Abstract:
I give an elementary introduction to the key algorithm used in recent applications of computational algebraic geometry to the subject of string phenomenology. I begin with a simple description of the algorithm itself and then give 3 examples of its use in physics. I describe how it can be used to obtain constraints on flux parameters, how it can simplify the equations describing vacua in 4D string models, and lastly how it can be used to compute the vacuum space of the electroweak sector of the MSSM.

Abstract:
Retail managers were examined to determine their leadership styles and any potential correlations to conflict management styles. Research findings suggest that successful retail managers exhibit transformational leadership styles, and those that exhibit laissez-faire leadership is strongly correlated with avoidance conflict management style. The Conflict Management Style (CMS) and Multi Leadership Questionnaire (MLQ) instruments were used to survey participants in this study. A MLQ scoring manual was used to identify leadership styles, and a CMS scoring manual was used to determine conflict management styles. Pearson correlation (SPSS, version 17.0) was used to correlate between MLQ and CMS findings.

Abstract:
We study the ideals of the partition, Brauer, and Jones monoids, establishing various combinatorial results on generating sets and idempotent generating sets via an analysis of their Graham-Houghton graphs. We show that each proper ideal of the partition monoid P_n is an idempotent generated semigroup, and obtain a formula for the minimal number of elements (and the minimal number of idempotent elements) needed to generate these semigroups. In particular, we show that these two numbers, which are called the rank and idempotent rank (respectively) of the semigroup, are equal to each other, and we characterize the generating sets of this minimal cardinality. We also characterize and enumerate the minimal idempotent generating sets for the largest proper ideal of P_n, which coincides with the singular part of P_n. Analogous results are proved for the ideals of the Brauer and Jones monoids; in each case, the rank and idempotent rank turn out to be equal, and all the minimal generating sets are described. We also show how the rank and idempotent rank results obtained, when applied to the corresponding twisted semigroup algebras (the partition, Brauer, and Temperley-Lieb algebras), allow one to recover formulas for the dimensions of their cell modules (viewed as cellular algebras) which, in the semisimple case, are formulas for the dimensions of the irreducible representations of the algebras. As well as being of algebraic interest, our results relate to several well-studied topics in graph theory including the problem of counting perfect matchings (which relates to the problem of computing permanents of {0,1}-matrices and the theory of Pfaffian orientations), and the problem of finding factorizations of Johnson graphs. Our results also bring together several well-known number sequences such as Stirling, Bell, Catalan and Fibonacci numbers.

Abstract:
Surgical reconstruction of the dislocated acromioclavicular joint often requires exposure and instrumentation of the coracoid. This carries risks to the surrounding neurovascular structures. We present a safe and simple technique of primary fixation of the acromioclavicular joint, relying on mechanical principles and biological repair, without the need for metalwork. By avoiding the coracoid we hope this approach will appeal to the general orthopedic surgeon. We have found that this technique is suited to both acute and chronic acromioclavicular joint dislocation.

Abstract:
We construct cosmological solutions of four-dimensional effective heterotic M-theory with a moving five-brane and evolving dilaton and T modulus. It is shown that the five-brane generates a transition between two asymptotic rolling-radii solutions. Moreover, the five-brane motion always drives the solutions towards strong coupling asymptotically. We present an explicit example of a negative-time branch solution which ends in a brane collision accompanied by a small-instanton transition. The five-dimensional origin of some of our solutions is also discussed.

Abstract:
We present an exhaustive, constructive, classification of the Calabi-Yau four-folds which can be described as complete intersections in products of projective spaces. A comprehensive list of 921,497 configuration matrices which represent all topologically distinct types of complete intersection Calabi-Yau four-folds is provided and can be downloaded at http://www-thphys.physics.ox.ac.uk/projects/CalabiYau/Cicy4folds/index.html . The manifolds have non-negative Euler characteristics in the range 0 - 2610. This data set will be of use in a wide range of physical and mathematical applications. Nearly all of these four-folds are elliptically fibered and are thus of interest for F-theory model building.

Abstract:
We study the partial Brauer monoid and its planar submonoid, the Motzkin monoid. We conduct a thorough investigation of the structure of both monoids, providing information on normal forms, Green's relations, regularity, ideals, idempotent generation, minimal (idempotent) generating sets, and so on. We obtain necessary and sufficient conditions under which the ideals of these monoids are idempotent-generated. We find formulae for the rank (smallest size of a generating set) of each ideal, and for the idempotent rank (smallest size of an idempotent generating set) of the idempotent-generated subsemigroup of each ideal; in particular, when an ideal is idempotent-generated, the rank and idempotent rank are equal. Along the way, we obtain a number of results of independent interest, and we demonstrate the utility of the semigroup theoretic approach by applying our results to obtain important representation theoretic results concerning the corresponding diagram algebras, the partial (or rook) Brauer algebra and Motzkin algebra.

Abstract:
We make explicit a larger structural phenomenon hidden behind the existence of normalizers in terms of existence of certain cartesian maps related to the kernel functor.

Abstract:
We analyse some aspects of the notion of algebraic exponentiation introduced by the second author [16] and satisfied by the category of groups. We show how this notion provides a new approach to the categorical-algebraic question of the centralization. We explore, in the category of groups, the unusual universal properties and constructions determined by this notion, and we show how it is the origin of various properties of this category.

Abstract:
We investigate the mathematical properties of the class of Calabi-Yau four-folds recently found in [arXiv:1303.1832]. This class consists of 921,497 configuration matrices which correspond to manifolds that are described as complete intersections in products of projective spaces. For each manifold in the list, we compute the full Hodge diamond as well as additional topological invariants such as Chern classes and intersection numbers. Using this data, we conclude that there are at least 36,779 topologically distinct manifolds in our list. We also study the fibration structure of these manifolds and find that 99.95 percent can be described as elliptic fibrations. In total, we find 50,114,908 elliptic fibrations, demonstrating the multitude of ways in which many manifolds are fibered. A sub-class of 26,088,498 fibrations satisfy necessary conditions for admitting sections. The complete data set can be downloaded at http://www-thphys.physics.ox.ac.uk/projects/CalabiYau/Cicy4folds/index.html .