Congruent families and invariant tensors

Classical results of Chentsov and Campbell state that -- up to constant multiples -- the only $2$-tensor field of a statistical model which is invariant under congruent Markov morphisms is the Fisher metric and the only invariant $3$-tensor field is the Amari-Chentsov tensor. We generalize this result for arbitrary degree $n$, showing that any family of $n$-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 $k$-th order statistical dependencies that cannot be reduced to interactions between $k-1$ 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 $J_+=FJ_-$ for the model chiral currents on the brane as a well posed first order differential problem and by solving it for Lie algebra isometries $F$ 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 $k$ actions whenever at most $k$ 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