An “analytic gravitational field”Z αβ(Z y ) is shown to include electromagnetic phenomena. In an almost flat and almost static complex geometryds 2 =zαβdzαdzβ of four complex variables zγ=t, x, y, x the field equationsR αβ $\frac{1}{2}$ Rz αβ= −κ(σU α U β − υZ αβ) imply the conventional equations of motion and the conventional electromagnetic field equations to first order if σ=σ(Z v) and ν=ν(z γ) are expressed in terms of the conventional mass density function $\hat (...) \sigma = \hat \sigma (x^\gamma )$ , the conventional charge density function $\hat \varepsilon = \hat \varepsilon (x^\gamma )$ , and a pressurep as follows: $\sigma = - 2v - 2iv\hat \varepsilon /\hat \sigma ,v = v + i(\frac{1}{4}\hat \varepsilon + v\hat \varepsilon /\hat \sigma ),$ v=const=p/c 2≈−10−29 gm/cm3. (shrink)

We generalize the notion of analytic/Borel equivalence relations, orbit equivalence relations, and Borel reductions between them to their continuous and quantitative counterparts: analytic/Borel pseudometrics, orbit pseudometrics, and Borel reductions between them. We motivate these concepts on examples and we set some basic general theory. We illustrate the new notion of reduction by showing that the Gromov–Hausdorff distance maintains the same complexity if it is defined on the class of all Polish metric spaces, spaces bounded from below, from above, (...) and from both below and above. Then we show that [Formula: see text] is not reducible to equivalences induced by orbit pseudometrics, generalizing the seminal result of Kechris and Louveau. We answer in negative a question of Ben Yaacov, Doucha, Nies, and Tsankov on whether balls in the Gromov–Hausdorff and Kadets distances are Borel. In appendix, we provide new methods using games showing that the distance-zero classes in certain pseudometrics are Borel, extending the results of Ben Yaacov, Doucha, Nies, and Tsankov. There is a complementary paper of the authors where reductions between the most common pseudometrics from functional analysis and metric geometry are provided. (shrink)

Suppose \ is a computable real. We extend previous work of Clanin, Stull, and McNicholl by determining the degrees of categoricity of the separable \ spaces whose underlying measure spaces are atomic but not purely atomic. In addition, we ascertain the complexity of associated projection maps.

Let E be a separable Banach space with separable dual. We show that the operation of subdifferentiation and the inverse operation are Borel from the convex functions on E into the monotone operators on E for the Effros–Borel structures.We also prove that the set of derivatives of differentiable convex functions is coanalytic non-Borel, by using the already known fact that the set of differentiable convex functions is itself coanalytic non-Borel, as proved in Bossard et al. 142).At last, we give (...) a new proof of this latter fact, for reflexive E's, by giving a coanalytic rank on those sets and constructing functions of “high ranks”. This approach, based on an ordinal rank which follows from a construction of trees, is quite different — not so general but actually more constructive — from the previous results of this kind, in Bossard et al. 142) and Godefroy et al. , based on reductions of arbitrary coanalytic or difference of analytic sets to the studied sets. (shrink)

In the modern scientific literature, there are many reports about the successful application of neural network technologies for solving complex applied problems, in particular, for modeling the urban real estate market. There are neural network models that can perform mass assessment of real estate objects taking into account their construction and operational characteristics. However, these models are static because they do not take into account the changing economic situation over time. Therefore, they quickly become outdated and need frequent updates. (...) In addition, if they are designed for a specific city, they are not suitable for other cities. On the other hand, there are several dynamic models taking into account the overall state of the economy and designed to predict and study the overall price situation in real estate markets. Such dynamic models are not intended for mass real estate appraisals. The aim of this article is to develop a methodology and create a complex model that has the properties of both static and dynamic models. Moreover, our comprehensive model should be suitable for evaluating real estate in many cities at once. This aim is achieved since our model is based on a neural network trained on examples considering both construction and operational characteristics, as well as geographical and environmental characteristics, along with time-changing macroeconomic parameters that describe the economic state of a specific region, country, and the world. A set of examples for training and testing the neural network were formed on the basis of statistical data of real estate markets in a number of Russian cities for the period from 2006 to 2020. Thus, many examples included the data relating to the periods of the economic calm for Russia, along with the periods of crisis, recovery, and growth of the Russian and global economy. Due to this, the model remains relevant with the changes of the international economic situation and it takes into account the specifics of regions. The model proved to be suitable for solving the following tasks: industrial economic analysis, company strategic and operational management, analytical and consulting support of investment, and construction activities of professional market participants. The model can also be used by government agencies authorized to conduct public cadastral assessment for calculating property taxes. (shrink)

The widely accepted two-dimensional circumplex model of emotions posits that most instances of human emotional experience can be understood within the two general dimensions of valence and activation. Currently, this model is facing some criticism, because complex emotions in particular are hard to define within only these two general dimensions. The present theory-driven study introduces an innovative analytical approach working in a way other than the conventional, two-dimensional paradigm. The main goal was to map and project semantic emotion (...) class='Hi'>space in terms of mutual positions of various emotion prototypical categories. Participants (N = 187; 54.5% females) judged 16 discrete emotions in terms of valence, intensity, controllability and utility. The results revealed that these four dimensional input measures were uncorrelated. This implies that valence, intensity, controllability and utility represented clearly different qualities of discrete emotions in the judgments of the participants. Based on this data, we constructed a 3D hypercube-projection and compared it with various two-dimensional projections. This contrasting enabled us to detect several sources of bias when working with the traditional, two-dimensional analytical approach. Contrasting two-dimensional and three-dimensional projections revealed that the 2D models provided biased insights about how emotions are conceptually related to one another along multiple dimensions. The results of the present study point out the reductionist nature of the two-dimensional paradigm in the psychological theory of emotions and challenge the widely accepted circumplex model. (shrink)

We characterise strongly minimal groups interpretable in elementary extensions of compact complex analytic spaces.

This paper provides a critical reflection on the nature of ethnic enclaves and segregation by presenting an analytical frame that can be used to capture the contested nature of spatiality in these spaces. By underscoring the dynamics in which differences constitute distinct subject positions, this paper posits a relational orientation to studying spatiality that is based on complex relations among and between subjects and space. To date, few attempts have been made to present an analytical frame for the (...) analysis of the spatiality of ethnic enclaves and segregation in which space becomes contested by different groups, occupants of space, and those external to space. This paper bridges this gap by synthesizing the relational approaches found in Bourdieusian field theory and Lefebvrian spatiality. This paper seeks to make three contributions. First, to provide an explicit theoretical anchor upon which relational and spatial theories converge since the underlying rationale for complementary is usually only implicitly evaluated. In detailing this convergence, the social constitution of reality and an emphasis on the duality between individuals and society as well as society and space are identified as a rationale for relational spatiality. Second, to demonstrate how a collective engagement with Bourdieu’s and Lefebvre’s approaches facilitates a recognition of spatiality as a polysemous social product and producer of social reality in addition to grounding this orientation as a critical dialectic engagement in which both the subjects and knowledge production cannot be neutral. Third, to present an analytical frame for the investigation of ethnic enclaves in and through which ethnic majorities, minorities, occupants of space, and those external to these enclaves constitute different views towards the same space. (shrink)

Complexified Liénard–Wiechert potentials simplify the mathematics of Kerr–Newman particles. Here we constrain them by fiat to move along Bohmian trajectories to see if anything interesting occurs, as their equations of motion are not known. A covariant theory due to Stueckelberg is used. This paper deviates from the traditional Bohmian interpretation of quantum mechanics since the electromagnetic interactions of Kerr–Newman particles are dictated by general relativity. A Gaussian wave function is used to produce the Bohmian trajectories, which are found to be (...) multi-valued. A generalized analytic continuation is introduced which leads to an infinite number of trajectories. These include the entire set of Bohmian trajectories. This leads to multiple retarded times which come into play in complex space-time. If one weights these trajectories by their natural Bohmian weighting factors, then it is found that the particles do not radiate, that they are extended, and that they can have a finite electrostatic self energy, thus avoiding the usual divergence of the charged point particle. This effort does not in any way criticize or downplay the traditional Bohmian interpretation which does not assume the standard electromagnetic coupling to charged particles, but it suggests that a hybridization of Kerr–Newman particle theory with Bohmian mechanics might lead to interesting new physics, and maybe even the possibility of emergent quantum mechanics. (shrink)

Let X be a non-reflexive Banach space such that X ∗ is separable. Let N be the set of all equivalent norms on X , equipped with the topology of uniform convergence on bounded subsets of X . We show that the subset Z of N consisting of Fréchet-differentiable norms whose dual norm is not strictly convex reduces any difference of analytic sets. It follows that Z is exactly a difference of analytic sets when N is equipped (...) with the standard Effros–Borel structure. Our main lemma elucidates the topological structure of the norm-attaining linear forms when the norm of X is locally uniformly rotund. (shrink)

A compact complex space X is viewed as a 1-st order structure by taking predicates for analytic subsets of X, X \times X, … as basic relations. Let f: X→ Y be a proper surjective holomorphic map between complex spaces and set Xy:=f-1(y). We show that the set Ak,d:={y∈ Y: the number of d-dimensional components of Xy is complex spaces and (...) f: X→ Y is a holomorphic map. The analogous result in the context of algebraic geometry gives rise to the definability of Morley degree. (shrink)

Let A be the category of all reduced compact complex spaces, viewed as a multi-sorted first order structure, in the standard way. Let U be a sub-category of A, which is closed under the taking of products and analytic subsets, and whose morphisms include the projections. Under the assumption that Th(U) is unidimensional, we show that Morley rank is equal to Noetherian dimension, in any elementary extension of U. As a result, we are able to show that Morley (...) degree is definable in Th(U), when Th(U) is unidimensional. (shrink)

Following the introduction and preliminary investigations of analytic Zariski structures in Peatfield and Zilber (Ann pure Appl Logic 132:125–180, 2005) an example of an analytic Zariski structure extending an algebraically closed field is provided. The example is constructed using Hrushovski’s method of free amalgamation, and a topology is introduced in which we can verify the analytic Zariski axioms.

This paper forges links between early analytic philosophy and the posits of semiotics. I show that there are some striking and potentially quite important, but perhaps unrecognized, connections between three key concepts in Wittgenstein’s middle and later philosophy, namely, complex, rule-following, and language games. This reveals the existence of a conceptual continuity between Wittgenstein’s “early” and “later” philosophy that can be applied to the analysis of the iterability of representation in computer-generated images. Methodologically, this paper clarifies to at (...) least some degree, the nature, progress and promise of an approach to doing philosophy and semiotics from a modally modest perspective that sees in the intellectual products of humanities, and not in unreflective empiricism, the future of scientific development. This hybrid, non-reductionist approach shows, among other things, that semiotic processes are encoded by specific types of complexes in computer-generated images that display iterability in time and space. (shrink)

The rise of networked social movements contesting neo-liberal globalization and protesting the summits of global finance and governance organizations has posed an analytical challenge to social movement theorists and called into question the applicability to this global milieu of the familiar concepts and heuristics utilized in social movement studies. In this article, we argue that the self-defining alter-globalization movement(s) might instead be engaged with as an expression and effect of global complexity, and we draw upon a ‘minor’ literature in social (...) movement studies that includes Gregory Bateson, Gilles Deleuze and Alberto Melucci to illustrate our claims. This article uses a Deleuzian reading of complexity to describe the phase space of the ‘movement of movements’, and its perturbation of global civil society through the iteration of sense-making processes (reflexive framing) and the exploration of singularities inhering in social movement ‘plateaux’. Those transnational gatherings, protests and social forums facilitated by computer-mediated communications and the advent of unprecedented mobility which constitute a ‘shadow realm’ that remains largely invisible to political exchange theories operating within the conceptual confines of the nation-state. (shrink)

Fundamental analytic, algebraic, and geometric properties of generalized Hamiltonian (Birkhoffian) theory are compared with the properties of a covering unitary phase-space formulation based on complex variables of the form (p+iq). Technical advantages in the unitary phase-space formulation are illustrated by a detailed discussion of the one-dimensional extended damped harmonic oscillator. One advantage is the ability to fully describe nonconservative constraint forces within a globally conservative system. Another advantage is that wider classes of gauge transformations are available (...) to simplify the construction of smooth solution manifolds. (shrink)

Coevolution between two antagonistic species has been widely studied theoretically for both ecologically- and genetically-driven Red Queen dynamics. A typical outcome of these systems is an oscillatory behavior causing an endless series of one species adaptation and others counter-adaptation. More recently, a mathematical model combining a three-species food chain system with an adaptive dynamics approach revealed genetically driven chaotic Red Queen coevolution. In the present article, we analyze this mathematical model mainly focusing on the impact of species rates of evolution (...) (mutation rates) in the dynamics. Firstly, we analytically proof the boundedness of the trajectories of the chaotic attractor. The complexity of the coupling between the dynamical variables is quantified using observability indices. By using symbolic dynamics theory, we quantify the complexity of genetically driven Red Queen chaos computing the topological entropy of existing one-dimensional iterated maps using Markov partitions. Co-dimensional two bifurcation diagrams are also built from the period ordering of the orbits of the maps. Then, we study the predictability of the Red Queen chaos, found in narrow regions of mutation rates. To extend the previous analyses, we also computed the likeliness of finding chaos in a given region of the parameter space varying other model parameters simultaneously. Such analyses allowed us to compute a mean predictability measure for the system in the explored region of the parameter space. We found that genetically driven Red Queen chaos, although being restricted to small regions of the analyzed parameter space, might be highly unpredictable. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:The Nature of Space by Milton SantosDave McLaughlinThe Nature of Spaceby milton santos (trans. by brenda baletti) Durham, N.C.: Duke University Press, 2021When asked to review Milton Santos’s The Nature of Space, I was interested mostly in the book’s core theme. As a literary geographer, my own research focuses heavily on space as an analytical concept and a lived experience; I was keen to read (...) and understand a fresh perspective on this topic. Little did I know that opening this book would connect me to a world of geography scholarship for the most part ignored, actively or otherwise, in the Anglophone academy. For my sins, I was not alone in this ignorance. In 2017, for example, one scholar felt confident in writing that:The English-speaking geographical community knows very little about the theoretical work in geography being produced in the so-called [End Page 147] “global South.” They are unaware, for example, of the work of Brazilian geographer Milton Santos.1It is not my place here to write about the reasons why this is such a mistake. Others, better qualified than me, have already done so.2 My aim here is to do three things. First, to put Santos’s arrival into English-language geography in context; second, to consider briefly his key contribution to defining the nature of space; and finally, to touch on what Santos’s book offers us more broadly.Published in 2021, Brenda Baletti’s translation of Santos’s great work arrived on the crest of a wave of discussions, debates, and scholarly interventions around decoloniality in Western geography. This movement emphasizes uncovering “still colonising frames of knowledge”3—frames “through which the world is apprehended and explained and modelled for the future”—and “craft[ing] ways of thinking harder about and against them.”4 Others have argued that the long wait for an English translation of Santos’s The Nature of Space is evidence of just such modes of thought continuing, unreflectively, among Anglophone academia. In 2019, an English-language translation of Santos’s For a New Geography was published by the University of Minnesota Press, followed by The Nature of Space in 2021. Hopefully, publications indicate that some publishers, at least, are following Stephen Legg’s call to think hard against certain predominant Western frames.The Nature of Space, despite its mere 280 pages, is an opus of sorts. Santos’s style eschews narrow conceptualization in favor of building a solid theory of space on a remarkably broad foundation of thinkers, including Braudel, Merleau-Ponty, Habermas, Latour, and many, many others. This broad foundation is a result not only of his long career and his own widely travelled life; it is necessary due to the slippery and almost-undefinable nature of space itself. In a wonderful section of For a New Geography, Santos lays out the problem facing geographers in defining this concept around which our discipline revolves:I understand why geographers have spent more time defining geography than space as the latter is extremely hard to do. The same could be said of space as Saint Augustine said of time: “if I ask myself if I know [End Page 148] what it is, I respond that I do; but, if I ask myself to define it, I respond that I do not know how.”5Part of this complication, recognized by Santos, is that “space” is a word with many meanings outside academia.6 Yet, geographers also face no simple task in defining this core concept for our own needs. Doreen Massey’s definition from For Space is one of my favorites, not only because it well illustrates the complexity of the term “space,” but also due to the range of reactions it produces in my first-year undergraduate students when I introduce it: Space is the sphere of the possibility of the existence of multiplicity in the sense of contemporaneous plurality.7 This is a very crunchy sentence! But it gets to the heart of a conceptually complex truth: that space is the dimension in which things happen, a dimension in which we must live at all times, as well as... (shrink)

ABSTRACT: In this chapter I argue that Sellars’s philosophy was deeply pragmatist both in its motivation and in its content, whether considered conceptually, historically, or in his own estimation, and that this is the case even in the important respects in which his views differ from most pragmatists. However, this assessment has been rejected by many recent pragmatists, with “classicalist” pragmatists frequently objecting to Sellars’s analytic-pragmatist privileging of language at the alleged expense of experience, while many analytic pragmatists (...) themselves emphasize that Sellars’s philosophy arguably runs against the grain of pragmatism in central respects, with Brandom for instance recently remarking that “Sellars never explicitly identified himself with pragmatism.” Part I explores the classical pragmatist influences on the development of Sellars’s philosophy, with reference to aspects of the intellectual background in which those views formed. Part II then outlines more abstractly some of the enduring pragmatist themes in Sellars’s philosophy, including his conceptions of the myth of the given, the space of reasons, and his normative-inferentialist theory of meaning. I conclude in Part III with Sellars’s views on truth and “picturing,” which present a complex case for the question of “how pragmatist” Sellars’s views both were and ought to be. (shrink)

With the rise of the so-called military-entertainment complex, critical scholars note with alarm the integration of the political economies of entertainment companies and the military, in particular its potential influence on millions of young people who consume its concomitant films, toys and especially video games. Seen from a broad perspective, a potentially productive means of understanding the complexities of this sphere is through the lens of Michel Foucault’s notion of governmentality—a concept that ties together the actions and preferred outcomes (...) of the modern surveillance state with the microlevel actions of individual behavior. In this analytical framework, social norms are inculcated through subtle forms of coercion, where the state establishes the field of action in which state subjects ultimately perform self-discipline. This article argues that the first person shooter genre inculcates what I refer to as the governmentality of battlefield space: a form of discipline in which players adhere to gamic norms of performance—efficiency, proficiency, and masculine performativity—which are delineated by ludic structures and largely understood on terms which originate within the social ecology of gaming. The genre accomplishes this though disciplinary techniques such as informational verisimilitude, statistics, and masculinized “gamer” discourse, particularly during multiplayer instances, in which players constitute social understandings of what is “good” and “bad” play. It is on these terms that virtual combat performance and player performance become conflated in a kind of masculinized performance, which both adheres to and undermines traditional, hegemonic norms of (Western) military masculinity. This phenomenon transcends local social realities, and highlights the ways in which particular aspects of gaming and combat appear to have increasingly overlapping phenomenological and ontological qualities, working to produce a form of self-performance that may be required of tomorrow’s soldiers. (shrink)

Electroencephalography is the measurement of neuronal activity in different areas of the brain through the use of electrodes. As EEG signal technology has matured over the years, it has been applied in various methods to EEG emotion recognition, most significantly including the use of convolutional neural network. However, these methods are still not ideal, and shortcomings have been found in the results of some models of EEG feature extraction and classification. In this study, two CNN models were selected for the (...) extraction and classification of preprocessed data, namely, common spatial patterns- CNN and wavelet transform- CNN. Using the CSP-CNN, we first used the common space model to reduce dimensionality and then applied the CNN directly to extract and classify the features of the EEG; while, with the WT-CNN model, we used the wavelet transform to extract EEG features, thereafter applying the CNN for classification. The EEG classification results of these two classification models were subsequently analyzed and compared, with the average classification accuracy of the CSP-CNN model found to be 80.56%, and the average classification accuracy of the WT-CNN model measured to 86.90%. Thus, the findings of this study show that the average classification accuracy of the WT-CNN model was 6.34% higher than that of the CSP-CNN. (shrink)

We show that if κ is a weakly compact cardinal then the embeddability relation on trees of size κ is invariantly universal. This means that for every analytic quasi-order R on the generalized Cantor space View the MathML source there is an Lκ+κ-sentence φ such that the embeddability relation on its models of size κ, which are all trees, is Borel bi-reducible to R. In particular, this implies that the relation of embeddability on trees of size κ is (...) complete for analytic quasi-orders on View the MathML source. These facts generalize analogous results for κ=ω obtained in Louveau and Rosendal [17] and Friedman and Motto Ros [6], and it also partially extends a result from Baumgartner [3] concerning the structure of the embeddability relation on linear orders of size κ. (shrink)

This paper is a tentative attempt to identify some basic-level conceptual and theoretical problems underlying the mainstream genre theory, which adversely affect the analysis of rapidly evolving, complex and hybrid genres in the modern communicative space. Having discussed these problems, I go on to I argue that the space of contemporary public communication should be viewed as not only an “analytic problem”, but also/rather a domain whose explorations could potentially revise the existing principles of genre theory. (...) In particular, I suggest such explorations should focus on the conception of genres as abstractions, activators and realizers of context, flexible macrostructures, social field entities, assigners of interpersonal roles. Notwithstanding a possible advancement of genre theory resulting from this approach, I conclude that it is only a first and admittedly uncertain step in trying to establish a sound theoretical framework for communicative genres in the modern discourse space. (shrink)

In considering two extended examples of educational reform efforts, this discussion traces relations that become visible through analytic approaches associated with actor-network theory (ANT). The strategy here is to present multiple readings of the two examples. The first reading adopts an ANT approach to follow ways that all actors—human and non-human entities, including the entity that is taken to be ‘educational reform’—are performed into being through the play of linkages among heterogeneous elements. Then, further readings focus not only on (...) the material practices that become enacted and distributed, but also on the otherings that occur: the various fluid spaces and ambivalent belongings that create actor-network(s) but also escape them. For educational research, particularly in educational reform and policy, it is argued that ANT analyses are particularly useful to examine the complex enactments in these dynamics. That is, ANT can illuminate movements of ordering and disordering that occur through minute socio-material connections in educational interventions. ANT readings also can discern, within these attempts to order people and practices, the spaces of flux and instability that enable and protect alternate possibilities. (shrink)

The quantum transition probability assignment is an equiareal transformation from the annulus of symplectic spinorial amplitudes to the disk of complex state vectors, which makes it equivalent to the equiareal projection of Archimedes. The latter corresponds to a symplectic synchronization method, which applies to the quantum phase space in view of Weyl’s quantization approach involving an Abelian group of unitary ray rotations. We show that Archimedes’ method of synchronization, in terms of a measure-preserving transformation to an equiareal disk, (...) imposes the integrality of the quantum of action, and requires the extension of the classical moment map from the real line to the circle. Additionally, the same synchronization method is encoded in the structure of the Heisenberg group, viewed as a principal bundle with a connection, whose curvature and anholonomy is expressed in terms of area bounding loops in relation to the underlying Abelian shadow on a symplectic plane. In this manner, we show that the geometric phase pertains to the minimal synchronized area \ of the 2-d symplectic Abelian shadow of the symplectic ball, modulo \. The integrality condition naturally leads to the consideration of modular commutative observables pertaining to the role of the discrete Heisenberg group. We prove that the structural transition from non-commutativity to modular commutativity in accordance to Weyl’s group-theoretic commutation relations takes place via universal factorization through the discrete Heisenberg group. In this way, we derive a homology-theoretic formulation of the synchronization method in terms of the area-bounding cells of the modular lattice \ in relation to any Abelian symplectic shadow. Thus, we finally obtain the physical interpretation of the analytic representation of quantum states as theta functions corresponding to the sections of a complex line bundle with an integral symplectic structure. (shrink)

The subject of the study is the ontological nature of the phenomenon of creativity in the context of conceptual constructions of the most important nominal layers of non-classical philosophy. The aim of the work is to reveal the ontological essence of creativity in the context of European philosophy of the XIX–XX centuries based on the works of A. Schopenhauer, A. Bergson, J.-P. Sartre, A. Camus and M. Heidegger. The theoretical and methodological basis of the research is the works of representatives (...) of the non-classical period of the development of philosophical thought, as well as the works of modern domestic and foreign researchers, in their works directly or indirectly touching on the problem of the ontological determinant of creativity. The central research methods are comparative and complex methods for establishing connections and relationships between phenomena that are part of the sphere of creative being, as well as an analytical and interpretive method for analyzing existing interpretations of the phenomenon under study and presenting the author's position. The scientific novelty of the research consists in the identification and systematization of philosophical ideas regarding the ontological determinant of creativity in the conceptual field of Western European non–classical philosophy of the XIX-XX centuries. As a result of the conducted research, the author comes to the conclusion that within the framework of non-classical philosophy, the ontological nature of creativity is revealed both at the level of objective reality and in the existential-personal space of the subject. Unlike the classical tradition of philosophizing, which absolutizes the epistemological component of the subject's creativity, in the subject field of non-classical philosophy, creativity regains its ontological rootedness, since it acts as the general existential of human existence, revealing itself through the prism of such concepts as the Will to live, pure duration, creative evolution, Vital impulse, imaginative consciousness, rebellion against the absurd, the promotion of truth and the way out of inauthenticity. (shrink)

We use tools of mathematical logic to analyse the notion of a path on a complex algebraic variety, and are led to formulate a “rigidity” property of fundamental groups specific to algebraic varieties, as well as to define a bona fide topology closely related to etale topology. These appear as criteria for ℵ1-categoricity, or rather stability and homogeneity, of the formal countable language we propose to describe homotopy classes of paths on a variety, or equivalently, its universal covering (...) class='Hi'>space.Technically, for a variety A defined over a finite field extension of the field Q of rational numbers, we introduce a countable language L describing the universal covering space of A, or, equivalently, homotopy classes of paths in A. Under some assumptions on A source we show that the universal covering space of A is an analytic Zariski structure [26]), and present an Lω1ω)-sentence axiomatising the class containing the structure and that is stable and homogeneous over elementary submodels. The “rigidity” condition on fundamental groups says that projection of the fundamental group of a variety is the fundamental group of the projection, up to finite index and under some irreducibility assumptions, and is used to prove that the projection of an irreducible closed set is closed in the analytic Zariski structure.In particular, we define an analytic Zariski structure on the universal covering space of an Abelian variety defined over a finite extension of the field Q of rational numbers. (shrink)

We calculate the mixing of real and imaginary components of space and time under the influence of superluminal boosts in thex direction. A unique mixing is determined for this superluminal Lorentz transformation when we consider the symmetry properties afforded by the inclusion of three temporal directions. Superluminal transformations in complex six-dimensional space exhibit unique tachyonic connections which have both remote and local space-time event connections.

It will be shown that the probability calculus of a quantum mechanical entity can be obtained in a deterministic framework, embedded in a real space, by introducing a lack of knowledge in the measurements on that entity. For all n ∃ ℕ we propose an explicit model in $\mathbb{R}^{n^2 } $ , which entails a representation for a quantum entity described by an n-dimensional complex Hilbert space þn, namely, the “þn,Euclidean hidden measurement representation.” This Euclidean hidden measurement (...) representation is also in a more general sense equivalent with the orthodox Hilbert space formulation of quantum mechanics, since every mathematical ingredient of ordinary quantum mechanics can easily be translated into the framework of these representations. (shrink)

A homeomorphism is built between the separable complex Hilbert space (quantum mechanics) and Minkowski space (special relativity) by meditation of quantum information (i.e. qubit by qubit). That homeomorphism can be interpreted physically as the invariance to a reference frame within a system and its unambiguous counterpart out of the system. The same idea can be applied to Poincaré’s conjecture (proved by G. Perelman) hinting at another way for proving it, more concise and meaningful physically. Furthermore, the conjecture (...) can be generalized and interpreted in relation to the pseudo-Riemannian space of general relativity therefore allowing for both mathematical and philosophical interpretations of the force of gravitation due to the mismatch of choice and ordering and resulting into the “curving of information” (e.g. entanglement). Mathematically, that homeomorphism means the invariance to choice, the axiom of choice, well-ordering, and well-ordering “theorem” (or “principle”) and can be defined generally as “information invariance”. Philosophically, the same homeomorphism implies transcendentalism once the philosophical category of the totality is defined formally. The fundamental concepts of “choice”, “ordering” and “information” unify physics, mathematics, and philosophy and should be related to their shared foundations. (shrink)

An isomorphism is built between the separable complex Hilbert space (quantum mechanics) and Minkowski space (special relativity) by meditation of quantum information (i.e. qubit by qubit). That isomorphism can be interpreted physically as the invariance between a reference frame within a system and its unambiguous counterpart out of the system. The same idea can be applied to Poincaré’s conjecture (proved by G. Perelman) hinting another way for proving it, more concise and meaningful physically. Mathematically, the isomorphism means (...) the invariance to choice, the axiom of choice, well-ordering, and well-ordering “theorem” (or “principle”) and can be defined generally as “information invariance”. (shrink)

Elementary particles are considered as local oscillators under the influence of zeropoint fields. Such oscillatory behavior of the particles leads to the deviations in their path of motion. The oscillations of the particle in general may be considered as complex rotations in complex vector space. The local particle harmonic oscillator is analyzed in the complex vector formalism considering the algebra of complex vectors. The particle spin is viewed as zeropoint angular momentum represented by a bivector. (...) It has been shown that the particle spin plays an important role in the kinematical intrinsic or local motion of the particle. From the complex vector formalism of harmonic oscillator, for the first time, a relation between mass $m$ and bivector spin $S$ has been derived in the form $\varvec{\sigma }_3 mc^2{\mathcal {J}}_{\pm } =\lambda \Omega _{\mathbf{s}} \cdot \mathrm{{S}} {\mathcal {J}}_{\pm }$ . Where, $\Omega _{s}$ is the angular velocity bivector of complex rotations, $c$ is the velocity of light. The unit vector $\varvec{\sigma }_3$ acts as an operator on the idempotents ${\mathcal {J}}_{+}$ and ${\mathcal {J}}_{-}$ to give the eigen values $\lambda =\pm 1.$ The constant $\lambda $ represents two fold nature of the equation corresponding to particle and antiparticle states. Further the above relation shows that the mass of the particle may be interpreted as a local spatial complex rotation in the rest frame. This gives an insight into the nature of fundamental particles. When a particle is observed from an arbitrary frame of reference, it has been shown that the spatial complex rotation dictates the relativistic particle motion. The mathematical structure of complex vectors in space and spacetime is developed. (shrink)

A generalized Schrödinger equation containing correction terms to classical kinetic energy, has been derived in the complex vector space by considering an extended particle structure in stochastic electrodynamics with spin. The correction terms are obtained by considering the internal complex structure of the particle which is a consequence of stochastic average of particle oscillations in the zeropoint field. Hence, the generalised Schrödinger equation may be called stochastic Schrödinger equation. It is found that the second order correction terms (...) are similar to corresponding relativistic corrections. When higher order correction terms are neglected, the stochastic Schrödinger equation reduces to normal Schrödinger equation. It is found that the Schrödinger equation contains an internal structure in disguise and that can be revealed in the form of internal kinetic energy. The internal kinetic energy is found to be equal to the quantum potential obtained in the Madelung fluid theory or Bohm statistical theory. In the rest frame of the particle, the stochastic Schrödinger equation reduces to a Dirac type equation and its Lorentz boost gives the Dirac equation. Finally, the relativistic Klein–Gordon equation is derived by squaring the stochastic Schrödinger equation. The theory elucidates a logical understanding of classical approach to quantum mechanical foundations. (shrink)

We consider a quaternionic quantum formalism for the description of quantum states and quantum dynamics. We prove that generalized quantum measurements on physical systems in quaternionic quantum theory can be simulated by usual quantum measurements with positive operator valued measures on complex Hilbert spaces. Furthermore, we prove that quaternionic quantum channels can be simulated by completely positive trace preserving maps on complex matrices. These novel results map all quaternionic quantum processes to algorithms in usual quantum information theory.

In lieu of an abstract, here is a brief excerpt of the content:Feminist Studies 47, no. 1. © 2021 by Feminist Studies, Inc. 15 Candice Lyons Behind the Scenes: Elizabeth Keckley, Slave Narratives, and the Queer Complexities of Space In the fall of 1867—just two years after the conclusion of the American Civil War—former First Lady Mary Todd Lincoln, finding herself in dire financial straits, traveled incognito to New York. She hoped to sell select pieces from her famed wardrobe (...) in order to supplement her income, which was, at the time, rather meager. Accompanying the recently widowed socialite was her self-described “modiste” and “confidante ” Elizabeth Keckley, a formerly enslaved African American dressmaker who had been “intimately associated” with Lincoln for years.1 Despite the various measures undertaken to ensure the scheme’s success, including attempts to extort monied East Coast Republicans and strategic appeals to the press, it ultimately proved fruitless. Political nemeses seized on the opportunity to publicly mock Lincoln, who was seen as an “extravagant and improper” social climber, for her “pecuniary embarrassment,” treating the public auction of her clothing as a spectacle akin to the World Fair.2 Eventually, the former First Lady was forced to retreat to her home in Chicago, leaving Keckley behind to tend to her affairs. 1. Elizabeth Keckley, Behind the Scenes: Or, Thirty Years a Slave and Four Years in the White House (New York: Open Road Integrated Media, 2015): Location no. 406, 54, 53. 2. Carolyn Sorisio, “Unmasking the Genteel Performer: Elizabeth Keckley’s Behind the Scenes and the Politics of Public Wrath,” African American Review 34 (2000): 20; Keckley, Behind the Scenes, Location no. 1321. 16 Candice Lyons This decision, however, left the ordinarily sought-after seamstress in dire straits of her own, given that the time she was compelled to dedicate to what would come to be known as “The Old Clothes Scandal ” necessitated closing down her then-thriving business in Washington, DC.3 This, coupled with the fact that indemnification for her services was not forthcoming from Mrs. Lincoln, was likely at least partially at the root of Keckley’s decision to publish her now-infamous memoir, Behind the Scenes: Or, Thirty Years A Slave and Four Years in the White House in 1868.4 Keckley explained that she penned her autobiographical text in a bid to “defend [her]self” and Lincoln against charges of impropriety following the New York incident. However, perhaps unsurprisingly, the book’s release had the exact opposite effect: Keckley’s literary disclosures were met with scorn, regarded by large swaths of white Americans, including some of the same people who had been most vocal in their condemnation of Mary Todd Lincoln, as constituting a set of socially impermissible transgressions of class, race, and gender. Sales of the book were subsequently suppressed, Keckley’s relationship with Lincoln (who had been caught off guard by the text’s release) came to an abrupt end, and there was even a brief, parodic pamphlet produced, titled Behind the Seams; by a Nigger Woman Who Took in Work from Mrs. Lincoln and Mrs. Davis, which cast the entire ordeal as a sort of (racist) cautionary tale.5 Given the clear disdain held for Lincoln by people across the political spectrum at the time, it can be difficult to make sense of the visceral reaction prompted by Keckley’s airing of the controversial figure’s dirty laundry (pun intended). Considering the ways Behind the Scenes implicitly challenged the fixity of hierarchical distinctions between Black and white, employee and employer, however, repudiation of the work might be understood as inevitable. Further, given the “intimate” and ambiguous nature of Lincoln and Keckley’s relationship, the book may also 3. Sorisio, “Unmasking the Genteel Performer,” 19. 4. The text’s infamy is in part attributable to its anomalous structure, which rendered it distinct from many of the era’s other book-length slave narratives ; whereas monographs such as Harriet Jacobs’s 1861 Incidents in the Life of a Slave Girl centered on the author’s experience of and eventual escape from slavery, Keckley’s work deals only briefly with these matters, primarily concerning itself with the intimate affairs of the author’s (white) employer. 5. Sorisio, “Unmasking the Genteel Performer,” 19. Candice... (shrink)

Mental state reasoning or theory-of-mind has been the subject of a rich body of imaging research. Although such investigations routinely tap a common set of regions, the precise function of each area remains a contentious matter. With the help of functional magnetic resonance imaging (fMRI), we sought to determine which areas are involved when processing mental state or intentional metarepresentations by focusing on the relational aspect of such representations. Using non-intentional relational representations such as spatial relations between persons and between (...) objects as a contrast, the results ascertained the involvement of the precuneus, the temporal poles, and the medial prefrontal cortex in the processing of intentional representations. In contrast, the anterior superior temporal sulcus and the left temporo-parietal junction were implicated when processing representations that refer to the presence of persons in relational contexts in general. The right temporo-parietal junction, however, was specifically activated for persons entering spatial relations. The level of representational complexity, a previously unexplored factor, was also found to modulate the neural response in some brain regions, such as the medial prefrontal cortex and the right temporo-parietal junction. These findings highlight the need to take into account the critical roles played by an extensive network of neural regions during mental state reasoning. (shrink)

We introduce a new Turing machine based concept of time complexity for functions on computable metric spaces. It generalizes the ordinary complexity of word functions and the complexity of real functions studied by Ko [19] et al. Although this definition of TIME as the maximum of a generally infinite family of numbers looks straightforward, at first glance, examples for which this maximum exists seem to be very rare. It is the main purpose of this paper to prove that, nevertheless, the (...) definition has a large number of important applications. Using the framework of TTE [40], we introduce computable metric spaces and computability on the compact subsets. We prove that every computable metric space has a c-proper c-admissible representation. We prove that Turing machine time complexity of a function computable relative to c-admissible c-proper representations has a computable bound on every computable compact subset. We prove that computably compact computable metric spaces have concise c-proper c-admissible representations and show by examples that many canonical representations are of this kind. Finally, we compare our definition with a similar one by Labhalla et al. [22]. Several examples illustrate the concepts. By these results natural and realistic definitions of computational complexity are now available for a variety of numerical problems such as image processing, integration, continuous Fourier transform or wave propagation. (shrink)

Here I shine light on the concept of and call for safe space and on the implicit argument that seems to undergird both the concept and the call, complicating and problematizing the taken for granted view of this issue with the goal of revealing a more complex dynamic worthy of interpretive attention when determining educational response. I maintain that the usual justification for safe space covers rather than clarifies the logic of safe space and makes it (...) difficult for an educator to respond to harassment in a constructive and fitting way. I also claim that calls for safe space can only be properly interpreted—and responded to—when the link between fear and safety is uncovered and deconstructed. In the process, I note that the assumption of “safety” as a “positive condition” for education is problematic and warrants careful consideration. (shrink)

The ArgumentThere can be no doubt about the moral and epistemological significance of what Shapin calls the “physical place” of the scientific laboratory. The physical place is defined by the locales, barriers, ports of entry, and lines of sight that bound the laboratory and separate it from other urban and architectural environments. Shapin's discussion of the emergence of the scientific laboratory in seventeenth-century England provides a convincing demonstration that credible knowledge is situated at an intersection between physical locales and social (...) distinctions. In this paper I take up Shapin's theme of the “siting of knowledge production,” but I give it a different treatment – one based on ethnomethodological studies of work. Without denying all that can be witnessed in the spectacle of the scientist at the bench and of the architectural habitat of the bench, I argue that the “place” of scientific work is defined by locally organizedtopical contextures. The paper describes two examples of such spatial orders – “opticism” and “digitality” – associated with distinct complexes of equipment and practice. These topical spaces might initially be viewed as “ideal” or “symbolic” spaces, but I argue that they are no less material than the “physical setting” of the laboratory; indeed, they are the physical setting. (shrink)

The basic concept of Type-2 Theory of Effectivity to define computability on topological spaces or limit spaces are representations, i. e. surjection functions from the Baire space onto X. Representations having the topological property of admissibility are known to provide a reasonable computability theory. In this article, we investigate several additional properties of representations which guarantee that such representations induce a reasonable Type-2 Complexity Theory on the represented spaces. For each of these properties, we give a nice characterization of (...) the class of spaces that are equipped with a representation having the respective property. (shrink)

Improving the evidence in public health is an important goal for the health promotion community. With better evidence, health professionals can make better decisions to achieve effectiveness in their interventions. The relative failure of such evidence in public health is well-known, and it is due to several factors. Briefly, from an epistemological point of view, it is not easy to develop evidence-based public health because public health interventions are highly complex and indeterminate. This paper proposes an analytical explanation of (...) the complexity and indeterminacy of public health interventions in terms of 12 points. Public health interventions are considered as a causal chain constituted by three elements and two levels of evaluation. Public health interventions thus differ from clinical interventions, which comprise two causal elements and one level of evaluation. From the two levels of evaluation, we suggest a classification of evidence into four typologies: evidence of both relations; evidence of the second but not of the first relation; evidence of the first but not of the second relation; and no evidence of either relation. In addition, a grading of indeterminacy of public health interventions is introduced. This theoretical point of view could be useful for public health professionals to better define and classify the public health interventions before acting. (shrink)

We develop a theory of LOGSPACE structures and apply it to construct a number of examples of Abelian Groups which have LOGSPACE presentations. We show that all computable torsion Abelian groups have LOGSPACE presentations and we show that the groups ${\mathbb {Z}, Z(p^{\infty})}$ , and the additive group of the rationals have LOGSPACE presentations over a standard universe such as the tally representation and the binary representation of the natural numbers. We also study the effective categoricity of such groups. For (...) example, we give conditions are given under which two isomorphic LOGSPACE structures will have a linear space isomorphism. (shrink)

The method of analytic tableaux is employed in many introductory texts and has also been used quite extensively as a basis for automated theorem proving. In this paper, we discuss the complexity of the system as a method for refuting contradictory sets of clauses, and resolve several open questions. We discuss the three forms of analytic tableaux: clausal tableaux, generalized clausal tableaux, and binary tableaux. We resolve the relative complexity of these three forms of tableaux proofs and also (...) resolve the relative complexity of analytic tableaux versus resolution. We show that there is a quasi-polynomial simulation of tree resolution by analytic tableaux; this simulation is close to optimal, since we give a matching lower bound that is tight to within a polynomial. (shrink)

Computability theory is used to evaluate the complexity of classifying various kinds of Lebesgue spaces and associated isometric isomorphism problems.

We prove that in the Polish group of isometries of the Baire space the collection of n-th powers is non-Borel. We also prove that in the Polish space of trees on $\mathbb{N}$ the collection of trees that have an automorphism under which every node has order exactly n is non-Borel.

I suggest that we can read Marx in the light of recent analytic, neo-Hegelian thought. I summarize the Pittsburgh School philosophers’ claims about the myth of the given, the claim that human experience is conceptual all the way out, and that we live in a space of reasons. I show how Hegel has been read in those terms, and then apply that reading of Hegel to Marx’s argument that capital is akin to what Hegel called Geist, or spirit. (...) We can understand capitalism as a space of reasons that is contradictory: while the space of reasons is supposed to make human freedom possible, our space of reasons makes freedom impossible. Reading Marx in this way is helpful, because it avoids the flaws of analytical Marxism, existentialism and structuralism. However, it raises a large problem of its own: Can the theory of the space of reasons be applied to a society that is not free of alienation? I argue that it can, but only in ways that would not satisfy the analytic neo-Hegelians themselves. (shrink)

In the dissertation we study the complexity of generalized quantifiers in natural language. Our perspective is interdisciplinary: we combine philosophical insights with theoretical computer science, experimental cognitive science and linguistic theories. -/- In Chapter 1 we argue for identifying a part of meaning, the so-called referential meaning (model-checking), with algorithms. Moreover, we discuss the influence of computational complexity theory on cognitive tasks. We give some arguments to treat as cognitively tractable only those problems which can be computed in polynomial time. (...) Additionally, we suggest that plausible semantic theories of the everyday fragment of natural language can be formulated in the existential fragment of second-order logic. -/- In Chapter 2 we give an overview of the basic notions of generalized quantifier theory, computability theory, and descriptive complexity theory. -/- In Chapter 3 we prove that PTIME quantifiers are closed under iteration, cumulation and resumption. Next, we discuss the NP-completeness of branching quantifiers. Finally, we show that some Ramsey quantifiers define NP-complete classes of finite models while others stay in PTIME. We also give a sufficient condition for a Ramsey quantifier to be computable in polynomial time. -/- In Chapter 4 we investigate the computational complexity of polyadic lifts expressing various readings of reciprocal sentences with quantified antecedents. We show a dichotomy between these readings: the strong reciprocal reading can create NP-complete constructions, while the weak and the intermediate reciprocal readings do not. Additionally, we argue that this difference should be acknowledged in the Strong Meaning hypothesis. -/- In Chapter 5 we study the definability and complexity of the type-shifting approach to collective quantification in natural language. We show that under reasonable complexity assumptions it is not general enough to cover the semantics of all collective quantifiers in natural language. The type-shifting approach cannot lead outside second-order logic and arguably some collective quantifiers are not expressible in second-order logic. As a result, we argue that algebraic (many-sorted) formalisms dealing with collectivity are more plausible than the type-shifting approach. Moreover, we suggest that some collective quantifiers might not be realized in everyday language due to their high computational complexity. Additionally, we introduce the so-called second-order generalized quantifiers to the study of collective semantics. -/- In Chapter 6 we study the statement known as Hintikka's thesis: that the semantics of sentences like ``Most boys and most girls hate each other'' is not expressible by linear formulae and one needs to use branching quantification. We discuss possible readings of such sentences and come to the conclusion that they are expressible by linear formulae, as opposed to what Hintikka states. Next, we propose empirical evidence confirming our theoretical predictions that these sentences are sometimes interpreted by people as having the conjunctional reading. -/- In Chapter 7 we discuss a computational semantics for monadic quantifiers in natural language. We recall that it can be expressed in terms of finite-state and push-down automata. Then we present and criticize the neurological research building on this model. The discussion leads to a new experimental set-up which provides empirical evidence confirming the complexity predictions of the computational model. We show that the differences in reaction time needed for comprehension of sentences with monadic quantifiers are consistent with the complexity differences predicted by the model. -/- In Chapter 8 we discuss some general open questions and possible directions for future research, e.g., using different measures of complexity, involving game-theory and so on. -/- In general, our research explores, from different perspectives, the advantages of identifying meaning with algorithms and applying computational complexity analysis to semantic issues. It shows the fruitfulness of such an abstract computational approach for linguistics and cognitive science. (shrink)