On Short Exponential Sums Involving Fourier Coefficients of Holomorphic Cusp Forms

By an exponential sum of the Fourier coefficients of a holomorphic cusp form we mean the sum which is formed by first taking the Fourier series of the said form,then cutting the beginning and the tail away and considering the remaining sum on the real axis. For simplicity’s sake, typically the coefficients are normalized. However, this isn’t so important as the normalization can be done and removed simply by using partial summation. We improve the approximate functional equation for the exponential sums of the Fourier coefficients of the holomorphic cusp forms by giving an explicit upper bound for the error term appearing in the equation. The approximate functional equation is originally due to Jutila [9] and a crucial tool for transforming sums into shorter sums. This transformation changes the point of the real axis on which the sum is to be considered. We also improve known upper bounds for the size estimates of the exponential sums. For very short sums we do not obtain any better estimates than the very easy estimate obtained by multiplying the upper bound estimate for a Fourier coefficient (they are bounded by the divisor function as Deligne [2] showed) by the number of coefficients. This estimate is extremely rough as no possible cancellation is taken into account. However, with small sums, it is unclear whether there happens any remarkable amounts of cancellation.

Abnormal Error Monitoring in Math-Anxious Individuals: Evidence from Error-Related Brain Potentials.

This study used event-related brain potentials to investigate whether math anxiety is related to abnormal error monitoring processing. Seventeen high math-anxious (HMA) and seventeen low math-anxious (LMA) individuals were presented with a numerical and a classical Stroop task. Groups did not differ in terms of trait or state anxiety. We found enhanced error-related negativity (ERN) in the HMA group when subjects committed an error on the numerical Stroop task, but not on the classical Stroop task. Groups did not differ in terms of the correct-related negativity component (CRN), the error positivity component (Pe), classical behavioral measures or post-error measures. The amplitude of the ERN was negatively related to participants" math anxiety scores, showing a more negative amplitude as the score increased. Moreover, using standardized low resolution electromagnetic tomography (sLORETA) we found greater activation of the insula in errors on a numerical task as compared to errors in a nonnumerical task only for the HMA group. The results were interpreted according to the motivational significance theory of the ERN.

The right dorsolateral prefrontal cortex prevents post-error slowing

Adjusting behavior following the detection of inappropriate actions allows flexible adaptation to task demands and environmental contingencies during goal-directed behaviors. Post-error behavioral adjustments typically consist in adopting more cautious response mode, which manifests as a slowing down of response speed. Although converging evidence involves the dorsolateral prefrontal cortex (DLPFC) in post-error behavioral adjustment, whether and when the left or right DLPFC is critical for post-error slowing (PES), as well as the underlying brain mechanisms, remain highly debated. To resolve these issues, we used single-pulse transcranial magnetic stimulation in healthy human adults to disrupt the left or right DLPFC selectively at various delays within the 30-180ms interval following false alarms commission, while participants preformed a standard visual Go/NoGo task. PES significantly increased after TMS disruption of the right, but not the left DLPFC at 150ms post-FA response. We discuss these results in terms of an involvement of the right DLPFC in reducing the detrimental effects of error detection on subsequent behavioral performance, as opposed to implementing adaptative error-induced slowing down of response speed.

Análisis del error de medición y variabilidad interespecífica morfométrica de Fourier en M2 de primates Hominoidea

Los análisis de Fourier permiten caracterizar el contorno del diente y obtener una serie de parámetros para un posterior análisis multivariante. Sin embargo, la gran complejidad que presentan algunas formas obliga a determinar el error de medición intrínseco que se produce. El objetivo de este trabajo es aplicar y validar los análisis de Fourier en el estudio de la forma dental del segundo molar inferior (M2) de cuatro especies de primates Hominoidea para explorar la variabilidad morfométrica interespecífica, así como determinar el error de medición a un nivel intra e interobservador. El contorno de la superficie oclusal del diente fue definido digitalmente y con las funciones derivadas del análisis de Fourier se realizaron Análisis Discriminantes y Test de Mantel (correlaciones de Pearson) para determinar las diferencias de forma a partir de las mediciones tomadas. Los resultados indican que el análisis de Fourier muestra la variabilidad de forma en dientes molares en especies de primates Hominoidea. Adicionalmente, los altos niveles de correlación a nivel intra (r>0,9) como interobservador (r>0,7) sugieren que la descripción morfométrica del diente a partir de métodos de Fourier realizados por diferentes observadores puede ser agrupada para posteriores análisis.

Time course of error detection and correction in humans: neurophysiological evidence.

Using event-related brain potentials, the time course of error detection and correction was studied in healthy human subjects. A feedforward model of error correction was used to predict the timing properties of the error and corrective movements. Analysis of the multichannel recordings focused on (1) the error-related negativity (ERN) seen immediately after errors in response- and stimulus-locked averages and (2) on the lateralized readiness potential (LRP) reflecting motor preparation. Comparison of the onset and time course of the ERN and LRP components showed that the signs of corrective activity preceded the ERN. Thus, error correction was implemented before or at least in parallel with the appearance of the ERN component. Also, the amplitude of the ERN component was increased for errors, followed by fast corrective movements. The results are compatible with recent views considering the ERN component as the output of an evaluative system engaged in monitoring motor conflict.

Error Modeling and Accuracy Analysis of a Novel Mobile Hybrid Parallel Robot

Over the last decades, calibration techniques have been widely used to improve the accuracy of robots and machine tools since they only involve software modification instead of changing the design and manufacture of the hardware. Traditionally, there are four steps are required for a calibration, i.e. error modeling, measurement, parameter identification and compensation. The objective of this thesis is to propose a method for the kinematics analysis and error modeling of a newly developed hybrid redundant robot IWR (Intersector Welding Robot), which possesses ten degrees of freedom (DOF) where 6-DOF in parallel and additional 4-DOF in serial. In this article, the problem of kinematics modeling and error modeling of the proposed IWR robot are discussed. Based on the vector arithmetic method, the kinematics model and the sensitivity model of the end-effector subject to the structure parameters is derived and analyzed. The relations between the pose (position and orientation) accuracy and manufacturing tolerances, actuation errors, and connection errors are formulated. Computer simulation is performed to examine the validity and effectiveness of the proposed method.

Error en el consentimiento en los contratos de SWAP

Cada cert temps hi ha assumptes d’alt interès social dins de la jurisdicció. En els últims anys, coincidint amb la crisi financera internacional, els assumptes relatius a contractes bancaris complexos, sobretot permutes financeres o swaps, han tingut una gran rellevància. En un context de crisi financera internacional, i també nacional, s'han estès el nombre de demandes dirigides contra bancs i entitats financeres. Són reclamacions en les quals se sol·licita la declaració de nul·litat dels citats contractes, principalment es basa en un error del consentiment, nul·litat que comporta la devolució de les quantitats invertides, de les rentabilitats esperades o de les penalitzacions aplicades davant la resolució anticipada d'us contractes pels clients defraudats en les seves expectatives. Les presents pàgines pretenen un estudi dels litigis sobre SWAPS, principalment dels “Interest Rate Swap”, identificar quins són els contractes bancaris complexes, quines són les normes de consentiment contractual que els regeixen. Respecte dels primers, cal destacar que l'elevat nombre de casos plantejats davant els nostres tribunals no es tradueix en una casuística tan àmplia com seria imaginable. La gran majoria versa sobre les peticions de nul·litat del contracte (total o parcial) realitzades pels clients, al moment en què l'Euribor va descendir, i que allò que molts havien contractat com un segur de cobertura enfront dels elevats tipus d'interès que havien de pagar per les seves hipoteques, veien com conforme als pactes en el contracte, havien de satisfer al seu contrapart (una entitat de crèdit) una liquidació.

Bias and standard error for social reciprocity measurements

The directional consistency and skew-symmetry statistics have been proposed as global measurements of social reciprocity. Although both measures can be useful for quantifying social reciprocity, researchers need to know whether these estimators are biased in order to assess descriptive results properly. That is, if estimators are biased, researchers should compare actual values with expected values under the specified null hypothesis. Furthermore, standard errors are needed to enable suitable assessment of discrepancies between actual and expected values. This paper aims to derive some exact and approximate expressions in order to obtain bias and standard error values for both estimators for round-robin designs, although the results can also be extended to other reciprocal designs.

Entrevista con Manuel Villegas sobre 'El error de Prometeo. Psico(pato)logía del desarrollo moral'

Entrevista con Manuel Villegas

Design and Analysis of Forward Error Control Coding and Signaling for Guaranteeing QoS in Wireless Broadcast Systems

Broadcasting systems are networks where the transmission is received by several terminals. Generally broadcast receivers are passive devices in the network, meaning that they do not interact with the transmitter. Providing a certain Quality of Service (QoS) for the receivers in heterogeneous reception environment with no feedback is not an easy task. Forward error control coding can be used for protection against transmission errors to enhance the QoS for broadcast services. For good performance in terrestrial wireless networks, diversity should be utilized. The diversity is utilized by application of interleaving together with the forward error correction codes. In this dissertation the design and analysis of forward error control and control signalling for providing QoS in wireless broadcasting systems are studied. Control signaling is used in broadcasting networks to give the receiver necessary information on how to connect to the network itself and how to receive the services that are being transmitted. Usually control signalling is considered to be transmitted through a dedicated path in the systems. Therefore, the relationship of the signaling and service data paths should be considered early in the design phase. Modeling and simulations are used in the case studies of this dissertation to study this relationship. This dissertation begins with a survey on the broadcasting environment and mechanisms for providing QoS therein. Then case studies present analysis and design of such mechanisms in real systems. The mechanisms for providing QoS considering signaling and service data paths and their relationship at the DVB-H link layer are analyzed as the first case study. In particular the performance of different service data decoding mechanisms and optimal signaling transmission parameter selection are presented. The second case study investigates the design of signaling and service data paths for the more modern DVB-T2 physical layer. Furthermore, by comparing the performances of the signaling and service data paths by simulations, configuration guidelines for the DVB-T2 physical layer signaling are given. The presented guidelines can prove useful when configuring DVB-T2 transmission networks. Finally, recommendations for the design of data and signalling paths are given based on findings from the case studies. The requirements for the signaling design should be derived from the requirements for the main services. Generally, these requirements for signaling should be more demanding as the signaling is the enabler for service reception.

Night admission is an independent risk factor for mortality in trauma patients - a systemic error approach

ABSTRACTObjective:to assess the impact of the shift inlet trauma patients, who underwent surgery, in-hospital mortality.Methods:a retrospective observational cohort study from November 2011 to March 2012, with data collected through electronic medical records. The following variables were statistically analyzed: age, gender, city of origin, marital status, admission to the risk classification (based on the Manchester Protocol), degree of contamination, time / admission round, admission day and hospital outcome.Results:during the study period, 563 patients injured victims underwent surgery, with a mean age of 35.5 years (± 20.7), 422 (75%) were male, with 276 (49.9%) received in the night shift and 205 (36.4%) on weekends. Patients admitted at night and on weekends had higher mortality [19 (6.9%) vs. 6 (2.2%), p=0.014, and 11 (5.4%) vs. 14 (3.9%), p=0.014, respectively]. In the multivariate analysis, independent predictors of mortality were the night admission (OR 3.15), the red risk classification (OR 4.87), and age (OR 1.17).Conclusion:the admission of night shift and weekend patients was associated with more severe and presented higher mortality rate. Admission to the night shift was an independent factor of surgical mortality in trauma patients, along with the red risk classification and age.

Novel Methods for Error Modeling and Parameter Identification of a Redundant Serial-Parallel Hybrid Robot

To obtain the desirable accuracy of a robot, there are two techniques available. The first option would be to make the robot match the nominal mathematic model. In other words, the manufacturing and assembling tolerances of every part would be extremely tight so that all of the various parameters would match the “design” or “nominal” values as closely as possible. This method can satisfy most of the accuracy requirements， but the cost would increase dramatically as the accuracy requirement increases. Alternatively, a more cost-effective solution is to build a manipulator with relaxed manufacturing and assembling tolerances. By modifying the mathematical model in the controller, the actual errors of the robot can be compensated. This is the essence of robot calibration. Simply put, robot calibration is the process of defining an appropriate error model and then identifying the various parameter errors that make the error model match the robot as closely as possible. This work focuses on kinematic calibration of a 10 degree-of-freedom (DOF) redundant serial-parallel hybrid robot. The robot consists of a 4-DOF serial mechanism and a 6-DOF hexapod parallel manipulator. The redundant 4-DOF serial structure is used to enlarge workspace and the 6-DOF hexapod manipulator is used to provide high load capabilities and stiffness for the whole structure. The main objective of the study is to develop a suitable calibration method to improve the accuracy of the redundant serial-parallel hybrid robot. To this end, a Denavit–Hartenberg (DH) hybrid error model and a Product-of-Exponential (POE) error model are developed for error modeling of the proposed robot. Furthermore, two kinds of global optimization methods, i.e. the differential-evolution (DE) algorithm and the Markov Chain Monte Carlo (MCMC) algorithm, are employed to identify the parameter errors of the derived error model. A measurement method based on a 3-2-1 wire-based pose estimation system is proposed and implemented in a Solidworks environment to simulate the real experimental validations. Numerical simulations and Solidworks prototype-model validations are carried out on the hybrid robot to verify the effectiveness, accuracy and robustness of the calibration algorithms.

Pulse response based control for positive definite systems

Pulse Response Based Control (PRBC) is a recently developed minimum time control method for flexible structures. The flexible behavior of the structure is represented through a set of discrete time sequences, which are the responses of the structure due to rectangular force pulses. The rectangular force pulses are given by the actuators that control the structure. The set of pulse responses, desired outputs, and force bounds form a numerical optimization problem. The solution of the optimization problem is a minimum time piecewise constant control sequence for driving the system to a desired final state. The method was developed for driving positive semi-definite systems. In case the system is positive definite, some final states of the system may not be reachable. Necessary conditions for reachability of the final states are derived for systems with a finite number of degrees of freedom. Numerical results are presented that confirm the derived analytical conditions. Numerical simulations of maneuvers of distributed parameter systems have shown a relationship between the error in the estimated minimum control time and sampling interval