Counterexamples to some pointwise estimates of the maximal Cauchy transform in terms of the Cauchy transform

Motivated by the work of Mateu, Orobitg, Pérez and Verdera, who proved inequalities of the form $T_*f\lesssim M(Tf)$ or $T_*f\lesssim M^2(Tf)$ for certain singular integral operators $T$, such as the Hilbert or the Beurling transforms, we study the possibility of establishing this type of control for the Cauchy transform along a Lipschitz graph. We show that this is not possible in general, and we give a partial positive result when the graph is substituted by a Jordan curve.

Al di là del fiume - attraverso il fiume: il basso corso del Ter in Catalogna

La ricerca prende in considerazione dal punto di vista dell’architettura e dell’urbanistica la relazione tra la città e il fiume che la attraversa o la lambisce; l’insediamento umano viene analizzato nel contesto del bacino idrografico al quale appartiene. La ricerca è stata sviluppata in seno alla tesi dottorale ora in fase di elaborazione presso il Departamento de Urbanismo y Ordenación del Territorio dell’Universidad Politecnica de Catalunya. La tesi ha come caso studio il tratto basso del fiume Ter in Catalogna. Nella discussione sul paesaggio urbano contemporaneo oggi la riflessione è centrata sulla città che si territorializza; la dimensione urbana interferisce con gran parte della superficie della terra facendo sfumare le tradizionali distinzioni tra urbano e non-urbano, tra spazio costruito e spazio aperto. In questo contesto, quale termine di conciliazione tra la dinamica naturale e la costruzione storica dei luoghi prodotta dall’intervento umano, il fiume si rivela uno strumento essenziale di analisi e progetto. L’obiettivo di questa ricerca è suggerire un’approssimazione al progetto della città che si sviluppa lungo il corso fluviale costruendo strumenti per la riflessione “attraverso il fiume”. Partendo dall’ipotesi che la città si insedia lungo un corso d’acqua secondo una sintassi territoriale stabilita dalla geografía e dalla geomorfologia del fiume stesso, il fine è fornire strumenti per il processo di recupero degli spazi fluviali in contesti urbanizzati. Il fiume diviene componente geografica chiave degli insediamenti dispersi e risorsa per costruirne l’abitabilità.

Energy partitioning for "fuzzy" atoms

The total energy of molecule in terms of 'fuzzy atoms' presented as sum of one- and two-atomic energy components is described. The divisions of three-dimensional physical space into atomic regions exhibit continuous transition from one to another. The energy components are on chemical energy scale according to proper definitions. The Becke's integration scheme and weight function determines realization of method which permits effective numerical integrations

Aitchison Geometry for Probability and Likelihood as a new approach to mathematical statistics

The Aitchison vector space structure for the simplex is generalized to a Hilbert space structure A2(P) for distributions and likelihoods on arbitrary spaces. Centralnotations of statistics, such as Information or Likelihood, can be identified in the algebraical structure of A2(P) and their corresponding notions in compositional data analysis, such as Aitchison distance or centered log ratio transform.In this way very elaborated aspects of mathematical statistics can be understoodeasily in the light of a simple vector space structure and of compositional data analysis. E.g. combination of statistical information such as Bayesian updating,combination of likelihood and robust M-estimation functions are simple additions/perturbations in A2(Pprior). Weighting observations corresponds to a weightedaddition of the corresponding evidence.Likelihood based statistics for general exponential families turns out to have aparticularly easy interpretation in terms of A2(P). Regular exponential families formfinite dimensional linear subspaces of A2(P) and they correspond to finite dimensionalsubspaces formed by their posterior in the dual information space A2(Pprior).The Aitchison norm can identified with mean Fisher information. The closing constant itself is identified with a generalization of the cummulant function and shown to be Kullback Leiblers directed information. Fisher information is the local geometry of the manifold induced by the A2(P) derivative of the Kullback Leibler information and the space A2(P) can therefore be seen as the tangential geometry of statistical inference at the distribution P.The discussion of A2(P) valued random variables, such as estimation functionsor likelihoods, give a further interpretation of Fisher information as the expected squared norm of evidence and a scale free understanding of unbiased reasoning

Forecasting the effects of global warming on biodiversity

The demand for accurate forecasting of the effects of global warming on biodiversity is growing, but current methods for forecasting have limitations. in this article, we compare and discuss the different uses of four forecasting methods: (1) models that consider species individually, (2) niche-theory models that group species by habitat (more specifically, by environmental conditions under which a species can persist or does persist), (3) general circulation models and coupled ocean-atmosphere-biosphere models, and (4) specics-area curve models that consider all species or large aggregates of species. After outlining the different uses and limitations of these methods, we make eight primary suggestions for improving forecasts. We find that greater use of the fossil record and of modern genetic studies would improve forecasting methods. We note a Quaternary conundrum: While current empirical and theoretical ecological results suggest that many species could be at risk from global warming, during the recent ice ages surprisingly few species became extinct. The potential resolution of this conundrum gives insights into the requirements for more accurate and reliable forecasting. Our eight suggestions also point to constructive synergies in the solution to the different problems.

Bounds on multisecant lines

The purpose of this paper is two fold. First, we give an upper bound on the orderof a multisecant line to an integral arithmetically Cohen-Macaulay subscheme in Pn of codimension two in terms of the Hilbert function. Secondly, we givean explicit description of the singular locus of the blow up of an arbitrary local ring at a complete intersection ideal. This description is used to refine standardlinking theorem. These results are tied together by the construction of sharp examples for the bound, which uses the linking theorems.

A numerical characterization of hypersurface singularities

In this note we give a numerical characterization of hypersurface singularities in terms of the normalized Hilbert-Samuel coefficients, and we interpret this result from the point of view of rigid polynomials.

Robustness of entanglement

In the quest to completely describe entanglement in the general case of a finite number of parties sharing a physical system of finite-dimensional Hilbert space an entanglement magnitude is introduced for its pure and mixed states: robustness. It corresponds to the minimal amount of mixing with locally prepared states which washes out all entanglement. It quantifies in a sense the endurance of entanglement against noise and jamming. Its properties are studied comprehensively. Analytical expressions for the robustness are given for pure states of two-party systems, and analytical bounds for mixed states of two-party systems. Specific results are obtained mainly for the qubit-qubit system (qubit denotes quantum bit). As by-products local pseudomixtures are generalized, a lower bound for the relative volume of separable states is deduced, and arguments for considering convexity a necessary condition of any entanglement measure are put forward.

Generalized adiabatic invariance

In this paper we find the quantities that are adiabatic invariants of any desired order for a general slowly time-dependent Hamiltonian. In a preceding paper, we chose a quantity that was initially an adiabatic invariant to first order, and sought the conditions to be imposed upon the Hamiltonian so that the quantum mechanical adiabatic theorem would be valid to mth order. [We found that this occurs when the first (m - 1) time derivatives of the Hamiltonian at the initial and final time instants are equal to zero.] Here we look for a quantity that is an adiabatic invariant to mth order for any Hamiltonian that changes slowly in time, and that does not fulfill any special condition (its first time derivatives are not zero initially and finally).

Alexandre Sauvaige. L'Etiquette du temps.

Manuscrit orné de dessins à la plume et aux armes de François de Rochechouart, gouverneur du Gênes sous Louis XII. Anciennes collections Mc Carthy, Georges Hilbert, Robert Hoe et comte Paul Durrieu.

Estimating biophysical variable dependences with kernels

This paper introduces a nonlinear measure of dependence between random variables in the context of remote sensing data analysis. The Hilbert-Schmidt Independence Criterion (HSIC) is a kernel method for evaluating statistical dependence. HSIC is based on computing the Hilbert-Schmidt norm of the cross-covariance operator of mapped samples in the corresponding Hilbert spaces. The HSIC empirical estimator is very easy to compute and has good theoretical and practical properties. We exploit the capabilities of HSIC to explain nonlinear dependences in two remote sensing problems: temperature estimation and chlorophyll concentration prediction from spectra. Results show that, when the relationship between random variables is nonlinear or when few data are available, the HSIC criterion outperforms other standard methods, such as the linear correlation or mutual information.

Life design: Un paradigma per la costruzione della vita professionale nel XXI secolo

In questo inizio di secolo, la nuova organizzazione sociale del lavoro pone una serie di domande e di sfide ai ricercatori che intendono aiutare le persone a progettare la loro vita lavorativa. Nell'era della globalizzazione anche per quanto riguarda il career counseling, abbiamo deciso di affrontare queste problematiche e di dare delle risposte che si caratterizzassero come innovative attraverso la costituzione di un forum di discussione internazionale. Si è proceduto in questo modo per evitare le difficoltà che generalmente si incontrano quando si mettono a punto dei modelli e dei metodi in un Paese e poi si esportano in altre culture con l'intento di adattarli alle stesse. Questo articolo presenta i primi risultati della collaborazione che si è registrata - un modello e dei metodi per la consulenza di orientamento. Il modello per l'intervento nell'ambito dell'approccio Life Design si caratterizza per cinque presupposti relativi al modo di vedere le persone e la loro vita lavorativa. Essi riguardano le possibilità contestuali, i processi dinamici, i progressi non-lineari, le molteplici prospettive e la presenza di pattern personali. Partendo da questi cinque presupposti abbiamo messo a punto un modello basato sull'epistemologia del costruzionismo sociale, che sostiene che la conoscenza e l'identità di un individuo sono i prodotti dell'interazione sociale e che il significato è costruito attraverso il discorso. Questo approccio fa riferimento anche alla teoria della costruzione di sé di Guichard (2005) e della costruzione della vita professionale di Savickas (2005), che descrivono le azioni utili a facilitare la progettazione del proprio futuro. Particolare attenzione viene data agli interventi nel corso dell'arco di vita, olistici, contestuali e preventivi.

Cross-frequency coupling in EEG revealed by adaptive oscillation tracking.

Introduction: Neuronal oscillations have been the focus of increasing interest in the neuroscientific community, in part because they have been considered as a possible integrating mechanism through which internal states can influence stimulus processing in a top-down way (Engel et al., 2001). Moreover, increasing evidence indicates that oscillations in different frequency bands interact with one other through coupling mechanisms (Jensen and Colgin, 2007). The existence and the importance of these cross-frequency couplings during various tasks have been verified by recent studies (Canolty et al., 2006; Lakatos et al., 2007). In this study, we measure the strength and directionality of two types of couplings - phase-amplitude couplings and phase-phase couplings - between various bands in EEG data recorded during an illusory contour experiment that were identified using a recently-proposed adaptive frequency tracking algorithm (Van Zaen et al., 2010). Methods: The data used in this study have been taken from a previously published study examining the spatiotemporal mechanisms of illusory contour processing (Murray et al., 2002). The EEG in the present study were from a subset of nine subjects. Each stimulus was composed of 'pac-man' inducers presented in two orientations: IC, when an illusory contour was present, and NC, when no contour could be detected. The signals recorded by the electrodes P2, P4, P6, PO4 and PO6 were averaged, and filtered into the following bands: 4-8Hz, 8-12Hz, 15-25Hz, 35-45Hz, 45-55Hz, 55-65Hz and 65-75Hz. An adaptive frequency tracking algorithm (Van Zaen et al., 2010) was then applied in each band in order to extract the main oscillation and estimate its frequency. This additional step ensures that clean phase information is obtained when taking the Hilbert transform. The frequency estimated by the tracker was averaged over sliding windows and then used to compare the two conditions. Two types of cross-frequency couplings were considered: phase-amplitude couplings and phase-phase couplings. Both types were measured with the phase locking value (PLV, Lachaux et al., 1999) over sliding windows. The phase-amplitude couplings were computed with the phase of the low frequency oscillation and the phase of the amplitude of the high frequency one. Different coupling coefficients were used when measuring phase-phase couplings in order to estimate different m:n synchronizations (4:3, 3:2, 2:1, 3:1, 4:1, 5:1, 6:1, 7:1, 8:1 and 9:1) and to take into account the frequency differences across bands. Moreover, the direction of coupling was estimated with a directionality index (Bahraminasab et al., 2008). Finally, the two conditions IC and NC were compared with ANOVAs with 'subject' as a random effect and 'condition' as a fixed effect. Before computing the statistical tests, the PLV values were transformed into approximately normal variables (Penny et al., 2008). Results: When comparing the mean estimated frequency across conditions, a significant difference was found only in the 4-8Hz band, such that the frequency within this band was significantly higher for IC than NC stimuli starting at ~250ms post-stimulus onset (Fig. 1; solid line shows IC and dashed line NC). Significant differences in phase-amplitude couplings were obtained only when the 4-8 Hz band was taken as the low frequency band. Moreover, in all significant situations, the coupling strength is higher for the NC than IC condition. An example of significant difference between conditions is shown in Fig. 2 for the phase-amplitude coupling between the 4-8Hz and 55-65Hz bands (p-value in top panel and mean PLV values in the bottom panel). A decrease in coupling strength was observed shortly after stimulus onset for both conditions and was greater for the condition IC. This phenomenon was observed with all other frequency bands. The results obtained for the phase-phase couplings were more complex. As for the phase-amplitude couplings, all significant differences were obtained when the 4-8Hz band was considered as the low frequency band. The stimulus condition exhibiting the higher coupling strength depended on the ratio of the coupling coefficients. When this ratio was small, the IC condition exhibited the higher phase-phase coupling strength. When this ratio was large, the NC condition exhibited the higher coupling strength. Fig. 3 shows the phase-phase couplings between the 4-8Hz and 35-45Hz bands for the coupling coefficient 6:1, and the coupling strength was significantly higher for the IC than NC condition. By contrast, for the coupling coefficient 9:1 the NC condition gave the higher coupling strength (Fig. 4). Control analyses verified that it is not a consequence of the frequency difference between the two conditions in the 4-8Hz band. The directionality measures indicated a transfer of information from the low frequency components towards the high frequency ones. Conclusions: Adaptive tracking is a feasible method for EEG analyses, revealing information both about stimulus-related differences and coupling patterns across frequencies. Theta oscillations play a central role in illusory shape processing and more generally in visual processing. The presence vs. absence of illusory shapes was paralleled by faster theta oscillations. Phase-amplitude couplings were decreased more for IC than NC and might be due to a resetting mechanism. The complex patterns in phase-phase coupling between theta and beta/gamma suggest that the contribution of these oscillations to visual binding and stimulus processing are not as straightforward as conventionally held. Causality analyses further suggest that theta oscillations drive beta/gamma oscillations (see also Schroeder and Lakatos, 2009). The present findings highlight the need for applying more sophisticated signal analyses in order to establish a fuller understanding of the functional role of neural oscillations.

The complete genome sequence of the gram-positive bacterium Bacillus subtilis.

Bacillus subtilis is the best-characterized member of the Gram-positive bacteria. Its genome of 4,214,810 base pairs comprises 4,100 protein-coding genes. Of these protein-coding genes, 53% are represented once, while a quarter of the genome corresponds to several gene families that have been greatly expanded by gene duplication, the largest family containing 77 putative ATP-binding transport proteins. In addition, a large proportion of the genetic capacity is devoted to the utilization of a variety of carbon sources, including many plant-derived molecules. The identification of five signal peptidase genes, as well as several genes for components of the secretion apparatus, is important given the capacity of Bacillus strains to secrete large amounts of industrially important enzymes. Many of the genes are involved in the synthesis of secondary metabolites, including antibiotics, that are more typically associated with Streptomyces species. The genome contains at least ten prophages or remnants of prophages, indicating that bacteriophage infection has played an important evolutionary role in horizontal gene transfer, in particular in the propagation of bacterial pathogenesis.