String theory imposes slight modifications to Einstein's equations of general relativity (GR). In (4), the authors claim that the gravitational field equations in empty space, which in GR are just R [subscript greek letters mu nu ] = 0, should hold one extra term which is first order in the string constant [alpha'] and proportional to the Riemann curvature tensor squared. They do admit, however, that this simple modification is just schematic. In (1) the authors use modified equations which are coupled to the dilation field. We show that equations given in (4) do not admit an isotropic solution; justification of these equations would require sacrificing isotropy. We thus investigate the consequences of the coupled equations from (1) and the black-hole solution they give there. We calculate the additional perihelion precession of Mercury, the added deflection of photons by the sun, and the extra gravitational redshift which should be present if these equations hold. We determine that additional effects due to string theory in each of these cases are quite minuscule.

This thesis describes the development and application of the new software MAXCOVER that computes maximal covers and non-extendible repeats (a.k.a. “maximal repeats”). A string is a finite array x[1..n] of elements chosen from a set of totally ordered symbols called an alphabet. A repeat is a substring that occurs at least twice in x. A repeat is left/right extendible if every occurrence is preceded/followed by the same symbol; otherwise, it is non-left/non-right extendible (NLE/NRE). A non-extendible (NE) repeat is both NLE and NRE. A repeat covers a position i if x[i] lies within the repeat. A maximal cover (a.k.a. “optimal cover”) is a repeat that covers the most positions in x. For simplicity, we first describe a quadratic O(n2) implementation of MAXCOVER to compute all maximal covers of a given string based on the pseudocode given in [1]. Then, we consider the logarithmic O(n log n) pseudocode in [1], in which we identify several errors. We leave a complete correction and implementation for future work. Instead, we propose two improved quadratic algorithms that, shown through experiments, will execute in linear time for the average case. We perform a benchmark evaluation of MAXCOVER’s performance and demonstrate its value to biologists in the protein context [2]. To do so, we develop an extension of MAXCOVER for the closely related task of computing NE repeats. Then, we compare MAXCOVER to the repeat-match feature of the well-known MUMmer software [3] (600+ citations). We determine that MAXCOVER is an order-of-magnitude faster than MUMmer with much lower space requirements. We also show that MAXCOVER produces a more compact, exact, and user-friendly output that specifies the repeats. Availability: Open source code, binaries, and test data are available on Github at https://github.com/hollykoponen/MAXCOVER. Currently runs on Linux, untested on other OS. / Thesis / Master of Science (MSc) / This thesis deals with a simple yet essential data structure called a string, a sequence of symbols drawn from an alphabet. For example, a DNA sequence is a string comprised of four letters. We describe a new software called MAXCOVER that identifies maximal covers of a given string x (a repeating substring that ‘covers’ the most positions in x). This software is based on the algorithms in [1]. We propose two new algorithms that perform faster in practice. We also extended MAXCOVER for the closely related task of computing non-extendible repeats. We compare this extension to the well-known MUMmer software (600+ citations). We find that MAXCOVER is many times faster than MUMmer with much lower space requirements and produces a more compact, exact and user-friendly output.

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