Statistics of Partial Minima

Motivated by multi-objective optimization, we study extrema of a set of N points independently distributed inside the d-dimensional hypercube. A point in this set is k-dominated by another point when at least k of its coordinates are larger, and is a k-minimum if it is not k-dominated by any other point. We obtain statistical properties of these partial minima using exact probabilistic methods and heuristic scaling techniques. The average number of partial minima, A, decays algebraically with the total number of points, A ~ N^{-(d-k)/k}, when 1<=k<d. Interestingly, there are k-1 distinct scaling laws characterizing the largest coordinates as the distribution P(y_j) of the jth largest coordinate, y_j, decays algebraically, P(y_j) ~ (y_j)^{-alpha_j-1}, with alpha_j=j(d-k)/(k-j) for 1<=j<=k-1. The average number of partial minima grows logarithmically, A ~ [1/(d-1)!](ln N)^{d-1}, when k=d. The full distribution of the number of minima is obtained in closed form in two-dimensions.Comment: 6 pages, 1 figur

Time-dependent postmortem redistribution of butyrfentanyl and its metabolites in blood and alternative matrices in a case of butyrfentanyl intoxication

A fatal case of butyrfentanyl poisoning was investigated at the Zurich Institute of Forensic Medicine. At admission at the institute approx. 9 h after death (first time point, t1), femoral and heart blood (right ventricle) was collected, as well as samples from the lung, liver, kidney, spleen, muscle and adipose tissue using computed tomography (CT)-guided biopsy sampling. At autopsy (t2), samples from the same body regions were collected manually. Additionally, urine, heart blood (left ventricle), gastric content, brain samples and hair were collected. Butyrfentanyl concentrations and relative concentrations of the metabolites carboxy-, hydroxy-, nor-, and desbutyrfentanyl were determined by LC⿿MS/MS and LC-QTOF. At t1, butyrfentanyl concentrations were 66 ng/mL in femoral blood, 39 ng/mL in heart blood, 110 ng/g in muscle, 57 ng/g in liver, 160 ng/g in kidney, 3100 ng/g in lung, 590 ng/g in spleen and 550 ng/g in adipose tissue. At t2, butyrfentanyl concentration in urine was 1100 ng/mL, in gastric content 2000 ng/mL, in hair 11,000 pg/mg and brain concentrations ranged between 200⿿340 ng/g. Carboxy- and hydroxybutyrfentanyl were identified as most abundant metabolites. Comparison of t1 and t2 showed a concentration increase of butyrfentanyl in femoral blood of 120%, in heart blood of 55% and a decrease in lung of 30% within 19 h. No clear concentration changes could be observed in the other matrices. Postmortem concentration changes were also observed for the metabolites. In conclusion, butyrfentanyl seems to be prone to postmortem redistribution processes and concentrations in forensic death cases should be interpreted with caution

Estimating Mutual Information

We present two classes of improved estimators for mutual information $M(X,Y)$, from samples of random points distributed according to some joint probability density $\mu(x,y)$. In contrast to conventional estimators based on binnings, they are based on entropy estimates from $k$-nearest neighbour distances. This means that they are data efficient (with $k=1$ we resolve structures down to the smallest possible scales), adaptive (the resolution is higher where data are more numerous), and have minimal bias. Indeed, the bias of the underlying entropy estimates is mainly due to non-uniformity of the density at the smallest resolved scale, giving typically systematic errors which scale as functions of $k/N$ for $N$ points. Numerically, we find that both families become {\it exact} for independent distributions, i.e. the estimator $\hat M(X,Y)$ vanishes (up to statistical fluctuations) if $\mu(x,y) = \mu(x) \mu(y)$. This holds for all tested marginal distributions and for all dimensions of $x$ and $y$. In addition, we give estimators for redundancies between more than 2 random variables. We compare our algorithms in detail with existing algorithms. Finally, we demonstrate the usefulness of our estimators for assessing the actual independence of components obtained from independent component analysis (ICA), for improving ICA, and for estimating the reliability of blind source separation.Comment: 16 pages, including 18 figure

Quasiperiodic time dependent current in driven superlattices: distorted Poincare maps and strange attractors

Intriguing routes to chaos have been experimentally observed in semiconductor superlattices driven by an ac field. In this work, a theoretical model of time dependent transport in ac driven superlattices is numerically solved. In agreement with experiments, distorted Poincare maps in the quasiperiodic regime are found. They indicate the appearance of very complex attractors and routes to chaos as the amplitude of the AC signal increases. Distorted maps are caused by the discrete well-to-well jump motion of a domain wall during spiky high-frequency self-sustained oscillations of the current.Comment: 10 pages, 4 figure

The transition between stochastic and deterministic behavior in an excitable gene circuit

We explore the connection between a stochastic simulation model and an ordinary differential equations (ODEs) model of the dynamics of an excitable gene circuit that exhibits noise-induced oscillations. Near a bifurcation point in the ODE model, the stochastic simulation model yields behavior dramatically different from that predicted by the ODE model. We analyze how that behavior depends on the gene copy number and find very slow convergence to the large number limit near the bifurcation point. The implications for understanding the dynamics of gene circuits and other birth-death dynamical systems with small numbers of constituents are discussed.Comment: PLoS ONE: Research Article, published 11 Apr 201

Decisional Conflict and User Acceptance of Multicriteria Decision-Making Aids *

Despite the development of increasingly sophisticated and refined multicriteria decision-making (MCDM) methods, an examination of the experimental evidence indicates that users most often prefer relatively unsophisticated methods. In this paper, we synthesize theories and empirical findings from the psychology of judgment and choice to provide a new theoretical explanation for such user preferences. Our argument centers on the assertion that the MCDM method preferred by decision makers is a function of the degree to which the method tends to introduce decisional conflict. The model we develop relates response mode, decision strategy, and the salience of decisional conflict to user preferences among decision aids. We then show that the model is consistent with empirical results in MCDM studies. Next, the role of decisional conflict in problem formulation aids is briefly discussed. Finally, we outline future research needed to thoroughly test the theoretical mechanisms we have proposed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73461/1/j.1540-5915.1991.tb00371.x.pd

Approximating the Pareto Front of Multi-criteria Optimization Problems

Abstract. We propose a general methodology for approximating the Pareto front of multi-criteria optimization problems. Our search-based methodology consists of submitting queries to a constraint solver. Hence, in addition to a set of solutions, we can guarantee bounds on the distance to the actual Pareto front and use this distance to guide the search. Our implementation, which computes and updates the distance efficiently, has been tested on numerous examples.

Determining and interpreting correlations in lipidomic networks found in glioblastoma cells

Background: Intelligent and multitiered quantitative analysis of biological systems rapidly evolves to a key technique in studying biomolecular cancer aspects. Newly emerging advances in both measurement as well as bio-inspired computational techniques have facilitated the development of lipidomics technologies and offer an excellent opportunity to understand regulation at the molecular level in many diseases. Results: We present computational approaches to study the response of glioblastoma U87 cells to gene- and chemo-therapy. To identify distinct biomarkers and differences in therapeutic outcomes, we develop a novel technique based on graph-clustering. This technique facilitates the exploration and visualization of co-regulations in glioblastoma lipid profiling data. We investigate the changes in the correlation networks for different therapies and study the success of novel gene therapies targeting aggressive glioblastoma. Conclusions: The novel computational paradigm provides unique “fingerprints” by revealing the intricate interactions at the lipidome level in glioblastoma U87 cells with induced apoptosis (programmed cell death) and thus opens a new window to biomedical frontiers. Background Glioblastoma are highly invasive brain tumors. Th

Systematic Analysis of Stability Patterns in Plant Primary Metabolism

Metabolic networks are characterized by complex interactions and regulatory mechanisms between many individual components. These interactions determine whether a steady state is stable to perturbations. Structural kinetic modeling (SKM) is a framework to analyze the stability of metabolic steady states that allows the study of the system Jacobian without requiring detailed knowledge about individual rate equations. Stability criteria can be derived by generating a large number of structural kinetic models (SK-models) with randomly sampled parameter sets and evaluating the resulting Jacobian matrices. Until now, SKM experiments applied univariate tests to detect the network components with the largest influence on stability. In this work, we present an extended SKM approach relying on supervised machine learning to detect patterns of enzyme-metabolite interactions that act together in an orchestrated manner to ensure stability. We demonstrate its application on a detailed SK-model of the Calvin-Benson cycle and connected pathways. The identified stability patterns are highly complex reflecting that changes in dynamic properties depend on concerted interactions between several network components. In total, we find more patterns that reliably ensure stability than patterns ensuring instability. This shows that the design of this system is strongly targeted towards maintaining stability. We also investigate the effect of allosteric regulators revealing that the tendency to stability is significantly increased by including experimentally determined regulatory mechanisms that have not yet been integrated into existing kinetic models