Explosion of smoothness from a point to everywhere for conjugacies between Markov families

For uniformly asymptotically affine (uaa) Markov maps on train tracks, we prove the following type of rigidity result: if a topological conjugacy between them is (uaa) at a point in the train track then the conjugacy is (uaa) everywhere. In particular, our methods apply to the case in which the domains of the Markov maps are Canter sets. We also present similar statements for (uaa:) and C-r Markov families. These results generalize the similar ones of Sullivan and de Faria for C-r expanding circle maps with r > 1 and have useful applications to hyperbolic dynamics on surfaces and laminations.

Hausdorff dimension bounds for smoothness of holonomies for codimension 1 hyperbolic dynamics

We prove that the stable holonomies of a proper codimension 1 attractor Λ, for a Cr diffeomorphism f of a surface, are not C1+θ for θ greater than the Hausdorff dimension of the stable leaves of f intersected with Λ. To prove this result we show that there are no diffeomorphisms of surfaces, with a proper codimension 1 attractor, that are affine on a neighbourhood of the attractor and have affine stable holonomies on the attractor.

Explosion of smoothness from a point to everywhere for conjugacies between diffeomorphisms on surfaces

For diffeomorphisms on surfaces with basic sets, we show the following type of rigidity result: if a topological conjugacy between them is differentiable at a point in the basic set then the conjugacy has a smooth extension to the surface. These results generalize the similar ones of D. Sullivan, E. de Faria and ours for one-dimensional expanding dynamics.

Hausdorff dimension versus smoothness

There is a one-to-one correspondence between C1+H Cantor exchange systems that are C1+H fixed points of renormalization and C1+H diffeomorphisms f on surfaces with a codimension 1 hyperbolic attractor Λ that admit an invariant measure absolutely continuous with respect to the Hausdorff measure on Λ. However, there is no such C1+α Cantor exchange system with bounded geometry that is a C1+α fixed point of renormalization with regularity α greater than the Hausdorff dimension of its invariant Cantor set. The proof of the last result uses that the stable holonomies of a codimension 1 hyperbolic attractor Λ are not C1+θ for θ greater than the Hausdorff dimension of the stable leaves of f intersected with Λ.

On moduli of smoothness of fractional order

In this paper we consider the properties of moduli of smoothness of fractional order. The main result of the paper describes the equivalence of the modulus of smoothness and a function from some class.

Moduli of smoothness and rate of a.e. convergence for some convolution operators

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Moduli of smoothness and growth properties of Fourier transforms: two-sided estimates

We prove two-sided inequalities between the integral moduli of smoothness of a function on R d[superscript] / T d[superscript] and the weighted tail-type integrals of its Fourier transform/series. Sharpness of obtained results in particular is given by the equivalence results for functions satisfying certain regular conditions. Applications include a quantitative form of the Riemann-Lebesgue lemma as well as several other questions in approximation theory and the theory of function spaces.

Evaluation of Lightweight Profilers for Construction Smoothness Evaluation, MLR-02-02, 2004

High-speed non-contact laser profilers have become the standard testing equipment for pavement management ride quality testing. The same technology used in the high-speed profilers is now being used in lightweight profilers for construction smoothness testing. The lightweight profilers have many advantages over the California 25-ft profilograph. Despite the many advantages of the lightweight profilers, there is resistance from the contracting industry toward eliminating the 25-ft profilograph for construction ride testing. One way to reduce or overcome the resistance is to evaluate and demonstrate the advantages/disadvantages of the lightweight profiler in actual field use in Iowa. The objective of the study was to purchase a lightweight profiler and to evaluate its suitability for construction smoothness quality verification and quality acceptance on Iowa projects. A lightweight profiler, an Ames Engineering, Inc. LISA single laser unit, was received in February 2003 for the study. Based on the work done during the 2003 construction season, the following conclusions can be made: (1) For hot mix asphalt surfaces, the LISA correlated well with the contractors' profilographs; (2) LISA results are significantly affected by longitudinal tining on portland cement concrete pavements, requiring a laser system upgrade to give accurate results; (3) A significant timesaving was realized by using the LISA; (4) Increasing visibility and reducing time in the construction zone improved safety; (5) One person with limited lifting capabilities could set up and operate the LISA; and (6) With the current Iowa Department of Transportation specification, the LISA cannot totally replace the profilograph, since bridges and short segments with no adjoining pavement would still require a profilograph.

Smoothness of scale functions for spectrally negative Lévy processes

Scale functions play a central role in the fluctuation theory of spectrally negative Lévy processes and often appear in the context of martingale relations. These relations are often require excursion theory rather than Itô calculus. The reason for the latter is that standard Itô calculus is only applicable to functions with a sufficient degree of smoothness and knowledge of the precise degree of smoothness of scale functions is seemingly incomplete. The aim of this article is to offer new results concerning properties of scale functions in relation to the smoothness of the underlying Lévy measure. We place particular emphasis on spectrally negative Lévy processes with a Gaussian component and processes of bounded variation. An additional motivation is the very intimate relation of scale functions to renewal functions of subordinators. The results obtained for scale functions have direct implications offering new results concerning the smoothness of such renewal functions for which there seems to be very little existing literature on this topic.

In vitro evaluation of surface roughness of 4 resin composites after the toothbrushing process and methods to recover superficial smoothness.

OBJECTIVE: This study evaluated the efficiency of repolishing, sealing with surface sealant, and the joining of both in decreasing the surface roughness of resin-based composites after a toothbrushing process. METHOD AND MATERIALS: Ten specimens of each composite (Alert, Z100, Definite, and Prodigy Condensable), measuring 2 mm in thickness and 4 mm in diameter, were made and submitted to finishing and polishing processes on both sides of the specimens using the Sof-Lex system. The specimens were then subjected to toothbrushing (30,000 cycles), and surface roughness (Ra) was analyzed with a Surfcorder SE 1700 profilometer. The upper surface of each composite was etched with 37% phosphoric acid, and the surface-penetrating sealant Protect-it was applied on 1 surface. The roughness of these surfaces was again measured. On the other side, the surface of the specimen was repolished, and the efficiency of this procedure was measured using the profilometer. The surface roughness resulting from the joining of the 2 methods was verified by applying, in the final stage, the surface-penetrating sealant on the repolished surface. Data were analyzed with analysis of variance and Tukey test (P <.05). RESULTS: Results showed that the lowest surface roughness values were obtained for Definite, Z100, and Prodigy Condensable after the repolishing process and after the repolishing plus sealing. For Alert, the joining of repolishing plus sealing promoted the lowest values of surface roughness. CONCLUSION: Of the resin-based composites, Alert demonstrated the highest values of surface roughness in all the techniques tested.

Constraining the dark energy and smoothness parameter with type Ia supernovae and gamma-ray bursts

The existence of inhomogeneities in the observed Universe modifies the distance-redshift relations thereby affecting the results of cosmological tests in comparison to the ones derived assuming spatially uniform models. By modeling the inhomogeneities through a Zeldovich-Kantowski-Dyer-Roeder approach which is phenomenologically characterized by a smoothness parameter alpha, we rediscuss the constraints on the cosmic parameters based on type Ia supernovae (SNe Ia) and gamma-ray bursts (GRBs) data. The present analysis is restricted to a flat Lambda CDM model with the reasonable assumption that Lambda does not clump. A chi(2) analysis using 557 SNe Ia data from the Union2 compilation data (R. Amanullah et al., Astrophys. J. 716, 712 (2010).) constrains the pair of parameters (Omega(m), alpha) to Omega(m) = 0.27(-0.03)(+0.08) (2 sigma) and alpha >= 0.25. A similar analysis based only on 59 Hymnium GRBs (H. Wei, J. Cosmol. Astropart. Phys. 08 (2010) 020.) constrains the matter density parameter to be Omega(m) = 0.35(-0.24)(+0.62) (2 sigma) while all values for the smoothness parameter are allowed. By performing a joint analysis, it is found that Omega(m) = 0.27(-0.06)(+0.06) and alpha >= 0.52. As a general result, although considering that current GRB data alone cannot constrain the smoothness alpha parameter, our analysis provides an interesting cosmological probe for dark energy even in the presence of inhomogeneities.

Metodologie di caratterizzazione della smoothness di movimenti volontari di arto superiore

Ormai da diversi anni vengono utilizzate tecnologie più o meno sofisticate in ambito riabilitativo, grazie alle conoscenze sviluppate nel campo della medicina riabilitativa e in altri ambiti tra i quali le neuroscienze, la neurofiiologia, la biomeccanica e l'imaging. La ricerca tecnologica più avanzata in questo settore coinvolge dispositivi robotici e realtà virtuale con lo scopo di arrivare ad ottenere tecniche sempre migliori. Questo approccio è anche la base di studi del movimento e l'interesse che si ha riguardo al modo in cui avvengono la pianificazione e l'esecuzione dell'atto motorio. Di particolare rilevanza sono i submovimenti, ovvero le frammentazioni che compongono un movimento continuo umano, i quali forniscono un'analisi compatta di codifica del moto e si rivelano i principali responsabili della caratteristica di smoothness delle traiettorie risultanti. Sotto l'ipotesi che esistano tali unità discrete, la capacità di isolarle e caratterizzarle accuratamente fornisce una descrizione dell'atto motorio, dunque un'analisi che può portare a nuove scoperte negli studi delle performance motorie, della riabilitazione e del sistema di controllo motorio nell'uomo. Il presente elaborato mostra una panoramica all'approccio dello studio del movimento e della sua decomposizione, partendo dal modo in cui viene generato e controllato all'interno del nostro organismo, fino alle tecniche computazionali sfruttate per modellare ciò che avviene nel sistema motorio. Il primo capitolo centra il problema nel suo contesto di utilizzo, ovvero quello della riabilitazione neuromotoria con la quale si cerca di sfruttare le tecniche più innovative per ottenere risultati più efficienti e soddisfacenti e sempre meno soggettivi. Il capitolo successivo fornisce la visione anatomo-fisiologica del problema, infatti si cerca di spiegare il funzionamento generale di produzione dei comandi motori a cui seguono la vera e propria attuazione e l'eventuale correzione; alla base di questo meccanismo sta anche la possibilità di rendere efficaci le suddette tecniche riabilitative. Sono, poi, introdotti i submovimenti e le conclusioni a cui si è arrivati nel corso degli anni grazie a varie ricerche di caratterizzazione della smoothness che mettono in relazione tale caratteristica con i submovimenti stessi. Nella terza parte si ha una visione d'insieme del modo in cui le tecnologie più recenti possono essere applicate nell'ambito di studio della tesi: la realtà virtuale, così come la robotica, giocano un ruolo fondamentale per la misurazione e la rilevazione della cinematica del corpo umano (nel caso specifico, la cinematica dell'arto superiore). Nel quarto capitolo vengono descritti alcuni modelli con cui si cerca di estrarre le proprietà del movimento per poterne comprendere al meglio la natura ed il modo in cui viene generato. Si conclude il lavoro spiegando come l'elaborato possa essere sfruttato quale base per costruire prove sperimentali e di come le tecniche presentate possano essere utilizzate in contesti ancora più innovativi.

Choosing Smoothness Parameters for Smoothing Splines by Minimizing and Estimate of Risk

Smoothing splines are a popular approach for non-parametric regression problems. We use periodic smoothing splines to fit a periodic signal plus noise model to data for which we assume there are underlying circadian patterns. In the smoothing spline methodology, choosing an appropriate smoothness parameter is an important step in practice. In this paper, we draw a connection between smoothing splines and REACT estimators that provides motivation for the creation of criteria for choosing the smoothness parameter. The new criteria are compared to three existing methods, namely cross-validation, generalized cross-validation, and generalization of maximum likelihood criteria, by a Monte Carlo simulation and by an application to the study of circadian patterns. For most of the situations presented in the simulations, including the practical example, the new criteria out-perform the three existing criteria.

Smoothness within ruggedness: the role of neutrality in adaptation.

RNA secondary structure folding algorithms predict the existence of connected networks of RNA sequences with identical structure. On such networks, evolving populations split into subpopulations, which diffuse independently in sequence space. This demands a distinction between two mutation thresholds: one at which genotypic information is lost and one at which phenotypic information is lost. In between, diffusion enables the search of vast areas in genotype space while still preserving the dominant phenotype. By this dynamic the success of phenotypic adaptation becomes much less sensitive to the initial conditions in genotype space.