Open Set Research Articles

Separation Axioms via $F$-open Sets

In this paper, we introduce some types of separation axioms via $F$-open sets, namely $FT_i$ ($i = 0, 1, 2, 3, 4$), $F$-regular and $F$-normal spaces, and investigate their properties, relationships and characterizations. We show that every $FT_i$ space is a Ti space for $i = 0, 1, 2, 3, 4$. However, the converse is true whenever X is finite.

On Some Functions Related to e*-θ-open Sets

In this study, we defined the concept of quasi $e^*$-$\theta$-closed sets by means of $e^*$-$\theta$-open sets. Depending on this concept, we introduced approximately $e^{\ast}\theta$-open functions and investigated some of its basic properties. Also, we defined and studied contra pre $e^{\ast}\theta$-open functions, which are stronger than the approximately $e^{\ast}\theta$-open functions. Moreover, we characterized the class of $e^*\theta$-$T_\frac {1}{2}$ spaces.

A robust defect detection method with a generalization enhancer and cross-modality aggregator for cylinder bores

High-quality cylinder bores in automobile engines enable drivers to respond quickly to emergencies. Automated detection methods are gradually being adopted across various industries. However, uncontrollable factors and improper preservation methods lead to various types of defects on cylinder bores, thereby causing existing high-performance detectors to exhibit not only undesirable generalizability for unseen defect types but also a certain degree of missed detection for defects of seen types, thereby allowing defective cylinder bores to flow into the market. To address these issues, we propose a foundation-model-based robust defect detection method with high generalizability for cylinder bores (RHG-Detector). Specifically, to address unseen defect categories, we propose a generalization enhancer comprising a box filter, a region extractor and a defect discriminator (DeDi) based on a foundation model to extend defect detection from a closed set to an open set. To reduce missed detections, we adopt a cross-modality aggregator to aggregate the detection results from different modalities. Additionally, we collected and annotated challenging defect classification and detection datasets for cylinder bores, named HIT-EngDC (Harbin Institute of Technology Engine defect classification dataset) and HIT-EngDD2 (Engine defect detection dataset-version 2), which cover nearly all types of cylinder bore defects. Extensive experiments on HIT-EngDC and HIT-EngDD2 demonstrate the state-of-the-art performance of RHG-Detector, with a classification accuracy of 92.0 and a mAP@50 (mean average precision under intersection over union = 0.5) score of 45.2, where the latter is increased by ∼6 and ∼3 compared to the corresponding FasterRCNN (faster region-based convolutional neural networks) and YOLOv7 (you only look once) scores, respectively.

NANO g* sr CLOSED SETS IN NANO TOPOLOGICAL SPACES

The primary focus of this article is to develop, a fresh concept of sets namely Ng*sr closed sets. The goal of this research is to go over the concepts of Ng*sr closed sets and open sets in nano topological spaces. An appropriate illustration is given to study the properties of the above sets. The present relations between some of these sets in nano topological space are provided.

Shape optimization for a nonlinear elliptic problem related to thermal insulation

In this paper, we consider a minimization problem of a nonlinear functional I_{\beta,p}(D,\Omega) related to a thermal insulation problem with a convection term, where \Omega is a bounded connected open set in \R^{n} and D\subset\overline{\Omega} is a compact set. The Euler–Lagrange equation relative to I_{\beta,p} is a p -Laplace equation, 1<p<\infty , with a Robin boundary condition with parameter \beta>0 . The main aim is to study extremum problems for I_{\beta,p}(D,\Omega) , among domains D with given geometrical constraints and \Omega\setminus D of fixed thickness. In the planar case, we show that under perimeter constraint the disk maximizes I_{\beta,p} . In the n -dimensional case we restrict our analysis to convex sets showing that the same is true for the ball but under different geometrical constraints.

The Role of Topology and Capacity in Some Bounds for Principal Frequencies

We prove a lower bound on the sharp Poincaré–Sobolev embedding constants for general open sets, in terms of their inradius. We consider the following two situations: planar sets with given topology; open sets in any dimension, under the restriction that points are not removable sets. In the first case, we get an estimate which optimally depends on the topology of the sets, thus generalizing a result by Croke, Osserman and Taylor, originally devised for the first eigenvalue of the Dirichlet–Laplacian. We also consider some limit situations, like the sharp Moser–Trudinger constant and the Cheeger constant. As a byproduct of our discussion, we also obtain a Buser-type inequality for open subsets of the plane, with given topology. An interesting problem on the sharp constant for this inequality is presented.

Interpretable machine learning boosting the discovery of targeted organometallic compounds with optimal bandgap

Organometallic compounds (OMCs) have attracted tremendous attention in various fields, such as photovoltaic cell and high-k dielectric application, due to their beneficial properties. Despite their potential, the progression of OMCs into industrial applications is hindered by the limited databases available for their properties and the absence of efficient surrogate models. To address this, in this study, optimally selected feature-based surrogate models for predicting the electronic properties of OMCs are constructed via various multiscale features and extensive database. To this end, high-throughput calculation was performed to obtain electronic properties of more than 18k materials generally known as organometallics, augmenting around 12k organic materials obtained from the public open data set, OMDB-GAP1. For generating features closely related to OMCs, descriptors encapsulating the information ranging local to global, also other widely-used composition-, structure-based features (more than 3.5k in total) were employed. Among these descriptors, we identified 48 critical features that elucidates the physicochemical underpinnings of OMCs’ properties, suggesting their impact on the properties of OMCs. The light gradient boosting machine model achieved high-accuracy predictions across the entire database with just 1 % of the total descriptors, sufficiently compared to the entire sets (decreased of around 0.01 by R2 score and 0.01 eV by MAE). Furthermore, the efficacy of active learning process was demonstrated to find OMCs with optimal properties rapidly. As a result, expected improvement outperforms other methods by identifying 69 % of the target materials only searching 46 % of the total search space. Our constructed platform with a high-throughput calculated database can pave the way for the rapid screening of OMCs for the targeted industrial application, and suggest a comprehensive grasp of the intrinsic properties of OMCs and related compounds.

Inexperienced water users can “Float to Live” in realistic open water conditions

BackgroundThe RNLI “Float to Live” campaign is based on research conducted in indoor pools with experienced open water swimmers. Study 1 investigated whether the RNLI “Float to Live” guidance would enable less experienced individuals to float in realistic open water conditions. Study 2 examined the separate effects of practice and coaching on floating competence.MethodsStudy 1: Inexperienced water users conducted floats in either still, open fresh (n = 22) or open sea water (n = 13), followed by moving sea (n = 6) or fresh water (n = 5). Participants undertook three 2-min floats in still water wearing swimwear and one clothed float: 1) naïve; 2) following RNLI “Float to live” messaging; 3) individual float coaching; 4) simulated fall wearing summer clothing. In moving sea water, participants undertook two floats equivalent to Floats 3 and 4. In moving fresh water, participants undertook 3 floats: 1) naïve; 2) following “defensive floating” coaching; 3) simulated fall wearing summer clothing. Study 2: Two groups matched for skinfold thickness undertook three 2-min floats in a flume wearing swimwear. PRAC group (n = 12): 1) naïve; 2) following float practice; 3) float coaching; COACH group (n = 11) coaching followed by practice. Floating difficulty, confidence, competence, “efficiency” and perceived exertion were analysed using either a Friedman test or mixed model ANOVA.ResultsIn both fresh water and sea water, participants’ floating competence and confidence increased after viewing the RNLI messaging, it was further improved with individualised float coaching. The additional helpful instructions included: 1) “head back with ears submerged”; 2) “relax”; 3) “breathe normally”; 4) “it is OK if your legs sink”; 5) an accurate description of sculling for “active” floaters that needed it; 6) spread arms and legs for stability. The simulated fall with clothing did not impair floating competence. No difference in floating competence was seen between PRAC and COACH, though confidence may be increased sooner in COACH.ConclusionsThe RNLI float advice can be applied in realistic open water settings by less experienced water users. Additional content could be included to make the messaging even more effective.

Walking fingerprinting

Abstract We consider the problem of predicting an individual’s identity from accelerometry data collected during walking. In a previous paper, we transformed the accelerometry time series into an image by constructing the joint distribution of the acceleration and lagged acceleration for a vector of lags. Predictors derived by partitioning this image into grid cells were used in logistic regression to predict individuals. Here, we (a) implement machine learning methods for prediction using the grid cell-derived predictors; (b) derive inferential methods to screen for the most predictive grid cells while adjusting for correlation and multiple comparisons; and (c) develop a novel multivariate functional regression model that avoids partitioning the predictor space. Prediction methods are compared on two open source acceleometry data sets collected from: (a) 32 individuals walking on a 1.06 km path; and (b) six repetitions of walking on a 20 m path on two occasions at least 1 week apart for 153 study participants. In the 32-individual study, all methods achieve at least 95% rank-1 accuracy, while in the 153-individual study, accuracy varies from 41% to 98%, depending on the method and prediction task. Methods provide insights into why some individuals are easier to predict than others.

Caloric functions and boundary regularity for the fractional Laplacian in Lipschitz open sets

AbstractWe give Martin representation of nonnegative functions caloric with respect to the fractional Laplacian in Lipschitz open sets. The caloric functions are defined in terms of the mean value property for the space-time isotropic $$\alpha $$ α -stable Lévy process. To derive the representation, we first establish the existence of the parabolic Martin kernel. This involves proving new boundary regularity results for both the fractional heat equation and the fractional Poisson equation with Dirichlet exterior conditions. Specifically, we demonstrate that the ratio of the solution and the Green function is Hölder continuous up to the boundary.

Uniquely Realisable Graphs in Analytic Normed Planes

Abstract A framework $(G,p)$ in Euclidean space $\mathbb{E}^{d}$ is globally rigid if it is the unique realisation, up to rigid congruences, of $G$ with the edge lengths of $(G,p)$. Building on key results of Hendrickson [28] and Connelly [14], Jackson and Jordán [29] gave a complete combinatorial characterisation of when a generic framework is global rigidity in $\mathbb{E}^{2}$. We prove an analogous result when the Euclidean norm is replaced by any norm that is analytic on $\mathbb{R}^{2} \setminus \{0\}$. Specifically, we show that a graph $G=(V,E)$ has an open set of globally rigid realisations in a non-Euclidean analytic normed plane if and only if $G$ is 2-connected and $G-e$ contains 2 edge-disjoint spanning trees for all $e\in E$. We also prove that the analogous necessary conditions hold in $d$-dimensional normed spaces.

Wearable Data From Subjects Playing Super Mario, Taking University Exams, or Performing Physical Exercise Help Detect Acute Mood Disorder Episodes via Self-Supervised Learning: Prospective, Exploratory, Observational Study.

Personal sensing, leveraging data passively and near-continuously collected with wearables from patients in their ecological environment, is a promising paradigm to monitor mood disorders (MDs), a major determinant of the worldwide disease burden. However, collecting and annotating wearable data is resource intensive. Studies of this kind can thus typically afford to recruit only a few dozen patients. This constitutes one of the major obstacles to applying modern supervised machine learning techniques to MD detection. In this paper, we overcame this data bottleneck and advanced the detection of acute MD episodes from wearables' data on the back of recent advances in self-supervised learning (SSL). This approach leverages unlabeled data to learn representations during pretraining, subsequently exploited for a supervised task. We collected open access data sets recording with the Empatica E4 wristband spanning different, unrelated to MD monitoring, personal sensing tasks-from emotion recognition in Super Mario players to stress detection in undergraduates-and devised a preprocessing pipeline performing on-/off-body detection, sleep/wake detection, segmentation, and (optionally) feature extraction. With 161 E4-recorded subjects, we introduced E4SelfLearning, the largest-to-date open access collection, and its preprocessing pipeline. We developed a novel E4-tailored transformer (E4mer) architecture, serving as the blueprint for both SSL and fully supervised learning; we assessed whether and under which conditions self-supervised pretraining led to an improvement over fully supervised baselines (ie, the fully supervised E4mer and pre-deep learning algorithms) in detecting acute MD episodes from recording segments taken in 64 (n=32, 50%, acute, n=32, 50%, stable) patients. SSL significantly outperformed fully supervised pipelines using either our novel E4mer or extreme gradient boosting (XGBoost): n=3353 (81.23%) against n=3110 (75.35%; E4mer) and n=2973 (72.02%; XGBoost) correctly classified recording segments from a total of 4128 segments. SSL performance was strongly associated with the specific surrogate task used for pretraining, as well as with unlabeled data availability. We showed that SSL, a paradigm where a model is pretrained on unlabeled data with no need for human annotations before deployment on the supervised target task of interest, helps overcome the annotation bottleneck; the choice of the pretraining surrogate task and the size of unlabeled data for pretraining are key determinants of SSL success. We introduced E4mer, which can be used for SSL, and shared the E4SelfLearning collection, along with its preprocessing pipeline, which can foster and expedite future research into SSL for personal sensing.

On second-order tensor representation of derivatives in shape optimization.

In this article, we study general properties of distributed shape derivatives admitting a volumetric tensor representation of order two. We obtain a general result providing a range of expressions for the shape derivative, with the distributed shape derivative at one end of the range and the standard Hadamard formula at the other end. We further apply this result to a cost functional depending on the solution of a fourth-order elliptic equation, and obtain the distributed shape derivative in the case of open sets, and the Hadamard formula for sets of class [Formula: see text]. We also consider the case of polygons, for which a description of the weak singularities of the solution appearing in the neighbourhood of the vertices is required to obtain the Hadamard formula. This article is part of the theme issue 'Non-smooth variational problems with applications in mechanics'.

On CR maps between hyperquadrics and Winkelmann hypersurfaces

In this paper, we study CR maps between hyperquadrics and Winkelmann hypersurfaces. Based on a previous study on the CR Ahlfors derivative of Lamel–Son and a recent result of Huang–Lu–Tang–Xiao on CR maps between hyperquadrics, we prove that a transversal CR map from a hyperquadric into a hyperquadric or a Winkelmann hypersurface extends to a local holomorphic isometric embedding with respect to certain Kähler metrics if and only if the Hermitian part of its CR Ahlfors derivative vanishes on an open set of the source. Our proof is based on relating the geometric rank of a CR map into a hyperquadric and its CR Ahlfors derivative.

Shrinking target problems in d-decaying Gauss-like iterated function systems

Let Φ={ϕn}n≥1 be an infinite iterated function system (IFS) on [0,1] satisfying the open set condition with the open set (0,1) and let J be its attractor. For any x∈J, there is a unique integer sequence {ωn(x)}n≥1, called the digit sequence of x, such thatx=limn→∞⁡ϕω1(x)∘⋯∘ϕωn(x)(1) except at countably many points. In this paper, we investigate the shrinking target problem in the infinite iterated function system with a polynomial decay of the derivative. More precisely, we consider the size of the setW(T,x0)={x∈J:Tn(x)∈Itn(x0) for infinitely many n∈N}, where T:J⟼J is the expanding map induced by the left shift and Itn(x0) denotes the tn-th cylinder of x0∈J. As a continuation of one result of Li et al. (2014) [11], we obtain the exact Hausdorff dimension of the set W(T,x0) in some general infinite function systems.

Generic properties of $3$-dimensional Reeb flows: Birkhoff sections and entropy

In this paper we use broken book decompositions to study Reeb flows on closed 3 -manifolds. We show that if the Liouville measure of a non-degenerate contact form can be approximated by periodic orbits, then there is a Birkhoff section for the associated Reeb flow. In view of Irie’s equidistribution theorem, this is shown to imply that the set of contact forms whose Reeb flows have a Birkhoff section contains an open and dense set in the C^{\infty} -topology. We also show that the set of contact forms whose Reeb flows have positive topological entropy is open and dense in the C^{\infty} -topology.

On GeneralizedNanoℕ?̌-Closed andNanoℕα̂-OpenSetsin Nano-Topological Spaces

This work aims to define a new class of sets in nano topological spaces called Nano (Nα) ̌- closed and (Nα) ̂-open sets, and to prove its verifiable properties and theorems.

Staircase patterns in Hirzebruch surfaces

The ellipsoidal capacity function of a symplectic four manifold X measures how much the form on X must be dilated in order for it to admit an embedded ellipsoid of eccentricity z . In most cases there are just finitely many obstructions to such an embedding besides the volume. If there are infinitely many obstructions, X is said to have a staircase. This paper gives an almost complete description of the staircases in the ellipsoidal capacity functions of the family of symplectic Hirzebruch surfaces H_{b} formed by blowing up the projective plane with weight b . We describe an interweaving, recursively defined, family of obstructions to symplectic embeddings of ellipsoids that show there is an open dense set of shape parameters b that are blocked, i.e. have no staircase, and an uncountable number of other values of b that do admit staircases. The remaining b -values form a countable sequence of special rational numbers that are closely related to the symmetries discussed in Magill–McDuff (arXiv:2106.09143). We show that none of them admit ascending staircases. Conjecturally, none admit descending staircases. Finally, we show that, as long as b is not one of these special rational values, any staircase in H_{b} has irrational accumulation point. A crucial ingredient of our proofs is the new, more indirect approach to using almost toric fibrations in the analysis of staircases by Magill (arXiv:2204.12460). In particular, the structure of the relevant mutations of the set of almost toric fibrations on H_{b} is echoed in the structure of the set of blocked b -intervals.

P-492 Providing implications counselling to SA anonymous oocyte donors donating to Australian recipients raising Australian DCC in an open- donor-identity context?

Abstract Study question How do counsellors manage mismatched expectations of stakeholders involved in cross-border oocyte donation between Australia and South Africa with different socio-legal frameworks regarding donor anonymity? Summary answer Cross-border oocyte donation can produce mismatched expectations due to different socio-legal frameworks around donor anonymity between two countries. Counsellors should alert stakeholders to these implications What is known already The demand for oocyte donation in Australia exceeds supply, influencing Australian women to undertake cross-border oocyte donation in South Africa. In Australia, oocyte donation is altruistic and open identity with guaranteed identity release. Conversely, South African oocyte donors are compensated and anonymous. The widespread utilisation of direct to consumer (DTC) ancestry DNA testing and internet-based forums to assist in the interpretation of these results has enabled recipients and donor conceived people (DCPs) to learn the identity of previously anonymous gamete donors. To better prepare stakeholders, some regulatory authorities require counsellors to discuss these implications with donors and recipients. Study design, size, duration Semi-structured in-depth interviews (lasting 45-60 mins) were conducted via zoom and in person in 2022 and 2023. The study included 9 South African infertility counsellors, 16 South African oocyte donors and 12 Australian recipients of cross-border oocyte donation in South Africa. Interviews were recorded and transcribed and transcripts were coded using NVivo software. Data were analysed using thematic analysis Participants/materials, setting, methods Infertility counsellors (9) were recruited through networks of SA fertility professionals. Research participant Australian recipients (12) were recruited through a Facebook peer fertility forum for recipients planning or having completed oocyte donation in SA. Research participant SA oocyte donors were recruited through Facebook advertisements and through snowball sampling resulting from recruitment advertisements placed in clinics and oocyte donor agencies Main results and the role of chance South African oocyte donors anticipated that they would remain anonymous. Some indicated that they would be open to contact should the legal framework in South Africa allow it. As Australian recipients were not required to undergo implications counselling with South African counsellors, the South African counsellors were not aware that recipients pursued the identity of their donors. The counsellors did not alert South African oocyte donors that Australian recipients and DCPs may engage in measures to determine their identity, including via DTC DNA testing and online sleuthing through forums. The Australian recipients believed donor conceived children had a right to know the donor’s identity and donor siblings’ identity, with some wanting early contact. Some recipients took steps to determine their donor’s identity and/or to discover whether their donor conceived children had donor siblings. They suggested that their children could pursue DNA testing in the future, if they wanted to know about their genetic origins. Limitations, reasons for caution The study findings are from 9 SA counsellors, 16 SA oocyte donors and 12 Australian recipients who agreed to be interviewed. They may not represent the views of all stakeholders involved in cross-border oocyte donation between Australia and South Africa. Wider implications of the findings Stakeholders involved in cross-border oocyte donation between anonymous donor and open identity settings should receive implications counselling to avoid a mismatch in the consequences of donor-conception. Trial registration number not applicable

Thermal comfort investigation of membrane-assisted radiant cooling in outdoor settings

The global warming and urban heat island effect call for mitigation strategies for improving thermal environments in open urban spaces. Radiant cooling can remove heat from the human body via direct thermal radiation, thereby creating the possibility to provide active cooling for people in outdoor environments. While using a transparent membrane, convection energy lost to the ambient airflow can be minimized. However, current research on the thermal comfort of radiant cooling systems is restricted to indoor applications, while outdoor applications remain unclear. To address this need, the study investigated the effect of membrane-assisted asymmetric radiant cooling on people's thermal perception in outdoor environments. A radiant cooling facility in an outdoor setting was built, and its cooling effects were assessed by using 248 human subjects across hot and transitional seasons. It is found that the radiant cooling facility can lower the mean thermal sensation vote (MTSV) by 0.6 to 1.5 units. The degree of cooling depends both on the panel temperature and environmental conditions. At the panel surface temperature of 14.3°C, MTSV was at the neutral zone (-0.5 ≤ MTSV ≤ 0.5) with the environmental UTCI as high as 38.1°C, whereas the thermal sensation of the group without radiant cooling was rated warm to hot. Under this condition, the ambient UTCI scope of no heat stress can be extended by 10.1°C higher. The strongest local cooling sensation appeared in the back, with an average decrease of 1.33 units in MTSV, contributing to lowering the overall thermal sensation of the body. For the first time, it is demonstrated that membrane-assisted radiant cooling panels can effectively improve thermal comfort in open outdoor settings.