Guaranteed optimal reachability control of reaction-diffusion equations using one-sided Lipschitz constants and model reduction

We show that, for any spatially discretized system of reaction-diffusion, the approximate solution given by the explicit Euler time-discretization scheme converges to the exact time-continuous solution, provided that diffusion coefficient be sufficiently large. By "sufficiently large", we mean that the diffusion coefficient value makes the one-sided Lipschitz constant of the reaction-diffusion system negative. We apply this result to solve a finite horizon control problem for a 1D reaction-diffusion example. We also explain how to perform model reduction in order to improve the efficiency of the method

Simulation-based reachability analysis for nonlinear systems using componentwise contraction properties

A shortcoming of existing reachability approaches for nonlinear systems is the poor scalability with the number of continuous state variables. To mitigate this problem we present a simulation-based approach where we first sample a number of trajectories of the system and next establish bounds on the convergence or divergence between the samples and neighboring trajectories. We compute these bounds using contraction theory and reduce the conservatism by partitioning the state vector into several components and analyzing contraction properties separately in each direction. Among other benefits this allows us to analyze the effect of constant but uncertain parameters by treating them as state variables and partitioning them into a separate direction. We next present a numerical procedure to search for weighted norms that yield a prescribed contraction rate, which can be incorporated in the reachability algorithm to adjust the weights to minimize the growth of the reachable set

Effect of high energy ball milling on compressibility and sintering behavior of alumina nanoparticles

The effect of high-energy ball milling on the textural evolution of alumina nanopowders (compaction response, sinter-ability, grain growth and the degree of agglomeration) during post sintering process is studied. The applied pressure required for the breakage of the agglomerates (Py) during milling was estimated and the key elements of compressibility (i.e. critical pressure (Pcr) and compressibility (b)) were calculated. Based on the results, the fracture point of the agglomerates decreased from 150 to 75 MPa with prolonged milling time from 3 to 60 min. Furthermore, the powders were formed by different shaping methods such as cold isostatic press (CIP) and uniaxial press (UP) to better illustrate the influence of green compact uniformity and powder deagglomeration on the densification behavior of nanopowders

Emergence of anti-cancer drug resistance: Exploring the importance of the microenvironmental niche via a spatial model.

Practically, all chemotherapeutic agents lead to drug resistance. Clinically, it is a challenge to determine whether resistance arises prior to, or as a result of, cancer therapy. Further, a number of different intracellular and microenvironmental factors have been correlated with the emergence of drug resistance. With the goal of better understanding drug resistance and its connection with the tumor microenvironment, we have developed a hybrid discrete-continuous mathematical model. In this model, cancer cells described through a particle-spring approach respond to dynamically changing oxygen and DNA damaging drug concentrations described through partial differential equations. We thoroughly explored the behavior of our self-calibrated model under the following common conditions: a fixed layout of the vasculature, an identical initial configuration of cancer cells, the same mechanism of drug action, and one mechanism of cellular response to the drug. We considered one set of simulations in which drug resistance existed prior to the start of treatment, and another set in which drug resistance is acquired in response to treatment. This allows us to compare how both kinds of resistance influence the spatial and temporal dynamics of the developing tumor, and its clonal diversity. We show that both pre-existing and acquired resistance can give rise to three biologically distinct parameter regimes: successful tumor eradication, reduced effectiveness of drug during the course of treatment (resistance), and complete treatment failure. When a drug resistant tumor population forms from cells that acquire resistance, we find that the spatial component of our model (the microenvironment) has a significant impact on the transient and long-term tumor behavior. On the other hand, when a resistant tumor population forms from pre-existing resistant cells, the microenvironment only has a minimal transient impact on treatment response. Finally, we present evidence that the microenvironmental niches of low drug/sufficient oxygen and low drug/low oxygen play an important role in tumor cell survival and tumor expansion. This may play role in designing new therapeutic agents or new drug combination schedules

Colibacillosis phytotherapy: An overview on the most important world medicinal plants effective on Escherichia coli

Escherichia coli is a Gram-negative, non-sporulating facultative anaerobe found in water and soil and is a normal flora in gastrointestinal tract of human, warm-blooded animals and reptiles. E. coli strains are categorized into six pathotypes caused different syndromes and shows high rate of resistance to different antibiotics. The aim of this study was to identify the most important native medicinal plants of world, effective on E. coli. All required information was obtained by searching keywords such as E.coli, medicinal plant extracts or essential oils in published articles in authentic scientific databases such as Science Direct, Wiley-blackwell, Springer, Google scholar, Scientific Information Database (SID) and Magiran. According to the literature review, our results showed 44 different native medicinal plants were effective against E.coli and used to colibacillosis treatment traditionally in all over the world. The results of this review indicated that some of the most important plants that have anti-E.coli effect include Rosmarinus officinalis (rosemary), Syzygium aromaticum (clove), Thymus vulgaris (Thyme), Zataria multiflora (Avishane shirazi), Salvia officinalis (Sage), Cymbopogon martini (Palmarosa), Aloysia triphylla (Lemon beebrush), Origanum vulgare (Oregano), Satureja cuneifolia (wild savory), Pluchea indica (Indian camphorweed), Eucalyptus tereticornis (Forest Red Gum), Aloe vera (Aloe) and Foeniculum vulgare (Fennel). An overview on phytochemical analysis has shown that bioactive compounds of medicinal plants with their antioxidant and antimicrobial properties are good alternative for synthetic drugs in food and drug industry and in other word to treatment microbial diseases in medicine. © 2017, Pharmainfo Publications. All rights reserved