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Dynamic Bayesian smooth transition autoregressive models applied to hourly electricity load in southern Brazil
Dynamic Bayesian Smooth Transition Autoregressive (DBSTAR) models are proposed for nonlinear autoregressive time series processes as alternative to both the classical Smooth Transition Autoregressive (STAR) models of Chan and Tong (1986) and the Bayesian Simulation STAR (BSTAR) models of Lopes and Salazar (2005). Unlike those, DBSTAR models are sequential polynomial dynamic analytical models suitable for inherently non-stationary time series with non-linear characteristics such as asymmetric cycles. As they are analytical, they also avoid potential computational problems associated with BSTAR models and allow fast sequential estimation of parameters.
Two types of DBSTAR models are defined here based on the method adopted to approximate the transition function of their autoregressive components, namely the Taylor and the B-splines DBSTAR models. A harmonic version of those models, that accounted for the cyclical component explicitly in a flexible yet parsimonious way, were applied to the well-known series of annual Canadian lynx trappings and showed improved fitting when compared to both the classical STAR and the BSTAR models. Another application to a long series of hourly electricity loading in southern Brazil, covering the period of the South-African Football World Cup in June 2010, illustrates the short-term forecasting accuracy of fast computing harmonic DBSTAR models that account for various characteristics such as periodic behaviour (both within-the-day and within-the-week) and average temperature
Nonequilibrium many-body quantum dynamics: from full random matrices to real systems
We present an overview of our studies on the nonequilibrium dynamics of
quantum systems that have many interacting particles. Our emphasis is on
systems that show strong level repulsion, referred to as chaotic systems. We
discuss how full random matrices can guide and support our studies of realistic
systems. We show that features of the dynamics can be anticipated from a
detailed analysis of the spectrum and the structure of the initial state
projected onto the energy eigenbasis. On the other way round, if we only have
access to the dynamics, we can use it to infer the properties of the spectrum
of the system. Our focus is on the survival probability, but results for other
observables, such as the spin density imbalance and Shannon entropy are also
mentioned.Comment: 14 pages, 7 figures, chapter for the book "Thermodynamics in the
Quantum Regime - Recent Progress and Outlook
Boundary Conditions for Kerr-AdS Perturbations
The Teukolsky master equation and its associated spin-weighted spheroidal
harmonic decomposition simplify considerably the study of linear gravitational
perturbations of the Kerr(-AdS) black hole. However, the formulation of the
problem is not complete before we assign the physically relevant boundary
conditions. We find a set of two Robin boundary conditions (BCs) that must be
imposed on the Teukolsky master variables to get perturbations that are
asymptotically global AdS, i.e. that asymptotes to the Einstein Static
Universe. In the context of the AdS/CFT correspondence, these BCs allow a
non-zero expectation value for the CFT stress-energy tensor while keeping fixed
the boundary metric. When the rotation vanishes, we also find the gauge
invariant differential map between the Teukolsky and the Kodama-Ishisbashi
(Regge-Wheeler-Zerilli) formalisms. One of our Robin BCs maps to the scalar
sector and the other to the vector sector of the Kodama-Ishisbashi
decomposition. The Robin BCs on the Teukolsky variables will allow for a
quantitative study of instability timescales and quasinormal mode spectrum of
the Kerr-AdS black hole. As a warm-up for this programme, we use the Teukolsky
formalism to recover the quasinormal mode spectrum of global AdS-Schwarzschild,
complementing previous analysis in the literature.Comment: 33 pages, 6 figure
AdS nonlinear instability: moving beyond spherical symmetry
Anti-de Sitter (AdS) is conjectured to be nonlinear unstable to a weakly
turbulent mechanism that develops a cascade towards high frequencies, leading
to black hole formation [1,2]. We give evidence that the gravitational sector
of perturbations behaves differently from the scalar one studied in [2]. In
contrast with [2], we find that not all gravitational normal modes of AdS can
be nonlinearly extended into periodic horizonless smooth solutions of the
Einstein equation. In particular, we show that even seeds with a single normal
mode can develop secular resonances, unlike the spherically symmetric scalar
field collapse studied in [2]. Moreover, if the seed has two normal modes, more
than one resonance can be generated at third order, unlike the spherical
collapse of [2]. We also show that weak turbulent perturbative theory predicts
the existence of direct and inverse cascades, with the former dominating the
latter for equal energy two-mode seeds.Comment: 7 pages, no figures, 2 table
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