Levy stable distributions via associated integral transform

We present a method of generation of exact and explicit forms of one-sided, heavy-tailed Levy stable probability distributions g(alpha)(x), 0 <= x < infinity, 0 < alpha < 1. We demonstrate that the knowledge of one such a distribution g a ( x) suffices to obtain exactly g(alpha)p ( x), p = 2, 3, .... Similarly, from known g(alpha)(x) and g(beta)(x), 0 < alpha, beta < 1, we obtain g(alpha beta)( x). The method is based on the construction of the integral operator, called Levy transform, which implements the above operations. For a rational, alpha = l/k with l < k, we reproduce in this manner many of the recently obtained exact results for g(l/k)(x). This approach can be also recast as an application of the Efros theorem for generalized Laplace convolutions. It relies solely on efficient definite integration. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4709443]

Translation and Cross-cultural Adaptation of the Lower Extremity Functional Scale Into a Brazilian Portuguese Version and Validation on Patients With Knee Injuries

STUDY DESIGN: Clinical measurement. OBJECTIVE: To translate and culturally adapt the Lower Extremity Functional Scale (LEFS) into a Brazilian Portuguese version, and to test the construct and content validity and reliability of this version in patients with knee injuries. BACKGROUND: There is no Brazilian Portuguese version of an instrument to assess the function of the lower extremity after orthopaedic injury. METHODS: The translation of the original English version of the LEFS into a Brazilian Portuguese version was accomplished using standard guidelines and tested in 31 patients with knee injuries. Subsequently, 87 patients with a variety of knee disorders completed the Brazilian Portuguese LEES, the Medical Outcomes Study 36-Item Short-Form Health Survey, the Western Ontario and McMaster Universities Osteoarthritis Index, and the International Knee Documentation Committee Subjective Knee Evaluation Form and a visual analog scale for pain. All patients were retested within 2 days to determine reliability of these measures. Validation was assessed by determining the level of association between the Brazilian Portuguese LEFS and the other outcome measures. Reliability was documented by calculating internal consistency, test-retest reliability, and standard error of measurement. RESULTS: The Brazilian Portuguese LEES had a high level of association with the physical component of the Medical Outcomes Study 36-Item Short-Form Health Survey (r = 0.82), the Western Ontario and McMaster Universities Osteoarthritis Index (r = 0.87), the International Knee Documentation Committee Subjective Knee Evaluation Form (r = 0.82), and the pain visual analog scale (r = -0.60) (all, P<.05). The Brazilian Portuguese LEES had a low level of association with the mental component of the Medical Outcomes Study 36-Item Short-Form Health Survey (r = 0.38, P<.05). The internal consistency (Cronbach alpha = .952) and test-retest reliability (intraclass correlation coefficient = 0.957) of the Brazilian Portuguese version of the LEES were high. The standard error of measurement was low (3.6) and the agreement was considered high, demonstrated by the small differences between test and retest and the narrow limit of agreement, as observed in Bland-Altman and survival-agreement plots. CONCLUSION: The translation of the LEFS into a Brazilian Portuguese version was successful in preserving the semantic and measurement properties of the original version and was shown to be valid and reliable in a Brazilian population with knee injuries. J Ort hop Sports Phys Ther 2012;42(11):932-939, Epub 9 October 2012. doi:10.2519/jospt.2012.4101

The log-exponentiated generalized gamma regression model for censored data

For the first time, we introduce a generalized form of the exponentiated generalized gamma distribution [Cordeiro et al. The exponentiated generalized gamma distribution with application to lifetime data, J. Statist. Comput. Simul. 81 (2011), pp. 827-842.] that is the baseline for the log-exponentiated generalized gamma regression model. The new distribution can accommodate increasing, decreasing, bathtub- and unimodal-shaped hazard functions. A second advantage is that it includes classical distributions reported in the lifetime literature as special cases. We obtain explicit expressions for the moments of the baseline distribution of the new regression model. The proposed model can be applied to censored data since it includes as sub-models several widely known regression models. It therefore can be used more effectively in the analysis of survival data. We obtain maximum likelihood estimates for the model parameters by considering censored data. We show that our extended regression model is very useful by means of two applications to real data.

A generalized finite element method with global-local enrichment functions for confined plasticity problems

The main feature of partition of unity methods such as the generalized or extended finite element method is their ability of utilizing a priori knowledge about the solution of a problem in the form of enrichment functions. However, analytical derivation of enrichment functions with good approximation properties is mostly limited to two-dimensional linear problems. This paper presents a procedure to numerically generate proper enrichment functions for three-dimensional problems with confined plasticity where plastic evolution is gradual. This procedure involves the solution of boundary value problems around local regions exhibiting nonlinear behavior and the enrichment of the global solution space with the local solutions through the partition of unity method framework. This approach can produce accurate nonlinear solutions with a reduced computational cost compared to standard finite element methods since computationally intensive nonlinear iterations can be performed on coarse global meshes after the creation of enrichment functions properly describing localized nonlinear behavior. Several three-dimensional nonlinear problems based on the rate-independent J (2) plasticity theory with isotropic hardening are solved using the proposed procedure to demonstrate its robustness, accuracy and computational efficiency.

Generalized Metropolis dynamics with a generalized master equation: An approach for time-independent and time-dependent Monte Carlo simulations of generalized spin systems

The extension of Boltzmann-Gibbs thermostatistics, proposed by Tsallis, introduces an additional parameter q to the inverse temperature beta. Here, we show that a previously introduced generalized Metropolis dynamics to evolve spin models is not local and does not obey the detailed energy balance. In this dynamics, locality is only retrieved for q = 1, which corresponds to the standard Metropolis algorithm. Nonlocality implies very time-consuming computer calculations, since the energy of the whole system must be reevaluated when a single spin is flipped. To circumvent this costly calculation, we propose a generalized master equation, which gives rise to a local generalized Metropolis dynamics that obeys the detailed energy balance. To compare the different critical values obtained with other generalized dynamics, we perform Monte Carlo simulations in equilibrium for the Ising model. By using short-time nonequilibrium numerical simulations, we also calculate for this model the critical temperature and the static and dynamical critical exponents as functions of q. Even for q not equal 1, we show that suitable time-evolving power laws can be found for each initial condition. Our numerical experiments corroborate the literature results when we use nonlocal dynamics, showing that short-time parameter determination works also in this case. However, the dynamics governed by the new master equation leads to different results for critical temperatures and also the critical exponents affecting universality classes. We further propose a simple algorithm to optimize modeling the time evolution with a power law, considering in a log-log plot two successive refinements.

Infantile Encephaloneuromyopathy and Defective Mitochondrial Translation Are Due to a Homozygous RMND1 Mutation

Defects of mitochondrial protein synthesis are clinically and genetically heterogeneous. We previously described a male infant who was born to consanguineous parents and who presented with severe congenital encephalopathy, peripheral neuropathy, myopathy, and lactic acidosis associated with deficiencies of multiple mitochondrial respiratory-chain enzymes and defective mitochondrial translation. In this work, we have characterized four additional affected family members, performed homozygosity mapping, and identified a homozygous splicing mutation in the splice donor site of exon 2 (c.504+1G>A) of RMND1 (required for meiotic nuclear division-1) in the affected individuals. Fibroblasts from affected individuals expressed two aberrant transcripts and had decreased wild-type mRNA and deficiencies of mitochondrial respiratory-chain enzymes. The RMND1 mutation caused haploinsufficiency that was rescued by overexpression of the wild-type transcript in mutant fibroblasts; this overexpression increased the levels and activities of mitochondrial respiratory-chain proteins. Knockdown of RMND1 via shRNA recapitulated the biochemical defect of the mutant fibroblasts, further supporting a loss-of-function pathomechanism in this disease. RMND1 belongs to the sif2 family, an evolutionary conserved group of proteins that share the DUF155 domain, have unknown function, and have never been associated with human disease. We documented that the protein localizes to mitochondria in mammalian and yeast cells. Further studies are necessary for understanding the function of this protein in mitochondrial protein translation.

Generalized non-commutative inflation

Non-commutative geometry indicates a deformation of the energy-momentum dispersion relation f (E) = E/pc (not equal 1) for massless particles. This distorted energy-momentum relation can affect the radiation-dominated phase of the universe at sufficiently high temperature. This prompted the idea of non-commutative inflation by Alexander et al (2003 Phys. Rev. D 67 081301) and Koh and Brandenberger (2007 JCAP06(2007) 021 and JCAP11(2007) 013). These authors studied a one-parameter family of a non-relativistic dispersion relation that leads to inflation: the a family of curves f (E) = 1 + (lambda E)(alpha). We show here how the conceptually different structure of symmetries of non-commutative spaces can lead, in a mathematically consistent way, to the fundamental equations of non-commutative inflation driven by radiation. We describe how this structure can be considered independently of (but including) the idea of non-commutative spaces as a starting point of the general inflationary deformation of SL(2, C). We analyze the conditions on the dispersion relation that leads to inflation as a set of inequalities which plays the same role as the slow-roll conditions on the potential of a scalar field. We study conditions for a possible numerical approach to obtain a general one-parameter family of dispersion relations that lead to successful inflation.

On Wald Residuals in Generalized Linear Models

A rigorous asymptotic theory for Wald residuals in generalized linear models is not yet available. The authors provide matrix formulae of order O(n(-1)), where n is the sample size, for the first two moments of these residuals. The formulae can be applied to many regression models widely used in practice. The authors suggest adjusted Wald residuals to these models with approximately zero mean and unit variance. The expressions were used to analyze a real dataset. Some simulation results indicate that the adjusted Wald residuals are better approximated by the standard normal distribution than the Wald residuals.

ON THE CONSISTENCY OF TWISTED GENERALIZED WEYL ALGEBRAS

A twisted generalized Weyl algebra A of degree n depends on a. base algebra R, n commuting automorphisms sigma(i) of R, n central elements t(i) of R and on some additional scalar parameters. In a paper by Mazorchuk and Turowska, it is claimed that certain consistency conditions for sigma(i) and t(i) are sufficient for the algebra to be nontrivial. However, in this paper we give all example which shows that this is false. We also correct the statement by finding a new set of consistency conditions and prove that the old and new conditions together are necessary and sufficient for the base algebra R to map injectively into A. In particular they are sufficient for the algebra A to be nontrivial. We speculate that these consistency relations may play a role in other areas of mathematics, analogous to the role played by the Yang-Baxter equation in the theory of integrable systems.

GENERALIZED FINITE ELEMENT METHOD ON NONCONVENTIONAL HYBRID-MIXED FORMULATION

The generalized finite element method (GFEM) is applied to a nonconventional hybrid-mixed stress formulation (HMSF) for plane analysis. In the HMSF, three approximation fields are involved: stresses and displacements in the domain and displacement fields on the static boundary. The GFEM-HMSF shape functions are then generated by the product of a partition of unity associated to each field and the polynomials enrichment functions. In principle, the enrichment can be conducted independently over each of the HMSF approximation fields. However, stability and convergence features of the resulting numerical method can be affected mainly by spurious modes generated when enrichment is arbitrarily applied to the displacement fields. With the aim to efficiently explore the enrichment possibilities, an extension to GFEM-HMSF of the conventional Zienkiewicz-Patch-Test is proposed as a necessary condition to ensure numerical stability. Finally, once the extended Patch-Test is satisfied, some numerical analyses focusing on the selective enrichment over distorted meshes formed by bilinear quadrilateral finite elements are presented, thus showing the performance of the GFEM-HMSF combination.

Bilateral subthalamic nucleus stimulation for generalized dystonia after bilateral pallidotomy

Background: Thalamotomies and pallidotomies were commonly performed before the deep brain stimulation (DBS) era. Although ablative procedures can lead to significant dystonia improvement, longer periods of analysis reveal disease progression and functional deterioration. Today, the same patients seek additional treatment possibilities. Methods: Four patients with generalized dystonia who previously had undergone bilateral pallidotomy came to our service seeking additional treatment because of dystonic symptom progression. Bilateral subthalamic nucleus DBS (B-STN-DBS) was the treatment of choice. The patients were evaluated with the BurkeFahnMarsden Dystonia Rating Scale (BFMDRS) and the Unified Dystonia Rating Scale (UDRS) before and 2 years after surgery. Results: All patients showed significant functional improvement, averaging 65.3% in BFMDRS (P = .014) and 69.2% in UDRS (P = .025). Conclusions: These results suggest that B-STN-DBS may be an interesting treatment option for generalized dystonia, even for patients who have already undergone bilateral pallidotomy. (c) 2012 Movement Disorder Society

Collybistin and gephyrin are novel components of the eukaryotic translation initiation factor 3 complex

Abstract Background Collybistin (CB), a neuron-specific guanine nucleotide exchange factor, has been implicated in targeting gephyrin-GABAA receptors clusters to inhibitory postsynaptic sites. However, little is known about additional CB partners and functions. Findings Here, we identified the p40 subunit of the eukaryotic translation initiation factor 3 (eIF3H) as a novel binding partner of CB, documenting the interaction in yeast, non-neuronal cell lines, and the brain. In addition, we demonstrated that gephyrin also interacts with eIF3H in non-neuronal cells and forms a complex with eIF3 in the brain. Conclusions Together, our results suggest, for the first time, that CB and gephyrin associate with the translation initiation machinery, and lend further support to the previous evidence that gephyrin may act as a regulator of synaptic protein synthesis.

A note on the use of the generalized odds ratio in meta-analysis of association studies involving bi- and tri-allelic polymorphisms

Abstract Background The generalized odds ratio (GOR) was recently suggested as a genetic model-free measure for association studies. However, its properties were not extensively investigated. We used Monte Carlo simulations to investigate type-I error rates, power and bias in both effect size and between-study variance estimates of meta-analyses using the GOR as a summary effect, and compared these results to those obtained by usual approaches of model specification. We further applied the GOR in a real meta-analysis of three genome-wide association studies in Alzheimer's disease. Findings For bi-allelic polymorphisms, the GOR performs virtually identical to a standard multiplicative model of analysis (e.g. per-allele odds ratio) for variants acting multiplicatively, but augments slightly the power to detect variants with a dominant mode of action, while reducing the probability to detect recessive variants. Although there were differences among the GOR and usual approaches in terms of bias and type-I error rates, both simulation- and real data-based results provided little indication that these differences will be substantial in practice for meta-analyses involving bi-allelic polymorphisms. However, the use of the GOR may be slightly more powerful for the synthesis of data from tri-allelic variants, particularly when susceptibility alleles are less common in the populations (≤10%). This gain in power may depend on knowledge of the direction of the effects. Conclusions For the synthesis of data from bi-allelic variants, the GOR may be regarded as a multiplicative-like model of analysis. The use of the GOR may be slightly more powerful in the tri-allelic case, particularly when susceptibility alleles are less common in the populations.

Prodromal Questionnaire: translation, adaptation to Portuguese and preliminary results in ultra-high risk individuals and first episode psychosis

OBJECTIVE: The Prodromal Questionnaire (PQ) is a 92-item self-report screening tool for individuals at ultra-high risk (UHR) to develop psychosis. This study aims to present the translation to Portuguese and preliminary results in UHR and first episode (FE) psychosis in a Portuguese sample. METHODS: The PQ was translated from English to Portuguese by two bilingual researchers from the research program on early psychosis of the Instituto de Psiquiatria HCFMUSP, São Paulo, Brazil (ASAS - "Evaluation and Follow up of Adolescents and Young Adults in São Paulo") and back translated by two other researchers. The study participants (n = 11-) were evaluated through the Portuguese version of the Prodromal Questionnaire (PQ) and SIPS. RESULTS: The individuals at UHR (n = 7) presented a lower score than first episode patients (n = 4). The UHR mean scores and standard deviation on Portuguese version of the PQ were: 13.0 ± 10.0 points on positive symptoms subscale, and FE patients: 33.0 ± 10.0. CONCLUSION: The UHR and FE patients' of this study presented PQ scores similar to the ones found in the literature; what suggests that it is possible to use the PQ in Brazilian help-seeking individuals as a screening tool.

Personal and Social Performance (PSP) scale for patients with schizophrenia: translation to Portuguese, cross-cultural adaptation and interrater reliability

INTRODUCTION: Schizophrenia is a chronic mental disorder associated with impairment in social functioning. The most widely used scale to measure social functioning is the GAF (Global Assessment of Functioning), but it has the disadvantage of measuring at the same time symptoms and functioning, as described in its anchors. OBJECTIVES:Translation and cultural adaptation of the PSP, proposing a final version in Portuguese for use in Brazil. METHODS: We performed five steps: 1) translation; 2) back translation; 3) formal assessment of semantic equivalence; 4) debriefing; 5) analysis by experts. Interrater reliability (Intraclass correlation, ICC) between two raters was also measured. RESULTS: The final version was applied by two independent investigators in 18 adults with schizophrenia (DSM-IV-TR). The interrater reliability (ICC) was 0.812 (p < 0.001). CONCLUSION: The translation and adaptation of the PSP had an adequate level of semantic equivalence between the Portuguese version and the original English version. There were no difficulties related to understanding the content expressed in the translated texts and terms. Its application was easy and it showed a good interrater reliability. The PSP is a valid instrument for the measurement of personal and social functioning in schizophrenia.