An algorithm for semi-infinite polynomial optimization

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A linear optimization technique for graph pebbling

Graph pebbling is a network model for studying whether or not a given supply of discrete pebbles can satisfy a given demand via pebbling moves. A pebbling move across an edge of a graph takes two pebbles from one endpoint and places one pebble at the other endpoint; the other pebble is lost in transit as a toll. It has been shown that deciding whether a supply can meet a demand on a graph is NP-complete. The pebbling number of a graph is the smallest t such that every supply of t pebbles can satisfy every demand of one pebble. Deciding if the pebbling number is at most k is NP 2 -complete. In this paper we develop a tool, called theWeight Function Lemma, for computing upper bounds and sometimes exact values for pebbling numbers with the assistance of linear optimization. With this tool we are able to calculate the pebbling numbers of much larger graphs than in previous algorithms, and much more quickly as well. We also obtain results for many families of graphs, in many cases by hand, with much simpler and remarkably shorter proofs than given in previously existing arguments (certificates typically of size at most the number of vertices times the maximum degree), especially for highly symmetric graphs. Here we apply theWeight Function Lemma to several specific graphs, including the Petersen, Lemke, 4th weak Bruhat, Lemke squared, and two random graphs, as well as to a number of infinite families of graphs, such as trees, cycles, graph powers of cycles, cubes, and some generalized Petersen and Coxeter graphs. This partly answers a question of Pachter, et al., by computing the pebbling exponent of cycles to within an asymptotically small range. It is conceivable that this method yields an approximation algorithm for graph pebbling.

A parameter-free approach for solving combinatorial optimization problems through biased randomization of efficient heuristics

This paper discusses the use of probabilistic or randomized algorithms for solving combinatorial optimization problems. Our approach employs non-uniform probability distributions to add a biased random behavior to classical heuristics so a large set of alternative good solutions can be quickly obtained in a natural way and without complex conguration processes. This procedure is especially useful in problems where properties such as non-smoothness or non-convexity lead to a highly irregular solution space, for which the traditional optimization methods, both of exact and approximate nature, may fail to reach their full potential. The results obtained are promising enough to suggest that randomizing classical heuristics is a powerful method that can be successfully applied in a variety of cases.

On the stability of the optimal value and the optimal set in optimization problems

The paper develops a stability theory for the optimal value and the optimal set mapping of optimization problems posed in a Banach space. The problems considered in this paper have an arbitrary number of inequality constraints involving lower semicontinuous (not necessarily convex) functions and one closed abstract constraint set. The considered perturbations lead to problems of the same type as the nominal one (with the same space of variables and the same number of constraints), where the abstract constraint set can also be perturbed. The spaces of functions involved in the problems (objective and constraints) are equipped with the metric of the uniform convergence on the bounded sets, meanwhile in the space of closed sets we consider, coherently, the Attouch-Wets topology. The paper examines, in a unified way, the lower and upper semicontinuity of the optimal value function, and the closedness, lower and upper semicontinuity (in the sense of Berge) of the optimal set mapping. This paper can be seen as a second part of the stability theory presented in [17], where we studied the stability of the feasible set mapping (completed here with the analysis of the Lipschitz-like property).

Artificial Snow Optimization in Winter Sport Destinations Using a Multi-agent Simulation

This paper presents the Juste-Neige system for predicting the snow height on the ski runs of a resort using a multi-agent simulation software. Its aim is to facilitate snow cover management in order to i) reduce the production cost of artificial snow and to improve the profit margin for the companies managing the ski resorts; and ii) to reduce the water and energy consumption, and thus to reduce the environmental impact, by producing only the snow needed for a good skiing experience. The software provides maps with the predicted snow heights for up to 13 days. On these maps, the areas most exposed to snow erosion are highlighted. The software proceeds in three steps: i) interpolation of snow height measurements with a neural network; ii) local meteorological forecasts for every ski resort; iii) simulation of the impact caused by skiers using a multi-agent system. The software has been evaluated in the Swiss ski resort of Verbier and provides useful predictions.

Optimization of spatial resolution for peripheral magnetic resonance angiography.

RATIONALE AND OBJECTIVES: To determine optimum spatial resolution when imaging peripheral arteries with magnetic resonance angiography (MRA). MATERIALS AND METHODS: Eight vessel diameters ranging from 1.0 to 8.0 mm were simulated in a vascular phantom. A total of 40 three-dimensional flash MRA sequences were acquired with incremental variations of fields of view, matrix size, and slice thickness. The accurately known eight diameters were combined pairwise to generate 22 "exact" degrees of stenosis ranging from 42% to 87%. Then, the diameters were measured in the MRA images by three independent observers and with quantitative angiography (QA) software and used to compute the degrees of stenosis corresponding to the 22 "exact" ones. The accuracy and reproducibility of vessel diameter measurements and stenosis calculations were assessed for vessel size ranging from 6 to 8 mm (iliac artery), 4 to 5 mm (femoro-popliteal arteries), and 1 to 3 mm (infrapopliteal arteries). Maximum pixel dimension and slice thickness to obtain a mean error in stenosis evaluation of less than 10% were determined by linear regression analysis. RESULTS: Mean errors on stenosis quantification were 8.8% +/- 6.3% for 6- to 8-mm vessels, 15.5% +/- 8.2% for 4- to 5-mm vessels, and 18.9% +/- 7.5% for 1- to 3-mm vessels. Mean errors on stenosis calculation were 12.3% +/- 8.2% for observers and 11.4% +/- 15.1% for QA software (P = .0342). To evaluate stenosis with a mean error of less than 10%, maximum pixel surface, the pixel size in the phase direction, and the slice thickness should be less than 1.56 mm2, 1.34 mm, 1.70 mm, respectively (voxel size 2.65 mm3) for 6- to 8-mm vessels; 1.31 mm2, 1.10 mm, 1.34 mm (voxel size 1.76 mm3), for 4- to 5-mm vessels; and 1.17 mm2, 0.90 mm, 0.9 mm (voxel size 1.05 mm3) for 1- to 3-mm vessels. CONCLUSION: Higher spatial resolution than currently used should be selected for imaging peripheral vessels.

Design of Novel Frequency Generation Circuit with Application to Ultra-Wideband Distributed Oscillators

Given the urgence of a new paradigm in wireless digital trasmission which should allow for higher bit rate, lower latency and tigher delay constaints, it has been proposed to investigate the fundamental building blocks that at the circuital/device level, will boost the change towards a more efficient network architecture, with high capacity, higher bandwidth and a more satisfactory end user experience. At the core of each transciever, there are inherently analog devices capable of providing the carrier signal, the oscillators. It is strongly believed that many limitations in today's communication protocols, could be relieved by permitting high carrier frequency radio transmission, and having some degree of reconfigurability. This led us to studying distributed oscillator architectures which work in the microwave range and possess wideband tuning capability. As microvave oscillators are essentially nonlinear devices, a full nonlinear analyis, synthesis, and optimization had to be considered for their implementation. Consequently, all the most used nonlinear numerical techniques in commercial EDA software had been reviewed. An application of all the aforementioned techniques has been shown, considering a systems of three coupled oscillator ("triple push" oscillator) in which the stability of the various oscillating modes has been studied. Provided that a certain phase distribution is maintained among the oscillating elements, this topology permits a rise in the output power of the third harmonic; nevertheless due to circuit simmetry, "unwanted" oscillating modes coexist with the intenteded one. Starting with the necessary background on distributed amplification and distributed oscillator theory, the design of a four stage reverse mode distributed voltage controlled oscillator (DVCO) using lumped elments has been presented. All the design steps have been reported and for the first time a method for an optimized design with reduced variations in the output power has been presented. Ongoing work is devoted to model a wideband DVCO and to implement a frequency divider.

On the analysis of travelling waves to a nonlinear flux limited reaction-diffusion equation

In this paper we study the existence and qualitative properties of travelling waves associated to a nonlinear flux limited partial differential equation coupled to a Fisher-Kolmogorov-Petrovskii-Piskunov type reaction term. We prove the existence and uniqueness of finite speed moving fronts of C2 classical regularity, but also the existence of discontinuous entropy travelling wave solutions.

Wellposedness of a nonlinear, logarithmic Schrödinger equation of Doebner-Goldin type modeling quantum dissipation

This paper is concerned with the modeling and analysis of quantum dissipation phenomena in the Schrödinger picture. More precisely, we do investigate in detail a dissipative, nonlinear Schrödinger equation somehow accounting for quantum Fokker–Planck effects, and how it is drastically reduced to a simpler logarithmic equation via a nonlinear gauge transformation in such a way that the physics underlying both problems keeps unaltered. From a mathematical viewpoint, this allows for a more achievable analysis regarding the local wellposedness of the initial–boundary value problem. This simplification requires the performance of the polar (modulus–argument) decomposition of the wavefunction, which is rigorously attained (for the first time to the best of our knowledge) under quite reasonable assumptions.

Optimization of the piggyBac Transposon Using mRNA and Insulators: Toward a More Reliable Gene Delivery System.

Integrating and expressing stably a transgene into the cellular genome remain major challenges for gene-based therapies and for bioproduction purposes. While transposon vectors mediate efficient transgene integration, expression may be limited by epigenetic silencing, and persistent transposase expression may mediate multiple transposition cycles. Here, we evaluated the delivery of the piggyBac transposase messenger RNA combined with genetically insulated transposons to isolate the transgene from neighboring regulatory elements and stabilize expression. A comparison of piggyBac transposase expression from messenger RNA and DNA vectors was carried out in terms of expression levels, transposition efficiency, transgene expression and genotoxic effects, in order to calibrate and secure the transposition-based delivery system. Messenger RNA reduced the persistence of the transposase to a narrow window, thus decreasing side effects such as superfluous genomic DNA cleavage. Both the CTF/NF1 and the D4Z4 insulators were found to mediate more efficient expression from a few transposition events. We conclude that the use of engineered piggyBac transposase mRNA and insulated transposons offer promising ways of improving the quality of the integration process and sustaining the expression of transposon vectors.

COMMIT: Convex Optimization Modeling for Microstructure Informed Tractography.

Tractography is a class of algorithms aiming at in vivo mapping the major neuronal pathways in the white matter from diffusion magnetic resonance imaging (MRI) data. These techniques offer a powerful tool to noninvasively investigate at the macroscopic scale the architecture of the neuronal connections of the brain. However, unfortunately, the reconstructions recovered with existing tractography algorithms are not really quantitative even though diffusion MRI is a quantitative modality by nature. As a matter of fact, several techniques have been proposed in recent years to estimate, at the voxel level, intrinsic microstructural features of the tissue, such as axonal density and diameter, by using multicompartment models. In this paper, we present a novel framework to reestablish the link between tractography and tissue microstructure. Starting from an input set of candidate fiber-tracts, which are estimated from the data using standard fiber-tracking techniques, we model the diffusion MRI signal in each voxel of the image as a linear combination of the restricted and hindered contributions generated in every location of the brain by these candidate tracts. Then, we seek for the global weight of each of them, i.e., the effective contribution or volume, such that they globally fit the measured signal at best. We demonstrate that these weights can be easily recovered by solving a global convex optimization problem and using efficient algorithms. The effectiveness of our approach has been evaluated both on a realistic phantom with known ground-truth and in vivo brain data. Results clearly demonstrate the benefits of the proposed formulation, opening new perspectives for a more quantitative and biologically plausible assessment of the structural connectivity of the brain.

Combination of enteral and parenteral nutrition in intensive care patients: A new concept of optimization

Undernutrition is a widespread problem in intensive care unit and is associated with a worse clinical outcome. A state of negative energy balance increases stress catabolism and is associated with increased morbidity and mortality in ICU patients. Undernutrition-related increased morbidity is correlated with an increase in the length of hospital stay and health care costs. Enteral nutrition is the recommended feeding route in critically ill patients, but it is often insufficient to cover the nutritional needs. The initiation of supplemental parenteral nutrition, when enteral nutrition is insufficient, could optimize the nutritional therapy by preventing the onset of early energy deficiency, and thus, could allow to reduce morbidity, length of stay and costs, shorten recovery period and, finally, improve quality of life. (C) 2009 Elsevier Masson SAS. All rights reserved.

Optimization of treatment with interferon beta in multiple sclerosis. Usefulness of automatic system application criteria

Background. A software based tool has been developed (Optem) to allow automatize the recommendations of the Canadian Multiple Sclerosis Working Group for optimizing MS treatment in order to avoid subjective interpretation. METHODS: Treatment Optimization Recommendations (TORs) were applied to our database of patients treated with IFN beta1a IM. Patient data were assessed during year 1 for disease activity, and patients were assigned to 2 groups according to TOR: "change treatment" (CH) and "no change treatment" (NCH). These assessments were then compared to observed clinical outcomes for disease activity over the following years. RESULTS: We have data on 55 patients. The "change treatment" status was assigned to 22 patients, and "no change treatment" to 33 patients. The estimated sensitivity and specificity according to last visit status were 73.9% and 84.4%. During the following years, the Relapse Rate was always higher in the "change treatment" group than in the "no change treatment" group (5 y; CH: 0.7, NCH: 0.07; p < 0.001, 12 m - last visit; CH: 0.536, NCH: 0.34). We obtained the same results with the EDSS (4 y; CH: 3.53, NCH: 2.55, annual progression rate in 12 m - last visit; CH: 0.29, NCH: 0.13). CONCLUSION: Applying TOR at the first year of therapy allowed accurate prediction of continued disease activity in relapses and disability progression.