scholarly journals Principal Bundle Structure of Matrix Manifolds

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1669
Author(s):  
Marie Billaud-Friess ◽  
Antonio Falcó ◽  
Anthony Nouy
Keyword(s):  
Principal Bundle ◽  
Full Rank ◽  
Geometric Description ◽  
Analytic Manifold ◽  
Matrix Space ◽  
Continuous Map ◽  
Starting Point ◽  
The Matrix ◽  
Fixed Rank ◽  
Definition Of

In this paper, we introduce a new geometric description of the manifolds of matrices of fixed rank. The starting point is a geometric description of the Grassmann manifold Gr(Rk) of linear subspaces of dimension r<k in Rk, which avoids the use of equivalence classes. The set Gr(Rk) is equipped with an atlas, which provides it with the structure of an analytic manifold modeled on R(k−r)×r. Then, we define an atlas for the set Mr(Rk×r) of full rank matrices and prove that the resulting manifold is an analytic principal bundle with base Gr(Rk) and typical fibre GLr, the general linear group of invertible matrices in Rk×k. Finally, we define an atlas for the set Mr(Rn×m) of non-full rank matrices and prove that the resulting manifold is an analytic principal bundle with base Gr(Rn)×Gr(Rm) and typical fibre GLr. The atlas of Mr(Rn×m) is indexed on the manifold itself, which allows a natural definition of a neighbourhood for a given matrix, this neighbourhood being proved to possess the structure of a Lie group. Moreover, the set Mr(Rn×m) equipped with the topology induced by the atlas is proven to be an embedded submanifold of the matrix space Rn×m equipped with the subspace topology. The proposed geometric description then results in a description of the matrix space Rn×m, seen as the union of manifolds Mr(Rn×m), as an analytic manifold equipped with a topology for which the matrix rank is a continuous map.

Holism, Chinese Medicine and Systems Ideologies: Rewriting the Past to Imagine the Future

2018 ◽  
Author(s):  
Volker Scheid
Keyword(s):  
Eighteenth Century ◽  
Chinese Medicine ◽  
Medical Humanities ◽  
Science And Technology Studies ◽  
Human Beings ◽  
The Past ◽  
Starting Point ◽  
The Us ◽  
Shared Objective ◽  
Definition Of

This chapter explores the articulations that have emerged over the last half century between various types of holism, Chinese medicine and systems biology. Given the discipline’s historical attachments to a definition of ‘medicine’ that rather narrowly refers to biomedicine as developed in Europe and the US from the eighteenth century onwards, the medical humanities are not the most obvious starting point for such an inquiry. At the same time, they do offer one advantage over neighbouring disciplines like medical history, anthropology or science and technology studies for someone like myself, a clinician as well as a historian and anthropologist: their strong commitment to the objective of facilitating better medical practice. This promise furthermore links to the wider project of critique, which, in Max Horkheimer’s definition of the term, aims at change and emancipation in order ‘to liberate human beings from the circumstances that enslave them’. If we take the critical medical humanities as explicitly affirming this shared objective and responsibility, extending the discipline’s traditional gaze is not a burden but becomes, in fact, an obligation.

Embracing Uncertainty: Modeling Uncertainty in EPMA—Part II

2021 ◽  
Vol 27 (1) ◽  
pp. 74-89
Author(s):  
Nicholas W.M. Ritchie
Keyword(s):  
Beam Energy ◽  
Uncertainty Modeling ◽  
Matrix Correction ◽  
Correction Model ◽  
X Ray ◽  
Starting Point ◽  
Uncertainty Calculation ◽  
The Matrix ◽  
Measurement Design ◽  
New Framework

AbstractThis, the second in a series of articles present a new framework for considering the computation of uncertainty in electron excited X-ray microanalysis measurements, will discuss matrix correction. The framework presented in the first article will be applied to the matrix correction model called “Pouchou and Pichoir's Simplified Model” or simply “XPP.” This uncertainty calculation will consider the influence of beam energy, take-off angle, mass absorption coefficient, surface roughness, and other parameters. Since uncertainty calculations and measurement optimization are so intimately related, it also provides a starting point for optimizing accuracy through choice of measurement design.

Digital competences of the workforce – a research topic?

2017 ◽  
Vol 23 (3) ◽  
pp. 721-734 ◽  
Author(s):  
Matthias Murawski ◽  
Markus Bick
Keyword(s):  
Research Topic ◽  
Future Research ◽  
Digital Competence ◽  
Content Type ◽  
Research Activities ◽  
Starting Point ◽  
Pros And Cons ◽  
Definition Of ◽  
The Individual ◽  
Practical Implications

Purpose Considering working in the digital age, questions on the consequences for the individual workers are, so far, often neglected. The purpose of this paper is to deal with the question of whether the digital competences of the workforce is a research topic. The authors argue for the thesis that it is indeed a research topic. Design/methodology/approach In addition to a literature analysis of the top IS, HR, and learning publications, non-scientific sources, as well as the opinions of the authors, are included. The authors’ thesis is challenged through a debate of corresponding pros and cons. Findings The definition of digital competences lacks scientific depth. Focussing on the workforce is valid, as a “lifelong” perspective is not mandatory for research. Digital competence research is a multidisciplinary task to which the IS field can make a valuable contribution. Research limitations/implications Although relevant references are included, some aspects are mainly driven by the opinions of the authors. The theoretical implications encompass a call for a scientific definition of digital competences. Furthermore, scholars should focus on the competences of the workforce, including occupations, roles, or industries. The authors conclude by providing a first proposal of a research agenda. Practical implications The practical implications include the alignment of multiple stakeholders for the design of “digital” curricula and the integration by HR departments of the construct of digital competences, e.g. for compensation matters and job requirements. Originality/value This paper is one of very few contributions in the area of the digital competences of the workforce, and it presents a starting point for future research activities.

On the Description and Definition of Human Factors/Ergonomics

1998 ◽  
Vol 42 (10) ◽  
pp. 671-674 ◽  
Author(s):  
Michael S. Wogalter ◽  
Peter A. Hancock ◽  
Patrick G. Dempsey
Keyword(s):  
Human Factors ◽  
Engineering Science ◽  
Human Factors Engineering ◽  
Lay Persons ◽  
Starting Point ◽  
Technical Report ◽  
Definition Of ◽  
Engineering Psychology

This work examines the terms most frequently used to describe our field, which has variously been named Ergonomics, Human Factors, Human Factors Engineering, and Engineering Psychology. A large number of definitions were collected, including those assembled in an earlier technical report by Licht, Polzella, and Boff (1990). First, the definitions were stripped of connector words. Second, the prefix root terms that had the same meaning were combined and third, the words were tabulated and sorted to reveal the content terms most frequently employed. These data may be used to develop core, concise definitions or longer more expository descriptions of the field. The list of terms could also be used as a starting point for the development of definitions oriented for different target audiences (e.g., lay persons vs. other engineering/science experts) as a method of disseminating information concerning what we do.

scholarly journals Infinite Matrix Products and the Representation of the Matrix Gamma Function

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
J.-C. Cortés ◽  
L. Jódar ◽  
Francisco J. Solís ◽  
Roberto Ku-Carrillo
Keyword(s):  
Gamma Function ◽  
Infinite Product ◽  
Infinite Matrix ◽  
Convergence Results ◽  
Matrix Products ◽  
The Matrix ◽  
Definition Of

We introduce infinite matrix products including some of their main properties and convergence results. We apply them in order to extend to the matrix scenario the definition of the scalar gamma function given by an infinite product due to Weierstrass. A limit representation of the matrix gamma function is also provided.

scholarly journals A History of Fluid Management—From “One Size Fits All” to an Individualized Fluid Therapy in Burn Resuscitation

Medicina ◽  
2021 ◽  
Vol 57 (2) ◽  
pp. 187
Author(s):  
Dorothee Boehm ◽  
Henrik Menke
Keyword(s):  
Fluid Therapy ◽  
Point Of Care ◽  
Fluid Management ◽  
Point Of Care Ultrasound ◽  
Burn Patients ◽  
Starting Point ◽  
History Of ◽  
Definition Of ◽  
Historical Developments ◽  
Burn Resuscitation

Fluid management is a cornerstone in the treatment of burns and, thus, many different formulas were tested for their ability to match the fluid requirements for an adequate resuscitation. Thereof, the Parkland-Baxter formula, first introduced in 1968, is still widely used since then. Though using nearly the same formula to start off, the definition of normovolemia and how to determine the volume status of burn patients has changed dramatically over years. In first instance, the invention of the transpulmonary thermodilution (TTD) enabled an early goal directed fluid therapy with acceptable invasiveness. Furthermore, the introduction of point of care ultrasound (POCUS) has triggered more individualized schemes of fluid therapy. This article explores the historical developments in the field of burn resuscitation, presenting different options to determine the fluid requirements without missing the red flags for hyper- or hypovolemia. Furthermore, the increasing rate of co-morbidities in burn patients calls for a more sophisticated fluid management adjusting the fluid therapy to the actual necessities very closely. Therefore, formulas might be used as a starting point, but further fluid therapy should be adjusted to the actual need of every single patient. Taking the developments in the field of individualized therapies in intensive care in general into account, fluid management in burn resuscitation will also be individualized in the near future.

The 3 C's of the Circular Economy for Food. A conceptual framework for circular design in the food system

2021 ◽  
Author(s):  
Franco Fassio
Keyword(s):  
Sustainable Development ◽  
Conceptual Framework ◽  
Circular Economy ◽  
Food System ◽  
Raw Material ◽  
Starting Point ◽  
Development Goals ◽  
Definition Of ◽  
Open Question ◽  
Circular Design

Food, the basic connecting unit of all the UN's Sustainable Development Goals, plays a crucial role in the ecological transition towards a circular economic paradigm. This paper takes scientific considerations as a starting point in order to contribute to the definition of a theoretical-operational framework in which to grow the Circular Economy for Food. This is a still-open question in a sector of the circular economy that is emerging as vital to sustainable development. The 3 C's of Capital, Cyclicality and Co-evolution offer a systemic, holistic vision of the food system's role. Within this conceptual framework, the designers can find the main boundaries of the system, within which to express their creativity. The aim must be to avoid damaging relationships with the best supplier of raw material known to humanity (Nature), respecting planetary boundaries and at the same time offering a fair space to civil society.

On the Very Idea of Civilisation

2021 ◽  
Vol 31 (2) ◽  
pp. 307-321
Author(s):  
Luke O’Sullivan ◽  
Keyword(s):  
Technological Development ◽  
Thomas Hobbes ◽  
Alternative Definition ◽  
Starting Point ◽  
Western Imperialism ◽  
Clash Of Civilisations ◽  
Definition Of ◽  
Contemporary Liberalism ◽  
Relationship Of ◽  
The Relationship

The concept of civilisation is a controversial one because it is unavoidably normative in its implications. Its historical associations with the effort of Western imperialism to impose substantive conditions of life have made it difficult for contemporary liberalism to find a definition of “civilization” that can be reconciled with progressive discourse that seeks to avoid exclusions of various kinds. But because we lack a way of identifying what is peculiar to the relationship of civilisation that avoids the problem of domination, it has tended to be conflated with other ideas. Taking Samuel Huntington's idea of a “Clash of Civilisations” as a starting point, this article argues that we suffer from a widespread confusion of civilisation with “culture,” and that we also confuse it with other ideas including modernity and technological development. Drawing on Thomas Hobbes, the essay proposes an alternative definition of civilisation as the existence of limits on how we may treat others.

The Intercity Origins of Diplomacy: Consuls, Empires, and the Sea

Diplomatica ◽  
2021 ◽  
Vol 3 (1) ◽  
pp. 147-156
Author(s):  
Halvard Leira ◽  
Benjamin de Carvalho
Keyword(s):  
Starting Point ◽  
Definition Of ◽  
Specific Definition

Abstract City diplomacy is a fairly new topic in the study of diplomacy, and, many would argue, a fairly recent empirical phenomenon. A counterpoint to this could be to reference how the alleged origin of diplomacy in Greek antiquity was city-centered, as were the earliest forms of Renaissance diplomacy in Italy. In this essay we want to probe the connections between cities and diplomacy through problematizing what has counted as diplomacy. Our starting point is that cities have always mattered to what we could analytically refer to as diplomatic practice. Being conscious of the conceptual ambiguities, we are thus not starting from a specific definition of “city diplomacy,” but from a conviction that cities have mattered and continue to matter to the practice of diplomacy.

scholarly journals TOWARDS A PANEVOLUTIONARY THEORY (PANEVO THEORY), FOLLOWING THE ACADEMIC OF FISIOCRITICI ENZO TIEZZI

2017 ◽  
Vol 8 (1-IT) ◽  
Author(s):  
Mario Tanga ◽  
Giacomo Gelati ◽  
Marco Casazza
Keyword(s):  
Charles Darwin ◽  
Current Knowledge ◽  
Close Contact ◽  
Rachel Carson ◽  
Starting Point ◽  
Science And Culture ◽  
History Of ◽  
Living Species ◽  
Definition Of ◽  
Scientific Fields

6Contemporary science and culture show more and more extended and meaningful signs about the increasing explaining power of evolutionary paradigm. This power overcomes the field of the history of living species. We consider “On the Origin of Species” of 1859 by Charles Darwin as the establishment of this paradigm, but this original and fruitful idea has received the several and different contributions from near and (seemingly) far scientific fields. This process happened according distinguishable waves and leaded the evolutionary theory very far from its starting point, making it something wider and different. The current knowledge of this theory involves many kinds of scholars: biologists, zoologists, botanists, development biologists, genetics/genomics scholars and also scholars of many other disciplines, as statistics, mathematics, ecology, environmental sciences, physics, chemistry, linguistics, sociology, neuro-sciences, epidemiology, informatics, immunology. During the end of XX Century, the study of complexity, of self-organization and of emerging properties has been a decisive factor to extend evolution until beyond the boundaries of Biology. These phenomena, or properties, or features, that are shown by “living” and “not-living” systems (so called basing ourselves on traditional definitions), have deeply modified even the “properly” biologic evolution itself and besides this has demonstrated that, mutatis mutandis, evolutionary processes or phenomena happen also out of biologic dominion, referring “biologic” to “wet-ware world”. This is to say the class of evolutionary phenomena is more widely and more inclusively extended than our opinion. We can mean this as a revolution (according to Kuhn’s definition) that imposes us to restructure the definition of evolution itself and even to redraw the boundaries and the map of Biology itself. Aiming to establish a name of this field of study we propose “PanEvolutionary Theory” (PanEvo Theory). No doubt Prigogine offered an important contribution to this area. The thinking and the work of Enzo Tiezzi can be placed seen in the same perspective. Disregarding direct connections and contacts with the Nobel Prize Prigogine, however the studies of Enzo Tiezzi are neither a fully unexpected work nor a theory lacking of important potentialities: it is not a strange or eccentric academic exercise. Except the close contact and the dense exchanges with Prigogine, we collocate Enzo Tiezzi in the same context of Gregory Chaitin, of Rachel Carson, of John Harte and Robert H. Socolow, of James Paul Wesley, of Sertorio, of Oort and Peixoto, just to cite the most strictly related. Our Academy had the privilege and the honor of having Enzo Tiezzi in its ranks. We think that merits and developments of the thinking of this scholar have to produce important and lasting fruits in the future.

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