Message passing for distributed optimisation of power allocation with renewable resources

The increase in renewable energy generators introduced into the electricity grid is putting pressure on its stability and management as predictions of renewable energy sources cannot be accurate or fully controlled. This, with the additional pressure of fluctuations in demand, presents a problem more complex than the current methods of controlling electricity distribution were designed for. A global approximate and distributed optimisation method for power allocation that accommodates uncertainties and volatility is suggested and analysed. It is based on a probabilistic method known as message passing [1], which has deep links to statistical physics methodology. This principled method of optimisation is based on local calculations and inherently accommodates uncertainties; it is of modest computational complexity and provides good approximate solutions.We consider uncertainty and fluctuations drawn from a Gaussian distribution and incorporate them into the message-passing algorithm. We see the effect that increasing uncertainty has on the transmission cost and how the placement of volatile nodes within a grid, such as renewable generators or consumers, effects it.

Robust Stereo Visual Odometry through a Probabilistic Combination of Points and Line Segments

Most approaches to stereo visual odometry reconstruct the motion based on the tracking of point features along a sequence of images. However, in low-textured scenes it is often difficult to encounter a large set of point features, or it may happen that they are not well distributed over the image, so that the behavior of these algorithms deteriorates. This paper proposes a probabilistic approach to stereo visual odometry based on the combination of both point and line segment that works robustly in a wide variety of scenarios. The camera motion is recovered through non-linear minimization of the projection errors of both point and line segment features. In order to effectively combine both types of features, their associated errors are weighted according to their covariance matrices, computed from the propagation of Gaussian distribution errors in the sensor measurements. The method, of course, is computationally more expensive that using only one type of feature, but still can run in real-time on a standard computer and provides interesting advantages, including a straightforward integration into any probabilistic framework commonly employed in mobile robotics.

Advanced Mission Synthesis Algorithms for Vibration-based Accelerated Life-testing

In the field of vibration qualification testing, with the popular Random Control mode of shakers, the specimen is excited by random vibrations typically set in the form of a Power Spectral Density (PSD). The corresponding signals are stationary and Gaussian, i.e. featuring a normal distribution. Conversely, real-life excitations are frequently non-Gaussian, exhibiting high peaks and/or burst signals and/or deterministic harmonic components. The so-called kurtosis is a parameter often used to statistically describe the occurrence and significance of high peak values in a random process. Since the similarity between test input profiles and real-life excitations is fundamental for qualification test reliability, some methods of kurtosis-control can be implemented to synthesize realistic (non-Gaussian) input signals. Durability tests are performed to check the resistance of a component to vibration-based fatigue damage. A procedure to synthesize test excitations which starts from measured data and preserves both the damage potential and the characteristics of the reference signals is desirable. The Fatigue Damage Spectrum (FDS) is generally used to quantify the fatigue damage potential associated with the excitation. The signal synthesized for accelerated durability tests (i.e. with a limited duration) must feature the same FDS as the reference vibration computed for the component’s expected lifetime. Current standard procedures are efficient in synthesizing signals in the form of a PSD, but prove inaccurate if reference data are non-Gaussian. This work presents novel algorithms for the synthesis of accelerated durability test profiles with prescribed FDS and a non-Gaussian distribution. An experimental campaign is conducted to validate the algorithms, by testing their accuracy, robustness, and practical effectiveness. Moreover, an original procedure is proposed for the estimation of the fatigue damage potential, aiming to minimize the computational time. The research is thus supposed to improve both the effectiveness and the efficiency of excitation profile synthesis for accelerated durability tests.

Automatic classification of stellar orbits in axisymmetric potentials

Within the classification of orbits in axisymmetric stellar systems, we present a new algorithm able to automatically classify the orbits according to their nature. The algorithm involves the application of the correlation integral method to the surface of section of the orbit; fitting the cumulative distribution function built with the consequents in the surface of section of the orbit, we can obtain the value of its logarithmic slope m which is directly related to the orbit’s nature: for slopes m ≈ 1 we expect the orbit to be regular, for slopes m ≈ 2 we expect it to be chaotic. With this method we have a fast and reliable way to classify orbits and, furthermore, we provide an analytical expression of the probability that an orbit is regular or chaotic given the logarithmic slope m of its correlation integral. Although this method works statistically well, the underlying algorithm can fail in some cases, misclassifying individual orbits under some peculiar circumstances. The performance of the algorithm benefits from a rich sampling of the traces of the SoS, which can be obtained with long numerical integration of orbits. Finally we note that the algorithm does not differentiate between the subtypes of regular orbits: resonantly trapped and untrapped orbits. Such distinction would be a useful feature, which we leave for future work. Since the result of the analysis is a probability linked to a Gaussian distribution, for the very definition of distribution, some orbits even if they have a certain nature are classified as belonging to the opposite class and create the probabilistic tails of the distribution. So while the method produces fair statistical results, it lacks in absolute classification precision.

Estimators and Tests based on Likelihood-Depth with Application to Weibull Distribution, Gaussian and Gumbel Copula

In dieser Arbeit werden mithilfe der Likelihood-Tiefen, eingeführt von Mizera und Müller (2004), (ausreißer-)robuste Schätzfunktionen und Tests für den unbekannten Parameter einer stetigen Dichtefunktion entwickelt. Die entwickelten Verfahren werden dann auf drei verschiedene Verteilungen angewandt. Für eindimensionale Parameter wird die Likelihood-Tiefe eines Parameters im Datensatz als das Minimum aus dem Anteil der Daten, für die die Ableitung der Loglikelihood-Funktion nach dem Parameter nicht negativ ist, und dem Anteil der Daten, für die diese Ableitung nicht positiv ist, berechnet. Damit hat der Parameter die größte Tiefe, für den beide Anzahlen gleich groß sind. Dieser wird zunächst als Schätzer gewählt, da die Likelihood-Tiefe ein Maß dafür sein soll, wie gut ein Parameter zum Datensatz passt. Asymptotisch hat der Parameter die größte Tiefe, für den die Wahrscheinlichkeit, dass für eine Beobachtung die Ableitung der Loglikelihood-Funktion nach dem Parameter nicht negativ ist, gleich einhalb ist. Wenn dies für den zu Grunde liegenden Parameter nicht der Fall ist, ist der Schätzer basierend auf der Likelihood-Tiefe verfälscht. In dieser Arbeit wird gezeigt, wie diese Verfälschung korrigiert werden kann sodass die korrigierten Schätzer konsistente Schätzungen bilden. Zur Entwicklung von Tests für den Parameter, wird die von Müller (2005) entwickelte Simplex Likelihood-Tiefe, die eine U-Statistik ist, benutzt. Es zeigt sich, dass für dieselben Verteilungen, für die die Likelihood-Tiefe verfälschte Schätzer liefert, die Simplex Likelihood-Tiefe eine unverfälschte U-Statistik ist. Damit ist insbesondere die asymptotische Verteilung bekannt und es lassen sich Tests für verschiedene Hypothesen formulieren. Die Verschiebung in der Tiefe führt aber für einige Hypothesen zu einer schlechten Güte des zugehörigen Tests. Es werden daher korrigierte Tests eingeführt und Voraussetzungen angegeben, unter denen diese dann konsistent sind. Die Arbeit besteht aus zwei Teilen. Im ersten Teil der Arbeit wird die allgemeine Theorie über die Schätzfunktionen und Tests dargestellt und zudem deren jeweiligen Konsistenz gezeigt. Im zweiten Teil wird die Theorie auf drei verschiedene Verteilungen angewandt: Die Weibull-Verteilung, die Gauß- und die Gumbel-Copula. Damit wird gezeigt, wie die Verfahren des ersten Teils genutzt werden können, um (robuste) konsistente Schätzfunktionen und Tests für den unbekannten Parameter der Verteilung herzuleiten. Insgesamt zeigt sich, dass für die drei Verteilungen mithilfe der Likelihood-Tiefen robuste Schätzfunktionen und Tests gefunden werden können. In unverfälschten Daten sind vorhandene Standardmethoden zum Teil überlegen, jedoch zeigt sich der Vorteil der neuen Methoden in kontaminierten Daten und Daten mit Ausreißern.

Gaussian entanglement for quantum key distribution from a single-mode squeezing source

We report the suitability of an Einstein-Podolsky-Rosen entanglement source for Gaussian continuous-variable quantum key distribution at 1550 nm. Our source is based on a single continuous-wave squeezed vacuum mode combined with a vacuum mode at a balanced beam splitter. Extending a recent security proof, we characterize the source by quantifying the extractable length of a composable secure key from a finite number of samples under the assumption of collective attacks. We show that distances in the order of 10 km are achievable with this source for a reasonable sample size despite the fact that the entanglement was generated including a vacuum mode. Our security analysis applies to all states having an asymmetry in the field quadrature variances, including those generated by superposition of two squeezed modes with different squeezing strengths.

Paste Residence Time in a Spouted Bed Dryer. IV: Effect of the Inert Particle Size Distribution

The residence time distribution and mean residence time of a 10% sodium bicarbonate solution that is dried in a conventional spouted bed with inert bodies were measured with the stimulus-response method. Methylene blue was used as a chemical tracer, and the effects of the paste feed mode, size distribution of the inert bodies, and mean particle size on the residence times and dried powder properties were investigated. The results showed that the residence time distributions could be best reproduced with the perfect mixing cell model or N = 1 for the continuous stirred tank reactor in a series model. The mean residence times ranged from 6.04 to 12.90 min and were significantly affected by the factors studied. Analysis of variance on the experimental data showed that mean residence times were affected by the mean diameter of the inert bodies at a significance level of 1% and by the size distribution at a level of 5%. Moreover, altering the paste feed from dripping to pneumatic atomization affected mean residence time at a 5% significance level. The dried powder characteristics proved to be adequate for further industrial manipulation, as demonstrated by the low moisture content, narrow range of particle size, and good flow properties. The results of this research are significant in the study of the drying of heat-sensitive materials because it shows that by simultaneously changing the size distribution and average size of the inert bodies, the mean residence times of a paste can be reduced by half, thus decreasing losses due to degradation.

Kinetic analysis of vascular marker distribution in perfused rat livers after regeneration following partial hepatectomy

Background/Aims: Liver clearance models are based on information (or assumptions) on solute distribution kinetics within the microvasculatory system, The aim was to study albumin distribution kinetics in regenerated livers and in livers of normal adult rats, Methods: A novel mathematical model was used to evaluate the distribution space and the transit time dispersion of albumin in livers following regeneration after a two-thirds hepatectomy compared to livers of normal adult rats. Outflow curves of albumin measured after bolus injection in single-pass perfused rat livers were analyzed by correcting for the influence of catheters and fitting a long-tailed function to the data. Results: The curves were well described by the proposed model. The distribution volume and the transit time dispersion of albumin observed in the partial hepatectomy group were not significantly different from livers of normal adult rats. Conclusions: These findings suggest that the distribution space and the transit time dispersion of albumin (CV2) is relatively constant irrespective of the presence of rapid and extensive repair. This invariance of CV2 implies, as a first approximation, a similar degree of intrasinusoidal mixing, The finding that a sum of two (instead of one) inverse Gaussian densities is an appropriate empirical function to describe the outflow curve of vascular indicators has consequences for an improved prediction of hepatic solute extraction.

Commentary: Using the convection-dispersion model and transit time density functions in the analysis of organ distribution kinetics

The convection-dispersion model and its extended form have been used to describe solute disposition in organs and to predict hepatic availabilities. A range of empirical transit-time density functions has also been used for a similar purpose. The use of the dispersion model with mixed boundary conditions and transit-time density functions has been queried recently by Hisaka and Sugiyanaa in this journal. We suggest that, consistent with soil science and chemical engineering literature, the mixed boundary conditions are appropriate providing concentrations are defined in terms of flux to ensure continuity at the boundaries and mass balance. It is suggested that the use of the inverse Gaussian or other functions as empirical transit-time densities is independent of any boundary condition consideration. The mixed boundary condition solutions of the convection-dispersion model are the easiest to use when linear kinetics applies. In contrast, the closed conditions are easier to apply in a numerical analysis of nonlinear disposition of solutes in organs. We therefore argue that the use of hepatic elimination models should be based on pragmatic considerations, giving emphasis to using the simplest or easiest solution that will give a sufficiently accurate prediction of hepatic pharmacokinetics for a particular application. (C) 2000 Wiley-Liss Inc. and the American Pharmaceutical Association J Pharm Sci 89:1579-1586, 2000.

Expectation Propagation with Factorizing Distributions: A Gaussian Approximation and Performance Results for Simple Models

We discuss the expectation propagation (EP) algorithm for approximate Bayesian inference using a factorizing posterior approximation. For neural network models, we use a central limit theorem argument to make EP tractable when the number of parameters is large. For two types of models, we show that EP can achieve optimal generalization performance when data are drawn from a simple distribution.

Microscopic origin of non-Gaussian distributions of financial returns

In this paper we study the possible microscopic origin of heavy-tailed probability density distributions for the price variation of financial instruments. We extend the standard log-normal process to include another random component in the so-called stochastic volatility models. We study these models under an assumption, akin to the Born-Oppenheimer approximation, in which the volatility has already relaxed to its equilibrium distribution and acts as a background to the evolution of the price process. In this approximation, we show that all models of stochastic volatility should exhibit a scaling relation in the time lag of zero-drift modified log-returns. We verify that the Dow-Jones Industrial Average index indeed follows this scaling. We then focus on two popular stochastic volatility models, the Heston and Hull-White models. In particular, we show that in the Hull-White model the resulting probability distribution of log-returns in this approximation corresponds to the Tsallis (t-Student) distribution. The Tsallis parameters are given in terms of the microscopic stochastic volatility model. Finally, we show that the log-returns for 30 years Dow Jones index data is well fitted by a Tsallis distribution, obtaining the relevant parameters. (c) 2007 Elsevier B.V. All rights reserved.

Derivation of the probability distribution function for the local density of states of a disordered quantum wire via the replica trick and supersymmetry

We consider the statistical properties of the local density of states of a one-dimensional Dirac equation in the presence of various types of disorder with Gaussian white-noise distribution. It is shown how either the replica trick or supersymmetry can be used to calculate exactly all the moments of the local density of states.' Careful attention is paid to how the results change if the local density of states is averaged over atomic length scales. For both the replica trick and supersymmetry the problem is reduced to finding the ground state of a zero-dimensional Hamiltonian which is written solely in terms of a pair of coupled spins which are elements of u(1, 1). This ground state is explicitly found for the particular case of the Dirac equation corresponding to an infinite metallic quantum wire with a single conduction channel. The calculated moments of the local density of states agree with those found previously by Al'tshuler and Prigodin [Sov. Phys. JETP 68 (1989) 198] using a technique based on recursion relations for Feynman diagrams. (C) 2001 Elsevier Science B.V. All rights reserved.

Mean anisotropy of homogeneous Gaussian random fields and anisotropic norms of linear translation-invariant operators on multidimensional integer lattices

Sensitivity of output of a linear operator to its input can be quantified in various ways. In Control Theory, the input is usually interpreted as disturbance and the output is to be minimized in some sense. In stochastic worst-case design settings, the disturbance is considered random with imprecisely known probability distribution. The prior set of probability measures can be chosen so as to quantify how far the disturbance deviates from the white-noise hypothesis of Linear Quadratic Gaussian control. Such deviation can be measured by the minimal Kullback-Leibler informational divergence from the Gaussian distributions with zero mean and scalar covariance matrices. The resulting anisotropy functional is defined for finite power random vectors. Originally, anisotropy was introduced for directionally generic random vectors as the relative entropy of the normalized vector with respect to the uniform distribution on the unit sphere. The associated a-anisotropic norm of a matrix is then its maximum root mean square or average energy gain with respect to finite power or directionally generic inputs whose anisotropy is bounded above by a≥0. We give a systematic comparison of the anisotropy functionals and the associated norms. These are considered for unboundedly growing fragments of homogeneous Gaussian random fields on multidimensional integer lattice to yield mean anisotropy. Correspondingly, the anisotropic norms of finite matrices are extended to bounded linear translation invariant operators over such fields.