Inference with multinomial data: why to weaken the prior strength

This paper considers inference from multinomial data and addresses the problem of choosing the strength of the Dirichlet prior under a mean-squared error criterion. We compare the Maxi-mum Likelihood Estimator (MLE) and the most commonly used Bayesian estimators obtained by assuming a prior Dirichlet distribution with non-informative prior parameters, that is, the parameters of the Dirichlet are equal and altogether sum up to the so called strength of the prior. Under this criterion, MLE becomes more preferable than the Bayesian estimators at the increase of the number of categories k of the multinomial, because non-informative Bayesian estimators induce a region where they are dominant that quickly shrinks with the increase of k. This can be avoided if the strength of the prior is not kept constant but decreased with the number of categories. We argue that the strength should decrease at least k times faster than usual estimators do.

Absolute Magnitudes of Pan-STARRS PS1 Asteroids

Absolute magnitude (H) of an asteroid is a fundamental parameter describing the size and the apparent brightness of the body. Because of its surface shape, properties and changing illumination, the brightness changes with the geometry and is described by the phase function governed by the slope parameter (G). Although many years have been spent on detailed observations of individual asteroids to provide H and G, vast majority of minor planets have H based on assumed G and due to the input photometry from multiple sources the errors of these values are unknown. We compute H of ~ 180 000 and G of few thousands asteroids observed with the Pan-STARRS PS1 telescope in well defined photometric systems. The mean photometric error is 0.04 mag. Because on average there are only 7 detections per asteroid in our sample, we employed a Monte Carlo (MC) technique to generate clones simulating all possible rotation periods, amplitudes and colors of detected asteroids. Known asteroid colors were taken from the SDSS database. We used debiased spin and amplitude distributions dependent on size, spectral class distributions of asteroids dependent on semi-major axis and starting values of G from previous works. H and G (G12 respectively) were derived by phase functions by Bowell et al. (1989) and Muinonen et al. (2010). We confirmed that there is a positive systematic offset between H based on PS1 asteroids and Minor Planet Center database up to -0.3 mag peaking at 14. Similar offset was first mentioned in the analysis of SDSS asteroids and was believed to be solved by weighting and normalizing magnitudes by observatory codes. MC shows that there is only a negligible difference between Bowell's and Muinonen's solution of H. However, Muinonen's phase function provides smaller errors on H. We also derived G and G12 for thousands of asteroids. For known spectral classes, slope parameters agree with the previous work in general, however, the standard deviation of G in our sample is twice as larger, most likely due to sparse phase curve sampling. In the near future we plan to complete the H and G determination for all PS1 asteroids (500,000) and publish H and G values online. This work was supported by NASA grant No. NNX12AR65G.

Performance assessment of cascade control loopswith non-Gaussian disturbances using entropy information

Cascade control is one of the routinely used control strategies in industrial processes because it can dramatically improve the performance of single-loop control, reducing both the maximum deviation and the integral error of the disturbance response. Currently, many control performance assessment methods of cascade control loops are developed based on the assumption that all the disturbances are subject to Gaussian distribution. However, in the practical condition, several disturbance sources occur in the manipulated variable or the upstream exhibits nonlinear behaviors. In this paper, a general and effective index of the performance assessment of the cascade control system subjected to the unknown disturbance distribution is proposed. Like the minimum variance control (MVC) design, the output variances of the primary and the secondary loops are decomposed into a cascade-invariant and a cascade-dependent term, but the estimated ARMA model for the cascade control loop based on the minimum entropy, instead of the minimum mean squares error, is developed for non-Gaussian disturbances. Unlike the MVC index, an innovative control performance index is given based on the information theory and the minimum entropy criterion. The index is informative and in agreement with the expected control knowledge. To elucidate wide applicability and effectiveness of the minimum entropy cascade control index, a simulation problem and a cascade control case of an oil refinery are applied. The comparison with MVC based cascade control is also included.

Identification and output tracking control of Hammerstein systems through wireless networks

his paper investigates the identification and output tracking control of a class of Hammerstein systems through a wireless network within an integrated framework and the statistic characteristics of the wireless network are modelled using the inverse Gaussian cumulative distribution function. In the proposed framework, a new networked identification algorithm is proposed to compensate for the influence of the wireless network delays so as to acquire the more precise Hammerstein system model. Then, the identified model together with the model-based approach is used to design an output tracking controller. Mean square stability conditions are given using linear matrix inequalities (LMIs) and the optimal controller gains can be obtained by solving the corresponding optimization problem expressed using LMIs. Illustrative numerical simulation examples are given to demonstrate the effectiveness of our proposed method.

Impact of Residual Transmit RF Impairments on Training-Based MIMO Systems

Radio-frequency (RF) impairments, which intimately exist in wireless communication systems, can severely limit the performance of multiple-input-multiple-output (MIMO) systems. Although we can resort to compensation schemes to mitigate some of these impairments, a certain amount of residual impairments always persists. In this paper, we consider a training-based point-to-point MIMO system with residual transmit RF impairments (RTRI) using spatial multiplexing transmission. Specifically, we derive a new linear channel estimator for the proposed model, and show that RTRI create an estimation error floor in the high signal-to-noise ratio (SNR) regime. Moreover, we derive closed-form expressions for the signal-to-noise-plus-interference ratio (SINR) distributions, along with analytical expressions for the ergodic achievable rates of zero-forcing, maximum ratio combining, and minimum mean-squared error receivers, respectively. In addition, we optimize the ergodic achievable rates with respect to the training sequence length and demonstrate that finite dimensional systems with RTRI generally require more training at high SNRs than those with ideal hardware. Finally, we extend our analysis to large-scale MIMO configurations, and derive deterministic equivalents of the ergodic achievable rates. It is shown that, by deploying large receive antenna arrays, the extra training requirements due to RTRI can be eliminated. In fact, with a sufficiently large number of receive antennas, systems with RTRI may even need less training than systems with ideal hardware.

Winter Is Coming: Seasonal Variation in Resting Metabolic Rate of the European Badger (Meles meles)

Resting metabolic rate (RMR) is a measure of the minimum energy requirements of an animal at rest, and can give an indication of the costs of somatic maintenance. We measured RMR of free-ranging European badgers (Meles meles) to determine whether differences were related to sex, age and season. Badgers were captured in live-traps and placed individually within a metabolic chamber maintained at 20 ± 1°C. Resting metabolic rate was determined using an open-circuit respirometry system. Season was significantly correlated with RMR, but no effects of age or sex were detected. Summer RMR values were significantly higher than winter values (mass-adjusted mean ± standard error: 2366 ± 70 kJ⋅d-1; 1845 ± 109 kJ⋅d-1, respectively), with the percentage difference being 24.7%. While under the influence of anaesthesia, RMR was estimated to be 25.5% lower than the combined average value before administration, and after recovery from anaesthesia. Resting metabolic rate during the autumn and winter was not significantly different to allometric predictions of basal metabolic rate for mustelid species weighing 1 kg or greater, but badgers measured in the summer had values that were higher than predicted. Results suggest that a seasonal reduction in RMR coincides with apparent reductions in physical activity and body temperature as part of the overwintering strategy ('winter lethargy') in badgers. This study contributes to an expanding dataset on the ecophysiology of medium-sized carnivores, and emphasises the importance of considering season when making predictions of metabolic rate.

Detecção multiutilizador do domínio da frequência para sistemas DS-CDMA

Os Sinais de Espalhamento de Espectro de Sequência Directa exibem propriedades cicloestacionárias que implicam redundância entre componentes de frequência espaçadas por múltiplos da taxa de símbolo. Nesta tese, é apresentado um cancelador de interferência multiutilizador (Cancelador por translação na frequência - FSC) que tira partido desta propriedade. Este cancelador linear opera no domínio da frequência no sinal espalhado de tal forma que minimiza a interferência e ruído na saída (Critério do Mínimo Erro Quadrado Médio). Além de testado para o caso de antena única, são avaliadas as performances das configurações de antenas múltiplas para o caso de beamforming e canais espacialmente descorrelacionados considerando sistemas síncronos e sistemas com desalinhamento no tempo dos perfis de canais (ambos UMTS-TDD). Essas configurações divergiam na ordem da combinação temporal, combinação espacial e detecção multiutilizador. As configurações FSC foram avaliadas quando concatenadas com o PIC-2D. Os resultados das simulações mostram consideráveis melhorias nos resultados relativamente ao RAKE-2D convencional e PIC-2D. Foi atingida performance próximo ao RAKE de utilizador único quando o FSC foi avaliado concatenado com PIC-2D em quase todas as configurações. Todas as configurações foram avaliadas com modulação QPSK, 8-PSK e 16-QAM. Foi introduzida codificação Turbo e identificou-se as situações da vantagem de utilização do FSC antes do PIC-2D. As modulações 8-PSK e 16-QAM foram igualmente testadas com codificação.

Forecasting overseas visitors into the United Kingdom using continuous time and autoregressive fractional integrated moving average models with discrete data

This paper applies Gaussian estimation methods to continuous time models for modelling overseas visitors into the UK. The use of continuous time modelling is widely used in economics and finance but not in tourism forecasting. Using monthly data for 1986–2010, various continuous time models are estimated and compared to autoregressive integrated moving average (ARIMA) and autoregressive fractionally integrated moving average (ARFIMA) models. Dynamic forecasts are obtained over different periods. The empirical results show that the ARIMA model performs very well, but that the constant elasticity of variance (CEV) continuous time model has the lowest root mean squared error (RMSE) over a short period.

O uso do smartphone na avaliação do risco de queda associado ao envelhecimento

Introdução: O declínio do equilíbrio, da força dos membros inferiores e o medo de cair são fatores de risco de queda associados ao envelhecimento e a sua avaliação pode ser realizada pelo teste One Leg Standing (OLS), Sit to Stand (STS) e pela Falls Eficacy Scale (FES), respetivamente. As aplicações para smartphone constituem uma alternativa para a avaliação dos fatores de risco de queda no envelhecimento. Objetivo: Analisar a capacidade de uma aplicação para smartphone na avaliação dos testes STS, OLS e FES. Metodologia: Realizou-se um estudo analítico numa amostra de 27 voluntários com idade ≥ 60 anos. Realizaram-se os testes STS, OLS e a FES (versão iconográfica, apresentada no smartphone). Os dados foram recolhidos simultaneamente por um smartphone e pelo Qualisys Motion Capture Systems associado a uma plataforma de forças. Foi utilizado o r de Pearson ou Spearman para analisar as possíveis correlações. Resultados: No STS obteve-se uma correlação muito forte (rp=0.97) no número de repetições de ciclos Sit Stand Sit (SLS) e forte na duração média do SLS (rp=0.85) e das subfases Sit to Stand (rp=0.69) e Stand to Sit (rp=0.778), com p<0.001. As medidas de inclinação do tronco apresentaram correlações fortes, com exceção do ângulo inicial (p≥0.05). No OLS, verificou-se uma correlação moderada entre o deslocamento do centro de pressão peak to peak médio-lateral (rs=0.45; p=0.017) e antero-posterior (rs=0.39; p=0.046), root mean square médio-lateral (rs=0.39; p=0.046) e antero-posterior (rs=0.46; p=0.017) e área do estatocinesiograma (rs=0.45; p=0.018). Na FES obteve-se uma correlação moderada em três categorias: ‘tomar banho/duche’ (rs=0.49; p=0.010), ‘deitar/levantar da cama (rs=0.43; p=0.024) e ‘chegar aos armários’ (rs=0.38; p=0.050). Conclusão: A aplicação para smartphone parece avaliar corretamente os ciclos e a variação da inclinação do tronco no STS, porém parece necessitar de ser reajustada na FES e na velocidade do deslocamento do centro de pressão, no OLS.

Wireless GPS-based phase-locked synchronization system for outdoor environment.

Synchronization of data coming from different sources is of high importance in biomechanics to ensure reliable analyses. This synchronization can either be performed through hardware to obtain perfect matching of data, or post-processed digitally. Hardware synchronization can be achieved using trigger cables connecting different devices in many situations; however, this is often impractical, and sometimes impossible in outdoors situations. The aim of this paper is to describe a wireless system for outdoor use, allowing synchronization of different types of - potentially embedded and moving - devices. In this system, each synchronization device is composed of: (i) a GPS receiver (used as time reference), (ii) a radio transmitter, and (iii) a microcontroller. These components are used to provide synchronized trigger signals at the desired frequency to the measurement device connected. The synchronization devices communicate wirelessly, are very lightweight, battery-operated and thus very easy to set up. They are adaptable to every measurement device equipped with either trigger input or recording channel. The accuracy of the system was validated using an oscilloscope. The mean synchronization error was found to be 0.39 μs and pulses are generated with an accuracy of <2 μs. The system provides synchronization accuracy about two orders of magnitude better than commonly used post-processing methods, and does not suffer from any drift in trigger generation.

High Altitude Increases Alteration in Maximal Torque but Not in Rapid Torque Development in Knee Extensors after Repeated Treadmill Sprinting.

We assessed knee extensor neuromuscular adjustments following repeated treadmill sprints in different normobaric hypoxia conditions, with special reference to rapid muscle torque production capacity. Thirteen team- and racquet-sport athletes undertook 8 × 5-s "all-out" sprints (passive recovery = 25 s) on a non-motorized treadmill in normoxia (NM; FiO2 = 20.9%), at low (LA; FiO2 = 16.8%) and high (HA; FiO2 = 13.3%) normobaric hypoxia (simulated altitudes of ~1800 m and ~3600 m, respectively). Explosive (~1 s; "fast" instruction) and maximal (~5 s; "hard" instruction) voluntary isometric contractions (MVC) of the knee extensors (KE), with concurrent electromyographic (EMG) activity recordings of the vastus lateralis (VL) and rectus femoris (RF) muscles, were performed before and 1-min post-exercise. Rate of torque development (RTD) and EMG (i.e., Root Mean Square or RMS) rise from 0 to 30, -50, -100, and -200 ms were recorded, and were also normalized to maximal torque and EMG values, respectively. Distance covered during the first 5-s sprint was similar (P > 0.05) in all conditions. A larger (P < 0.05) sprint decrement score and a shorter (P < 0.05) cumulated distance covered over the eight sprints occurred in HA (-8 ± 4% and 178 ± 11 m) but not in LA (-7 ± 3% and 181 ± 10 m) compared to NM (-5 ± 2% and 183 ± 9 m). Compared to NM (-9 ± 7%), a larger (P < 0.05) reduction in MVC torque occurred post-exercise in HA (-14 ± 9%) but not in LA (-12 ± 7%), with no difference between NM and LA (P > 0.05). Irrespectively of condition (P > 0.05), peak RTD (-6 ± 11%; P < 0.05), and normalized peak RMS activity for VL (-8 ± 11%; P = 0.07) and RF (-14 ± 11%; P < 0.01) muscles were reduced post-exercise, whereas reductions (P < 0.05) in absolute RTD occurred within the 0-100 (-8 ± 9%) and 0-200 ms (-10 ± 8%) epochs after contraction onset. After normalization to MVC torque, there was no difference in RTD values. Additionally, the EMG rise for VL muscle was similar (P > 0.05), whereas it increased (P < 0.05) for RF muscle during all epochs post-exercise, independently of the conditions. In summary, alteration in repeated-sprint ability and post-exercise MVC decrease were greater at high altitude than in normoxia or at low altitude. However, the post-exercise alterations in RTD were similar between normoxia and low-to-high hypoxia.

Effects of isometric elbow flexion on electromyographic spike analysis

The main objective of this research was to examine the relationship between surface electromyographic (SEMG) spike activity and force. The secondary objective was to determine to what extent subcutaneous tissue impacts the high frequency component of the signal, as well as, examining the relationship between measures of SEMG spike shape and their traditional time and frequency analogues. A total of96 participants (46 males and 50 females) ranging in age (18-35 years), generated three 5-second isometric step contractions at each force level of 40, 60, 80, and 100 percent of maximal voluntary contraction (MVC). The presentation of the contractions was balanced across subjects. The right arm of the subject was positioned in the sagittal plane, with the shoulder and elbow flexed to 90 degrees. The elbow rested on a support in a neutral position (mid pronation/mid supination) and placed within a wrist cuff, fastened below the styloid process. The wrist cuff was attached to a load cell (JR3 Inc., Woodland, CA) recording the force produced. Biceps brachii activity was monitored with a pair of Ag/AgCI recording electrodes (Grass F-E9, Astro-Med Inc., West Warwick, RI) placed in a bipolar configuration, with an interelectrode distance (lED) of 2cm distal to the motor point. Data analysis was performed on a I second window of data in the middle of the 5-second contraction. The results indicated that all spike shape measures exhibited significant (p < 0.01) differences as force increase~ from 40 to 100% MVC. The spike shape measures suggest that increased motor unit (MU) recruitment was responsible for increasing force up to 80% MVC. The results suggested that further increases in force relied on MU III synchronization. The results also revealed that the subcutaneous tissue (skin fold thickness) had no relationship (r = 0.02; P > 0.05) with the mean number of peaks per spike (MNPPS), which was the high frequency component of the signal. Mean spike amplitude (MSA) and mean spike frequency (MSF) were highly correlated with their traditional measures root mean square (RMS) and mean power frequency (MPF), respectively (r = 0.99; r = 0.97; P < 0.01).

The surface electromyography-force relationship during isometric dorsiflexion in males and females

This study evaluated sex-related differences in the tibialis anterior (TA) surface electromyography (EMG) to force relationship. One-hundred participants (50 males and 50 females) performed three isometric contractions at 20, 40, 60, 80, and 100% of maximal voluntary contraction (MVC) in an apparatus designed to isolate the action of the dorsiflexors. The surface EMG signal was amplified (lOOOx), band-pass filtered (10-500Hz), and sampled at 2048 Hz. The load cell signal was low-passed filtered at 100 Hz and sampled at the same rate. Males were stronger than females {P <0.05). However, there was no significant difference in root-mean-square (RMS) values between sexes {P <0.05). Both sexes exhibited a quadratic increase in RMS across force levels (P <0.05). The mean power frequency (MNF) for males was greater than for females {P <0.05). Males and females exhibited a linear increase in both frequency measures up to 80% of MVC (P <0.05). Between 80 and 100% MVC, the frequency values for the females plateaued while males showed a decrease {P <0.05). The magnitude of the difference in MNF between males and females was consistent with sex-specific TA physiology. In general, the pattern of means for RMS and MNF between males and females revealed no sex-related differences in the surface EMG/force relationship. We therefore conclude that there are no sex-related differences in the gradation of muscle force.

An analysis of decoupling procedures in generating thermal Green's functions of O([lambda]â ´) by the Zubarev equation of motion method

The Zubarev equation of motion method has been applied to an anharmonic crystal of O( ,,4). All possible decoupling schemes have been interpreted in order to determine finite temperature expressions for the one phonon Green's function (and self energy) to 0()\4) for a crystal in which every atom is on a site of inversion symmetry. In order to provide a check of these results, the Helmholtz free energy expressions derived from the self energy expressions, have been shown to agree in the high temperature limit with the results obtained from the diagrammatic method. Expressions for the correlation functions that are related to the mean square displacement have been derived to 0(1\4) in the high temperature limit.

Training distribution and the acquisition of maximal isometric elbow flexion strength

Twenty-six sedentary, college-aged females were matched and randomly assigned to one of two groups. The massed group (n=13) completed 15 maximal isometric elbow flexion strength trials in one session, while the distributed group (n=13) performed five such contractions on three successive days. After a two-week and three month rest interval, both groups returned to perfonn another five maximal isometric elbow flexion strength trials to assess retention of any potential strength gains. Elbow flexion torque and surface electromyography (SEMG) of the biceps and triceps were monitored concurrently. There was a significant (P < 0.05) increase in strength in both groups from block one (first five contractions) to block four (first retest) and from block one to block five (second retest). Both groups exhibited a similar linear increasing (P < 0.05) trend in biceps root-mean-square (RMS) SEMG amplitude. A significant (P < 0.05) decrease in triceps RMS SEMG amplitude was found between block one and block four for the distributed group. However, a significant (P < 0.05) increase was then found between block one and five for the massed group, and between blocks four and five for distributed group. These results suggest that there is flexibility in resistive exercise schedules. An increase in neural drive to the agonist muscle continued throughout testing. This was accompanied by a reduction in antagonist co activation that was a short-tenn (two weeks) training effect, dissipated over the longer rest interval (three months).