Zeta-like Multizeta Values for higher genus curves

We prove or conjecture several relations between the multizeta values for positive genus function fields of class number one, focusing on the zeta-like values, namely those whose ratio with the zeta value of the same weight is rational (or conjecturally equivalently algebraic). These are the first known relations between multizetas, which are not with prime field coefficients. We seem to have one universal family. We also find that interestingly the mechanism with which the relations work is quite different from the rational function field case, raising interesting questions about the expected motivic interpretation in higher genus. We provide some data in support of the guesses.Comment: Expository revisions plus appendices containing proofs of more cases of conjecture

Induction, minimization and collection for Δ n+1 (T)–formulas

For a theory T, we study relationships among IΔ n +1 (T), LΔ n+1 (T) and B * Δ n+1 (T). These theories are obtained restricting the schemes of induction, minimization and (a version of) collection to Δ n+1 (T) formulas. We obtain conditions on T (T is an extension of B * Δ n+1 (T) or Δ n+1 (T) is closed (in T) under bounded quantification) under which IΔ n+1 (T) and LΔ n+1 (T) are equivalent. These conditions depend on Th Πn +2 (T), the Π n+2 –consequences of T. The first condition is connected with descriptions of Th Πn +2 (T) as IΣ n plus a class of nondecreasing total Π n –functions, and the second one is related with the equivalence between Δ n+1 (T)–formulas and bounded formulas (of a language extending the language of Arithmetic). This last property is closely tied to a general version of a well known theorem of R. Parikh. Using what we call Π n –envelopes we give uniform descriptions of the previous classes of nondecreasing total Π n –functions. Π n –envelopes are a generalization of envelopes (see [10]) and are closely related to indicators (see [12]). Finally, we study the hierarchy of theories IΔ n+1 (IΣ m ), m≥n, and prove a hierarchy theorem.Ministerio de Educación y Cultura DGES PB96-134

Risk Assessment Algorithms Based On Recursive Neural Networks

The assessment of highly-risky situations at road intersections have been recently revealed as an important research topic within the context of the automotive industry. In this paper we shall introduce a novel approach to compute risk functions by using a combination of a highly non-linear processing model in conjunction with a powerful information encoding procedure. Specifically, the elements of information either static or dynamic that appear in a road intersection scene are encoded by using directed positional acyclic labeled graphs. The risk assessment problem is then reformulated in terms of an inductive learning task carried out by a recursive neural network. Recursive neural networks are connectionist models capable of solving supervised and non-supervised learning problems represented by directed ordered acyclic graphs. The potential of this novel approach is demonstrated through well predefined scenarios. The major difference of our approach compared to others is expressed by the fact of learning the structure of the risk. Furthermore, the combination of a rich information encoding procedure with a generalized model of dynamical recurrent networks permit us, as we shall demonstrate, a sophisticated processing of information that we believe as being a first step for building future advanced intersection safety system

HAWC response to atmospheric electricity activity

The HAWC Gamma Ray observatory consists of 300 water Cherenkov detectors (WCD) instrumented with four photo multipliers tubes (PMT) per WCD. HAWC is located between two of the highest mountains in Mexico. The high altitude (4100 m asl), the relatively short distance to the Gulf of Mexico (~100 km), the large detecting area (22 000 m$^2$) and its high sensitivity, make HAWC a good instrument to explore the acceleration of particles due to the electric fields existing inside storm clouds. In particular, the scaler system of HAWC records the output of each one of the 1200 PMTs as well as the 2, 3, and 4-fold multiplicities (logic AND in a time window of 30 ns) of each WCD with a sampling rate of 40 Hz. Using the scaler data, we have identified 20 enhancements of the observed rate during periods when storm clouds were over HAWC but without cloud-earth discharges. These enhancements can be produced by electrons with energy of tens of MeV, accelerated by the electric fields of tens of kV/m measured at the site during the storm periods. In this work, we present the recorded data, the method of analysis and our preliminary conclusions on the electron acceleration by the electric fields inside the clouds.Comment: Presented at the 35th International Cosmic Ray Conference (ICRC2017), Bexco, Busan, Korea. See arXiv:1708.02572 for all HAWC contribution