Dependence in Stochastic Simulation Models

There is a growing need for the ability to model and generate samples of dependent random variables as primitive inputs to stochastic models. We consider the case where this dependence is modeled in terms of a partially-specified finite-dimensional random vector. A random vector sampler is commonly required to match a given set of distributions for each of its components (the marginal distributions) and values of their pairwise covariances. The NORTA method, which produces samples via a transformation of a joint-normal random vector sample, is considered the state-of-the-art method for matching this specification. We begin by showing that the NORTA method has certain flaws in its design which limit its applicability. A covariance matrix is said to be feasible for a given set of marginal distributions if a random vector exists with these properties. We develop a computational tool that can establish the feasibility of (almost) any covariance matrix for a fixed set of marginals. This tool is used to rigorously establish that there are feasible combinations of marginals and covariance matrices that the NORTA method cannot match. We further determine that as the dimension of the random vector increases, this problem rapidly becomes acute, in the sense that NORTA becomes increasingly likely to fail to match feasible specifications. As part of this analysis, we propose a random matrix sampling technique that is possibly of wider interest. We extend our study along two natural paths. First, we investigate whether NORTA can be modified to approximately match a desired covariance matrix that the original NORTA procedure fails to match. Results show that simple, elegant modifications to the NORTA procedure can help it achieve close approximations to the desired covariance matrix, and these modifications perform well with increasing dimension. Second, the feasibility testing procedure suggests a random vector sampling technique that can exactly match (almost) any given feasible set of marginals and covariances, i.e., be free of the limitations of NORTA. We develop a strong characterization of the computational effort needed by this new sampling technique. This technique is computationally competitive with NORTA in low to moderate dimensions, while matching the desired covariances exactly

COMPLEX SELF-SORTING SYSTEMS

Over the past century scientists have taken a reductionist approach towards much of the physical and biological sciences. More recently scientists have become interested in constructing complex systems from their components and thereby controlling their emerging behaviors. As supramolcular chemists we have been pursuing an approach to the creation of complex functional systems - systems chemistry - by preparation of self-sorting systems. Self-sorting system displays ability to efficiently distinguish between self- and non-self even within complex mixture. This dissertation is divided into four chapters that describe increasingly complex self-sorting systems. Chapter 1 describes a literature review on self-sorting. First, we introduced the concept of self-sorting and then described the previously studied self-sorting phenomenon in the Isaacs group followed by a description of the examples of self-sorting systems in the literature. Chapter 2 describes the synthesis and characterization of eleven C-shaped methylene bridged glycoluril dimers (II-1 - II-11) bearing H-bonding groups on their aromatic rings. Compounds II-1, II-2, (±)-II-4a, (±)-II-5, and II-7 form tightly associated homodimers in CDCl3 due to π - π and H-bonding interactions. Compounds II-2, (±)-II-5 and II-7, having disparate spatial distribution of their H-bonding groups show the ability to efficiently distinguish between self and non-self within three component mixtures in CDCl3. The effect of various structural modifications (e.g. chirality, side chain steric bulk, relative orientation, number and pattern of H-bonds) on the strength of self-assembly and the fidelity of self-sorting are presented. Chapter 3 describes the stepwise construction of an 8-component self-sorted system (III-1 - III-8) by the sequential addition of components. This process occurs via a large number of states (28 = 256) and even a larger number of pathways (8! = 40320). A pathway (III-5, III-6, III-7, III-8, III-4, III-3, III-2, then III-1) that is self-sorted at every step along the way. Another pathway (III-1, III-8, III-3, III-5, III-4, III-7, III-2, then III-6) exhibits interesting shuttling of guest molecules among hosts. The majority of pathways - unlike the special ones described above - proceed through several non self-sorted states. We characterized the remainder of the 40320 pathways by simulation using GEPASI and describe the influence of concentration, mean binding constants and standard deviation on the fidelity of the self-sorting pathways. Chapter 4 describes a method to control biological catalysis using synthetic self-sorting systems. We report the synthesis of IV-1 - IV-5 which contain both enzyme inhibitor and cucurbit[n]uril binding domains. The enzyme binding domains of IV-1 - IV-5 bind to the active sites of Bovine Carbonic Anhydrase or Acetylcholinesterase and inhibit their catalytic activities. Addition of CB[7] catalyzes the dissociation of IV-1 and IV-2 from the active site of BCA and thereby regenerates the enzymatic activity. In contrast, addition of CB[7] to AChE*IV-44 and AChE*IV-54 results in the formation of a ternary complex that does not regenerate the enzymatic activity

Deconvolution of a multi-component interaction network using systems chemistry

Abstract We describe the stepwise construction of an 8-component self-sorted system (1 - 8) by the sequential addition of components. This process occurs via a large number of states (28 = 256) and even a larger number of pathways (8! = 40320). A pathway (5, 6, 7, 8, 4, 3, 2, then 1) that is self-sorted at every step along the way has been demonstrated experimentally. Another pathway (1, 8, 3, 5, 4, 7, 2, then 6) resembles a game of musical chairs and exhibits interesting shuttling of guest molecules among hosts. The majority of pathways - unlike the special ones described above - proceed through several non self-sorted states. We characterized the remainder of the 40320 pathways by simulation using Gepasi and describe the influence of concentration and binding constants on the fidelity of the self-sorting pathways

A study on the effects of 6 weeks of training on body composition, physical fitness and physiological variables of female football players

Background: Female football becomes popular in last decades. The body fat, strength, power, endurance etc are playing an important role in female football. The present study has been designed to investigate the effects of 6 weeks of training on body composition, physical fitness and physiological variables of female football players. Materials and Methods: A total of eighty two female football players (age 16-18 yrs.) participated were included and twenty two were excluded from the study, the remaining were divided into control group (CG, n = 30) and experimental group (EG, n = 30). The volunteers of the experimental group followed a training programme (2 hrs/day, 5day/week, for 6 weeks), whereas no training was given volunteers of the control group. Selected body composition, physical fitness and physiological variables were performed at the beginning (0 week) and at the end of the study (6 weeks). Results: A significant reduction (p < .05) in body mass, body fat, resting heart rate, recovery heart rate, and systolic blood pressure; and an increase (p < .05) in strength, anaerobic power, VO2max, FEV1, FVC and PEFR was noted after 6 weeks of training. Body fat showed negative correlation with back strength (r = - 0.26, p < .05), grip strength (r = -0.46, p < .01), anaerobic capacity (r = -0.30, p < .05) and flexibility (r = -0.32, p < .05) of the volunteers. LBM showed positive correlation with grip strength right (r = 0.59, p < .05), grip strength left (r = 0.53, p < .05), back strength (r = 0.73, p < .05), flexibility (r = 0.41, p < .05). The anaerobic power showed a significant positive correlation with VO2max (r = 0.51, p < .01). Conclusions: Regular monitoring of the indicators is essential to obtain optimal performance of the players