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

Vegeu el resum a l'inici del document del fitxer adjunt.

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.

Embedding theorems of funcitional classes, III

In this paper we obtain the necessary and sufficient conditions for embedding results of different function classes. The main result is a criterion for embedding theorems for the so-called generalized Weyl-Nikol'skii class and the generalized Lipschitz class. To define the Weyl-Nikol'skii class, we use the concept of a (λ,β)-derivative, which is a generalization of the derivative in the sense of Weyl. As corollaries, we give estimates of norms and moduli of smoothness of transformed Fourier series.

On Boas-Type Problem

R.P. Boas has found necessary and sufficient conditions of belonging of function to Lipschitz class. From his findings it turned out, that the conditions on sine and cosine coefficients for belonging of function to Lip α(0 & α & 1) are the same, but for Lip 1 are different. Later his results were generalized by many authors in the viewpoint of generalization of condition on the majorant of modulus of continuity. The aim of this paper is to obtain Boas-type theorems for generalized Lipschitz classes. To define generalized Lipschitz classes we use the concept of modulus of smoothness of fractional order.

A parameter-free approach for solving combinatorial optimization problems through biased randomization of efficient heuristics

This paper discusses the use of probabilistic or randomized algorithms for solving combinatorial optimization problems. Our approach employs non-uniform probability distributions to add a biased random behavior to classical heuristics so a large set of alternative good solutions can be quickly obtained in a natural way and without complex conguration processes. This procedure is especially useful in problems where properties such as non-smoothness or non-convexity lead to a highly irregular solution space, for which the traditional optimization methods, both of exact and approximate nature, may fail to reach their full potential. The results obtained are promising enough to suggest that randomizing classical heuristics is a powerful method that can be successfully applied in a variety of cases.

The HP-filter in cross-country comparisons

Many empirical studies of business cycles have followed the practise ofapplying the Hodrick-Prescott filter for cross-country comparisons. Thestandard procedure is to set the weight \lambda, which determines the'smoothness' of the trend equal to 1600. We show that if this value isused for against common wisdom about business cycles. As an example, weshow that the long recession occurred inSpain between 1975 and 1985 goesunnotoced by the HP filter. We propose a method for adjusting \lambda byreinterpreting the HP-filter as the solution to a constrained minimizationproblem. We argue that the common practice of fixing \lambda across countriesamounts to chankging the constraints on trend variability across countries.Our proposed method is easy to apply, retains all the virtues of thestandard HP-filter and when applied to Spanish data the results are inthe line with economic historian's view. Applying the method to a numberof OECD countries we find that, with the exception of Spain, Italy andJapan, the standard choice of \lambda=1600 is sensible.

Variable Kernel estimates: On the impossibility of tuning the parameters

For the standard kernel density estimate, it is known that one can tune the bandwidth such that the expected L1 error is within a constant factor of the optimal L1 error (obtained when one is allowed to choose the bandwidth with knowledge of the density). In this paper, we pose the same problem for variable bandwidth kernel estimates where the bandwidths are allowed to depend upon the location. We show in particular that for positive kernels on the real line, for any data-based bandwidth, there exists a densityfor which the ratio of expected L1 error over optimal L1 error tends to infinity. Thus, the problem of tuning the variable bandwidth in an optimal manner is ``too hard''. Moreover, from the class of counterexamples exhibited in the paper, it appears thatplacing conditions on the densities (monotonicity, convexity, smoothness) does not help.

Sensorimotor Plasticity after Music-Supported Therapy in Chronic Stroke Patients Revealed by Transcranial Magnetic Stimulation

BACKGROUND: Several recently developed therapies targeting motor disabilities in stroke sufferers have shown to be more effective than standard neurorehabilitation approaches. In this context, several basic studies demonstrated that music training produces rapid neuroplastic changes in motor-related brain areas. Music-supported therapy has been recently developed as a new motor rehabilitation intervention. METHODS AND RESULTS: In order to explore the plasticity effects of music-supported therapy, this therapeutic intervention was applied to twenty chronic stroke patients. Before and after the music-supported therapy, transcranial magnetic stimulation was applied for the assessment of excitability changes in the motor cortex and a 3D movement analyzer was used for the assessment of motor performance parameters such as velocity, acceleration and smoothness in a set of diadochokinetic movement tasks. Our results suggest that the music-supported therapy produces changes in cortical plasticity leading the improvement of the subjects' motor performance. CONCLUSION: Our findings represent the first evidence of the neurophysiological changes induced by this therapy in chronic stroke patients, and their link with the amelioration of motor performance. Further studies are needed to confirm our observations.

Sensorimotor Plasticity after Music-Supported Therapy in Chronic Stroke Patients Revealed by Transcranial Magnetic Stimulation

BACKGROUND: Several recently developed therapies targeting motor disabilities in stroke sufferers have shown to be more effective than standard neurorehabilitation approaches. In this context, several basic studies demonstrated that music training produces rapid neuroplastic changes in motor-related brain areas. Music-supported therapy has been recently developed as a new motor rehabilitation intervention. METHODS AND RESULTS: In order to explore the plasticity effects of music-supported therapy, this therapeutic intervention was applied to twenty chronic stroke patients. Before and after the music-supported therapy, transcranial magnetic stimulation was applied for the assessment of excitability changes in the motor cortex and a 3D movement analyzer was used for the assessment of motor performance parameters such as velocity, acceleration and smoothness in a set of diadochokinetic movement tasks. Our results suggest that the music-supported therapy produces changes in cortical plasticity leading the improvement of the subjects' motor performance. CONCLUSION: Our findings represent the first evidence of the neurophysiological changes induced by this therapy in chronic stroke patients, and their link with the amelioration of motor performance. Further studies are needed to confirm our observations.

Sensorimotor Plasticity after Music-Supported Therapy in Chronic Stroke Patients Revealed by Transcranial Magnetic Stimulation

BACKGROUND: Several recently developed therapies targeting motor disabilities in stroke sufferers have shown to be more effective than standard neurorehabilitation approaches. In this context, several basic studies demonstrated that music training produces rapid neuroplastic changes in motor-related brain areas. Music-supported therapy has been recently developed as a new motor rehabilitation intervention. METHODS AND RESULTS: In order to explore the plasticity effects of music-supported therapy, this therapeutic intervention was applied to twenty chronic stroke patients. Before and after the music-supported therapy, transcranial magnetic stimulation was applied for the assessment of excitability changes in the motor cortex and a 3D movement analyzer was used for the assessment of motor performance parameters such as velocity, acceleration and smoothness in a set of diadochokinetic movement tasks. Our results suggest that the music-supported therapy produces changes in cortical plasticity leading the improvement of the subjects' motor performance. CONCLUSION: Our findings represent the first evidence of the neurophysiological changes induced by this therapy in chronic stroke patients, and their link with the amelioration of motor performance. Further studies are needed to confirm our observations.

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.