Deep Impact: Unintended consequences of journal rank

Very interesting article,

» “Unintended Consequences of Journal Ranking”, http://mathbabe.org/2013/03/08/unintended-consequences-of-journal-ranking/

And here’s a link straight to the paper itself,

» “Deep Impact: Unintended consequences of journal rank”, http://arxiv.org/abs/1301.3748

From MRIs to shrink wrap, particle physics technology improves the world we live in.

Zipf’s law unzipped

Why does Zipf’s law give a good description of data from seemingly completely unrelated phenomena? Here it is argued that the reason is that they can all be described as outcomes of a ubiquitous random group division: the elements can be citizens of a country and the groups family names, or the elements can be all the words making up a novel and the groups the unique words, or the elements could be inhabitants and the groups the cities in a country and so on. A random group formation (RGF) is presented from which a Bayesian estimate is obtained based on minimal information: it provides the best prediction for the number of groups with k elements, given the total number of elements, groups and the number of elements in the largest group. For each specification of these three values, the RGF predicts a unique group distribution N(k)∝exp(−bk)/kγ, where the power-law index γ is a unique function of the same three values. The universality of the result is made possible by the fact that no system-specific assumptions are made about the mechanism responsible for the group division. The direct relation between γ and the total number of elements, groups and the number of elements in the largest group is calculated. The predictive power of the RGF model is demonstrated by direct comparison with data from a variety of systems. It is shown that γ usually takes values in the interval 1≤γ≤2 and that the value for a given phenomenon depends in a systematic way on the total size of the dataset. The results are put in the context of earlier discussions on Zipf’s and Gibrat’s laws, N(k)∝k−2 and the connection between growth models and RGF is elucidated.

Seung Ki Baek et al 2011 New J. Phys. 13 043004 doi: 10.1088/1367-2630/13/4/043004

Lectures on localization and matrix models in supersymmetric Chern-Simons-matter theories. (arXiv:1104.0783 [hep-th])

In these lectures I give a pedagogical presentation of some of the recent progress in supersymmetric Chern-Simons-matter theories, coming from the use of localization and matrix model techniques. The goal is to provide a simple derivation of the exact interpolating function for the free energy of ABJM theory on the three-sphere, which implies in particular the N^{3/2} behavior at strong coupling. I explain in detail part of the background needed to understand this derivation, like holographic renormalization, localization of path integrals, and large N techniques in matrix models. arXiv:1104.0783 [hep-th]

Exact Superconformal and Yangian Symmetry of Scattering Amplitudes. (arXiv:1104.0700 [hep-th])

We review recent progress in the understanding of symmetries for scattering amplitudes in N=4 superconformal Yang-Mills theory. It is summarized how the superficial breaking of superconformal symmetry by collinear anomalies and the renormalization process can be cured at tree and loop level. This is achieved by correcting the representation of the superconformal group on amplitudes. Moreover, we comment on the Yangian symmetry of scattering amplitudes and how it inherits these correction terms from the ordinary Lie algebra symmetry. Invariants under this algebra and their relation to the Grassmannian generating function for scattering amplitudes are discussed. Finally, parallel developments in N=6 superconformal Chern-Simons theory are summarized. This article is an invited review for a special issue of Journal of Physics A devoted to Scattering Amplitudes in Gauge Theories. arXiv:1104.0700 [hep-th]

Hamilton-Jacobi Diffieties. (arXiv:1104.0162 [math.DG])

Diffieties formalize geometrically the concept of differential equation. We introduce and study Hamilton-Jacobi diffieties. They are finite dimensional subdiffieties of a given diffiety and appear to play a special role in the field theoretic version of the geometric Hamilton-Jacobi theory. arXiv:1104.0162 [math.DG]

Lectures on 2D Yang-Mills Theory, Equivariant Cohomology and Topological Field Theories. (arXiv:hep-th/9411210)

These are expository lectures reviewing

1. recent developments in two-dimensional Yang-Mills theory, and
2. the construction of topological field theory Lagrangians. Topological field theory is discussed from the point of view of infinite-dimensional differential geometry. We emphasize the unifying role of equivariant cohomology both as the underlying principle in the formulation of BRST transformation laws and as a central concept in the geometrical interpretation of topological field theory path integrals.

Localization and Diagonalization: A review of functional integral techniques for low-dimensional gauge theories and topological field theories. (arXiv:hep-th/9501075)

We review localization techniques for functional integrals which have recently been used to perform calculations in and gain insight into the structure of certain topological field theories and low-dimensional gauge theories. These are the functional integral counterparts of the Mathai-Quillen formalism, the Duistermaat-Heckman theorem, and the Weyl integral formula respectively. In each case, we first introduce the necessary mathematical background (Euler classes of vector bundles, equivariant cohomology, topology of Lie groups), and describe the finite dimensional integration formulae. We then discuss some applications to path integrals and give an overview of the relevant literature. The applications we deal with include supersymmetric quantum mechanics, cohomological field theories, phase space path integrals, and two-dimensional Yang-Mills theory. arXiv:hep-th/9501075.

TASI lectures on complex structures. (arXiv:1104.0254 [hep-th])

These lecture notes give an introduction to a number of ideas and methods that have been useful in the study of complex systems ranging from spin glasses to D-branes on Calabi-Yau manifolds. Topics include the replica formalism, Parisi’s solution of the Sherrington-Kirkpatrick model, overlap order parameters, supersymmetric quantum mechanics, D-brane landscapes and their black hole duals.

Gerhard Hochschild (1915/2010) A Mathematician of the XXth Century. (arXiv:1104.0335 [math.HO])

Gerhard Hochschild’s contribution to the development of mathematics in the XX century is succinctly surveyed. We start with a personal and mathematical biography, and then consider with certain detail his contributions to algebraic groups and Hopf algebras. arXiv:1104.0335 [math.HO]

A motivic approach to phase transitions in Potts models. (arXiv:1102.3462 [math-ph])

We describe an approach to the study of phase transitions in Potts models based on an estimate of the complexity of the locus of real zeros of the partition function, computed in terms of the classes in the Grothendieck ring of the affine algebraic varieties defined by the vanishing of the multivariate Tutte polynomial. We give completely explicit calculations for the examples of the chains of linked polygons and of the graphs obtained by replacing the polygons with their dual graphs. These are based on a deletion-contraction formula for the Grothendieck classes and on generating functions for splitting and doubling edges. arXiv:1102.3462 [math-ph]

Crystals, instantons and quantum toric geometry. (arXiv:1102.3861 [hep-th])

We describe the statistical mechanics of a melting crystal in three dimensions and its relation to a diverse range of models arising in combinatorics, algebraic geometry, integrable systems, low-dimensional gauge theories, topological string theory and quantum gravity. Its partition function can be computed by enumerating the contributions from noncommutative instantons to a six-dimensional cohomological gauge theory, which yields a dynamical realization of the crystal as a discretization of spacetime at the Planck scale. We describe analogous relations between a melting crystal model in two dimensions and N=4 supersymmetric Yang-Mills theory in four dimensions. We elaborate on some mathematical details of the construction of the quantum geometry which combines methods from toric geometry, isospectral deformation theory and noncommutative geometry in braided monoidal categories. In particular, we relate the construction of noncommutative instantons to deformed ADHM data, torsion-free modules and a noncommutative twistor correspondence. arXiv:1102.3861 [hep-th]

Crystal Melting and Wall Crossing Phenomena. (arXiv:1002.1709 [hep-th])

This paper summarizes recent developments in the theory of Bogomol’nyi-Prasad-Sommerfield (BPS) state counting and the wall crossing phenomena, emphasizing in particular the role of the statistical mechanical model of crystal melting. This paper is divided into two parts, which are closely related to each other. In the first part, we discuss the statistical mechanical model of crystal melting counting BPS states. Each of the BPS state contributing to the BPS index is in one-to-one correspondence with a configuration of a molten crystal, and the statistical partition function of the melting crystal gives the BPS partition function. We also show that smooth geometry of the Calabi-Yau manifold emerges in the thermodynamic limit of the crystal. This suggests a remarkable interpretation that an atom in the crystal is a discretization of the classical geometry, giving an important clue as to the geometry at the Planck scale.In the second part we discuss the wall crossing phenomena. Wall crossing phenomena states that the BPS index depends on the value of the moduli of the Calabi-Yau manifold, and jumps along real codimension one subspaces in the moduli space. We show that by using type IIA/M-theory duality, we can provide a simple and an intuitive derivation of the wall crossing phenomena, furthermore clarifying the connection with the topological string theory. This derivation is consistent with another derivation from the wall crossing formula, motivated by multi-centered BPS extremal black holes. We also explain the representation of the wall crossing phenomena in terms of crystal melting, and the generalization of the counting problem and the wall crossing to the open BPS invariants. arXiv:1002.1709 [hep-th]