Spaces Of Type Research Articles

Representing type spaces as signal allocations

Representing type spaces as signal allocations

Cluster Assembly Dynamics Drive Fidelity of Planar Cell Polarity Polarization.

The planar cell polarity (PCP) signaling pathway polarizes epithelial cells in the tissue plane by segregating distinct molecular subcomplexes to opposite sides of each cell, where they interact across intercellular junctions to form asymmetric clusters. The role of clustering in this process is unknown. We hypothesized that protein cluster size distributions could be used to infer the underlying molecular dynamics and function of cluster assembly and polarization. We developed a method to count the number of monomers of core PCP proteins within individual clusters in live animals, and made measurements over time and space in wild type and in strategically chosen mutants. The data demonstrate that clustering is required for polarization, and together with mathematical modeling provide evidence that cluster assembly dynamics dictate that larger clusters are more likely to be strongly asymmetric and correctly oriented. We propose that cluster assembly dynamics thereby drive fidelity of cell- and tissue-level polarization.

Fractional Sobolev type spaces of functions of two variables via Riemann-Liouville derivatives

AbstractWe introduce and study the spaces of fractionally absolutely continuous functions of two variables of any order and the fractional Sobolev type spaces of functions of two variables. Our approach is based on the Riemann-Liouville fractional integrals and derivatives. We investigate relations between these spaces as well as between the Riemann-Liouville and weak derivatives.

Complex Structure That Admits Complete Nevanlinna–Pick Spaces of Hardy Type

Abstract In this paper, we will characterize those sets, over which every irreducible complete Nevanlinna–Pick space enjoys that its multiplier and supremum norms coincide. Moreover, we will prove that, if there exists an irreducible complete Nevanlinna–Pick space of holomorphic functions on a reduced complex space $X$ whose multiplier algebra is isometrically equal to the algebra of bounded holomorphic functions (we will say that such a space is of Hardy type in this paper), then $X$ must be biholomorphic to the unit disk minus a zero analytic capacity set. This means that the Hardy space is characterized as a unique irreducible complete Nevanlinna–Pick space of Hardy type.

Correlation between soundscape and sense of culture in historic public space

Soundscapes, as part of cultural heritage, have attracted attention for their role in crafting atmospheres and fostering a sense of place. It is still unclear how soundscapes and the sense of culture interlink within historic public spaces. This research explores how soundscape elements influence the sense of culture in historic towns. Twenty-five typical railway-type historic town public spaces in northern China are selected as examples. We restored the field situation in the laboratory. Through correlation analysis in SPSS, we analyzed the relationships between soundscape elements (encompassing objective environmental attributes and subjective perception) and cultural senses. The result shows: 1) Natural sounds, people sounds, and cultural activities sounds like music/shows significantly influence the sense of culture in historical spaces along the Chinese Eastern Railway (CER). 2)Calm and stable sound environments contribute to creating a cultural atmosphere. 3)Pleasure and eventful sounds strengthen people's connection to culture. 4)Enclosed spaces, pedestrian-friendly environments, and bustling crowds enhance the cultural ambience. 5)Visual perception correlates more strongly with the sense of culture than auditory evaluation. This research provides valuable insights for enhancing cultural senses in historic towns through soundscape design.

Selling to a manager and a budget-constrained agent

We analyze a model of selling a single object to a manager-agent pair who want to acquire the object for a firm. The manager and the agent have different assessments of the object’s value to the firm. The agent is budget-constrained while the manager is not. The agent participates in the mechanism, but she can (strategically) approach the manager for decision-making. We derive the revenue-maximizing mechanism in a two-dimensional type space (values of the agent and the manager). We show that below a threshold budget, a mechanism involving two posted prices and three outcomes (one of which involves randomization) is the optimal mechanism for the seller. Otherwise, a single posted price mechanism is optimal.

A necessary condition for the boundedness of the maximal operator on $$L^{p(\cdot)}$$ over reverse doubling spaces of homogeneous type

AbstractLet $$(X,d,\mu)$$ ( X , d , μ ) be a space of homogeneous type and $$p(\cdot) \colon X \to[1,\infty]$$ p ( · ) : X → [ 1 , ∞ ] be a variable exponent. We show that if the measure $$\mu$$ μ is Borel-semiregular and reverse doubling, then the condition $${ess\,inf}_{x\in X}p(x)>1$$ e s s i n f x ∈ X p ( x ) > 1 is necessary for the boundedness of the Hardy–Littlewood maximal operator $$M$$ M on the variable Lebesgue space $$L^{p(\cdot)}(X,d,\mu)$$ L p ( · ) ( X , d , μ ) .

Exploring strong controlled partial metric type spaces: Analysis of fixed points and theoretical contributions

This study involves the generalization of partial metric spaces and strong controlled metric type spaces through the introduction of the notion of strong controlled partial metric type spaces. This research pursues a dual objective: firstly, to scrutinize fixed points related to contractions of the Kannan type within the framework of strong controlled partial metric type spaces, encompassing both linear and nonlinear contractions; secondly, to furnish illustrative examples and applications that underscore the consequential implications of our theoretical contributions.

Accept/Reject games

Many properties of topological spaces, like compactness, have the form that any cover of the space of a certain type contains a subcover of some other type. We introduce a game theoretic analogue of this selection prototype, the Accept/Reject game, and relate it to classical games and selection principles. Modified versions of this game are shown to be equivalent to standard selection principles games.

Characterization of solutions in Besov spaces for fractional Rayleigh–Stokes equations

This paper considers fractional Rayleigh–Stokes equations with a power-type nonlinearity. The linear equation can be simulated a non-Newtonian fluid for a generalized second grade fluid and display a nonlocal behavior in time. Because the coexistence of fractional and classical derivatives leads to the lack of semigroup structure of the solution operator, we need to develop a suitable tool to establish some Lp−Lq estimates in the framework of Lp spaces and Besov spaces, respectively. Further, global existence of solutions is showed in spaces of Besov type.

Evaluating and enhancing the applicability of thermal comfort indices in diverse outdoor environments using Bayesian and random forest regression

This research aims to evaluate and improve the applicability of three commonly utilized thermal comfort indices—standard effective temperature (SET), physiological equivalent temperature (PET), and universal thermal climate index (UTCI)—in outdoor environments. The study was conducted in four typical spaces of a university in Xi’an, China, covering different environmental settings: East Lake (Place 1), tree-lined path (Place 2), campus playground (Place 3), and campus square (Place 4). A total of 322 volunteers participated by completing a subjective sensory questionnaire in randomized environments, and on-place meteorological data were collected. The study yielded three primary findings. First, the tree-lined path (Place 2) was identified as the most comfortable outdoor space on the university campus during summer, whereas East Lake (Place 1) was the least comfortable. Second, substantial residuals were observed for SET, PET, and UTCI across different places when assessing the thermal comfort variations experienced by the subjects. Third, Bayesian regression and random forest regression were employed to analyze and adjust the thermal comfort indices. The comparative study found that after correction, the model explanatory power of PET increased by up to 20%, with the standard deviation of residuals decreasing by up to 0.314 and MSE decreasing by up to 0.1912. The model explanatory power of SET increased by up to 31.2%, with the standard deviation of residuals decreasing by up to 0.3867 and MSE decreasing by up to 0.3012. For UTCI, the model explanatory power increased by up to 10.5%, the standard deviation of residuals decreased by up to 0.2215, and the MSE decreased by up to 0.1002.

Harmonic Riemannian submersions between Riemannian symmetric spaces of noncompact type

AbstractWe construct harmonic Riemannian submersions that are retractions from symmetric spaces of noncompact type onto their rank‐one totally geodesic subspaces. Among the consequences, we prove the existence of a nonconstant, globally defined complex‐valued harmonic morphism from the Riemannian symmetric space associated to a split real semisimple Lie group. This completes an affirmative proof of a conjecture of Gudmundsson.

Geometrical Penrose tilings are characterized by their 1-atlas

Penrose rhombus tilings are tilings of the plane by two decorated rhombi such that the decorations match at the junction between two tiles (like in a jigsaw puzzle). In dynamical terms, they form a tiling space of finite type. If we remove the decorations, we get, by definition, a sofic tiling space that we here call geometrical Penrose tilings. Here, we show how to compute the patterns of a given size which appear in these tilings by three different methods: two based on the substitutive structure of the Penrose tilings and the last on their definition by the cut and projection method. We use this to prove that the geometrical Penrose tilings are characterized by a small set of patterns called vertex-atlas, i.e., they form a tiling space of finite type. Though considered as folklore, no complete proof of this result has been published, to our knowledge.

Fixed points of regular set-valued mappings in quasi-metric spaces

Metric fixed point theory is becoming increasingly significant across various fields, including data science and iterative methods for solving optimization problems. This paper aims to introduce new fixed point theorems for set-valued mappings under novel regularity conditions, such as orbital regularity and orbital pseudo-Lipschitzness. Instead of traditional metric spaces, we adopt the framework of quasi-metric spaces, motivated by the need to address problems in spaces that are not necessarily metric, such as function spaces of homogeneous type. We also explore the stability of the set of fixed points under variations of the set-valued mapping. Additionally, we provide estimates for the distances from a given point to the set of fixed points and between two sets of fixed points. Building on these findings, we extend the discussion to similar problems involving fixed, coincidence, and cyclic/double fixed points within this framework. Our results generalize recent findings from the literature, including those in Ait Mansour M, Bahraoui MA, El Bekkali A. [Metric regularity and Lyusternik-Graves theorem via approximate fixed points of set-valued maps in noncomplete metric spaces. Set-Valued Var Anal. 2022;30(1):233–256. doi: 10.1007/s11228-020-00553-1], Dontchev AL, Rockafellar RT. [Implicit functions and solution mappings. a view from variational analysis. Dordrecht: Springer; 2009. Springer Monographs in Mathematics], Ioffe AD. [Variational analysis of regular mappings. Springer, Cham; 2017. Springer Monographs in Mathematics; theory and applications. doi: 10.1007/978-3-319-64277-2], Lim TC. [On fixed point stability for set-valued contractive mappings with applications to generalized differential equations. J Math Anal Appl. 1985;110(2):436–441. doi: 10.1016/0022-247X(85)90306-3] and Tron NH. [Coincidence and fixed points of set-valued mappings via regularity in metric spaces. Set-Valued Var Anal. 2023;31(2):22. Paper No. 17. doi: 10.1007/s11228-023-00680-5].

The role of acetabular cement augmentation in 2-stage revision arthroplasty for prosthetic joint infection of the hip.

In the treatment of chronic prosthetic joint infection (PJI) of the hip, two-stage exchange arthroplasty is commonly employed. Various spacer designs, including Hemi-Spacers and Articulating Spacers, are utilized during this process. However, these spacers are associated with a high rate of mechanical complications and pose a risk of progressive bone loss. This study aims to compare these two types of spacers in terms of mechanical complications, center of rotation (COR) restoration, and preservation of acetabular bone stock. From 2019 to 2022, patients who underwent two-stage exchange arthroplasty for hip PJI across three hospitals were retrospectively reviewed. Data including demographic, clinical, and microbiological information were collected. Radiographic imaging was analyzed to measure acetabular bone erosion, COR, and periacetabular bone resected. Additionally, the average surgical time in the first and second stages, mechanical complications, and the mean duration of the inter-stage period were recorded. Forty patients were divided into two groups: Group A (Articulating Spacer, n = 23) received a preformed femur spacer with acetabular cement augmentation, while Group B (Hemi-Spacer, n = 17) received a preformed femur spacer alone. Acetabular cement augmentation slightly prolonged the first stage but facilitated a faster second stage during subsequent reimplantation. Spacer dislocation rates were 8.7% in Group A and 17.6% in Group B during the interstage period. Radiographic analysis revealed a statistically significant greater degree of acetabular erosion in Group B. A significant difference in Vertical-COR differential was observed, with a more proximalized revision cup compared to the primary cup in Group B, and Horizontal-COR values closer to the native hip in Group A. Dynamic spacers with acetabular cement augmentation help preserve peri-acetabular bone stock and prevent progression of acetabular bone erosion during the inter-stage period. Additionally, these spacers reduce the dislocation rates, making reimplantation easier and leading to better restoration of hip biomechanics during the second procedure.

Wardowski Contraction on Controlled S-Metric Type Spaces with Fixed Point Results

This article presents the concept of a triple controlled S-metric type space, characterized by three control functions: β, µ, and γ. This extends the idea of controlled S-metric type spaces. We explore several properties and provide illustrative examples. Furthermore, we introduce αs-admissible mappings and enhance Wardowski’s contraction principle by introducing (αs-F)-contractive mappings specifically designed for triple controlled S-metric type spaces. The article establishes the existence and uniqueness of fixed points within a complete triple controlled S-metric type space. Finally, we apply our main theorem to demonstrate the determination of a unique solution for an mth degree polynomial.

A Fixed Point Theorem on Partial Metric Spaces of Hyperbolic Type

A Fixed Point Theorem on Partial Metric Spaces of Hyperbolic Type

Targeted nano-energetic material exploration through active learning algorithm implementation

This paper presents an active learning-based method designed to guide experiments towards user-defined specific regions, termed ”regions of interest,” within vast and multi-dimensional thermite design spaces. Thermites composed of metallic reactant coupled to an inorganic oxidizer are non-explosive energetic materials which stay inert and stable until subjected to a sufficiently strong thermal stimulus, after which they undergo fast burning with release of high amount of chemical energy (up to 16 kJ.cm−3). They represent an interesting class of nano-engineered energetic material because of their high adiabatic flame temperature (> 2600 °C) and customizable combustion properties. We introduced a new acquisition function combining linearly two factors with the usual standard deviation of a Gaussian Process Regression algorithm. A first factor guides the sampling towards the defined zone of interest, and a second, is an incentive function that encourages the exploration of under-sampled regions of the design space. We found that our algorithm effectively provides up to several tens of nanothermites that achieve specific desired properties well-distributed within the design space, after only 200 samplings, whereas, Latin Hypercube Sampling procedure samples less than 10 points of interest. Our framework is tailored for typical discrete search spaces involving multiple measured physical properties and when only a small dataset is available, as it is the case in thermite materials. But more generally, this research represents a significant advancement for large-scale problems in energetic materials science and engineering, where predicting the effect of feature modification is desired but limited simulations or experiments can be afforded due to their high cost.

A Review on Analysis of Seismic Impact of Improvements with Rigid and Semi Rigid RC Structure with having Podium

Abstract: The growing population and limited land in urban areas are driving up demand for towering buildings on a daily basis. India and other emerging countries are seeing an increase in the use of tall buildings. Land becomes unavailable for further expansion in any city, particularly in major cities, beyond a certain point of horizontal development. Consequently, multi-story skyscrapers gained popularity as a means of optimising land use. The design principles used for low- and mediumrise structures are not applicable to high-rise skyscrapers. Tall structures demand the most advanced design techniques since they are intricate engineering tasks. Architects and engineers proposed/put forward the new idea of Podium sort constructions in order to meet the demands of both the growing population and the present bye-laws requiring a minimum parking space for such types of buildings. These days, tower-podium style structures are quite common since they provide for the best possible use of available space on the property and the financial leverage to meet the need for more commercial space. A portion of a structure known as a podium has lateral load resistance greater than that of a tower.

Differences in human thermal and physiological responses under corridor and greenway in summer in guangzhou

As urbanization and the heat island effect intensify, comfortable and healthy outdoor micro-environments are particularly important for sustainable urban development, encouraging more outdoor activities. Fewer studies have focused on differences in thermal comfort and thermal physiology of users in potential outdoor open spaces. Therefore, this study aims to examine the differences in thermal comfort and thermal stress among users of common outdoor open shady spaces, contributing towards a better thermal experience and mitigating heat stress. In this study, a field investigation of corridors and greenways was conducted on a campus in Guangzhou in the summer based on subjective questionnaires and objective measurements of thermal environment, and thermal physiological parameters. The results found that people were more likely to experience good thermal comfort and weaker intensity of thermal stress in corridors with significant differences in physiological responses. Furthermore, the upper limit comfort temperatures of the corridor and greenway were 34.0 and 33.4 °C, respectively. In addition, it can be concluded that the corridor was a more optimal space for outdoor shade before evening, whereas the greenway was more optimal in the evening in summer. The findings determine the thermal benchmarks for typical outdoor shady spaces in hot and humid regions in summer, which can help designers create comfortable outdoor public spaces that improve thermal comfort and people's health.