Functional equations from generating functions: a novel approach to deriving identities for the Bernstein basis functions

The main aim of this paper is to provide a novel approach to deriving identities for the Bernstein polynomials using functional equations. We derive various functional equations and differential equations using generating functions. Applying these equations, we give new proofs for some standard identities for the Bernstein basis functions, including formulas for sums, alternating sums, recursion, subdivision, degree raising, differentiation and a formula for the monomials in terms of the Bernstein basis functions. We also derive many new identities for the Bernstein basis functions based on this approach. Moreover, by applying the Laplace transform to the generating functions for the Bernstein basis functions, we obtain some interesting series representations for the Bernstein basis functions.Comment: 1

Signal Propagation in Feedforward Neuronal Networks with Unreliable Synapses

In this paper, we systematically investigate both the synfire propagation and firing rate propagation in feedforward neuronal network coupled in an all-to-all fashion. In contrast to most earlier work, where only reliable synaptic connections are considered, we mainly examine the effects of unreliable synapses on both types of neural activity propagation in this work. We first study networks composed of purely excitatory neurons. Our results show that both the successful transmission probability and excitatory synaptic strength largely influence the propagation of these two types of neural activities, and better tuning of these synaptic parameters makes the considered network support stable signal propagation. It is also found that noise has significant but different impacts on these two types of propagation. The additive Gaussian white noise has the tendency to reduce the precision of the synfire activity, whereas noise with appropriate intensity can enhance the performance of firing rate propagation. Further simulations indicate that the propagation dynamics of the considered neuronal network is not simply determined by the average amount of received neurotransmitter for each neuron in a time instant, but also largely influenced by the stochastic effect of neurotransmitter release. Second, we compare our results with those obtained in corresponding feedforward neuronal networks connected with reliable synapses but in a random coupling fashion. We confirm that some differences can be observed in these two different feedforward neuronal network models. Finally, we study the signal propagation in feedforward neuronal networks consisting of both excitatory and inhibitory neurons, and demonstrate that inhibition also plays an important role in signal propagation in the considered networks.Comment: 33pages, 16 figures; Journal of Computational Neuroscience (published

Complexity without chaos: Plasticity within random recurrent networks generates robust timing and motor control

It is widely accepted that the complex dynamics characteristic of recurrent neural circuits contributes in a fundamental manner to brain function. Progress has been slow in understanding and exploiting the computational power of recurrent dynamics for two main reasons: nonlinear recurrent networks often exhibit chaotic behavior and most known learning rules do not work in robust fashion in recurrent networks. Here we address both these problems by demonstrating how random recurrent networks (RRN) that initially exhibit chaotic dynamics can be tuned through a supervised learning rule to generate locally stable neural patterns of activity that are both complex and robust to noise. The outcome is a novel neural network regime that exhibits both transiently stable and chaotic trajectories. We further show that the recurrent learning rule dramatically increases the ability of RRNs to generate complex spatiotemporal motor patterns, and accounts for recent experimental data showing a decrease in neural variability in response to stimulus onset

Age and growth of the smooth hammerhead, Sphyrna zygaena, in the Atlantic Ocean: comparison with other hammerhead species

The smooth hammerhead Sphyrna zygaena (Sphyrnidae) is a pelagic shark occasionally caught as bycatch in pelagic longline fisheries, but is one of the least studied of all pelagic sharks. Age and growth of S. zygaena was studied along a wide Atlantic region covering both the northern and southern hemispheres. Data from 304 specimens, caught between October 2009 and September 2014, ranging in size from 126 to 253 cm fork length (FL), were analysed. Growth models were fitted using the three-parameter von Bertalanffy growth function (VBGF) re-parameterized to calculate L0 (size at birth). Growth models were fitted to the sample data and data from several back-calculation models. The model fit to the quadratic modified Dahl-Lea back-calculated data seems to be the most appropriate to describe growth in this species, with resulting growth parameters of Linf = 285 cm FL, k = 0.09 year−1 for males and Linf = 293 cm FL, k = 0.09 year−1 for females. Compared with other species of the same genus, estimated growth coefficients for S. zygaena seem to fall in the low to middle range. Although further work is still needed, this study adds to knowledge of the vital life-history parameters of smooth hammerheads in the Atlantic Ocean, which can be used in the management and conservation of this species.Programa Operacional Potencial Humano: IF/00253/2014info:eu-repo/semantics/publishedVersio

PhyloSim - Monte Carlo simulation of sequence evolution in the R statistical computing environment

<p>Abstract</p> <p>Background</p> <p>The Monte Carlo simulation of sequence evolution is routinely used to assess the performance of phylogenetic inference methods and sequence alignment algorithms. Progress in the field of molecular evolution fuels the need for more realistic and hence more complex simulations, adapted to particular situations, yet current software makes unreasonable assumptions such as homogeneous substitution dynamics or a uniform distribution of indels across the simulated sequences. This calls for an extensible simulation framework written in a high-level functional language, offering new functionality and making it easy to incorporate further complexity.</p> <p>Results</p> <p><monospace>PhyloSim</monospace> is an extensible framework for the Monte Carlo simulation of sequence evolution, written in R, using the Gillespie algorithm to integrate the actions of many concurrent processes such as substitutions, insertions and deletions. Uniquely among sequence simulation tools, <monospace>PhyloSim</monospace> can simulate arbitrarily complex patterns of rate variation and multiple indel processes, and allows for the incorporation of selective constraints on indel events. User-defined complex patterns of mutation and selection can be easily integrated into simulations, allowing <monospace>PhyloSim</monospace> to be adapted to specific needs.</p> <p>Conclusions</p> <p>Close integration with <monospace>R</monospace> and the wide range of features implemented offer unmatched flexibility, making it possible to simulate sequence evolution under a wide range of realistic settings. We believe that <monospace>PhyloSim</monospace> will be useful to future studies involving simulated alignments.</p

Strongly hyperpolarized gas from parahydrogen by rational design of ligand-capped nanoparticles

The production of hyperpolarized fluids in continuous mode would broaden substantially the range of applications in chemistry, materials science, and biomedicine. Here we show that the rational design of a heterogeneous catalyst based on a judicious choice of metal type, nanoparticle size and surface decoration with appropriate ligands leads to highly efficient pairwise addition of dihydrogen across an unsaturated bond. This is demonstrated in a parahydrogen-induced polarization (PHIP) experiment by a 508-fold enhancement (±78) of a CH3 proton signal and a corresponding 1219-fold enhancement (±187) of a CH2 proton signal using nuclear magnetic resonance (1H-NMR). In contrast, bulk metal catalyst does not show this effect due to randomization of reacting dihydrogen. Our approach results in the largest gas-phase NMR signal enhancement by PHIP known to date. Sensitivity-enhanced NMR with this technique could be used to image microfluidic reactions in-situ, to probe nonequilibrium thermodynamics or for the study of metabolic reactions

Evolutionary distances in the twilight zone -- a rational kernel approach

Phylogenetic tree reconstruction is traditionally based on multiple sequence alignments (MSAs) and heavily depends on the validity of this information bottleneck. With increasing sequence divergence, the quality of MSAs decays quickly. Alignment-free methods, on the other hand, are based on abstract string comparisons and avoid potential alignment problems. However, in general they are not biologically motivated and ignore our knowledge about the evolution of sequences. Thus, it is still a major open question how to define an evolutionary distance metric between divergent sequences that makes use of indel information and known substitution models without the need for a multiple alignment. Here we propose a new evolutionary distance metric to close this gap. It uses finite-state transducers to create a biologically motivated similarity score which models substitutions and indels, and does not depend on a multiple sequence alignment. The sequence similarity score is defined in analogy to pairwise alignments and additionally has the positive semi-definite property. We describe its derivation and show in simulation studies and real-world examples that it is more accurate in reconstructing phylogenies than competing methods. The result is a new and accurate way of determining evolutionary distances in and beyond the twilight zone of sequence alignments that is suitable for large datasets.Comment: to appear in PLoS ON

A unique cause of hemoperitoneum: spontaneous rupture of a splenic hemangiopericytoma

Non-traumatic hemoperitoneum may be catastrophic if it is not promptly diagnosed and treated. It is critical to identify this clinical picture and treat any active bleeding. We report the first case in the literature (to our knowledge) of spontaneous hemoperitoneum caused by a cystic splenic hemangiopericytoma. Hemangiopericytomas represent a small subset of soft tissue sarcomas. They rarely originate in the spleen as a primary tumor, with only ten cases having been previously described. The difficulty of predicting the prognosis and clinical behavior of these lesions has been repeatedly stressed. The literature concerning this rare and unusual neoplasm is reviewed