaluation Bayesienne de l'élément de preuve au niveau de la source et au niveau de l'activité. Finalement des exemples pratiques sont présentés et la méthodologie est discutée afin de définir le rôle précis de l'expert et des statistiques dans la procédure globale d'analyse des peintures. -- Infrared spectroscopy (FTIR) is a technique of choice for analyzing spray paint speciments (i.e. traces) and reference samples (i.e. cans seized from suspects) due to its high discriminating power, sensitivity and sampling possibilities. The comparison of the spectra is currently carried out visually, but this procedure has limitations such as the subjectivity in the decision due to its dependency on the experience and training of the expert. This implies that small differences in the relative intensity of two peaks can be perceived differently by experts, even between analysts working in the same laboratory. When it comes to justifying these differences, some will explain them by the analytical technique, while others will estimate that the observed differences are mostly due to an intrinsic variability from the paint sample and/or its acquired characteristics (for example homogeneity, spraying, or degradation). This work proposes to statistically study the different sources of variability observed in infrared spectra, to identify them, understand them and try to minimize them. The second goal is to propose a procedure for spectra comparison that is more transparent, and allows obtaining reproducible answers being independent from the expert. The first part of the manuscript focuses on the optimization of infrared measurement and on the main analytical parameters. The necessary conditions to obtain reproducible spectra with a minimized variation within a sample (intra-variability) are presented. Following that a procedure of spectral correction is then proposed using pretreatments and variable selection methods, in order to minimize systematic and random errors, and increase simultaneously relevant chemical information. The second part presents a market study of 74 spray paints representative of the Swiss market. The discrimination capabilities of FTIR at the brand and model level are evaluated by means of visual and statistical procedures. The inferior limits of discrimination are tested on paints coming from the same brand and model, but from different production batches. The results showed that the pigment composition was particularly discriminatory, because of the corrections and adjustments made to the paint color during its manufacturing process. The features associated with spray paint traces (graffitis, droplets) were also tested. Three elements were identified and their influence on the resulting infrared spectra were tested: 1) the minimum shaking time necessary to obtain a sufficient homogeneity of the paint and subsequently of the painted surface, 2) the degradation initiated by ultraviolet radiation in an exterior environment, and 3) the contamination from the support when paint is recovered. Finally a population study was performed on 35 graffitis coming from the city of Lausanne and surroundings areas, and the results were compared to the previous market study of spray cans. The last part concentrated on the decision process during the pairwise comparison of spectra. First, an understanding of the actual practice among laboratories was initiated by submitting a questionnaire. Then, a proposition for a statistical method of comparison was advanced to improve the objectivity and transparency during the decision process. A method of comparison based on the correlation between spectra is proposed, followed by the integration into a Bayesian framework at both source and activity levels. Finally, some case examples are presented and the recommended methodology is discussed in order to define the role of the expert as well as the contribution of the tested statistical approach within a global analytical sequence for paint examinations.

Priming psychic and conjuring abilities of a magic demonstration influences event interpretation and random number generation biases

Magical ideation and belief in the paranormal is considered to represent a trait-like character; people either believe in it or not. Yet, anecdotes indicate that exposure to an anomalous event can turn skeptics into believers. This transformation is likely to be accompanied by altered cognitive functioning such as impaired judgments of event likelihood. Here, we investigated whether the exposure to an anomalous event changes individuals' explicit traditional (religious) and non-traditional (e.g., paranormal) beliefs as well as cognitive biases that have previously been associated with non-traditional beliefs, e.g., repetition avoidance when producing random numbers in a mental dice task. In a classroom, 91 students saw a magic demonstration after their psychology lecture. Before the demonstration, half of the students were told that the performance was done respectively by a conjuror (magician group) or a psychic (psychic group). The instruction influenced participants' explanations of the anomalous event. Participants in the magician, as compared to the psychic group, were more likely to explain the event through conjuring abilities while the reverse was true for psychic abilities. Moreover, these explanations correlated positively with their prior traditional and non-traditional beliefs. Finally, we observed that the psychic group showed more repetition avoidance than the magician group, and this effect remained the same regardless of whether assessed before or after the magic demonstration. We conclude that pre-existing beliefs and contextual suggestions both influence people's interpretations of anomalous events and associated cognitive biases. Beliefs and associated cognitive biases are likely flexible well into adulthood and change with actual life events.

Optimization of Radiation Dose and Image Quality in Musculoskeletal CT: Emphasis on Iterative Reconstruction Techniques (Part 1).

Computed tomography (CT) is a modality of choice for the study of the musculoskeletal system for various indications including the study of bone, calcifications, internal derangements of joints (with CT arthrography), as well as periprosthetic complications. However, CT remains intrinsically limited by the fact that it exposes patients to ionizing radiation. Scanning protocols need to be optimized to achieve diagnostic image quality at the lowest radiation dose possible. In this optimization process, the radiologist needs to be familiar with the parameters used to quantify radiation dose and image quality. CT imaging of the musculoskeletal system has certain specificities including the focus on high-contrast objects (i.e., in CT of bone or CT arthrography). These characteristics need to be taken into account when defining a strategy to optimize dose and when choosing the best combination of scanning parameters. In the first part of this review, we present the parameters used for the evaluation and quantification of radiation dose and image quality. In the second part, we discuss different strategies to optimize radiation dose and image quality at CT, with a focus on the musculoskeletal system and the use of novel iterative reconstruction techniques.

Optimization of Radiation Dose and Image Quality in Musculoskeletal CT: Emphasis on Iterative Reconstruction Techniques (Part 2).

Computed tomography (CT) is a modality of choice for the study of the musculoskeletal system for various indications including the study of bone, calcifications, internal derangements of joints (with CT arthrography), as well as periprosthetic complications. However, CT remains intrinsically limited by the fact that it exposes patients to ionizing radiation. Scanning protocols need to be optimized to achieve diagnostic image quality at the lowest radiation dose possible. In this optimization process, the radiologist needs to be familiar with the parameters used to quantify radiation dose and image quality. CT imaging of the musculoskeletal system has certain specificities including the focus on high-contrast objects (i.e., in CT of bone or CT arthrography). These characteristics need to be taken into account when defining a strategy to optimize dose and when choosing the best combination of scanning parameters. In the first part of this review, we present the parameters used for the evaluation and quantification of radiation dose and image quality. In the second part, we discuss different strategies to optimize radiation dose and image quality of CT, with a focus on the musculoskeletal system and the use of novel iterative reconstruction techniques.

Accelerated Microstructure Imaging via Convex Optimization (AMICO) in crossing fibers

Mapping the microstructure properties of the local tissues in the brain is crucial to understand any pathological condition from a biological perspective. Most of the existing techniques to estimate the microstructure of the white matter assume a single axon orientation whereas numerous regions of the brain actually present a fiber-crossing configuration. The purpose of the present study is to extend a recent convex optimization framework to recover microstructure parameters in regions with multiple fibers.