Quantum discrete Dubrovin equations

The discrete equations of motion for the quantum mappings of KdV type are given in terms of the Sklyanin variables (which are also known as quantum separated variables). Both temporal (discrete-time) evolutions and spatial (along the lattice at a constant time-level) evolutions are considered. In the classical limit, the temporal equations reduce to the (classical) discrete Dubrovin equations as given in a previous publication. The reconstruction of the original dynamical variables in terms of the Sklyanin variables is also achieved.Comment: 25 page

Learning Temporal Dependence from Time-Series Data with Latent Variables

We consider the setting where a collection of time series, modeled as random processes, evolve in a causal manner, and one is interested in learning the graph governing the relationships of these processes. A special case of wide interest and applicability is the setting where the noise is Gaussian and relationships are Markov and linear. We study this setting with two additional features: firstly, each random process has a hidden (latent) state, which we use to model the internal memory possessed by the variables (similar to hidden Markov models). Secondly, each variable can depend on its latent memory state through a random lag (rather than a fixed lag), thus modeling memory recall with differing lags at distinct times. Under this setting, we develop an estimator and prove that under a genericity assumption, the parameters of the model can be learned consistently. We also propose a practical adaption of this estimator, which demonstrates significant performance gains in both synthetic and real-world datasets

Temporal and spatial variation of limnological variables and biomass of different macrophyte species in a Neotropical reservoir (São Paulo - Brazil)

Aim: This study reports an investigation of limnological characteristics and aquatic macrophyte occurrence in a neotropical reservoir in order to assess the spatio-temporal variation of water and sediment variables and their influence on plant distribution. Methods: Macrophytes, water and sediment samples were collected from a Brazilian reservoir in different seasons from four main arms of the reservoir. In total sixteen water-sediment variables were analyzed including N:P ratio and Trophic State Index. The plants were collected using a quadrat sampling procedure and the dry weight per sample was measured. MANOVA was performed to evaluate spatial and temporal variation of environmental variables as well as seasonal biomass differences. To assess the relationship among environmental variables and macrophytes an ordination analysis (using Canonical Correspondence Analysis: CCA) was carried out. Results: The spatial and temporal variation of limnological variables generated a heterogeneous system which supports the presence of different species of macrophyte. pH, dissolved oxygen and sediment composition were important predictors of Polygonum lapathifolium occurrence while nutrients were associated with Eichhornia crassipes and Pistia stratiotes. Inorganic substances were related to biomass variation of Eichhornia azurea and Myriophyllum aquaticum. Conclusions: The spatial variation of the environmental variables has caused heterogeneity in the reservoir and it may support the occurrence of different species of macrophyte. Limnological variables highlighted in CCA are important to predict the species occurrence and their control in the study area

Self-adjoint Lyapunov variables, temporal ordering and irreversible representations of Schroedinger evolution

In non relativistic quantum mechanics time enters as a parameter in the Schroedinger equation. However, there are various situations where the need arises to view time as a dynamical variable. In this paper we consider the dynamical role of time through the construction of a Lyapunov variable - i.e., a self-adjoint quantum observable whose expectation value varies monotonically as time increases. It is shown, in a constructive way, that a certain class of models admit a Lyapunov variable and that the existence of a Lyapunov variable implies the existence of a transformation mapping the original quantum mechanical problem to an equivalent irreversible representation. In addition, it is proved that in the irreversible representation there exists a natural time ordering observable splitting the Hilbert space at each t>0 into past and future subspaces.Comment: Accepted for publication in JMP. Supercedes arXiv:0710.3604. Discussion expanded to include the case of Hamiltonians with an infinitely degenerate spectru

Multivariate Covariance Generalized Linear Models

We propose a general framework for non-normal multivariate data analysis called multivariate covariance generalized linear models (McGLMs), designed to handle multivariate response variables, along with a wide range of temporal and spatial correlation structures defined in terms of a covariance link function combined with a matrix linear predictor involving known matrices. The method is motivated by three data examples that are not easily handled by existing methods. The first example concerns multivariate count data, the second involves response variables of mixed types, combined with repeated measures and longitudinal structures, and the third involves a spatio-temporal analysis of rainfall data. The models take non-normality into account in the conventional way by means of a variance function, and the mean structure is modelled by means of a link function and a linear predictor. The models are fitted using an efficient Newton scoring algorithm based on quasi-likelihood and Pearson estimating functions, using only second-moment assumptions. This provides a unified approach to a wide variety of different types of response variables and covariance structures, including multivariate extensions of repeated measures, time series, longitudinal, spatial and spatio-temporal structures.Comment: 21 pages, 5 figure