Implementing the key functions, any company is faced with issues related to the formation and analysis of the range of goods, products, services. Regardless of the field of activity, enterprises need to analyze each product line separately in order to make timely adjustments to the product range policy, which directly affects the economic efficiency of the enterprise as a whole. The purpose of the study is to reveal the content of matrix methods of assortment analysis. The article deals with (...) the concepts of "assortment", "product assortment", their meaning and impact on the company's activities; matrix methods: BKG matrix; Dibb-Simkin matrix; Markon matrix. The scientific novelty lies in the author's interpretation of the comparative characteristics of these methods, summarized in a tabular form, allowing enterprises to choose the optimal method when analyzing assortment positions in real business conditions. (shrink)

Taking metaphysics in its aristotelian sense to mean the investigation of being qua being, The author contends that its "matrix" (its place of origin, Field of operations, And continuing and ultimate point of reference) is everyday life, Characterized by its practical or existential inescapability. He then examines the charge that the truths of metaphysics illegitimately claim to be both necessary and factual, And argues in response that the objection rests upon a confusion of the character of one's intentional instrument (...) (the sentence or proposition) with that of the object intended. (staff). (shrink)

Resolution Matrix Semantics (RMS) introduces the alternative truth-value-based framework for modal logic, providing a substantive alternative to Kripke’s relational semantics of possible worlds. Drawing inspiration from Y. Ivlev’s substantive semantics, RMS utilizes a 4-valued structure—necessary truth (tn), contingent truth (tc), contingent false (fc), and necessary false (fn)—augmented by indeterminate values (t, f, t/f) to define modal systems Km, KDm, KTm, S4m, and S5m, analogous to Kripke’s K, KD, T, S4, and S5. By directly assigning determined and indeterminate truth values (...) via an interpretation function, RMS validates formulas without relying on accessibility relations, as demonstrated through soundness and completeness proofs and a tailored tableau method. The framework’s versatility extends to applications in deontic logic, artificial intelligence, and quantum computing, enabling context-dependent reasoning with computational efficiency. RMS thus bridges philosophical logic and practical domains, offering a truth-centric perspective on modal reasoning’s complexities. (shrink)

The Ethical Matrix was developed to help decision-makers explore the ethical issues raised by agri-food biotechnologies. Over the decade since its inception the Ethical Matrix has been used by a number of organizations and the philosophical basis of the framework has been discussed and analyzed extensively. The role of tools such as the Ethical Matrix in public policy decision-making has received increasing attention. In order to further develop the methodological aspects of the Ethical Matrix method, (...) work was carried out to study the potential role of the Ethical Matrix as a decision support framework. When considering which frameworks to apply when analyzing the ethical dimensions of the application of agri-food biotechnologies, it is important to clarify the substantive nature of any prospective framework. In order to further investigate this issue, reflections on the neologism “ethical soundness” of an ethical framework are presented here. This concept is introduced in order to provide more structured evaluations of a range of ethical tools, including ethical frameworks such as the Ethical Matrix. As well as examining the philosophical dimensions of the method, theoretical analysis and literature studies were combined with stakeholder engagement exercises and consultations in order to review the Ethical Matrix from a user perspective. This work resulted in the development of an Ethical Matrix Manual, which is intended to act as a guide for potential user groups. (shrink)

The ethical matrix approach was developed by Prof Ben Mepham and his colleagues at the University of Nottingham in the early 1990s. Since then the approach has received increasing attention and has been used by several researchers in different projects related to assessing ethical impacts of different food production technologies and other policy options of societal concern. The ethical matrix is sometimes understood simply as a checklist of ethical concerns, but might also be seen as a guide to (...) coming to conclusions on moral questions. The problem I discuss in this paper relates to how using the ethical matrix method as a decision guide can be combined with respecting pluralism. The aim of the paper is to suggest a framework making it possible to – at the same time – enhance public justification of judgments and respect pluralism. I argue that pluralism is fundamental to the ethical matrix approach; I distinguish between intuitionist principled pluralism and societal value pluralism; and I show how both kinds of pluralism imply restrictions on how conclusions can be made. No substantive moral decision principles can be allowed. Still, I argue, decision principles of a more epistemological or procedural character can be acceptable even within pluralism. The pragmatist principle of inquiry is defended as an account of moral problem solving compatible with both principled pluralism and value pluralism. When an ethical matrix is used within such a participatory inquiry process substantive conclusions can be drawn. (shrink)

'The Matrix Project' comprises two contexts, namely photographic work of architect Thierry Lagrange and the self-reflective trajectory that he developed during his doctorate at KULeuven. Lagrange's practice-based research developed to an autonomous artistic project, in which he studied the signification and nature of observation within a creative process. Through his multifaceted practice as an architect, photographer and researcher, Lagrange developed 'The Matrix Method'; a method that stimulates creativity within different contexts and can be implemented for example (...) in art education. For the Matrix Project, 25 years' worth of photographs was entered into a context of research and presents a new perspective on different ways of seeing in our present visual culture. (shrink)

We propose a rational method for addressing an important question—who deserves to be an author of a scientific article? We review various contentious issues associated with this question and recommend that the scientific community should view authorship in terms of contributions and responsibilities, rather than credits. We propose a new paradigm that conceptually divides a scientific article into four basic elements: ideas, work, writing, and stewardship. We employ these four fundamental elements to modify the well-known International Committee of Medical (...) Journal Editors (ICMJE) authorship guidelines. The modified ICMJE guidelines are then used as the basis to develop an approach to quantify individual contributions and responsibilities in multi-author articles. The outcome of the approach is an authorship matrix, which can be used to answer several nagging questions related to authorship. (shrink)

This paper defends the idea that Cassirer's methodology is idealistic in regard to validity claims and the structuralist views he holds and at the same time empiric in regard to the facts and genealogy of culture. This perspective is best to be unfolded along Cassirer's model of representation. The author does so by showing that Cassirer's triad of symbolic articulation (expressive, presentational, significative) and the triad of symbolic development (mimetic, analogical, symbolic) form a coherent and exhaustive theory of symbolic formation. (...) In order to defend this view, two main objections from the secondary literature against the consistency of this essential theory piece of The Philosophy of Symbolic Forms have to be rejected. (shrink)

This article presents a Pauli-Dirac matrix approach to Clifford Algebras. It is shown that the algebra C2 is generated by two Pauli matrices iσ2 and iσ3; C3 is generated by the three Pauli matrices σ1, σ2, σ3; C4 is generated by four Dirac matrices γ0, γ1, γ2, γ3 and C5 is generated by five Dirac matrices iγ0, iγ1, iγ2, iγ3, iγ5. The higher dimensional anticommuting matrices which generate arbitrarily high order Clifford algebras are given in closed form. The results (...) obtained with this Clifford algebra approach are compared with the vector product method which was described in a recent article [Found. Phys. 10, 531–553 (1980) by Poole, Farach and Aharonov] and with the Dirac, Rashevskii and Ramakrishnan methods of matrix generation. (shrink)

A recent rethinking of the early history of Quantum Mechanics deemed the late 1920s agreement on the equivalence of Matrix Mechanics and Wave Mechanics, prompted by Schrödinger's 1926 proof, a myth. Schrödinger supposedly failed to prove isomorphism, or even a weaker equivalence (“Schrödinger-equivalence”) of the mathematical structures of the two theories; developments in the early 1930s, especially the work of mathematician von Neumann provided sound proof of mathematical equivalence. The alleged agreement about the Copenhagen Interpretation, predicated to a large (...) extent on this equivalence, was deemed a myth as well. In response, I argue that Schrödinger's proof concerned primarily a domain-specific ontological equivalence, rather than the isomorphism or a weaker mathematical equivalence. It stemmed initially from the agreement of the eigenvalues of Wave Mechanics and energy-states of Bohr's Model that was discovered and published by Schrödinger in his first and second communications of 1926. Schrödinger demonstrated in this proof that the laws of motion arrived at by the method of Matrix Mechanics are satisfied by assigning the auxiliary role to eigenfunctions in the derivation of matrices (while he only outlined the reversed derivation of eigenfunctions from Matrix Mechanics, which was necessary for the proof of both isomorphism and Schrödinger-equivalence of the two theories). This result was intended to demonstrate the domain-specific ontological equivalence of Matrix Mechanics and Wave Mechanics, with respect to the domain of Bohr's atom. And although the mathematical equivalence of the theories did not seem out of the reach of existing theories and methods, Schrödinger never intended to fully explore such a possibility in his proof paper. In a further development of Quantum Mechanics, Bohr's complementarity and Copenhagen Interpretation captured a more substantial convergence of the subsequently revised (in light of the experimental results) Wave and Matrix Mechanics. -/- I argue that both the equivalence and Copenhagen Interpretation can be deemed myths if one predicates the philosophical and historical analysis on a narrow model of physical theory which disregards its historical context, and focuses exclusively on its formal aspects and the exploration of the logical models supposedly implicit in it. -/- . (shrink)

In metazoans, the extracellular matrix (ECM) provides a dynamic, heterogeneous microenvironment that has important supportive and instructive roles. Although the primary site of action of ECM proteins is extracellular, evidence is emerging for non‐canonical intracellular roles. Examples include osteopontin, thrombospondins, IGF‐binding protein 3 and biglycan, and relate to roles in transcription, cell‐stress responses, autophagy and cancer. These findings pose conceptual problems on how proteins signalled for secretion can be routed to the cytosol or nucleus, or can function in environments (...) with diverse redox, pH and ionic conditions. We review evidence for intracellular locations and functions of ECM proteins, and current knowledge of the mechanisms by which they may enter intracellular compartments. We evaluate the experimental methods that are appropriate to obtain rigorous evidence for intracellular localisation and function. Better insight into this under‐researched topic is needed to decipher the complete spectrum of physiological and pathological roles of ECM proteins. -/- . (shrink)

A recent rethinking of the early history of Quantum Mechanics deemed the late 1920s agreement on the equivalence of Matrix Mechanics and Wave Mechanics, prompted by Schrödinger’s 1926 proof, a myth. Schrödinger supposedly failed to achieve the goal of proving isomorphism of the mathematical structures of the two theories, while only later developments in the early 1930s, especially the work of mathematician John von Neumman (1932) provided sound proof of equivalence. The alleged agreement about the Copenhagen Interpretation, predicated to (...) a large extent on this equivalence, was deemed a myth as well. If such analysis is correct, it provides considerable evidence that, in its critical moments, the foundations of scientific practice might not live up to the minimal standards of rigor, as such standards are established in the practice of logic, mathematics, and mathematical physics, thereby prompting one to question the rationality of the practice of physics. In response, I argue that Schrödinger’s proof concerned primarily a domain-specific ontological equivalence, rather than the isomorphism. It stemmed initially from the agreement of the eigenvalues of Wave Mechanics and energy-states of Bohr’s Model that was discovered and published by Schrödinger in his First and Second Communications of 1926. Schrödinger demonstrated in this proof that the laws of motion arrived at by the method of Matrix Mechanics could be derived successfully from eigenfunctions as well (while he only outlined the reversed derivation of eigenfunctions from Matrix Mechanics, which was necessary for the proof of isomorphism of the two theories). This result was intended to demonstrate the domain-specific ontological equivalence of Matrix Mechanics and Wave Mechanics, with respect to the domain of Bohr’s atom. And although the full-fledged mathematico-logical equivalence of the theories did not seem out of the reach of existing theories and methods, Schrödinger never intended to fully explore such a possibility in his proof paper. In a further development of Quantum Mechanics, Bohr’s complementarity and Copenhagen Interpretation captured a more substantial convergence of the subsequently revised (in light of the experimental results) Wave and Matrix Mechanics. I argue that both the equivalence and Copenhagen Interpretation can be deemed myths if one predicates the philosophical and historical analysis on a narrow model of physical theory which disregards its historical context, and focuses exclusively on its formal aspects and the exploration of the logical models supposedly implicit in it. (shrink)

The concept of time-coarsened density matrix for open systems has frequently featured in equilibrium and non-equilibrium statistical mechanics, without being probed as to the detailed consequences of the time averaging procedure. In this work we introduce and prove the need for a selective and non-uniform time-sampling, whose form depends on the properties of the bath. It is also applicable when an open microscopic sub-system is coupled to another finite system. By use of a time-periodic minimal coupling model between these (...) two systems, we present detailed quantitative consequences of time coarsening, which include initial state independence of equilibration, deviations from long term averages, their environment size dependence and the approach to classicality, as measured by a Leggett–Garg type inequality. An interacting multiple qubit model affords comparison between the time integrating procedure and the more conventional environment tracing method. (shrink)

The Norwegian National Committee for Research Ethics inScience and Technology (NENT), collaborating with The NorwegianFisherman''s Association and The Research Council of Norway,started in 1999 a project aiming at an ethical assessment of Norwegian fisheries for the year 2020. The project was to preparethe ground for ethical debate in and of the fishery sector inview of pending important decisions on long term strategies. Thispaper has its focus on the method used for achieving these aims,rather than the substantive results concerning the (...) fisheries. Amethod was developed for this purpose, called the ethicalscenario process. This included the construction of scenarios forthe future of Norwegian fisheries, using an ethical matrix for evaluating strategies, and organizing a ``value workshop'''' whereparticipants from different stakeholder groups came together todo ethical evaluations. The positive achievements and theshortcomings of this method are discussed in this paper. The useof an ethical matrix was meant to combine a participatory approachwith insights from theoretical ethics. The project revealedinherent tensions between these two objectives. Possible ways ofdealing with this tension are indicated, but in general a goodgrasp of the socio-political context might be the best guardianagainst the possible pitfalls involved in such an approach. (shrink)

India’s sacred texts provide deep insights into people management, with the Triguna theory offering a culturally rooted framework to understand workplace personality and behaviour. In Indian higher education, non-teaching duties are as vital as teaching for faculty development; yet, aligning these roles with faculty’s natural strengths is often overlooked, leading to dissatisfaction and anxiety. Despite their importance, this issue remains under-researched. This study develops a competency mapping matrix based on the Triguna theory to align non-teaching roles with inherent faculty (...) traits. Non-teaching tasks were grouped into six clusters, and seven personality types were defined using the Triguna framework, linked to specific competencies. The study adopted a qualitative exploratory design involving input from 15 faculty members across Indian higher education institutions. Participants were purposively selected from public and private universities, with 8–25 years of teaching experience and active involvement in administrative and committee roles. Non-teaching roles were clustered through thematic grouping based on the nature of work and competency requirements. The clustering was independently reviewed by academic experts, and discrepancies were resolved through consensus to enhance face validity. An adapted version of the Questionnaire Measure of Sahya (Manickam, 2014, Journal of Psychological Researches, 58[2], 75–83) was used to identify dominant Guna traits, with items reworded for faculty context and reviewed for contextual clarity. The resulting Guna-based competency mapping matrix offers a practical, culturally relevant method for allocating non-teaching duties, offering a culturally grounded framework that may support improved role alignment and faculty engagement. (shrink)

Contemporary changes in favor of the populist matrix thematization involve examination of the signifier-inaugural power of conspiratorial discourses as a symptom and political method of Serbian society democratic structure marginalization. Admittedly, the state's re-dramatization of conspiracists? phantasms of the enemy's horrifying hidden actions is not interpreted exclusively in the light of the political contagion that global, populist mind employs to write contemporary history. It is neither the central epistemic structure of the post-factual world which mandates the state's manipulation (...) of paranoid fear should be exclusively interpreted as part of the competition of multiple discourses for a hegemonic position. This study suggests political effects of creating phantasmatic content are reflected in maintaining the counter-revolutionary fervor of populist rule and traditional affiliation politics. Fully comprehending democratic standards? self discrediting relies on psychoanalytical assumptions about the predetermination of the subject by its phantasms having been placed in the field of the unconscious and the Lacanian anticipation of the permanent impossibility of bearing one's own self and desires. Ensuring proofs that the systemic incitement of irrational suspicion through the regime's media supports the self-establishment of ruling-class credibility, as well as getting to know the way in which the familiar dramaturgy of guilt is applied to ensure new legitimization procedures points to the interpretation of change as a difference in the relationship between social and phantasmatic forces. (shrink)

The objective of this chapter is to study abstract sentential calculi (alternatively, abstract propositional logics) construed as pairs (ℒ,⊢)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\mathcal {L}, \vdash )$$\end{document}. Here, ℒ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {L}$$\end{document} is the sentential language (absolutely free algebra) generated by a countably infinite set of propositional variables and a finite set of finitary connectives, and ⊢\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\vdash $$\end{document} is a multiple-conclusion (...) consequence relation. To call a binary relation between arbitrary sets of formulas of ℒ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {L}$$\end{document} a (multiple-conclusion) consequence relation, it is assumed that it fulfills the three laws—(R), (M), and (C): (R)If X∩Y≠∅\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$X\cap Y\neq \varnothing $$\end{document}, then X⊢Y\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$X\vdash Y$$\end{document}. (Reflexivity)(M)If X1⊢Y1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$X_1\vdash Y_1$$\end{document}, where X1⊆X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$X_1\subseteq X$$\end{document} and Y1⊆Y\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Y_1\subseteq Y$$\end{document}, then X⊢Y\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$X\vdash Y$$\end{document}. (Monotonicity or Dilution)(C)If X,S⊢Y,T\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$X, S\vdash Y, T$$\end{document} for all S and T such that S∩T=∅\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S\cap T=\varnothing $$\end{document} and S∪T=L\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S\cup T = L$$\end{document}, then X⊢Y\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$X\vdash Y$$\end{document}. (Cut)Some relations may be additionally structural in the sense that they satisfy the following condition, which takes into account the algebraic structure of ℒ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {L}$$\end{document}: (S)If X⊢Y\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$X\vdash Y$$\end{document}, then {e(α):α∈X}⊢{e(β):β∈Y}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\{e(\alpha ): \alpha \in X\} \vdash \{e(\beta ): \beta \in Y\}$$\end{document} for every endomorphism e of ℒ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {L}$$\end{document}.Section 3 reviews the basic properties of consequence relations from a lattice-theoretical point of view. In particular, a description is given of the least consequence relation extending a fixed set of pairs (X, Y ), where X and Y are finite sets of formulas.The main thread of discussion appears in Sect. 4, extends to the rest of the work, and concerns consequence relations determined by (logical) matrices, i.e., the relations of the form ⊢M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\vdash _M$$\end{document}, where M=(A,D)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M = (\mathcal {A}, D)$$\end{document} is a matrix for ℒ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {L}$$\end{document}. One defines X⊢MY\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$X\vdash _{M} Y$$\end{document} to mean that, for every homomorphism h from ℒ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {L}$$\end{document} to A\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {A}$$\end{document}, either h(α)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h(\alpha )$$\end{document} is undesignated (does not belong to D) for some α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document} in X or h(β)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h(\beta )$$\end{document} is designated for some β\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta $$\end{document} in Y. Since every such a relation ⊢M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\vdash _M$$\end{document} is structural, in discussing the problem of representing a consequence relation ⊢\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\vdash $$\end{document} by a class of matrices, one naturally has to assume that ⊢\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\vdash $$\end{document} is structural. Much attention is devoted to the study of strongly finite logics, i.e., logics whose consequence relations may be determined by a finite set of finite matrices. In Sect. 4.3, a criterion, expressed in terms of Lindenbaum-type matrices, for ⊢\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\vdash $$\end{document} to be strongly finite is given, and in Sect. 4.4 by the well-known method of ultraproducts it is proved that every strongly finite consequence relation is compact. The subject of strengthenings of logics is treated in Sects. 4.5 and 4.6, where the so-called (A, B)-strengthenings are examined in detail. Intuitively, given two arbitrary sets of formulas A and B, the (A, B)-strengthening of consequence relation ⊢\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\vdash $$\end{document} is obtained by treating formulas in A as new axiom schemas, while those from B as counter-axiom schemas. It is shown (by two methods) that any (A, B)-strengthening of a strongly finite ⊢\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\vdash $$\end{document} is strongly finite, and the number of such strengthenings is finite.The remaining part of our work (Sect. 5) is devoted to a purely model-theoretical proof of Shoesmith and Smiley’s finite basis theorem, which states that every strongly finite logic is finitely based, i.e., generated by a finite set of pairs (X, Y ) with X and Y being finite sets of formulas.In the Appendix, we abandon multiple-conclusion consequence relations and turn briefly to single-conclusion ones (i.e., consequence operations in Tarski’s sense) and furnish other proofs of two important theorems: Czelakowski’s characterization theorem for the class Matr(CnK\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Cn_K$$\end{document}) and Wojtylak’s representation theorem for consequence operations that are ≥\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\geq $$\end{document} than CnK\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Cn_K$$\end{document}. (shrink)

In today’s era of rapid development in science and technology, the development of digital technology has increasingly higher requirements for data processing functions. The matrix signal commonly used in engineering applications also puts forward higher requirements for processing speed. The eigenvalues of the matrix represent many characteristics of the matrix. Its mathematical meaning represents the expansion of the inherent vector, and its physical meaning represents the spectrum of vibration. The eigenvalue of a matrix is the focus (...) of matrix theory. The problem of matrix eigenvalues is widely used in many research fields such as physics, chemistry, and biology. A neural network is a neuron model constructed by imitating biological neural networks. Since it was proposed, the application research of its typical models, such as recurrent neural networks and cellular neural networks, has become a new hot spot. With the emergence of deep neural network theory, scholars continue to combine deep neural networks to calculate matrix eigenvalues. This article aims to study the estimation and application of matrix eigenvalues based on deep neural networks. This article introduces the related methods of matrix eigenvalue estimation based on deep neural networks, and also designs experiments to compare the time of matrix eigenvalue estimation methods based on deep neural networks and traditional algorithms. It was found that under the serial algorithm, the algorithm based on the deep neural network reduced the calculation time by about 7% compared with the traditional algorithm, and under the parallel algorithm, the calculation time was reduced by about 17%. Experiments are also designed to calculate matrix eigenvalues with Obj and recurrent neural networks (RNNS) models, which proves that the Oja algorithm is only suitable for calculating the maximum eigenvalues of non-negative matrices, while RNNS is commonly used in general models. (shrink)

Phenomenology, Sociology, Hermeneutics and Psychoanalysis have accumulated different methods and knowledge on the imaginary. Nevertheless, the crucial connection between the social imagining and communication has not always been truly examined. In this article, we take the imaginary (seen as a symbolic thought of images) and communication (seen as a process of symbolic reproduction) as correlated notions, and work upon a communicational matrix of the imaginary. We emphasize three key elements of the imaginary: by pointing to the verbal-iconic, technical and (...) mediatized dimensions we will be paying special attention to the media imaginary and the effects of its commemorative logic to the propagation of public imaginaries. (shrink)

Purpose. The article highlights the demand for critical thinking in everyday life at the present stage of development of globalized culture and emphasizes the role of philosophy as a source of rationality. Philosophizing, which is determined by the psychosociocultural matrix, sets the toposes, vocabulary and rhythms of meaning making, their preservation and transformation. The purpose of the article is to concretize the practices of socio-cultural communication, primarily through the social institute of education, where individuals interact with the psychosociocultural (...) class='Hi'>matrix of philosophizing, which mediate the general and individual level in philosophical culture. Theoretical basis of the study are cultural anthropology and phenomenological methods. Originality of the study: based on the philosophy of intersubjectivity, we actualized the rational grounds for formation of adequate judgments in modern culture at the level of everyday life. This justifies the inevitability of the spread of various forms and types of philosophical education, philosophical thinking, ideas and values developed in philosophical communities beyond the narrow circle of professional philosophers. This implies the systemic involvement of philosophers as professionals of meaning-making in solving problems in various non-academic fields – politics, economics, law, etc. The formation of skills of philosophical critical thinking in the process of preparing young people for active civil life is no less important aspect of this. Conclusions lead to an understanding of the existential importance of philosophy and philosophizing and the need for organized forms of knowledge transfer such as the Faculty of Philosophy of the Classical University. There is a mutual interest and interaction of the general culture of society and philosophy as a special kind of culture. Because philosophy actively configures other forms of culture, contributes to the creation of sociocultural identities precisely because of its ability to conceptually reproduce the core of the psychosociocultural matrix that underlies the existence of all these different forms within one society. The sociocultural macro level of philosophical spiritual practices is formed by the psychosociocultural matrix of the philosophical tradition, which retains its longevity from the emergence of philosophy and goes through its history, demonstrating the features of the national reception of philosophy as a national-specific embodiment of sociocultural macro level of the psychosociocultural matrix. (shrink)

The advent of intelligent technologies, notably Brain–Computer Interfaces (BCIs), has introduced novel privacy dilemmas. Ensuring judicious privacy transfer is imperative for the application of BCI technology and pivotal for fostering economic and technological progress. This study adopts privacy transfer as the research perspective and employs an ethical matrix as the research method. It establishes BCI users as the central core interests, with marketers, developers, and medical personnel as stakeholders. Departing from the binary opposition of public and private in (...) traditional privacy theory, this article proposes ethical principles such as maximizing benefits, minimizing harm, and respecting independent decision-making power. It constructs a judgment matrix for the privacy transfer of BCIs, utilizing this matrix to identify ethical risks like privacy disclosure and hijacking. This study analyzes the reasons for risks, aiming to overcome dilemmas and construct an ethical matrix to explore privacy transfer boundary division methods suitable for BCI technology and tailored to different stakeholders. (shrink)

Several studies have indicated that scientists are likely to have an outlook on both facts and values that are different to that of lay people in important ways. This is one significant reason it is currently believed that in order for scientists to exercise a reliable ethical reflection about their research it is necessary for them to engage in dialogue with other stakeholders. This paper reports on an exercise to encourage a group of scientists to reflect on ethical issues without (...) the presence of external stakeholders. It reports on the use of a reflection process with scientists working in the area of animal disease genomics (mainly drawn from the EADGENE EC Network of Excellence). This reflection process was facilitated by using an ethical engagement framework, a modified version of the Ethical Matrix. As judged by two criteria, a qualitative assessment of the outcomes and the participants’ own assessment of the process, this independent reflective exercise was deemed to be successful. The discussions demonstrated a high level of complexity and depth, with participants demonstrating a clear perception of uncertainties and the context in which their research operates. Reflection on stakeholder views and values appeared to be embedded within the discussions. The finding from this exercise seems to indicate that even without the involvement of the wider stakeholder community, valuable reflection and worthwhile discourse can be generated from ethical reflection processes involving only scienitific project partners. Hence, the previous assumption that direct stakeholder engagement is necessary for ethical reflection does not appear to hold true in all cases; however, other reasons for involving a broad group of stakeholders relating to governance and social accountability of science remain. (shrink)

By using the general expression of the matrix elements of the transitions S1/2-P1/2, S1/2-P3/2, established in previous papers, and the Sommerfeld and Schur method of integration, the matrix elements of the transitions 1S1/2-continuum are carried out, in a first step, without retardation.

We motivate and introduce a new method of abduction, Matrix Abduction, and apply it to modelling the use of non-deductive inferences in the Talmud such as Analogy and the rule of Argumentum A Fortiori. Given a matrix $${\mathbb {A}}$$ with entries in {0, 1}, we allow for one or more blank squares in the matrix, say a i,j =?. The method allows us to decide whether to declare a i,j = 0 or a i,j = (...) 1 or a i,j =? undecided. This algorithmic method is then applied to modelling several legal and practical reasoning situations including the Talmudic rule of Kal-Vachomer. We add an Appendix showing that this new rule of Matrix Abduction, arising from the Talmud, can also be applied to the analysis of paradoxes in voting and judgement aggregation. In fact we have here a general method for executing non-deductive inferences. (shrink)

Service process optimization is conducive to the innovation of enterprise services, but the poor logic design of multiple touchpoints can easily lead to problems in the service process, such as scattered layouts and repeated paths. Aiming at the promotion of service innovation and user experience, this paper takes the optimization of a single service touchpoint as the prerequisite and proposes a service process optimization method based on service touchpoint association and the design structure matrix. The association of service (...) touchpoints is categorized into two types, namely, noncoupled and coupled association. The DSM is used to describe the two types of association between service touchpoints, and the matrix operation is used for modular identification and layering of the two kinds of association. Finally, through the above steps, the problematic service process was replanned. By using the service process optimization of a new retail convenience store as an example, the service process is divided into 6 relatively independent modules, and the order of module execution is arranged. Moreover, the optimal service process of the convenience store system is determined, and the method is verified to be feasible. Through optimization both from single service touchpoint and service process modularization, the study provides a reference for process optimization of the complex service system. (shrink)

The motor modules during human walking are identified using non-negative matrix factorization from surface electromyography signals. The extraction of motor modules in healthy participants is affected by the change in pre-processing of EMG signals, such as low-pass filters ; however, the effect of different pre-processing methods, such as the number of necessary gait cycles in post-stroke patients with varying steps, remains unknown. We aimed to specify that the number of GCs influenced the motor modules extracted in the consideration of (...) LPFs in post-stroke patients. In total, 10 chronic post-stroke patients walked at a self-selected speed on an overground walkway, while EMG signals were recorded from the eight muscles of paretic lower limb. To verify the number of GCs, five GC conditions were set, namely, 25, 20, 15, 10, and 5 gate cycles with three LPFs. First, the number of modules, variability accounted for, and muscle weightings extracted by the NNMF algorithm were compared between the conditions. Next, a modified NNMF algorithm, in which the activation timing profiles among different GCs were unified, was performed to compare the muscle weightings more robustly between GCs. The number of motor modules was not significantly different, regardless of the GCs. The difference in VAF and muscle weightings in the different GCs decreased with the LPF of 4 Hz. Muscle weightings in 15 GCs or less were significantly different from those in 25 GCs using the modified NNMF. Therefore, we concluded that the variability extracted motor modules by different GCs was suppressed with lower LPFs; however, 20 GCs were needed for more representative extraction of motor modules during walking in post-stroke patients. (shrink)

Educational research suggests that the response biases of educators can negatively influence student performance and aptitude (Blanchett 2006; Bloom 2001; Darity et al. 2001; Gordon 2005; and Skiba et al. 2000). This article introduces ?good enough methods? for autoethnography as an alternative approach to this problem. Luttrell (2000, 13) conceptualizes ?good enough methods? researchers as those seeking to understand and appreciate difference and accept errors often made because of their blind spots and intense involvement. Evidence of this approach via autoethnography (...) is provided here from cases of graduate student-practitioners and their Intergroup/Intercultural Education professor. Moreover, the article highlights (a) a connection of autoethnography to research in Education, (b) five key decisions of a ?good enough methods? approach to autoethnography, and (c) how this approach can be applied to expose and address educator biases relating to ?the matrix? (Hill-Collins 1990) of race, class, and gender. (shrink)

In 1999, the first episode of The Matrix movie trilogy was released, marking the beginning of a new trend in science fiction movies and also in the perception of motion pictures as interactive social and commercial events. This paper will analyze an aspect of The Matrix trilogy promotional campaign (1999–2003) focusing on the interplay between verbal and visual semiotics through a select corpus of posters. The method of analysis will be based both on the grammar of visual (...) design developed by Kress and van Leeuwen, and on the Hallidayan model of analysis. The Matrix movies are set in a present (not future) ‘real’ world that is actually a ‘fiction of science,’ rather than a science fiction vision of a future reality. They are based on the idea of a very fuzzy border between real and virtual reality, which has become a major issue in these last fifteen years due to the advent of the internet and the fast growing number of internet users all over the world. This analysis will show how posters encode different kinds of promotional messages according to the social impact of each movie. (shrink)

Management decision-making is a daily task that managers of various levels solve in every organization. Degree of difficulty of this process depends on the scope of authority, responsibility level, manager’s position in organizational hierarchy; on the changes in the environment, unpredictability of which causes emergence of significant amounts of alternatives. For this reason, managers do not rely only on intuition or personal experience (which limited with selective perception, cognitive ability, ability to withstand stress and/or the presence of bias), but use (...) tools (methods) that have stood the test of time and practice; are based at the analysis of a significant amount of primary and secondary information; involve team-building to find the optimal option or to generate ideas. A significant amount of research papers are devoted to such methods, however, the author forms a synergetic approach which contains a detailed analysis of their correlation with the key factors of the competitiveness of enterprise, such as organizational culture and leadership. Existing decision-making practices, problems and style of management at the tourism enterprises are revealed from conducted survey (the first half of 2014) in tourism firms of Dnepropetrovsk and Zaporizhzhia regions of Ukraine, in which 729 tourism managers took part. The most popular decision-making practices in tourism branch were specified, among them are modeling and monitoring of previous results. The study proved the hypothesis of the author concerning strong connection of decision-making management and type of organizational culture. Moreover, 63% of managers were dissatisfied with low attention to organizational culture at their companies. The basis for future research and the synergetic matrix for decision-making management were worked out in the article which give preconditions for further studies and improvements in tourism management of Ukrainian enterprises. (shrink)

In the big data era, sequencing technology has produced a large number of biological sequencing data. Different views of the cancer genome data provide sufficient complementary information to explore genetic activity. The identification of differentially expressed genes from multiview cancer gene data is of great importance in cancer diagnosis and treatment. In this paper, we propose a novel method for identifying differentially expressed genes based on tensor robust principal component analysis, which extends the matrix method to the (...) processing of multiway data. To identify differentially expressed genes, the plan is carried out as follows. First, multiview data containing cancer gene expression data from different sources are prepared. Second, the original tensor is decomposed into a sum of a low-rank tensor and a sparse tensor using TRPCA. Third, the differentially expressed genes are considered to be sparse perturbed signals and then identified based on the sparse tensor. Fourth, the differentially expressed genes are evaluated using Gene Ontology and Gene Cards tools. The validity of the TRPCA method was tested using two sets of multiview data. The experimental results showed that our method is superior to the representative methods in efficiency and accuracy aspects. (shrink)

This chapter elaborates on the approaches, methods, and key concepts used in the research. This chapter goes more deeply into the details about the book’s chosen approach and research methods which have been adopted from modern matriarchal, Indigenous, and archeomythological studies, something never before applied to sauna research. The book brings together, at the same time, the author’s life’s work as it has focused for decades on the links between saunas, sweat lodges, and the bear religion.The notion of proxemics is (...) defined as a useful tool for clarifying the architectonics of space as a semiotic system, relevant also to different saunas in terms of their structures and spiritual or ritual meaning. The notion of proxemics has to do with the study of intentional human use of space for symbolic meanings. The notion is relevant to all of the sweating ritual studies just as they fit the task of comparing architectural arrangements of the Big House among the Delaware. The obvious ecofeminist approach is to revisit patriarchal history for its gendered biases and exclusions and to complement the research in this field with what we know of the past through the lens of indigeneity and gender.In this chapter I elaborate on the different gendered notions of spirituality as part of a deeper and broader worldview and life ways. After having provided an overview of the theories of the spiritual and of the sacred, I apply their relevance specifically to the sauna as a matrix of rebirth and healing. The issue of appropriation is, on the other hand, relevant to any comparative study touching on Indigenous peoples and their sacred rituals. Hence my self-reflection on how I came to include this perspective and how I have sought to avoid the politics of unconscious or even well-intentioned cultural appropriation. In this chapter I also elaborate on different terms for the sacred from sanctus and spiritus to holy and Hel contrasting various historical and contemporary definitions within religious studies. The terms themselves reveal the subjective and constructed nature of spiritual terminology. I also refer to the Finnish notion of väki, a particular strong energy charge linked with women and bears, which becomes relevant in the following chapters on different types of primal saunas and a protective life force rooted in female sexuality. (shrink)