Spectral synthesis for Banach Algebras II

This paper continues the study of spectral synthesis and the topologies tau-infinity and tau-r on the ideal space of a Banach algebra, concentrating particularly on the class of Haagerup tensor products of C*-algebras. For this class, it is shown that spectral synthesis is equivalent to the Hausdorffness of tau_infinity. Under a weak extra condition, spectral synthesis is shown to be equivalent to the Hausdorffness of tau_r.

Operatory kompozycji i miary Carlesona w teorii przestrzeni Hardy’ego-Orlicza na obszarach

Wydział Matematyki i Informatyki: Zakład Teorii Interpolacji i Aproksymacji

Solutions of Tikhonov functional equations and applications to multiplication operators on Szegö spaces

We consider a natural representation of solutions for Tikhonov functional equations. This will be done by applying the theory of reproducing kernels to the approximate solutions of general bounded linear operator equations (when defined from reproducing kernel Hilbert spaces into general Hilbert spaces), by using the Hilbert-Schmidt property and tensor product of Hilbert spaces. As a concrete case, we shall consider generalized fractional functions formed by the quotient of Bergman functions by Szegö functions considered from the multiplication operators on the Szegö spaces.

A space-time hybrid hourly rainfall model for derived flood frequency analysis

For derived flood frequency analysis based on hydrological modelling long continuous precipitation time series with high temporal resolution are needed. Often, the observation network with recording rainfall gauges is poor, especially regarding the limited length of the available rainfall time series. Stochastic precipitation synthesis is a good alternative either to extend or to regionalise rainfall series to provide adequate input for long-term rainfall-runoff modelling with subsequent estimation of design floods. Here, a new two step procedure for stochastic synthesis of continuous hourly space-time rainfall is proposed and tested for the extension of short observed precipitation time series. First, a single-site alternating renewal model is presented to simulate independent hourly precipitation time series for several locations. The alternating renewal model describes wet spell durations, dry spell durations and wet spell intensities using univariate frequency distributions separately for two seasons. The dependence between wet spell intensity and duration is accounted for by 2-copulas. For disaggregation of the wet spells into hourly intensities a predefined profile is used. In the second step a multi-site resampling procedure is applied on the synthetic point rainfall event series to reproduce the spatial dependence structure of rainfall. Resampling is carried out successively on all synthetic event series using simulated annealing with an objective function considering three bivariate spatial rainfall characteristics. In a case study synthetic precipitation is generated for some locations with short observation records in two mesoscale catchments of the Bode river basin located in northern Germany. The synthetic rainfall data are then applied for derived flood frequency analysis using the hydrological model HEC-HMS. The results show good performance in reproducing average and extreme rainfall characteristics as well as in reproducing observed flood frequencies. The presented model has the potential to be used for ungauged locations through regionalisation of the model parameters.

On the size of the fibers of spectral maps induced by semialgebraic embeddings

Let S(M) be the ring of (continuous) semialgebraic functions on a semialgebraic set M and S*(M) its subring of bounded semialgebraic functions. In this work we compute the size of the fibers of the spectral maps Spec(j)1:Spec(S(N))→Spec(S(M)) and Spec(j)2:Spec(S*(N))→Spec(S*(M)) induced by the inclusion j:N M of a semialgebraic subset N of M. The ring S(M) can be understood as the localization of S*(M) at the multiplicative subset WM of those bounded semialgebraic functions on M with empty zero set. This provides a natural inclusion iM:Spec(S(M)) Spec(S*(M)) that reduces both problems above to an analysis of the fibers of the spectral map Spec(j)2:Spec(S*(N))→Spec(S*(M)). If we denote Z:=ClSpec(S*(M))(M N), it holds that the restriction map Spec(j)2|:Spec(S*(N)) Spec(j)2-1(Z)→Spec(S*(M)) Z is a homeomorphism. Our problem concentrates on the computation of the size of the fibers of Spec(j)2 at the points of Z. The size of the fibers of prime ideals "close" to the complement Y:=M N provides valuable information concerning how N is immersed inside M. If N is dense in M, the map Spec(j)2 is surjective and the generic fiber of a prime ideal p∈Z contains infinitely many elements. However, finite fibers may also appear and we provide a criterium to decide when the fiber Spec(j)2-1(p) is a finite set for p∈Z. If such is the case, our procedure allows us to compute the size s of Spec(j)2-1(p). If in addition N is locally compact and M is pure dimensional, s coincides with the number of minimal prime ideals contained in p. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Modular continuous crystallizer: operation, experimental arrangement and identification of process parameters

Crystallization is employed in different industrial processes. The method and operation can differ depending on the nature of the substances involved. The aim of this study is to examine the effect of various operating conditions on the crystal properties in a chemical engineering design window with a focus on ultrasound assisted cooling crystallization. Batch to batch variations, minimal manufacturing steps and faster production times are factors which continuous crystallization seeks to resolve. Continuous processes scale-up is considered straightforward compared to batch processes owing to increase of processing time in the specific reactor. In cooling crystallization process, ultrasound can be used to control the crystal properties. Different model compounds were used to define the suitable process parameters for the modular crystallizer using equal operating conditions in each module. A final temperature of 20oC was employed in all experiments while the operating conditions differed. The studied process parameters and configuration of the crystallizer were manipulated to achieve a continuous operation without crystal clogging along the crystallization path. The results from the continuous experiment were compared with the batch crystallization results and analysed using the Malvern Morphologi G3 instrument to determine the crystal morphology and CSD. The modular crystallizer was operated successfully with three different residence times. At optimal process conditions, a longer residence time gives smaller crystals and narrower CSD. Based on the findings, at a constant initial solution concentration, the residence time had clear influence on crystal properties. The equal supersaturation criterion in each module offered better results compared to other cooling profiles. The combination of continuous crystallization and ultrasound has large potential to overcome clogging, obtain reproducible and narrow CSD, specific crystal morphologies and uniform particle sizes, and exclusion of milling stages in comparison to batch processes.

On the construction of new bent functions from the max-weight and min-weight functions of old bent functions

Given a bent function f (x) of n variables, its max-weight and min-weight functions are introduced as the Boolean functions f + (x) and f − (x) whose supports are the sets {a ∈ Fn2 | w( f ⊕la) = 2n−1+2 n 2 −1} and {a ∈ Fn2 | w( f ⊕la) = 2n−1−2 n 2 −1} respectively, where w( f ⊕ la) denotes the Hamming weight of the Boolean function f (x) ⊕ la(x) and la(x) is the linear function defined by a ∈ Fn2 . f + (x) and f − (x) are proved to be bent functions. Furthermore, combining the 4 minterms of 2 variables with the max-weight or min-weight functions of a 4-tuple ( f0(x), f1(x), f2(x), f3(x)) of bent functions of n variables such that f0(x) ⊕ f1(x) ⊕ f2(x) ⊕ f3(x) = 1, a bent function of n + 2 variables is obtained. A family of 4-tuples of bent functions satisfying the above condition is introduced, and finally, the number of bent functions we can construct using the method introduced in this paper are obtained. Also, our construction is compared with other constructions of bent functions.

Multivariate orthogonal polynomials and integrable systems

Multivariate orthogonal polynomials in D real dimensions are considered from the perspective of the Cholesky factorization of a moment matrix. The approach allows for the construction of corresponding multivariate orthogonal polynomials, associated second kind functions, Jacobi type matrices and associated three term relations and also Christoffel-Darboux formulae. The multivariate orthogonal polynomials, their second kind functions and the corresponding Christoffel-Darboux kernels are shown to be quasi-determinants as well as Schur complements of bordered truncations of the moment matrix; quasi-tau functions are introduced. It is proven that the second kind functions are multivariate Cauchy transforms of the multivariate orthogonal polynomials. Discrete and continuous deformations of the measure lead to Toda type integrable hierarchy, being the corresponding flows described through Lax and Zakharov-Shabat equations; bilinear equations are found. Varying size matrix nonlinear partial difference and differential equations of the 2D Toda lattice type are shown to be solved by matrix coefficients of the multivariate orthogonal polynomials. The discrete flows, which are shown to be connected with a Gauss-Borel factorization of the Jacobi type matrices and its quasi-determinants, lead to expressions for the multivariate orthogonal polynomials and their second kind functions in terms of shifted quasi-tau matrices, which generalize to the multidimensional realm, those that relate the Baker and adjoint Baker functions to ratios of Miwa shifted tau-functions in the 1D scenario. In this context, the multivariate extension of the elementary Darboux transformation is given in terms of quasi-determinants of matrices built up by the evaluation, at a poised set of nodes lying in an appropriate hyperplane in R^D, of the multivariate orthogonal polynomials. The multivariate Christoffel formula for the iteration of m elementary Darboux transformations is given as a quasi-determinant. It is shown, using congruences in the space of semi-infinite matrices, that the discrete and continuous flows are intimately connected and determine nonlinear partial difference-differential equations that involve only one site in the integrable lattice behaving as a Kadomstev-Petviashvili type system. Finally, a brief discussion of measures with a particular linear isometry invariance and some of its consequences for the corresponding multivariate polynomials is given. In particular, it is shown that the Toda times that preserve the invariance condition lay in a secant variety of the Veronese variety of the fixed point set of the linear isometry.

Average-case analysis of power consumption in embedded systems

Power efficiency is one of the most important constraints in the design of embedded systems since such systems are generally driven by batteries with limited energy budget or restricted power supply. In every embedded system, there are one or more processor cores to run the software and interact with the other hardware components of the system. The power consumption of the processor core(s) has an important impact on the total power dissipated in the system. Hence, the processor power optimization is crucial in satisfying the power consumption constraints, and developing low-power embedded systems. A key aspect of research in processor power optimization and management is “power estimation”. Having a fast and accurate method for processor power estimation at design time helps the designer to explore a large space of design possibilities, to make the optimal choices for developing a power efficient processor. Likewise, understanding the processor power dissipation behaviour of a specific software/application is the key for choosing appropriate algorithms in order to write power efficient software. Simulation-based methods for measuring the processor power achieve very high accuracy, but are available only late in the design process, and are often quite slow. Therefore, the need has arisen for faster, higher-level power prediction methods that allow the system designer to explore many alternatives for developing powerefficient hardware and software. The aim of this thesis is to present fast and high-level power models for the prediction of processor power consumption. Power predictability in this work is achieved in two ways: first, using a design method to develop power predictable circuits; second, analysing the power of the functions in the code which repeat during execution, then building the power model based on average number of repetitions. In the first case, a design method called Asynchronous Charge Sharing Logic (ACSL) is used to implement the Arithmetic Logic Unit (ALU) for the 8051 microcontroller. The ACSL circuits are power predictable due to the independency of their power consumption to the input data. Based on this property, a fast prediction method is presented to estimate the power of ALU by analysing the software program, and extracting the number of ALU-related instructions. This method achieves less than 1% error in power estimation and more than 100 times speedup in comparison to conventional simulation-based methods. In the second case, an average-case processor energy model is developed for the Insertion sort algorithm based on the number of comparisons that take place in the execution of the algorithm. The average number of comparisons is calculated using a high level methodology called MOdular Quantitative Analysis (MOQA). The parameters of the energy model are measured for the LEON3 processor core, but the model is general and can be used for any processor. The model has been validated through the power measurement experiments, and offers high accuracy and orders of magnitude speedup over the simulation-based method.

Design of experiment in drug development: optimal allocations in multi-arm clinical trials and design space for multi-step processes

In this thesis, we deal with the design of experiments in the drug development process, focusing on the design of clinical trials for treatment comparisons (Part I) and the design of preclinical laboratory experiments for proteins development and manufacturing (Part II). In Part I we propose a multi-purpose design methodology for sequential clinical trials. We derived optimal allocations of patients to treatments for testing the efficacy of several experimental groups by also taking into account ethical considerations. We first consider exponential responses for survival trials and we then present a unified framework for heteroscedastic experimental groups that encompasses the general ANOVA set-up. The very good performance of the suggested optimal allocations, in terms of both inferential and ethical characteristics, are illustrated analytically and through several numerical examples, also performing comparisons with other designs proposed in the literature. Part II concerns the planning of experiments for processes composed of multiple steps in the context of preclinical drug development and manufacturing. Following the Quality by Design paradigm, the objective of the multi-step design strategy is the definition of the manufacturing design space of the whole process and, as we consider the interactions among the subsequent steps, our proposal ensures the quality and the safety of the final product, by enabling more flexibility and process robustness in the manufacturing.

Task analysis for HMI design. Level of automation study of aircraft navigation functions

Advancements in technology have enabled increasingly sophisticated automation to be introduced into the flight decks of modern aircraft. Generally, this automation was added to accomplish worthy objectives such as reducing flight crew workload, adding additional capability, or increasing fuel economy. Automation is necessary due to the fact that not all of the functions required for mission accomplishment in today’s complex aircraft are within the capabilities of the unaided human operator, who lacks the sensory capacity to detect much of the information required for flight. To a large extent, these objectives have been achieved. Nevertheless, despite all the benefits from the increasing amounts of highly reliable automation, vulnerabilities do exist in flight crew management of automation and Situation Awareness (SA). Issues associated with flight crew management of automation include: • Pilot understanding of automation’s capabilities, limitations, modes, and operating principles and techniques. • Differing pilot decisions about the appropriate automation level to use or whether to turn automation on or off when they get into unusual or emergency situations. • Human-Machine Interfaces (HMIs) are not always easy to use, and this aspect could be problematic when pilots experience high workload situations. • Complex automation interfaces, large differences in automation philosophy and implementation among different aircraft types, and inadequate training also contribute to deficiencies in flight crew understanding of automation.

Deploying and processing neural representations of signals

Neural representations (NR) have emerged in the last few years as a powerful tool to represent signals from several domains, such as images, 3D shapes, or audio. Indeed, deep neural networks have been shown capable of approximating continuous functions that describe a given signal with theoretical infinite resolution. This finding allows obtaining representations whose memory footprint is fixed and decoupled from the resolution at which the underlying signal can be sampled, something that is not possible with traditional discrete representations, e.g., grids of pixels for images or voxels for 3D shapes. During the last two years, many techniques have been proposed to improve the capability of NR to approximate high-frequency details and to make the optimization procedures required to obtain NR less demanding both in terms of time and data requirements, motivating many researchers to deploy NR as the main form of data representation for complex pipelines. Following this line of research, we first show that NR can approximate precisely Unsigned Distance Functions, providing an effective way to represent garments that feature open 3D surfaces and unknown topology. Then, we present a pipeline to obtain in a few minutes a compact Neural Twin® for a given object, by exploiting the recent advances in modeling neural radiance fields. Furthermore, we move a step in the direction of adopting NR as a standalone representation, by considering the possibility of performing downstream tasks by processing directly the NR weights. We first show that deep neural networks can be compressed into compact latent codes. Then, we show how this technique can be exploited to perform deep learning on implicit neural representations (INR) of 3D shapes, by only looking at the weights of the networks.

The Effect Of Celastrol, A Triterpene With Antitumorigenic Activity, On Conformational And Functional Aspects Of The Human 90kda Heat Shock Protein Hsp90α, A Chaperone Implicated In The Stabilization Of The Tumor Phenotype.

Hsp90 is a molecular chaperone essential for cell viability in eukaryotes that is associated with the maturation of proteins involved in important cell functions and implicated in the stabilization of the tumor phenotype of various cancers, making this chaperone a notably interesting therapeutic target. Celastrol is a plant-derived pentacyclic triterpenoid compound with potent antioxidant, anti-inflammatory and anticancer activities; however, celastrol's action mode is still elusive. In this work, we investigated the effect of celastrol on the conformational and functional aspects of Hsp90α. Interestingly, celastrol appeared to target Hsp90α directly as the compound induced the oligomerization of the chaperone via the C-terminal domain as demonstrated by experiments using a deletion mutant. The nature of the oligomers was investigated by biophysical tools demonstrating that a two-fold excess of celastrol induced the formation of a decameric Hsp90α bound throughout the C-terminal domain. When bound, celastrol destabilized the C-terminal domain. Surprisingly, standard chaperone functional investigations demonstrated that neither the in vitro chaperone activity of protecting against aggregation nor the ability to bind a TPR co-chaperone, which binds to the C-terminus of Hsp90α, were affected by celastrol. Celastrol interferes with specific biological functions of Hsp90α. Our results suggest a model in which celastrol binds directly to the C-terminal domain of Hsp90α causing oligomerization. However, the ability to protect against protein aggregation (supported by our results) and to bind to TPR co-chaperones are not affected by celastrol. Therefore celastrol may act primarily by inducing specific oligomerization that affects some, but not all, of the functions of Hsp90α. To the best of our knowledge, this study is the first work to use multiple probes to investigate the effect that celastrol has on the stability and oligomerization of Hsp90α and on the binding of this chaperone to Tom70. This work provides a novel mechanism by which celastrol binds Hsp90α.

A metalinguagem como lugar da interpretação: terminologia e bases de dados informatizadas

The main objective of this work is to discuss the notion of metalanguage concerning the use of thesaurus (symbols systems, functions indicators, descriptors) utilized by indexers for article representation in computerized bibliographical databases. Our corpus comprises article abstracts and bibliographical database descriptors LILACS (Literatura Latino-Americana em Ciências da Saúde) and SOCIOFILE Sociological Abstracts. We aim at clarifying the effects of subjectivity in the functioning of indexing taking account the grounds for interpretation that allow different meanings.

A descriptive analysis of the seasonal variation of physical oceanographic characteristics in the northern region of the Todos os Santos Bay (Bahia, Brazil)

The results obtained in the August and December 2003, August 2004 and January 2005 oceanographic campaigns in the northern region of the Todos os Santos Bay (lat. 12º44.5'S; long. 038º35.00'W) between the Madre de Deus and Maré islands are analyzed. Instruments of continuous and discrete samplings were used to measure hydrographic properties currents and tides. The water mass of the northern region of the bay is forced by semidiurnal and mesotides of form number 0.08 and the lunar component M2 height was estimated at 91cm. The time series of the surface currents indicated movements in the N/S direction, forced by the tide with maximum magnitudes of 0.73 m.s-1 on the December 2003 campaign. However, in August 2004 the currents were dominated by the wind stress forcing, with a maximum speed of 1.85 m.s-1 and SE direction. Near the bottom, the influence of the tide is not as evident, with a decrease in intensity due to internal and bottom friction, with a maximum velocity of 0.17 m.s-1. The thermal and haline structures were weakly horizontally, as well as vertically stratified, with extreme values varying in the intervals 23ºC (August, 2004) to 28ºC (December, 2003) and 31.0 psu (August, 2003) to 36.0 psu (December, 2003), respectively. Some conclusions may be drawn from these results: i) The signs of the dilution of the fresh water discharges of the Caípe, Mataripe and São Paulo rivers in the region under the influence of the RLAM were observed only during the winter periods, but in the summer the region was flooded by waters of oceanic origin and the salinities above 36.0 indicated TW mass intrusion; ii) The N-S circulation near the RLAM is strongly dominated by the tide, and the importance of the M2 component was unequivocal, however, the E-W component presented some tidal modulation away from abrupt bottom topographical changes, and iii) The residual series, calculated as the difference between the original and modeled, is about ¼ of the original and confirmed its semidiurnal character.