Factor analysis with finite data

Factor analysis aims to describe high dimensional random vectors by means of a small number of unknown common factors. In mathematical terms, it is required to decompose the covariance matrix $\Sigma$ of the random vector as the sum of a diagonal matrix $D$ | accounting for the idiosyncratic noise in the data | and a low rank matrix $R$ | accounting for the variance of the common factors | in such a way that the rank of $R$ is as small as possible so that the number of common factors is minimal. In practice, however, the matrix $\Sigma$ is unknown and must be replaced by its estimate, i.e. the sample covariance, which comes from a finite amount of data. This paper provides a strategy to account for the uncertainty in the estimation of $\Sigma$ in the factor analysis problem.Comment: Draft, the final version will appear in the 56th IEEE Conference on Decision and Control, Melbourne, Australia, 201

Factor Models with Real Data: a Robust Estimation of the Number of Factors

Factor models are a very efficient way to describe high dimensional vectors of data in terms of a small number of common relevant factors. This problem, which is of fundamental importance in many disciplines, is usually reformulated in mathematical terms as follows. We are given the covariance matrix Sigma of the available data. Sigma must be additively decomposed as the sum of two positive semidefinite matrices D and L: D | that accounts for the idiosyncratic noise affecting the knowledge of each component of the available vector of data | must be diagonal and L must have the smallest possible rank in order to describe the available data in terms of the smallest possible number of independent factors. In practice, however, the matrix Sigma is never known and therefore it must be estimated from the data so that only an approximation of Sigma is actually available. This paper discusses the issues that arise from this uncertainty and provides a strategy to deal with the problem of robustly estimating the number of factors.Comment: arXiv admin note: text overlap with arXiv:1708.0040

Robust Identification of "Sparse Plus Low-rank" Graphical Models: An Optimization Approach

Motivated by graphical models, we consider the "Sparse Plus Low-rank" decomposition of a positive definite concentration matrix -- the inverse of the covariance matrix. This is a classical problem for which a rich theory and numerical algorithms have been developed. It appears, however, that the results rapidly degrade when, as it happens in practice, the covariance matrix must be estimated from the observed data and is therefore affected by a certain degree of uncertainty. We discuss this problem and propose an alternative optimization approach that appears to be suitable to deal with robustness issues in the "Sparse Plus Low-rank" decomposition problem.The variational analysis of this optimization problem is carried over and discussed

Regularized transport between singular covariance matrices

We consider the problem of steering a linear stochastic system between two end-point degenerate Gaussian distributions in finite time. This accounts for those situations in which some but not all of the state entries are uncertain at the initial, t = 0, and final time, t = T . This problem entails non-trivial technical challenges as the singularity of terminal state-covariance causes the control to grow unbounded at the final time T. Consequently, the entropic interpolation (Schroedinger Bridge) is provided by a diffusion process which is not finite-energy, thereby placing this case outside of most of the current theory. In this paper, we show that a feasible interpolation can be derived as a limiting case of earlier results for non-degenerate cases, and that it can be expressed in closed form. Moreover, we show that such interpolation belongs to the same reciprocal class of the uncontrolled evolution. By doing so we also highlight a time-symmetry of the problem, contrasting dual formulations in the forward and reverse time-directions, where in each the control grows unbounded as time approaches the end-point (in the forward and reverse time-direction, respectively).Comment: 8 page

Desarrollo de una propuesta metodológica para cuantificar en forma práctica la evolución de las geoformas en un sector del Arroyo Saladillo

El presente trabajo final de la carrera de Ingeniería en Agrimensura plantea tres objetivos bien definidos. En primera instancia un estudio de la cuenca del Arroyo Saladillo, partiendo de la ubicación, límites y divisoria de la cuenca, transitando por sus rasgos tectónicos y estratigráficos, su hidrología, topografía, diversidad biológica, tipo de suelo, características climáticas, etc. La principal finalidad de este estudio es poder conocer la dinámica y los rasgos característicos de la cuenca. El segundo objetivo será establecer e identificar las principales problemáticas existentes en zonas aledañas al Arroyo Saladillo, realizando una breve descripción de cada una. No es incumbencia del presente trabajo determinar soluciones a los inconvenientes planteados, sino mencionarlos para establecer un antecedente de los hechos descriptos. Por último, realizar un monitoreo de la cascada del arroyo ubicada en el parque Regional Sur accediendo desde la localidad de Villa Gobernador Gálvez. El control se hará en el período Octubre - Marzo. Los datos obtenidos de estas sucesivas mediciones, serán relacionados con diversos factores con la finalidad de obtener una propuesta metodológica para cuantificar en forma práctica la evolución del proceso erosivo retrogradante que presenta la cascada del Arroyo Saladillo en su tramo final. En esta última instancia, se realizaran mediciones topográficas con el objetivo de dejar puntos de control con coordenadas en el sistema de referencia Gauss-Krugger, quedando a disposición de cualquier persona u ente interesado. A su vez se confeccionará cartografía temática actualizada de la cuenca del Arroyo Saladillo.Fil: Ciccone, Betina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura; Argentin

Intermittent versus continuous energy restriction on weight loss and cardiometabolic outcomes: A systematic review and meta-analysis of randomized controlled trials

Additional file 1. Electronic search strategy

The Anemonia sulcata Toxin BDS-I Protects Astrocytes Exposed to Aβ1–42 Oligomers by Restoring [Ca2+]i Transients and ER Ca2+ Signaling

Intracellular calcium concentration ([Ca2+]i) transients in astrocytes represent a highly plastic signaling pathway underlying the communication between neurons and glial cells. However, how this important phenomenon may be compromised in Alzheimer’s disease (AD) remains unexplored. Moreover, the involvement of several K+ channels, including KV3.4 underlying the fast-inactivating currents, has been demonstrated in several AD models. Here, the effect of KV3.4 modulation by the marine toxin blood depressing substance-I (BDS-I) extracted from Anemonia sulcata has been studied on [Ca2+]i transients in rat primary cortical astrocytes exposed to Aβ1–42 oligomers. We showed that: (1) primary cortical astrocytes expressing KV3.4 channels displayed [Ca2+]i transients depending on the occurrence of membrane potential spikes, (2) BDS-I restored, in a dose-dependent way, [Ca2+]i transients in astrocytes exposed to Aβ1–42 oligomers (5 µM/48 h) by inhibiting hyperfunctional KV3.4 channels, (3) BDS-I counteracted Ca2+ overload into the endoplasmic reticulum (ER) induced by Aβ1–42 oligomers, (4) BDS-I prevented the expression of the ER stress markers including active caspase 12 and GRP78/BiP in astrocytes treated with Aβ1–42 oligomers, and (5) BDS-I prevented Aβ1–42-induced reactive oxygen species (ROS) production and cell suffering measured as mitochondrial activity and lactate dehydrogenase (LDH) release. Collectively, we proposed that the marine toxin BDS-I, by inhibiting the hyperfunctional KV3.4 channels and restoring [Ca2+]i oscillation frequency, prevented Aβ1–42-induced ER stress and cell suffering in astrocytes