7,346 research outputs found
Two-step Nonnegative Matrix Factorization Algorithm for the Approximate Realization of Hidden Markov Models
We propose a two-step algorithm for the construction of a Hidden Markov Model
(HMM) of assigned size, i.e. cardinality of the state space of the underlying
Markov chain, whose -dimensional distribution is closest in divergence to a
given distribution. The algorithm is based on the factorization of a pseudo
Hankel matrix, defined in terms of the given distribution, into the product of
a tall and a wide nonnegative matrix. The implementation is based on the
nonnegative matrix factorization (NMF) algorithm. To evaluate the performance
of our algorithm we produced some numerical simulations in the context of HMM
order reduction.Comment: presented at MTNS2010 - Budapest, July 201
Super Quantum Mechanics in the Integral Form Formalism
We reformulate Super Quantum Mechanics in the context of integral forms. This
framework allows to interpolate between different actions for the same theory,
connected by different choices of Picture Changing Operators (PCO). In this way
we retrieve component and superspace actions, and prove their equivalence. The
PCO are closed integral forms, and can be interpreted as super Poincar\'e duals
of bosonic submanifolds embedded into a supermanifold.. We use them to
construct Lagrangians that are top integral forms, and therefore can be
integrated on the whole supermanifold. The and the
cases are studied, in a flat and in a curved supermanifold. In this formalism
we also consider coupling with gauge fields, Hilbert space of quantum states
and observables.Comment: 41 pages, no figures. Use birkjour.cls. Minor misprints, moved
appendix A and B in the main text. Version to be published in Annales H.
Poincar\'
The Geometry of Supermanifolds and New Supersymmetric Actions
We construct the Hodge dual for supermanifolds by means of the Grassmannian
Fourier transform of superforms. In the case of supermanifolds it is known that
the superforms are not sufficient to construct a consistent integration theory
and that the integral forms are needed. They are distribution-like forms which
can be integrated on supermanifolds as a top form can be integrated on a
conventional manifold. In our construction of the Hodge dual of superforms they
arise naturally. The compatibility between Hodge duality and supersymmetry is
exploited and applied to several examples. We define the irreducible
representations of supersymmetry in terms of integral and superforms in a new
way which can be easily generalised to several models in different dimensions.
The construction of supersymmetric actions based on the Hodge duality is
presented and new supersymmetric actions with higher derivative terms are
found. These terms are required by the invertibility of the Hodge operator.Comment: LateX2e, 51 pages. Corrected some further misprint
The Quantum Theory of Chern-Simons Supergravity
We consider -extended Chern-Simons supergravity (\`a la
Achucarro-Tonswend) and we study its gauge symmetries. We promote those gauge
symmetries to a BRST symmetry and we perform its quantization by choosing
suitable gauge-fixings. The resulting quantum theories have different features
which we discuss in the present work. In particular, we show that a special
choice of the gauge-fixing correctly reproduces the Ansatz by Alvarez,
Valenzuela and Zanelli for the graphene fermion.Comment: 25 pages. Some points clarified and conclusion section extended;
content of sections 3 and 4 reorganized. Version to be published on JHE
Dualities of Deformed SCFTs from Link Monodromy on D3-brane States
We study D3-brane theories that are dually described as deformations of two
different superconformal theories with massless monopoles and
dyons. These arise at the self-intersection of a seven-brane in F-theory, which
cuts out a link on a small three-sphere surrounding the self-intersection. The
spectrum is studied by taking small loops in the three-sphere, yielding a
link-induced monodromy action on string junction D3-brane states, and
subsequently quotienting by the monodromy. This reduces the differing flavor
algebras of the theories to the same flavor algebra, as
required by duality, and projects out charged states, yielding an
superconformal theory on the D3-brane. In one, a deformation of
a rank one Argyres-Douglas theory retains its flavor symmetry and
exhibits a charge neutral flavor triplet that is comprised of electron, dyon,
and monopole string junctions. From duality we argue that the monodromy
projection should also be imposed away from the conformal point, in which case
the D3-brane field theory appears to exhibit confinement of electrons, dyons,
and monopoles. We will address the mathematical counterparts in a companion
paper.Comment: 28+20 pages, 8 figures 6 table
Fermionic Corrections to Fluid Dynamics from BTZ Black Hole
We reconstruct the complete fermionic orbit of the non-extremal BTZ black
hole by acting with finite supersymmetry transformations. The solution
satisfies the exact supergravity equations of motion to all orders in the
fermonic expansion and the final result is given in terms of fermionic
bilinears. By fluid/gravity correspondence, we derive linearized Navier-Stokes
equations and a set of new differential equations from Rarita-Schwinger
equation. We compute the boundary energy-momentum tensor and we interpret the
result as a perfect fluid with a modified definition of fluid velocity.
Finally, we derive the modified expression for the entropy of the black hole in
terms of the fermionic bilinears.Comment: 21 pages, Latex2e, no figure
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