A simpler characterization of Sheffer polynomial

We characterize the Sheffer sequences by a single convolution identity $$F^{(y)} p_{n}(x) = \sum _{k=0}^{n}\ p_{k}(x)\ p_{n-k}(y)$$ where $F^{(y)}$ is a shift-invariant operator. We then study a generalization of the notion of Sheffer sequences by removing the requirement that $F^{(y)}$ be shift-invariant. All these solutions can then be interpreted as cocommutative coalgebras. We also show the connection with generalized translation operators as introduced by Delsarte. Finally, we apply the same convolution to symmetric functions where we find that the ``Sheffer'' sequences differ from ordinary full divided power sequences by only a constant factor

Automatic Construction of Predictive Neuron Models through Large Scale Assimilation of Electrophysiological Data.

We report on the construction of neuron models by assimilating electrophysiological data with large-scale constrained nonlinear optimization. The method implements interior point line parameter search to determine parameters from the responses to intracellular current injections of zebra finch HVC neurons. We incorporated these parameters into a nine ionic channel conductance model to obtain completed models which we then use to predict the state of the neuron under arbitrary current stimulation. Each model was validated by successfully predicting the dynamics of the membrane potential induced by 20-50 different current protocols. The dispersion of parameters extracted from different assimilation windows was studied. Differences in constraints from current protocols, stochastic variability in neuron output, and noise behave as a residual temperature which broadens the global minimum of the objective function to an ellipsoid domain whose principal axes follow an exponentially decaying distribution. The maximum likelihood expectation of extracted parameters was found to provide an excellent approximation of the global minimum and yields highly consistent kinetics for both neurons studied. Large scale assimilation absorbs the intrinsic variability of electrophysiological data over wide assimilation windows. It builds models in an automatic manner treating all data as equal quantities and requiring minimal additional insight

An Optimized and Scalable Eigensolver for Sequences of Eigenvalue Problems

In many scientific applications the solution of non-linear differential equations are obtained through the set-up and solution of a number of successive eigenproblems. These eigenproblems can be regarded as a sequence whenever the solution of one problem fosters the initialization of the next. In addition, in some eigenproblem sequences there is a connection between the solutions of adjacent eigenproblems. Whenever it is possible to unravel the existence of such a connection, the eigenproblem sequence is said to be correlated. When facing with a sequence of correlated eigenproblems the current strategy amounts to solving each eigenproblem in isolation. We propose a alternative approach which exploits such correlation through the use of an eigensolver based on subspace iteration and accelerated with Chebyshev polynomials (ChFSI). The resulting eigensolver is optimized by minimizing the number of matrix-vector multiplications and parallelized using the Elemental library framework. Numerical results show that ChFSI achieves excellent scalability and is competitive with current dense linear algebra parallel eigensolvers.Comment: 23 Pages, 6 figures. First revision of an invited submission to special issue of Concurrency and Computation: Practice and Experienc

Citation Success: Evidence from Economic History Journal Publications

This study examines the determinants of citation success among authors who recently published their work in economic history journals. We find that full professors, authors from non-economic history departments, and authors working in Anglo-Saxon countries are all more likely to get cited than others whereas affiliation at a top-ranked university has no seeming effect. A number of bibliometric features like article length and number of co-authors also matter for citation success. Our most novel finding is that active diffusion of one’s research, e.g., academic presentations (at conferences, workshops or seminars) or online publication of working papers, has a first-order impact on subsequent citation success.Bibliometrics; Citation Analysis; Citation Success; Economic History; Scientometrics; Poisson Regression

Citation Success: Evidence from Economic History Journal Publications

This study analyses determinants of citation success among authors publishing in economic history journals. Bibliometric features, like article length and number of authors, are positively correlated with the citation rate up to a certain point. Remarkably, publishing in top-ranked journals hardly affects citations. In regard to author-specific characteristics, male authors, full professors and authors working economics or history departments, and authors employed in Anglo-Saxon countries, are more likely to get cited than others. As a ‘shortcut’ to citation success, we find that research diffusion, measured by number of presentations and people mentioned in acknowledgement, boosts the citation rate.bibliometrics; citation analysis; citation success; economic history; scientometrics; Poisson regression