19,483 research outputs found
Congruent families and invariant tensors
Classical results of Chentsov and Campbell state that -- up to constant
multiples -- the only -tensor field of a statistical model which is
invariant under congruent Markov morphisms is the Fisher metric and the only
invariant -tensor field is the Amari-Chentsov tensor. We generalize this
result for arbitrary degree , showing that any family of -tensors which
is invariant under congruent Markov morphisms is algebraically generated by the
canonical tensor fields defined in an earlier paper
Comparing Information-Theoretic Measures of Complexity in Boltzmann Machines
In the past three decades, many theoretical measures of complexity have been
proposed to help understand complex systems. In this work, for the first time,
we place these measures on a level playing field, to explore the qualitative
similarities and differences between them, and their shortcomings.
Specifically, using the Boltzmann machine architecture (a fully connected
recurrent neural network) with uniformly distributed weights as our model of
study, we numerically measure how complexity changes as a function of network
dynamics and network parameters. We apply an extension of one such
information-theoretic measure of complexity to understand incremental Hebbian
learning in Hopfield networks, a fully recurrent architecture model of
autoassociative memory. In the course of Hebbian learning, the total
information flow reflects a natural upward trend in complexity as the network
attempts to learn more and more patterns.Comment: 16 pages, 7 figures; Appears in Entropy, Special Issue "Information
Geometry II
Complexity Measures from Interaction Structures
We evaluate new complexity measures on the symbolic dynamics of coupled tent
maps and cellular automata. These measures quantify complexity in terms of
-th order statistical dependencies that cannot be reduced to interactions
between units. We demonstrate that these measures are able to identify
complex dynamical regimes.Comment: 11 pages, figures improved, minor changes to the tex
Primary Signet-Ring Carcinoma (Linitus Plastica) of the Colorectum presenting as Subacute Intestinal Obstruction
Primary Signet-ring cell carcinoma (Linitus Plastica) of the colon and rectum is a rare form of adenocarcinoma of the large intestine and has been reported to have an extremely poor prognosis. We report a case of Primary Signet-ring cell carcinoma of the colorectum in a thirty one year old man presented in Surgical OPD of our hospital with chief complaints of persistent pain in abdomen and vomiting since two days. Since the prognosis of primary signet ring cell carcinoma (SRCC) is extremely poor (in view of more malignant behavior than ordinary colorectal carcinoma), early diagnosis and aggressive treatment strategy are necessary
D-branes with Lorentzian signature in the Nappi-Witten model
Lorentzian signature D-branes of all dimensions for the Nappi-Witten string
are constructed. This is done by rewriting the gluing condition for
the model chiral currents on the brane as a well posed first order differential
problem and by solving it for Lie algebra isometries other than Lie algebra
automorphisms. By construction, these D-branes are not twined conjugacy
classes. Metrically degenerate D-branes are also obtained.Comment: 22 page
Lipid peroxidation is essential for α-synuclein-induced cell death.
Parkinson's disease is the second most common neurodegenerative disease and its pathogenesis is closely associated with oxidative stress. Deposition of aggregated α-synuclein (α-Syn) occurs in familial and sporadic forms of Parkinson's disease. Here, we studied the effect of oligomeric α-Syn on one of the major markers of oxidative stress, lipid peroxidation, in primary co-cultures of neurons and astrocytes. We found that oligomeric but not monomeric α-Syn significantly increases the rate of production of reactive oxygen species, subsequently inducing lipid peroxidation in both neurons and astrocytes. Pre-incubation of cells with isotope-reinforced polyunsaturated fatty acids (D-PUFAs) completely prevented the effect of oligomeric α-Syn on lipid peroxidation. Inhibition of lipid peroxidation with D-PUFAs further protected cells from cell death induced by oligomeric α-Syn. Thus, lipid peroxidation induced by misfolding of α-Syn may play an important role in the cellular mechanism of neuronal cell loss in Parkinson's disease. We have found that aggregated α-synuclein-induced production of reactive oxygen species (ROS) that subsequently stimulates lipid peroxidation and cell death in neurons and astrocytes. Specific inhibition of lipid peroxidation by incubation with reinforced polyunsaturated fatty acids (D-PUFAs) completely prevented the effect of α-synuclein on lipid peroxidation and cell death
Geometry of Policy Improvement
We investigate the geometry of optimal memoryless time independent decision
making in relation to the amount of information that the acting agent has about
the state of the system. We show that the expected long term reward, discounted
or per time step, is maximized by policies that randomize among at most
actions whenever at most world states are consistent with the agent's
observation. Moreover, we show that the expected reward per time step can be
studied in terms of the expected discounted reward. Our main tool is a
geometric version of the policy improvement lemma, which identifies a
polyhedral cone of policy changes in which the state value function increases
for all states.Comment: 8 page
On acceleration of Krylov-subspace-based Newton and Arnoldi iterations for incompressible CFD: replacing time steppers and generation of initial guess
We propose two techniques aimed at improving the convergence rate of steady
state and eigenvalue solvers preconditioned by the inverse Stokes operator and
realized via time-stepping. First, we suggest a generalization of the Stokes
operator so that the resulting preconditioner operator depends on several
parameters and whose action preserves zero divergence and boundary conditions.
The parameters can be tuned for each problem to speed up the convergence of a
Krylov-subspace-based linear algebra solver. This operator can be inverted by
the Uzawa-like algorithm, and does not need a time-stepping. Second, we propose
to generate an initial guess of steady flow, leading eigenvalue and eigenvector
using orthogonal projection on a divergence-free basis satisfying all boundary
conditions. The approach, including the two proposed techniques, is illustrated
on the solution of the linear stability problem for laterally heated square and
cubic cavities
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