Bounds on edit metric codes with combinatorial DNA constraints

The design of a large and reliable DNA codeword library is a key problem in DNA based computing. DNA codes, namely sets of fixed length edit metric codewords over the alphabet {A, C, G, T}, satisfy certain combinatorial constraints with respect to biological and chemical restrictions of DNA strands. The primary constraints that we consider are the reverse--complement constraint and the fixed GC--content constraint, as well as the basic edit distance constraint between codewords. We focus on exploring the theory underlying DNA codes and discuss several approaches to searching for optimal DNA codes. We use Conway's lexicode algorithm and an exhaustive search algorithm to produce provably optimal DNA codes for codes with small parameter values. And a genetic algorithm is proposed to search for some sub--optimal DNA codes with relatively large parameter values, where we can consider their sizes as reasonable lower bounds of DNA codes. Furthermore, we provide tables of bounds on sizes of DNA codes with length from 1 to 9 and minimum distance from 1 to 9.

Charting developmental EEG gamma changes in the auditory modality /

The oscillation of neuronal circuits reflected in the EEG gamma frequency may be fundamental to the perceptual process referred to as binding (the integration of various thoughts and perceptions into a coherent picture). The aim of our study was to expand our knowledge of the developmental course ofEEG gamma in the auditory modality. 2 We investigated EEG 40 Hz gamma band responses (35.2 to 43.0 Hz) using an auditory novelty oddball paradigm alone and with a visual-number-series distracter task in 208 participants as a function of age (7 years to adult) at 9 sites across the sagital and lateral axes (F3, Fz, F4, C3, Cz, C4, P3, Pz, P4). Gamma responses were operationally defined as change in power or a change in phase synchrony level from baseline within two time windows. The evoked gamma response was defined as a significant change from baseline occurring between 0 to 150 ms after stimulus onset; the induced gamma response was measured from 250 to 750 ms after stimulus onset. A significant evoked gamma band response was found when measuring changes in both power and phase synchrony. The increase in both measures was maximal at frontal regions. Decreases in both measures were found when participants were distracted by a secondary task. For neither measure were developmental effects noted. However, evoked gamma power was significantly enhanced with the presentation of a novel stimulus, especially at the right frontal site (F4); frontal evoked gamma phase synchrony also showed enhancement for novel stimuli but only for our two oldest age groups (16-18 year olds and adults). Induced gamma band responses also varied with task-dependent cognitive stimulus properties. In the induced gamma power response in all age groups, target stimuli generated the highest power values at the parietal region, while the novel stimuli were always below baseline. Target stimuli increased induced synchrony in all regions for all participants, but the novel stimulus selectively affected participants dependent on their age and gender. Adult participants, for example, exhibited a reduction in gamma power, but an increase in synchrony to the novel stimulus within the same region. Induced gamma synchrony was more sensitive to the gender of the participant than was induced gamma power. While induced gamma power produced little effects of age, gamma synchrony did have age effects. These results confirm that the perceptual process which regulates gamma power is distinct from that which governs the synchronization for neuronal firing, and both gamma power and synchrony are important factors to be considered for the "binding" hypothesis. However, there is surprisingly little effect of age on the absolute levels of or distribution of EEG gamma in the age range investigated.

Particle swarm optimization for two-connected networks with bounded rings

The Two-Connected Network with Bounded Ring (2CNBR) problem is a network design problem addressing the connection of servers to create a survivable network with limited redirections in the event of failures. Particle Swarm Optimization (PSO) is a stochastic population-based optimization technique modeled on the social behaviour of flocking birds or schooling fish. This thesis applies PSO to the 2CNBR problem. As PSO is originally designed to handle a continuous solution space, modification of the algorithm was necessary in order to adapt it for such a highly constrained discrete combinatorial optimization problem. Presented are an indirect transcription scheme for applying PSO to such discrete optimization problems and an oscillating mechanism for averting stagnation.

Zero-sum problems in finite cyclic groups

The purpose of this thesis is to investigate some open problems in the area of combinatorial number theory referred to as zero-sum theory. A zero-sequence in a finite cyclic group G is said to have the basic property if it is equivalent under group automorphism to one which has sum precisely IGI when this sum is viewed as an integer. This thesis investigates two major problems, the first of which is referred to as the basic pair problem. This problem seeks to determine conditions for which every zero-sequence of a given length in a finite abelian group has the basic property. We resolve an open problem regarding basic pairs in cyclic groups by demonstrating that every sequence of length four in Zp has the basic property, and we conjecture on the complete solution of this problem. The second problem is a 1988 conjecture of Kleitman and Lemke, part of which claims that every sequence of length n in Zn has a subsequence with the basic property. If one considers the special case where n is an odd integer we believe this conjecture to hold true. We verify this is the case for all prime integers less than 40, and all odd integers less than 26. In addition, we resolve the Kleitman-Lemke conjecture for general n in the negative. That is, we demonstrate a sequence in any finite abelian group isomorphic to Z2p (for p ~ 11 a prime) containing no subsequence with the basic property. These results, as well as the results found along the way, contribute to many other problems in zero-sum theory.

Bio-inspired optimization & sampling technique for side-chain packing in MCCE

The prediction of proteins' conformation helps to understand their exhibited functions, allows for modeling and allows for the possible synthesis of the studied protein. Our research is focused on a sub-problem of protein folding known as side-chain packing. Its computational complexity has been proven to be NP-Hard. The motivation behind our study is to offer the scientific community a means to obtain faster conformation approximations for small to large proteins over currently available methods. As the size of proteins increases, current techniques become unusable due to the exponential nature of the problem. We investigated the capabilities of a hybrid genetic algorithm / simulated annealing technique to predict the low-energy conformational states of various sized proteins and to generate statistical distributions of the studied proteins' molecular ensemble for pKa predictions. Our algorithm produced errors to experimental results within .acceptable margins and offered considerable speed up depending on the protein and on the rotameric states' resolution used.

George H. Cornish Fonds

George Henry Cornish (1834-1912) was a Methodist minister whose circuits included Clinton, Ont. (1859), Newcastle, Ont. (1861), and Caledonia/Binbrook/Glanford, Ont. (1864- 1865). He wrote several books on the Methodist Church in Canada, including the Cyclopaedia of Methodism in Canada (1881) and the Handbook of Canadian Methodism (1867).

The Salmon Algorithm - A New Population Based Search Metaheuristic

This thesis introduces the Salmon Algorithm, a search meta-heuristic which can be used for a variety of combinatorial optimization problems. This algorithm is loosely based on the path finding behaviour of salmon swimming upstream to spawn. There are a number of tunable parameters in the algorithm, so experiments were conducted to find the optimum parameter settings for different search spaces. The algorithm was tested on one instance of the Traveling Salesman Problem and found to have superior performance to an Ant Colony Algorithm and a Genetic Algorithm. It was then tested on three coding theory problems - optimal edit codes, optimal Hamming distance codes, and optimal covering codes. The algorithm produced improvements on the best known values for five of six of the test cases using edit codes. It matched the best known results on four out of seven of the Hamming codes as well as three out of three of the covering codes. The results suggest the Salmon Algorithm is competitive with established guided random search techniques, and may be superior in some search spaces.

Generator Matrix Based Search for Extremal Self-Dual Binary Error-Correcting Codes

Self-dual doubly even linear binary error-correcting codes, often referred to as Type II codes, are codes closely related to many combinatorial structures such as 5-designs. Extremal codes are codes that have the largest possible minimum distance for a given length and dimension. The existence of an extremal (72,36,16) Type II code is still open. Previous results show that the automorphism group of a putative code C with the aforementioned properties has order 5 or dividing 24. In this work, we present a method and the results of an exhaustive search showing that such a code C cannot admit an automorphism group Z6. In addition, we present so far unpublished construction of the extended Golay code by P. Becker. We generalize the notion and provide example of another Type II code that can be obtained in this fashion. Consequently, we relate Becker's construction to the construction of binary Type II codes from codes over GF(2^r) via the Gray map.

Investigation of the role of the nucleus accumbens in amphetamine-induced 50 kHz ultrasonic vocalizations in the rat

There is extensive evidence that the mesolimbic dopamine system underlies the production of 50 kHz ultrasonic vocalizations in rats. In particular, the shell of the nucleus accumbens is associated with generation of frequency modulated 50 kHz calls (a specific type of 50 kHz call which can be subdivided into various subtypes). There is also evidence that amphetamine administered systemically preferentially increases the proportion of trill and step calls compared to other frequency modulated 50 kHz subtypes. The purpose of this study was to investigate the effect of drug administration route and the role of the nucleus accumbens shell in amphetamine-induced 50 kHz call profile in the rat. Three experiments investigated this by using subcutaneous and intra-accumbens microinjections of amphetamine, as well as procaine (a local anesthetic) blockade of the nucleus accumbens. Ultrasonic vocalizations were recorded digitally from 24 rats and were analysed for sonographic structure based on general call parameters. The results of the three experiments were partially supportive of the hypotheses. Systemic amphetamine was found to induce greater bandwidth in 50 kHz calling compared to spontaneous calls in a vehicle condition. Systemic amphetamine was also found to preferentially increase the proportion of trill and step subtypes compared to vehicle. Moreover, there was no difference in the proportions of 50 kHz subtypes resulting from intracerebral or systemic application of amphetamine. There was, however, a significant difference for bandwidth, with systemic amphetamine inducing greater bandwidth over intraaccumbens application. Procaine blockade of the nucleus accumbens shell paired with subcutaneous amphetamine produced no difference in bandwidth of calls compared with those after a vehicle pre-treatment similarly paired. There was no reduction in the proportions of trill and step 50 kHz subtypes as well, with the procaine condition showing significantly greater proportion of step calls. The results of the study support a role for the iii nucleus accumbens shell in the amphetamine-induced changes on 50 kHz call profile. They also indicate there are more regions and pathways involved in generating 50 kHz calls than the projections from the ventral tegmental area to the nucleus accumbens. The implications of this work are that frequency modulated 50 kHz subtypes may be generated by distinct neurophysiological mechanisms and may represent a profitable avenue for investigating different circuits of 50 kHz call categories in the rat.