Riesz-Nágy singular functions revisited

In 1952 F. Riesz and Sz.Nágy published an example of a monotonic continuous function whose derivative is zero almost everywhere, that is to say, a singular function. Besides, the function was strictly increasing. Their example was built as the limit of a sequence of deformations of the identity function. As an easy consequence of the definition, the derivative, when it existed and was finite, was found to be zero. In this paper we revisit the Riesz-N´agy family of functions and we relate it to a system for real numberrepresentation which we call (t, t-1) expansions. With the help of these real number expansions we generalize the family. The singularity of the functions is proved through some metrical properties of the expansions used in their definition which also allows us to give a more precise way of determining when the derivative is 0 or infinity.

Programació d'una aplicació gràfica per l'anàlisi de senyals usant LDB (Local Discriminant Bases) i MLDB (Modified LDB)

Tot seguit presentem un entorn per analitzar senyals de tot tipus amb LDB (Local Discriminant Bases) i MLDB (Modified Local Discriminant Bases). Aquest entorn utilitza funcions desenvolupades en el marc d’una tesi en fase de desenvolupament. Per entendre part d’aquestes funcions es requereix un nivell de coneixement avançat de processament de senyals. S’han extret dels treballs realitzats per Naoki Saito [3], que s’han agafat com a punt de partida per la realització de l’algorisme de la tesi doctoral no finalitzada de Jose Antonio Soria. Aquesta interfície desenvolupada accepta la incorporació de nous paquets i funcions. Hem deixat un menú preparat per integrar Sinus IV packet transform i Cosine IV packet transform, tot i que també podem incorporar-n’hi altres. L’aplicació consta de dues interfícies, un Assistent i una interfície principal. També hem creat una finestra per importar i exportar les variables desitjades a diferents entorns. Per fer aquesta aplicació s’han programat tots els elements de les finestres, en lloc d’utilitzar el GUIDE (Graphical User Interface Development Enviroment) de MATLAB, per tal que sigui compatible entre les diferents versions d’aquest programa. En total hem fet 73 funcions en la interfície principal (d’aquestes, 10 pertanyen a la finestra d’importar i exportar) i 23 en la de l’Assistent. En aquest treball només explicarem 6 funcions i les 3 de creació d’aquestes interfícies per no fer-lo excessivament extens. Les funcions que explicarem són les més importants, ja sigui perquè s’utilitzen sovint, perquè, segons la complexitat McCabe, són les més complicades o perquè són necessàries pel processament del senyal. Passem cada entrada de dades per part de l’usuari per funcions que ens detectaran errors en aquesta entrada, com eliminació de zeros o de caràcters que no siguin números, com comprovar que són enters o que estan dins dels límits màxims i mínims que li pertoquen.

Neuroprotective role of PrPC against kainate-induced epileptic seizures and cell death depends on the modulation of JNK3 activation by GluR6/7-PSD-95 binding

Cellular prion protein (PrPC) is a glycosyl-phosphatidylinositol¿anchored glycoprotein. When mutated or misfolded, the pathogenic form (PrPSC) induces transmissible spongiform encephalopathies. In contrast, PrPC has a number of physiological functions in several neural processes. Several lines of evidence implicate PrPC in synaptic transmission and neuroprotection since its absence results in an increase in neuronal excitability and enhanced excitotoxicity in vitro and in vivo. Furthermore, PrPC has been implicated in the inhibition of N-methyl-D-aspartic acid (NMDA)¿mediated neurotransmission, and prion protein gene (Prnp) knockout mice show enhanced neuronal death in response to NMDA and kainate (KA). In this study, we demonstrate that neurotoxicity induced by KA in Prnp knockout mice depends on the c-Jun N-terminal kinase 3 (JNK3) pathway since Prnpo/oJnk3o/o mice were not affected by KA. Pharmacological blockage of JNK3 activity impaired PrPC-dependent neurotoxicity. Furthermore, our results indicate that JNK3 activation depends on the interaction of PrPC with postsynaptic density 95 protein (PSD-95) and glutamate receptor 6/7 (GluR6/7). Indeed, GluR6¿PSD-95 interaction after KA injections was favored by the absence of PrPC. Finally, neurotoxicity in Prnp knockout mice was reversed by an AMPA/KA inhibitor (6,7-dinitroquinoxaline-2,3-dione) and the GluR6 antagonist NS-102. We conclude that the protection afforded by PrPC against KA is due to its ability to modulate GluR6/7-mediated neurotransmission and hence JNK3 activation.

Neuroprotective role of PrPC against kainate-induced epileptic seizures and cell death depends on the modulation of JNK3 activation by GluR6/7-PSD-95 binding

Cellular prion protein (PrPC) is a glycosyl-phosphatidylinositol¿anchored glycoprotein. When mutated or misfolded, the pathogenic form (PrPSC) induces transmissible spongiform encephalopathies. In contrast, PrPC has a number of physiological functions in several neural processes. Several lines of evidence implicate PrPC in synaptic transmission and neuroprotection since its absence results in an increase in neuronal excitability and enhanced excitotoxicity in vitro and in vivo. Furthermore, PrPC has been implicated in the inhibition of N-methyl-D-aspartic acid (NMDA)¿mediated neurotransmission, and prion protein gene (Prnp) knockout mice show enhanced neuronal death in response to NMDA and kainate (KA). In this study, we demonstrate that neurotoxicity induced by KA in Prnp knockout mice depends on the c-Jun N-terminal kinase 3 (JNK3) pathway since Prnpo/oJnk3o/o mice were not affected by KA. Pharmacological blockage of JNK3 activity impaired PrPC-dependent neurotoxicity. Furthermore, our results indicate that JNK3 activation depends on the interaction of PrPC with postsynaptic density 95 protein (PSD-95) and glutamate receptor 6/7 (GluR6/7). Indeed, GluR6¿PSD-95 interaction after KA injections was favored by the absence of PrPC. Finally, neurotoxicity in Prnp knockout mice was reversed by an AMPA/KA inhibitor (6,7-dinitroquinoxaline-2,3-dione) and the GluR6 antagonist NS-102. We conclude that the protection afforded by PrPC against KA is due to its ability to modulate GluR6/7-mediated neurotransmission and hence JNK3 activation.

Energy and structure of dilute hard- and soft-sphere gases

The energy and structure of dilute hard- and soft-sphere Bose gases are systematically studied in the framework of several many-body approaches, such as the variational correlated theory, the Bogoliubov model, and the uniform limit approximation, valid in the weak-interaction regime. When possible, the results are compared with the exact diffusion Monte Carlo ones. Jastrow-type correlation provides a good description of the systems, both hard- and soft-spheres, if the hypernetted chain energy functional is freely minimized and the resulting Euler equation is solved. The study of the soft-sphere potentials confirms the appearance of a dependence of the energy on the shape of the potential at gas paremeter values of x~0.001. For quantities other than the energy, such as the radial distribution functions and the momentum distributions, the dependence appears at any value of x. The occurrence of a maximum in the radial distribution function, in the momentum distribution, and in the excitation spectrum is a natural effect of the correlations when x increases. The asymptotic behaviors of the functions characterizing the structure of the systems are also investigated. The uniform limit approach is very easy to implement and provides a good description of the soft-sphere gas. Its reliability improves when the interaction weakens.

Nonempirical cluster-model study of the chemisorption of atomic hydrogen on the (111) surface of diamondlike crystals

The interaction of atomic hydrogen with C4H9, Si4H9, and Ge4H9 model clusters has been studied using all-electron and pseudopotential ab initio Hartree-Fock computations with basis sets of increasing flexibility. The results show that the effect of polarization functions is important in order to reproduce the experimental findings, but their inclusion only for the atoms directly involved in the chemisorption bond is usually sufficient. For the systems H-C4H9 and H-Si4H9 all-electron and pseudopotential results are in excellent agreement when basis sets of comparable quality are used. Besides, semiempirical modified-neglect-of-differential-overlap computations provide quite reliable results both for diamond and silicon and have been used to investigate larger model clusters. The results confirm the local nature of chemisorption and further justify the use of minimal X4H9 model clusters.

Ab initio cluster-model study of the on-top chemisorption of F and Cl on Si(111) and Ge(111) surfaces

The interaction of atomic F and Cl with Si4H9 and Ge4H9 cluster models has been studied by using ab initio pseudopotentials and basis sets of increasing complexity. The results show that the effect of d orbitals is important in order to reproduce the experimental findings. However, the use of polarization functions in the atoms which are directly involved in the chemisorption bond leads to results which are very close to those obtained using extended basis sets. The local nature of the chemisorption bond is also interpreted by means of a Mulliken population analysis. For F-Si4H9 and Cl-Si4H9 the present results are in good agreement with previous ab initio all-electron calculations, and for the chemisorption of Cl on Si(111) and Ge(111) surfaces, good agreement is found with respect to the available experimental results as well as with previous slab calculations based on the local-density-functional formalism.

On the relationship between connections and the asymptotic properties of predictive distributions

In a recent paper, Komaki studied the second-order asymptotic properties of predictive distributions, using the Kullback-Leibler divergence as a loss function. He showed that estimative distributions with asymptotically efficient estimators can be improved by predictive distributions that do not belong to the model. The model is assumed to be a multidimensional curved exponential family. In this paper we generalize the result assuming as a loss function any f divergence. A relationship arises between alpha connections and optimal predictive distributions. In particular, using an alpha divergence to measure the goodness of a predictive distribution, the optimal shift of the estimate distribution is related to alpha-covariant derivatives. The expression that we obtain for the asymptotic risk is also useful to study the higher-order asymptotic properties of an estimator, in the mentioned class of loss functions.

R functions for quantifying nonindependence in standard dyadic and SRM designs

Interdependence is the main feature of dyadic relationships and, in recent years, various statistical procedures have been proposed for quantifying and testing this social attribute in different dyadic designs. The purpose of this paper is to develop several functions for this kind of statistical tests in an R package, known as nonindependence, for use by applied social researchers. A Graphical User Interface (GUI) is also developed to facilitate the use of the functions included in this package. Examples drawn from psychological research and simulated data are used to illustrate how the software works.

Cardiac motion estimation by joint alignment of tagged MRI sequences

Image registration has been proposed as an automatic method for recovering cardiac displacement fields from Tagged Magnetic Resonance Imaging (tMRI) sequences. Initially performed as a set of pairwise registrations, these techniques have evolved to the use of 3D+t deformation models, requiring metrics of joint image alignment (JA). However, only linear combinations of cost functions defined with respect to the first frame have been used. In this paper, we have applied k-Nearest Neighbors Graphs (kNNG) estimators of the -entropy (H ) to measure the joint similarity between frames, and to combine the information provided by different cardiac views in an unified metric. Experiments performed on six subjects showed a significantly higher accuracy (p < 0.05) with respect to a standard pairwise alignment (PA) approach in terms of mean positional error and variance with respect to manually placed landmarks. The developed method was used to study strains in patients with myocardial infarction, showing a consistency between strain, infarction location, and coronary occlusion. This paper also presentsan interesting clinical application of graph-based metric estimators, showing their value for solving practical problems found in medical imaging.

Bandlimited Lipschitz functions

We study the space of bandlimited Lipschitz functions in one variable. In particular we provide a geometrical description of interpolating and sampling sequences for this space. We also give a description of the trace of such functions to sequences of critical density in terms of a cancellation condition.

Characterization of an antennal carboxylesterase from the pest moth Spodoptera littoralis degrading a host plant odorant.

Background: Carboxyl/cholinesterases (CCEs) are highly diversified in insects. These enzymes have a broad range of proposed functions, in neuro/developmental processes, dietary detoxification, insecticide resistance or hormone/pheromone degradation. As few functional data are available on purified or recombinant CCEs, the physiological role of most of these enzymes is unknown. Concerning their role in olfaction, only two CCEs able to metabolize sex pheromones have been functionally characterized in insects. These enzymes are only expressed in the male antennae, and secreted into the lumen of the pheromone-sensitive sensilla. CCEs able to hydrolyze other odorants than sex pheromones, such as plant volatiles, have not been identified. Methodology: In Spodoptera littoralis, a major crop pest, a diversity of antennal CCEs has been previously identified. We have employed here a combination of molecular biology, biochemistry and electrophysiology approaches to functionally characterize an intracellular CCE, SlCXE10, whose predominant expression in the olfactory sensilla suggested a role in olfaction. A recombinant protein was produced using the baculovirus system and we tested its catabolic properties towards a plant volatile and the sex pheromone components. Conclusion: We showed that SlCXE10 could efficiently hydrolyze a green leaf volatile and to a lesser extent the sex pheromone components. The transcript level in male antennae was also strongly induced by exposure to this plant odorant. In antennae, SlCXE10 expression was associated with sensilla responding to the sex pheromones and to plant odours. These results suggest that a CCE-based intracellular metabolism of odorants could occur in insect antennae, in addition to the extracellular metabolism occurring within the sensillar lumen. This is the first functional characterization of an Odorant- Degrading Enzyme active towards a host plant volatile.

Integrated regulation of the type III secretion system and other virulence determinants in Ralstonia solanacearum

In many plant and animal bacterial pathogens, the Type III secretion system (TTSS) that directly translocates effector proteins into the eukaryotic host cells is essential for the development of disease. In all species studied, the transcription of the TTSS and most of its effector substrates is tightly regulated by a succession of consecutively activated regulators. However, the whole genetic programme driven by these regulatory cascades is still unknown, especially in bacterial plant pathogens. Here, we have characterised the programme triggered by HrpG, a host-responsive regulator of the TTSS activation cascade in the plant pathogen Ralstonia solanacearum. We show through genome-wide expression analysis that, in addition to the TTSS, HrpG controls the expression of a previously undescribed TTSS-independent pathway that includes a number of other virulence determinants and genes likely involved in adaptation to life in the host. Functional studies revealed that this second pathway co-ordinates the bacterial production of plant cell wall-degrading enzymes, exopolysaccharide, and the phytohormones ethylene and auxin. We provide experimental evidence that these activities contribute to pathogenicity. We also show that the ethylene produced by R. solanacearum is able to modulate the expression of host genes and can therefore interfere with the signalling of plant defence responses. These results provide a new, integrated view of plant bacterial pathogenicity, where a common regulator activates synchronously upon infection the TTSS, other virulence determinants and a number of adaptive functions, which act co-operatively to cause disease.

Consequences of lineage-specific gene loss on functional evolution of surviving paralogs: ALDH1A and retinoic acid signaling in vertebrate genomes

Genome duplications increase genetic diversity and may facilitate the evolution of gene subfunctions. Little attention, however, has focused on the evolutionary impact of lineage-specific gene loss. Here, we show that identifying lineage-specific gene loss after genome duplication is important for understanding the evolution of gene subfunctions in surviving paralogs and for improving functional connectivity among human and model organism genomes. We examine the general principles of gene loss following duplication, coupled with expression analysis of the retinaldehyde dehydrogenase Aldh1a gene family during retinoic acid signaling in eye development as a case study. Humans have three ALDH1A genes, but teleosts have just one or two. We used comparative genomics and conserved syntenies to identify loss of ohnologs (paralogs derived from genome duplication) and to clarify uncertain phylogenies. Analysis showed that Aldh1a1 and Aldh1a2 form a clade that is sister to Aldh1a3-related genes. Genome comparisons showed secondarily loss of aldh1a1 in teleosts, revealing that Aldh1a1 is not a tetrapod innovation and that aldh1a3 was recently lost in medaka, making it the first known vertebrate with a single aldh1a gene. Interestingly, results revealed asymmetric distribution of surviving ohnologs between co-orthologous teleost chromosome segments, suggesting that local genome architecture can influence ohnolog survival. We propose a model that reconstructs the chromosomal history of the Aldh1a family in the ancestral vertebrate genome, coupled with the evolution of gene functions in surviving Aldh1a ohnologs after R1, R2, and R3 genome duplications. Results provide evidence for early subfunctionalization and late subfunction-partitioning and suggest a mechanistic model based on altered regulation leading to heterochronic gene expression to explain the acquisition or modification of subfunctions by surviving ohnologs that preserve unaltered ancestral developmental programs in the face of gene loss.

Music-supported training is more efficient than functional motor training for recovery of fine motor skills in stroke patients

MOTOR IMPAIRMENTS ARE COMMON AFTER STROKE but efficacious therapies for these dysfunctions are scarce. Extending an earlier study on the effects of music-supported training (MST), behavioral indices of motor function were obtained before and after a series of training sessions to assess whether this new treatment leads to improved motor functions. Furthermore, music-supported training was contrasted to functional motor training according to the principles of constraint-induced therapy (CIT). In addition to conventional physiotherapy, 32 stroke patients with moderately impaired motor function and no previous musical experience received 15 sessions of MST over a period of three weeks, using a manualized, step-bystep approach. A control group consisting of 15 patients received 15 sessions of CIT in addition to conventional physiotherapy. A third group of 30 patients received exclusively conventional physiotherapy and served as a control group for the other three groups. Fine as well as gross motor skills were trained by using either a MIDI-piano or electronic drum pads programmed to emit piano tones. Motor functions were assessed by an extensive test battery. MST yielded significant improvement in fine as well as gross motor skills with respect to speed, precision, and smoothness of movements. These improvements were greater than after CIT or conventional physiotherapy. In conclusion, with equal treatment intensity, MST leads to more pronounced improvements of motor functions after stroke than CIT.