Max-convex decompositions for cooperative TU games

We show that any cooperative TU game is the maximum of a finite collection of convex games. This max-convex decomposition can be refined by using convex games with non-negative dividends for all coalitions of at least two players. As a consequence of the above results we show that the class of modular games is a set of generators of the distributive lattice of all cooperative TU games. Finally, we characterize zero-monotonic games using a strong max-convex decomposition

Non-constant discounting in finite horizon: The free terminal time case

This paper derives the HJB (Hamilton-Jacobi-Bellman) equation for sophisticated agents in a finite horizon dynamic optimization problem with non-constant discounting in a continuous setting, by using a dynamic programming approach. A simple example is used in order to illustrate the applicability of this HJB equation, by suggesting a method for constructing the subgame perfect equilibrium solution to the problem.Conditions for the observational equivalence with an associated problem with constantdiscounting are analyzed. Special attention is paid to the case of free terminal time. Strotz¿s model (an eating cake problem of a nonrenewable resource with non-constant discounting) is revisited.

Optimization of Soil Stabilization with Class C Fly Ash, January 1987

Previous Iowa DOT sponsored research has shown that some Class C fly ashes are ementitious (because calcium is combined as calcium aluminates) while other Class C ashes containing similar amounts of elemental calcium are not (1). Fly ashes from modern power plants in Iowa contain significant amounts of calcium in their glassy phases, regardless of their cementitious properties. The present research was based on these findings and on the hyphothesis that: attack of the amorphous phase of high calcium fly ash could be initiated with trace additives, thus making calcium available for formation of useful calcium-silicate cements. Phase I research was devoted to finding potential additives through a screening process; the likely chemicals were tested with fly ashes representative of the cementitious and non-cementitious ashes available in the state. Ammonium phosphate, a fertilizer, was found to produce 3,600 psi cement with cementitious Neal #4 fly ash; this strength is roughly equivalent to that of portland cement, but at about one-third the cost. Neal #2 fly ash, a slightly cementitious Class C, was found to respond best with ammonium nitrate; through the additive, a near-zero strength material was transformed into a 1,200 psi cement. The second research phase was directed to optimimizing trace additive concentrations, defining the behavior of the resulting cements, evaluating more comprehensively the fly ashes available in Iowa, and explaining the cement formation mechanisms of the most promising trace additives. X-ray diffraction data demonstrate that both amorphous and crystalline hydrates of chemically enhanced fly ash differ from those of unaltered fly ash hydrates. Calciumaluminum- silicate hydrates were formed, rather than the expected (and hypothesized) calcium-silicate hydrates. These new reaction products explain the observed strength enhancement. The final phase concentrated on laboratory application of the chemically-enhanced fly ash cements to road base stabilization. Emphasis was placed on use of marginal aggregates, such as limestone crusher fines and unprocessed blow sand. The nature of the chemically modified fly ash cements led to an evaluation of fine grained soil stabilization where a wide range of materials, defined by plasticity index, could be stabilized. Parameters used for evaluation included strength, compaction requirements, set time, and frost resistance.

Max-convex decompositions for cooperative TU games

We show that any cooperative TU game is the maximum of a finite collection of convex games. This max-convex decomposition can be refined by using convex games with non-negative dividends for all coalitions of at least two players. As a consequence of the above results we show that the class of modular games is a set of generators of the distributive lattice of all cooperative TU games. Finally, we characterize zero-monotonic games using a strong max-convex decomposition

Non-constant discounting in finite horizon: The free terminal time case

This paper derives the HJB (Hamilton-Jacobi-Bellman) equation for sophisticated agents in a finite horizon dynamic optimization problem with non-constant discounting in a continuous setting, by using a dynamic programming approach. A simple example is used in order to illustrate the applicability of this HJB equation, by suggesting a method for constructing the subgame perfect equilibrium solution to the problem.Conditions for the observational equivalence with an associated problem with constantdiscounting are analyzed. Special attention is paid to the case of free terminal time. Strotz¿s model (an eating cake problem of a nonrenewable resource with non-constant discounting) is revisited.

Optimization and regeneration kinetics of lymphatic-specific photodynamic therapy in the mouse dermis.

Lymphatic vessels transport fluid, antigens, and immune cells to the lymph nodes to orchestrate adaptive immunity and maintain peripheral tolerance. Lymphangiogenesis has been associated with inflammation, cancer metastasis, autoimmunity, tolerance and transplant rejection, and thus, targeted lymphatic ablation is a potential therapeutic strategy for treating or preventing such events. Here we define conditions that lead to specific and local closure of the lymphatic vasculature using photodynamic therapy (PDT). Lymphatic-specific PDT was performed by irradiation of the photosensitizer verteporfin that effectively accumulates within collecting lymphatic vessels after local intradermal injection. We found that anti-lymphatic PDT induced necrosis of endothelial cells and pericytes, which preceded the functional occlusion of lymphatic collectors. This was specific to lymphatic vessels at low verteporfin dose, while higher doses also affected local blood vessels. In contrast, light dose (fluence) did not affect blood vessel perfusion, but did affect regeneration time of occluded lymphatic vessels. Lymphatic vessels eventually regenerated by recanalization of blocked collectors, with a characteristic hyperplasia of peri-lymphatic smooth muscle cells. The restoration of lymphatic function occurred with minimal remodeling of non-lymphatic tissue. Thus, anti-lymphatic PDT allows control of lymphatic ablation and regeneration by alteration of light fluence and photosensitizer dose.

Dosage optimization of treatments using population pharmacokinetic modeling and simulation.

Pharmacokinetic variability in drug levels represent for some drugs a major determinant of treatment success, since sub-therapeutic concentrations might lead to toxic reactions, treatment discontinuation or inefficacy. This is true for most antiretroviral drugs, which exhibit high inter-patient variability in their pharmacokinetics that has been partially explained by some genetic and non-genetic factors. The population pharmacokinetic approach represents a very useful tool for the description of the dose-concentration relationship, the quantification of variability in the target population of patients and the identification of influencing factors. It can thus be used to make predictions and dosage adjustment optimization based on Bayesian therapeutic drug monitoring (TDM). This approach has been used to characterize the pharmacokinetics of nevirapine (NVP) in 137 HIV-positive patients followed within the frame of a TDM program. Among tested covariates, body weight, co-administration of a cytochrome (CYP) 3A4 inducer or boosted atazanavir as well as elevated aspartate transaminases showed an effect on NVP elimination. In addition, genetic polymorphism in the CYP2B6 was associated with reduced NVP clearance. Altogether, these factors could explain 26% in NVP variability. Model-based simulations were used to compare the adequacy of different dosage regimens in relation to the therapeutic target associated with treatment efficacy. In conclusion, the population approach is very useful to characterize the pharmacokinetic profile of drugs in a population of interest. The quantification and the identification of the sources of variability is a rational approach to making optimal dosage decision for certain drugs administered chronically.

Current state of vaccine therapies in non-small-cell lung cancer.

A large variety of cancer vaccines have undergone extensive testing in early-phase clinical trials. A limited number have also been tested in randomized phase II clinical trials. Encouraging trends toward increased survival in the vaccine arms have been recently observed for 2 vaccine candidates in patients with non-small-cell lung cancer. These have provided the impetus for the initiation of phase III trials in large groups of patients with lung cancer. These vaccines target 2 antigens widely expressed in lung carcinomas: melanoma-associated antigen 3, a cancer testis antigen; and mucin 1, an antigen overexpressed in a largely deglycosylated form in advanced tumors. Therapeutic cancer vaccines aim at inducing strong CD8 and CD4 T-cell responses. The majority of vaccines recently tested in phase I clinical trials show efficacy in terms of induction of specific tumor antigen immunity. However, clinical efficacy remains to be determined but appears limited. Efforts are thus aimed at understanding the basis for this apparent lack of effect on tumors. Two major factors are involved. On one hand, current vaccines are suboptimal. Strong adjuvant agents and appropriate tumor antigens are needed. Moreover, dose, route, and schedule also need optimization. On the other hand, it is now clear that large tumors often present a tolerogenic microenvironment that hampers effective antitumor immunity. The partial understanding of the molecular pathways leading to functional inactivation of T cells at tumor sites has provided new targets for intervention. In this regard, blockade of cytotoxic T-lymphocyte antigen-4 and programmed death-1 with humanized monoclonal antibodies has reached the clinical testing stage. In the future, more potent cancer vaccines will benefit from intense research in antigen discovery and adjuvant agents. Furthermore, it is likely that vaccines need to be combined with compounds that reverse major tolerogenic pathways that are constitutively active at the tumor site. Developing these combined approaches to vaccination in cancer promises new, exciting findings and, at the same time, poses important challenges to academic research institutions and the pharmaceutical industry.

Optimization of Snow Drifting Mitigation and Control Methods for Iowa Conditions Part II, TR-626, 2015

Blowing and drifting of snow is a major concern for transportation efficiency and road safety in regions where their development is common. One common way to mitigate snow drift on roadways is to install plastic snow fences. Correct design of snow fences is critical for road safety and maintaining the roads open during winter in the US Midwest and other states affected by large snow events during the winter season and to maintain costs related to accumulation of snow on the roads and repair of roads to minimum levels. Of critical importance for road safety is the protection against snow drifting in regions with narrow rights of way, where standard fences cannot be deployed at the recommended distance from the road. Designing snow fences requires sound engineering judgment and a thorough evaluation of the potential for snow blowing and drifting at the construction site. The evaluation includes site-specific design parameters typically obtained with semi-empirical relations characterizing the local transport conditions. Among the critical parameters involved in fence design and assessment of their post-construction efficiency is the quantification of the snow accumulation at fence sites. The present study proposes a joint experimental and numerical approach to monitor snow deposits around snow fences, quantitatively estimate snow deposits in the field, asses the efficiency and improve the design of snow fences. Snow deposit profiles were mapped using GPS based real-time kinematic surveys (RTK) conducted at the monitored field site during and after snow storms. The monitored site allowed testing different snow fence designs under close to identical conditions over four winter seasons. The study also discusses the detailed monitoring system and analysis of weather forecast and meteorological conditions at the monitored sites. A main goal of the present study was to assess the performance of lightweight plastic snow fences with a lower porosity than the typical 50% porosity used in standard designs of such fences. The field data collected during the first winter was used to identify the best design for snow fences with a porosity of 50%. Flow fields obtained from numerical simulations showed that the fence design that worked the best during the first winter induced the formation of an elongated area of small velocity magnitude close to the ground. This information was used to identify other candidates for optimum design of fences with a lower porosity. Two of the designs with a fence porosity of 30% that were found to perform well based on results of numerical simulations were tested in the field during the second winter along with the best performing design for fences with a porosity of 50%. Field data showed that the length of the snow deposit away from the fence was reduced by about 30% for the two proposed lower-porosity (30%) fence designs compared to the best design identified for fences with a porosity of 50%. Moreover, one of the lower-porosity designs tested in the field showed no significant snow deposition within the bottom gap region beneath the fence. Thus, a major outcome of this study is to recommend using plastic snow fences with a porosity of 30%. It is expected that this lower-porosity design will continue to work well for even more severe snow events or for successive snow events occurring during the same winter. The approach advocated in the present study allowed making general recommendations for optimizing the design of lower-porosity plastic snow fences. This approach can be extended to improve the design of other types of snow fences. Some preliminary work for living snow fences is also discussed. Another major contribution of this study is to propose, develop protocols and test a novel technique based on close range photogrammetry (CRP) to quantify the snow deposits trapped snow fences. As image data can be acquired continuously, the time evolution of the volume of snow retained by a snow fence during a storm or during a whole winter season can, in principle, be obtained. Moreover, CRP is a non-intrusive method that eliminates the need to perform man-made measurements during the storms, which are difficult and sometimes dangerous to perform. Presently, there is lots of empiricism in the design of snow fences due to lack of data on fence storage capacity on how snow deposits change with the fence design and snow storm characteristics and in the estimation of the main parameters used by the state DOTs to design snow fences at a given site. The availability of such information from CRP measurements should provide critical data for the evaluation of the performance of a certain snow fence design that is tested by the IDOT. As part of the present study, the novel CRP method is tested at several sites. The present study also discusses some attempts and preliminary work to determine the snow relocation coefficient which is one of the main variables that has to be estimated by IDOT engineers when using the standard snow fence design software (Snow Drift Profiler, Tabler, 2006). Our analysis showed that standard empirical formulas did not produce reasonable values when applied at the Iowa test sites monitored as part of the present study and that simple methods to estimate this variable are not reliable. The present study makes recommendations for the development of a new methodology based on Large Scale Particle Image Velocimetry that can directly measure the snow drift fluxes and the amount of snow relocated by the fence.

Optimization of the procedure for removing iron deposits on ceramic filter media

In this thesis, cleaning of ceramic filter media was studied. Mechanisms of fouling and dissolution of iron compounds, as well as methods for cleaning ceramic membranes fouled by iron deposits were studied in the literature part. Cleaning agents and different methods were closer examined in the experimental part of the thesis. Pyrite is found in the geologic strata. It is oxidized to form ferrous ions Fe(II) and ferric ions Fe(III). Fe(III) is further oxidized in the hydrolysis to form ferric hydroxide. Hematite and goethite, for instance, are naturally occurring iron oxidesand hydroxides. In contact with filter media, they can cause severe fouling, which common cleaning techniques competent enough to remove. Mechanisms for the dissolution of iron oxides include the ligand-promoted pathway and the proton-promoted pathway. The dissolution can also be reductive or non-reductive. The most efficient mechanism is the ligand-promoted reductive mechanism that comprises two stages: the induction period and the autocatalytic dissolution.Reducing agents(such as hydroquinone and hydroxylamine hydrochloride), chelating agents (such as EDTA) and organic acids are used for the removal of iron compounds. Oxalic acid is the most effective known cleaning agent for iron deposits. Since formulations are often more effective than organic acids, reducing agents or chelating agents alone, the citrate¿bicarbonate¿dithionite system among others is well studied in the literature. The cleaning is also enhanced with ultrasound and backpulsing.In the experimental part, oxalic acid and nitric acid were studied alone andin combinations. Also citric acid and ascorbic acid among other chemicals were tested. Soaking experiments, experiments with ultrasound and experiments for alternative methods to apply the cleaning solution on the filter samples were carried out. Permeability and ISO Brightness measurements were performed to examine the influence of the cleaning methods on the samples. Inductively coupled plasma optical emission spectroscopy (ICP-OES) analysis of the solutions was carried out to determine the dissolved metals.

Ranking-Dominance Relation for (Evolutionary) Multi-Objective Optimization

An alternative relation to Pareto-dominance relation is proposed. The new relation is based on ranking a set of solutions according to each separate objective and an aggregation function to calculate a scalar fitness value for each solution. The relation is called as ranking-dominance and it tries to tackle the curse of dimensionality commonly observedin evolutionary multi-objective optimization. Ranking-dominance can beused to sort a set of solutions even for a large number of objectives when Pareto-dominance relation cannot distinguish solutions from one another anymore. This permits search to advance even with a large number of objectives. It is also shown that ranking-dominance does not violate Pareto-dominance. Results indicate that selection based on ranking-dominance is able to advance search towards the Pareto-front in some cases, where selection based on Pareto-dominance stagnates. However, in some cases it is also possible that search does not proceed into direction of Pareto-front because the ranking-dominance relation permits deterioration of individual objectives. Results also show that when the number of objectives increases, selection based on just Pareto-dominance without diversity maintenance is able to advance search better than with diversity maintenance. Therefore, diversity maintenance is connive at the curse of dimensionality.

Identifying the preferred subset of enzymatic profiles in nonlinear kinetic metabolic models via multiobjective global optimization and pareto filters

Optimization models in metabolic engineering and systems biology focus typically on optimizing a unique criterion, usually the synthesis rate of a metabolite of interest or the rate of growth. Connectivity and non-linear regulatory effects, however, make it necessary to consider multiple objectives in order to identify useful strategies that balance out different metabolic issues. This is a fundamental aspect, as optimization of maximum yield in a given condition may involve unrealistic values in other key processes. Due to the difficulties associated with detailed non-linear models, analysis using stoichiometric descriptions and linear optimization methods have become rather popular in systems biology. However, despite being useful, these approaches fail in capturing the intrinsic nonlinear nature of the underlying metabolic systems and the regulatory signals involved. Targeting more complex biological systems requires the application of global optimization methods to non-linear representations. In this work we address the multi-objective global optimization of metabolic networks that are described by a special class of models based on the power-law formalism: the generalized mass action (GMA) representation. Our goal is to develop global optimization methods capable of efficiently dealing with several biological criteria simultaneously. In order to overcome the numerical difficulties of dealing with multiple criteria in the optimization, we propose a heuristic approach based on the epsilon constraint method that reduces the computational burden of generating a set of Pareto optimal alternatives, each achieving a unique combination of objectives values. To facilitate the post-optimal analysis of these solutions and narrow down their number prior to being tested in the laboratory, we explore the use of Pareto filters that identify the preferred subset of enzymatic profiles. We demonstrate the usefulness of our approach by means of a case study that optimizes the ethanol production in the fermentation of Saccharomyces cerevisiae.

Vitamin D time profile based on the contribution of non-genetic and genetic factors in HIV-infected individuals of European ancestry.

BACKGROUND: Vitamin D deficiency is prevalent in HIV-infected individuals and vitamin D supplementation is proposed according to standard care. This study aimed at characterizing the kinetics of 25(OH)D in a cohort of HIV-infected individuals of European ancestry to better define the influence of genetic and non-genetic factors on 25(OH)D levels. These data were used for the optimization of vitamin D supplementation in order to reach therapeutic targets. METHODS: 1,397 25(OH)D plasma levels and relevant clinical information were collected in 664 participants during medical routine follow-up visits. They were genotyped for 7 SNPs in 4 genes known to be associated with 25(OH)D levels. 25(OH)D concentrations were analysed using a population pharmacokinetic approach. The percentage of individuals with 25(OH)D concentrations within the recommended range of 20-40 ng/ml during 12 months of follow-up and several dosage regimens were evaluated by simulation. RESULTS: A one-compartment model with linear absorption and elimination was used to describe 25(OH)D pharmacokinetics, while integrating endogenous baseline plasma concentrations. Covariate analyses confirmed the effect of seasonality, body mass index, smoking habits, the analytical method, darunavir/ritonavir and the genetic variant in GC (rs2282679) on 25(OH)D concentrations. 11% of the inter-individual variability in 25(OH)D levels was explained by seasonality and other non-genetic covariates, and 1% by genetics. The optimal supplementation for severe vitamin D deficient patients was 300,000 IU two times per year. CONCLUSIONS: This analysis allowed identifying factors associated with 25(OH)D plasma levels in HIV-infected individuals. Improvement of dosage regimen and timing of vitamin D supplementation is proposed based on those results.

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.

Accelerated Microstructure Imaging via Convex Optimisation for regions with multiple fibres (AMICOx)

This paper reviews and extends our previous work to enable fast axonal diameter mapping from diffusion MRI data in the presence of multiple fibre populations within a voxel. Most of the existing mi-crostructure imaging techniques use non-linear algorithms to fit their data models and consequently, they are computationally expensive and usually slow. Moreover, most of them assume a single axon orientation while numerous regions of the brain actually present more complex configurations, e.g. fiber crossing. We present a flexible framework, based on convex optimisation, that enables fast and accurate reconstructions of the microstructure organisation, not limited to areas where the white matter is coherently oriented. We show through numerical simulations the ability of our method to correctly estimate the microstructure features (mean axon diameter and intra-cellular volume fraction) in crossing regions.