scholarly journals From the Kalman Filter to the Particle Filter: A Geometrical Perspective of the Curse of Dimensionality

2016 ◽  
Vol 2016 ◽  
pp. 1-18
Author(s):  
Olivier Pannekoucke ◽  
Pierrick Cébron ◽  
Niels Oger ◽  
Philippe Arbogast
Keyword(s):  
Kalman Filter ◽  
Particle Filter ◽  
High Dimension ◽  
Convergence Property ◽  
Curse Of Dimensionality ◽  
Finite Sample ◽  
New Approach ◽  
The Mean ◽  
Finite Sampling ◽  
The Difference

The aim of this contribution is to provide a description of the difference between Kalman filter and particle filter when the state space is of high dimension. In the Gaussian framework, KF and PF give the same theoretical result. However, in high dimension and using finite sampling for the Gaussian distribution, the PF is not able to reproduce the solution produced by the KF. This discrepancy is highlighted from the convergence property of the Gaussian law toward a hypersphere: in high dimension, any finite sample of a Gaussian law lies within a hypersphere centered in the mean of the Gaussian law and of radius square-root of the trace of the covariance matrix. This concentration of probability suggests the use of norm as a criterium that discriminates whether a forecast sample can be compatible or not with a given analysis state. The contribution illustrates important characteristics that have to be considered for the high dimension but does not introduce a new approach to face the curse of dimensionality.

Sequential decisions in the control of a space-ship (finite fuel)

1967 ◽  
Vol 4 (3) ◽  
pp. 584-604 ◽  
Author(s):  
John Bather ◽  
Herman Chernoff
Keyword(s):  
Optimal Policy ◽  
Point Of View ◽  
Control Procedure ◽  
Theoretical Point ◽  
New Approach ◽  
Final Approach ◽  
The Mean ◽  
The Difference ◽  
Miss Distance ◽  
Quadratic Case

This paper is a sequel to [1] and considers a more realistic formulation of the same question: that of finding an optimal policy for controlling the path of a space-ship as it moves towards its target. The difference here is that we no longer suppose there is an infinite quantity of fuel, always available at a fixed price, for modifying the current direction of motion. This complicates the problem of reducing the final miss distance, by introducing an extra variable. As before, we shall be particularly concerned to find a control procedure which always minimizes the mean square terminal miss. From the theoretical point of view we are also interested to see whether the techniques used to approximate the optimal policy can be extended, and how far we shall be forced to adopt a new approach. Results are derived which provide bounds on the form of the optimal policy. The derivation depends on a comparison technique whose validity is intuitively obvious, but which is still only a conjecture. However, further confirmation is obtained in the quadratic case from asymptotic expansions giving the form of the solution both when the space-ship is far away from its target and during its final approach.

A new approach to the measurement of the quantitative effects of inherent and environmental factors on the composition of the milk of individual cows and of herds, with particular reference to lactose content

1968 ◽  
Vol 35 (1) ◽  
pp. 91-105 ◽  
Author(s):  
J. P. Walsh ◽  
J. A. F. Rook ◽  
F. H. Dodd
Keyword(s):  
Quantitative Estimation ◽  
Relative Importance ◽  
New Approach ◽  
Mean Values ◽  
Stage Of Lactation ◽  
Bulk Milk ◽  
Wide Range ◽  
The Mean ◽  
The Difference ◽  
Effect Of Age

Summary(1) A tentative scheme is proposed for the quantitative estimation of the effects of various factors on one major milk constituent, lactose, from analyses of the milk of individual cows within herds. The potential lactose content in the milk of individual cows is predicted from the observed potassium-to-lactose ratio in the milk, and the difference between the predicted potential and the actual lactose content is partitioned into fractions that are attributed to effects due to age, inter-quarter difference and changes with stage of lactation. The scheme was applied to 2 commercial herds, one (herd A) producing milk of low and the other (herd B) milk of normal SNF content.(2) Lactation mean values for fat, SNF and lactose contents of the milk of individual cows showed a wide range of the same order in each of the 2 herds. Of the mean difference in SNF percentage of 0·30 between the herds, 0·14, or 47%, was due to a difference in lactose content.(3) The predicted potential milk lactose content of the cows in the 2 herds ranged from 5·04 to 5·66 (g/100 g milk water). Herd mean values were 5·394 for herd A and 5·244 for herd B.(4) Herd mean values for the effect on the lactose content (g/100 g milk water) of age, of changes with stage of lactation and of inter-quarter difference were −0·127, −0·080, and 0·073 respectively in herd A, and −0·197, −0·058 and −0·078, respectively, in herd B.(5) The relative importance of the various factors in accounting for differences between the herds in the lactose content of their bulk milk were: predicted potential lactose content 61%, effect of age 28%, effect of changes with stage of lactation 9% and effect of inter-quarter difference 2%.(6) The errors attached to the estimation of potential milk lactose content and the effects of age, of changes with stage of lactation and of inter-quarter difference are discussed.

scholarly journals A New Approach for Estimating Rock Discontinuity Trace Intensity Based on Rectangular Sampling Windows

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Xiaoxue Huo ◽  
Qiong Wu ◽  
Huiming Tang ◽  
Zhen Meng ◽  
Di Wang ◽  
...  
Keyword(s):  
Cross Sections ◽  
Unit Area ◽  
Estimation Method ◽  
Finite Sample ◽  
Intensity Estimation ◽  
New Approach ◽  
Trace Length ◽  
Discontinuity Orientation ◽  
Finite Sample Size ◽  
The Mean

Trace intensity is defined as mean total trace length of discontinuities per unit area, which is an important geometric parameter to describe fracture networks. The probability of each trace appearing in the sampling surface is different since discontinuity orientation has a scatter and is probabilistically distributed, so this factor should be taken into account in trace intensity estimation. This paper presents an approach to estimate the two-dimensional trace intensity by considering unequal appearing probability for discontinuities sampled by rectangular windows. The estimation method requires the number of discontinuities intersecting the window, the appearing probability of discontinuities with both ends observed, one end observed, and both ends censored, and the mean trace length of discontinuities intersecting the window. The new estimator is validated by using discontinuity data from an outcrop in Wenchuan area in China. Similarly, circular windows are used along with Mauldon’s equation to calculate trace intensity using discontinuity trace data of the same outcrop as a contrast. Results indicate that the proposed new method based on rectangular windows shows close accuracy and less variability than that of the method based on circular windows due to the influence of finite sample size and the variability of location of the window and has advantage in application to sampling surfaces longer in one direction than in the other such as tunnel cross sections and curved sampling surfaces such as outcrops that show some curvature.

Sequential decisions in the control of a space-ship (finite fuel)

1967 ◽  
Vol 4 (03) ◽  
pp. 584-604 ◽  
Author(s):  
John Bather ◽  
Herman Chernoff
Keyword(s):  
Optimal Policy ◽  
Point Of View ◽  
Control Procedure ◽  
Theoretical Point ◽  
New Approach ◽  
Final Approach ◽  
The Mean ◽  
The Difference ◽  
Miss Distance ◽  
Quadratic Case

This paper is a sequel to [1] and considers a more realistic formulation of the same question: that of finding an optimal policy for controlling the path of a space-ship as it moves towards its target. The difference here is that we no longer suppose there is an infinite quantity of fuel, always available at a fixed price, for modifying the current direction of motion. This complicates the problem of reducing the final miss distance, by introducing an extra variable. As before, we shall be particularly concerned to find a control procedure which always minimizes the mean square terminal miss. From the theoretical point of view we are also interested to see whether the techniques used to approximate the optimal policy can be extended, and how far we shall be forced to adopt a new approach. Results are derived which provide bounds on the form of the optimal policy. The derivation depends on a comparison technique whose validity is intuitively obvious, but which is still only a conjecture. However, further confirmation is obtained in the quadratic case from asymptotic expansions giving the form of the solution both when the space-ship is far away from its target and during its final approach.

The Effect of Vocabulary Intervention on Text Comprehension: Who Benefits?

2019 ◽  
Vol 50 (4) ◽  
pp. 562-578 ◽  
Author(s):  
Dawna Duff
Keyword(s):  
Middle School ◽  
Reading Comprehension ◽  
Text Comprehension ◽  
Classroom Instruction ◽  
Vocabulary Instruction ◽  
Clinical Intervention ◽  
Vocabulary Knowledge ◽  
Vocabulary Intervention ◽  
The Mean ◽  
The Difference

Purpose Vocabulary intervention can improve comprehension of texts containing taught words, but it is unclear if all middle school readers get this benefit. This study tests 2 hypotheses about variables that predict response to vocabulary treatment on text comprehension: gains in vocabulary knowledge due to treatment and pretreatment reading comprehension scores. Method Students in Grade 6 ( N = 23) completed a 5-session intervention based on robust vocabulary instruction (RVI). Knowledge of the semantics of taught words was measured pre- and posttreatment. Participants then read 2 matched texts, 1 containing taught words (treated) and 1 not (untreated). Treated texts and taught word lists were counterbalanced across participants. The difference between text comprehension scores in treated and untreated conditions was taken as a measure of the effect of RVI on text comprehension. Results RVI resulted in significant gains in knowledge of taught words ( d RM = 2.26) and text comprehension ( d RM = 0.31). The extent of gains in vocabulary knowledge after vocabulary treatment did not predict the effect of RVI on comprehension of texts. However, untreated reading comprehension scores moderated the effect of the vocabulary treatment on text comprehension: Lower reading comprehension was associated with greater gains in text comprehension. Readers with comprehension scores below the mean experienced large gains in comprehension, but those with average/above average reading comprehension scores did not. Conclusion Vocabulary instruction had a larger effect on text comprehension for readers in Grade 6 who had lower untreated reading comprehension scores. In contrast, the amount that children learned about taught vocabulary did not predict the effect of vocabulary instruction on text comprehension. This has implications for the identification of 6th-grade students who would benefit from classroom instruction or clinical intervention targeting vocabulary knowledge.

Inter-country inequality as a dynamic process and the problem of post-industrial development

2018 ◽  
pp. 5-29 ◽  
Author(s):  
L. M. Grigoryev ◽  
V. A. Pavlyushina
Keyword(s):  
Economic Growth ◽  
Political Institutions ◽  
Industrial Development ◽  
Modern World ◽  
New Approach ◽  
Development Level ◽  
The World ◽  
Long Time ◽  
The Difference ◽  
Post Industrial

The phenomenon of economic growth is studied by economists and statisticians in various aspects for a long time. Economic theory is devoted to assessing factors of growth in the tradition of R. Solow, R. Barrow, W. Easterly and others. During the last quarter of the century, however, the institutionalists, namely D. North, D. Wallis, B. Weingast as well as D. Acemoglu and J. Robinson, have shown the complexity of the problem of development on the part of socioeconomic and political institutions. As a result, solving the problem of how economic growth affects inequality between countries has proved extremely difficult. The modern world is very diverse in terms of development level, and the article offers a new approach to the formation of the idea of stylized facts using cluster analysis. The existing statistics allows to estimate on a unified basis the level of GDP production by 174 countries of the world for 1992—2016. The article presents a structured picture of the world: the distribution of countries in seven clusters, different in levels of development. During the period under review, there was a strong per capita GDP growth in PPP in the middle of the distribution, poverty in various countries declined markedly. At the same time, in 1992—2016, the difference increased not only between rich and poor groups of countries, but also between clusters.

Efficacy and Safety of Oral Ivermectin and Topical Permethrin in the Treatment of Scabies

2020 ◽  
Vol 33 (1) ◽  
pp. 41-47
Author(s):  
Mohsena Akhter ◽  
Ishrat Bhuiyan ◽  
Zulfiqer Hossain Khan ◽  
Mahfuza Akhter ◽  
Gulam Kazem Ali Ahmad ◽  
...  
Keyword(s):  
Skin Diseases ◽  
Close Contact ◽  
Randomized Study ◽  
Sarcoptes Scabiei ◽  
Efficacy And Safety ◽  
Common Skin ◽  
Group A ◽  
The Mean ◽  
The Difference ◽  
Group B

Background: Scabies is one of the most common skin diseases in our country. It is caused by the mite Sarcoptes scabiei var hominis, which is an ecto-parasite infesting the epidermis. Scabies is highly contagious. Prevalence is high in congested or densely populated areas. Individuals with close contact with an affected person should be treated with scabicidal which is available in both oral and topical formulations. The only oral but highly effective scabicidal known to date is Ivermectin. Amongst topical preparations, Permethrin 5 % cream is the treatment of choice. Objective: To evaluate the efficacy & safety of oral Ivermectin compared to topical Permethrin in the treatment of scabies. Methodology: This prospective, non-randomized study was conducted at the out-patient department of Dermatology and Venereology of Shaheed Suhrawardy Medical College & Hospital over a period of 6 months, from August 2016 to January 2017. The study population consisted of one hundred patients having scabies, enrolled according to inclusion criteria. They were divided into two groups. group A was subjected to oral Ivermectin and the group B to Permethrin 5% cream. Patients were followed up on day 7 and 14 for assessment of efficacy and safety. Result: The mean scoring with SD in group A (Ivermectin) and group B (Permethrin) were 8.26 ± 2.22 and 7.59 ± 2.01 respectively at the time of observation. The difference between the mean score of the two group is not significant (p=0.117) the mean scoring with SD in group A and group B were 4.54 ± 2.05 and 1.64 ± 1.84 respectively at 7thdays. The difference between the mean score of the two group is significant (p<0.001). The mean scoring with SD in group A and group B were 2.68± 2.35 and .36± 1.10 respectively at 14th day difference between the mean score of the group is significant (p<0.001). Conclusion: Topical application of permethrin 5% cream is more effective and safer than oral Ivermectin in the treatment of scabies. TAJ 2020; 33(1): 41-47

EFFECTS OF SYNTHETIC LH/FSH-RELEASING HORMONE (LRH) ON PLASMA LH AND FSH IN AMENORRHOEIC WOMEN

1974 ◽  
Vol 75 (4) ◽  
pp. 647-652 ◽  
Author(s):  
G. Rannevik ◽  
J. Thorell
Keyword(s):  
Urinary Excretion ◽  
Initial Response ◽  
Releasing Hormone ◽  
The Mean ◽  
The Difference ◽  
Serial Measurements

ABSTRACT Eight amenorrhoeic women were given 100 μg synthetic LRH (Hoechst) iv and im, respectively, at an interval of 2 weeks. Four of the women received the iv injection first and four the im injection. The urinary excretion of oestrogens and pregnanediol was low and unaltered throughout the test weeks. The effects of LRH were compared by serial measurements of the plasma LH and FSH during 8 h. The initial response of LH for up to 25 min and that of FSH for up to 60 min were equal whether LRH was given iv or im. The difference appeared later. Four hours after the injection the mean increase of LH to iv injection was 0.5 ng/ml (N. S.), while that to im injection was 1.9 ng/ml (P < 0.01). The corresponding values for FSH were 1.3 (P < 0.05) and 3.2 (P < 0.001). The effect of LRH administration im was thus found to be larger and more prolonged.

Development of Prolonged Delivery of Tramadol and Dissolution Translation by Statistical Data Treatment

2011 ◽  
Vol 4 (1) ◽  
pp. 1331-1337
Author(s):  
P B Parejiya ◽  
B S Barot ◽  
P K Shelat
Keyword(s):  
Drug Release ◽  
Study Data ◽  
Stability Study ◽  
Dissolution Time ◽  
Matrix Tablet ◽  
Burst Effect ◽  
The Matrix ◽  
The Mean ◽  
The Difference ◽  
Dissolution Efficiency

The present study was carried out to fabricate a prolonged design for tramadol using Kollidon SR (Polyvinyl acetate and povidone based matrix retarding polymer). Matrix tablet formulations were prepared by direct compression of Kollidon SR of a varying proportion with a fixed percentage of tramadol. Tablets containing a 1:0.5 (Drug: Kollidon SR) ratio exhibited a rapid rate of drug release with an initial burst effect. Incorporation of more Kollidon SR in the matrix tablet extended the release of drug with subsequent minimization of the burst effect as confirmed by the mean dissolution time, dissolution efficiency and f2 value. Among the formulation batches, a direct relationship was obtained between release rate and the percentage of Kollidon SR used. The formulation showed close resemblance to the commercial product Contramal and compliance with USP specification. The results were explored and explained by the difference of micromeritic characteristics of the polymers and blend of drug with excipients. Insignificant effects of various factors, e.g. pH of dissolution media, ionic strength, speed of paddle were found on the drug release from Kollidon-SR matrix. The formulation followed the Higuchi kinetic model of drug release. Stability study data indicated stable character of Batch T6 after short-term stability study.

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