A New Mechanism of Spontaneous SUSY Breaking

We propose a new mechanism of spontaneous supersymmetry breaking. The existence of extra dimensions with nontrivial topology plays an important role. We investigate new features resulted from the mechanism in two simple supersymmetric Z_2 and U(1) models. One of remarkable features is that there exists a phase in which the translational invariance for the compactified directions is broken spontaneously, accompanying the breakdown of the supersymmetry. The mass spectrum of the models appeared in reduced dimensions is a full of variety, reflecting the highly nontrivial vacuum structure of the models. The Nambu-Goldstone bosons (fermions) associated with breakdown of symmetries are found in the mass spectrum. Our mechanism also yields quite different vacuum structures if models have different global symmetries.Comment: 43 pages, 3 figure

Complementary vertices and adjacency testing in polytopes

Our main theoretical result is that, if a simple polytope has a pair of complementary vertices (i.e., two vertices with no facets in common), then it has at least two such pairs, which can be chosen to be disjoint. Using this result, we improve adjacency testing for vertices in both simple and non-simple polytopes: given a polytope in the standard form {x \in R^n | Ax = b and x \geq 0} and a list of its V vertices, we describe an O(n) test to identify whether any two given vertices are adjacent. For simple polytopes this test is perfect; for non-simple polytopes it may be indeterminate, and instead acts as a filter to identify non-adjacent pairs. Our test requires an O(n^2 V + n V^2) precomputation, which is acceptable in settings such as all-pairs adjacency testing. These results improve upon the more general O(nV) combinatorial and O(n^3) algebraic adjacency tests from the literature.Comment: 14 pages, 5 figures. v1: published in COCOON 2012. v2: full journal version, which strengthens and extends the results in Section 2 (see p1 of the paper for details

ATM-CMG control system stability

Stability analyses and simulation data and results are presented for an initial Control Moment Gyroscope system proposed for the Apollo Telescope Mount cluster (later named Skylab) using momentum vector feedback. A compensation filtering technique is presented which significantly improved analytical and simulation performance of the system. This technique is quite similar to the complementary filtering technique and represents an early NASA application

On the Relationship between Convex Bodies Related to Correlation Experiments with Dichotomic Observables

In this paper we explore further the connections between convex bodies related to quantum correlation experiments with dichotomic variables and related bodies studied in combinatorial optimization, especially cut polyhedra. Such a relationship was established in Avis, Imai, Ito and Sasaki (2005 J. Phys. A: Math. Gen. 38 10971-87) with respect to Bell inequalities. We show that several well known bodies related to cut polyhedra are equivalent to bodies such as those defined by Tsirelson (1993 Hadronic J. S. 8 329-45) to represent hidden deterministic behaviors, quantum behaviors, and no-signalling behaviors. Among other things, our results allow a unique representation of these bodies, give a necessary condition for vertices of the no-signalling polytope, and give a method for bounding the quantum violation of Bell inequalities by means of a body that contains the set of quantum behaviors. Optimization over this latter body may be performed efficiently by semidefinite programming. In the second part of the paper we apply these results to the study of classical correlation functions. We provide a complete list of tight inequalities for the two party case with (m,n) dichotomic observables when m=4,n=4 and when min{m,n}<=3, and give a new general family of correlation inequalities.Comment: 17 pages, 2 figure

Race and vocational education and training in England

Black and minority ethnic students (BME) are a significant constituency in VET and FE in England. Despite this recent research on race and VET has become a marginal concern. Insofar as current VET research addresses social justice, race appears to be a supplementary concern. Although there is a substantial literature addressing race and education, this focuses primarily on schools and higher education. This paper examines why there is a need to develop a research agenda that analyses participation, outcomes and experiences of BME VET students, particularly those on ‘non-advanced’ programmes (equivalent to European Qualification Framework Level 1-3) with uncertain labour market outcomes and who are arguably being ‘warehoused’ in low status courses. The paper reflects on the historically specific reasons for the dearth of research on race and VET, drawing on a scoping exercise of the literature to evidence this. We conclude by offering a provisional analysis that identifies recent shifts in participation among BME groups, locating this in its socio-economic and historical context. Our analysis reaffirms that VET remains a significant educational site for BME groups, but it is a complex racialised site which makes the current neglect of race and VET in academic research deeply problematic

A robust pseudo-inverse spectral filter applied to the Earth Radiation Budget Experiment (ERBE) scanning channels

Computer simulations of a least squares estimator operating on the ERBE scanning channels are discussed. The estimator is designed to minimize the errors produced by nonideal spectral response to spectrally varying and uncertain radiant input. The three ERBE scanning channels cover a shortwave band a longwave band and a ""total'' band from which the pseudo inverse spectral filter estimates the radiance components in the shortwave band and a longwave band. The radiance estimator draws on instantaneous field of view (IFOV) scene type information supplied by another algorithm of the ERBE software, and on a priori probabilistic models of the responses of the scanning channels to the IFOV scene types for given Sun scene spacecraft geometry. It is found that the pseudoinverse spectral filter is stable, tolerant of errors in scene identification and in channel response modeling, and, in the absence of such errors, yields minimum variance and essentially unbiased radiance estimates

Efficient Enumeration of Induced Subtrees in a K-Degenerate Graph

In this paper, we address the problem of enumerating all induced subtrees in an input k-degenerate graph, where an induced subtree is an acyclic and connected induced subgraph. A graph G = (V, E) is a k-degenerate graph if for any its induced subgraph has a vertex whose degree is less than or equal to k, and many real-world graphs have small degeneracies, or very close to small degeneracies. Although, the studies are on subgraphs enumeration, such as trees, paths, and matchings, but the problem addresses the subgraph enumeration, such as enumeration of subgraphs that are trees. Their induced subgraph versions have not been studied well. One of few example is for chordless paths and cycles. Our motivation is to reduce the time complexity close to O(1) for each solution. This type of optimal algorithms are proposed many subgraph classes such as trees, and spanning trees. Induced subtrees are fundamental object thus it should be studied deeply and there possibly exist some efficient algorithms. Our algorithm utilizes nice properties of k-degeneracy to state an effective amortized analysis. As a result, the time complexity is reduced to O(k) time per induced subtree. The problem is solved in constant time for each in planar graphs, as a corollary

Spacetime structure of the global vortex

We analyse the spacetime structure of the global vortex and its maximal analytic extension in an arbitrary number of spacetime dimensions. We find that the vortex compactifies space on the scale of the Hubble expansion of its worldvolume, in a manner reminiscent of that of the domain wall. We calculate the effective volume of this compactification and remark on its relevance to hierarchy resolution with extra dimensions. We also consider strongly gravitating vortices and derive bounds on the existence of a global vortex solution.Comment: 19 pages revtex, 2 figures, minor changes, references adde

Confinement and the AdS/CFT Correspondence

We study the thermodynamics of the confined and unconfined phases of superconformal Yang-Mills in finite volume and at large N using the AdS/CFT correspondence. We discuss the necessary conditions for a smooth phase crossover and obtain an N-dependent curve for the phase boundary.Comment: 12 pages, 1 figure, RevTe

Noise Thresholds for Higher Dimensional Systems using the Discrete Wigner Function

For a quantum computer acting on d-dimensional systems, we analyze the computational power of circuits wherein stabilizer operations are perfect and we allow access to imperfect non-stabilizer states or operations. If the noise rate affecting the non-stabilizer resource is sufficiently high, then these states and operations can become simulable in the sense of the Gottesman-Knill theorem, reducing the overall power of the circuit to no better than classical. In this paper we find the depolarizing noise rate at which this happens, and consequently the most robust non-stabilizer states and non-Clifford gates. In doing so, we make use of the discrete Wigner function and derive facets of the so-called qudit Clifford polytope i.e. the inequalities defining the convex hull of all qudit Clifford gates. Our results for robust states are provably optimal. For robust gates we find a critical noise rate that, as dimension increases, rapidly approaches the the theoretical optimum of 100%. Some connections with the question of qudit magic state distillation are discussed.Comment: 14 pages, 1 table; Minor changes vs. version