14,435 research outputs found
A Note on the Stringy Embeddings of Certain N = 2 Dualities
Seiberg-Witten theory can be embedded in F-theory using D3 branes probing an
orientifold geometry. The non-perturbative corrections in the orientifold
picture map directly to the instanton corrections in the corresponding gauge
theory that convert the classical moduli space to the quantum one. In this
short review we argue that the recently proposed class of conformal Gaiotto
models may also be embedded in F-theory. The F-theory constructions help us not
only to understand the Gaiotto dualities but also to extend to the
non-conformal cases with and without cascading behaviors. For the conformal
cases, the near horizon geometries in F-theory capture both the UV and IR
behaviors succinctly.Comment: 6 pages, LaTeX, Based on the talk given by K. D at the Theory Canada
Conference June 2012; v2: Typos corrected and references adde
2D Black Hole and Holographic Renormalization Group
In hep-th/0311177, the Large renormalization group (RG) flows of a
modified matrix quantum mechanics on a circle, capable of capturing effects of
nonsingets, were shown to have fixed points with negative specific heat. The
corresponding rescaling equation of the compactified matter field with respect
to the RG scale, identified with the Liouville direction, is used to extract
the two dimensional Euclidean black hole metric at the new type of fixed
points. Interpreting the large RG flows as flow velocities in holographic
RG in two dimensions, the flow equation of the matter field around the black
hole fixed point is shown to be of the same form as the radial evolution
equation of the appropriate bulk scalar coupled to 2D black hole.Comment: 21 page
Effective Superpotentials for SO/Sp with Flavor from Matrix Models
We study matrix models related to gauge theories with flavors. We
give the effective superpotentials for gauge theories with arbitrary tree level
superpotential up to first instanton level. For quartic tree level
superpotential we obtained exact one-cut solution. We also derive
Seiberg-Witten curve for these gauge theories from matrix model argument.Comment: 17pp,2 figures, v2;refs added and to appear in MPL
Critical dynamics in homeostatic memory networks
Critical behavior in neural networks characterized by scale-free event distributions and brought about by self-regulatory mechanisms such as short-term synaptic dynamics or homeostatic plasticity, is believed to optimize sensitivity to input and information transfer in the system. Although theoretical predictions of the spike distributions have been confirmed by in-vitro experiments, in-vivo data yield a more complex picture which might be due to the in-homogeneity of the network structure, leakage in currents or massive driving inputs which has so far not been comprehensively covered by analytical or numerical studies.

We address these questions by the study of a neural model of memory that allows for storage and retrieval of patterns and for recombining such patterns as needed for search in problem solving. The model features critical dynamics in the neural assembly as a result of the interplay of synaptic depression and facilitation (Levina e.a 2007, 2009). Model simulations show that the prolonged consolidation of memory patterns induces a bias towards the memories which affects the scale-free spike-frequency distribution. However, selective modification of neuronal circuitry in the form of controlled homeostatic regulation in the form of recalibration of the synaptic weights towards the critical value preserved criticality although characterized by fluctuations between learned random patterns, as observed by the dynamics of stored pattern retrieval quality. The resulting spike statistics depends on the assumed coding scheme, but even sparse or orthogonal memory patterns introduce a typical event size which is incompatible with critical dynamics below the maximal memory capacity. Specifically results obtained for de-correlated patterns show an immediate jump from the sub-critical regime to a state of super-criticality in contrast to a more structured wave-like formation in the avalanche dynamics obtained from a general set of random patterns, pointing towards an eventual evolution of the network connectivity and the optimization of the critical regime. Specifically results obtained for de-correlated patterns show an immediate jump from the sub-critical regime to a state of super-criticality in contrast to a more structured wave-like formation in the avalanche dynamics obtained from a general set of random patterns, pointing towards an eventual evolution of the network connectivity and the optimization of the critical regime (Pearlmutter and Houghton, 2009).

The combination of memory and ongoing dynamics in the model was chosen for its implications in the context of cognitive aging. Following the paradigm of aging as a multi-criteria optimization process, we posit aging effects as a result of an increasing incompatibility of learning goals. In aging, a shift from fluid intelligence (flexibility to recombine memory content) towards crystalline intelligence (optimal memory organization) appears as a lifelong trend against the general decrease of resources. We show that in young age memory and criticality can be maintained simultaneously by a homeostatic leveling of the synaptic conductances. This balance is lost in the aging brain where the memory attractors cannot be kept sufficiently shallow due to neural and synaptic loss, a reduction of activity while experiencing a growth in memories. The value of the memory organization is therefore protected on the cost of the partial loss of the capability of recombining memory patterns in a task-dependent way
A Probabilistic Analysis of EM for Mixtures of Separated, Spherical Gaussians
We show that, given data from a mixture of k well-separated spherical Gaussians in ℜ^d, a simple two-round variant of EM will, with high probability, learn the parameters of the Gaussians to near-optimal precision, if the dimension is high (d >> ln k). We relate this to previous theoretical and empirical work on the EM algorithm
A Lorentzian cure for Euclidean troubles
There is strong evidence coming from Lorentzian dynamical triangulations that
the unboundedness of the gravitational action is no obstacle to the
construction of a well-defined non-perturbative path integral. In a continuum
approach, a similar suppression of the conformal divergence comes about as the
result of a non-trivial path-integral measure.Comment: 3 page
Investigation of the role of neutron transfer in the fusion of 32,34S with 197Au,208Pb using quasi-elastic scattering
Excitation functions for quasi-elastic scattering have been measured at backward angles for the systems 32,34S+197Au and 32,34S+208Pb for energies spanning the Coulomb barrier. Representative distributions, sensitive to the low energy part of the fusion barrier distribution, have been extracted from the data. For the fusion reactions of 32,34S with 197Au couplings related to the nuclear structure of 197Au appear to be dominant in shaping the low energy part of the barrier distibution. For the system 32S+208Pb the barrier distribution is broader and extends further to lower energies, than in the case of 34S+208Pb. This is consistent with the interpretation that the neutron pick-up channels are energetically more favoured in the 32S induced reaction and therefore couple more strongly to the relative motion. It may also be due to the increased collectivity of 32S, when compared with 34S
Fusion and breakup in the reactions of 6,7Li and 9Be
We develop a three body classical trajectory Monte Carlo (CTMC) method to
dicsuss the effect of the breakup process on heavy-ion fusion reactions induced
by weakly bound nuclei. This method follows the classical trajectories of
breakup fragments after the breakup takes place, and thus provides an
unambiguous separation between complete and incomplete fusion cross sections.
Applying this method to the fusion reaction Li + Bi, we find that
there is a significant contribution to the total complete fusion cross sections
from the process where all the breakup fragments are captured by the target
nucleus (i.e., the breakup followed by complete fusion).Comment: 4 pages, 3 eps figures. Uses espcrc1.sty. To be published in the
proceedings of the 8th international conference on clustering aspects of
nuclear structure and dynamics, November 24 - 29, 2003, Nara, Japan (Nucl.
Phys. A
Quiver Gauge Theory of Nonabelian Vortices and Noncommutative Instantons in Higher Dimensions
We construct explicit BPS and non-BPS solutions of the Yang-Mills equations
on the noncommutative space R^{2n}_\theta x S^2 which have manifest spherical
symmetry. Using SU(2)-equivariant dimensional reduction techniques, we show
that the solutions imply an equivalence between instantons on R^{2n}_\theta x
S^2 and nonabelian vortices on R^{2n}_\theta, which can be interpreted as a
blowing-up of a chain of D0-branes on R^{2n}_\theta into a chain of spherical
D2-branes on R^{2n} x S^2. The low-energy dynamics of these configurations is
described by a quiver gauge theory which can be formulated in terms of new
geometrical objects generalizing superconnections. This formalism enables the
explicit assignment of D0-brane charges in equivariant K-theory to the
instanton solutions.Comment: 45 pages, 4 figures; v2: minor correction
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