Regular Sets Research Articles

Obstructions to Integrability of Nearly Integrable Dynamical Systems Near Regular Level Sets

Obstructions to Integrability of Nearly Integrable Dynamical Systems Near Regular Level Sets

On the undecidability and descriptional complexity of synchronized regular expressions

In Freydenberger (Theory Comput Syst 53(2):159–193, 2013. https://doi.org/10.1007/s00224-012-9389-0), Freydenberger shows that the set of invalid computations of an extended Turing machine can be recognized by a synchronized regular expression [as defined in Della Penna et al. (Acta Informatica 39(1):31–70, 2003. https://doi.org/10.1007/s00236-002-0099-y)]. Therefore, the widely discussed predicate “={0,1}^*” is not recursively enumerable for synchronized regular expressions (SRE). In this paper, we employ a stronger form of non-recursive enumerability called productiveness and show that the set of invalid computations of a deterministic Turing machine on a single input can be recognized by a synchronized regular expression. Hence, for a polynomial-time decidable subset of SRE, where each expression generates either {0, 1}^* or {0, 1}^* -{w} where w in {0, 1}^*, the predicate “={0,1}^*” is productive. This result can be easily applied to other classes of language descriptors due to the simplicity of the construction in its proof. This result also implies that many computational problems, especially promise problems, for SRE are productive. These problems include language class comparison problems (e.g., does a given synchronized regular expression generate a context-free language?), and equivalence and containment problems of several types (e.g., does a given synchronized regular expression generate a language equal to a fixed unbounded regular set?). In addition, we study the descriptional complexity of SRE. A generalized method for studying trade-offs between SRE and many classes of language descriptors is established.

Two simple assays for assessing the seeding activity of proteopathic tau.

The regional distribution of neurofibrillary tangles of hyperphosphorylated tau aggregates is associated with the progression of Alzheimer's disease (AD). Misfolded proteopathic tau recruits naïve tau and templates its misfolding and aggregation in a prion-like fashion, which is believed to be the molecular basis of propagation of tau pathology. A practical way to assess tau seeding activity is to measure its ability to recruit/bind other tau molecules and to induce tau aggregation. Based on the properties of proteopathic tau, here we report the development of two simple assays to assess tau seeding activity ----- capture assay in vitro and seeded-tau aggregation assay in cultured cells. In the capture assay, proteopathic tau was applied onto a nitrocellulose membrane and the membrane was incubated with cell lysate containing HA-tagged tau151-391 (HA-tau151-391). The captured tau on the membrane was determined by immuno-blots developed with anti-HA. For the seeded-tau aggregation assay, HEK-293FT cells transiently expressing HA-tau151-391 were treated with proteopathic tau in the presence of Lipofectamine 2000 and then lysed with RIPA buffer. RIPA-insoluble fraction containing aggregated tau was obtained by ultracentrifugation and analyzed by immuno-blot developed with anti-HA. To validate these two assays, we assessed the seeding activity of tau in the middle frontal gyrus, middle temporal gyrus and basal forebrain of AD and control brains and found that AD, but not control, brain extracts effectively captured and seeded tau151-391 aggregation. Basal forebrain contained less phospho-tau and tau seeding activity. The levels of captured tau or seeded-tau aggregates were positively correlated to the levels of phospho-tau, Braak stages and tangle sores. These two assays are specific and sensitive and can be carried out in a regular biomedical laboratory setting by using routine biochemical techniques.

The Plateau-Douglas Problem for Singular Configurations and in General Metric Spaces

Assume you are given a finite configuration Gamma of disjoint rectifiable Jordan curves in {mathbb {R}}^n. The Plateau-Douglas problem asks whether there exists a minimizer of area among all compact surfaces of genus of at most p which span Gamma . While the solution to this problem is well-known, the classical approaches break down if one allows for singular configurations Gamma , where the curves are potentially non-disjoint or self-intersecting. Our main result solves the Plateau-Douglas problem for such potentially singular configurations. Moreover, our proof works not only in {mathbb {R}}^n but in general proper metric spaces. In particular, the existence of an area minimizer is new for disjoint configurations of Jordan curves in general complete Riemannian manifolds. A minimal surface of fixed genus p bounding a given configuration Gamma need not always exist, even in the most regular settings. Concerning this problem, we also generalize the approach for singular configurations via minimal sequences satisfying conditions of cohesion and adhesion to the setting of metric spaces.

Evaluation of the properties of a new super quick-setting (2 min) polyether impression material

ObjectivesAlthough a new super-quick setting polyether impression material has been commercially recently introduced, its properties have not been yet reported. Thus, it was the aim of this study to assess the dimensional stability, tear strength, and elastic recovery of the new material and to compare it with another commonly used polyether and polyvinyl siloxane.Materials and methodsA new super-quick set polyether, a regular set polyether and a polyvinylsiloxane (PVS) impression material have been used in the study. Dimensional changes were measured using a modified mold as per ISO 4823:2000 after 1 h and 7 days. Tear strength was evaluated by subjecting specimens to tension until failure with a crosshead speed of 250 mm/min. Elastic recovery was measured by deforming specimens using a materials testing machine to a height of 16 mm (20% strain). The change in length (ΔL) was measured afterwards and elastic recovery was calculated in percentages.ResultsDimensional changes of the super quick and regular set polyether were comparable in both the vertical and horizontal dimensions after 24 h and 7 days. All the tested materials showed dimensional change values far below the maximum accepted ISO requirement (1.5%). The super quick setting polyether showed significantly improved tear strength (4.9 N/mm) in comparison to the regular set polyether (3.5 N/mm) and similar to PVS (5.2 N/mm). The elastic recovery of PVS (99.6%) was the highest among all the groups.Conclusions and clinical relevanceThe newly available super-fast set polyether offers a great potential for a reduced chair side time and comfort for both, the patient and the dentist. Super quick polyether showed as well improved tear strength, which is considered one of the shortcomings of the regular set polyether. In addition, the new polyether was as accurate as the regular set polyether and with good elastic recovery.

Generalized Investigated in Topological Space

Abstract: In this paper, some characterizations and proportion of notion a investigated. Throughout this paper (X, τ) and (Y, σ ) (simply, X and Y) represent topological spaces on which separation axioms are assumed unless otherwise mentioned. We introduce a new class of sets called regular generalized open sets which is properly placed in between the class of open sets and the class of - open sets. Throughout this paper (X, ) represents a topological space on which no separation axiom is assumed unless otherwise mentioned. For a subset A of a topological space X, cl (A) and int (A) denote the closure of A and the interior of A respectively. X/A or Ac denotes the complement of A in X. introduced and investigated semi open sets, generalized closed sets, regular semi open sets, weakly closed sets, semi generalized closed sets , weakly generalized closed sets, strongly generalized closed sets, generalized pre - regular closed sets, regular generalized closed sets, and generalized -generalized closed sets respectively.

Regular Open Sets on The Intuitionistic Fuzzy Topological Spaces in Sostak's Sense

The aim of this paper is to introduce and study the concepts of intuitionistic r-fuzzy regular open sets and their related notions in topological spaces.

The Upper Capacity Topological Entropy of Free Semigroup Actions for Certain Non-compact Sets, II

This paper’s major purpose is to continue the work of Zhu and Ma in [J Stat Phys 182(1):19, 2021]. To begin, the $${\textbf{g}}$$ -almost product property, more general irregular and regular sets, and some new notions of the Banach upper density recurrent points and transitive points of free semigroup actions are introduced. Furthermore, under the $${\textbf{g}}$$ -almost product property and other conditions, we coordinate the Banach upper recurrence, transitivity with (ir)regularity, and obtain lots of generalized multifractal analyses for general observable functions of free semigroup actions. Finally, statistical $$\omega $$ -limit sets are used to consider the upper capacity topological entropy of the sets of Banach upper recurrent points and transitive points of free semigroup actions, respectively. Our analysis generalizes the results obtained by Huang et al. in [Nonlinearity 32(7):2721–2757, 2019] and Pfister and Sullivan in [Ergodic Theory Dynam Syst 27(3):929–956, 2007].

Uniqueness of free boundary minimal hypersurfaces in rotational domains

In this work, we investigate the existence of compact free boundary minimal hypersurfaces immersed in several domains. Using an original integral identity for compact free boundary minimal hypersurfaces that are immersed in a domain whose boundary is a regular level set, we study the case where this domain is a quadric or, more generally, a rotational domain. This existence study is done without topological restrictions. We also obtain a new gap theorem for free boundary hypersurfaces immersed in an Euclidean ball and in a rotational ellipsoid.

Equivalence between pure point diffractive sets and cut-and-project sets on substitution tilings

Quasicrystals are characterized by the property of pure point diffractive spectrum mathematically. We look at substitution tilings and characterize the pure point diffractive spectrum by regular model sets defined from a cut-and-project scheme. The cut-and-project scheme is built with a physical space ℝ d and an internal space which is a product of a Euclidean space and a profinite group. The assumptions we make here are that the expansion map of the substitution is diagonalizable and its eigenvalues are all algebraically conjugate with same multiplicity. We give a precise argument for the proof on a specific example.

Teaching science to students with special educational needs: a systematic review of science teaching-learning approaches in regular and special education settings

ABSTRACT In this systematic review, a series of didactic proposals and experiences that have been developed over recent years in formal education are presented with the common purpose of ensuring that students with special educational needs learn science. Initially, only 54 publications on the topic were identified, which underlines the scarce research over the last 20 years and the small percentage of papers published in research journals and conference proceedings within this area. From among those publications, our review is focused on the 27 that report the implementation of didactic interventions: 11 at specific special education centres and 16 at regular educational centres. Explicit instruction was considered a fundamental strategy in the first group, while varied experiences and methods were among the most relevant approach in the second group. In addition, both educational environments involve learner-centred teaching approaches, with the implementation of inquiry-based and hands-on activities, in line with the general results of research in Science Education that does not specifically deal with SSEN. Ensuring that all learners have the opportunity to learn science requires more specific and complementary studies that consolidate the evidence of these results, taking into account the diversity of learners in classrooms for the benefit of all.

APSN: Adversarial Pseudo-Siamese Network for Fake News Stance Detection

Fake news is a longstanding issue that has existed on the social network, whose negative impact has been increasingly recognized since the US presidential election. During the election, numerous fake news about the candidates distributes vastly in the online social networks. Identifying inauthentic news quickly is an essential purpose for this research to enhance the trustworthiness of news in online social networks, which will be the task studied in this paper. The fake news stance detection can contribute to detect a startling amount of fake news, which aims at evaluating the relevance between the headline and text bodies. There exists a significant difference between news article headline and text body, since headlines with several key phrases are usually much shorter than the text bodies. Such an information imbalance challenge may cause serious problems for the stance detection task. Furthermore, news article data in online social networks is usually exposed to various types of noise and can be contaminated, which poses more challenges for the stance detection task. In this paper, we propose a novel fake news stance detection model, namely Adversarial Pseudo-Siamese Network model (APSN), to solve these challenges. With coupled input components with imbalanced parameters, APSN can learn and compute feature vectors and similarity score of news article headlines and text bodies simultaneously. In addition, by adopting adversarial setting, besides the regular training set, a set of noisy training instances will be generated and fed to APSN in the learning process, which can significantly enhance the robustness of the model. Extensive experiments have been conducted on a real-world fake news dataset, and the experimental results reveal that the presented model exceeds compared suspicious information detection models with significant advantages.

A NOTE ON REGULAR SETS IN CAYLEY GRAPHS

AbstractA subset R of the vertex set of a graph $\Gamma $ is said to be $(\kappa ,\tau )$ -regular if R induces a $\kappa $ -regular subgraph and every vertex outside R is adjacent to exactly $\tau $ vertices in R. In particular, if R is a $(\kappa ,\tau )$ -regular set of some Cayley graph on a finite group G, then R is called a $(\kappa ,\tau )$ -regular set of G. Let H be a nontrivial normal subgroup of G, and $\kappa $ and $\tau $ a pair of integers satisfying $0\leq \kappa \leq |H|-1$ , $1\leq \tau \leq |H|$ and $\gcd (2,|H|-1)\mid \kappa $ . It is proved that (i) if $\tau $ is even, then H is a $(\kappa ,\tau )$ -regular set of G; (ii) if $\tau $ is odd, then H is a $(\kappa ,\tau )$ -regular set of G if and only if it is a $(0,1)$ -regular set of G.

Transnormal Functions and Focal Varieties on Finsler Manifolds

In this paper, we study transnormal functions and their level sets and focal varieties on complete Finsler manifolds. We prove that the focal varieties of a $$C^{2}$$ transnormal function are smooth submanifolds and each regular level set is a tube over either of the focal varieties.

Finite Algebras for Solid Modeling using Julia’s Sparse Arrays

An early research in solid modeling led by Herbert Voelcker at the University of Rochester and later at Cornell suggested that every solid representation scheme corresponds to an algebra, where the elements of the algebra are solid representations constructed and edited using operations in the algebra. For example, every CSG representation describes an element in a finite Boolean algebra of closed regular sets, whereas every boundary representation describes an element of a vector space of 2-chains in an algebraic topological chain complex. In this paper, we elucidate the precise relationships (functors) between all algebras used for CSG and boundary representations of solids. Based on these properties, we show that many solid modeling operations, including boundary evaluation, reduce to straightforward algebraic operations or application of identified functors that are efficiently implemented using point membership tests and sparse matrix operations. To fully exploit the efficacy of the new algebraic approach to solid modeling, all algorithms are fully implemented in Julia, the modern language of choice for numerical and scientific computing. • New research direction in solid modeling. • Algebraic relationships between CSG and boundary representations of PL solids. • Arrangements are isomorphic to the finite Boolean algebra of regularized sets. • This algebra is isomorphic to a linear vector space of 3-chains. • Operations on CSG and b-reps reduce to composition of algebraic operations. operations.

Teachers' perspectives toward integrating special education need learners in normal classrooms: A case study of Arab teachers in Israel

This paper constitutes a relatively new area that has emerged from the relationship between Special Education Need (SEN) students in normal classrooms and teachers’ perspectives. The purpose of this study was to investigate factors that could contribute to differences in attitudes of public-school teachers toward the inclusion of students with special needs in general education classes in the Arab schools in Israel. The study used a quantitative methodology, adopting an online survey method of data collection, addressed to a total number of 237 teachers working in government public schools. The findings indicated that teachers who hold a master’s degree were more likely to accept the idea of integrating SEN students in regular settings and suggested that teachers' education level affected their emotional attitude towards SEN integration. These findings embody significant practical meanings. A change is needed in the way Arab society perceives students with SEN, and how this society treats their integration into the framework of regular students. A practical recommendation of this study is that the Ministry of Education should offer intensive training for a wide range of teachers to be able to deal with students with special needs.

Research on air conditioning energy use and indoor thermal environment with Private Finance Initiative data monitoring of junior high schools before and during the COVID-19 pandemic in Japan

The COVID-19 pandemic began to spread at the beginning of 2020 in the world and in Japan, which is expected to impact the air conditioning (AC) energy use (EU) in educational buildings when AC and natural ventilation are used together as a new regulation to decrease infectious disease transmission. Furthermore, this regulation of natural ventilation is expected to impact the AC EU when the outside temperature affects indoor comfort causing changes in the regular AC setting temperature and AC operating times. This study aims to evaluate the AC EU, and the indoor thermal environment changes with Private Finance Initiative (PFI) data monitoring in junior high schools in Oita City before and during the COVID-19 pandemic during summer and winter through a sensitivity analysis method. The result found that AC EU significantly increased during the pandemic, 2 times escalation in summer and 1.9 times in winter. Besides, during the pandemic, indoor air temperature comfort was achieved with longer AC operation time, lower AC setting temperature in summer, and higher AC setting temperature in winter. The result of this research can be expected to be beneficial for future studies regarding AC energy saving and indoor thermal comfort-related investigation and valuable for new regulations related to air conditioner settings and operations for the new normal during the pandemic.

Partially dissipative systems in the critical regularity setting, and strong relaxation limit

Many physical phenomena may be modeled by first order hyperbolic equations with degenerate dissipative or diffusive terms. This is the case for example in gas dynamics, where the mass is conserved during the evolution, but the momentum balance includes a diffusion (viscosity) or damping (relaxation) term, or, in numerical simulations, of conservation laws by relaxation schemes. Such so-called partially dissipative systems have been first pointed out by S. K. Godunov in a short note in 1961. Much later, in 1984, S. Kawashima highlighted in his PhD thesis a simple criterion ensuring the existence of global strong solutions in the vicinity of a linearly stable constant state. This criterion has been revisited in a number of research works. In particular, K. Beauchard and E. Zuazua proposed in 2010 an explicit method for constructing a Lyapunov functional allowing to refine Kawashima’s results and to establish global existence results in some situations that were not covered before. These notes originate essentially from the PhD thesis of T. Crin-Barat that was initially motivated by an earlier observation of the author in a chapter of the handbook edited by Y. Giga and A. Novotný. Our main aim is to adapt the method of Beauchard and Zuazua to a class of symmetrizable quasilinear hyperbolic systems (containing the compressible Euler equations), in a critical regularity setting that allows to keep track of the dependence with respect to e.g. the relaxation parameter. Compared to Beauchard and Zuazua’s work, we exhibit a ‘damped mode’ that will have a key role in the construction of global solutions with critical regularity, in the proof of optimal time-decay estimates and, last but not least, in the study of the strong relaxation limit. For simplicity, we here focus on a simple class of partially dissipative systems, but the overall strategy is rather flexible, and adaptable to much more general situations.

Orbit closed permutation groups, relation groups, and simple groups

A permutation group G on a set Omega is called orbit closed if every permutation of Omega preserving the orbits of G in its action on the power set P(Omega ) belongs to G. It is called a relation group if there exists a family R subseteq P(Omega ) such that G is the group of all permutations preserving R. We prove that if a finite orbit closed permutation group G is simple, or is a subgroup of a simple group, then it is a relation group. This result justifies our general conjecture that with a few exceptions every finite orbit closed group is a relation group. To obtain the result, we prove that most of the finite simple permutation groups are relation groups. We also obtain a complete description of those finite simple permutation groups that have regular sets, and prove that (with one exception) if a finite simple permutation group G is a relation group, then every subgroup of G is a relation group.

Amorphic complexity of group actions with applications to quasicrystals

In this article, we define amorphic complexity for actions of locally compact σ \sigma -compact amenable groups on compact metric spaces. Amorphic complexity, originally introduced for Z \mathbb {Z} -actions, is a topological invariant which measures the complexity of dynamical systems in the regime of zero entropy. We show that it is tailor-made to study strictly ergodic group actions with discrete spectrum and continuous eigenfunctions. This class of actions includes, in particular, Delone dynamical systems related to regular model sets obtained via Meyer’s cut and project method. We provide sharp upper bounds on amorphic complexity of such systems. In doing so, we observe an intimate relationship between amorphic complexity and fractal geometry.