scholarly journals Estimating the Mutual Information between Two Discrete, Asymmetric Variables with Limited Samples

Entropy ◽  
2019 ◽  
Vol 21 (6) ◽  
pp. 623 ◽  
Author(s):  
Damián G. Hernández ◽  
Inés Samengo

Determining the strength of nonlinear, statistical dependencies between two variables is a crucial matter in many research fields. The established measure for quantifying such relations is the mutual information. However, estimating mutual information from limited samples is a challenging task. Since the mutual information is the difference of two entropies, the existing Bayesian estimators of entropy may be used to estimate information. This procedure, however, is still biased in the severely under-sampled regime. Here, we propose an alternative estimator that is applicable to those cases in which the marginal distribution of one of the two variables—the one with minimal entropy—is well sampled. The other variable, as well as the joint and conditional distributions, can be severely undersampled. We obtain a consistent estimator that presents very low bias, outperforming previous methods even when the sampled data contain few coincidences. As with other Bayesian estimators, our proposal focuses on the strength of the interaction between the two variables, without seeking to model the specific way in which they are related. A distinctive property of our method is that the main data statistics determining the amount of mutual information is the inhomogeneity of the conditional distribution of the low-entropy variable in those states in which the large-entropy variable registers coincidences.

1975 ◽  
Vol 34 (02) ◽  
pp. 426-444 ◽  
Author(s):  
J Kahan ◽  
I Nohén

SummaryIn 4 collaborative trials, involving a varying number of hospital laboratories in the Stockholm area, the coagulation activity of different test materials was estimated with the one-stage prothrombin tests routinely used in the laboratories, viz. Normotest, Simplastin-A and Thrombotest. The test materials included different batches of a lyophilized reference plasma, deep-frozen specimens of diluted and undiluted normal plasmas, and fresh and deep-frozen specimens from patients on long-term oral anticoagulant therapy.Although a close relationship was found between different methods, Simplastin-A gave consistently lower values than Normotest, the difference being proportional to the estimated activity. The discrepancy was of about the same magnitude on all the test materials, and was probably due to a divergence between the manufacturers’ procedures used to set “normal percentage activity”, as well as to a varying ratio of measured activity to plasma concentration. The extent of discrepancy may vary with the batch-to-batch variation of thromboplastin reagents.The close agreement between results obtained on different test materials suggests that the investigated reference plasma could be used to calibrate the examined thromboplastin reagents, and to compare the degree of hypocoagulability estimated by the examined PIVKA-insensitive thromboplastin reagents.The assigned coagulation activity of different batches of the reference plasma agreed closely with experimentally obtained values. The stability of supplied batches was satisfactory as judged from the reproducibility of repeated measurements. The variability of test procedures was approximately the same on different test materials.


1975 ◽  
Vol 14 (3) ◽  
pp. 370-375
Author(s):  
M. A. Akhtar

I am grateful to Abe, Fry, Min, Vongvipanond, and Yu (hereafter re¬ferred to as AFMVY) [1] for obliging me to reconsider my article [2] on the demand for money in Pakistan. Upon careful examination, I find that the AFMVY results are, in parts, misleading and that, on the whole, they add very little to those provided in my study. Nevertheless, the present exercise as well as the one by AFMVY is useful in that it furnishes us with an opportunity to view some of the fundamental problems involved in an empi¬rical analysis of the demand for money function in Pakistan. Based on their elaborate critique, AFMVY reformulate the two hypo¬theses—the substitution hypothesis and the complementarity hypothesis— underlying my study and provide us with some alternative estimates of the demand for money in Pakistan. Briefly their results, like those in my study, indicate that income and interest rates are important in deter¬mining the demand for money. However, unlike my results, they also suggest that the price variable is a highly significant determinant of the money demand function. Furthermore, while I found only a weak support for the complementarity between money demand and physical capital, the results obtained by AFMVY appear to yield a strong support for that rela¬tionship.1 The difference in results is only a natural consequence of alter¬native specifications of the theory and, therefore, I propose to devote most of this reply to the criticisms raised by AFMVY and the resulting reformulation of the two mypotheses.


2019 ◽  
Vol 67 (6) ◽  
pp. 483-492
Author(s):  
Seonghyeon Baek ◽  
Iljae Lee

The effects of leakage and blockage on the acoustic performance of particle filters have been examined by using one-dimensional acoustic analysis and experimental methods. First, the transfer matrix of a filter system connected to inlet and outlet pipes with conical sections is measured using a two-load method. Then, the transfer matrix of a particle filter only is extracted from the experiments by applying inverse matrices of the conical sections. In the analytical approaches, the one-dimensional acoustic model for the leakage between the filter and the housing is developed. The predicted transmission loss shows a good agreement with the experimental results. Compared to the baseline, the leakage between the filter and housing increases transmission loss at a certain frequency and its harmonics. In addition, the transmission loss for the system with a partially blocked filter is measured. The blockage of the filter also increases the transmission loss at higher frequencies. For the simplicity of experiments to identify the leakage and blockage, the reflection coefficients at the inlet of the filter system have been measured using two different downstream conditions: open pipe and highly absorptive terminations. The experiments show that with highly absorptive terminations, it is easier to see the difference between the baseline and the defects.


Author(s):  
Sagar Suman Panda ◽  
Ravi Kumar B.V.V.

Three new analytical methods were optimized and validated for the estimation of tigecycline (TGN) in its injection formulation. A difference UV spectroscopic, an area under the curve (AUC), and an ultrafast liquid chromatographic (UFLC) method were optimized for this purpose. The difference spectrophotometric method relied on the measurement of amplitude when equal concentration solutions of TGN in HCl are scanned against TGN in NaOH as reference. The measurements were done at 340 nm (maxima) and 410nm (minima). Further, the AUC under both the maxima and minima were measured at 335-345nm and 405-415nm, respectively. The liquid chromatographic method utilized a reversed-phase column (150mm×4.6mm, 5µm) with a mobile phase of methanol: 0.01M KH2PO4 buffer pH 3.5 (using orthophosphoric acid) in the ratio 80:20 %, v/v. The flow rate was 1.0ml/min, and diode array detection was done at 349nm. TGN eluted at 1.656min. All the methods were validated for linearity, precision, accuracy, stability, and robustness. The developed methods produced validation results within the satisfactory limits of ICH guidance. Further, these methods were applied to estimate the amount of TGN present in commercial lyophilized injection formulations, and the results were compared using the One-Way ANOVA test. Overall, the methods are rapid, simple, and reliable for routine quality control of TGN in the bulk and pharmaceutical dosage form. 


Author(s):  
M. Rahul ◽  
R. Ganesan

Leaders in the global arena are the one who face the challenges never seen before, while coordinating work and managing relationship between team members coming from varied ethnic groups. Globalization has undoubtedly opened up endless growth opportunities for both, businesses and individuals, by collaborating with each other, but with certain inherent challenges. These challenges are the difference in the cultural background of the team members, which gets predominantly reflected in their behavior at workplace too. The cultural differences exist primarily due to differences in shared values, which form the basis for difference in perception and practices of decision making by an individual (Hofstede, 1980). Juana Bordas has rightly described that any business that fails to adapt their leadership style aligning with multi-cultural approach will find it difficult to thrive in a more colorful world. Leadership style has witnessed various facets of changing work environment that has demanded from leaders to modify their approach to adapt along and be effective and survive in the ever-changing environment of business (Bordas,2007).A cross-culture leader plays a significant role in knitting the diverse workforce into an efficient team; which requires a leader to very well understand the various dimensions of culture. This understanding of the leader enables him to learn about blending of leadership styles to address the challenges of such work environment. This paper is an extended work on 'Leadership in Cross-Cultural Environment – A Comparison of Asian and Non-Asian Managers' (Rahul and Ganesan, 2015). The extended research study has identified that enhanced work experience of cross-culture leaders enables them in effective team management, than the rise in designation, as it results in creation of hierarchical distance between the leaders and subordinates.


Dreyfus argues that there is a basic methodological difference between the natural sciences and the social sciences, a difference that derives from the different goals and practices of each. He goes on to argue that being a realist about natural entities is compatible with pluralism or, as he calls it, “plural realism.” If intelligibility is always grounded in our practices, Dreyfus points out, then there is no point of view from which one can ask about or provide an answer to the one true nature of ultimate reality. But that is consistent with believing that the natural sciences can still reveal the way the world is independent of our theories and practices.


2021 ◽  
Vol 13 (4) ◽  
pp. 2197
Author(s):  
Seongmin Kang ◽  
Joonyoung Roh ◽  
Eui-chan Jeon

NH3 is one of the major substances contributing to the secondary generation of PM2.5; therefore, management is required. In Korea, the management of NH3 is insufficient, and the emission factor used by EPA is the same as the one used when calculating emissions. In particular, waste incineration facilities do not currently calculate NH3 emissions. In the case of combustion facilities, the main ammonia emission source is the De-NOx facility, and, in the case of a power plant with a De-NOx facility, NH3 emission is calculated. Therefore, in the case of a Municipal Solid Waste (MSW) incinerator with the same facility installed, it is necessary to calculate NH3 emissions. In this study, the necessity of developing NH3 emission factors for an MSW incinerator and calculating emission was analyzed. In addition, elements to be considered when developing emission factors were analyzed. The study found that the NH3 emission factors for each MSW incinerator technology were calculated as Stoker 0.010 NH3 kg/ton and Fluidized Beds 0.004 NH3 kg/ton, which was greater than the NH3 emission factor 0.003 NH3 kg/ton for the MSW incinerator presented in EMEP/EEA (2016). As a result, it was able to identify the need for the development of NH3 emission factors in MSW incinerators in Korea. In addition, the statistical analysis of the difference between the incineration technology of MSW and the NH3 emission factor by the De-NOx facility showed a difference in terms of both incineration technology and De-NOx facilities, indicating that they should be considered together when developing the emission factor. In addition to MSW, it is believed that it will be necessary to review the development of emission factors for waste at workplaces and incineration facilities of sewage sludge.


2015 ◽  
Vol 54 (06) ◽  
pp. 500-504 ◽  
Author(s):  
A. G. Maglione ◽  
A. Scorpecci ◽  
P. Malerba ◽  
P. Marsella ◽  
S. Giannantonio ◽  
...  

SummaryObjectives: The aim of the present study is to investigate the variations of the electroencephalographic (EEG) alpha rhythm in order to measure the appreciation of bilateral and unilateral young cochlear implant users during the observation of a musical cartoon. The cartoon has been modified for the generation of three experimental conditions: one with the original audio, another one with a distorted sound and, finally, a mute version.Methods: The EEG data have been recorded during the observation of the cartoons in the three experimental conditions. The frontal alpha EEG imbalance has been calculated as a measure of motivation and pleasantness to be compared across experimental populations and conditions.Results: The EEG frontal imbalance of the alpha rhythm showed significant variations during the perception of the different cartoons. In particular, the pattern of activation of normal-hearing children is very similar to the one elicited by the bilateral implanted patients. On the other hand, results related to the unilateral subjects do not present significant variations of the imbalance index across the three cartoons.Conclusion: The presented results suggest that the unilateral patients could not appreciate the difference in the audio format as well as bilaterally implanted and normal hearing subjects. The frontal alpha EEG imbalance is a useful tool to detect the differences in the appreciation of audiovisual stimuli in cochlear implant patients.


1930 ◽  
Vol 51 (5) ◽  
pp. 769-776 ◽  
Author(s):  
Max B. Lurie

Under conditions closely simulating the natural modes of tuberculous infection in man normal guinea pigs have acquired tuberculosis by being exposed under two degrees of crowding to tuberculous cage mates in ordinary cages, where the food became soiled with excreta, bearing tubercle bacilli, and in special cages, with wire-mesh floors, where this source of infection was almost entirely eliminated. Guinea pigs were also exposed in the same room but not in the same cage with tuberculous animals. It was found that the relative tuberculous involvement of the mesenteric and tracheobronchial nodes showed a gradation of change from an almost completely alimentary infection to a completely respiratory infection. The disease involved the mesenteric nodes predominantly in the crowded ordinary cages, with much less or no affection of the tracheobronchial nodes. It was similarly, but less markedly, enteric in origin in the less crowded ordinary cages, the mesenteric nodes again being larger than the tracheobronchial nodes, but the difference in size was not so great. In the more crowded special cages the relative affection of these two groups of nodes alternated, so that in some the mesenteric, in some the tracheobronchial nodes were more extensively tuberculous. A disease characterized by less or no affection of the mesenteric nodes and by extensive lesions of the tracheobronchial nodes was seen in the less crowded special cages. Finally there was a massive tuberculosis of the tracheobronchial nodes with usually no affection of the mesenteric nodes in the frankly air-borne tuberculosis acquired by guinea pigs exposed in the same room but not to tuberculous cage mates. This gradation in the rô1e played by the enteric and respiratory routes of infection, as first the one and then the other becomes the more frequent channel of entrance for tuberculosis, would indicate that the penetration of tubercle bacilli by the one portal of entry inhibits the engrafting of tuberculosis in the tissues by way of the other portal of entry. It is apparent that in the special cages the opportunities for inhaling tubercle bacilli are at most equal to if not much less than in the ordinary cages; for in the latter dust from the bedding, laden with tubercle bacilli, is stirred up almost constantly by the animals, whereas in the special cages there is no bedding at all, and therefore, presumably, no more tubercle bacilli in the air than may occur in any part of the room. Nevertheless the route of infection was predominantly the respiratory tract in the special cages, especially in the less crowded, apparently because the enteric route had been largely eliminated. The greater predominance of the respiratory route amongst guinea pigs that acquired tuberculosis in the less crowded ordinary cages as compared to the lesser significance of this route in the more crowded ordinary cages would point in the same direction. These observations are in harmony with our knowledge that tuberculosis once implanted in an organism confers a certain degree of immunity to the disease. It is noteworthy that in a study of human autopsy material Opie (3) has found that when healed lesions are present in the mesentery focal tuberculosis in the lungs is seldom found, and that when first infection occurs by way of the lungs it tends to prevent the engrafting of the disease by way of the intestinal tract.


1998 ◽  
Vol 30 (04) ◽  
pp. 1027-1057 ◽  
Author(s):  
Philippe Picard

Modelling malaria with consistency necessitates the introduction of at least two families of interconnected processes. Even in a Markovian context the simplest fully stochastic model is intractable and is usually transformed into a hybrid model, by supposing that these two families are stochastically independent and linked only through two deterministic connections. A model closer to the fully stochastic model is presented here, where one of the two families is subordinated to the other and just a unique deterministic connection is required. For this model a threshold theorem can be proved but the threshold level is not the one obtained in a hybrid model. The difference disappears only when the human population size approaches infinity.


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