Equivariant Poincar\'e series of filtrations and topology

Earlier, for an action of a finite group $G$ on a germ of an analytic variety, an equivariant $G$-Poincar\'e series of a multi-index filtration in the ring of germs of functions on the variety was defined as an element of the Grothendieck ring of $G$-sets with an additional structure. We discuss to which extend the $G$-Poincar\'e series of a filtration defined by a set of curve or divisorial valuations on the ring of germs of analytic functions in two variables determines the (equivariant) topology of the curve or of the set of divisors

Human summating potential using continuous loop averaging deconvolution: Response amplitudes vary with tone burst repetition rate and duration

Electrocochleography (ECochG) to high repetition rate tone bursts may have advantages over ECochG to clicks with standard slow rates. Tone burst stimuli presented at a high repetition rate may enhance summating potential (SP) measurements by reducing neural contributions resulting from neural adaptation to high stimulus repetition rates. To allow for the analysis of the complex ECochG responses to high rates, we deconvolved responses using the Continuous Loop Averaging Deconvolution (CLAD) technique. We examined the effect of high stimulus repetition rate and stimulus duration on SP amplitude measurements made with extratympanic ECochG to tone bursts in 20 adult females with normal hearing. We used 500 and 2,000 Hz tone bursts of various stimulus durations (12, 6, 3 ms) and repetition rates (five rates ranging from 7.1 to 234.38/s). A within-subject repeated measures (rate x duration) analysis of variance was conducted. We found that, for both 500 and 2,000 Hz stimuli, the mean deconvolved SP amplitudes were larger at faster repetition rates (58.59 and 97.66/s) compared to slower repetition rates (7.1 and 19.53/s), and larger at shorter stimulus duration compared longer stimulus duration. Our concluding hypothesis is that large SP amplitude to short duration stimuli may originate primarily from neural excitation, and large SP amplitudes to long duration, fast repetition rate stimuli may originate from hair cell responses. While the hair cell or neural origins of the SP to various stimulus parameters remains to be validated, our results nevertheless provide normative data as a step toward applying the CLAD technique to understanding diseased ears

Optimal Control Realizations of Lagrangian Systems with Symmetry

A new relation among a class of optimal control systems and Lagrangian systems with symmetry is discussed. It will be shown that a family of solutions of optimal control systems whose control equation are obtained by means of a group action are in correspondence with the solutions of a mechanical Lagrangian system with symmetry. This result also explains the equivalence of the class of Lagrangian systems with symmetry and optimal control problems discussed in \cite{Bl98}, \cite{Bl00}. The explicit realization of this correspondence is obtained by a judicious use of Clebsch variables and Lin constraints, a technique originally developed to provide simple realizations of Lagrangian systems with symmetry. It is noteworthy to point out that this correspondence exchanges the role of state and control variables for control systems with the configuration and Clebsch variables for the corresponding Lagrangian system. These results are illustrated with various simple applications

A hierarchical Bayesian model to infer PL(Z) relations using Gaia parallaxes

Aims. We aim at creating a Bayesian model to infer the coefficients of PL or PLZ relations that propagates uncertainties in the observables in a rigorous and well founded way. Methods. We propose a directed acyclic graph to encode the conditional probabilities of the inference model that will allow us to infer probability distributions for the PL and PL(Z) relations. We evaluate the model with several semi-synthetic data sets and apply it to a sample of 200 fundamental mode and first overtone mode RR Lyrae stars for which Gaia DR1 parallaxes and literature Ks-band mean magnitudes are available. We define and test several hyperprior probabilities to verify their adequacy and check the sensitivity of the solution with respect to the prior choice. Results. The main conclusion of this work is the absolute necessity of incorporating the existing correlations between the observed variables (periods, metallicities and parallaxes) in the form of model priors in order to avoid systematically biased results, especially in the case of non-negligible uncertainties in the parallaxes. The tests with the semi-synthetic data based on the data set used in Gaia Collaboration et al. (2017) reveal the significant impact that the existing correlations between parallax, metallicity and periods have on the inferred parameters. The relation coefficients obtained here have been superseded by those presented in Muraveva et al. (2018a), that incorporates the findings of this work and the more recent Gaia DR2 measurements.Comment: 14 pages, 12 figures. Submitted to A&

Exact Mapping of the 2+1 Dirac Oscillator onto the Jaynes-Cummings Model: Ion-Trap Experimental Proposal

We study the dynamics of the 2+1 Dirac oscillator exactly and find spin oscillations due to a {\it Zitterbewegung} of purely relativistic origin. We find an exact mapping of this quantum-relativistic system onto a Jaynes-Cummings model, describing the interaction of a two-level atom with a quantized single-mode field. This equivalence allows us to map a series of quantum optical phenomena onto the relativistic oscillator, and viceversa. We make a realistic experimental proposal, at reach with current technology, for studying the equivalence of both models using a single trapped ion.Comment: Revtex4, submitted for publicatio

Interference and complementarity for two-photon hybrid entangled states

In this work we generate two-photon hybrid entangled states (HES), where the polarization of one photon is entangled with the transverse spatial degree of freedom of the second photon. The photon pair is created by parametric down-conversion in a polarization-entangled state. A birefringent double-slit couples the polarization and spatial degrees of freedom of these photons and finally, suitable spatial and polarization projections generate the HES. We investigate some interesting aspects of the two-photon hybrid interference, and present this study in the context of the complementarity relation that exists between the visibilities of the one- and two-photon interference patterns.Comment: 10 pages, 4 figures. Accepted in Physical Review

Density Matrix and Renormalization for Classical Lattice Models

We review the variational principle in the density matrix renormalization group (DMRG) method, which maximizes an approximate partition function within a restricted degrees of freedom; at zero temperature, DMRG mini- mizes the ground state energy. The variational principle is applied to two-dimensional (2D) classical lattice models, where the density matrix is expressed as a product of corner transfer matrices. (CTMs) DMRG related fields and future directions of DMRG are briefly discussed.Comment: 21 pages, Latex, 14 figures in postscript files, Proc. of the 1996 El Escorial Summer School on "Strongly Correlated Magnetic and Superconducting Systems