This is a quartet in three movements: allegro ben marcato (free form); adagio appasionato (passacaglia); and presto (scherzo). These three movements comprise an arch-form, the first and third being similar stylistically and thematically, the second forming the "pillar".

This quartet shows the composer's development from a highly chromatic, freely melodic, un-serialized style in movement I, through a still free, but disjunct, somewhat more ordered style in movement II, to a style in movement III which makes much use of serial techniques. This last usage, however, no longer employs the twelve-tone method in a stiff and fettered manner.

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This thesis is divided into two parts. The first part concerns the study of the ambitwistor string and the scattering equations, while the second concerns the interplay of the symmetries of the asymptotic null boundary of Minkowski space, called [scri], and scattering amplitudes. The first part begins with a review of the CHY formulas for scattering amplitudes, the scattering equations and the ambitwistor string including its pure spinor version. Next are the results of this thesis concerning these topics, they are: generalizing the ambitwistor model to higher genus surfaces; calculating the one-loop NS-NS scattering amplitudes and studying their modular and factorization properties; deriving the one-loop scattering equations and analyzing their factorization; showing that, in the case of the four graviton amplitude, the ambitwistor amplitude gives the expected kinematical prefactor; matching this amplitude to the field theory expectation in a particular kinematical regime; solving the one loop scattering equations in this kinematical regime; a conjecture for the IR behaviour of the one-loop ambitwistor integrand; computing the four graviton, two-loop amplitude using pure spinors; showing that this two-loop amplitude has the correct kinematical prefactor and factorizes as expected for a field theory amplitude; generalizing the ambitwistor string to curved backgrounds; obtaining the field equations for type II supergravity as anomaly cancellation on the worldsheet; generalizing the scattering equations for curved backgrounds. The second part begins with a review of the definition of the null asymptotic boundary of four dimensional Minkowski space, its symmetry algebra, and their relation to soft particles in the S-matrix. Next are the results of this thesis concerning these topics, they are: constructing two models consisting of maps from a worldsheet to [scri], one containing the spectrum of N=8 supergravity, and the other the spectrum of N=4 super Yang-Mills; showing how certain correlators in these theories calculate the tree-level S-matrix of N=8 sugra and N=4 sYM respectively; defining worldsheet charges which encode the action of the appropriate asymptotic symmetry algebra and showing that their Ward-identities recover the soft graviton, and soft gluon factors; defining worldsheet charges for proposed extensions of these symmetry algebras and showing that their Ward-identities give the subleading soft graviton and subleading soft gluon factors.

Music educators admit that there is a great need for research in the field o public school music. Instrumental class teaching has suffered the trial and error method since its introduction into the schools. There is still an appalling lack of material on the subject. The two or three books published on instrumental class teaching are from twelve to seventeen years old. The Reader's Guide lists only nine magazine articles in the past ten years concerning the class teaching of string instruments. Yet, the successful teaching of instrumental classes requires a high type of organization and a specialized teaching technique. It is not only necessary for the teacher to be a good musician, but he must have a knowledge of proper classroom methods and apply it. The purpose of this study is to analyze and evolve from six recognized beginning string methods a course of study suitable for use in training a beginning string section.

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Approximate string matching consists in identifying strings as similar even ifthere is a number of mismatch between them. This technique is one of thesolutions to reduce the exact matching strictness in data comparison. In manycases it is useful to identify stream variation (e.g. audio) or word declension (e.g.prefix, suffix, plural). Approximate string matching can be used to score terms in InformationRetrieval (IR) systems. The benefit is to return results even if query terms doesnot exactly match indexed terms. However, as approximate string matchingalgorithms only consider characters (nor context neither meaning), there is noguarantee that additional matches are relevant matches. This paper presents the effects of some approximate string matchingalgorithms on search results in IR systems. An experimental research design hasbeen conducting to evaluate such effects from two perspectives. First, resultrelevance is analysed with precision and recall. Second, performance is measuredthanks to the execution time required to compute matches. Six approximate string matching algorithms are studied. Levenshtein andDamerau-Levenshtein computes edit distance between two terms. Soundex andMetaphone index terms based on their pronunciation. Jaccard similarity calculatesthe overlap coefficient between two strings. Tests are performed through IR scenarios regarding to different context,information need and search query designed to query on a technicaldocumentation related to software development (man pages from Ubuntu). Apurposive sample is selected to assess document relevance to IR scenarios andcompute IR metrics (precision, recall, F-Measure). Experiments reveal that all tested approximate matching methods increaserecall on average, but, except Metaphone, they also decrease precision. Soundexand Jaccard Similarity are not advised because they fail on too many IR scenarios.Highest recall is obtained by edit distance algorithms that are also the most timeconsuming. Because Levenshtein-Damerau has no significant improvementcompared to Levenshtein but costs much more time, the last one is recommendedfor use with a specialised documentation. Finally some other related recommendations are given to practitioners toimplement IR systems on technical documentation.

String-to-String Correction is the process of transforming some mutable string M into an exact copy of some other string (the target string T), using a shortest sequence of well-defined edit operations. The formal STRING-TO-STRING CORRECTION problem asks for the optimal solution using just two operations: symbol deletion, and swap of adjacent symbols. String correction problems using only swaps and deletions are computationally interesting; in his paper On the Complexity of the Extended String-to-String Correction Problem (1975), Robert Wagner proved that the String-to-String Correction problem under swap and deletion operations only is NP-complete for unbounded alphabets. In this thesis, we present the first careful examination of the binary-alphabet case, which we call Binary String-to-String Correction (BSSC). We present several special cases of BSSC for which an optimal solution can be found in polynomial time; in particular, the case where T and M have an equal number of occurrences of a given symbol has a polynomial-time solution. As well, we demonstrate and prove several properties of BSSC, some of which do not necessarily hold in the case of String-to-String Correction. For instance: that the order of operations is irrelevant; that symbols in the mutable string, if swapped, will only ever swap in one direction; that the length of the Longest Common Subsequence (LCS) of the two strings is monotone nondecreasing during the execution of an optimal solution; and that there exists no correlation between the effect of a swap or delete operation on LCS, and the optimality of that operation. About a dozen other results that are applicable to Binary String-to-String Correction will also be presented. / Graduate / 0984 / 0715 / tspreen@gmail.com