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.

People favour imperfect catching by assuming a stable world

The visual angle that is projected by an object (e.g. a ball) on the retina depends on the object's size and distance. Without further information, however, the visual angle is ambiguous with respect to size and distance, because equal visual angles can be obtained from a big ball at a longer distance and a smaller one at a correspondingly shorter distance. Failure to recover the true 3D structure of the object (e.g. a ball's physical size) causing the ambiguous retinal image can lead to a timing error when catching the ball. Two opposing views are currently prevailing on how people resolve this ambiguity when estimating time to contact. One explanation challenges any inference about what causes the retinal image (i.e. the necessity to recover this 3D structure), and instead favors a direct analysis of optic flow. In contrast, the second view suggests that action timing could be rather based on obtaining an estimate of the 3D structure of the scene. With the latter, systematic errors will be predicted if our inference of the 3D structure fails to reveal the underlying cause of the retinal image. Here we show that hand closure in catching virtual balls is triggered by visual angle, using an assumption of a constant ball size. As a consequence of this assumption, hand closure starts when the ball is at similar distance across trials. From that distance on, the remaining arrival time, therefore, depends on ball's speed. In order to time the catch successfully, closing time was coupled with ball's speed during the motor phase. This strategy led to an increased precision in catching but at the cost of committing systematic errors.

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.

General Equilibrium Long-Run Determinants for Spanish FDI: A Spatial Panel Data Approach

While general equilibrium theories of trade stress the role of third-country effects, little work has been done in the empirical foreign direct investment (FDI) literature to test such spatial linkages. This paper aims to provide further insights into long-run determinants of Spanish FDI by considering not only bilateral but also spatially weighted third-country determinants. The few studies carried out so far have focused on FDI flows in a limited number of countries. However, Spanish FDI outflows have risen dramatically since 1995 and today account for a substantial part of global FDI. Therefore, we estimate recently developed Spatial Panel Data models by Maximum Likelihood (ML) procedures for Spanish outflows (1993-2004) to top-50 host countries. After controlling for unobservable effects, we find that spatial interdependence matters and provide evidence consistent with New Economic Geography (NEG) theories of agglomeration, mainly due to complex (vertical) FDI motivations. Spatial Error Models estimations also provide illuminating results regarding the transmission mechanism of shocks.

Power line communication in motor cables of variable-speed electric drives − analysis and

Data transmission between an electric motor and a frequency converter is required in variablespeed electric drives because of sensors installed at the motor. Sensor information can be used for various useful applications to improve the system reliability and its properties. Traditionally, the communication medium is implemented by an additional cabling. However, the costs of the traditional method may be an obstacle to the wider application of data transmission between a motor and a frequency converter. In any case, a power cable is always installed between a motor and a frequency converter for power supply, and hence it may be applied as a communication medium for sensor level data. This thesis considers power line communication (PLC) in inverter-fed motor power cables. The motor cable is studied as a communication channel in the frequency band of 100 kHz−30 MHz. The communication channel and noise characteristics are described. All the individual components included in a variable-speed electric drive are presented in detail. A channel model is developed, and it is verified by measurements. A theoretical channel information capacity analysis is carried out to estimate the opportunities of a communication medium. Suitable communication and forward error correction (FEC) methods are suggested. A general method to implement a broadband and Ethernet-based communication medium between a motor and a frequency converter is proposed. A coupling interface is also developed that allows to install the communication device safely to a three-phase inverter-fed motor power cable. Practical tests are carried out, and the results are analyzed. Possible applications for the proposed method are presented. A speed feedback motor control application is verified in detail by simulations and laboratory tests because of restrictions for the delay in the feedback loop caused by PLC. Other possible applications are discussed at a more general level.

Avaliando as aproximações usadas no ensino de Físico-Química

The approaches are part of the everyday of the Physical Chemistry. In many didactic books in the area of Chemistry, the approaches are validated starting from qualitative and not quantitative approaches. We elaborated some examples that allow evaluating the quantitative impact of the approaches, being considered the mistake tolerated for the approximate calculation. The estimate of the error in the approaches should serve as guide to establish the validity of the calculation, which use them. Thus, the shortcut that represents a calculation approached to substitute accurate calculations; it can be used without it loses of quality in the results, besides indicating, as they are valid the adopted criterions.

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.

3D Surface Modeling From Point Clouds

The goal of this thesis is to implement software for creating 3D models from point clouds. Point clouds are acquired with stereo cameras, monocular systems or laser scanners. The created 3D models are triangular models or NURBS (Non-Uniform Rational B-Splines) models. Triangular models are constructed from selected areas from the point clouds and resulted triangular models are translated into a set of quads. The quads are further translated into an estimated grid structure and used for NURBS surface approximation. Finally, we have a set of NURBS surfaces which represent the whole model. The problem wasn’t so easy to solve. The selected triangular surface reconstruction algorithm did not deal well with noise in point clouds. To handle this problem, a clustering method is introduced for simplificating the model and removing noise. As we had better results with the smaller point clouds produced by clustering, we used points in clusters to better estimate the grids for NURBS models. The overall results were good when the point cloud did not have much noise. The point clouds with small amount of error had good results as the triangular model was solid. NURBS surface reconstruction performed well on solid models.

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.

Microcontroller-based interface circuit for inductive sensors

This work proposes a fully-digital interface circuit for the measurement of inductive sensors using a low-cost microcontroller (µC) and without any intermediate active circuit. Apart from the µC and the sensor, the circuit just requires an external resistor and a reference inductance so that two RL circuits with a high-pass filter (HPF) topology are formed. The µC appropriately excites such RL circuits in order to measure the discharging time of the voltage across each inductance (i.e. sensing and reference) and then it uses such discharging times to estimate the sensor inductance. Experimental tests using a commercial µC show a non-linearity error (NLE) lower than 0.5%FSS (Full-Scale Span) when measuring inductances from 1 mH to 10 mH, and from 10 mH to 100 mH.

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.