Correction to “The Importance of Convexity in Learning With Squared Loss” [Sep 98 1974-1980]

The paper "the importance of convexity in learning with squared loss" gave a lower bound on the sample complexity of learning with quadratic loss using a nonconvex function class. The proof contains an error. We show that the lower bound is true under a stronger condition that holds for many cases of interest.

Using a video camera to measure the radius of the Earth

A simple but accurate method for measuring the Earth’s radius using a video camera is described. A video camera was used to capture a shadow rising up the wall of a tall building at sunset. A free program called ImageJ was used to measure the time it took the shadow to rise a known distance up the building. The time, distance and length of the sidereal day were used to calculate the radius of the Earth. The radius was measured as 6394.3 +/- 118 km, which is within 1.8% of the accepted average value of 6371 km and well within the experimental error. The experiment is suitable as a high school or university project and should produce a value for Earth’s radius within a few per cent at latitudes towards the equator, where at some times of the year the ecliptic is approximately normal to the horizon.

An alternative approach to describing agility in sports through establishment of a relationship between velocity and radius of curvature

Agility is an essential part of many athletic activities. Currently, agility drill duration is the sole criterion used for evaluation of agility performance. The relationship between drill duration and factors such as acceleration, deceleration and change of direction, however, has not been fully explored. This paper provides a mathematical description of the relationship between velocity and radius of curvatures in an agility drill through implementation of a power law (PL). Two groups of skilled and unskilled participants performed a cyclic forward/backward shuttle agility test. Kinematic data was recorded using motion capture system at a sampling rate of 200 Hz. The logarithmic relationship between tangential velocity and radius of curvature of participant trajectories in both groups was established using the PL. The slope of the regression line was found to be 0.26 and 0.36, for the skilled and unskilled groups, respectively. The magnitudes of regression line slope for both groups were approximately 0.3 which is close to the expected 1/3 value. Results are an indication of how the PL could be implemented in an agility drill thus opening the way for establishment of a more representative measure of agility performance instead of drill duration.

The nature of the charge-ordered state in Y0.5Ca0.5MnO3 with a very small average radius of the A-site cations

A detailed investigation of Y0.5Ca0.5MnO3 with a very small radius of the A-site cations ([r(A)] approximate to 1.13 Angstrom reveals the occurrence of a charge-ordering transition in the paramagnetic state, at a relatively high temperature of 260 K. The orthorhombic lattice distortion, as measured by the dimensionless index D, is large (similar to 1.75%) over the entire 300-100 K range, but the antiferromagnetic interactions become prominent only at low temperatures (< 160 K). The charge-ordering gap in Y0.5Ca0.5MnO3, measured by low-temperature vacuum tunnelling spectroscopy, is large (similar to 0.5 eV) and the charge-ordered state is unaffected by the application of a magnetic field of 6 T. The study indicates that the nature of charge-ordering in Y0.5Ca0.5MnO3 which is dominated by the cooperative Jahn-Teller effect and the associated lattice distortion is distinctly different from analogous manganates with larger [r(A)].

A method for estimation of the radius of elastic-plastic boundary around cold-worked holes

The radius of an elastic-plastic boundary was measured by the strain gage method around the cold-worked region in L72-aluminum alloy. The relative radial expansion was varied from 2.5 to 6.5 percent during the cold-working process using mandrel and split sleeve. The existing theoretical studies in this area are reviewed. The experimental results are compared with existing experimental data of various investigators and with various theoretical formulations. A model is developed to predict the radius of elastic-plastic boundary, and the model is assessed by comparing with the present experiments.

Relation Between the Diffusivity, Viscosity, and Ionic Radius of LiCl in Water, Methanol, and Ethylene Glycol: A Molecular Dynamics Simulation

A molecular dynamics (MD) investigation of LiCl in water, methanol, and ethylene glycol (EG) at 298 K is reported. Several; structural and dynamical properties of the ions as well as the solvent such as self-diffusivity, radial distribution functions, void and neck distributions, velocity autocorrelation functions, and mean residence times of solvent in the first solvation shell have been computed. The results show that the reciprocal relationship between the self-diffusivity of the ions and the viscosity is valid in almost all solvents with the exception of water. From an analysis of radial distribution functions and coordination numbers the nature of hydrogen bonding within the solvent and its influence on the void and neck distribution becomes evident. It is seen that the solvent solvent interaction is important in EG while solute solvent interactions dominate in water and methanol. From Voronoi tessellation, it is seen that the voids and necks within methanol are larger as compared to those within water or EG. On the basis of the void and neck distributions obtained from MD simulations and literature experimental data of limiting ion conductivity for various ions of different sizes we show that there is a relation between the void and neck radius on e one hand and dependence of conductivity on the ionic radius on the other. It is shown that the presence of large diameter voids and necks in methanol is responsible for maximum in limiting ion conductivity (lambda(0)) of TMA(+), while in water in EG, the maximum is seen for Rb+. In the case of monovalent anions, maximum in lambda(0) as a function ionic radius is seen for Br- in water EG but for the larger ClO4- ion in methanol. The relation between the void and neck distribution and the variation in lambda(0) with ionic radius arises via the Levitation effect which is discussed. These studies show the importance of the solvent structure and the associated void structure.

Radius of curvature measurements for laser beams: A simple method

A simple method for measuring the radius of curvature of laser beams is introduced. It has been developed to estimate the astigmatic aberration of a diode laser. Compared with the interferornetry, this method is convenient and straightforward. (c) 2005 Elsevier GmbH. All rights reserved.

Anaerobic performance in ice hockey : the effect of skate blade radius of hollow

The purpose of the study was to investigate the effect of skate blade radius of hollow (ROH) on anaerobic performance, specifically during the acceleration and stopping phases of an on-ice skating test. Fifteen, male Junior B hockey players (mean age 19 y ± 1.46) were recruited to participate. On-icc testing required each participant to complete an on-ice anaerobic performance test [Reed Repeat Skate (RRS)) on three separate days. During each on-ice test, the participant's skate blades were sharpened to one of three, randomly assigned, ROH values (0.63 cm, 1.27 cm, 1.90 cm). Performance times were recorded during each RRS and used to calculate anaerobic variables [anaerobic power (W), anaerobic capacity (W), and fatigue index (s, %)). Each RRS was video recorded for the purpose of motion analysis. Video footage was imported into Peak Motus™ to measure kinematic variables of the acceleration and stopping phases. The specific variables calculated from the acceleration phase were: average velocity over 6 m (m/s), average stride length (m), and mean stride rate (strides/s). The specific variables calculated from the stopping phase were: velocity at initiation of stopping (rn/s), stopping distance (m), stopping time (s). A repeated measures ANOV A was used to assess differences in mean performance and kinematic variables across the three selected hollows. Further analysis was conducted to assess differences in trial by trial performance and kinematic variables for all hollows. The primary findings of the study suggested that skate blade ROH can have a significant effect on kinematic variables, namely stride length and stride rate during the acceleration phase and stopping distance and stopping time during the stopping phase of an on-ice anaerobic performance test. During the acceleration phase, no significant difdifferences were found in SR and SL across the three selected hollows. Mean SR on the 1.27 cm hollow was significantly slower than both the 0.63 cm and 1.90 cm hollows and SL was significantly longer when skating on the 1.27 cm hollow in comparison to the 1.90 cm hollow. During the stopping phase, stopping distance on the 0.63 cm hollow (4.12 m ± 0.14) was significantly shorter than both the 1.27 cm hollow (4.43 m ± 0.08) (p < 0.05) and the 1.90 cm ho])ow (4.35 m ± 0.12) (p < 0.05). Mean ST was also significantly shorter when stopping on the 0.63 cm hollow then both the 1.27 cm and 1.90 cm hollows. Trial by trial results clearly illustrated the affect of fatigue on kinematic variables; AV, SR, IV decreased from trial 1 to 6. There was no significant effect on anaerobic performance variables during the RRS. Altering the skate blade ROH has a significant and practical affect on accelerating and stopping performance will be discussed in this paper.

The Effect of Skate Blade Radius of Contour and Radius of Hollow on Skating Performance in Male Ice Hockey Players

The primary purpose of this study was to investigate the effect of skate blade shape on skating performance. A secondary purpose was to evaluate if a change in hollow shape can create additional effects on skating performance. Thirty-seven male ice hockey players (age=18 years, SD=3.4) participated. The intervention consisted of four sharpening trials assessed using three on-ice tests. Participant feedback was also assessed using a Likert scale questionnaire. Statistical analysis included within-subject repeated measures MANOVA of trial by skating variables (p≤0.05). Results revealed Contour 1 enhanced performance compared to baseline on six variables at varsity level and five variables at midget level. Contour 1 enhanced performance compared to Contour 2 on six variables at the varsity and midget levels. Contour 1 also scored highest on the feedback questionnaire. Findings of this study indicate that contouring is a necessary practice to achieve optimal skating performance.

On the stability radius of a generalized state-space system

The concept of “distance to instability” of a system matrix is generalized to system pencils which arise in descriptor (semistate) systems. Difficulties arise in the case of singular systems, because the pencil can be made unstable by an infinitesimal perturbation. It is necessary to measure the distance subject to restricted, or structured, perturbations. In this paper a suitable measure for the stability radius of a generalized state-space system is defined, and a computable expression for the distance to instability is derived for regular pencils of index less than or equal to one. For systems which are strongly controllable it is shown that this measure is related to the sensitivity of the poles of the system over all feedback matrices assigning the poles.

On the radius of centrality in evolving communication networks

In this article, we investigate how the choice of the attenuation factor in an extended version of Katz centrality influences the centrality of the nodes in evolving communication networks. For given snapshots of a network, observed over a period of time, recently developed communicability indices aim to identify the best broadcasters and listeners (receivers) in the network. Here we explore the attenuation factor constraint, in relation to the spectral radius (the largest eigenvalue) of the network at any point in time and its computation in the case of large networks. We compare three different communicability measures: standard, exponential, and relaxed (where the spectral radius bound on the attenuation factor is relaxed and the adjacency matrix is normalised, in order to maintain the convergence of the measure). Furthermore, using a vitality-based measure of both standard and relaxed communicability indices, we look at the ways of establishing the most important individuals for broadcasting and receiving of messages related to community bridging roles. We compare those measures with the scores produced by an iterative version of the PageRank algorithm and illustrate our findings with two examples of real-life evolving networks: the MIT reality mining data set, consisting of daily communications between 106 individuals over the period of one year, a UK Twitter mentions network, constructed from the direct \emph{tweets} between 12.4k individuals during one week, and a subset the Enron email data set.

Breaks in the radial oxygen abundance and corotation radius of three spiral galaxies

The correlation between the breaks in the metallicity distribution and the corotation radius of spiral galaxies has been already advocated in the past and is predicted by a chemodynamical model of our Galaxy that effectively introduces the role of spiral arms in the star formation rate. In this work, we present photometric and spectroscopic observations made with the Gemini Telescope for three of the best candidates of spiral galaxies to have the corotation inside the optical disc: IC 0167, NGC 1042 and NGC 6907. We observed the most intense and well-distributed H ii regions of these galaxies, deriving reliable galactocentric distances and oxygen abundances by applying different statistical methods. From these results, we confirm the presence of variations in the gradients of metallicity of these galaxies that are possibly correlated with the corotation resonance.