Generalized Onsager-Machlup's theory of thermal fluctuations for non-equilibrium systems

In this work a generalization of Onsager-Machlup's theory of time-dependent thermal fluctuations of equilibrium systems is proposed, to the case in which the system relaxes irreversibly along a non-equilibrium trajectory that can be approximated as a sequence of stationary states. This generalization is summarized by a canonical description of the dependence of the two-time correlation function C(t+\tau,t), and of the equal-time correlation function \sigma(t)= C(t,t) (the covariance of the fluctuations), on the non-equilibrium relaxation time t

An Axiomatic Characterization of Steenrod's cup-ii Products

We introduce new formulae for the cup-$i$ products on the cochains of spaces. We prove that any set of choices for the cup-$i$ products is isomorphic to the one defined by our formulae if it is natural, minimal, non-degenerate, and free. We also show that Steenrod's original set of choices, as well as all of those induced from operadic and prop theoretic constructions known to the author satisfy these axioms

Persistence Steenrod modules

We develop the theory of persistence modules equipped with an action of the Steenrod algebra and effectively incorporate part of the added information into the persistence computational pipeline

Functional Analysis of Variance for Hilbert-Valued Multivariate Fixed Effect Models

This paper presents new results on Functional Analysis of Variance for fixed effect models with correlated Hilbert-valued Gaussian error components. The geometry of the Reproducing Kernel Hilbert Space (RKHS) of the error term is considered in the computation of the total sum of squares, the residual sum of squares, and the sum of squares due to the regression. Under suitable linear transformation of the correlated functional data, the distributional characteristics of these statistics, their moment generating and characteristic functions, are derived. Fixed effect linear hypothesis testing is finally formulated in the Hilbert-valued multivariate Gaussian context considered

Spectral analysis of long range dependence functional time series

Long Range Dependence (LRD) in functional sequences is characterized in the spectral domain under suitable conditions. Particularly, multifractionally integrated functional autoregressive moving averages processes can be introduced in this framework. The convergence to zero in the Hilbert-Schmidt operator norm of the integrated bias of the periodogram operator is proved. Under a Gaussian scenario, a weak--consistent parametric estimator of the long--memory operator is then obtained by minimizing, in the norm of bounded linear operators, a divergence information functional loss.Comment: 36 page

A finitely presented E∞{E}_{\infty}-prop II: cellular context

We construct, using finitely many generating cell and relations, props in the category of CW-complexes with the property that their associated operads are models of the $E_\infty$-operad. We use one of these to construct a cellular $E_\infty$-bialgebra structure on the interval and derive from it natural cellular $E_\infty$-coalgebra structures on the geometric realization of simplicial sets. We use another, a quotient of the first, to relate our constructions to earlier work of Kaufmann and prove a conjecture of his. This is the second of two papers in a series, the first investigates analogue constructions in the category of differential graded modules.Comment: Removed the application to cubical sets. The E-infinity coalgebra associated to cubical chains can be found in a separate notebook in the authors webpag

`Tight Binding' methods in quantum transport through molecules and small devices: From the coherent to the decoherent description

We discuss the steady-state electronic transport in solid-state and molecular devices in the quantum regime. The decimation technique allows a comprehensive description of the electronic structure. Such a method is used, in conjunction with the generalizations of Landauer's tunneling formalism, to describe a wide range of transport regimes. We analize mesoscopic and semiclassical metallic transport, the metal-insulator transition, and the resonant tunneling regime. The effects of decoherence on transport is discussed in terms of the D'Amato-Pastawski model. A brief presentation of the time dependent phenomena is also included.Comment: 25 pages 20 figure

Sampling basis in reproducing kernel Banach spaces

We present necessary and sufficient conditions to hold true a Kramer type sampling theorem over semi-inner product reproducing kernel Banach spaces. Under some sampling-type hypotheses over a sequence of functions on these Banach spaces it results necessary that such sequence must be a $X_d$-Riesz basis and a sampling basis for the space. These results are a generalization of some already known sampling theorems over reproducing kernel Hilbert spaces

Symplectic or contact structures on Lie Groups

We study left invariant contact forms and left invariant symplectic forms on Lie groups. We give the classification of all symplectic structures on nilpotent Lie algebras up the dimension 6.Comment: 18 page

The effect of the spatial domain in FANOVA models with ARH(1) error term

Functional Analysis of Variance (FANOVA) from Hilbert-valued correlated data with spatial rectangular or circular supports is analyzed, when Dirichlet conditions are assumed on the boundary. Specifically, a Hilbert-valued fixed effect model with error term defined from an Autoregressive Hilbertian process of order one (ARH(1) process) is considered, extending the formulation given in Ruiz-Medina (2016). A new statistical test is also derived to contrast the significance of the functional fixed effect parameters. The Dirichlet conditions established at the boundary affect the dependence range of the correlated error term. While the rate of convergence to zero of the eigenvalues of the covariance kernels, characterizing the Gaussian functional error components, directly affects the stability of the generalized least-squares parameter estimation problem. A simulation study and a real-data application related to fMRI analysis are undertaken to illustrate the performance of the parameter estimator and statistical test derived.Comment: 56 pages (with 11 figures). Supplementary material is also include