Nonlinear deterministic equations in biological evolution

We review models of biological evolution in which the population frequency changes deterministically with time. If the population is self-replicating, although the equations for simple prototypes can be linearised, nonlinear equations arise in many complex situations. For sexual populations, even in the simplest setting, the equations are necessarily nonlinear due to the mixing of the parental genetic material. The solutions of such nonlinear equations display interesting features such as multiple equilibria and phase transitions. We mainly discuss those models for which an analytical understanding of such nonlinear equations is available.Comment: Invited review for J. Nonlin. Math. Phy

Numerical Modeling of Fluid Flow in Solid Tumors

A mathematical model of interstitial fluid flow is developed, based on the application of the governing equations for fluid flow, i.e., the conservation laws for mass and momentum, to physiological systems containing solid tumors. The discretized form of the governing equations, with appropriate boundary conditions, is developed for a predefined tumor geometry. The interstitial fluid pressure and velocity are calculated using a numerical method, element based finite volume. Simulations of interstitial fluid transport in a homogeneous solid tumor demonstrate that, in a uniformly perfused tumor, i.e., one with no necrotic region, because of the interstitial pressure distribution, the distribution of drug particles is non-uniform. Pressure distribution for different values of necrotic radii is examined and two new parameters, the critical tumor radius and critical necrotic radius, are defined. Simulation results show that: 1) tumor radii have a critical size. Below this size, the maximum interstitial fluid pressure is less than what is generally considered to be effective pressure (a parameter determined by vascular pressure, plasma osmotic pressure, and interstitial osmotic pressure). Above this size, the maximum interstitial fluid pressure is equal to effective pressure. As a consequence, drugs transport to the center of smaller tumors is much easier than transport to the center of a tumor whose radius is greater than the critical tumor radius; 2) there is a critical necrotic radius, below which the interstitial fluid pressure at the tumor center is at its maximum value. If the tumor radius is greater than the critical tumor radius, this maximum pressure is equal to effective pressure. Above this critical necrotic radius, the interstitial fluid pressure at the tumor center is below effective pressure. In specific ranges of these critical sizes, drug amount and therefore therapeutic effects are higher because the opposing force, interstitial fluid pressure, is low in these ranges

Exact solution for mean energy of 2d Dyson gas at beta = 1

Mean Coulomb energy of 2d Dyson gas in quadratic potential is examined from combinatorial viewpoint. For beta = 1, we find a recursive relation on mean energy and obtain its exact (finite N) solution in closed form in terms of the hypergeometric function 3F2. Using this exact solution, we derive the large-N asymptotic expansion of mean energy and show, that this expansion contains half-integer powers of N.Comment: 10 pages, 1 figur

Equilibrium analysis in multi-echelon supply chain with multi-dimensional utilities of inertial players

In a supply chain, the importance of information elicitation from the supply chain players is vital to design supply chain network. The rationality and self-centredness of these players causes the information asymmetry in the supply chain and thus situation of conflict and non-participation of the players in the network design process. In such situations, it is required to analyse the supply chain players’ behaviour in order to explore potential for coordination through incentives. In this paper, a novel approach of social utility analysis is proposed to elicit the information for supply chain coordination among the supply chain players in a dyadic relationship – supplier and buyer. In principal, we consider a monopsony situation where buyer is a dominant player. With the objective of maximizing the social utility, efforts have been made to value behavioural issues in supply chain. On the other hand, the reluctance of player due to the information asymmetry is measured in the form of inertia – an offset to the supply chain profit. The suppliers’ behaviour is analysed with three distinct level of risk for two types of the product in procurement process. The useful insight from this paper is in supplier selection process where the reluctance of supplier offsets supply chain profit. The paper provides recommendations to supply chain managers for efficient decision-making ability in supplier selection process

Decolorization of synthetic melanoidins-containing wastewater by a bacterial consortium

The presence of melanoidins in molasses wastewater leads to water pollution both due to its dark brown color and its COD contents. In this study, a bacterial consortium isolated from waterfall sediment was tested for its decolorization. The identification of culturable bacteria by 16S rDNA based approach showed that the consortium composed of Klebsiella oxytoca, Serratia mercescens, Citrobacter sp. and unknown bacterium. In the context of academic study, prevention on the difficulties of providing effluent as well as its variations in compositions, several synthetic media prepared with respect to color and COD contents based on analysis of molasses wastewater, i.e., Viandox sauce (13.5% v/v), caramel (30% w/v), beet molasses wastewater (41.5% v/v) and sugarcane molasses wastewater (20% v/v) were used for decolorization using consortium with color removal 9.5, 1.13, 8.02 and 17.5%, respectively, within 2 days. However, Viandox sauce was retained for further study. The effect of initial pH and Viandox concentration on decolorization and growth of bacterial consortium were further determined. The highest decolorization of 18.3% was achieved at pH 4 after 2 day of incubation. Experiments on fresh or used medium and used or fresh bacterial cells, led to conclusion that the limitation of decolorization was due to nutritional deficiency. The effect of aeration on decolorization was also carried out in 2 L laboratory-scale suspended cell bioreactor. The maximum decolorization was 19.3% with aeration at KLa = 2.5836 h-1 (0.1 vvm)

The Schro¨\ddot{o}dinger-Poisson equations as the large-N limit of the Newtonian N-body system: applications to the large scale dark matter dynamics

In this paper it is argued how the dynamics of the classical Newtonian N-body system can be described in terms of the Schr$\ddot{o}$dinger-Poisson equations in the large $N$ limit. This result is based on the stochastic quantization introduced by Nelson, and on the Calogero conjecture. According to the Calogero conjecture, the emerging effective Planck constant is computed in terms of the parameters of the N-body system as $\hbar \sim M^{5/3} G^{1/2} (N/)^{1/6}$, where is $G$ the gravitational constant, $N$ and $M$ are the number and the mass of the bodies, and $$ is their average density. The relevance of this result in the context of large scale structure formation is discussed. In particular, this finding gives a further argument in support of the validity of the Schr$\ddot{o}$dinger method as numerical double of the N-body simulations of dark matter dynamics at large cosmological scales.Comment: Accepted for publication in the Euro. Phys. J.

How effective is tetracaine 4% gel, before a venipuncture, in reducing procedural pain in infants: a randomized double-blind placebo controlled trial

BACKGROUND: Procedural pain relief is sub-optimal in neonates. Topical tetracaine provides pain relief in children. Evidence of its efficacy and safety in neonates is limited. The objective of this study was to assess the efficacy and safety of topical tetracaine on the pain response of neonates during a venipuncture. METHODS: Medically stable infants greater than or equal to 24 weeks gestation, requiring a venipuncture, were included. Following randomization and double blinding, 1.1 g of tetracaine or placebo was applied to the skin for 30 minutes. Participants received oral sucrose if they met local eligibility criteria. The venipuncture was performed according to a standard protocol. A medium effect size in the pain score (corresponding to about 2 point difference in the PIPP score) was considered clinically significant, leading to a sample size of 142 infants, with 80% statistical power. Local skin reactions and immediate adverse cardiorespiratory events were noted. The primary outcome, PIPP score at 1 minute, was analysed using an independent Student's t-test. RESULTS: One hundred and forty two infants were included, 33 +/- 4 weeks gestation, 2100 +/- 900 grams and 6 +/- 3 days of age. There was almost no difference in PIPP scores at 1 minute between groups (mean difference -0.09; 95% confidence interval [CI]: -1.68 to 1.50; P = . 91). Similarly, there were no differences in PIPP scores during the 2(nd), 3(rd )and 4th minute. Duration of cry did not differ between the groups (median difference, 0; 95% CI, -3 to 0; P = . 84). The majority of infants in both groups received sucrose 24%. Sucrose had a significant effect on the PIPP score, as assessed by an ANOVA model (p = 0.0026). Local skin erythema was observed transiently in 11 infants (7 in the tetracaine and 4 in the placebo group). No serious side effect was observed. CONCLUSION: Tetracaine did not significantly decrease procedural pain in infants undergoing a venipuncture, when used in combination with routine sucrose administration

How effective is tetracaine 4% gel, before a peripherally inserted central catheter, in reducing procedural pain in infants: a randomized double-blind placebo controlled trial [ISRCTN75884221]

BACKGROUND: Procedural pain relief is sub-optimal in infants, especially small and vulnerable ones. Tetracaine gel 4% (Ametop(®), Smith-Nephew) provides pain relief in children and larger infants, but its efficacy in smaller infants and for peripherally inserted central catheters (PICC) remains uncertain. The objective of this trial was to assess the safety and efficacy of tetracaine gel on the pain response of very low birth weight (VLBW) infants during insertion of a PICC. METHODS: Medically stable infants greater than or equal to 24 weeks gestation, requiring a non-urgent PICC, were included. Following randomization and double blinding, 1.1 g of tetracaine or placebo was applied to the skin for 30 minutes. The PICC was inserted according to a standard protocol. Pain was assessed using the Premature Infant Pain Profile (PIPP). A 3-point change in the pain score was considered clinically significant, leading to a sample size of 54 infants, with 90% statistical power. Local skin reactions and immediate adverse cardiorespiratory events were noted. The primary outcome, PIPP score at 1 minute, was analysed using an independent Student's t-test. RESULTS: Fifty-four infants were included, 27 +/- 2 weeks gestation, 916 +/- 292 grams and 6.5 +/- 3.2 days of age. Baseline characteristics were similar between groups. The mean PIPP score in the first minute was 10.88 in the treatment group as compared to 11.74 in the placebo group (difference 0.86, 95% CI -1.86, 3.58). Median duration of crying in non-intubated infants was 181 seconds in the tetracaine group compared to 68 seconds in the placebo group (difference -78, 95% CI -539, 117). Local skin erythema was observed transiently in 4 infants (3 in the treatment and 1 in the placebo group). No serious harms were observed. CONCLUSION: Tetracaine 4% when applied for 30 minutes was not beneficial in decreasing procedural pain associated with a PICC in very small infants