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Culture change initiatives in older adult and dementia care have called for a new care paradigm informed by a relational ontology and relational theories. Yet translating these humanizing principles into practice has proven difficult; traditional approaches to knowledge translation have not had a sustained impact. One of the most significant impediments to transforming the culture of care has been the lack of understanding of what it means to be and act relational in practice. A growing body of research is demonstrating the potential of critical arts-based inquiry/pedagogy (CABI/P) for translating theory in accessible and relevant ways for diverse audiences and for shifting images, understandings and actions in healthcare in more effective ways. As part of a larger longitudinal project, this paper explores the immediate impacts of a research-informed drama called ‘Cracked: new light on dementia,’ and how it might enhance understandings of relational caring for staff working in long-term care (LTC) homes. Data from post-performance focus group/interview discussions with staff working in two different LTC settings point to the effectiveness of Cracked in translating key principles of relational theories into older adult and dementia care and the possibilities of CABI/P in gerontological education more broadly. Although organizational and broader system change is needed to achieve sustained impact of relational caring practices, CABI/P, such as Cracked, has the potential to expose and challenge entrenched assumptions, policies, practices, and to imagine and effect more compassionate, humane, and equitable care. [ABSTRACT FROM AUTHOR]

Imaging antiferromagnetic 180° domains with actively controlled visibility is vital for both fundamental science and sophisticated applications. While optical second-harmonic generation (SHG) is a well-known technique for distinguishing such domains in non-centrosymmetric antiferromagnets, a general material-based strategy to control domain contrast remains elusive. Using van der Waals antiferromagnet MnPS3 as a proof of concept, we demonstrate the tuning of nonreciprocity-induced domain contrast in SHG through applying an in-plane electric field that transforms the magnetic point group to its unitary subgroup. The interference among intrinsic electric-dipole, magnetic-dipole, and field-induced electric-dipole transitions, each carrying distinct characters under space-inversion (P ) and time-reversal (T ) operations, enables large tuning of domain contrast and nonreciprocity in a broad spectral range. This strategy, generically applicable to systems characterized by P T -symmetric magnetic groups with a polar unitary subgroup, offers a path to fast electrical modulation of nonlinear nonreciprocal photonic behaviors using antiferromagnets. Controlling properties associated with antiferromagnetic states could unlock numerous applications, though this has long seemed elusive. Here, Wang et al. demonstrate how electric fields can manipulate the coupling between light and antiferromagnetic domains in a nonlinear optical interaction. [ABSTRACT FROM AUTHOR]

Let (an)n=0∞ be a second-order linear recurrence sequence with constant coefficients over the field of p-adic numbers Qp. We study the set of limit points of the sequence of consecutive ratios (an+1/an)n=0∞ in Qp. [ABSTRACT FROM AUTHOR]

Objective: Patients with Postherpetic Neuralgia (PHN) often exhibit depressive-like symptoms, significantly impacting their quality of life. Esketamine, known for its analgesic properties, has also been recognized for its rapid antidepressant effects. However, its efficacy in the treatment of PHN requires further exploration. This study aims to evaluate the impact of intravenous patient-controlled analgesia(PICA) with esketamine on depressive mood in PHN patients. Methods: This retrospective study analyzed PHN patients hospitalized and treated at the affiliated hospital of Southwest Medical University from June 2021 to March 2023. Patients were divided into the esketamine group (E group) and the sufentanil group (S group) based on their treatment regimens. Primary outcomes included pain numerical rating scale(NRS), depression patient health questionaire-9(PHQ-9), and anxiety generalized anxiety disorder-7(GAD-7) scores measured before treatment, and at 3 days, 7 days, 1 month, 2 months, and 3 months post-treatment. Results: A total of 83 patients were included in the analysis. Before treatment, there were no statistically significant differences in pain NRS, depression PHQ-9, and anxiety GAD-7 scores between the two groups (P > 0.05). Compared to before treatment, significant reductions in pain NRS scores were observed at all post-treatment time points in both groups (P < 0.05), with no differences between groups (P > 0.05). The E group exhibited significantly lower depression PHQ-9 scores than the S group at 3 days and 7 days post-treatment (P < 0.05), but no significant differences were observed at 1 month, 2 months, and 3 months (P > 0.05). Anxiety GAD-7 scores were significantly lower in the E group compared to the S group at 3 days, 7 days post-treatment (P < 0.05), with no statistical differences at 1 month, 2 months, and 3 months post-treatment (P > 0.05). Conclusion: Both PICA with esketamine and sufentanil alleviated pain equally in PHN patients. However, PICA with esketamine specifically improved early symptoms of anxiety and depression. [ABSTRACT FROM AUTHOR]

For 0-cycles on a variety over a number field, we define an analogue of the classical descent set for rational points. This leads to, among other things, a definition of the étale-Brauer obstruction set for 0-cycles. We show that all these constructions are compatible with Suslin's singular homology of degree 0. We then transfer some tools and techniques used to study the arithmetic of rational points into the setting of 0-cycles. For example, we extend the strategy developed by Y. Liang, relating the arithmetic of rational points over finite extensions of the base field to that of 0-cycles, to torsors. We give applications of our results to study the arithmetic behaviour of 0-cycles for Enriques surfaces, torsors given by (twisted) Kummer varieties, universal torsors, and torsors under tori. [ABSTRACT FROM AUTHOR]

A convex fair partition of a convex polygonal region is defined as a partition on which all regions are convex and have equal area and equal perimeter. The existence of such a partition for any number of regions remains an open question. In this paper, we address this issue by developing an algorithm to find such a convex fair partition without restrictions on the number of regions. Our approach utilizes the normal flow algorithm (a generalization of Newton's method) to find a zero for the excess areas and perimeters of the convex hulls of the regions. The initial partition is generated by applying Lloyd's algorithm to a randomly selected set of points within the polygon, after appropriate scaling. We performed extensive experimentation, and our algorithm can find a convex fair partition for 100% of the tested problem. Our findings support the conjecture that a convex fair partition always exists. [ABSTRACT FROM AUTHOR]

For K an infinite field of characteristic other than two, consider the action of the special orthogonal group SOt(K) on a polynomial ring via copies of the regular representation. When K has characteristic zero, Boutot’s theorem implies that the invariant ring has rational singularities; when K has positive characteristic, the invariant ring is F-regular, as proven by Hashimoto using good filtrations. We give a new proof of this, viewing the invariant ring for SOt(K) as a cyclic cover of the invariant ring for the corresponding orthogonal group; this point of view has a number of useful consequences, for example, it readily yields the a-invariant and information on the Hilbert series. Indeed, we use this to show that the h-vector of the invariant ring for SOt(K) need not be unimodal. [ABSTRACT FROM AUTHOR]

To address the scientific inquiry regarding the dynamic mechanism of deformation of droplets on the jet surface, this study establishes a stochastic differential equation describing deformation of a droplet on a uniform jet surface, considering the affine deformation of a semi-ellipsoidal droplet driven by the pulsation velocity of the jet. The results indicate that the equilibrium point set of the model conforms to an inverse proportional function concerning the major and minor axes of the droplet. Additionally, the assumption of the physical model is satisfied only when the droplet position parameter . The solution process, initialized with the equilibrium point set, tends to reach the state of mean square instability within a very short duration. For dimensionless initial semi-minor axes of the droplet below 0.1 and within the constraint of the equilibrium point set, the probability of the droplet being in a stretched state during the later stages of deformation ranges between 60 and 65%. In this model, during the late stage of droplet deformation, the dimensionless semi-minor axis of the droplet approaches zero. Thus, when the droplet is in the stretched state, it is close to breaking. During retraction, the length of semi-major axis of the droplet fluctuates and gradually decreases. However, in the stretched state, the length of semi-major axis of the droplet increases rapidly, with its growth rate accelerating with time. [ABSTRACT FROM AUTHOR]

Given an action of a discrete group on a closed smooth manifold, we consider the class of nonlocal elliptic operators generated by pseudodifferential operators on the manifold and shift operators. The operators in this class are Fredholm under suitable ellipticity conditions. In the present paper, we give an index formula for these operators for the case of the group , where is an arbitrary finite group. To solve this index problem, we explicitly write the contribution to the index by the fixed points of finite-order elements of the group. The index formula is stated in terms of characteristic classes in periodic cyclic cohomology. [ABSTRACT FROM AUTHOR]

Objective To investigate indoor and outdoor air absorption dose rates of γ radiation in Changning District for the estimation of public exposure doses and the health impacts. Methods From June to December 2022, using a grid - layout sampling approach, 12 households from each of 10 communities in Changning District were selected based on the construction year, and 15 monitoring points were set for each household. Concurrently, 2 roads and 1 green space were selected as outdoor monitoring points in the center of each community, and a total of 30 outdoor monitoring points were set up. Air dose rates of γ-radiation were measured at each monitoring point using the environment-grade γ dose rate meter. Calculate the annual average effective dose equivalent of environmental gamma radiation for the public, and assess the excess lifetime cancer risk (ELCR) due to environmental gamma radiation. Results The average values of the absorbed dose rate of γ-radiation in Changning District for indoor and outdoor monitoring points were (125.80 ± 11.72) nGy/h and (76.63 ± 16.15) nGy/h. Indoor air dose rates of γ-radiation were higher than outdoor rates (P < 0.05). Indoor air dose rates of γ -radiation in households constructed after 2000 were lower compared to those constructed before 2000 (P < 0.05). The annual average of indoor and outdoor effective doses for the public were 0.617 mSv/year and 0.094 mSv/year, respectively. The average excess lifetime cancer risk (ELCR) was 2.56 × 10 -3 indoors and 4.28 × 10 -4 outdoors. Conclusions The air dose rates of γ -radiation in different regions of Changning District varied. The annual average effective dose equivalent and ELCR in Changning District were slightly higher than the global average level and still within the normal fluctuation range nationwide. [ABSTRACT FROM AUTHOR]

The objective of this research is to present a novel approach to enhance the extragradient algorithm's efficiency for finding an element within a set of fixed points of nonexpansive mapping and the set of solutions for equilibrium problems. Specifically, we focus on applications involving a pseudomonotone, Lipschitz-type continuous bifunction. Our main contribution lies in establishing a strong convergence theorem for this method, without relying on the assumption of lim n → ∞ ∥ x n + 1 − x n ∥ = 0 . Moreover, the main theorem can be applied to effectively solve the combination of variational inequality problem (CVIP). In support of our main result, numerical examples are also presented. [ABSTRACT FROM AUTHOR]

Reconstructing 2D curves from sample points has long been a critical challenge in computer graphics, finding essential applications in vector graphics. The design and editing of curves on surfaces has only recently begun to receive attention, primarily relying on human assistance, and where not, limited by very strict sampling conditions. In this work, we formally improve on the state‐of‐the‐art requirements and introduce an innovative algorithm capable of reconstructing closed curves directly on surfaces from a given sparse set of sample points. We extend and adapt a state‐of‐the‐art planar curve reconstruction method to the realm of surfaces while dealing with the challenges arising from working on non‐Euclidean domains. We demonstrate the robustness of our method by reconstructing multiple curves on various surface meshes. We explore novel potential applications of our approach, allowing for automated reconstruction of curves on Riemannian manifolds. [ABSTRACT FROM AUTHOR]

Working with pushbroom imagery in photogrammetry and remote sensing presents a fundamental challenge in object-to-image space transformation. For this transformation, accurate estimation of Exterior Orientation Parameters (EOPs) for each scanline is required. To tackle this challenge, Best Scanline Search or Determination (BSS/BSD) methods have been developed. However, the current BSS/BSD methods are not efficient for real-time applications due to their complex procedures and interpolations. This paper introduces a new non-iterative BSD method specifically designed for line-type pushbroom images. The method involves simulating a pair of sets of points, Simulated Control Points (SCOPs), and Simulated Check Points (SCPs), to train and test a Multilayer Perceptron (MLP) model. The model establishes a strong relationship between object and image spaces, enabling a direct transformation and determination of best scanlines. This proposed method does not rely on the Collinearity Equation (CE) or iterative search. After training, the MLP model is applied to the SCPs for accuracy assessment. The proposed method is tested on ten images with diverse landscapes captured by eight sensors, exploiting five million SCPs per image for statistical assessments. The Root Mean Square Error (RMSE) values range between 0.001 and 0.015 pixels across ten images, demonstrating the capability of achieving the desired sub-pixel accuracy within a few seconds. The proposed method is compared with conventional and state-of-the-art BSS/BSD methods, indicating its higher applicability regarding accuracy and computational efficiency. These results position the proposed BSD method as a practical solution for transforming object-to-image space, especially for real-time applications. [ABSTRACT FROM AUTHOR]

Let the circle group act on a compact oriented manifold |$M$| with a non-empty discrete fixed point set. Then the dimension of |$M$| is even. If |$M$| has one fixed point, |$M$| is the point. In any even dimension, such a manifold |$M$| with two fixed points exists, a rotation of an even dimensional sphere. Suppose that |$M$| has three fixed points. Then the dimension of |$M$| is a multiple of 4. Under the assumption that each isotropy submanifold is orientable, we show that if |$\dim M=8$|⁠ , then the weights at the fixed points agree with those of an action on the quaternionic projective space |$\mathbb{H}\mathbb{P}^{2}$|⁠ , and show that there is no such 12-dimensional manifold |$M$|⁠. [ABSTRACT FROM AUTHOR]

In this study, we propose an algorithmic framework for solving a class of optimal control problems. This class is associated with the minimum-time interception of moving target problems, where a plant with a given state equation must approach a moving target whose trajectory is known a priori. Our framework employs an analytical description of the distance from an arbitrary point to the reachable set of the plant. The proposed algorithm is always convergent and cannot be improved without losing the guarantee of its convergence to the correct solution for arbitrary Lipschitz continuous trajectories of the moving target. In practice, it is difficult to obtain an analytical description of the distance to the reachable set for the sophisticated state equation of the plant. Nevertheless, it was shown that the distance can be obtained for some widely used models, such as the Dubins car, in an explicit form. Finally, we illustrate the generality and effectiveness of the proposed framework for simple motions and the Dubins model. [ABSTRACT FROM AUTHOR]

Aiming at the problem that the Osprey Optimization Algorithm (OOA) does not have high optimization accuracy and is prone to falling into local optimum, an Improved Osprey Optimization Algorithm Based on a Two-Color Complementary Mechanism for Global Optimization (IOOA) is proposed. The core of the IOOA algorithm lies in its unique two-color complementary mechanism, which significantly improves the algorithm's global search capability and optimization performance. Firstly, in the initialization stage, the population is created by combining logistic chaos mapping and the good point set method, and the population is divided into four different color groups by drawing on the four-color theory to enhance the population diversity. Secondly, a two-color complementary mechanism is introduced, where the blue population maintains the OOA core exploration strategy to ensure the stability and efficiency of the algorithm; the red population incorporates the Harris Hawk heuristic strategy in the development phase to strengthen the ability of local minima avoidance; the green group adopts the strolling and wandering strategy in the searching phase to add stochasticity and maintain the diversity; and the orange population implements the optimized spiral search and firefly perturbation strategies to deepen the exploration and effectively perturb the local optimums, respectively, to improve the overall population diversity, effectively perturbing the local optimum to improve the performance of the algorithm and the exploration ability of the solution space as a whole. Finally, to validate the performance of IOOA, classical benchmark functions and CEC2020 and CEC2022 test sets are selected for simulation, and ANOVA is used, as well as Wilcoxon and Friedman tests. The results show that IOOA significantly improves convergence accuracy and speed and demonstrates high practical value and advantages in engineering optimization applications. [ABSTRACT FROM AUTHOR]

We discuss the structure of idempotent uninorms defined on bounded lattices such that the set of all points incomparable with the neutral element contains at most one point. We show that the structure of idempotent uninorms on lattices with one point incomparable with the neutral element is much more complex than the structure of those defined on lattices where all points are comparable with the neutral element. In Part I of this two-part paper, we completely characterize idempotent uninorms defined on bounded lattices such that all points are comparable with the neutral element. Moreover, we show some basic properties and observations on idempotent uninorms on bounded lattices with one point incomparable with the neutral element and we completely characterize the class of internal uninorms on such lattices. In Part II, we will characterize two special classes of idempotent uninorms defined on bounded lattices with one point incomparable with the neutral element, including idempotent uninorms with annihilator incomparable with the neutral element, and by the composition of these special cases, we will show the complete characterization of idempotent uninorms on such lattices. [ABSTRACT FROM AUTHOR]

The geproci property is a recent development in the world of geometry. We call a set of points Z\subseteq \mathbb {P}_k^3 an (a,b)-geproci set (for GEneral PROjection is a Complete Intersection) if its projection from a general point P to a plane is a complete intersection of curves of degrees a\leq b. Nondegenerate examples known as grids have been known since 2011. Nondegenerate nongrids were first described in 2018, working in characteristic 0. Almost all of these new examples are of a special kind called half grids. In this paper, based partly on the author's thesis, we use a feature of geometry in positive characteristic to give new methods of producing geproci half grids and non-half grids. [ABSTRACT FROM AUTHOR]

In this work, we propose a multi-level protocol for routine theoretical studies of chemical reaction mechanisms. The initial reaction paths of our investigated systems are sampled using the Nudged Elastic Band (NEB) method driven by a cheap electronic structure method. Forces recalculated at the more accurate electronic structure theory for a set of points on the path are fitted with a machine learning technique (in our case symmetric gradient domain machine learning or sGDML) to produce a semi-local reactive potential energy surface (PES), embracing reactants, products and transition state (TS) regions. This approach has been successfully applied to a unimolecular (Bergman cyclization of enediyne) and a bimolecular (SN2 substitution) reaction. In particular, we demonstrate that with only 50 to 150 energy-force evaluations with the accurate reference methods (here complete-active-space self-consistent field, CASSCF, and coupled-cluster singles and doubles, CCSD) it is possible to construct a semi-local PES giving qualitative agreement for stationary-point geometries, intrinsic reaction coordinates and barriers. Furthermore, we find a qualitative agreement in vibrational frequencies and reaction rate coefficients. The key aspect of the method's performance is its multi-level nature, which not only saves computational effort but also allows extracting meaningful information along the reaction path, characterized by zero gradients in all but one direction. Agnostic to the nature of the TS and computationally economic, the protocol can be readily automated and routinely used for mechanistic reaction studies. [ABSTRACT FROM AUTHOR]

Contrary to the second-order Phase field model (PFM) of fracture, fourth-order PFM provides a more precise representation of the crack surface by incorporating higher-order derivatives (curvature) of the phase-field order parameter in the so-called crack density functional. As a result, in a finite element setting, the weak form of the phase-field governing differential equation requires C 1 continuity in the basis function. C 0 Sibson interpolants or Natural element interpolants are obtained by the ratio of area traced by the second-order Voronoi cell over the first-order Voronoi cells, which is based on the natural neighbor of a nodal point set. C 1 Sibson interpolants are obtained by degree elevating the evaluated C 0 interpolants in the Bernstein-Bezier patch of a cubic simplex. For better computational efficiency while accounting only for the tensile part for driving fracture, a hybrid PFM is adopted. In this work, the numerical implementation of higher-order PFM with C 1 Sibson interpolants along with some benchmark examples are presented to showcase the performance of this method for simulating fracture in brittle materials. [ABSTRACT FROM AUTHOR]

When two tasks are presented simultaneously or in close succession, such as in the overlapping task paradigm of the psychological refractory period, dual-task performance on those tasks is usually impaired compared with separate single-task performance. Numerous theories explain these emerging dual-task costs in terms of the existence of capacity limitations in the constituent component tasks. The current paper proposes active dual-task coordination processes that work on the scheduling of these capacity-limited processes. Further, there are recent findings that point to a meta-cognitive control level in addition to these active coordination processes. This additional level's responsibility is to adjust the dual-task coordination of capacity-limited stages (i.e., coordination adjustment). I review evidence focusing on the existence of dual-task coordination processes and processes of coordination adjustment. The remainder of the paper elaborates on preliminary findings and points to the separability of these sets of processes, which is a key assumption of the framework of dual-task coordination adjustment. [ABSTRACT FROM AUTHOR]

A strong blocking set in a finite projective space is a set of points that intersects each hyperplane in a spanning set. We provide a new graph theoretic construction of such sets: combining constant-degree expanders with asymptotically good codes, we explicitly construct strong blocking sets in the (k-1)-dimensional projective space over \mathbb {F}_q that have size at most c q k for some universal constant c. Since strong blocking sets have recently been shown to be equivalent to minimal linear codes, our construction gives the first explicit construction of \mathbb {F}_q-linear minimal codes of length n and dimension k, for every prime power q, for which n \leq c q k. This solves one of the main open problems on minimal codes. [ABSTRACT FROM AUTHOR]

We apply a real-space block renormalization group approach to study the critical properties of the random transverse-field Ising spin chain with multispin interactions. First, we recover the known properties of the traditional model with two-spin interactions by applying the renormalization approach for the arbitrary size of the block. For the model with three-spin couplings, we calculate the critical point and demonstrate that the phase transition is controlled by an infinite disorder fixed point. We have determined the typical correlation-length critical exponent, which seems to be different from that of the random transverse Ising chain with nearest-neighbor couplings. Thus, this model represents a new infinite disorder universality class. [ABSTRACT FROM AUTHOR]

We consider entropy solutions to the eikonal equation $|\nabla u|=1$ in two-space dimensions. These solutions are motivated by a class of variational problems and fail in general to have bounded variation. Nevertheless, they share several of their fine properties with BV functions: we show in particular that the set of non-Lebesgue points has at least one co-dimension. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Chongqing University of Posts & Telecommunications (Natural Science Edition) is the property of Chongqing University of Posts & Telecommunications and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

A monotone function interval is the set of monotone functions that lie pointwise between two fixed, -monotone functions. We characterize the set of extreme points of monotone function intervals and apply this to a number of economic settings. First, we leverage the main result to characterize the set of distributions of posterior quantiles that can be induced by a signal, with applications to political economy, Bayesian persuasion, and the psychology of judgment. Second, we combine our characterization with properties of convex optimization problems to unify and generalize seminal results in the literature on security design under adverse selection and moral hazard. (JEL C61, C65, D72, D82, D91, G12) [ABSTRACT FROM AUTHOR]

Conical tanks have a high application rate in industrial processes, especially in colloidal mills, chemical processes, and food processing. The use of conical tanks presents significant benefits because they contribute to sedimentation and reduce the accumulation of impurities compared to conventional cylindrical tanks. However, level control of a conical tank due to its shape requires advanced strategies to guarantee efficient control. In this research, a model predictive control (MPC) method was designed and implemented for the level control of a conical tank on a laboratory scale. To evaluate the performance of the controller, it was compared with a traditional proportional–integral (PI) controller, and the rise time, settling time, overshoot, and error in the steady state were analyzed when different set point changes were tested. In addition, the system was subjected to disturbances, and the MPC demonstrated better performance in a transient state, as well as smooth and stable action controls that allowed for an increase in the useful life of the actuator. In addition, an interactive graphical interface was developed that allowed a dynamic response in a real plant to be experienced; this provides an academic tool for designing control strategies before implementation in a real process. [ABSTRACT FROM AUTHOR]

In this paper, we classified Hadamard 2-(51, 25, 12) designs having a non-abelian automorphism group of order 10, i.e., Frob10 ≌ Z5: Z2, where a subgroup isomorphic to Z2 fixed setwise all the Z5-orbits of the sets of points and blocks. Furthermore, we classified 2-(59, 29, 14) designs having a non-abelian automorphism group of order 14, i.e., Frob14 ≌ Z7: Z2, where a subgroup isomorphic to Z2 fixed setwise all the Z7-orbits of the sets of points and blocks. We also showed that there was no Hadamard 2-(59, 29, 14) design with automorphism group Frob21 ≌ Z7: Z3, where a subgroup of order 3 fixed setwise all the Z7-orbits of points and blocks. Additionally, we used Hadamard 2-(59, 29, 14) designs obtained to construct ternary linear codes and linear codes over the finite field of order 5. We constructed ternary self-dual codes and self-dual codes over the finite field of order 5 from the corresponding Hadamard matrices of order 60. [ABSTRACT FROM AUTHOR]

The concept of contraction mappings plays a significant role in mathematics, particularly in the study of fixed points and the existence of solutions for various equations. In this study, we described two types of enriched contractions: enriched F-contraction and enriched F'-contraction associated with u-fold averaged mapping, which are involved with Kirk's iterative technique with order u. The contractions extracted from this paper generalized and unified many previously common super contractions. Furthermore, u-fold averaged mappings can be seen as a more general form of both averaged mappings and double averaged mappings. Moreover, we demonstrated that the ufold averaged mapping with enriched contractions has a unique fixed point. Our work examined the necessary conditions for the u-fold averaged mapping and weak enriched contractions to have equal sets of fixed points. Additionally, we illustrated that an appropriate Kirk's iterative algorithm can effectively approximate a fixed point of a u-fold averaged mapping as well as the two enriched contractions. Also, we delved into the well-posedness, limit shadowing property, and Ulam-Hyers stability of the u-fold averaged mapping. Furthermore, we established necessary conditions that guaranteed the periodic point property for each of the illustrated strengthened contractions. To underscore the generality of our findings, we presented several examples that aligned with comparable results found in the existing literature. [ABSTRACT FROM AUTHOR]

Copyright of Electric Machines & Control / Dianji Yu Kongzhi Xuebao is the property of Electric Machines & Control and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this study, we investigate the connection between the efficient frontier (EF) of a general multiobjective mixed integer linear optimization problem (MILP) and the so-called restricted value function (RVF) of a closely related single-objective MILP. In the first part of the paper, we detail the mathematical structure of the RVF, including characterizing the set of points at which it is differentiable, the gradients at such points, and the subdifferential at all nondifferentiable points. We then show that the EF of the multiobjective MILP is comprised of points on the boundary of the epigraph of the RVF and that any description of the EF suffices to describe the RVF and vice versa. Because of the close relationship of the RVF to the EF, we observe that methods for constructing the so-called value function (VF) of an MILP and methods for constructing the EF of a multiobjective optimization problem are effectively interchangeable. Exploiting this observation, we propose a generalized cutting-plane algorithm for constructing the EF of a multiobjective MILP that arises from an existing algorithm for constructing the classical MILP VF. The algorithm identifies the set of all integer parts of solutions on the EF. We prove that the algorithm converges finitely under a standard boundedness assumption and comes with a performance guarantee if terminated early. [ABSTRACT FROM AUTHOR]

The k-nearest neighbor algorithm is a powerful classification method. However, its classification performance will be affected in small-size samples with existing outliers. To address this issue, a pre-averaged pseudo nearest neighbor classifier (PAPNN) is proposed to improve classification performance. In the PAPNN rule, the pre-averaged categorical vectors are calculated by taking the average of any two points of the training sets in each class. Then, k-pseudo nearest neighbors are chosen from the preprocessed vectors of every class to determine the category of a query point. The pre-averaged vectors can reduce the negative impact of outliers to some degree. Extensive experiments are conducted on nineteen numerical real data sets and three high dimensional real data sets by comparing PAPNN to other twelve classification methods. The experimental results demonstrate that the proposed PAPNN rule is effective for classification tasks in the case of small-size samples with existing outliers. [ABSTRACT FROM AUTHOR]

The steady states of an antitone electric system are described by an antitone function with respect to the componentwise order. When this function is bounded from below by a positive vector, it has only one fixed point. This fixed point is attractive for the fixed point iteration method. In the general case, we find existence and uniqueness results of fixed points using the set of ℙ$$ \mathrm{\mathbb{P}} $$‐matrices. [ABSTRACT FROM AUTHOR]

We provide a definition of a ≺-asymptotic (we suggest the pronunciation "prec-asymptotic") pair in a topological action (X , G) of a countable amenable group G , where ≺ is an order on G of type Z. In the case where for some G -invariant Borel probability measure μ on X , the measure-preserving system (X , μ , G) factors, via a map φ , onto a multiorder (O ˜ , ν , G) , we also introduce the notion of a φ -asymptotic pair. Then we prove that if μ has positive measure-theoretic conditional entropy with respect to the multiorder factor, then the set of points which belong to φ -asymptotic pairs has positive measure μ. This result is a generalization of the Blanchard-Host-Ruette Theorem for classical topological dynamical systems (actions of Z). As a strengthening of our theorem, we show that for any system (X , G) of positive topological entropy, any multiorder (O ˜ , ν , G) and ν -almost every ≺ ∈ O ˜ , there exist ≺-asymptotic pairs in X. Finally, we characterize systems (X , G) of topological entropy zero as factors of topologically multiordered systems (in which case φ is defined μ -almost everywhere for every G -invariant measure μ) with no φ -asymptotic pairs. [ABSTRACT FROM AUTHOR]

We investigate a general boundary-value problem for nonuniformly 2 b → -parabolic equations with degeneration. The coefficients of parabolic equations and boundary conditions admit power singularities of any order in any variables on a certain set of points. By using a priori estimates and the Arzelà and Riesz theorems, we establish the existence and integral representation for the unique solution of the formulated boundary-value problems. The estimates of the solution of the general parabolic boundary- value problem and its derivatives in Hölder spaces with power weight are obtained. The order of the power weight is determined via the values of the orders of power singularities and degenerations of the coefficients of 2 b → -parabolic equations and boundary conditions. [ABSTRACT FROM AUTHOR]

Recently, the growing demand for autonomous driving in the industry has led to a lot of interest in 3D object detection, resulting in many excellent 3D object detection algorithms. However, most 3D object detectors focus only on a single set of LiDAR points, ignoring their potential ability to improve performance by leveraging the information provided by the consecutive set of LIDAR points. In this paper, we propose a novel 3D object detection method called temporal motion-aware 3D object detection (TM3DOD), which utilizes temporal LiDAR data. In the proposed TM3DOD method, we aggregate LiDAR voxels over time and the current BEV features by generating motion features using consecutive BEV feature maps. First, we present the temporal voxel encoder (TVE), which generates voxel representations by capturing the temporal relationships among the point sets within a voxel. Next, we design a motion-aware feature aggregation network (MFANet), which aims to enhance the current BEV feature representation by quantifying the temporal variation between two consecutive BEV feature maps. By analyzing the differences and changes in the BEV feature maps over time, MFANet captures motion information and integrates it into the current feature representation, enabling more robust and accurate detection of 3D objects. Experimental evaluations on the nuScenes benchmark dataset demonstrate that the proposed TM3DOD method achieved significant improvements in 3D detection performance compared with the baseline methods. Additionally, our method achieved comparable performance to state-of-the-art approaches. [ABSTRACT FROM AUTHOR]

Addressing the issues of the sand cat swarm optimization algorithm (SCSO), such as its weak global search ability and tendency to fall into local optima, this paper proposes an improved strategy called the multi-strategy integrated sand cat swarm optimization algorithm (MSCSO). The MSCSO algorithm improves upon the SCSO in several ways. Firstly, it employs the good point set strategy instead of a random strategy for population initialization, effectively enhancing the uniformity and diversity of the population distribution. Secondly, a nonlinear adjustment strategy is introduced to dynamically adjust the search range of the sand cats during the exploration and exploitation phases, significantly increasing the likelihood of finding more high-quality solutions. Lastly, the algorithm integrates the early warning mechanism of the sparrow search algorithm, enabling the sand cats to escape from their original positions and rapidly move towards the optimal solution, thus avoiding local optima. Using 29 benchmark functions of 30, 50, and 100 dimensions from CEC 2017 as experimental subjects, this paper further evaluates the MSCSO algorithm through Wilcoxon rank-sum tests and Friedman's test, verifying its global solid search ability and convergence performance. In practical engineering problems such as reducer and welded beam design, MSCSO also demonstrates superior performance compared to five other intelligent algorithms, showing a remarkable ability to approach the optimal solutions for these engineering problems. [ABSTRACT FROM AUTHOR]

The formation of unmanned surface vehicles (USVs) stands as a paramount concern in USV formation control research. In addressing this, this paper introduces a novel formation strategy for USVs, which accounts for their arbitrary initial positions and headings. Firstly, given the random distribution of the USVs' initial positions, to enhance the efficiency of formation assembly, the point set of the USVs is matched with basic formations using the Hausdorff distance to establish the formation. Building upon this foundation and acknowledging the potential hindrance posed by the arbitrary initial headings of the USVs, which could hinder their ability to reach the designated formation target points, a cost matrix is constructed based on the designed distance–azimuth evaluation function. Subsequently, the Hungarian algorithm is utilized to efficiently assign formation target points for the USVs. Ultimately, the effectiveness of the proposed strategy is validated through simulation experiments. [ABSTRACT FROM AUTHOR]

The increasing application of virtual surgical planning (VSP) in orthognathic surgery implies a critical need for accurate prediction of facial and skeletal shapes. The craniofacial relationship in patients with dentofacial deformities is still not understood, and transformations between facial and skeletal shapes remain a challenging task due to intricate anatomical structures and nonlinear relationships between the facial soft tissue and bones. In this study, a novel bidirectional 3-dimensional (3D) deep learning framework, named P2P-ConvGC, was developed and validated based on a large-scale data set for accurate subject-specific transformations between facial and skeletal shapes. Specifically, the 2-stage point-sampling strategy was used to generate multiple nonoverlapping point subsets to represent high-resolution facial and skeletal shapes. Facial and skeletal point subsets were separately input into the prediction system to predict the corresponding skeletal and facial point subsets via the skeletal prediction subnetwork and facial prediction subnetwork. For quantitative evaluation, the accuracy was calculated with shape errors and landmark errors between the predicted skeleton or face with corresponding ground truths. The shape error was calculated by comparing the predicted point sets with the ground truths, with P2P-ConvGC outperforming existing state-of-the-art algorithms including P2P-Net, P2P-ASNL, and P2P-Conv. The total landmark errors (Euclidean distances of craniomaxillofacial landmarks) of P2P-ConvGC in the upper skull, mandible, and facial soft tissues were 1.964 ± 0.904 mm, 2.398 ± 1.174 mm, and 2.226 ± 0.774 mm, respectively. Furthermore, the clinical feasibility of the bidirectional model was validated using a clinical cohort. The result demonstrated its prediction ability with average surface deviation errors of 0.895 ± 0.175 mm for facial prediction and 0.906 ± 0.082 mm for skeletal prediction. To conclude, our proposed model achieved good performance on the subject-specific prediction of facial and skeletal shapes and showed clinical application potential in postoperative facial prediction and VSP for orthognathic surgery. [ABSTRACT FROM AUTHOR]

Introduction: n-of-1 trials are undertaken to optimise the evaluation of health technologies in individual patients. They involve a single patient receiving treatments, both interventional and control, consecutively over set periods of time, the order of which is decided at random. Although n-of-1 trials are undertaken in medical research it could be argued they have the utility to be undertaken more frequently. We undertook the National Institute for Health Research (NIHR) commissioned DIAMOND (Development of generalisable methodology for n-of-1 trials delivery for very low volume treatments) project to develop key points to assist clinicians and researchers in designing and conducting n-of-1 trials. Methods: The key points were developed by undertaking a stakeholder workshop, followed by a discussion within the study team and then a stakeholder dissemination and feedback event. The stakeholder workshop sought to gain the perspectives of a variety of stakeholders (including clinicians, researchers and patient representatives) on the design and use of n-of-1 trials. A discussion between the study team was held to reflect on the workshop and draft the key points. Lastly, the stakeholders from the workshop were invited to a dissemination and feedback session where the proposed key points were presented and their feedback gained. Results: A set of 22 key points were developed based on the insights from the workshop and subsequent discussions. They provide guidance on when an n-of-1 trial might be a viable or appropriate study design and discuss key decisions involved in the design of n-of-1 trials, including determining an appropriate number of treatment periods and cycles, the choice of comparator, recommended approaches to randomisation and blinding, the use of washout periods and approaches to analysis. Conclusions: The key points developed in the project will support clinical researchers to understand key considerations when designing n-of-1 trials. It is hoped they will support the wider implementation of the study design. [ABSTRACT FROM AUTHOR]

AbstractIn a vascular interventional surgery robot(VISR), a high transparency master-slave system can aid physicians in the more precise manipulation of guidewires for navigation and operation within blood vessels. However, deformations arising from the movement of the guidewire can affect the accuracy of the registration, thus reducing the transparency of the master-slave system. In this study, the degree of the guidewire’s deformation is analyzed based on the Kirchhoff model. An unsupervised learning-based guidewire shape registration method(UL-GSR) is proposed to estimate geometric transformations by learning displacement field functions. It can effectively achieve precise registration of flexible bodies. This method not only demonstrates high registration accuracy but also performs robustly under different complexity degrees of guidewire shapes. The experiments have demonstrated that the UL-GSR method significantly improves the accuracy of shape point set registration between the master and slave sides, thus enhancing the transparency and operational reliability of the VISR system. [ABSTRACT FROM AUTHOR]

Focussing on the life-long activism of former suffragette and feminist Hazel Hunkins-Hallinan this article presents an innovative re-appraisal of histories of the women’s movement in England during the 1960s and 1970s. Adopting a micro-history approach the article uses Hunkins-Hallinan’s experience of feminist activism to make two connected arguments. The first is to challenge the suggestion that post-suffrage feminist societies such as the Six Point Group lost their ability to participate in and influence campaigns for gender equality into the second half of the twentieth century. The second is to ensure that the contributions made by older women to the women’s movement during the 1960s and 1970s are no longer obscured by the emergence of the Women’s Liberation Movement. Drawing on both arguments the article reveals the previously hidden co-operation and intersection between older and younger generations of women campaigning for women’s rights during these two pivotal decades. [ABSTRACT FROM AUTHOR]

We investigate the quantum modified cosmological dynamical equations in a Friedmann–Lemaître–Robertson–Walker universe filled with a barotropic fluid and a general non-canonical scalar field characterized by a Lagrangian similar to k-essence model but with a potential term. Quantum corrections are incorporated by considering the running of the gravitational and potential couplings, employing the functional renormalization group approach. Covariant conservation of the non-canonical scalar field and the background barotropic fluid is considered separately, imposing a constraint resulting from the Bianchi identity. This constraint determines the evolution of the cut-off scale with the scale factor and also reveals the cosmic fixed points, depending on whether the flow ceases or continues to evolve. We explore how the general non-canonical scalar field parameter affects the different types of cosmic fixed points and how it differs from the canonical case. Furthermore, we establish a bound on the ratio of the renormalization group parameters involving the non-canonical parameter for which the universe may exhibit accelerated expansion for mixed fixed points. This bound indicates the non-canonical scalar field includes larger sets of asymptotically safe renormalization group fixed point which may give rise to an accelerated universe. [ABSTRACT FROM AUTHOR]

The characterization of the solution set for a class of algebraic Riccati inequalities is studied. This class arises in the passivity analysis of linear time-invariant control systems. Eigenvalue perturbation theory for the Hamiltonian matrix associated with the Riccati inequality is used to analyze the extremal points of the solution set. [ABSTRACT FROM AUTHOR]

We study the set of eventually always hitting points for symbolic dynamics with specification. The measure and Hausdorff dimension of such fractal set are obtained. Moreover, we establish the stronger metric results by introducing a new quantity L N (ω) which describes the maximal length of string of zeros of the prefix among the first N iterations of ω in symbolic space. The Hausdorff dimensions of the level sets for this quantity are also completely determined. [ABSTRACT FROM AUTHOR]

In this paper, we consider a new class of generalized enriched cyclic contraction and establish a related fixed point theorem in the setting of a Banach space. As an application to the fractals, we develop a new iterated function system (IFS) consisting of enriched cyclic (bn, ...n(t), βn(t))-contractions. [ABSTRACT FROM AUTHOR]

In this paper, we study the following Minimum Cost Multicovering (MCMC) problem: Given a set of n client points C and a set of m server points S in a fixed dimensional Rd space, determine a set of disks centered at these server points so that each client point c is covered by at least k(c) disks and the total cost of these disks is minimized, where k(·) is a function that maps every client point to some nonnegative integer no more than m and the cost of each disk is measured by the \alpha th power of its radius for some constant α >0. MCMC is a fundamental optimization problem with applications in many areas such as wireless/sensor networking. Despite extensive research on this problem for about two decades, only constant approximations were known for general k. It has been a long standing open problem to determine whether a PTAS is possible. In this paper, we give an affirmative answer to this question by presenting the first PTAS for it. Our approach is based on a number of novel techniques, such as balanced recursive realization and bubble charging, and new counterintuitive insights to the problem. Particularly, we approximate each disk with a set of sub-boxes and optimize them at the subdisk level. This allows us to first compute an approximate disk cover through dynamic programming, and then obtain the desired disk cover through a balanced recursive realization procedure. [ABSTRACT FROM AUTHOR]

Coverings of convex bodies have emerged as a central component in the design of efficient solutions to approximation problems involving convex bodies. Intuitively, given a convex body K and ϵ>0, a covering is a collection of convex bodies whose union covers K such that a constant factor expansion of each body lies within an ϵ expansion of K. Coverings have been employed in many applications, such as approximations for diameter, width, and ϵ-kernels of point sets, approximate nearest neighbor searching, polytope approximations, and approximations to the Closest Vector Problem (CVP). It is known how to construct coverings of size nO(n)/ϵ(n-1)/2 for general convex bodies in Rn. In special cases, such as when the convex body is the ℓp unit ball, this bound has been improved to 2O(n)/ϵ(n-1)/2. This raises the question of whether such a bound generally holds. In this paper we answer the question in the affirmative. We demonstrate the power and versatility of our coverings by applying them to the problem of approximating a convex body by a polytope, under the Banach-Mazur metric. Given a well-centered convex body K and an approximation parameter ϵ>0, we show that there exists a polytope P consisting of 2O(n)/ϵ(n-1)/2 vertices (facets) such that K⊂P⊂K(1+ϵ). This bound is optimal in the worst case up to factors of 2O(n). As an additional consequence, we obtain the fastest (1+ϵ)-approximate CVP algorithm that works in any norm, with a running time of 2O(n)/ϵ(n-1)/2 up to polynomial factors in the input size, and we obtain the fastest (1+ϵ)-approximation algorithm for integer programming. We also present a framework for constructing coverings of optimal size for any convex body (up to factors of 2O(n)). [ABSTRACT FROM AUTHOR]

When developing numerical methods for solving nonlinear minimax problems, the following auxiliary problem arose: in the convex hull of a certain finite set in Euclidean space, find a point that has the smallest norm. In 1971, B. Mitchell, V. Demyanov and V. Malozemov proposed a non-standard algorithm for solving this problem, which was later called the MDM algorithm (based on the first letters of the authors' last names). This article considers a specific minimax problem: finding the smallest volume ball containing a given finite set of points. It is called the Sylvester problem and is a special case of the problem about the Chebyshev center of a set. The Sylvester problem is associated with a convex quadratic programming problem with simplex constraints. To solve this problem, it is proposed to use a variant of the MDM algorithm. With its help, a minimizing sequence of feasible solutions is constructed such that two consecutive feasible solutions differ in only two components. The indices of these components are selected based on certain optimality conditions. We prove the weak convergence of the resulting sequence of feasible solutions that implies that the corresponding sequence of vectors converges in norm to a unique solution to the Sylvester problem. Four typical examples on a plane are given. [ABSTRACT FROM AUTHOR]

The Delaunay triangulation of a set of points P on a hyperbolic surface is the projection of the Delaunay triangulation of the set P ~ of lifted points in the hyperbolic plane. Since P ~ is infinite, the algorithms to compute Delaunay triangulations in the plane do not generalize naturally. Using a Dirichlet domain, we exhibit a finite set of points that captures the full triangulation. We prove that an edge of a Delaunay triangulation has a combinatorial length (a notion we define in the paper) smaller than 12 g - 6 with respect to a Dirichlet domain. To achieve this, we introduce new tools, of intrinsic interest, that capture the properties of length-minimizing curves in the context of closed curves. We then use these to derive structural results on Delaunay triangulations and exhibit certain distance minimizing properties of both the edges of a Delaunay triangulation and of a Dirichlet domain. The bounds produced in this paper depend only on the topology of the surface. They provide mathematical foundations for hyperbolic analogs of the algorithms to compute periodic Delaunay triangulations in Euclidean space. [ABSTRACT FROM AUTHOR]