Space Version Research Articles

Approximation properties for dynamical W⁎-correspondences

Let G be a locally compact quantum group, and A,B von Neumann algebras on which G acts. We refer to these as G-dynamical W⁎-algebras. We make a study of G-equivariant A-B-correspondences, that is, Hilbert spaces H with an A-B-bimodule structure by ⁎-preserving normal maps, and equipped with a unitary representation of G which is equivariant with respect to the above bimodule structure. Such structures are a Hilbert space version of the theory of G-equivariant Hilbert C⁎-bimodules. We show that there is a well-defined Fell topology on equivariant correspondences, and use this to formulate approximation properties for them. Within this formalism, we then characterize amenability of the action of a locally compact group on a von Neumann algebra, using recent results due to Bearden and Crann. We further consider natural operations on equivariant correspondences such as taking opposites, composites and crossed products, and examine the continuity of these operations with respect to the Fell topology.

A Fixed Point Approach to the Stability of a Quadratic Functional Equation in Modular Spaces Without Δ2-Conditions

Abstract In this paper, we investigate the Hyers-Ulam-Rassias stability property of a quadratic functional equation. The even and odd cases for the corresponding function are treated separately before combining them into a single stability result. The study is undertaken in a relatively new structure of modular spaces. The theorems are deduced without using the familiar Δ2-property of that space. This complicated the proofs. In the proofs, a fixed point methodology is used for which a modular space version of Banach contraction mapping principle is utilized. Several corollaries and an illustrative example are provided.

The impact of individual, scientific and organizational factors on the adoption of AR in university education

PurposeAugmented reality (AR) is an advanced version of the dynamic physical space that is perceived and received via visual, audio, digital and other sensory stimuli. The capabilities of virtual technologies change the field of university and education considerably. The necessity of using virtual technologies in the education field was revealed more in unforeseen disasters such as the COVID-19 pandemic. The adoption of a technology by its users is an important factor in the successful implementation of the technology. The present study evaluates several factors affecting the adoption of AR technology in the realm of tertiary education.Design/methodology/approachThis study is applied in nature, and the necessary data were gathered through a survey questionnaire. The opinions of 621 students were investigated using a simple random sampling method. The multinomial logit test was used in this research.FindingsIt was found that individual and social factors such as age, education level, major and economic characteristics such as one’s income in a month, expenses of a person in a month, the level of access to high-speed internet and access to a laptop or smartphone are effective in AR technology adoption in the field of academic education.Originality/valueThe theoretical contribution of this study is to identify the key factors that influence the adoption of AR technology and develop a model specifically applicable to the educational field. The results of this research can be used by university managers and educational policymakers for the efficient and effective use of this technology.

An index theorem for loop spaces

We formulate and prove an index theorem for loop spaces of compact manifolds in the framework of KK-theory. It is a strong candidate for the noncommutative geometrical definition (or the analytic counterpart) of the Witten genus. In order to specify an “appropriate form” of the index theorem to formulate a loop space version, we formulate and prove an equivariant index theorem for non-compact S1-manifolds with a compact fixed-point set. In order to formulate it, we use a ring of formal power series.

The Deck-of-cards-based Ordinal Regression method and its application for the development of an ecovillage

This paper presents the deck-of-cards-based Ordinal Regression (DOR), a new multicriteria decision-aiding procedure that conjugates the deck-of-cards method with an ordinal regression approach to define a multicriteria value function representing the preferences of the decision maker (DM). The deck-of-cards method allows the DM to express the ranking order of a set of reference alternatives along with the intensity of preferences between reference alternatives. An ordinal regression procedure is then used to define a multicriteria value function that represents the ranking of the reference alternatives as well as the preference intensity. This approach can be applied to define value functions with different formulations, such as weighted sum, additive value, or Choquet integral. The value function thus obtained can be used to comprehensively evaluate alternatives of a multi-criteria decision problem. The value function provided by DOR can also be applied to a multi-objective optimisation problem. In this study, we applied DOR to handle urban and regional planning decisions in which facilities are required to be selected, located, and planned. In particular, we consider the interactions between criteria and synergies between facilities in an enriched version of the so-called space–time model. We applied this methodology to a real-world problem to plan the development of a sustainable ecovillage in the province of Turin (Italy), thus supporting the president of the cooperative owning the ecovillage in his decisions regarding which structures to select, where to locate them, and when to plan their realisation.

UMAP-SMOTENC: A simple, efficient, and consistent alternative for privacy-aware synthetic data generation

The intensification of governmental legislation and the social awareness around data privacy protection severely constrains organizations' data utilization capabilities. As a result, the interest in data anonymization techniques, which should preserve the patterns present in the original data but mitigate the risks of privacy leakage, has also increased. While conventional methods may compromise privacy, recently proposed deep learning generative approaches are computationally expensive and unreliable when used in tabular datasets, hindering the democratization and usability of data. In this paper, we explore this trade-off between privacy and the quality of the anonymized data, establishing a new equilibrium obtained using a synthetic oversampling technique, SMOTE-NC, on a non-linear compressed version of the input space, achieved with the application of UMAP. The introduced approach, UMAP-SMOTENC, constitutes an efficient and consistent solution that can be used without significant efforts on hyperparameter tuning or resourcing to massive computing infrastructures. An experiment was conducted to evaluate the robustness of the proposed solution, comparing several metrics and models across eight datasets with diverse characteristics. The results achieved suggest that the presented method can efficiently synthesize privacy-aware data while conserving the relevant patterns of the real dataset, particularly those required for classification tasks.

Large time asymptotics for partially dissipative hyperbolic systems without Fourier analysis: Application to the nonlinearly damped $p$-system

A new framework to obtain time-decay estimates for partially dissipative hyperbolic systems set on the real line is developed. Under the classical Shizuta–Kawashima (SK) stability condition, equivalent to the Kalman rank condition in control theory, the solutions of these systems decay exponentially in time for high frequencies and polynomially for low ones. This allows us to derive a sharp description of the space-time decay of solutions for large time. However, such analysis relies heavily on the use of the Fourier transform, which we avoid here, developing the “physical space version” of the hyperbolic hypocoercivity approach introduced in Beauchard and Zuazua [Arch. Ration. Mech. Anal. 199 (2011), 177–227], to prove new asymptotic results in the linear and nonlinear settings. The new physical space version of the hyperbolic hypocoercivity approach allows us to recover the natural heat-like time decay of solutions under sharp rank conditions, without employing Fourier analysis or L^{1} assumptions on the initial data. Taking advantage of this Fourier-free framework, we establish new enhanced time-decay estimates for initial data belonging to weighted Sobolev spaces. These results are then applied to the nonlinear compressible Euler equations with linear damping. We also prove the logarithmic stability of the nonlinearly damped p -system.

A note on Köthe–Toeplitz duals and multiplier spaces of sequence spaces involving bicomplex numbers

Abstract In this paper, we generalize the notions of the Köthe–Toeplitz duals of sequence spaces by introducing the concepts of bicomplex α-dual, bicomplex β-dual and bicomplex γ-dual, and also we compute them for some bicomplex sequence spaces l p ⁢ ( 𝔹 ⁢ ℂ ) {l_{p}(\mathbb{BC})} for 1 ≤ p ≤ ∞ {1\leq p\leq\infty} , c 0 ⁢ ( 𝔹 ⁢ ℂ ) {c_{0}(\mathbb{BC})} and c ⁢ ( 𝔹 ⁢ ℂ ) {c(\mathbb{BC})} . Furthermore, we define a concept of bicomplex multiplier space as the bicomplex version of multiplier space of two sequence spaces and support this definition with examples.

The lowest-order weak Galerkin finite element method for linear elasticity problems on convex polygonal grids

This paper presents the lowest-order weak Galerkin finite element method for linear elasticity problems on the convex polygonal meshes. This method uses piecewise constant vector-valued spaces on element interiors and edges. The discrete weak gradient space introduced by this paper is the matrix version of CW0 space. The discrete weak divergence space is piecewise constant space on each element. This method is simple, efficient, stabilizer-free and symmetric positive-definite. The optimal error estimates in discrete H1 and L2 norms are presented. Numerical results are given to demonstrate the efficiency of algorithm and the locking-free property.

A New Logic, a New Information Measure, and a New Information-Based Approach to Interpreting Quantum Mechanics.

The new logic of partitions is dual to the usual Boolean logic of subsets (usually presented only in the special case of the logic of propositions) in the sense that partitions and subsets are category-theoretic duals. The new information measure of logical entropy is the normalized quantitative version of partitions. The new approach to interpreting quantum mechanics (QM) is showing that the mathematics (not the physics) of QM is the linearized Hilbert space version of the mathematics of partitions. Or, putting it the other way around, the math of partitions is a skeletal version of the math of QM. The key concepts throughout this progression from logic, to logical information, to quantum theory are distinctions versus indistinctions, definiteness versus indefiniteness, or distinguishability versus indistinguishability. The distinctions of a partition are the ordered pairs of elements from the underlying set that are in different blocks of the partition and logical entropy is defined (initially) as the normalized number of distinctions. The cognate notions of definiteness and distinguishability run throughout the math of QM, e.g., in the key non-classical notion of superposition (=ontic indefiniteness) and in the Feynman rules for adding amplitudes (indistinguishable alternatives) versus adding probabilities (distinguishable alternatives).

Fundamental Characteristics of the Product-Operated Metric Spaces

In the field of metric fixed point theory, there are several generalized or modified types of metric space. One such type is called multiplicative metric space. It was initially introduced as a modified version of the metric space, but was later found to be equivalent to the metric space. However, it allows the researchers to view the concept of metric space from a different perspective. Consequently, the idea of product-operated metric space is introduced in this article, which is obtained by removing the slackness of the multiplicative metric space. This article also presents some fundamental characteristics of the product-operated metric space and investigates the existence of fixed points for self-maps in product-operated metric spaces.

A deep learning-based illumination transform for devignetting photographs of dermatological lesions

Photographs of skin lesions taken with standard digital cameras (macroscopic images) have gained wide acceptance in dermatology. However, uneven background lighting caused by nonstandard image acquisition negatively impacts lesion segmentation and diagnosis. To address this, we propose an automated illumination equalization method based on a counter exponential transform (IECET). A modified residual network (ResNet) regressor is used to automate the selection of the operational parameter of the IECET. The regressor is designed by modifying the final fully-connected layer of the baseline ResNet-50 model. The modified fully-connected layer is coupled to a regression layer in the modified ResNet regressor. A prior knowledge base is created to train the modified ResNet regressor. For this, a set of corrupted images are generated by simulating uneven background illumination on pristine images. The knowledge base is created by including pairs of value components obtained from the HSV color space version of the corrupted macroscopic images and ideal operational parameter values that maximize the peak signal-to-noise ratio (PSNR) between the pristine images and the IECET outputs. We evaluated segmentation accuracies of the deep threshold prediction network (DTP-Net), DeepLabV3+, fully convolutional network (FCN), and U-Net on the corrupted macroscopic images and output images of the IECET. The DTP-Net, DeepLabV3+, FCN, and U-Net exhibited Dice similarity coefficient (DSC) of 0.71 ± 0.26, 0.85 ± 0.15, 0.75 ± 0.22, and 0.66 ± 0.28 on corrupted images and 0.81 ± 0.17, 0.87 ± 0.12, 0.79 ± 0.18, and 0.79 ± 0.15, on the outputs of the IECET. Increase in DSC proves the ability of the IECET to improve the performance of deep learning models used to segment skin lesions on macroscopic images.

Dollo-CDP: a polynomial-time algorithm for the clade-constrained large Dollo parsimony problem

The last decade of phylogenetics has seen the development of many methods that leverage constraints plus dynamic programming. The goal of this algorithmic technique is to produce a phylogeny that is optimal with respect to some objective function and that lies within a constrained version of tree space. The popular species tree estimation method ASTRAL, for example, returns a tree that (1) maximizes the quartet score computed with respect to the input gene trees and that (2) draws its branches (bipartitions) from the input constraint set. This technique has yet to be used for parsimony problems where the input are binary characters, sometimes with missing values. Here, we introduce the clade-constrained character parsimony problem and present an algorithm that solves this problem for the Dollo criterion score in O(|Sigma |^{3.726}(n+k) + |Sigma |^{1.726}nk) time, where n is the number of leaves, k is the number of characters, and Sigma is the set of clades used as constraints. Dollo parsimony, which requires traits/mutations to be gained at most once but allows them to be lost any number of times, is widely used for tumor phylogenetics as well as species phylogenetics, for example analyses of low-homoplasy retroelement insertions across the vertebrate tree of life. This motivated us to implement our algorithm in a software package, called Dollo-CDP, and evaluate its utility for analyzing retroelement insertion presence / absence patterns for bats, birds, toothed whales as well as simulated data. Our results show that Dollo-CDP can improve upon heuristic search from a single starting tree, often recovering a better scoring tree. Moreover, Dollo-CDP scales to data sets with much larger numbers of taxa than branch-and-bound while still having an optimality guarantee, albeit a more restricted one. Lastly, we show that our algorithm for Dollo parsimony can easily be adapted to Camin-Sokal parsimony but not Fitch parsimony.

Linguistic and pragmatic characteristics of self-presentational discourse (based on the material of the content of English-language corporate websites)

The article explores the self-presentational discourse essence in the communicative and pragmatic aspects. The relevance of this study lies in self-presentation applicability and importance in the information age. The purpose of the study is to determine the linguistic and pragmatic features of self-presentational discourse. The research was carried out using methods of linguapragmatic, discursive, interpretive and contextual analysis. The research material is English-language text content of corporate website “Company Mission” and “Company History” subsections. Scientific novelty of the article lies in the analysis of self-presentational discourse through the prism of transdiscoursivity idea, proposed by Michel Foucault. Such approach is applicable thanks to the discovery of transdiscursive signs of self-presentation. These include adaptability, universality, significance for social interaction. Self-presentation process manifests itself in the form of self-presentation strategy. Its purpose, which is abstract and constant, is to create a positive image of a speaker. Only communicative and pragmatic conditions of a concrete discourse specify the purpose. The transdiscursive discourse-forming strategy and its purpose serve as the main differentiating criteria of self-presentational discourse. Its communicative space is heterogeneous due to consisting of all possible situations of self-presentation. Each fragment of the space is treated as a specific version of self-presentational discourse realization within one discourse. Such an example is PR discourse, which concretizes PR version of self-presentational communicative space. It acts like any other version and adopts all linguistic and pragmatic features of corresponding discourse. Backgrounder as a PR discourse and PR variant genre is analyzed through “Company History” and “Company Mission” corporate website subsections. The genre embodies several tactics of the strategy. This supports the conclusion that self-presentation discourse is a transdiscursive phenomenon.

Ternary Instantaneous Noise-Based Logic with Exponential Hilbert Space

A tree-valued instantaneous noise-based logic with exponential Hilbert space is proposed. The third value is an uncertain bit value, which can be useful in artificial intelligence applications. The signal carrying the ternary universe has a significant advantage over the signal of the standard binary universe: its amplitude is never zero during any clock period. All known binary logic gates for exponential Hilbert space work for the binary sub-space in the ternary logic in the same way as they do in binary logic. This is useful when zeros cause problems in the exponential Hilbert space version of binary logic. Ternary logic is advantageous in various applications, including AI and natural language processing.

The continuity equation in the phase space quantum mechanics

A quantum phase space version of the continuity equation for systems with internal degrees of freedom is derived. The 1-D Dirac equation is introduced and its phase space counterpart is found. The phase space representation of free motion and of scattering in a nonrelativistic and relativistic case for setups with internal degrees of freedom is discussed and illustrated. Properties of Wigner functions of unbound states are analysed.

MAX FREI’S TEXT OF VILNIUS: THE WAYS, MEANS AND RESULTS OF URBAN SPACE OBJECTIVIZATION

Studying the city as a text of culture on the material of literary works is usually associated with the identification of its “inner meaning”, “feeling” and / or the main “idea”. We proceed from understanding objectification as fixation of the author’s perception of urban space in a literary text which leads us to the question of the ways and linguistic means that allow turning the thoughtform into a holistic, visible, in some cases almost tangible image determining the possibility of transmitting the author’s vision of the city to the readership. “Tales of Old Vilnius” by Max Frei has been chosen as a source for the research because it can be regarded as one of the most interesting urban texts which have appeared in the 21st century, where the characteristics of the existing city are combined with the author’s fantasy, as a result of which there appears a literary version of urban space which differs greatly from its invariant. The methods of linguostylistic analysis (with elements of linguosemiotic analysis) have been chosen, which enable us to reveal not only verbal, but also visual ways and means of objectivization of the city in fiction. As the analysis has shown, the specifics of the Tales are stipulated by its composition and the combination of verbal and visual ways of author’s objectivisation: they are implemented with the help of linguistic means of different semiotics, however, they complement each other in the process of creating the image of the city, where the real and the imaginary are closely connected. As a result, it can be concluded that not only the urban supertext can be enriched by the creation of a new literary image of the city, but that the new fictional image as well has the potential to foster the real future development of urban space.

Moduli of formal torsors II

Applying the authors' preceding work, we construct a version of the moduli space of $G$-torsors over the formal punctured disk for a finite group $G$. To do so, we introduce two Grothendieck topologies, the sur (surjective) and luin (locally universally injective) topologies, and define P-schemes using them as variants of schemes. Our moduli space is defined as a P-scheme approximating the relevant moduli functor. We then prove that Fr\"ohlich's module resolvent gives a locally constructible function on this moduli space, which implies that motivic integrals appearing the wild McKay correspondence are well-defined.

IDENTIFICATION OF INDOOR HEALTH COMFORT (IHC) AT TANJUNGPURA UNIVERSITY LIBRARY BASED ON GBCI RATING TOOLS

Most human activities are carried out in an indoors space. The room as an activity support facility must be able to provide a sense of comfort and safety and provide the health impacts needed by its occupants. Unhealthy working conditions can cause SBS (Sick Building Syndrome). SBS is a health problem and discomfort during activities in the room, which gradually disappears when the room user leaves the building. SBS causes a decrease in room user’s health, comfort, and productivity. To prevent this, identification of indoor health and comfort or IHC based on Greenship Interior Space is required. The object of this research is the Tanjungpura University Library, which has fulfiled the green construction criteria in terms of previous research. The study used an evaluative method by measuring the assessment referring to the Greenship Interior Space version 1 standard with field observations, simulations, manual calculations, and evaluation interviews. The results of analysis shows that the building achieves a score of 14 out of the maximum score of 28 with a value of 50%. The building successfully fulfilled prerequisite criteria, CO2 levels, chemical pollutants, biological pollutants, visual comfort, views from the outside and sunlight, and user comfort. It is hoped that the research results can be proposed as the right strategy to improve indoor health and comfort conditions at the Tanjungpura University Library building.

The exponential Orlicz space in quantum information geometry

We review the construction of a quantum version of the exponential statistical manifold over the set of all faithful normal positive functionals on a von Neumann algebra. The construction is based on the relative entropy approach to state perturbation. We construct a quantum version of the exponential Orlicz space and discuss the properties of this space and its dual with respect to Kosaki $$L_p$$ -spaces. We show that the constructed manifold admits a canonical divergence satisfying a Pythagorean relation. We also prove that the manifold structure is invariant under sufficient channels.