Search

This letter addresses experimental validation of the reduced-order natural speed observer design for position sensorless drive with nonsalient permanent magnet synchronous motor. The natural speed observer and the active flux estimator are connected in a cascaded fashion, which results in a simple sensorless algorithm that needs only to tune one bandwidth parameter for flux estimation and one bandwidth parameter for speed observation. Experimental results of high speed reversal test, zero speed stopping test, and slow speed reversal test are included, where the practice of applying nonzero d-axis current at zero speed has shown to be effective for loaded zero speed stopping test, but it causes zero-speed lockedup at slow speed reversal with acceleration rate of 50 r/min/s. Four remedies are compared to improve the slow speed reversal test and the proposed method gives almost ramp actual speed waveform, nondiverging q-axis current and smooth transition in position waveform during slow zero speed crossing. A new dynamic expression of the active flux is proposed and with the aid of the active flux concept, the proposed sensorless algorithm is also applicable to various types of ac motors. National Research Foundation (NRF) Accepted version This work was supported by National Research Foundation (NRF) Singapore, under its NRF Fellowship under Grant no: NRF-NRFF12-2020-0003.

The midsession reversal paradigm confronts an animal with a two-choice discrimination task where the reward contingencies are reversed at the midpoint of the session. Species react to the reversal with either win-stay/lose-shift, using local information of reinforcement, or reversal estimation, using global information, e.g. time, to estimate the point of reversal. Besides pigeons, only mammalian species were tested in this paradigm so far and analyses were conducted on pooled data, not considering possible individually different responses. We tested twelve kea parrots with a 40-trial midsession reversal test and additional shifted reversal tests with a variable point of reversal. Birds were tested in two groups on a touchscreen, with the discrimination task having either only visual or additional spatial information. We used Generalized Linear Mixed Models to control for individual differences when analysing the data. Our results demonstrate that kea can use win-stay/lose-shift independently of local information. The predictors group, session, and trial number as well as their interactions had a significant influence on the response. Furthermore, we discovered notable individual differences not only between birds but also between sessions of individual birds, including the ability to quite accurately estimate the reversal position in alternation to win-stay/lose-shift. Our findings of the kea’s quick and flexible responses contribute to the knowledge of diversity in avian cognitive abilities and emphasize the need to consider individuality as well as the limitation of pooling the data when analysing midsession reversal data. Supplementary Information The online version contains supplementary material available at 10.1007/s10071-021-01524-1.

Acute stress has been found to impair the flexible updating of stimulus-outcome associations. However, there is a lack of studies investigating the effect of acute stress on the flexible updating of stimulus-response associations, like active avoidance responses. The current study used an avoidance reversal learning paradigm to address this question. Sixty-one participants learned that a red dot was associated with an aversive sound, whereas a green dot was not (Pavlovian Acquisition phase). Next, they were trained to avoid the aversive stimulus by selectively pressing a button in response to the red, but not the green, dot (Avoidance Acquisition phase). Subsequently, participants either underwent a stress induction task or a no-stress control task. The flexible updating of expectancies of the US and avoidance responses were assessed after reversal of the original contingencies (Reversal Test). Acute stress did not impair the flexible updating of avoidance responses during the Reversal Test. In contrast, results showed that in the stress group the expectancies of the aversive sound were more in accordance with the reversed contingencies compared to the ratings of control participants. Additionally, cortisol responders avoided less often in comparison to cortisol non-responders. Increased noradrenergic activity in stressed participants was related to impairments in the flexible updating of avoidance responses after contingency reversal, while this association was absent in the control participants. In conclusion, our results suggest that the autonomic response might account for shifting the balance towards inflexible updating of stimulus-outcome awareness while stress does not impair flexible updating of avoidance responses.

Thirty years ago, Rob Van der Voo proposed an elegant and simple system for evaluating the quality of paleomagnetic data. As a second-year Ph.D. student, the lead author remembers Rob waxing philosophical about the need to have an appropriate, but not overly rigid evaluation system. The end result was a 7-point system that assigned a (1) or (0) for any paleomagnetic result based on objective criteria. The goal was never to reject or blindly accept any particular result, but merely to indicate the degree of quality for any paleomagnetic pole. At the time, the global paleomagnetic database was burgeoning and it was deemed useful to rank older paleo magnetic results with the newer data being developed in modern laboratories. Van der Voo's, 1990 paper launched a silent revolution in paleomagnetism. Researchers began to evaluate their data against those seven criteria with the anticipation that reviewers would be similarly critical. Today, paleomagnetism is a mature science. Our methods, analyses, and results are more sophisticated than they were 30 years ago. Therefore, we feel it is appropriate to revisit the Van der Voo (1990) criteria in light of those developments. We hope to honor the intention of the original paper by keeping the criteria simple and easy to evaluate while also acknowledging the advances in science. This paper aims to update the criteria and modernize the process. We base our changes on advances in paleomagnetism and geochronology with a faithful adherence to the simplicity of the original publication. We offer the "Reliability" or "R" index as the next generation of the Van der Voo "Quality" or "Q" index. The new R-criteria evaluate seven different information items for each paleomagnetic pole including age, statistical requirements, identification of magnetic carriers, field tests, structural integrity, presence of reversals and an evaluation for possible remagnetization.

Understanding both inter- and intraspecific variation in animals' cognitive abilities is one of the central goals of cognitive ecology. We developed a field system for testing spatial learning in wild chickadees using radio frequency identification (RFID)-enabled feeders that allowed us to track individuals across multiple years. Mountain chickadees, Poecile gambeli, inhabit a continuous montane gradient, and individuals inhabiting higher elevations experience harsher winters than those at lower elevations. Previous studies found that chickadees at higher elevations cached more food and demonstrated better spatial memory, but they performed worse during reversal learning than chickadees at lower elevations. Here, we employed spatial learning, reversal learning and memory retention tasks to compare elevation-related performance of first-year juvenile birds with that of adults that had survived at least 1 year. Chickadees from high elevation performed better in the initial learning task but worse in the reversal task than birds from low elevation. There were no differences between first-year birds and adults in the initial learning task, but adults performed significantly better in the reversal test. First-year birds also made more errors associated with the initial target, which suggests higher levels of proactive interference. There were no significant differences between elevations or between juvenile and adults in memory performance after a 16-day retention. After retention, chickadees did not discriminate between the feeders that provided food during the initial task or during the reversal task prior to retention. These results are also consistent with the effects of proactive interference, as birds should have only visited the most recently rewarding feeder. Our findings suggest that the ability to quickly learn changing information is critical for chickadees at both elevations as surviving adults did better in the reversal task than first-year birds. Our results also suggest that selection may favour better reversal learning abilities associated with lower levels of proactive interference.

Aim This study aimed to find a more sensitive and systematic behavioral evaluation protocol to evaluate the cognitive impairment in rats with heart failure (HF). Methods and results An HF rat model was built by ligating the left anterior descending coronary artery. The cardiac function and structure were detected using echocardiography. Myocardial histopathological changes were observed by nitro blue tetrazolium and hematoxylin–eosin staining. The cognitive functions were evaluated using the acquisition task, probe trial, reversal test, and matching‐to‐sample test of the Morris water maze. In the probe trial, the number of times the rats in the model group crossed the platform site significantly decreased compared with that in the sham group. In the reversal test, the average latency was significantly longer in the sham group compared with the model group in the first trial but was shorter in the second and third trials. In the matching‐to‐sample test, the average latency of Trial1 increased significantly in the model group compared with the sham group, while no obvious difference was observed in Trial2. Therefore, the difference in the average latency between Trial1 and Trial2 of the model group was significantly larger. Conclusions The cognitive impairment in rats with HF mainly reflected in the long‐term and working memory, spatial learning, and reversal learning ability. The probe trial and reversal test in the water maze may be more sensitive and preferred to evaluate cognitive function after HF. These findings would provide a brief evaluation protocol for further studies on the relationship between cognitive function and HF., This study aimed to find a more sensitive and systematic behavioral evaluation protocol to evaluate the cognitive impairment in rats with heart failure (HF).The cognitive impairment in rats with HF mainly reflected in the long‐term and working memory, spatial learning and reversal learning ability.

The reversal of voltage polarity is essential in HVDC cable systems with Current Source Converters (CSC), since it enables to revert the direction of the power flow. In a previous paper by the authors a life model for HVDC cables subjected to voltage polarity reversal was developed and applied for predicting the life of HVDC cables subjected to a voltage polarity reversal test. In that model, a heuristic procedure was developed for determining the relaxation time constant for the redistribution of space charges within the insulation after voltage polarity reversal. In this paper the model is refined according to a novel approach based on manufacturers’ experience with MIND HVDC cables.

Background Cocaine use disorder is characterized by compulsive drug-seeking that persists long into abstinence. Work using rodent models of cocaine addiction has found evidence for reversal learning deficits 21 days after non-contingent cocaine administration and 60 days after self-administration. Here we sought to determine if a deficit in reversal learning is present 3–4 weeks after cessation of cocaine self-administration, when relapse to cocaine-seeking is robust. Conversely, we hypothesized that reversal learning training would protect against relapse, similar to other forms of environmental enrichment. Methods Male rats underwent short access (ShA, 2 h/10d) or long access (LgA, 1 h/7d then 6 h/10d) cocaine self-administration, followed by 21–29 days of abstinence. During abstinence, a subset of rats underwent training in a plus-maze that required an egocentric strategy to earn a sucrose reward. Following response acquisition and retention, the ability to reverse the spatial navigation strategy was tested. Results Total trials to criteria and total errors made did not differ between the groups during response acquisition, retention, or reversal. On the first reversal test, ShA rats performed better than LgA and control rats. ShA rats’ performance worsened over time. There were no effects of cognitive training or length of cocaine access on context-primed relapse of cocaine-seeking. Conclusions The present data indicate that perhaps LgA cocaine self-administration does not produce adaptations to regions mediating context-primed relapse as it does for cocaine and cocaine-associated cue-induced reinstatement of drug-seeking. A time-dependent deficit in reversal learning was found only in ShA rats. Reversal learning training did not protect against cocaine relapse.

Of interest is comparing the out-of-sample forecasting performance of two competing models in the presence of possible instabilities. To that effect, we suggest using simple structural change tests, sup-Wald and UDmax as proposed by Andrews (1993) and Bai and Perron (1998), for changes in the mean of the loss-differences. Giacomini and Rossi (2010) proposed a Aiuctuations test and a one-time reversal test also applied to the loss-differences. When properly constructed to account for potential serial correlation under the null hypothesis to have a pivotal limit distribution, it is shown that their tests have undesirable power properties, power that can be low and non-increasing as the alternative gets further from the null hypothesis. The good power properties they reported is simply an artifact of imposing a priori that the loss di§erentials are serially uncorrelated and using the simple sample variance to scale the tests. On the contrary, our statistics are shown to have higher monotonic power, especially the UDmax version. We use their empirical examples to show the practical relevance of the issues raised.

The Sato–Vartia (SV) index for bilateral price comparisons has impressive analytical properties and is used intensively in recent international trade and macroeconomic analyses. We show that the SV index is only one of many logarithmic indices that satisfy the factor reversal test discussed in index number theory. In this paper we propose several transitive multilateral versions of the SV index but note that these do not satisfy factor reversal test. We derive closed form expressions for the transitive logarithmic indices and empirically implement the new indices for cross-country price comparisons using World Bank data from the 2011 International Comparison Program.

There has been a long-standing need to develop efficient and standardized behavioral test methods for evaluating higher-order brain functions in mice. Here, we developed and validated a behavioral flexibility test in mice using IntelliCage, a fully automated behavioral analysis system for mice in a group-housed environment. We first developed a "behavioral sequencing task" in the IntelliCage that enables us to assess the learning ability of place discrimination and behavioral sequence for reward acquisition. In the serial reversal learning using the task, the discriminated spatial patterns of the rewarded and never-rewarded places were serially reversed, and thus, mice were accordingly expected to realign the previously acquired behavioral sequence. In general, the tested mice showed rapid acquisition of the behavioral sequencing task and behavioral flexibility in the subsequent serial reversal stages both in intra- and inter-session analyses. It was found that essentially the same results were obtained among three different laboratories, which confirm the high stability of the present test protocol in different strains of mice (C57BL/6, DBA/2, and ICR). In particular, the most trained cohort of C57BL/6 mice achieved a markedly rapid adaptation to the reversal task in the final phase of the long-term serial reversal test, which possibly indicated that the mice adapted to the "reversal rule" itself. In conclusion, the newly developed behavioral test was shown to be a valid assay of behavioral flexibility in mice, and is expected to be utilized in tests of mouse models of cognitive deficits.

We propose new methods for comparing the out-of-sample forecasting performance of two competing models in the presence of possible instabilities. The main idea is to develop a measure of the relative local forecasting performance for the two models, and to investigate its stability over time by means of statistical tests. We propose two tests (the Fluctuation test and the One-Time Reversal test) that analyze the evolution of the models' relative performance over historical samples. In contrast to previous approaches to forecast comparison, which are based on measures of global performance, we focus on the entire time path of the models' relative performance, which may contain useful information that is lost when looking for the model that forecasts best on average. We apply our tests to the analysis of the time variation in the out-of-sample forecasting performance of monetary models of exchange rate determination relative to the random walk. Copyright © 2010 John Wiley & Sons, Ltd.

People with early-stage Huntington's disease have been found to have a specific deficit in performing an extra-dimensional shift. To date no evidence of this deficit has been identified in transgenic or knock-in rodent models of the disease. The aim of the present paper then, was to test whether homozygous knock-in mice derived from the Hdh(CAG(150)) mouse line were impaired in any of five 2-choice discrimination tasks (simple, compound, compound reversal, intra-dimensional shift and extra-dimensional shift), and whether these mice were impaired at recalling these tasks on the following day. On the extra-dimensional shift task the Hdh(CAG(150)) homozygous mice required a greater number of trials to reach criteria than mice and the percentage of correct choices within the trials was also significantly reduced compared with the animals. For the recall tasks, a deficit for recalling the compound reversal test was found in the Hdh(CAG(150)) homozygous mice for both number of trials required to reach criteria and percentage of correct choices within the trials. Recall for the intra-dimensional shift task was also impaired in these animals when measured by the percentage of correct choices. Our results demonstrate a pronounced deficit in the Hdh(CAG(150)) mice not only on extra-dimensional shift performance in agreement with human studies, but also on recall tasks for both the compound reversal and the intra-dimensional shift tasks.

After reviewing existing environmental performance indices the paper suggests an index of overall environmental performance in terms of geometric mean and avoiding scaling or finding weights for component indicators which may be independent or have correlations with different degrees. The suggested index satisfies many desired properties including monotonically increasing, time reversal test, formation of chain indices, independent of change of scale, reduction of substitutability between component indicators, etc. and facilitates further statistical analysis like estimation, confidence interval and test of significance and identifies the critical areas requiring corrective measures. Such identification is important from a policy point of view. Separate indices for core areas or drivers can be constructed easily by clumping relevant indicators pertaining to each core area. The method helps to reflect path of improvement registered by a country or a region over time. Such paths may provide new criteria for comparison of countries across time.

Taste aversion learning is induced through two different behavioral procedures: a short-term or concurrent (two-daily flavors) and a long-term or sequential (one-daily flavor) procedure. For the concurrent group of animals, two gustatory/olfactory stimuli are presented separately but at the same time on a daily basis. One is paired with simultaneous intragastric administration of hypertonic NaCl and the other with physiological saline. For the sequential group, the two stimuli are presented on alternate days, one of them followed by intragastric injection of the aversive stimulus and the other by saline, both after a delay of 15 min. The two groups learned the task, but when they were subjected to a flavor-placement reversal test only the sequential group was successful in achieving it. In a second experiment, three groups of animals had to learn concurrent or sequential discrimination tasks (with either simultaneous or delayed administration of the visceral stimulus) using only spatial/proprioceptive cues. The data show that none of the groups learned them under these conditions. The results are discussed in terms of the different modalities of learning. Short-term and long-term taste aversion learning are different in the anatomical structures involved, the number of trials required for acquisition and, as shown in this paper, flexibility.

English-speaking subjects were taught 16 English-French word pairs. Within any given trial, one word from each pair was presented; for eight items, subjects were to select its counterpart from an array of words in the other language (selection-based training), and for the other eight items there was no array and subjects were to type its counterpart (topography-based training). In Experiment 1, all items were trained from French to English, and later, interspersed no-feedback probe trials tested for the emergence of the reversed relations. Half of the eight selection-trained items were tested in the selection-based mode and half were tested in the topography-based mode; similarly, half of the eight topography-trained items were tested in the selection-based mode and half were tested in the topography-based mode. On the first reversal test trial, all 7 subjects scored 100% correct for the selection-tested items; in contrast, 5 of the 7 subjects scored 0% or near 0% correct for the topography-tested items, which improved to varying degrees with repeated testing. The training response mode affected neither acquisition rate nor reversal test trial performance. In Experiment 2, all items were tested in the topography-based mode only, and subjects were exposed to nine consecutive reversal test trials prior to interspersed probe testing. Improved accuracy across reversal test trials was not observed until the conditions of probe testing were instated, an indication that reexposure to the trained relations was a crucial component of delayed emergence. In Experiment 3, all items were trained from English to French, resulting in subjects typing a familiar rather than an unfamiliar word on reversal test trials. Accuracy on reversal test trials was considerably better than in the previous two experiments. We discuss the implications of our findings for stimulus equivalence research.

In “Imposing Genetic Diversity,” Robert Sparrow (2015) offers a means to assess the value of genetic diversity. He proposes a number of thought experiments that draw on a particular argumentative s...

In his target article, Sparrow (2015) argues that we ought to be wary of our positive intuitions toward genetic diversity because they result in problematic conclusions when a “reversal test” is ap...

Cognitive flexibility can be assessed in reversal learning tests, which are sensitive to modulation of 5-HT2C receptor (5-HT2CR) function. Successful performance in these tests depends on at least two dissociable cognitive mechanisms which may separately dissipate associations of previous positive and negative valence. The first is opposed by perseverance and the second by learned non-reward. The current experiments explored the effect of reducing function of the 5-HT2CR on the cognitive mechanisms underlying egocentric reversal learning in the mouse. Experiment 1 used the 5-HT2CR antagonist SB242084 (0.5 mg/kg) in a between-groups serial design and Experiment 2 used 5-HT2CR KO mice in a repeated measures design. Animals initially learned to discriminate between two egocentric turning directions, only one of which was food rewarded (denoted CS+, CS−), in a T- or Y-maze configuration. This was followed by three conditions; (1) Full reversal, where contingencies reversed; (2) Perseverance, where the previous CS+ became CS− and the previous CS− was replaced by a novel CS+; (3) Learned non-reward, where the previous CS− became CS+ and the previous CS+ was replaced by a novel CS-. SB242084 reduced perseverance, observed as a decrease in trials and incorrect responses to criterion, but increased learned non-reward, observed as an increase in trials to criterion. In contrast, 5-HT2CR KO mice showed increased perseverance. 5-HT2CR KO mice also showed retarded egocentric discrimination learning. Neither manipulation of 5-HT2CR function affected performance in the full reversal test. These results are unlikely to be accounted for by increased novelty attraction, as SB242084 failed to affect performance in an unrewarded novelty task. In conclusion, acute 5-HT2CR antagonism and constitutive loss of the 5-HT2CR have opposing effects on perseverance in egocentric reversal learning in mice. It is likely that this difference reflects the broader impact of 5HT2CR loss on the development and maintenance of cognitive function.

Paleomagnetic data frequently display bipolar data that are not exactly antipodal. One cause of this biasing is the addition of another later (secondary) magnetization that cannot be removed by laboratory demagnetization experiments. The magnitude of this hidden secondary magnetization can be calculated when only two values are known : the non-antipodal angle (measured), and the angle between the Normal direction (measured) and secondary direction (measured or assumed). Furthermore, a minimum magnitude of the secondary magnetization can be calculated with knowledge only of the non-antipodal angle. Applied to three published data sets (sandstone, limestone and diorite intrusion) with non-antipodal angles of 11°, 28° and 11° respectively ; a secondary component is calculated at 25%, 28% and 16% of the characteristic magnetization remaining after laboratory cleaning. Near surface alteration (weathering) appears to be the source of secondary magnetization in two of these cases. A directionally consistent, biasing effect of a few degrees is made on the mean direction as compared to the conventional calculation of averaging the non-antipodal directions.

In the present study we extended errorless learning to a conditional temporal discrimination. Pigeons’ responses to a left–red key after a 2-s sample and to a right–green key after a 10-s sample were reinforced. There were two groups: One learned the discrimination through trial and error and the other through an errorless learning procedure. Then, both groups were presented with three types of tests. First, they were exposed to intermediate durations between 2 s and 10 s, and given a choice between both keys (stimulus generalization test). Second, a delay from 1 s to 16 s was included between the offset of the sample and the onset of the choice keys (delay test). Finally, pigeons learned a new discrimination in which the stimuli were switched (reversal test). Results showed that pigeons from the Errorless group made significantly fewer errors than those in the Trial-and-Error group. Both groups performed similarly during the stimulus generalization test and the reversal test, but results of the delay test suggested that, on long stimulus trials, responding in the errorless training group was less disrupted by delays., This research was presented in part at the 33rd Annual Convention of the Association of Behavioral Analysis (ABA) in San Diego, California. The authors were supported by the Portuguese Foundation for Science and Technology (FT). The authors thank Herbert S. Terrace for his valuable thoughts at the 31st Annual Meeting of the Society for the Quantitative Analyses of Behavior (SQAB) about this research.

For a change in prices, the common-scaling social cost-of-living index is the equal scaling of every individual's expenditure level needed to restore the level of social welfare to its pre-change value. This index does not, in general, satisfy two standard index-number tests. The reversal test requires the index value for the reverse change to be the reciprocal of the original index. And the circular test requires the product of index values for successive price changes to be equal to the index value for the whole change. We show that both tests are satisfied if and only if the Bergson-Samuelson indirect social-welfare function is homothetic in prices, a condition which does not require individual preferences to be homothetic. If individual preferences are homothetic, however, stronger conditions on the Bergson-Samuelson indirect must be satisfied. Given these results, we ask whether the restrictions are empirically reasonable and find, in the case that individual preferences are not homothetic, that the restrictions make little difference to estimates of the index.

The Jordan Left-Right Reversal Test (JLRRT) was first published in 1974 (1) as a convenient measure of symbol reversals in children. A current revision of the test, based on 3,000 children, showed error scores to be inversely related to age and sex. Learning disabled children and a group of below average readers made significantly more errors, indicating that visual reversals are dysfunctional for reading skills.

Potential long-term effects of intrapartum meperidine were studied in rhesus monkey infants whose dams received 0,2, or 3 mg/kg meperidine, i.v., during labor (n = 5, 5, 3). Spontaneous behavior and cognitive performance were evaluated at 3–12 months of age. Observation of spontaneous behaviors indicated less age-related increase in quiet activities in drug-exposed infants. In the discrimination reversal test, drug-exposed infants had more balks (p = 0.008) and fewer correct choices (p = 0.008) during initial phases of the first reversal. Due to sex differences in the delayed alternation test, evaluation of drug effects on short-term memory was not possible. In the continuous performance test, drug-exposed infants performed better (NS) and had fewer omission errors (p = 0.034) during the second half of the test period. These initial findings suggest that short-term opiate exposure during labor can alter later behavior of infant monkeys.

We examine time reversal invariance in the beta-decays of 8B(2+) and 8Li(2+) to 8Be(2+) in detail, with particular attention to final state interactions of the two alpha particles from the decay of 8Be, and of the electron (positron) with the daughter nucleus. A R-matrix formulation is used, with the initial state described by a shell model. The R-matrix parameters are obtained by fitting the alpha-\alpha scattering phase shifts and allowed beta-decay rates. Because the nuclear final state interaction effects on the time reversal test come from second forbidden beta-decays, they are small and can be minimized by a suitable choice of kinematic conditions. The e(+/-)-nucleus Coulomb interaction induced T-violation effects depend on the first forbidden operators., Comment: 64 pages, latex, 26 figures (available upon request)

Letter reversal errors, both expressive (written) and receptive (read), are common among children and adults with reading problems. Educators have long wrestled with the problem of eliminating letter reversal errors. This investigation examined whether a program which trains directional awareness can reduce the letter reversal discrimination errors of deficient readers. We chose to examine receptive letter reversal errors for two reasons: first, because they represent a significant reading problem; and second, because a standardized measure of these errors exists in the form of the Jordan Left/Right Reversal Test. Ten deficient readers, ranging from 6 to 19 years of age, were selected to participate in the study. Although the older students exceeded the norms range of the Jordan Test, they were included in order to examine the viability of maturational and "critical period" hypotheses which might have some bearing upon skill gains among learners of different ages. Eight of the ten had achieved scores within the normal range on standardized

As Vartia (1976, p. 32) has noted correctly there still does not exist a sufficient number of different axiom systems each characterizing one and only one index. By characterization we mean the deduction of a certain index from a set of given conditions such that the index in question not only meets the required conditions but also represents the only index that can be deduced from these conditions. If for some reason these conditions are considered to be basic or natural requirements they are often called axioms or tests. The so-called test approach in the theory of the price index heavily makes use of certain axioms/tests and special conditions in order to define or characterize price indices as well as to evaluate their distinct merits. A rather comprehensive presentation of this branch of index theory is provided in Eichhorn/Voeller (1976b) where the general solution of the inconsistency problem of Fisher's tests is proven I). Also, characterization s of many well-known price indices are introduced including a characterization of Fisher's "ideal index". This latter index deserves particular attention since it satisfies all of Fisher's tests for price and quantity indices except for the Circular Test. Consequently, Fisher himself (1922, p. 271) proposed to discard the Circular Test 2) The problem, however, as to Fisher's assumed superiority of the "ideal index" over all other indices remained unsolved. Furthermore, the inconsistency of different subsets of Fisher's original test system calls for new and consistent axiom/test systems to define or even characterize indices. In the following, we shall state three tests each imposing a kind of reversal procedure on an index function. Two of the reversal tests, the Time Reversal Test and the Factor Reversal Test, are taken from Fisher's original test system. The third test which we call Price Reversal Test is new but very reasonable. As will be shown below, Fisher's "ideal index" represents the only index satisfying all three reversal tests simultaneously, i.e., can be characterized by them.

RICE and quantum indexes (P, Q) are dual to each other if PQ = E where E is the expenditure index. They satisfy the weak factor reversal test.' If they share an identical weighting formula as weighted averages of price and quantity relatives, they satisfy the strong factor reversal test, that is, they are ideal. The most celebrated ideal economic index is the one associated with the name of Irving Fisher though it was discovered before him. No ideal index as simple as Fisher's has been discovered since. Log-change index numbers have become increasingly popular in recent years, particularly as an approximation to the theoretically desirable Divisia index. Theil (1973) proposed a new log-change index number that alhnost satisfies the strong factor reversal test. I derived several alternative formulas that improve in the degree of approximation (Sato, 1974b). But neither Theil nor I was able to obtain the ideal log-change index. In section II, I report its discovery. Our pessimism has proved premature. Indeed, the formula was self-evident from the very beginning -we simply failed to see it.2 There are dual dualities between economic indexes and homothetic preferences (Samuelson and Swamy, 1974). A price or quantum index is associated with a homothetic indirect or direct preference ordering. If P and Q are dual to each other, so are the direct and indirect preference orderings corresponding to them. If P and Q are ideal, the latter are not only dual but also share an identical mathematical form. They are strictly self-dual as I call them elsewhere.3 An obvious example is the association of Cobb-Douglas indexes and preferences. A less obvious example is the association of Fisher's ideal indexes and quadratic preferences. The association itself was discovered by Konuis and Buscheguence a half century ago in 1926.4 Note that homothetic quadratic preferences are self-dual. Then, what is the selfdual preference ordering that corresponds to our ideal log-change index? We shall show in section III that it is the CES function that has become so popular in the economic literature, originally discussed by Bergson (1936), rediscovered by Solow (1956), and popularized by Arrow et al. (1961). The CES function is known to be self-dual (Samuelson, 1965) and yet the economic index associated with it has eluded discovery until now. Economic indexes are useful because they apply even when underlying preferences are not homothetic.5 We shall show in section IV that the ideal log-change index corresponds to the addilog preference ordering introduced by Houthakker (1960).

The Jordan Left-Right Reversal Test was constructed in order to standardize a measure for symbol reversals (letters and numbers) in normal children, ages 6 through 10. A random sample of 2,500 subjects was tested in schools selected in six different states. Results established age-sex norms for symbol reversals. Error scores were inversely related to age of all subjects and generally lower for girls. Younger children (6–8.5) made significantly more number reversals than letter reversals. Boys in this age grouping made the highest percentage of number errors. When the Reversal Test was administered to a sample of minimally brain dysfunction children, results indicated that the test has adequate discrimination ability and suggest that visual reversals are a symptom of this childhood disorder.

Support for the hypothesis that adaptive responses reduce the drive component in behaviour was found in an experiment involving two groups of rats placed, for different periods, in a water tank. After being detained in a delay chamber, the rats were allowed to escape after making a brightness discrimination. A discrimination reversal test was undertaken in order to establish whether the original learning had been affected by the length of the water-detention period. It was found that a long prediscrimination detention period facilitated reversal learning. This result was taken to support the major contention of the paper, that prolonged exposure to a potential stress situation encouraged the elaboration of drive-minimizing responses and, in consequence, favoured discrimination learning.

A classically conditioned discrimination was established between two rates of intermittent stimulation in the auditory modality for four rabbits and in the visual modality for four additional rabbits. Following acquisition in the original modality, both stimulus modality and stimulus contingencies were changed in a cross-modal reversal test. All rabbits were subsequently tested in reacquisition of the original discrimination. Results were compared to a previous test of direct cross-modal transfer. It was concluded that results of cross-modal reversal support the earlier finding of cross-modal transfer in the rabbit.

Index number theory, and the theory of price indices in particular, tends to run in terms of arithmetic properties. Such questions as whether a particular index satisfies a chain property or a reversal test are well discussed and relatively well understood. Important as such properties and such discussions are, however, they are only one side of the index number story. The other side lies in what I shall term the economic theory of index numbers: What are we trying to measure? What would we do if we had all the information possible? What, if anything, are we attempting to approximate with the index numbers computed in practice?

The study was designed to investigate the relationship of reversal of letters and numbers to academic achievement to decide if the tendency to reversal might be used to predict achievement. Two groups of 45 predominantly white third-grade students whose chronological ages were 9.0 yr. or above were administered the California Achievement Tests and the Jordan Left-Right Reversal Test. A statistical comparison was made using scaled scores on the California Achievement Tests and raw errors on the Jordan Left-Right Reversal Test. Reversal was significantly correlated with academic achievement. Children who exhibit reversals at 9 yr. of age or older may be expected to perform less well academically than children who do not reverse letters.

This investigation established the reliability of the Jordan Left-Right Reversal Test for learning disabled children. Test-retest reliability coefficients ranged from .89 to .92 for a sample of 91 children, 5 through 12 yr., attending private schools for children with learning disabilities. Reversal errors decreased with age for boys and girls, although girls 9 through 12 made significantly fewer errors than did boys in the same age range. Learning disabled children made more errors at all ages than normal children. This test instrument was determined to be a measure of the global tendency to make visual reversal errors and was viewed as an appropriate part of the learning disabilities diagnostic procedure.