Dirac-K\"ahler particle in Riemann spherical space: boson interpretation

In the context of the composite boson interpretation, we construct the exact general solution of the Dirac--K\"ahler equation for the case of the spherical Riemann space of constant positive curvature, for which due to the geometry itself one may expect to have a discrete energy spectrum. In the case of the minimal value of the total angular momentum, $j=0$, the radial equations are reduced to second-order ordinary differential equations, which are straightforwardly solved in terms of the hypergeometric functions. For non-zero values of the total angular momentum, however, the radial equations are reduced to a pair of complicated fourth-order differential equations. Employing the factorization approach, we derive the general solution of these equations involving four independent fundamental solutions written in terms of combinations of the hypergeometric functions. The corresponding discrete energy spectrum is then determined via termination of the involved hypergeometric series, resulting in quasi-polynomial wave-functions. The constructed solutions lead to notable observations when compared with those for the ordinary Dirac particle. The energy spectrum for the Dirac-K\"ahler particle in spherical space is much more complicated. Its structure substantially differs from that for the Dirac particle since it consists of two paralleled energy level series each of which is twofold degenerate. Besides, none of the two separate series coincides with the series for the Dirac particle. Thus, the Dirac--K\"ahler field cannot be interpreted as a system of four Dirac fermions. Additional arguments supporting this conclusion are discussed

Type-I contributions to the one and two level densities of quadratic Dirichlet LL--functions over function fields

Using the Ratios Conjecture, we write down precise formulas with lower order terms for the one and the two level densities of zeros of quadratic Dirichlet $L$--functions over function fields. We denote the various terms arising as Type-$0$, Type-I and Type-II contributions. When the support of the Fourier transform of the test function is sufficiently restricted, we rigorously compute the Type-$0$ and Type-I terms and confirm that they match the conjectured answer. When the restrictions on the support are relaxed, our results suggest that Type-II contributions become important in the two level density.Comment: 23 page

Using neural networks to obtain indirect information about the state variables in an alcoholic fermentation process

This work provides a manual design space exploration regarding the structure, type, and inputs of a multilayer neural network (NN) to obtain indirect information about the state variables in the alcoholic fermentation process. The main benefit of our application is to help experts reduce the time needed for making the relevant measurements and to increase the lifecycles of sensors in bioreactors. The novelty of this research is the flexibility of the developed application, the use of a great number of variables, and the comparative presentation of the results obtained with different NNs (feedback vs. feed-forward) and different learning algorithms (Back-Propagation vs. Levenberg–Marquardt). The simulation results show that the feedback neural network outperformed the feed-forward neural network. The NN configuration is relatively flexible (with hidden layers and a number of nodes on each of them), but the number of input and output nodes depends on the fermentation process parameters. After laborious simulations, we determined that using pH and CO2 as inputs reduces the prediction errors of the NN. Thus, besides the most commonly used process parameters like fermentation temperature, time, the initial concentration of the substrate, the substrate concentration, and the biomass concentration, by adding pH and CO2, we obtained the optimum number of input nodes for the network. The optimal configuration in our case was obtained after 1500 iterations using a NN with one hidden layer and 12 neurons on it, seven neurons on the input layer, and one neuron as the output. If properly trained and validated, this model can be used in future research to accurately predict steady-state and dynamic alcoholic fermentation process behaviour and thereby improve process control performance

A method for identifying alternative or cryptic donor splice sites within gene and mRNA sequences. Comparisons among sequences from vertebrates, echinoderms and other groups

<p>Abstract</p> <p>Background</p> <p>As the amount of genome sequencing data grows, so does the problem of computational gene identification, and in particular, the splicing signals that flank exon borders. Traditional methods for identifying splicing signals have been created and optimized using sequences from model organisms, mostly vertebrate and yeast species. However, as genome sequencing extends across the animal kingdom and includes various invertebrate species, the need for mechanisms to recognize splice signals in these organisms increases as well. With that aim in mind, we generated a model for identifying donor and acceptor splice sites that was optimized using sequences from the purple sea urchin, <it>Strongylocentrotus purpuratus</it>. This model was then used to assess the possibility of alternative or cryptic splicing within the highly variable immune response gene family known as <it>185/333</it>.</p> <p>Results</p> <p>A donor splice site model was generated from <it>S. purpuratus </it>sequences that incorporates non-adjacent dependences among positions within the 9 nt splice signal and uses position weight matrices to determine the probability that the site is used for splicing. The <it>Purpuratus </it>model was shown to predict splice signals better than a similar model created from vertebrate sequences. Although the <it>Purpuratus </it>model was able to correctly predict the true splice sites within the <it>185/333 </it>genes, no evidence for alternative or trans-gene splicing was observed.</p> <p>Conclusion</p> <p>The data presented herein describe the first published analyses of echinoderm splice sites and suggest that the previous methods of identifying splice signals that are based largely on vertebrate sequences may be insufficient. Furthermore, alternative or trans-gene splicing does not appear to be acting as a diversification mechanism in the <it>185/333 </it>gene family.</p