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On Copositive Matrices and Completely Mixed Games
No full textIn 1945, Kaplansky [4] introduced the concept of the games being completely mixed and presented a necessary and sufficient condition for a game associated with a skew-symmetric matrix to be completely mixed. Recently, we have provided an additional condition for such games. It is known that skew symmetric matrices are Q0 and P0. In 1997, Murthy and Parthasarathy proved that if a matrix B belongs to fully copositive (C0f) and Q0, then B also belongs to P0. Building upon these results, our main result states that if the game associated with a fully copositive Q0-matrix B is completely mixed, then B+Dj∈Q for all j from 1 to n, where Dj is a diagonal matrix whose jth diagonal entry is 1 and else 0. Additionally, we prove that if B∈C0f∩Q0 but not a Q-matrix, then GB is completely mixed game if and only if B+Dj∈Q for all j from 1 to n
Parameter-Free Undersampling for Multi-Label Data
No full textThis work presents a novel undersampling scheme to tackle the imbalance problem in multi-label datasets. We use the principles of the natural nearest neighborhood and follow a paradigm of label-specific undersampling. Natural-nearest neighborhood is a parameter-free principle. Our scheme’s novelty lies in exploring the parameter-optimization-free natural nearest neighborhood principles. The class imbalance problem is particularly challenging in a multi-label context, as the imbalance ratio and the majority-minority distributions vary from label to label. Consequently, the majority-minority class overlaps also vary across the labels. Working on this aspect, we propose a framework where a single natural neighbor search is sufficient to identify all the label-specific overlaps. Natural neighbor information is also used to find the key lattices of the majority class (which we do not undersample). The performance of the proposed method, NaNUML, indicates its ability to mitigate the class-imbalance issue in multi-label datasets to a considerable extent. We could also establish a statistically superior performance over other competing methods several times. An empirical study involving twelve real-world multi-label datasets, seven competing methods, and four evaluating metrics - shows that the proposed method effectively handles the class-imbalance issue in multi-label datasets. In this work, we have presented a novel label-specific undersampling scheme, NaNUML, for multi-label datasets. NaNUML is based on the parameter-free natural neighbor search and the key factor, neighborhood size ’k’ is determined without invoking any parameter optimization
Tight Lower Bound on Equivalence Testing in Conditional Sampling Model
No full textWe study the equivalence testing problem where the goal is to determine if the given two unknown distributions on [n] are equal or ε-far in the total variation distance in the conditional sampling model (CFGM, SICOMP16; CRS, SICOMP15) wherein a tester can get a sample from the distribution conditioned on any subset. Equivalence testing is a central problem in distribution testing, and there has been a plethora of work on this topic in various sampling models. Despite significant efforts over the years, there remains a gap in the current best-known upper bound of Õ(log log n) [FJOPS, COLT 2015] and lower bound of Ω(√log log n)[ACK, RANDOM 2015, Theory of Computing 2018]. Closing this gap has been repeatedly posed as an open problem (listed as problems 66 and 87 at sublinear.info). In this paper, we completely resolve the query complexity of this problem by showing a lower bound of Ω̃(log log n). For that purpose, we develop a novel and generic proof technique that enables us to break the √log log n barrier, not only for the equivalence testing problem but also for other distribution testing problems, such as uniblock property
Transport phenomena in phononic lattices: Effect of positional correlation
No full textWe make a comparative study of phonon transmission and phonon thermal conductance considering perfect and quasiperiodic lattices. Describing the lattice using spring bound masses, we compute transmission function based on Green\u27s function formalism. From our detailed analysis we find that positional correlations among substituted atoms greatly suppress phonon thermal conductance. Our study provides a suitable hint for the regulation of phonon transport and designing of efficient thermoelectric devices
Attitudes towards the environment: A study of farmers in India
No full textThis chapter summarises a series of studies that examined the salience of a sense of environmental protection in the minds of residents of three villages in West Bengal. India. It considers how their level of awareness and concern could initiate some public action and the formation of pressure groups for checking wasteful exploitation of natural resources. The investigation was based on a Household survey (n = 368), a Social Ecological Survey (n = 168) and an indepth study of 57 Village Council (Panchayat) members. It indicated a high level of awareness of environmental problems but superficial concern. Even among the new Panchayat members who expressed some anxiety over wasteful depletion of natural resources, their concern was not sufficiently crystallised so as to lead to any public action. People’s confidence in the ability of the panchayat and the government was also found to be low in general. Although a large number of respondents mentioned the possibility of an acute food shortage resulting from population explosion, few of them explicitly identified population growth as a contributor to environmental crisis. The findings suggest that in addition to non-formal ecological education, there is need for carefully designed activities aimed at the establishment of effective resource management institutions at the local level which may be empowered to control various forms of environmental degradation
Empowerment of Mothers and its Impact on the Health of Children: A Comparative Analysis of North-Eastern Region and the Rest of India
No full textIntroduction: There is no denying of mothers\u27 crucial role in nurturing a child. Studies have shown the greater contribution of mothers in raising children, especially in the early days of childhood, than their male counterparts. Therefore, empowering mothers would enhance their capacity in shaping the future of their children. This paper tries to understand how empowerment of mothers indicated by several factors affects not only the health status of the mothers but also the health of children in North-East India vis a vis the rest of India. Methods: Analysis is done by using NFHS Round 5 data on child\u27s (0–5 years) weight at birth, age, sex, height, status of BCG, DPT, Polio, Measles other vaccinations, hemoglobin, and mothers\u27 level of education, mothers\u27 age, various other healthcare measures. Bivariate frequency tables were computed, and Chi-square tests were performed to see if the relevant variables were dependent. Empowerment of North-East mothers in comparison to the rest of India is examined through the indicators of education, extent of reading newspaper, watching television, wealth index, religion, etc. that raise awareness and affect empowerment as reflected through their participation in decision making in the family, their psychological thinking about wife beating and undertake breastfeeding, BMI, anemia, etc. Health status of children is examined through HAZ, WAZ, WHZ, anemia, and BMI level. Logistic regression is used to examine the impact on status of each health variable of children of various attributes of mothers and empowerment indicators.Results: The result reveals relatively better health status of mothers in North-East as compared to the rest of India. Excepting preference for birth in hospital, immunization, and post-natal care, in other respects North-Eastern mothers take care of children including breastfeeding and maintaining mothers\u27 health during pregnancy which resulted in better child health in North-East India. As usual, in education and earning North-Eastern mothers are better placed as compared to the rest of India, and thus they are comparatively more empowered, which can be correlated with better health conditions as measured by HAZ, WAZ, WHZ, and BMI. The logistic regression results also suggest that conditions of empowerment lead to better child health. Conclusion: The findings suggest that in comparison to women in other parts of the country, being more literate, and having more social empowerment as evidenced from the indicators, women in North-East India take some extra care by extended breast feeding and maintaining mothers\u27 health so that healthy baby is born and they need not go for a higher number of vaccinations of children apart from basic immunizations provided by the government free of cost. Also, mothers\u27 empowerment level in all respects is very important for their healthcare, which puts North-Eastern region a little ahead in many respects
A New Symmetry-Based Transformer for Text Spotting in Person and Vehicle Re-Identification Images
No full textText spotting in person and vehicle re-identification images is complex due to the presence of multiple views of the same person and vehicle. Most existing models focus on text spotting in natural scene images, our work focuses on spotting in person and vehicle re-identification images. The rationale behind this work is that the person and the vehicles share symmetry properties and the bib number in the torso and license plate number in the vehicle are text. The method divides the input image into patches, and it explores vision transformation for encoding the patches into linear patches. The linearly embedded patches are fed to the feature similarity index step, which involves phase congruency and gradient magnitude to detect symmetric patches. The transformer is proposed to encode and capture textual information from the symmetry patches for text detection and recognition. The decoder receives the attention features from the encoder and fetches a multi-task head with the information about the detected and recognized text. The experiments on person and vehicle image benchmark, viz. (Person) Re-ID, RBNR, UFPR-ALPR and RodoSol datasets show significant improvement in performance when compared to other text spotting models. The effectiveness of the proposed model is validated by testing on the benchmark datasets, namely, ICDAR 2015, Total-Text and CTW1500 of natural scene images. Furthermore, cross-data validation shows the proposed method is independent of domains
A note on statistical analysis of Cpk for autocorrelated data in the presence of random measurement errors
No full textProcess capability indices (PCIs) have been widely used for process performance assessment. It provides a quantitative measure of performance of an industrial production process. Several PCIs have been proposed in the literature. C pk is one of the most useful capability index. Statistical properties of the estimator of C pk have been discussed by many researches under the assumption of identically and independently normal distribution. Some statistical properties of the estimator of C pk for autocorrelated data in presence of gauge measurement errors have studied by Scagliarini (2010). However, we found some critical error in the expression of expectation and variance of the estimator when process is autocorrelated as well as measurement error is present. Through this article, we present a corrected version of expectation and variance of the estimator
A note on the simultaneous 3-divisibility of class numbers of tuples of real quadratic fields
No full textLet r be a positive integer, and let k1,k2,⋯,kr be integers such that ki≡±1(mod9) for all 1≤i≤r. In this article, we prove the existence of infinitely many positive integers D such that the class numbers of the real quadratic fields Q(3D),Q(3(D-1)),Q(3(D-k12)),…,Q(3(D-kr2)) are simultaneously divisible by 3. This result gives an affirmative answer to a weaker version of a conjecture of Iizuka (J Number Theory 184:122–127, 2018)
Abelian surfaces and the non-Archimedean Hodge-D-conjecture – The semi-stable case
No full textIf X is a smooth projective variety over R, the Hodge D-conjecture of Beilinson asserts the surjectivity of the regulator map to Deligne cohomology with real coefficients. It is known to be false in general, but is true in some special cases like Abelian surfaces and K3-surfaces – and still expected to be true when the variety is defined over a number field. We prove an analogue of this for Abelian surfaces at a non-Archimedean place where the surface has bad reduction. Here, the Deligne cohomology is replaced by a certain Chow group of the special fibre. The case of good reduction is harder and was first studied by Spiess (1999) in the case of products of elliptic curves and by the author in general (Sreekantan, 2014). The case of bad reduction was also studied by the author in Sreekantan (2008)