It is shown that in any model of constructive mathematics in which a certain omniscience principle is false, for strongly extensional functions on an interval the distinction between sequentially continuous and regulated disappears. It follows, without the use of Markov's Principle, that any recursive function of bounded variation on a bounded closed interval is recursively sequentially continuous.

It is shown constructively that a strongly extensional function of bounded variation on an interval is regulated, in a sequential sense that is classically equivalent to the usual one.

Photovoltaic power forecasting can provide strong support for the safe operation of the power system. Existing forecasting methods are ineffective for grid scheduling decisions or risk analysis. The novel multicluster interval prediction method is proposed to consider the volatility and randomness of PV power output. First, this method utilizes the sparse autoencoder and Bayesian regularized NARX network for point forecasting of PV power. Second, density peak clustering improved by kernel Mahalanobis distance is applied to classify the dataset into multiple (...) clusters, including forecasting error and meteorological factors. Finally, the joint probability density is established by multivariate kernel density estimation to accomplish the PV power interval prediction. The proposed hybrid method is applied for the interval prediction of PV power at Yulara, Australia. Comparative research of point forecasting is implemented to evaluate the machine learning and deep learning methods, with the proposed SAE-BRNARX under four different periods. Results shows that the average values of nRMSE, MRE, nMAE, and R2 for the four periods are 4.45%, 0.90%, −0.15%, 3.39%, and 95.93%, respectively. Moreover, the results of interval prediction obtained by the other interval prediction approaches are compared with the proposed KMDDPC-MKDE. It shows that the average values of PICP, PINAW, ACE, and nMPICD for four periods are 93.93%, 9.50%, 3.93%, and 7.10% at 90% confidence level, respectively. Outcomes demonstrate that the proposed method can obtain more accuracy, a higher coverage rate, narrower average bandwidth, and a closer distance between the middle of interval and actual value than other methods. (shrink)

Nehru’s vision found near unanimous support from the relevant constituencies. Even the rare dissenting voices did not question the core strategy of primacy to heavy industries. At Nehru’s instance, his close associate and a self-taught statistician, P. C. Mahalanobis, prepared the Draft Plan-frame of the second plan, which was extensively discussed and endorsed by a panel of twenty-one leading economists of India, including V. K. R. V. Rao, D. R. Gadgil, K. N. Raj, A. K. Das Gupta, Vakil, and (...) D. T. Lakdawala. Only Shenoy submitted a dissent note questioning the wisdom of the large deficit financing. All foreign economists invited by the government supported the Plan-frame. Milton Friedman, independently sent by the US government, provided a trenchant critique that proved prophetic later but had no salience at the time. Some dissenting voices in the parliament notwithstanding, politicians overwhelmingly endorsed Nehru’s vision, while leading businessmen had already given it a nod through their 1945 Bombay Plan. (shrink)

Nowadays, the quality standards of higher education institutions pay special attention to the performance and evaluation of the students. Then, having a complete academic record of each student, such as number of attempts, average grade and so on, plays a key role. In this context, the existence of missing data, which can happen for different reasons, leads to affect adversely interesting future analysis. Therefore, the use of imputation techniques is presented as a helpful tool to estimate the value of missing (...) data. This work deals with the academic records of engineering students, in which imputation techniques are applied. More specifically, it is assessed and compared to the performance of the multivariate imputation by chained equations methodology, the adaptive assignation algorithm based on multivariate adaptive regression splines and a hybridization based on self-organisation maps with Mahalanobis distances and AAA algorithm. The results show that proposed methods obtain successfully results regardless the number of missing values, in general terms. (shrink)

The “Coefficient of Racial Likeness” (CRL) ascribed to Karl Pearson (1857–1936) was born in the Biometric Laboratory in London. It was developed with the purpose to determine the distance between two samples of different origins. Widely used but also distrusted before being ultimately replaced by a true statistical measure of divergence, the Mahalanobis distance (D2), the global biography of the CRL reveals the social, scientific, and historical forces at play that determined the lifespan of the coefficient, its success and (...) fall from grace. Closely linked to Pearson personally, he could no longer control its fate once the CRL had escaped his laboratory and gotten into the hands of critical mathematicians, or to China where results of racial classification based on a single number and the assumption of homogeneity did not please the audience. (shrink)

This chapter examines the effectiveness of five weighting and matching techniques, including propensity score matching (PSM), in improving covariate balance and reducing bias when estimating treatment effects in finite-sample situations through Monte Carlo simulations. King and Nielsen (2019) argue that pruning observations based on PSM with 1-to-1 greedy matching can worsen, rather than improve, covariate balance and increase bias in treatment effect estimates. In our simulations, we observed this phenomenon not only in PSM with 1-to-1 greedy matching but also in (...) other covariate balancing techniques that King and Nielsen (2019) recommend as better matching methods, i.e., Mahalanobis distance matching (MDM) and coarsened exact matching (CEM). Across all weighting and matching techniques and data-generating processes examined in this study, our findings indicate that matching and weighting under extreme caliper or cut-point settings do not improve covariate balance. In addition, once covariate balance is substantially improved, the estimated bias tends to increase slightly as balance continues to improve. Moreover, our simulation results suggest that OLS with appropriately specified covariates reduces selection bias as effectively as the other weighting and matching methods. These findings highlight the importance of avoiding a one-size-fits-all approach and of carefully identifying the appropriate nonexperimental estimator for a given sample by thoroughly examining the characteristics of the available data. (shrink)

In late 1960s and 1970s, electronics was an emerging sector of technology development and industrial production. It was seen as a sunrise industry, with potential applications of electronics in varied sectors such as defence, atomic energy, entertainment, communication and education. All these factors attracted the governments, policy makers and Indian industry to this field. The government’s entry into electronics and computing sectors was driven by the desire to achieve self reliance, ending multinational monopoly and dependence on imports. In the run (...) up to the formation of the Department of Electronics and soon afterwards, scientists and technocrats took upon themselves the task of setting up an electronics industry. They started looking for opportunities in R & D, design, production, export and import. Electronics was considered strategic—on par with space and atomic energy, so they strived for national control over it. This gave rise to the phenomenon of ‘government entrepreneurship’, whereby scientific departments planned commercial ventures for production of components, computers and software. Several ventures were conceived at ISI, TIFR, DAE and DoE under Mahalanobis, Bhabha, Sarabahi and M G K Menon. Most of them failed for lack of business and market orientation. The ones that took shape helped India develop certain capabilities and manpower in advanced areas of R & D and production. This helped created nuclei to human capital and expertise that eventually helped the private sector in seeding the software revolution in the decades that followed. (shrink)

BackgroundAlthough gait patterns disturbances are known to be related to cognitive decline, there is no consensus on the possibility of predicting one from the other. It is necessary to find the optimal gait features, experimental protocols, and computational algorithms to achieve this purpose.PurposesTo assess the efficacy of the Stable Sparse Classifiers procedure for discriminating young and healthy older adults, as well as healthy and cognitively impaired elderly groups from their gait patterns. To identify the walking tasks or combinations of tasks (...) and specific spatio-temporal gait features that allow the best prediction with SSC.MethodsA sample of 125 participants was studied. They underwent assessment with five neuropsychological tests that explore different cognitive domains. A summarized cognitive index, based on the Mahalanobis distance from normative data, was calculated. The sample was divided into three groups using k-means clustering of MDCog in addition to Age. The participants executed four walking tasks and their gait patterns, measured with a body-fixed Inertial Measurement Unit, were used to calculate 16 STGF and dual-task costs. SSC was then employed to predict which group the participants belonged to. The classification's performance was assessed using the area under the receiver operating curves and the stable biomarkers were identified.ResultsThe discrimination HE vs. MCI-E revealed that the combination of the easy dual-task and the fast walking task had the best prediction performance. The features related to gait variability and to the amplitude of vertical acceleration had the largest predictive power. SSC prediction accuracy was better than the accuracies obtained with linear discriminant analysis and support vector machine classifiers.ConclusionsThe study corroborated that the changes in gait patterns can be used to discriminate between young and healthy older adults and more importantly between healthy and cognitively impaired adults. A subset of gait tasks and STGF optimal for achieving this goal with SSC were identified, with the latter method superior to other classification techniques. (shrink)

There are three main problems in track fastener defect detection based on image: The number of abnormal fastener pictures is scarce, and supervised learning detection model is difficult to establish. The potential data features obtained by different feature extraction methods are different. Some methods focus on edge features, and some methods focus on texture features. Different features have different detection capabilities, and these features are not effectively fused and utilized. The detection of the track fastener clip will be interfered by (...) the track fastener bolt subimage. Aiming at the above three problems, a method for track fastener defects detection based on Local Deep Feature Fusion Network is proposed. Firstly, the track fastener image segmentation method is used to obtain the track fastener clip subimage, which can effectively reduce the interference of bolt subimage features on the track fastener clip detection. Secondly, the edge features and texture features of track fastener clip subimages are extracted by Autoencoder and Restricted Boltzmann Machine, and the features are fused. Finally, the similarity measurement method Mahalanobis Distance is used to detect defects in track fasteners. The effectiveness of the proposed method is verified by real Pandrol track fastener images. (shrink)

With the development of communication and computer technology, the application of big data technology has become increasingly widespread. Reasonable, effective, and fast retrieval methods for querying information from massive data have become an important content of current research. This article provides an image retrieval method based on the weighted nearest neighbor label prediction for the problem of automatic image annotation and keyword image retrieval. In order to improve the performance of the test method, scientific experimental verification was implemented. The nearest (...) neighbor weights are determined by maximizing the training image annotation, and experiments are carried out from multiple angles based on the Mahalanobis metric learning integration model. The experimental results show that the proposed tag correlation prediction propagation model has obvious improvements in accuracy, recall rate, break-even point, and overall average accuracy performance compared with other widely used algorithm models. (shrink)

erative clustering. First, we show formally that the common heuristic agglomerative clustering algorithms – Ward’s method, single-link, complete-link, and a variant of group-average – are each equivalent to a hierarchical model-based method. This interpretation gives a theoretical explanation of the empirical behavior of these algorithms, as well as a principled approach to resolving practical issues, such as number of clusters or the choice of method. Second, we show how a model-based viewpoint can suggest variations on these basic agglomerative algorithms. We (...) introduce adjusted complete-link, Mahalanobis-link, and line-link as variants, and demonstrate their utility. (shrink)

The research aims to theoretically substantiate the application of robust clustering algorithms to enhance the effectiveness of teaching methodologies for the Russian language. The authors explore the potential use of mathematical algorithms for predicting student behavior. The problem of forecasting learning activity related to the mastery of linguistic material necessitates the use of analytical tools capable of identifying differences among learners. This approach creates opportunities for designing individualized educational trajectories that consider the cognitive and behavioral characteristics of schoolchildren, which vary (...) depending on the dominance of the right or left hemisphere of the brain. The methodological foundation of this research comprises fundamental research on hemispheric asymmetry and higher mental functions, as well as machine learning theory. The primary research method involves robust clustering algorithms, which allow for more accurate classification of students based on data analysis, including academic performance, task completion time, and common grammatical errors. Methods based on Mahalanobis distance facilitate the selection of individualized Russian language learning trajectories that align with specific didactic tasks set by the teacher. The research opens new perspectives in Russian language teaching methodologies by integrating mathematical modeling to improve the quality of philological education and adapt to the contemporary demands of the digital society. The research is original in that it establishes a connection between the cognitive approach in Russian language teaching methodologies and the application of robust clustering algorithms for predicting student behavior. (shrink)

Evidence, as viewed through the lens of statistical significance, is not always as it appears! In the investigation of clinical research findings arising from statistical analyses, a fundamental initial step for the emerging fraud detective is to retrieve the source data for cross-examination with the study data. Recognizing that source data are not always forthcoming and that, realistically speaking, the investigator may be uninitiated in fraud detection and investigation, this paper will highlight some key methodological procedures for providing a sounder (...) evidence base for withdrawing from a study on grounds of integrity. The promotion of patient safety is paramount. However, there is a broader rationale for disseminating these ideas. This includes empowering researchers to optimize their personal integrity, make informed choices regarding membership of future research collaborations and successfully voice their concerns to journal editors, particularly where a conflict of interests can render such dialogues particularly difficult. Recommendations will be supported by topical case studies and practical steps involving data exploration, testing of baseline data and application of Benford’s Law. While this paper has a clinical focus, the advice provided is transferrable to a wide range of multidisciplinary research settings outside of Medicine. (shrink)

At independence in 1947, Prime Minister Jawaharlal Nehru embarked upon two foundational projects to build modern India: a political project aimed at establishing democracy and an economic one aimed at ending poverty. Three-quarters of a century later, his political project is a resounding success, but the opposite is true of the economic one. While much has been written in recent years on the Nehru-era political history and thought and its impact on post-independence India, no such work on the economic side (...) exists. The present volume fills this gap. It draws on numerous contemporary documents and writings to examine the evolution of Nehru’s economic philosophy with socialism, self-sufficiency, and heavy-industry development at its core. It discusses in full detail the historical circumstances and contemporary thought that led to near unanimity on adopting a development model that, in hindsight, was deeply and obviously flawed. It goes on to highlight how the focus on heavy industry and self-sufficiency translated into myriad inefficiencies and an exclusionary development model that left all but a small elite out of the mainstream growth process. The volume goes on to argue that the entrenchment of socialist thought within the country’s democratic polity effectively ruled out any major change of course for many decades. The bequest of socialist thought from one generation to the next led to its perpetuation among politicians, bureaucrats, intellectuals, and even businessmen. The result was that alternative ideas failed to germinate, with a change of course ruled out until an economic crisis closed all other options. (shrink)

This chapter provides a crisp summary of the book, pointing out that the volume is divided into three parts. The primary focus of Part I is on Nehru-era economic thought. It describes Nehru’s own evolution from a radical to a moderate socialist and documents the all-around consensus prevailing around his development strategy at the time of the launch of the foundational second development plan. Part II turns to the history of the implementation of Nehru’s development strategy and its consequences for (...) growth, transformation, and poverty. In particular, it describes the evolution of investment licensing, the highly restrictive import policy after a decade of liberal phase, and the myriad inefficiencies resulting from them. Part III turns to the long-run implications of the Nehru-era strategy. It shows that the entrenchment of socialist thought among nearly all relevant actors made a change of course difficult and greatly slowed down the transition to a market economy. (shrink)