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In the short duration of six months, one week, and two days, Einstein, in 1905, wrote five papers that stand today at the bedrock of physics. Only one of these papers was, according to Einstein himself, revolutionary. This paper, on the nature of light, made him the father of quantum physics. In the other four papers, Einstein clearly eschewed trivialities as he demonstrated the reality of atoms and examined their dimensions (the reality of atoms was still debated in 1905), put the laws of thermodynamics on a new footing as he established the validity of the kinetic theory, enhanced the significance of the speed of light, and purged the basic concepts of space, time, mass, and energy of profound fallacies. But Einstein did not retire after 1905. He continued a career that, in sum, stands alone in the annals of physics.

In this paper “wobulation” is presented. Wobulation is a cost-effective method of increasing the resolution of digital projection systems without changing the spatial light modulator (SLM). Multiple sub-frames of data are generated from each frame of image data. An optical image shifting mechanism displaces the projected image of each sub-frame by a fraction of a pixel. The sub-frames are projected in rapid succession, thereby appearing as if they were projected simultaneously and superimposed. The resulting image has significantly higher resolution than images produced by unwobulated systems having the same number of SLM pixels.

This advanced high definition flat-panel television display has 4096 × 2160 pixels and can realize good moving picture resolution, good color viewing angle, and crisp beautiful images over the entire screen. The single-panel device is made from a mother glass which could fit nine 50 inch diagonal substrates.

We have developed a new front projector with a super-short projection distance of 0.65 m at 100″. We installed a newly developed reflective-type projection optical system in this projector, which was composed of only four aspheric mirrors that were free of color aberrations. Using this new system and a single-chip DMD™*, we projected a picture that had excellent sharpness and high contrast from 40″–100″. This paper describes the principles, design, and characteristics of the new WT600™ front projector.

Schneider misinterpreted the rhetorical question about the second law, which the authors firmly believe not violated. Their main purpose is to show, under the Boussinesq approximation and the Navier-Stokes, there exist non-trivial solutions even for quiescent boundary conditions.

Traditionally, the fixed-length linear paper-and-pencil (P&P) mode of administration has been the standard method of test delivery. With the advancement of technology, however, the popularity of administering tests using adaptive methods like computerized adaptive testing (CAT) and multistage testing (MST) has grown in the field of measurement in both theory and practice. In practice, several standardized tests have sections that include only set-based items. To date, there is no study in the literature that compares these testing procedures when a test is completely set-based under various item response theory (IRT) models. This study investigates the measurement precision of MST compared to CAT and compared to P&P tests for the one-, two-, and three-parameter logistic (1-, 2-, and 3PL) models when the test is completely set-based. Results showed that MST performed better for the 2- and 3PL models than an equivalent-length P&P test in terms of reliability and conditional standard error of measurement. In addition, findings showed that MST performed better for the 1- and 2PL models than for an equivalent-length CAT test. For the 3PL model, MST and CAT performed about the same.

Focus cues specify inappropriate 3d scene parameters in conventional displays because the light comes from a single surface, independent of the depth relations in the portrayed scene. We examine the efficacy of a stereo-display prototype designed to minimize these problems by using multiple image planes to present near-correct focus cues. Each eye's view is the sum of several images presented at different focal distances. Variation in focal distance is provided by either multiple beam splitters or by use of a switchable lens. The stimulus to accommodation is more consistent with the portrayed depth than with conventional displays. Compared to a normal, fixed-distance display, observers show improved stereoscopic performance in different psychophysical tasks including speed of fusing stereoscopic images. The multiple image-planes approach provides a practical solution for some shortcomings of conventional displays.

This paper provides a methodology which bridges the gap between a simple color-difference metric and a full spatio-chromatic vision model to predict color differences. Because luminance and chromatic visual channels differ greatly in their spatial sensitivities, more than a single number is needed for specific applications—e.g., performance of softcopy displays. On the other hand, a full vision model implies dependence on the displayed images as well as on the display device, and may be impractical to implement. The compromise proposed here is to adopt in certain cases two color-difference metrics, one for luminance and the other for chrominance. Because chromatic coordinates are not luminance-independent in uniform color spaces such as CIELAB, the endpoints of the color difference are made isoluminous prior to transformation to a uniform-color space.

In this note we point out that a simple proof of the lower bound of the sets (b, c), and so also of Ξ(b, c), defined in the previous paper [1] can be obtained as a simple application of a general method. By Example 4.6 from [2], if [0, 1] = E0⊃E1⊃ … are sets each of which is a finite union of disjoint closed intervals such that each interval of Ek−1, contains at least mk intervals of Ek which are separated by gaps of lengths at least ek, and if mk≥2 and ek≥ek+1>0, then the dimension of the intersection of Ek is at least

The recent paper [1] presents a formula for an interval containing all eigenvalues of a real symmetric matrix. The formula requires only the trace of the matrix and the trace of its square. This formula is here generalised to complex matrices.

Blackman et al. [1994] describe an experiment that purports to show that weak 45 Hz magnetic fields inhibit the growth of neurites from PC-12 cells treated with a growth stimulation factor. I present a statistical analysis of the data in that paper that shows that the data were corrupted in some way; hence, the results are invalid.

Mechanisms of the artifacts accompanying with image motion on Flat Panel Displays (FPDs), e.g. motion blur, jerky motion, and dynamic false contour, etc deteriorating picture quality, will be explained on the bases of image projected on the retina. The solutions for decreasing the artifacts will be reviewed and other possible artifacts will be discussed.

Multiple endpoints are tested to assess an overall treatment effect and also to identify which endpoints or subsets of endpoints contributed to treatment differences. The conventional p-value adjustment methods, such as single-step, step-up, or step-down procedures, sequentially identify each significant individual endpoint. Closed test procedures can also detect individual endpoints that have effects via a step-by-step closed strategy. This paper proposes a global-based statistic for testing an a priori number, say, r of the k endpoints, as opposed to the conventional approach of testing one (r = 1) endpoint. The proposed test statistic is an extension of the single-step p-value-based statistic based on the distribution of the smallest p-value. The test maintains strong control of the FamilyWise Error (FWE) rate under the null hypothesis of no difference in any (sub)set of r endpoints among all possible combinations of the k endpoints. After rejecting the null hypothesis, the individual endpoints in the sets that are rejected can be tested further, using a univariate test statistic in a second step, if desired. However, the second step test only weakly controls the FWE. The proposed method is illustrated by application to a psychosis data set.

A reflection-type integral imaging scheme for displaying three-dimensional images and its modifications are proposed. A concave mirror array instead of a lens array is adopted for the image integration. Its feasibility is demonstrated by basic experiments.

We have developed a new scaling technique, which we call “Advanced Scaling with Preserving Extracted Contour's Transition (ASPECT)”. When an image is expanded, it generally lose uniformity and become blurred. ASPECT change the scaling ratio at the contour of an image so that it can maintain sharpness of the expanded image. Thus the technology can create a crisp expanded image without producing artifacts caused by non-uniformity or overshooting.

Adaptive two-stage designs allow a data-driven change of design characteristics during the ongoing trial. One of the available options is an adaptive choice of the test statistic for the second stage of the trial based on the results of the interim analysis. Since there is often only a vague knowledge of the distribution shape of the primary endpoint in the planning phase of a study, a change of the test statistic may then be considered if the data indicate that the assumptions underlying the initial choice of the test are not correct. Collings and Hamilton proposed a bootstrap method for the estimation of the power of the two-sample Wilcoxon test for shift alternatives. We use this approach for the selection of the test statistic. By means of a simulation study, we show that the gain in terms of power may be considerable when the initial assumption about the underlying distribution was wrong, whereas the loss is relatively small when in the first instance the optimal test statistic was chosen. The results also hold true for comparison with a one-stage design. Application of the method is illustrated by a clinical trial example.

Poisson processes {X(t), t > 0} are suitable models for a broad variety of counting processes in Ecology. For example, when analyzing data that apparently came from Poisson population, over-dispersion [i.e. V(X(t)) > E(X(t))] or under-dispersion [i.e. V(X(t)) < E(X(t))] is encountered. This led CONSUL and JAIN (1973), and JANARDAN and SCHAEFFER (1977) to consider a generalization of the Poisson distribution called Lagrangian Poisson distribution. JANARDAN (1980) modified the Poisson process and derived a stochastic model for the number of eggs laid by a parasite on a host. This distribution is very suitable for fitting data with over- (or under-) dispersion. JANARDAN et al. (1981) considered this stochastic model and applied it to study the variation of the distribution of chromosome aberrations in human and animal cells subject to radiation or chemical insults. Here, we present a new approach for the derivation of this distribution and provide some alternative chance mechanisms for the genesis of the distribution. Moments, moment properties, and some applications are also given.

This report summarizes a study conducted to assess the comparability of paper-and-pencil (P&P) and computer adaptive test (CAT) scores on the GRE® General Test. Volunteer examinees from around the country were randomly assigned to take the test in either CAT mode or P&P mode. Results indicated that for each measure (verbal, quantitative, analytical), mean scores on the CAT were higher than mean scores on P&P. It was hypothesized that CAT examinee test-taking behavior with regard to the CAT scoring method that was in place at the time of the study (allowing student to receive a score by answering only 80% or more of the questions) may have affected CAT scores. Investigation of this hypothesis indicated that CAT examinees who did not complete their CATs obtained higher mean scores than would be predicted. However, mean scores for examinees who completed their CATs were similar to mean scores for P&P examinees. A new psychometrically-defensible CAT scoring method, called proportional scoring, was developed in which it is to the examinees' advantage, in terms of maximizing their scores, to carefully consider and answer as many items as they can. The proportional scoring method has been implemented in the operational GRE CAT program, and it is believed that this scoring method will result in CAT scores that are comparable to P&P scores. GRE CAT scores will continue to be closely monitored.

The deadly coronavirus disease 2019 (COVID-19) has recently affected each corner of the world. Many governments of different countries have imposed strict measures in order to reduce the severity of the infection. In this present paper, we will study a mathematical model describing COVID-19 dynamics taking into account the government action and the individuals reaction. To this end, we will suggest a system of seven fractional deferential equations (FDEs) that describe the interaction between the classical susceptible, exposed, infectious, and removed (SEIR) individuals along with the government action and individual reaction involvement. Both human-to-human and zoonotic transmissions are considered in the model. The well-posedness of the FDEs model is established in terms of existence, positivity, and boundedness. The basic reproduction number (BRN) is found via the new generation matrix method. Different numerical simulations were carried out by taking into account real reported data from Wuhan, China. It was shown that the governmental action and the individuals' risk awareness reduce effectively the infection spread. Moreover, it was established that with the fractional derivative, the infection converges more quickly to its steady state.

OBJECTIVES Current human infant urine collection methods for the field are problematic for the researcher and potentially uncomfortable for the infant. In this study, we compared two minimally invasive methods for collecting infant urine: organic cotton balls and filter paper. MATERIALS AND METHODS We first collected urine from infants using the clean catch method. We then used those samples to compare the performance of filter paper and cotton ball collection protocols. We analyzed the clean catch and cotton samples using commercial estrone-3-glucuronide (E1G) kits and tried two different extraction methods for the filter paper. Using a paired t-test (n = 10), we compared clean catch and cotton samples. We also compared effect sizes within and between methods. RESULTS We were unable to extract enough urine from the filter paper to successfully assay the samples for E1G. The paired t-test revealed a statistically significant difference between the clean catch and cotton methods (t = 2.63, p-value = 0.03). However, the effect size was small (5.91 μg/ml, n = 10, 95% CI = 3.80, 8.02) and similar to or larger than the difference seen between duplicate wells for clean catch and cotton values. DISCUSSION While this study is limited by sample size, our results indicate that filter paper is not a field-friendly method for collecting infant urine. However, we found that organic cotton balls showed similar values to the clean catch method, and we propose this method as an alternative, minimally invasive method for study of E1G in human infant urine.

The anterolateral thigh flap and the tensor fasciae latae flap are supplied by the lateral circumflex femoral artery (LCFA). Different branching patterns of the LCFA have been described, leading to confusion, discrepancies and difficulties in clinical and cadaveric study comparisons. The aim of this study was to evaluate the branching patterns of the LCFA in dissected lower limbs and propose a simplified nomenclature. One hundred and two lower limbs fixed with Thiel's method were investigated. Meticulous dissection was performed, and the branching pattern of the arteries was documented by illustration and photography. These were analysed and allocated to the currently existing terminologies regarding the numbers of the branches (Part 1), and these subgroups were evaluated according to the variability of the trunk formations (Part 2). In Part 1, four subgroups could be classified (A, B, C and D). Group A included a total number of three branches (n = 50), Group B included four (n = 41), Group C included five (n = 5) and Group D included only two branches (n = 6). Part 2 showed in total 11 different trunk variations. Group A had four trunk variations: A1 (n = 38), A2 (n = 5), A3 (n = 2) and A4 (n = 6); Group B also had four variations: B1 (n = 16), B2 (n = 18), B3 (n = 3) and B4 (n = 4); Group C displayed two variations: C1 (n = 1) and C2 (n = 4); and in Group D, there was only one variation observed D1 (n = 6). Branching patterns were highly variable and inconsistent in terms of the number of branches and trunk variations, which resulted in different possible and justified interpretations and classifications. A new terminology should be defined cooperatively among anatomists and clinicians that will be useful for everybody. We propose a terminology oriented to the associated muscles., The manuscript indicates confusing terminologies used for the branching pattern of the lateral circumflex femoral artery. No existing terminology could be used for the results found in this manuscript, as they do not include trunk formations which were found in this investigation. Therfore, we recommend a new terminology focussing on the supplied muscles.

An alternative proof of the main results of the preceding paper by J. Howard Redfield is provided in modern terminology. The relationship of Redfield's results with a number of more recent articles is discussed. This is necessitated by the delay of over forty years between the submission and publication of his lost paper.

Summary. Examiners are often advised that, if one examination paper is to have twice the weight of another, it is only by the former's having twice the S.D. of the latter that the required effect will be achieved. But precisely what is the effect which is called ‘having twice the weight’? And will doubling the S.D., in fact, achieve it? The answers call for a definition of Weight. Some established definitions are examined, and it is shown that, on these, doubling the S.D. will only rarely have the effect promised. A simple definition is proposed, which appears to be in accord with examiners' intentions, and which is such that a paper's weight is directly proportional to its S.D.

The paper is a survey on some practical aspects of stochastic geometry in the sense of D. G. KENDALL's and G. MATHERON's & J. SERRA's schools.

Summary The maximum possible autocorrelations, for moving average processes of order q, have recently been discussed. In this paper, we give the corresponding process parameter values when greatest (or least) autocorrelations are attained. The attainment of an individual autocorrelation bound often does not fully define the process, and for such cases we also investigate the possible conditional bounds for the remaining autocorrelations.

Summary Recently Theodoresu and Wolff have proposed a sequence of random variables for estimating a sequence of constants satisfying a certain recurrence equation. Their problem, which is similar to some arising in stochastic approximation theory, was solved by using techniques from this theory. The present paper shows that the theory of sums of independent random variables is a more natural tool for tackling this problem.