Note on the space group selection rule for closed strings on orbifolds

It is well-known that the space group selection rule constrains the interactions of closed strings on orbifolds. For some examples, this rule has been described by an effective Abelian symmetry that combines with a permutation symmetry to a non-Abelian flavor symmetry like $D_4$ or $\Delta(54)$. However, the general case of the effective Abelian symmetries was not yet fully understood. In this work, we formalize the computation of the Abelian symmetry that results from the space group selection rule by imposing two conditions only: (i) well-defined discrete charges and (ii) their conservation. The resulting symmetry, which we call the space group flavor symmetry $D_S$, is uniquely specified by the Abelianization of the space group. For all Abelian orbifolds with $N=1$ supersymmetry we compute $D_S$ and identify new cases, for example, where $D_S$ contains a $Z_2$ dark matter-parity with charges 0 and 1 for massless and massive strings, respectively.Comment: 28 pages, 1 tabl

Mean Field Theory for Sigmoid Belief Networks

We develop a mean field theory for sigmoid belief networks based on ideas from statistical mechanics. Our mean field theory provides a tractable approximation to the true probability distribution in these networks; it also yields a lower bound on the likelihood of evidence. We demonstrate the utility of this framework on a benchmark problem in statistical pattern recognition---the classification of handwritten digits.Comment: See http://www.jair.org/ for any accompanying file

Better Late Than Early: Vertical Differentiation in the Adoption of a New Technology

After the initial breakthrough in the research phase of R&D a new product undergoes a process of change, improvement and adaptation to market conditions. We model the strategic behavior of firms in this development phase of R&D. We emphasize that a key dimension to this competition is the innovations that lead to product differentiation and quality improvement. In a duopoly model with a single adoption choice, we derive endogeneously the level and diversity of product innovations. We demonstrate the existence of equilibria in which one firm enters early with a low quality product while the other continues to develop the technology and eventually markets a high quality good. In such an equilibrium, no monopoly rent is dissipated and the later innovator makes more profits. Incumbent firms may well be the early innovators, contrary to the predictions of the hypothesis.

The systemic environment: at the interface of aging and adult neurogenesis.

Aging results in impaired neurogenesis in the two neurogenic niches of the adult mammalian brain, the dentate gyrus of the hippocampus and the subventricular zone of the lateral ventricle. While significant work has characterized intrinsic cellular changes that contribute to this decline, it is increasingly apparent that the systemic environment also represents a critical driver of brain aging. Indeed, emerging studies utilizing the model of heterochronic parabiosis have revealed that immune-related molecular and cellular changes in the aging systemic environment negatively regulate adult neurogenesis. Interestingly, these studies have also demonstrated that age-related decline in neurogenesis can be ameliorated by exposure to the young systemic environment. While this burgeoning field of research is increasingly garnering interest, as yet, the precise mechanisms driving either the pro-aging effects of aged blood or the rejuvenating effects of young blood remain to be thoroughly defined. Here, we review how age-related changes in blood, blood-borne factors, and peripheral immune cells contribute to the age-related decline in adult neurogenesis in the mammalian brain, and posit both direct neural stem cell and indirect neurogenic niche-mediated mechanisms

Mirage Torsion

Z_NxZ_M orbifold models admit the introduction of a discrete torsion phase. We find that models with discrete torsion have an alternative description in terms of torsionless models. More specifically, discrete torsion can be 'gauged away' by changing the shifts by lattice vectors. Similarly, a large class of the so-called generalized discrete torsion phases can be traded for changing the background fields (Wilson lines) by lattice vectors. We further observe that certain models with generalized discrete torsion are equivalent to torsionless models with the same gauge embedding but based on different compactification lattices. We also present a method of classifying heterotic Z_NxZ_M orbifolds.Comment: 26 pages, 3 figures, v2: matches version published in JHE

A note on discrete R symmetries in Z6-II orbifolds with Wilson lines

We re-derive the R symmetries for the Z6-II orbifold with non-trivial Wilson lines and find expressions for the R charges which differ from those in the literature.Comment: 13 pages, 3 figure

Modeling Distances in Large-Scale Networks by Matrix Factorization

In this paper, we propose a model for representing and predicting distances in large-scale networks by matrix factorization. The model is useful for network distance sensitive applications, such as content distribution networks, topology-aware overlays, and server selections. Our approach overcomes several limitations of previous coordinates-based mechanisms, which cannot model sub-optimal routing or asymmetric routing policies. We describe two algorithms -- singular value decomposition (SVD) and nonnegative matrix factorization (NMF) -- for representing a matrix of network distances as the product of two smaller matrices. With such a representation, we build a scalable system -- Internet Distance Estimation Service (IDES) -- that predicts large numbers of network distances from limited numbers of measurements. Extensive simulations on real-world data sets show that IDES leads to more accurate, efficient and robust predictions of latencies in large-scale networks than previous approaches