Monotonicity preserving approximation of multivariate scattered data

This paper describes a new method of monotone interpolation and smoothing of multivariate scattered data. It is based on the assumption that the function to be approximated is Lipschitz continuous. The method provides the optimal approximation in the worst case scenario and tight error bounds. Smoothing of noisy data subject to monotonicity constraints is converted into a quadratic programming problem. Estimation of the unknown Lipschitz constant from the data by sample splitting and cross-validation is described. Extension of the method for locally Lipschitz functions is presented.

Interpolation of Lipschitz functions

This paper describes a new computational approach to multivariate scattered data interpolation. It is assumed that the data is generated by a Lipschitz continuous function f. The proposed approach uses the central interpolation scheme, which produces an optimal interpolant in the worst case scenario. It provides best uniform error bounds on f, and thus translates into reliable learning of f. This paper develops a computationally efficient algorithm for evaluating the interpolant in the multivariate case. We compare the proposed method with the radial basis functions and natural neighbor interpolation, provide the details of the algorithm and illustrate it on numerical experiments. The efficiency of this method surpasses alternative interpolation methods for scattered data.

Dead man walking : an empirical reassessment of the deterrent effect of capital punishment using the bounds testing approach to cointegration

This paper empirically estimates a murder supply equation for the United States from 1965 to 2001 within a cointegration and error correction framework. Our findings suggest that any support for the deterrence hypothesis is sensitive to the inclusion of variables for the effects of guns and other crimes. In the long run we find that real income and the conditional probability of receiving the death sentence are the main factors explaining variations in the homicide rate. In the short run the aggravated assault rate and robbery rate are the most important determinants of the homicide rate.

The residential demand for electricity in Australia : an application of the bounds testing approach to cointegration

This paper reports estimates of the long- and short-run elasticities of residential demand for electricity in Australia using the bounds testing procedure to cointegration, within an autoregressive distributive lag framework. In the long run, we find that income and own price are the most important determinants of residential electricity demand, while temperature is significant some of the time and gas prices are insignificant. Our estimates of long-run income elasticity and price elasticity of demand are consistent with previous studies, although they are towards the lower end of existing estimates. As expected, the short-run elasticities are much smaller than the long-run elasticities, and the coefficients on the error-correction coefficients are small consistent with the fact that in the short-run energy appliances are fixed.

Achievable rate and error performance of an amplify and forward multi-way relay network in the presence of imperfect channel estimation

In this paper, we investigate the impact of channel estimation error on the achievable common rate and error performance of amplify and forward (AF) multi-way relay networks (MWRNs). Assuming lattice codes with large dimensions, we provide the analytical expressions for the end-to-end SNR at the users and obtain upper bounds on the achievable common rate for an AF MWRN. Moreover, considering binary phase shift keying (BPSK) modulation as the simplest case of lattice codes, we obtain the average bit error rate (BER) for a user in an AF MWRN. The analysis shows that the average BER is a linearly increasing function and the achievable common rate is a linearly decreasing function of the channel estimation error. On the other hand, the average BER decreases and the achievable common rate increases with increasing correlation between the true and the estimated channel. Also, we observe that the AFprotocol is robust against increasing number of users in terms of error performance. We show that when the decoding user has better channel conditions compared to other users, AF relaying gives a better error performance and common rate. Finally, simulation results are provided to verify the validity of our analysis.

Some unusual applications of the `Error-bar` feature in Excel spreadsheets

This paper demonstrates how the "error-bar" feature can be used to extend the utility of "worldware" spreadsheet packages in producing high-quality graphs for university teaching and learning, and for research. To further utilize the advantages of spreadsheets in university education, this paper seeks to overcome some of the earlier reservations about the lack of scientific plotting capabilities of spreadsheet applications. Specific examples of educational material in the areas of enzyme kinetics, vibrational spectroscopy, vibronic spectroscopy, and mass spectrometry are discussed. It is argued that, where practical, university educators should use "worldware" packages to prepare teaching aids, since these would better prepare their students for future employment. The use of software features for purposes that were not envisioned by the programmers has additional educational benefits in fostering flexibility and innovation. Other graphing packages can also use the "error-bar" feature in a manner similar to that described here for Excel.

A shape error metric for sheet metal forming and its application to springback

There are many variations within sheet metal forming, some of which are manifest in the final geometry of the formed component. It is important that this geometric variation be quantified and measured for use in a process or quality control system. The contribution of this paper is to propose a novel way of measuring the geometric difference between the desired shape and an actual formed "U" channel. The metric is based upon measuring errors in terms of the significant manufacturing variations. The metric accords with the manually measured errors of the channel set. The shape error metric is then extended to develop a simple empirical, whole-component, springback error measure. The springback error measure combines into one value all the angle springback and side wall curl geometric errors for a single channel. Two trends were observed: combined springback decreases when the blank holder force is increased; and the combined springback marginally decreases when the die radii is increased.

Prediction error property of the Lasso Estimator and its generalization

The lasso procedure is an estimator-shrinkage and variable selection method. This paper shows that there always exists an interval of tuning parameter values such that the corresponding mean squared prediction error for the lasso estimator is smaller than for the ordinary least squares estimator. For an estimator satisfying some condition such as unbiasedness, the paper defines the corresponding generalized lasso estimator. Its mean squared prediction error is shown to be smaller than that of the estimator for values of the tuning parameter in some interval. This implies that all unbiased estimators are not admissible. Simulation results for five models support the theoretical results.

Accelerating linear causal model discovery using hoeffding bounds

Efficiently inducing precise causal models accurately reflecting given data sets is the ultimate goal of causal discovery. The algorithms proposed by Dai et al. has demonstrated the ability of the Minimum Message Length (MML) principle in discovering Linear Causal Models from training data. In order to further explore ways to improve efficiency, this paper incorporates the Hoeffding Bounds into the learning process. At each step of causal discovery, if a small number of data items is enough to distinguish the better model from the rest, the computation cost will be reduced by ignoring the other data items. Experiments with data set from related benchmark models indicate that the new algorithm achieves speedup over previous work in terms of learning efficiency while preserving the discovery accuracy.

Eulerian superpath approach to correct sequencing error in shotgun assembly

This work describes an error correction method based on the Euler Superpath problem. Sequence data is mapped to an Euler Superpath dynamically by Merging Transformation. With restriction and guiding rules, data consistency is maintained and error paths are separated from correct data: Error edges are mapped to the correct ones and after substitution (of error edges with right paths), corresponding errors in the sequencing data are eliminated.

What explains dissent on the High Court of Australia? An empirical assessment using a cointegration and error correction approach

This article examines the factors influencing the annual dissent rate on the High Court of Australia from its first full year of operation in 1904 up to 2001 within a cointegration and error correction framework. We hypothesize that institutional factors, socioeconomic complexity, and leadership style explain variations in the dissent rate on the High Court of Australia over time. The institutional factors that we consider are the Court's caseload, whether it had discretion to select the cases it hears, and whether it was a final court of appeal. To measure socioeconomic complexity we use the divorce rate, urbanization rate, and real GDP per capita. Our main finding is that in the long run and short run, caseload and real income are the main factors influencing dissent. We find that a 1 percent increase in caseload and real income reduce the dissent rate on the High Court of Australia by 0.3 percent and 0.6 percent, respectively, holding other factors constant.

Lower bounds for stability margin of n-dimensional discrete systems

This paper derives lower bounds for the stability margin of n-dimensional discrete systems in the Roesser’s state space setting. The lower bounds for stability margin are derived based on the MacLaurine series expansion. Numerical examples are given to illustrate the results.

EStream: online mining of frequent sets with precise error guarantee

In data stream applications, a good approximation obtained in a timely  manner is often better than the exact answer that’s delayed beyond the window of opportunity. Of course, the quality of the approximate is as important as its timely delivery. Unfortunately, algorithms capable of online processing do not conform strictly to a precise error guarantee. Since online processing is essential and so is the precision of the error, it is necessary that stream algorithms meet both criteria. Yet, this is not the case for mining frequent sets in data streams. We present EStream, a novel algorithm that allows online processing while producing results strictly within the error bound. Our theoretical and experimental results show that EStream is a better candidate for finding frequent sets in data streams, when both constraints need to be satisfied.

Reducing position error of cantilevered loads in motion systems

The positioning error of a large cantilevered mass that is actuated at its supported end is minimized as this mass travels at challenging high speeds and accelerations. An integrated approach is adopted to realize the task. After selecting the appropriate actuator that would provide higher rigidity, the system is viewed as a multi-degree of freedom system, and hence the concept of system-generated disturbance is introduced. This allows the use of appropriate mechanical design considerations and a proper generation of the kinematics commands to minimize such disturbance. A disturbance observer is then designed to detect and compensate the remaining disturbance, hence minimizing the positioning error.

An evolutionary computing approach to minimize dynamic hedging error

The objective of our present paper is to derive a computationally efficient genetic pattern learning algorithm to evolutionarily derive the optimal rebalancing weights (i.e. dynamic hedge ratios) to engineer a structured financial product out of a multiasset, best-of option. The stochastic target function is formulated as an expected squared cost of hedging (tracking) error which is assumed to be partly dependent on the governing Markovian process underlying the individual asset returns and partly on
randomness i.e. pure white noise. A simple haploid genetic algorithm is advanced as an alternative numerical scheme, which is deemed to be
computationally more efficient than numerically deriving an explicit solution to the formulated optimization model. An extension to our proposed scheme is suggested by means of adapting the Genetic Algorithm parameters based on fuzzy logic controllers.