Numerical enclosures of the optimal cost of the Kantorovitch’s mass transportation problem

International audience

Nested Sampling and its Applications in Stable Compressive Covariance Estimation and Phase Retrieval with Near-Minimal Measurements

Compressed covariance sensing using quadratic samplers is gaining increasing interest in recent literature. Covariance matrix often plays the role of a sufficient statistic in many signal and information processing tasks. However, owing to the large dimension of the data, it may become necessary to obtain a compressed sketch of the high dimensional covariance matrix to reduce the associated storage and communication costs. Nested sampling has been proposed in the past as an efficient sub-Nyquist sampling strategy that enables perfect reconstruction of the autocorrelation sequence of Wide-Sense Stationary (WSS) signals, as though it was sampled at the Nyquist rate. The key idea behind nested sampling is to exploit properties of the difference set that naturally arises in quadratic measurement model associated with covariance compression. In this thesis, we will focus on developing novel versions of nested sampling for low rank Toeplitz covariance estimation, and phase retrieval, where the latter problem finds many applications in high resolution optical imaging, X-ray crystallography and molecular imaging. The problem of low rank compressive Toeplitz covariance estimation is first shown to be fundamentally related to that of line spectrum recovery. In absence if noise, this connection can be exploited to develop a particular kind of sampler called the Generalized Nested Sampler (GNS), that can achieve optimal compression rates. In presence of bounded noise, we develop a regularization-free algorithm that provably leads to stable recovery of the high dimensional Toeplitz matrix from its order-wise minimal sketch acquired using a GNS. Contrary to existing TV-norm and nuclear norm based reconstruction algorithms, our technique does not use any tuning parameters, which can be of great practical value. The idea of nested sampling idea also finds a surprising use in the problem of phase retrieval, which has been of great interest in recent times for its convex formulation via PhaseLift, By using another modified version of nested sampling, namely the Partial Nested Fourier Sampler (PNFS), we show that with probability one, it is possible to achieve a certain conjectured lower bound on the necessary measurement size. Moreover, for sparse data, an l1 minimization based algorithm is proposed that can lead to stable phase retrieval using order-wise minimal number of measurements.

Bidirectional Helmholtz Machines

L'entraînement sans surveillance efficace et inférence dans les modèles génératifs profonds reste un problème difficile. Une approche assez simple, la machine de Helmholtz, consiste à entraîner du haut vers le bas un modèle génératif dirigé qui sera utilisé plus tard pour l'inférence approximative. Des résultats récents suggèrent que de meilleurs modèles génératifs peuvent être obtenus par de meilleures procédures d'inférence approximatives. Au lieu d'améliorer la procédure d'inférence, nous proposons ici un nouveau modèle, la machine de Helmholtz bidirectionnelle, qui garantit qu'on peut calculer efficacement les distributions de haut-vers-bas et de bas-vers-haut. Nous y parvenons en interprétant à les modèles haut-vers-bas et bas-vers-haut en tant que distributions d'inférence approximative, puis ensuite en définissant la distribution du modèle comme étant la moyenne géométrique de ces deux distributions. Nous dérivons une borne inférieure pour la vraisemblance de ce modèle, et nous démontrons que l'optimisation de cette borne se comporte en régulisateur. Ce régularisateur sera tel que la distance de Bhattacharyya sera minisée entre les distributions approximatives haut-vers-bas et bas-vers-haut. Cette approche produit des résultats de pointe en terme de modèles génératifs qui favorisent les réseaux significativement plus profonds. Elle permet aussi une inférence approximative amérliorée par plusieurs ordres de grandeur. De plus, nous introduisons un modèle génératif profond basé sur les modèles BiHM pour l'entraînement semi-supervisé.

Bidirectional Helmholtz Machines

L'entraînement sans surveillance efficace et inférence dans les modèles génératifs profonds reste un problème difficile. Une approche assez simple, la machine de Helmholtz, consiste à entraîner du haut vers le bas un modèle génératif dirigé qui sera utilisé plus tard pour l'inférence approximative. Des résultats récents suggèrent que de meilleurs modèles génératifs peuvent être obtenus par de meilleures procédures d'inférence approximatives. Au lieu d'améliorer la procédure d'inférence, nous proposons ici un nouveau modèle, la machine de Helmholtz bidirectionnelle, qui garantit qu'on peut calculer efficacement les distributions de haut-vers-bas et de bas-vers-haut. Nous y parvenons en interprétant à les modèles haut-vers-bas et bas-vers-haut en tant que distributions d'inférence approximative, puis ensuite en définissant la distribution du modèle comme étant la moyenne géométrique de ces deux distributions. Nous dérivons une borne inférieure pour la vraisemblance de ce modèle, et nous démontrons que l'optimisation de cette borne se comporte en régulisateur. Ce régularisateur sera tel que la distance de Bhattacharyya sera minisée entre les distributions approximatives haut-vers-bas et bas-vers-haut. Cette approche produit des résultats de pointe en terme de modèles génératifs qui favorisent les réseaux significativement plus profonds. Elle permet aussi une inférence approximative amérliorée par plusieurs ordres de grandeur. De plus, nous introduisons un modèle génératif profond basé sur les modèles BiHM pour l'entraînement semi-supervisé.

Efficient algorithms for beacon routing in polygons

In a paper by Biro et al. [7], a novel twist on guarding in art galleries is introduced. A beacon is a fixed point with an attraction pull that can move points within the polygon. Points move greedily to monotonically decrease their Euclidean distance to the beacon by moving straight towards the beacon or sliding on the edges of the polygon. The beacon attracts a point if the point eventually reaches the beacon. Unlike most variations of the art gallery problem, the beacon attraction has the intriguing property of being asymmetric, leading to separate definitions of attraction region and inverse attraction region. The attraction region of a beacon is the set of points that it attracts. For a given point in the polygon, the inverse attraction region is the set of beacon locations that can attract the point. We first study the characteristics of beacon attraction. We consider the quality of a "successful" beacon attraction and provide an upper bound of $\sqrt{2}$ on the ratio between the length of the beacon trajectory and the length of the geodesic distance in a simple polygon. In addition, we provide an example of a polygon with holes in which this ratio is unbounded. Next we consider the problem of computing the shortest beacon watchtower in a polygonal terrain and present an $O(n \log n)$ time algorithm to solve this problem. In doing this, we introduce $O(n \log n)$ time algorithms to compute the beacon kernel and the inverse beacon kernel in a monotone polygon. We also prove that $\Omega(n \log n)$ time is a lower bound for computing the beacon kernel of a monotone polygon. Finally, we study the inverse attraction region of a point in a simple polygon. We present algorithms to efficiently compute the inverse attraction region of a point for simple, monotone, and terrain polygons with respective time complexities $O(n^2)$, $O(n \log n)$ and $O(n)$. We show that the inverse attraction region of a point in a simple polygon has linear complexity and the problem of computing the inverse attraction region has a lower bound of $\Omega(n \log n)$ in monotone polygons and consequently in simple polygons.

Keeping Variables within Bounds: Using Information between Observations

This research develops an econometric framework to analyze time series processes with bounds. The framework is general enough that it can incorporate several different kinds of bounding information that constrain continuous-time stochastic processes between discretely-sampled observations. It applies to situations in which the process is known to remain within an interval between observations, by way of either a known constraint or through the observation of extreme realizations of the process. The main statistical technique employs the theory of maximum likelihood estimation. This approach leads to the development of the asymptotic distribution theory for the estimation of the parameters in bounded diffusion models. The results of this analysis present several implications for empirical research. The advantages are realized in the form of efficiency gains, bias reduction and in the flexibility of model specification. A bias arises in the presence of bounding information that is ignored, while it is mitigated within this framework. An efficiency gain arises, in the sense that the statistical methods make use of conditioning information, as revealed by the bounds. Further, the specification of an econometric model can be uncoupled from the restriction to the bounds, leaving the researcher free to model the process near the bound in a way that avoids bias from misspecification. One byproduct of the improvements in model specification is that the more precise model estimation exposes other sources of misspecification. Some processes reveal themselves to be unlikely candidates for a given diffusion model, once the observations are analyzed in combination with the bounding information. A closer inspection of the theoretical foundation behind diffusion models leads to a more general specification of the model. This approach is used to produce a set of algorithms to make the model computationally feasible and more widely applicable. Finally, the modeling framework is applied to a series of interest rates, which, for several years, have been constrained by the lower bound of zero. The estimates from a series of diffusion models suggest a substantial difference in estimation results between models that ignore bounds and the framework that takes bounding information into consideration.

On polynomials with given Hilbert function and applications

Using Macaulay's correspondence we study the family of Artinian Gorenstein local algebras with fixed symmetric Hilbert function decomposition. As an application we give a new lower bound for the dimension of cactus varieties of the third Veronese embedding. We discuss the case of cubic surfaces, where interesting phenomena occur.

Protein cutoff scanning: a comparative analysis of cutoff dependent and cutoff free methods for prospecting contacts in proteins.

In this study, we carried out a comparative analysis between two classical methodologies to prospect residue contacts in proteins: the traditional cutoff dependent (CD) approach and cutoff free Delaunay tessellation (DT). In addition, two alternative coarse-grained forms to represent residues were tested: using alpha carbon (CA) and side chain geometric center (GC). A database was built, comprising three top classes: all alpha, all beta, and alpha/beta. We found that the cutoff value? at about 7.0 A emerges as an important distance parameter.? Up to 7.0 A, CD and DT properties are unified, which implies that at this distance all contacts are complete and legitimate (not occluded). We also have shown that DT has an intrinsic missing edges problem when mapping the first layer of neighbors. In proteins, it may produce systematic errors affecting mainly the contact network in beta chains with CA. The almost-Delaunay (AD) approach has been proposed to solve this DT problem. We found that even AD may not be an advantageous solution. As a consequence, in the strict range up ? to 7.0 A, the CD approach revealed to be a simpler, more complete, and reliable technique than DT or AD. Finally, we have shown that coarse-grained residue representations may introduce bias in the analysis of neighbors in cutoffs up to ? 6.8 A, with CA favoring alpha proteins and GC favoring beta proteins. This provides an additional argument pointing to ? the value of 7.0 A as an important lower bound cutoff to be used in contact analysis of proteins.

Analisi sperimentale di un sistema di localizzazione UWB per applicazioni robotiche

Data la pervasività dell’elettronica nella vita moderna, sempre più interesse è stato posto nelle applicazioni di localizzazione. In ambienti indoor e outdoor, dove sono richieste precisioni dell’ordine delle decine di centimetri, i classici servizi GNSS non sono applicabili. Una tecnologia promettente è quella a banda ultra-larga (UWB), affermata recentemente sul mercato. Un’alternativa potrebbe essere l’utilizzo di sensori ottici con marker di riferimento, però la presenza di fumo e idrometeore presenti nell’ambiente potrebbero andare ad oscurare i marker, rendendo impossibile la localizzazione. Lo scopo della tesi è volto a studiare un sistema di localizzazione UWB, progettato dall’Università di Bologna, ora sviluppato e commercializzato, in un’applicazione robotica. In particolare, l’idea è quella di porre il sistema di localizzazione sopra un elemento mobile, per esempio nella parte terminale di un braccio meccanico, al fine di localizzare un oggetto dotato di nodo UWB, ricavando dinamicamente la posizione relativa tra il braccio e l’oggetto. La tesi si concentra inizialmente a livello teorico sulle caratteristiche delle principali tecnologie coinvolte, in particolare i sistemi UWB e il filtraggio Bayesiano, per poi trattare i limiti teorici della localizzazione, nei concetti di Cramér-Rao lower bound (CRLB) e geometric dilution of precision (GDOP). Da questi, si motiva l’utilizzo della tecnica two-way ranging (TWR) come principio di raccolta delle misure per la localizzazione, per poi ricavare le curve teoriche dell’errore di localizzazione, tenendo conto dei limiti geometrici imposti, utilizzate come riferimento per l’analisi dell’errore ottenuto con il sistema reale. La tecnologia viene testata in tre campagne di misura. Nelle prime due si osserva la presenza di un piano metallico parallelo alla direzione di propagazione, per esaminare gli effetti delle riflessioni sulla localizzazione, mentre nella terza campagna si considera la presenza di acqua dolce.

Periodicals in the Central library as currently received in the Periodical reading room and kept bound on the shelves of the Lower hall and Bates hall.

Caption title.

Channel model and lower capacity bound for the transmission based on nonlinear Fourier transform

The integrability of the nonlinear Schräodinger equation (NLSE) by the inverse scattering transform shown in a seminal work [1] gave an interesting opportunity to treat the corresponding nonlinear channel similar to a linear one by using the nonlinear Fourier transform. Integrability of the NLSE is in the background of the old idea of eigenvalue communications [2] that was resurrected in recent works [3{7]. In [6, 7] the new method for the coherent optical transmission employing the continuous nonlinear spectral data | nonlinear inverse synthesis was introduced. It assumes the modulation and detection of data using directly the continuous part of nonlinear spectrum associated with an integrable transmission channel (the NLSE in the case considered). Although such a transmission method is inherently free from nonlinear impairments, the noisy signal corruptions, arising due to the ampli¯er spontaneous emission, inevitably degrade the optical system performance. We study properties of the noise-corrupted channel model in the nonlinear spectral domain attributed to NLSE. We derive the general stochastic equations governing the signal evolution inside the nonlinear spectral domain and elucidate the properties of the emerging nonlinear spectral noise using well-established methods of perturbation theory based on inverse scattering transform [8]. It is shown that in the presence of small noise the communication channel in the nonlinear domain is the additive Gaussian channel with memory and signal-dependent correlation matrix. We demonstrate that the effective spectral noise acquires colouring", its autocorrelation function becomes slow decaying and non-diagonal as a function of \frequencies", and the noise loses its circular symmetry, becoming elliptically polarized. Then we derive a low bound for the spectral effiency for such a channel. Our main result is that by using the nonlinear spectral techniques one can significantly increase the achievable spectral effiency compared to the currently available methods [9]. REFERENCES 1. Zakharov, V. E. and A. B. Shabat, Sov. Phys. JETP, Vol. 34, 62{69, 1972. 2. Hasegawa, A. and T. Nyu, J. Lightwave Technol., Vol. 11, 395{399, 1993. 3. Yousefi, M. I. and F. R. Kschischang, IEEE Trans. Inf. Theory, Vol. 60, 4312{4328, 2014. 4. Yousefi, M. I. and F. R. Kschischang, IEEE Trans. Inf. Theory, Vol. 60, 4329{4345 2014. 5. Yousefi, M. I. and F. R. Kschischang, IEEE Trans. Inf. Theory, Vol. 60, 4346{4369, 2014. 6. Prilepsky, J. E., S. A. Derevyanko, K. J. Blow, I. Gabitov, and S. K. Turitsyn, Phys. Rev. Lett., Vol. 113, 013901, 2014. 7. Le, S. T., J. E. Prilepsky, and S. K. Turitsyn, Opt. Express, Vol. 22, 26720{26741, 2014. 8. Kaup, D. J. and A. C. Newell, Proc. R. Soc. Lond. A, Vol. 361, 413{446, 1978. 9. Essiambre, R.-J., G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, J. Lightwave Technol., Vol. 28, 662{701, 2010.

Lower Bounds on the Exchange-Correlation Energy in Reduced Dimensions

Bounds on the exchange-correlation energy of many-electron systems are derived and tested. By using universal scaling properties of the electron-electron interaction, we obtain the exponent of the bounds in three, two, one, and quasione dimensions. From the properties of the electron gas in the dilute regime, the tightest estimate to date is given for the numerical prefactor of the bound, which is crucial in practical applications. Numerical tests on various low-dimensional systems are in line with the bounds obtained and give evidence of an interesting dimensional crossover between two and one dimensions.

Considerations on the Least Upper Bound for Mixed-Criticality Real-Time Systems

5th Brazilian Symposium on Computing Systems Engineering, SBESC 2015 (SBESC 2015). 3 to 6, Nov, 2015. Foz do Iguaçu, Brasil.

Purification and partial characterization of a midgut membrane-bound alpha-glucosidase from Quesada gigas (Hemiptera: Cicadidae)

Adults of Quesada gigas (Hemiptera: Cicadidae) have a major alpha-glucosidase bound to the perimicrovillar membranes, which are lipoprotein membranes that surround the midgut cell microvilli in Hemiptera and Thysanoptera. Determination of the spatial distribution of alpha-glucosidases in Q. gigas midgut showed that this activity is not equally distributed between soluble and membrane-bound isoforms. The major membrane-bound enzyme was solubilized in the detergent Triton X-100 and purified to homogeneity by means of gel filtration on Sephacryl S-100, and ion-exchange on High Q and Mono Q columns. The purified alpha-glucosidase is a protein with a pH optimum of 6.0 against the synthetic substrate p-nitrophenyl alpha-D-glucoside and M(r) of 61,000 (SDS-PAGE). Taking into account V(Max)/K(M) ratios, the enzyme is more active on maltose than sucrose and prefers oligomaltodextrins up to maltopentaose, with lower efficiency for longer chain maltodextrins. The Q gigas alpha-glucosidase was immunolocalized in perimicrovillar membranes by using a monospecific polyclonal antibody raised against the purified enzyme from Dysdercus peruvianus. The role of this enzyme in xylem fluid digestion and its possible involvement in osmoregulation is discussed. (C) 2009 Elsevier Inc. All rights reserved.

Ionically bound peroxidase from peach fruit

Soluble, ionically bound peroxidase (POD) and polyphenoloxidase (PPO) were extracted from the pulp of peach fruit during ripening at 20degreesC Ionically bound form was purified 6.1 -fold by DEAE-cellulose and Sephadex G-100 chromatography. The purified enzyme showed only one peak of activity on Sephadex G-100 and PAGE revealed that the enzyme was purified by the procedures adopted. The purified enzyme showed a molecular weight of 29000 Da, maximum activity at pH 5.0 and at 40degreesC the calculated apparent activation energy (Ea) for the reaction was 10.04 kcal/mol. The enzyme was heat-labile in the temperature range of 60 to 75degreesC with a fast inactivation at 75degreesC Measurement of residual activity showed a stabilizing effect of sucrose at various temperature/sugar concentrations (0, 10, 20 %, w/w), with an activation energy (Ea) for inactivation increasing with sucrose concentration from 0 to 20% (w/w). The Km and V-max values were 9.35 and 15.38 mM for O-dianisidine and H2O2, respectively. The bound enzyme was inhibited competitively by (.)ferulic, caffeic and protocatechuic acids with different values of Ki,. L-cysteine, p-coumaric and indolacetic acid and Fe++ also inhibited the enzyme but at a lower grade. N-ethylmaleimide and p-CMB were not effective to inhibit the enzyme demonstrating the non-essentiality of SH groups.