During inflation quantum fluctuations of the field driving inflation, known as inflaton, were stretched by inflationary expansion to galactic size scales or even larger. A possible implication of inflation -- if it is correct -- is that our observable universe was once of sub-Planckian size. Thus inflation could act as a magnifier to probe the short distance structure of space-time. General arguments about the quantum theory of gravity suggest that the short distance structure of space-time can be modeled as arising from some corrections to the well-known uncertainty relation between the position and momentum operators. Such modifications have been predicted by more fundamental theories such as string theory. This modified commutation relation has been implemented at the first quantized level to the theory of cosmological perturbations. In this thesis, we will show that the aforementioned scenario of implementing the minimal length to the action has an ambiguity: total time derivatives that in continuous space-time could be neglected and do not contribute to the equations of motion, cease to remain total time derivatives as we implement minimal length. Such an ambiguity opens up the possibility for trans-Planckian physics to leave an imprint on the ratio of tensor to scalar fluctuations. In near de-Sitter space, we obtain the explicit dependence of the tensor/scalar on the minimal length. Also the first consistency relation is examined in a power-law background, where it is found that despite the ambiguity that exists in choosing the action, Planck scale physics modifies the consistency relation considerably as it leads to large oscillations in the scalar spectral index in the observable range of scales. In the second part of the thesis, I demonstrate how the assumption of existence of invariant minimal length can assist us to explain the origin of cosmic magnetic fields. The third part of the thesis is dedicated to the study of signatures of M-theory Cascade inflation.

A number of models of nature incorporate dimensions beyond our observed four. In this thesis we examine some examples and consequences of classical instabilities that emerge in the higher-dimensional theories of gravity which can describe their low energy phenomenology. <br /><br /> We first investigate a gravitational instability for black strings carrying momentum along an internal direction. We argue that this implies a new type of solution that is nonuniform along the extra dimension and find that there is a boost dependent critical dimension for which they are stable. Our analysis implies the existence of an analogous instability for the five-dimensional black ring. We construct a simple mode of the black ring to aid in applying these results and argue that such rings should exist in any number of space-time dimensions. <br /><br /> Next we consider a recently constructed class of nonsupersummetric solutions of type IIB supergravity which are everywhere smooth and have no horizon. We demonstrate that these solutions are all classically unstable. The instability is a generic feature of horizonless geometries with an ergoregion. We consider the endpoint of this instability and argue that the solutions decay to supersymmetric configurations. We also comment on the implications of the ergoregion instability for Mathur's 'fuzzball' proposal. <br /><br /> Finally, we consider an interesting braneworld cosmology in the Randall-Sundrum scenario constructed using a bulk space-time which corresponds to a charged AdS black hole. In particular, these solutions appear to 'bounce', making a smooth transition from a contracting to an expanding phase. By considering the space-time geometry more carefully, we demonstrate that generically in these solutions the brane will encounter a singularity in the transition region.

During inflation quantum fluctuations of the field driving inflation, known as inflaton, were stretched by inflationary expansion to galactic size scales or even larger. A possible implication of inflation -- if it is correct -- is that our observable universe was once of sub-Planckian size. Thus inflation could act as a magnifier to probe the short distance structure of space-time. General arguments about the quantum theory of gravity suggest that the short distance structure of space-time can be modeled as arising from some corrections to the well-known uncertainty relation between the position and momentum operators. Such modifications have been predicted by more fundamental theories such as string theory. This modified commutation relation has been implemented at the first quantized level to the theory of cosmological perturbations. In this thesis, we will show that the aforementioned scenario of implementing the minimal length to the action has an ambiguity: total time derivatives that in continuous space-time could be neglected and do not contribute to the equations of motion, cease to remain total time derivatives as we implement minimal length. Such an ambiguity opens up the possibility for trans-Planckian physics to leave an imprint on the ratio of tensor to scalar fluctuations. In near de-Sitter space, we obtain the explicit dependence of the tensor/scalar on the minimal length. Also the first consistency relation is examined in a power-law background, where it is found that despite the ambiguity that exists in choosing the action, Planck scale physics modifies the consistency relation considerably as it leads to large oscillations in the scalar spectral index in the observable range of scales. In the second part of the thesis, I demonstrate how the assumption of existence of invariant minimal length can assist us to explain the origin of cosmic magnetic fields. The third part of the thesis is dedicated to the study of signatures of M-theory Cascade inflation.

Photovoltaics offers a unique solution to energy and environmental problems simultaneously. However, widespread application of photovoltaics will not be realized until costs are reduced by about a factor of four without sacrificing performance. Silicon crystallization and wafering account for about 55% of the photovoltaic module manufacturing cost, but can be reduced significantly if a ribbon silicon material, such as String Ribbon Si, is used as an alternative to cast Si. However, the growth of String Ribbon leads to a high density of electrically active bulk defects that limit the minority carrier lifetime and solar cell performance. The research tasks of this thesis focus on the understanding, development, and implementation of defect passivation techniques to increase the bulk carrier lifetime in String Ribbon Si in order to enhance solar cell efficiency. Hydrogen passivation of defects in Si can be performed during solar cell processing by utilizing the hydrogen available during plasma-enhanced chemical vapor deposition (PECVD) of SiNx:H films. It is shown in this thesis that hydrogen passivation of defects during the simultaneous anneal of a screen-printed Al layer on the back and a PECVD SiNx:H film increases the bulk lifetime in String Ribbon by more than 30 ?A three step physical model is proposed to explain the hydrogen defect passivation. Appropriate implementation of the Al-enhanced defect passivation treatment leads to String Ribbon solar cell efficiencies as high as 14.7%. Further enhancement of bulk lifetime up to 92 ?s achieved through in-situ NH3 plasma pretreatment and low-frequency (LF) plasma excitation during SiNx:H deposition followed by a rapid thermal anneal (RTA). Development of an optimized two-step RTA firing cycle for hydrogen passivation, the formation of an Al-doped back surface field, and screen-printed contact firing results in solar cell efficiencies as high as 15.6%. In the final task of this thesis, a rapid thermal treatment performed in a conveyer belt furnace is developed to achieve a peak efficiency of 15.9% with a bulk lifetime of 140 ?Simulations of further solar cell efficiency enhancement up to 17-18% are presented to provide guidance for future research.

The low-energy supersymmetry phenomenology for specific classes of string compactifications is investigated given that the low-energy physics may provide a clue as to the structure of the fundamental theory at high energy scales. The one-parameter model (OPM), a highly constrained subset of minimal Supergravity where all the soft-supersymmetry breaking terms may be fixed in terms of the gaugino mass, is studied, in addition to a three-family Pati-Salam model constructed from intersecting D6-branes. Furthermore, the phenomenology of gravity mediated supersymmetry breaking F-theory SU(5) and SO(10) models, as well as F-SU(5) models with vector- like particles, are examined. We determine the viable parameter space that satisfies all the latest experimental constraints, including the most recent WMAP relic neutralino abundance observations, and find it to be consistent with the CDMS II and other concurrent direct-detection experiments. Moreover, we compute the gamma-ray flux and cross-sections of neutralino annihilations into gamma-rays and compare to the published Fermi-LAT satellite telescope measurements. In F-theory SU(5) and SO(10) models, we predict the exact small deviation of the gaugino mass relation at two-loop level near the electroweak scale, which can be tested at the colliders. More- over, in F-SU(5), we predict the precise deviations from the mSUGRA gaugino mass relations due to the presence of the vector-like particles, also testable at the colliders. The compilation of all these results form a comprehensive collection of predictions with which to evaluate these string models alongside anticipated experimental dis- coveries in the coming decade.

Genomic sequence databases, like GenBank, EMBL, are widely used by molecular biologists for homology searching. Because of the long length of each genomic sequence and the increase of the size of genomic sequence databases, the importance of efficient searching methods for fast queries grows. The DNA sequences are composed of four kinds of nucleotides, and these genomic sequences can be regarded as the text strings. However, there is no concept of words in a genomic sequence, which makes the search of the genomic sequence in the genomic database much difficult. Approximate String Matching (ASM) with k errors is considered for genomic sequences, where k errors would be caused by insertion, deletion, and replacement operations. Filtration of the DNA sequence is a widely adopted technique to reduce the number of the text areas (i.e., candidates) for further verification. In most of the filter methods, they first split the database sequence into q-grams. A sequence of grams (subpatterns) which match some part of the text will be passed as a candidate. The match problem of grams with the part of the text could be speed up by using the index structure for the exact match. Candidates will then be examined by dynamic programming to get the final result. However, in the previous methods for ASM, most of them considered the local order within each gram. Only the (k + s) h-samples filter considers the global order of the sequence of matched grams. Although the (k + s) h-samples filter keeps the global order of the sequence of the grams, it still has some disadvantages. First, to be a candidate in the (k + s) h-samples filter, the number of the ordered matched grams, s, is always fixed to 2 which results in low precision. Second, the (k + s) h-samples filter uses the query time to build the index for query patterns. In this thesis, we propose a new approximate string matching method, the hash trie filter, for efficiently searching in genomic databases. We build a hash trie in the pre-computing time for the genomic sequence stored in database. Although the size q of each split grams is also decided by the same formula used in the (k + s) h-samples filter, we have proposed a different way to find the ordered subpatterns in text T. Moreover, we reduce the number of candidates by pruning some unreasonable matched positions. Furthermore, unlike the (k + s) h-samples filter which always uses s = 2 to decide whether s matched subpatterns could be a candidate or not, our method will dynamically decide s, resulting in the increase of precision. The simulation results show that our hash trie filter outperforms the (k +s) h-samples filter in terms of the response time, the number of verified candidates, and the precision under different length of the query patterns and different error levels.

In this study, the focus is on predicting the subcellular localization of a protein, since subcellular localization is helpful in understanding a protein&rsquo / s functions. Function of a protein may be estimated from its sequence. Motifs or conserved subsequences are strong indicators of function. In a given sample set of protein sequences known to perform the same function, a certain subsequence or group of subsequences should be common / that is, occurrence (frequency) of common subsequences should be high. Our idea is to find the common subsequences through clustering and use these common groups (implicit motifs) to classify proteins. To calculate the distance between two subsequences, traditional string edit distance is modified so that only replacement is allowed and the cost of replacement is related to an amino acid substitution matrix. Based on the modified string edit distance, spectral clustering embeds the subsequences into some transformed space for which the clustering problem is expected to become easier to solve. For a given protein sequence, distribution of its subsequences over the clusters is the feature vector which is subsequently fed to a classifier. The most important aspect if this approach is the use of spectral clustering based on modified string edit distance.

In this thesis, we present a content based packet filtering Architecture in Linux using Deterministic Finite Automata and iptables framework. New generation firewalls and intrusion detection systems not only filter or inspect network packets according to their header fields but also take into account the content of payload. These systems use a set of signatures in the form of regular expressions or plain strings to scan network packets. This scanning phase is a CPU intensive task which may degrade network performance. Currently, the Linux kernel firewall scans network packets separately for each signature in the signature set provided by the user. This approach constitutes a considerable bottleneck to network performance. We implement a content based packet filtering architecture and a multiple string matching extension for the Linux kernel firewall that matches all signatures at once, and show that we are able to filter network traffic by consuming constant bandwidth regardless of the number of signatures. Furthermore, we show that we can do packet filtering in multi-gigabit rates.

Support Vector Machines (SVM) have recently gained prominence in the field of machine learning and pattern classification (Vapnik, 1995, Herbrich, 2002, Scholkopf and Smola, 2002). Classification is achieved by finding a separating hyperplane in a feature space, which can be mapped back onto a non-linear surface in the input space. However, training an SVM involves solving a quadratic optimization problem, which tends to be computationally intensive. Furthermore, it can be subject to stability problems and is non-trivial to implement. This thesis proposes an fast iterative Support Vector training algorithm which overcomes some of these problems. Our algorithm, which we christen Simple SVM, works mainly for the quadratic soft margin loss (also called the l2 formulation). We also sketch an extension for the linear soft-margin loss (also called the l1 formulation). Simple SVM works by incrementally changing a candidate Support Vector set using a locally greedy approach, until the supporting hyperplane is found within a finite number of iterations. It is derived by a simple (yet computationally crucial) modification of the incremental SVM training algorithms of Cauwenberghs and Poggio (2001) which allows us to perform update operations very efficiently. Constant-time methods for initialization of the algorithm and experimental evidence for the speed of the proposed algorithm, when compared to methods such as Sequential Minimal Optimization and the Nearest Point Algorithm are given. We present results on a variety of real life datasets to validate our claims. In many real life applications, especially for the l2 formulation, the kernel matrix K є R n x n can be written as K = Z T Z + Λ , where, Z є R n x m with m << n and Λ є R n x n is diagonal with nonnegative entries. Hence the matrix K - Λ is rank-degenerate, Extending the work of Fine and Scheinberg (2001) and Gill et al. (1975) we propose an efficient factorization algorithm which can be used to find a L D LT factorization of K in 0(nm2) time. The modified factorization, after a rank one update of K, can be computed in 0(m2) time. We show how the Simple SVM algorithm can be sped up by taking advantage of this new factorization. We also demonstrate applications of our factorization to interior point methods. We show a close relation between the LDV factorization of a rectangular matrix and our LDLT factorization (Gill et al., 1975). An important feature of SVM's is that they can work with data from any input domain as long as a suitable mapping into a Hilbert space can be found, in other words, given the input data we should be able to compute a positive semi definite kernel matrix of the data (Scholkopf and Smola, 2002). In this thesis we propose kernels on a variety of discrete objects, such as strings, trees, Finite State Automata, and Pushdown Automata. We show that our kernels include as special cases the celebrated Pair-HMM kernels (Durbin et al., 1998, Watkins, 2000), the spectrum kernel (Leslie et al., 20024, convolution kernels for NLP (Collins and Duffy, 2001), graph diffusion kernels (Kondor and Lafferty, 2002) and various other string-matching kernels. Because of their widespread applications in bio-informatics and web document based algorithms, string kernels are of special practical importance. By intelligently using the matching statistics algorithm of Chang and Lawler (1994), we propose, perhaps, the first ever algorithm to compute string kernels in linear time. This obviates dynamic programming with quadratic time complexity and makes string kernels a viable alternative for the practitioner. We also propose extensions of our string kernels to compute kernels on trees efficiently. This thesis presents a linear time algorithm for ordered trees and a log-linear time algorithm for unordered trees. In general, SVM's require time proportional to the number of Support Vectors for prediction. In case the dataset is noisy a large fraction of the data points become Support Vectors and thus time required for prediction increases. But, in many applications like search engines or web document retrieval, the dataset is noisy, yet, the speed of prediction is critical. We propose a method for string kernels by which the prediction time can be reduced to linear in the length of the sequence to be classified, regardless of the number of Support Vectors. We achieve this by using a weighted version of our string kernel algorithm. We explore the relationship between dynamic systems and kernels. We define kernels on various kinds of dynamic systems including Markov chains (both discrete and continuous), diffusion processes on graphs and Markov chains, Finite State Automata, various linear time-invariant systems etc Trajectories arc used to define kernels introduced on initial conditions lying underlying dynamic system. The same idea is extended to define Kernels on a. dynamic system with respect to a set of initial conditions. This framework leads to a large number of novel kernels and also generalize many previously proposed kernels. Lack of adequate training data is a problem which plagues classifiers. We propose n new method to generate virtual training samples in the case of handwritten digit data. Our method uses the two dimensional suffix tree representation of a set of matrices to encode an exponential number of virtual samples in linear space thus leading to an increase in classification accuracy. This in turn, leads us naturally to a, compact data dependent representation of a test pattern which we call the description tree. We propose a new kernel for images and demonstrate a quadratic time algorithm for computing it by wing the suffix tree representation of an image. We also describe a method to reduce the prediction time to quadratic in the size of the test image by using techniques similar to those used for string kernels.

<p>Of the many waveforms the bowed string can assume, theso-called "Helmholtz motion" (Helmholtz 1862) gives the fullestsound in terms of power and overtone richness. The developmentof this steady-state oscillation pattern can take manydifferent paths, most of which would include noise caused bystick-slip irregularities of the bow-string contact. Of thefive papers included in the thesis, the first one shows, notsurprisingly, that tone onsets are considered superior when theattack noise has a very limited duration. It was found,however, that in this judgment the<i>character</i>of the noise plays an important part, as thelistener’s tolerance of noise in terms of duration isalmost twice as great for "slipping noise" as for "creaks" or"raucousness" during the tone onsets. The three followingpapers contain analyses focusing on how irregular slip-sticktriggering may be avoided, as is quite often the case inpractical playing by professionals. The fifth paper describesthe triggering mechanism of a peculiar tone production referredto as "Anomalous Low Frequencies" (ALF). If properly skilled, aplayer can achieve pitches below the normal range of theinstrument. This phenomenon is related to triggering wavestaking "an extra turn" on the string before causing thestring’s release from the bow-hair grip. Since transverseand torsional propagation speeds are both involved, twodifferent sets of "sub-ranged" notes can be produced this way.In the four last papers wave patterns are analysed andexplained through the use of computer simulations.</p><p>Key words:</p><p>Key words:</p><p>Bowed string, violin, musicalacoustics, musical transient, anomalous low frequencies,Helmholtz motion</p>