Non-normal Recurrent Neural Network (nnRNN): learning long time dependencies while improving expressivity with transient dynamics

A recent strategy to circumvent the exploding and vanishing gradient problem in RNNs, and to allow the stable propagation of signals over long time scales, is to constrain recurrent connectivity matrices to be orthogonal or unitary. This ensures eigenvalues with unit norm and thus stable dynamics and training. However this comes at the cost of reduced expressivity due to the limited variety of orthogonal transformations. We propose a novel connectivity structure based on the Schur decomposition and a splitting of the Schur form into normal and non-normal parts. This allows to parametrize matrices with unit-norm eigenspectra without orthogonality constraints on eigenbases. The resulting architecture ensures access to a larger space of spectrally constrained matrices, of which orthogonal matrices are a subset. This crucial difference retains the stability advantages and training speed of orthogonal RNNs while enhancing expressivity, especially on tasks that require computations over ongoing input sequences

Direct data-driven control of constrained linear parameter-varying systems: A hierarchical approach

In many nonlinear control problems, the plant can be accurately described by a linear model whose operating point depends on some measurable variables, called scheduling signals. When such a linear parameter-varying (LPV) model of the open-loop plant needs to be derived from a set of data, several issues arise in terms of parameterization, estimation, and validation of the model before designing the controller. Moreover, the way modeling errors affect the closed-loop performance is still largely unknown in the LPV context. In this paper, a direct data-driven control method is proposed to design LPV controllers directly from data without deriving a model of the plant. The main idea of the approach is to use a hierarchical control architecture, where the inner controller is designed to match a simple and a-priori specified closed-loop behavior. Then, an outer model predictive controller is synthesized to handle input/output constraints and to enhance the performance of the inner loop. The effectiveness of the approach is illustrated by means of a simulation and an experimental example. Practical implementation issues are also discussed.Comment: Preliminary version of the paper "Direct data-driven control of constrained systems" published in the IEEE Transactions on Control Systems Technolog

GPU-accelerated stochastic predictive control of drinking water networks

Despite the proven advantages of scenario-based stochastic model predictive control for the operational control of water networks, its applicability is limited by its considerable computational footprint. In this paper we fully exploit the structure of these problems and solve them using a proximal gradient algorithm parallelizing the involved operations. The proposed methodology is applied and validated on a case study: the water network of the city of Barcelona.Comment: 11 pages in double column, 7 figure

Rational Multi-Curve Models with Counterparty-Risk Valuation Adjustments

We develop a multi-curve term structure setup in which the modelling ingredients are expressed by rational functionals of Markov processes. We calibrate to LIBOR swaptions data and show that a rational two-factor lognormal multi-curve model is sufficient to match market data with accuracy. We elucidate the relationship between the models developed and calibrated under a risk-neutral measure Q and their consistent equivalence class under the real-world probability measure P. The consistent P-pricing models are applied to compute the risk exposures which may be required to comply with regulatory obligations. In order to compute counterparty-risk valuation adjustments, such as CVA, we show how positive default intensity processes with rational form can be derived. We flesh out our study by applying the results to a basis swap contract.Comment: 34 pages, 9 figure

Observational hints on the Big Bounce

In this paper we study possible observational consequences of the bouncing cosmology. We consider a model where a phase of inflation is preceded by a cosmic bounce. While we consider in this paper only that the bounce is due to loop quantum gravity, most of the results presented here can be applied for different bouncing cosmologies. We concentrate on the scenario where the scalar field, as the result of contraction of the universe, is driven from the bottom of the potential well. The field is amplified, and finally the phase of the standard slow-roll inflation is realized. Such an evolution modifies the standard inflationary spectrum of perturbations by the additional oscillations and damping on the large scales. We extract the parameters of the model from the observations of the cosmic microwave background radiation. In particular, the value of inflaton mass is equal to $m=(2.6 \pm 0.6) \cdot 10^{13}$ GeV. In our considerations we base on the seven years of observations made by the WMAP satellite. We propose the new observational consistency check for the phase of slow-roll inflation. We investigate the conditions which have to be fulfilled to make the observations of the Big Bounce effects possible. We translate them to the requirements on the parameters of the model and then put the observational constraints on the model. Based on assumption usually made in loop quantum cosmology, the Barbero-Immirzi parameter was shown to be constrained by $\gamma<1100$ from the cosmological observations. We have compared the Big Bounce model with the standard Big Bang scenario and showed that the present observational data is not informative enough to distinguish these models.Comment: 25 pages, 8 figures, JHEP3.cl

Negative fluctuation-dissipation ratios in the backgammon model

We analyze fluctuation-dissipation relations in the Backgammon model: a system that displays glassy behavior at zero temperature due to the existence of entropy barriers. We study local and global fluctuation relations for the different observables in the model. For the case of a global perturbation we find a unique negative fluctuation-dissipation ratio that is independent of the observable and which diverges linearly with the waiting time. This result suggests that a negative effective temperature can be observed in glassy systems even in the absence of thermally activated processes.Comment: 32 pages, 10 figures. Accepted in PR