Disjoint Elements Research Articles

Physics‐based iterative scheme for computing antenna array embedded element patterns

AbstractRigorously accounting for mutual coupling effects in antenna array synthesis, generally requires that embedded element patterns (EEPs) be determined. The method of moments (MoM) is typically used. Multiple linear system solutions are required, corresponding to every excitation vector associated with an EEP. This paper presents the direct coupling technique (DCT) to obtain the MoM solution for arrays with disjoint elements, by iteratively solving a series of localized subproblems, one associated with each array element. It utilizes a physics‐based, direct‐coupling approximation to incorporate global coupling into the local problems. Local matrices do not change between iterations or with excitation vectors, hence they can be inverted as a preprocessing step, allowing for efficient solution of multiple excitation configurations. Numerical results demonstrate rapid convergence. The convergence rate can be controlled via local problem domain sizing. Since the DCT is ideally suited to parallelization, it is applicable to very large arrays.

Morphing Triangle Contact Representations of Triangulations

A morph is a continuous transformation between two representations of a graph. We consider the problem of morphing between contact representations of a plane graph. In an {mathcal {F}}-contact representation of a plane graph G, vertices are realized by internally disjoint elements from a family {mathcal {F}} of connected geometric objects. Two such elements touch if and only if their corresponding vertices are adjacent. These touchings also induce the same embedding as in G. In a morph between two {mathcal {F}}-contact representations we insist that at each time step (continuously throughout the morph) we have an {mathcal {F}}-contact representation. We focus on the case when mathcal {F} is the family of triangles in mathbb {R}^2 that are the lower-right half of axis-parallel rectangles. Such RT-representations exist for every plane graph and right triangles are one of the simplest families of shapes supporting this property. Moreover, they naturally correspond to 3-orientations. Thus, they provide a natural case to study regarding morphs of contact representations of plane graphs. We characterize the pairs of RT-representations admitting a morph between each other via the respective 3-orientations. Our characterization leads to a polynomial-time algorithm to decide whether there is a morph between two RT-representations of an n-vertex plane triangulation, and, if so, computes a morph with {mathcal {O}}(n^2) steps. Each of these steps is a linear morph moving the endpoints of each triangle at constant speed along straight-line trajectories. Our characterization also implies that for 4-connected plane triangulations there is a morph between every pair of RT-representations where the “top-most” triangle in both representations corresponds to the same vertex.

Hot Spots in Sgr A* Accretion Disk: Hydrodynamic Insights

The recent image of our galaxy’s supermassive black hole Sgr A* derived from the 7 April 2017 data of the Event Horizon Telescope Collaboration shows multiple hot spots in its accretion disk. Using the analytical framework, we demonstrate that the observed hot spots may not be disjoint elements but causally linked components (“petals”) of one rotating quasi-stationary macro-structure formed in the thermo-vorticial field within the accretion disk.

Matching Logic for Concurrent Programs Based on Rely/Guarantee and Abstract Patterns

This paper combines rely/guarantee, abstract patterns and matching logic to reason about concurrent programs in a modular and compositional manner. According to the separation property, the state can be divided into two disjoint parts, the local state and the shared state. We use matching logic to deal with the local state, and use rely/guarantee and abstract patterns to deal with the shared state. The power of rely/guarantee is to describe interference between concurrent programs. The advantage of abstract patterns is supporting fictional separation, which indicates that we logically consider abstract patterns to represent disjoint elements, although these elements are not disjoint under a certain implementation. By combining the advantages of rely/guarantee, abstract patterns and matching logic, our approach realize that clients of the module can be verified completely according to the specification of the module, regardless of the implementation of the module. In addition, we use several examples to illustrate our approach, define our logic judgments, and prove the soundness of our logic.

Numerable open covers and representability of topological stacks

We prove that the class of numerable open covers of topological spaces is the smallest class that contains covers with pairwise disjoint elements and numerable covers with two elements, closed under composition and coarsening of covers. We apply this result to establish an analogue of the Brown–Gersten property for numerable open covers of topological spaces: a simplicial presheaf on the site of topological spaces satisfies the homotopy descent property for all numerable open covers if and only if it satisfies it for numerable covers with two elements and covers with pairwise disjoint elements. We also prove a strengthening of these results for manifolds, ensuring that covers with two elements can be taken to have a specific simple form. We apply these results to deduce a representability criterion for stacks on topological spaces similar to arXiv:1912.10544. We also use these results to establish new simple criteria for chain complexes of sheaves of abelian groups to satisfy the homotopy descent property. This article is available at arXiv:2203.03120v2.

Reconceptualising Sense of Place: Towards a Conceptual Framework for Investigating Individual-Community-Place Interrelationships

While sense of place has been increasingly used in planning literature over the last five decades, its conceptualisation varies by discipline and theoretical orientation, with disjointed elements. This study develops a three-theme conceptual framework articulating individual-community-place interrelationships by critically reviewing the literature on sense of place and place-based constructs of attachment, identity, and satisfaction. Theorising the interactions in-between contributes to theoretical debates on sense of place and developing conceptual clarity to understand the planning context, processes, and outcomes, informing decision- and policy-making. It also facilitates the analysis and synthesis of complex narratives in qualitative studies of people-place relations.

A Robust Approach to CCRM Interval Regression considering Interval Coincidence Degree

Traditional CCRMs (Constrained Center-and-Range Methods) in solving the problem of interval regression could hardly make tradeoffs between the overall fitting accuracy and the coincidence degree between the observed and predicted intervals and could also hardly reduce the number of disjoint elements between the observed and predicted intervals, as well as raise the average ratio of all predicted intervals contained within their observed intervals. This paper constructed a nonlinear regression model based on center-and-range method, in which the maximization of coincidence degree for the sample with the worst coincidence degree between the observed and predicted interval was incorporated into the traditional CCRM model’s objective. This novel nonlinear programming model was proven to be a convex one that satisfied K-T condition. Monte Carlo simulation shows that the model is degenerated to the compared CCRM+ model as the objective only contains the minimization of the overall fitting accuracy for both center and range sample series. In this situation, it could obtain a better solution than the use of the compared CCRM model. In addition, when the proposed model only takes into account the maximization of coincidence degree for the sample with the worst coincidence degree between the observed and predicted interval, the model shows a better performance than the CCRM+ model in terms of the average ratio of all predicted intervals contained within their observed intervals, as well as the average number of forecasts with 0% accuracy.

Operators in pre-Riesz spaces: moduli and homomorphisms

We focus on two topics that are related to moduli of elements in partially ordered vector spaces. First, we relate operators that preserve moduli to generalized notions of lattice homomorphisms, such as Riesz homomorphisms, Riesz* homomorphisms, and positive disjointness preserving operators. We also consider complete Riesz homomorphisms, which generalize order continuous lattice homomorphisms. Second, we characterize elements with a modulus by means of disjoint elements and apply this result to obtain moduli of functionals and operators in various settings. On spaces of continuous functions, we identify those differences of Riesz* homomorphisms that have a modulus. Many of our results for pre-Riesz spaces of continuous functions lead to results on order unit spaces, where the functional representation is used.

Disjoint elements and semi solids in Riesz lG−module

Disjoint elements and semi solids in Riesz lG - module are introduced and properties are studied.

A quantitative criterion with which to distinguish lithofacies belts from mosaics in carbonate deposystems

The planform pattern of carbonate lithofacies in shallow tropical systems have been described as both relatively simple (i.e. the lithofacies belt model) and highly complex (i.e., the lithofacies mosaic model). The lateral continuity of the lithofacies elements differs between these two descriptions with the former containing continuous strike-oriented elements while the latter contains numerous disjointed elements with no specified orientation under two conditions. First, we consider the lithofacies elements solely by their sediment texture, and second, we do not consider ecological constraints on the benthic communities. Using variography, we develop the spatial correlation index (SCI) for distinguishing between the two types of lithofacies arrangements and deploy the index to visualize the spatial distribution of belt-like and mosaic-like patterning for 7 lithofacies in 36 carbonate platforms. The visualizations suggest that the belt versus mosaic dichotomy does not adequately capture the complexity of lithofacies arrangements in modern carbonate systems. This limitation exists because carbonates primarily consist of biogenic sediments whose distribution is controlled by physical and ecological controls. Thus, taxonomy must be considered when examining these spatial patterns. Furthermore, there appears to be a co-occurrence of arrangements within each of the systems. Four motifs in the statistical distribution of the SCI values observed within the systems are identified. The motifs appear to depend on the biotic and abiotic factors of the sedimentary system under study. Belt-like arrangements for a framestone class appeared to be strongly associated with the higher energy environments, while mosaic-like arrangement for this class often occurred in sheltered, low-energy areas. For grainstone and wackestone classes, belt-like arrangements were located along the transition from platform rim to lagoon. Finally, the results suggest that a greater variety of sediment-texture arrangements may be observed in Modern shallow-water carbonate depositional systems than may be visible in Ancient systems observed within the rock record.

Bok binds to a largely disordered loop in the coupling domain of type 1 inositol 1,4,5-trisphosphate receptor

Bcl-2-related ovarian killer (Bok) binds tightly to inositol 1,4,5-trisphosphate receptors (IP3Rs). To better understand this interaction, we sought to elucidate the Bok binding determinants in IP3R1, focusing on the ∼75 amino acid loop (residues 1882–1957) between α helices 72 and 73. Bioinformatic analysis revealed that the majority of this loop is intrinsically disordered, with two flanking regions of high disorder next to a low disorder central region (∼residues 1914–1926) that is predicted to contain two fused, disjointed transient helical elements. Experiments with IP3R1 mutants, combined with computational analysis, indicated that small deletions in this central region block Bok binding due to perturbation of the helical elements. Studies in vitro with purified Bok and IP3R1-derived peptides revealed high affinity binding to amino acids 1898–1940 of IP3R1 (Kd ∼65 nM) and that binding affinity is also dependent upon both of the high disorder flanking regions. The strength of the Bok-IP3R1 interaction was demonstrated by the ability of IP3R1 or Bok to recruit transmembrane domain-free Bok or IP3R1 mutants, respectively, to membranes in intact cells, and that these two mutants can bind in the cytosol independently of membrane association. Overall, we show that Bok binding to IP3R1 occurs within a largely disordered loop between α helices 72 and 73 and that high affinity binding is mediated by multivalent interactions.

A hierarchical clustering and data fusion approach for disease subtype discovery

Recent advances in multi-omics clustering methods enable a more fine-tuned separation of cancer patients into clinical relevant clusters. These advancements have the potential to provide a deeper understanding of cancer progression and may facilitate the treatment of cancer patients. Here, we present a simple hierarchical clustering and data fusion approach, named HC-fused, for the detection of disease subtypes. Unlike other methods, the proposed approach naturally reports on the individual contribution of each single-omic to the data fusion process. We perform multi-view simulations with disjoint and disjunct cluster elements across the views to highlight fundamentally different data integration behavior of various state-of-the-art methods. HC-fused combines the strengths of some recently published methods and shows superior performance on real world cancer data from the TCGA (The Cancer Genome Atlas) database. An R implementation of our method is available on GitHub (pievos101/HC-fused).

Disjointness graphs of segments in the space

AbstractThe disjointness graph G = G(𝒮) of a set of segments 𝒮 in ${\mathbb{R}^d}$, $$d \ge 2$$, is a graph whose vertex set is 𝒮 and two vertices are connected by an edge if and only if the corresponding segments are disjoint. We prove that the chromatic number of G satisfies $\chi (G) \le {(\omega (G))^4} + {(\omega (G))^3}$, where ω(G) denotes the clique number of G. It follows that 𝒮 has Ω(n1/5) pairwise intersecting or pairwise disjoint elements. Stronger bounds are established for lines in space, instead of segments.We show that computing ω(G) and χ(G) for disjointness graphs of lines in space are NP-hard tasks. However, we can design efficient algorithms to compute proper colourings of G in which the number of colours satisfies the above upper bounds. One cannot expect similar results for sets of continuous arcs, instead of segments, even in the plane. We construct families of arcs whose disjointness graphs are triangle-free (ω(G) = 2), but whose chromatic numbers are arbitrarily large.

Mental geometry of three-dimensional size perception

Judging the poses, sizes, and shapes of objects accurately is necessary for organisms and machines to operate successfully in the world. Retinal images of three-dimensional objects are mapped by the rules of projective geometry and preserve the invariants of that geometry. Since Plato, it has been debated whether geometry is innate to the human brain, and Poincare and Einstein thought it worth examining whether formal geometry arises from experience with the world. We examine if humans have learned to exploit projective geometry to estimate sizes and aspects of three-dimensional shape that are related to relative lengths and aspect ratios.Numerous studies have examined size invariance as a function of physical distance, which changes scale on the retina. However, it is surprising that possible constancy or inconstancy of relative size seems not to have been investigated for object pose, which changes retinal image size differently along different axes. We show systematic underestimation of length for extents pointing toward or away from the observer, both for static objects and dynamically rotating objects. Observers do correct for projected shortening according to the optimal back-transform, obtained by inverting the projection function, but the correction is inadequate by a multiplicative factor. The clue is provided by the greater underestimation for longer objects, and the observation that they seem to be more slanted toward the observer. Adding a multiplicative factor for perceived slant in the back-transform model provides good fits to the corrections used by observers. We quantify the slant illusion with two different slant matching measurements, and use a dynamic demonstration to show that the slant illusion perceptually dominates length nonrigidity.In biological and mechanical objects, distortions of shape are manifold, and changes in aspect ratio and relative limb sizes are functionally important. Our model shows that observers try to retain invariance of these aspects of shape to three-dimensional rotation by correcting retinal image distortions due to perspective projection, but the corrections can fall short. We discuss how these results imply that humans have internalized particular aspects of projective geometry through evolution or learning, and if humans assume that images are preserving the continuity, collinearity, and convergence invariances of projective geometry, that would simply explain why illusions such as Ames’ chair appear cohesive despite being a projection of disjointed elements, and thus supplement the generic viewpoint assumption.

Completely additive and C-compact operators in lattice-normed spaces

In this article, we investigate some classes of dominated orthogonally additive operators in lattice-normed spaces. We say that an orthogonally additive operator T from a lattice-normed space (V, E) to a lattice-normed space (W, F) is completely additive if, for every order summable family of pairwise disjoint elements $$(v_{\alpha })_{\alpha \in \Lambda }$$ of V, the family $$(Tv_{\alpha })_{\alpha \in \Lambda }$$ is order summable in W. The first part of the article is devoted to completely additive operators. We prove that a dominated orthogonally additive operator $$T:V\rightarrow W$$ from a Banach–Kantorovich space V to a Banach–Kantorovich space W is completely additive if and only if so is its exact dominant $$\left\bracevert T\right\bracevert :E\rightarrow F$$ . One of the our main results asserts that an orthogonally additive map defined on a lateral ideal and dominated by a positive completely additive operator can be extended to a dominated completely additive operator defined on the whole space. In the second part of the article, we consider C-compact dominated orthogonally additive operators. We show that the C-compactness of a dominated orthogonally additive operator $$T:V\rightarrow W$$ from a decomposable lattice-normed space (V, E) to an order continuous Banach lattice W implies the C-compactness of its exact dominant $$\left\bracevert T\right\bracevert :E\rightarrow W$$ .

Model-completions for Abelian lattice-ordered groups with finitely many disjoint elements

This paper axiomatizes classes of Abelian lattice-ordered groups with a finite upper bound on the number of pairwise disjoint positive elements; finds model-completions for these theories; derives corresponding Nullstellensätze; determines which model-completions eliminate quantifiers; and examines quantifier elimination in a different language and for positive formulas.

Les monnaies virtuelles décentralisées sont-elles des dispositifs d’avenir ?

In this article, we show that decentralized virtual currencies can be powerful tools for societal transformation. Indeed, the study of the joint and disjoint elements between the first Bitcoin currencies, SELs and local currencies, reveals that these projects are not so far. Then, we present the current evolution of crypto-currencies towards new energy aware, community-based, useful and fundamentally innovative protocols, emphazing their strong potential. Finally, some recent crypto-currencies are close to the values of the Social and Solidarity Economy, and even though they have some technical and theoretical problems, they have the merit of offering new perspectives. Finally, we propose an idea of decentralized money geolocalized melty, which would allow us to meet a certain number of limits that are experienced by traditional local currencies.

Points of narrowness and uniformly narrow operators

It is known that the sum of every two narrow operators on $L_1$ is narrow, however the same is false for $L_p$ with $1 < p < \infty$. The present paper continues numerous investigations of the kind. Firstly, we study narrowness of a linear and orthogonally additive operators on Kothe function spaces and Riesz spaces at a fixed point. Theorem 1 asserts that, for every Kothe Banach space $E$ on a finite atomless measure space there exist continuous linear operators $S,T: E \to E$ which are narrow at some fixed point but the sum $S+T$ is not narrow at the same point. Secondly, we introduce and study uniformly narrow pairs of operators $S,T: E \to X$, that is, for every $e \in E$ and every $\varepsilon > 0$ there exists a decomposition $e = e' + e''$ to disjoint elements such that $\|S(e') - S(e'')\| < \varepsilon$ and $\|T(e') - T(e'')\| < \varepsilon$. The standard tool in the literature to prove the narrowness of the sum of two narrow operators $S+T$ is to show that the pair $S,T$ is uniformly narrow. We study the question of whether every pair of narrow operators with narrow sum is uniformly narrow. Having no counterexample, we prove several theorems showing that the answer is affirmative for some partial cases.

Three-dimensional-printed membrane-type acoustic metamaterial for low frequency sound attenuation.

Membrane-type acoustic metamaterials have received much attention for low-frequency sound manipulation, especially in the form of decorated membrane resonators. In this paper, such resonators are obtained using fused deposition modeling. Beyond the practical aspects provided by this manufacturing method, the low density of the flexible filament used increases their effectiveness. Indeed, the mass usually added to the membrane center can easily be divided into several disjoint elements. Using rotary inertia of the added structures, new peaks of efficiency in both absorption and normal transmission loss appear when compared to usual decorated membrane resonators.

Subjective? Emotional? Emotive?: Language Combinatorics based Automatic Detection of Emotionally Loaded Sentences

In this paper presents our research in automatic detection of emotionally loaded, or emotive sentences. We define the problem from a linguistic point of view assuming that emotive sentences stand out both lexically and grammatically. To verify this assumption we prepare a text classification experiment. In the experiment we apply language combinatorics approach to automatically extract emotive patterns from training sentences. The applied approach allows automatic extraction of not only widely used unigrams (tokens), or n-grams, but also more sophisticated patterns with disjointed elements. The results of experiments are explained with the use of means such as standard Precision, Recall and balanced F-score. The algorithm also provides a refined list of most frequent sophisticated patterns typical for both emotive and non-emotive context. The method reached results comparable to the state of the art, while the fact that it is fully automatic makes it more efficient and language independent.