LEAST‐SQUARES INVERSE FILTERING

Geophysics ◽  
1966 ◽  
Vol 31 (5) ◽  
pp. 917-926 ◽  
Author(s):  
Wayne T. Ford ◽  
James H. Hearne

Suppose we are given the autocorrelation function of a certain unknown sampled signal. Although a number of different signals might produce the given autocorrelation function, only one of these is minimum‐delay. Denoting this minimum‐delay unknown signal by the matrix K, the given autocorrelation may be written in the form K′K where K′ is the transpose of K. It is desired to determine approximately the inverse of this unknown signal K; that is, we wish to determine a vector X so that KX is as close to B′=(1, 0, 0, ⋯, 0) as possible in a least‐squares sense. If K were known, Rice shows that [Formula: see text] At first glance, the above formula appears useless as K′ is unknown. However, although K′ is indeed unknown, K′B has the form K′B=(c, 0, 0, ⋯, 0)′ where the scalar c simply plays the role of a scale factor. Thus, we determine X by simply selecting a convenient multiple of the first column of the inverse of the known matrix K′K. Although we do not present the details of the computer programming involved in the above calculation, we do present some simple examples to illustrate the process.

2021 ◽  
Author(s):  
Laura Miller ◽  
Raimondo Penta

AbstractWe derive the balance equations for a double poroelastic material which comprises a matrix with embedded subphases. We assume that the distance between the subphases (the local scale) is much smaller than the size of the domain (the global scale). We assume that at the local scale both the matrix and subphases can be described by Biot’s anisotropic, heterogeneous, compressible poroelasticity (i.e. the porescale is already smoothed out). We then decompose the spatial variations by means of the two-scale homogenization method to upscale the interaction between the poroelastic phases at the local scale. This way, we derive the novel global scale model which is formally of poroelastic-type. The global scale coefficients account for the complexity of the given microstructure and heterogeneities. These effective poroelastic moduli are to be computed by solving appropriate differential periodic cell problems. The model coefficients possess properties that, once proved, allow us to determine that the model is both formally and substantially of poroelastic-type. The properties we prove are a) the existence of a tensor which plays the role of the classical Biot’s tensor of coefficients via a suitable analytical identity and b) the global scale scalar coefficient $$\bar{\mathcal {M}}$$ M ¯ is positive which then qualifies as the global Biot’s modulus for the double poroelastic material.


Geophysics ◽  
1975 ◽  
Vol 40 (2) ◽  
pp. 358-359
Author(s):  
A. J. Berkhout

In this publication Treitel determines the complex normal equations and proposes a solution method (Robinson’s block‐Toeplitz algorithm). With respect to these results, I would like to draw attention to the paper Berkhout (1973). In Appendix B of that paper the complex normal equations were also derived: [Formula: see text]for n = 0, 1, ⋯ , N. In (1a), [Formula: see text] is the autocorrelation function of a complex input signal x(t), [Formula: see text] is the complex least‐squares filter of duration (N + 1)Δt, [Formula: see text] is the complex desired output, and Δt represents the sampling interval. Note that in matrix notation expression (1a) equals expression (3) of Treitel’s paper. In the case of least‐squares inverse filtering, (1a) takes on a different form.


2019 ◽  
Vol 47 (5) ◽  
pp. 1543-1555 ◽  
Author(s):  
Maurizio Mongiat ◽  
Simone Buraschi ◽  
Eva Andreuzzi ◽  
Thomas Neill ◽  
Renato V. Iozzo

Abstract The extracellular matrix is a network of secreted macromolecules that provides a harmonious meshwork for the growth and homeostatic development of organisms. It conveys multiple signaling cascades affecting specific surface receptors that impact cell behavior. During cancer growth, this bioactive meshwork is remodeled and enriched in newly formed blood vessels, which provide nutrients and oxygen to the growing tumor cells. Remodeling of the tumor microenvironment leads to the formation of bioactive fragments that may have a distinct function from their parent molecules, and the balance among these factors directly influence cell viability and metastatic progression. Indeed, the matrix acts as a gatekeeper by regulating the access of cancer cells to nutrients. Here, we will critically evaluate the role of selected matrix constituents in regulating tumor angiogenesis and provide up-to-date information concerning their primary mechanisms of action.


2019 ◽  
Vol 16 (2) ◽  
pp. 1
Author(s):  
Shamsatun Nahar Ahmad ◽  
Nor’Aini Aris ◽  
Azlina Jumadi

Concepts from algebraic geometry such as cones and fans are related to toric varieties and can be applied to determine the convex polytopes and homogeneous coordinate rings of multivariate polynomial systems. The homogeneous coordinates of a system in its projective vector space can be associated with the entries of the resultant matrix of the system under consideration. This paper presents some conditions for the homogeneous coordinates of a certain system of bivariate polynomials through the construction and implementation of the Sylvester-Bèzout hybrid resultant matrix formulation. This basis of the implementation of the Bèzout block applies a combinatorial approach on a set of linear inequalities, named 5-rule. The inequalities involved the set of exponent vectors of the monomials of the system and the entries of the matrix are determined from the coefficients of facets variable known as brackets. The approach can determine the homogeneous coordinates of the given system and the entries of the Bèzout block. Conditions for determining the homogeneous coordinates are also given and proven.


Author(s):  
Ирина Викторовна Евстафьева

В статье исследуются вопросы попечительства в отношении несовершеннолетних, отбывающих наказание в виде лишения свободы. Проблема, поднимаемая автором настоящей статьи, многогранна, касается различных аспектов отбывания наказания несовершеннолетними в воспитательных колониях и требует комплексного исследования, способного ответить на определенно значимый вопрос: является ли колония законным представителем находящихся в ней несовершеннолетних со всеми вытекающими из статуса законных представителей последствиями. При этом необходимо обращать внимание на специфику правового статуса лиц, отбывающих наказание в воспитательных колониях, которые, во-первых, являются несовершеннолетними, то есть не обладают дееспособностью в полном объеме и нуждаются в особой заботе, защите и представительстве, а во-вторых, осуждены за совершение тяжкого или особо тяжкого преступления, влекущего изоляцию от общества и определенные ограничения и лишения. Отечественное законодательство достаточно детально регламентирует особенности режима отбывания наказания в виде лишения свободы несовершеннолетними, не определяя при этом статуса воспитательных колоний, кем они являются: воспитателями, попечителями или исключительно учреждениями исполнения наказаний. Между тем правильное понимание значения и роли воспитательной колонии в жизни находящихся в ней несовершеннолетних преступников, по мнению автора, поможет избежать ряда проблем, объективно складывающихся в учреждениях подобного рода. С этой точки зрения предлагаемая тема представляет интерес не только для ученых-теоретиков, но и для практиков - сотрудников соответствующих учреждений. Особо следует подчеркнуть, что исследований по данной тематике в специальной литературе нет. Отдельные исследования, встречающиеся в современной литературе, касаются исключительно общего гражданско-правового статуса несовершеннолетних осужденных. Однако это обстоятельство может свидетельствовать только о новизне данной темы, но никак не об отсутствии самой проблемы. The article analyzes the issues of the status of educational colonies as guardians of minors serving a sentence of imprisonment. In fact, the problem raised by the author of this article is multifaceted, concerns various aspects of the serving of punishment by minors in educational colonies and requires a comprehensive study that can answer, it seems, a definitely significant question: whether the colony is the legal representative of the minors in it with all the consequences arising from the status of legal representatives in the form of duties and responsibilities. At the same time, it seems, it is necessary to pay attention to the specifics of the legal status of citizens serving sentences in educational colonies, who, firstly, are minors, i.e. do not have full legal capacity and need special care, protection and representation, and, secondly, are convicted of committing a serious or particularly serious crime, entailing isolation from society and certain restrictions and deprivation. Domestic legislation regulates in sufficient detail the peculiarities of the regime of serving sentences in the form of deprivation of liberty by minors, without determining the status of educational colonies. Who are they: educators, Trustees or only institutions of execution of punishments. Meanwhile, the correct understanding of the importance and role of the educational colony in the life of juvenile offenders in it, according to the author, will help to avoid a number of problems that objectively develop in institutions of this kind. From this point of view, the proposed topic is of interest not only for theoretical scientists, but for practitioners-employees of relevant institutions. It should be emphasized that there are no studies on this subject in the special literature. However, this circumstance can testify only about novelty of the given subject, but in any way about absence of the problem. It seems that the relevance and importance of a problem is not always measured by the number of studies devoted to it. Sometimes these its traits are manifest only under particularly careful consideration.


Antioxidants ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 188
Author(s):  
Małgorzata Makarewicz ◽  
Iwona Drożdż ◽  
Tomasz Tarko ◽  
Aleksandra Duda-Chodak

This review presents the comprehensive knowledge about the bidirectional relationship between polyphenols and the gut microbiome. The first part is related to polyphenols’ impacts on various microorganisms, especially bacteria, and their influence on intestinal pathogens. The research data on the mechanisms of polyphenol action were collected together and organized. The impact of various polyphenols groups on intestinal bacteria both on the whole “microbiota” and on particular species, including probiotics, are presented. Moreover, the impact of polyphenols present in food (bound to the matrix) was compared with the purified polyphenols (such as in dietary supplements) as well as polyphenols in the form of derivatives (such as glycosides) with those in the form of aglycones. The second part of the paper discusses in detail the mechanisms (pathways) and the role of bacterial biotransformation of the most important groups of polyphenols, including the production of bioactive metabolites with a significant impact on the human organism (both positive and negative).


2020 ◽  
Vol 7 (1) ◽  
Author(s):  
Badiaa Hamama ◽  
Jian Liu

Abstract During the rapid process of urbanization in post-reform China, cities assumed the role of a catalyst for economic growth and quantitative construction. In this context, territorially bounded and well delimited urban cells, globally known as ‘gated communities’, xiaoqu, continued to define the very essence of Chinese cities becoming the most attractive urban form for city planners, real estate developers, and citizens alike. Considering the guidelines in China’s National New Urbanization Plan (2014–2020), focusing on the promotion of humanistic and harmonious cities, in addition to the directive of 2016 by China’s Central Urban Work Conference to open up the gates and ban the construction of new enclosed residential compounds, this paper raises the following questions: As the matrix of the Chinese urban fabric, what would be the role of the gated communities in China’s desire for a human-qualitative urbanism? And How to rethink the gated communities to meet the new urban challenges? Seeking alternative perspectives, this paper looks at the gated communities beyond the apparent limits they seem to represent, considering them not simply as the ‘cancer’ of Chinese cities, rather the container of the primary ingredients to reshape the urban fabric dominated by the gate.


Author(s):  
Thomas Köllen ◽  
Susanne Kopf

AbstractSo far, management research on mechanisms of exclusion of employee groups has mainly applied constructs of racism to understanding issues of origin-based ostracism. This research has primarily focused on issues faced by employees whose heritage is markedly different from the heritage shared by the norm group in the given socio-cultural, linguistic, and geographical setting. Against this backdrop, the present study investigates how ostracism plays out when the heritages involved are similar, as exemplified by German employees in Austria. Study 1 examines the discursive production of Austrian stereotyping of Germans in the usage of different terms of reference for ‘Germans’ in Austrian discourse. A corpus analysis of online comments on newspaper sites highlights the implicit Austrian need for delineation against Germany. Study 2 analyzes Germans’ perception of Austrians’ exclusionary linguistic practices and how this impacts on their employment experience and turnover intention. A quantitative analysis of survey data from 600 German nationals employed in Austria reveals that the degree of exposure to these demarcating practices is associated with lower job satisfaction, a higher burnout level and an increase in turnover intention. This study is amongst the first to shed light on the central role of nationalism and national identities in organizational mechanisms of exclusion.


2021 ◽  
Vol 5 (sup1) ◽  
pp. 73-73
Author(s):  
Megan E. Schroeder ◽  
Andrea Gonzalez Rodriguez ◽  
Kelly F. Speckl ◽  
Cierra J. Walker ◽  
Firaol S. Midekssa ◽  
...  

2021 ◽  
pp. 1-27
Author(s):  
Anna Naszodi ◽  
Francisco Mendonca

Abstract We develop a method which assumes that marital preferences are characterized either by the scalar-valued measure proposed by Liu and Lu, or by the matrix-valued generalized Liu–Lu measure. The new method transforms an observed contingency table into a counterfactual table while preserving its (generalized) Liu–Lu value. After exploring some analytical properties of the new method, we illustrate its application by decomposing changes in the prevalence of homogamy in the US between 1980 and 2010. We perform this decomposition with two alternative transformation methods as well where both methods capture preferences differently from Liu and Lu. Finally, we use survey evidence to support our claim that out of the three considered methods, the new transformation method is the most suitable for identifying the role of marital preferences at shaping marriage patterns. These data are also in favor of measuring assortativity in preferences à la Liu and Lu.


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