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Silicon (Si) holds promise as an anode material for lithium-ion batteries (LIBs) as it is widely available and characterized by high specific capacity and suitable working potential. However, the relatively low electrical conductivity of Si and the significantly high extent of volume expansion realized during lithiation hinder its practical application. We prepared N-doped carbon polyhedral micro cage encapsulated Si nanoparticles derived from Co-Mo bimetal metal-organic framework (MOFs) (denoted as Si/CoMo@NCP) and explored their lithium storage performance as anode materials to address these problems. The Si/CoMo@NCP anode exhibited a high reversible lithium storage capacity (1013 mAh g−1 at 0.5 A g−1 after 100 cycles), stable cycle performance (745 mAh g−1 at 1 A g−1 after 400 cycles), and excellent rate performance (723 mAh g−1 at 2 A g−1). Also, the constructed the full-cell NCM 811 //Si/CoMo@NCP exhibited well reversible capacity. The excellent electrochemical performances of Si/CoMo@NCP were attributed to two unique properties. The encapsulation of NCP with doped nitrogen and porous structural carbon improves the electrical conductivity and cycling stability of the molecules. The introductions of metallic cobalt and its oxides help to improve the rate capability and lithiation capacity of the materials following multi-electron reaction mechanisms. [ABSTRACT FROM AUTHOR]

Mathematicians have discovered a new class of mathematical shapes called soft cells that can be used to describe patterns in living organisms. These shapes, which contain as few sharp corners as possible, are able to fit together snugly and are found in various biological processes and structures, such as muscle cells and nautilus shells. Soft cells have been found to be widespread in the real world, including in architecture and biological growth. The discovery of these shapes could improve our understanding of the geometry and material properties of biological systems. [Extracted from the article]

• A high-precision polyhedron algorithm with mixed-order interpolation is proposed. • An optional solution scheme for the efficient octree meshes has been offered. • The accuracy approaches quadratic elements with less computational burden. Computational accuracy and solution efficiency are crucial indicators for evaluating the performance of finite element numerical algorithms, and the corresponding improvements in these areas are the motivation for the development of computational science. In this paper, a flexible and high-precision polyhedron algorithm is proposed in conjunction with SBFEM and the triangle/quadrilateral interpolation functions. The main content can be summarized as follows: The construction equations for a mixed-order polyhedron element are derived, meanwhile, a generalized procedural framework is designed for multi-performance applications, including automatic elements type identification, coupled solutions, and dynamic storage, and the integrated development is completed based on self-developed software GEODYNA. The correctness, convergence and practicability of the proposed method are demonstrated through several examples in different dimensions. The results show that the proposed method obtains results with an error of <3 % compared to theoretical solutions and the fine numerical solutions, while significantly reducing computational costs; Besides, the proposed method overcomes the limitations of conventional methods on mesh shape and can be seamlessly integrated with octree algorithms, which offers a powerful technical means for the efficient and high-precision analyses of bending deformation and stress concentration problems. It is foreseeable that a good application potential in high-precision structural analysis would be revealed. [ABSTRACT FROM AUTHOR]

Credal sets are one of the most important models for describing probabilistic uncertainty. They usually arise as convex sets of probabilistic models compatible with judgments provided in terms of coherent lower previsions or more specific models such as coherent lower probabilities or probability intervals. In finite spaces, credal sets usually take the form of convex polytopes. Many properties of convex polytopes can be derived from their normal cones, which form polyhedral complexes called normal fans. We analyze the properties of normal cones corresponding to credal sets of coherent lower probabilities. For two important classes of coherent lower probabilities, 2-monotone lower probabilities and probability intervals, we provide a detailed description of the normal fan structure. These structures are related to the structure of the extreme points of the credal sets. To arrive at our main results, we provide some general results on triangulated normal fans of convex polyhedra and their adjacency structure. [ABSTRACT FROM AUTHOR]

A high-order accurate, efficient and easy-to-implement method is presented for computing the fluid volume bounded by an arbitrary polyhedron, whether it is convex or non-convex, and an implicitly-defined fluid body. This method is an improved version of a previous one that used a recursive local grid refinement of the polyhedron and linear interpolations to determine the intersections of the interface that delimits the fluid body (or simply fluid-body interface) with the polyhedron boundaries. The proposed method first determines the volume of a polyhedral approximation of the bounded fluid region by using a general clipping-lookup and capping procedure valid for arbitrary polyhedra, where the points of intersection between the polyhedron and the fluid-body interface are obtained using a root-finding method rather than linear interpolations. The approximated polyhedral volume is subsequently corrected by using simple Gaussian quadrature rules over a triangulated approximation of the intersected fluid-body interface to achieve high-order accuracy. Recursive local grid refinement of the polyhedron also enables reductions in fluid volume errors. The proposed method requires no assumption of any particular local parametrization of the fluid-body interface, whether paraboloidal or of any other type, or deriving any complex analytical expressions to compute the volume of fluid contained within the polyhedron, thereby making the method easy to implement and generally applicable to any implicitly-defined function. A detailed assessment shows global fourth-order convergent accuracies on structured and unstructured grids even for complex fluid-body interfaces of a high degree. Speedups of several orders of magnitude with respect to the previous refinement method with linear interpolations are achieved even for relatively coarse grids. Comparisons with other methods are also presented, and the software with the implemented method and tests used for the assessment is freely available. • Novel method for volume of fluid fraction initialization on an arbitrary polyhedron. • Method based on recursive local grid refinement and simple Gaussian quadrature. • Easy to implement method generally applicable to any implicitly defined function. • High-order accuracy is achieved on structured and unstructured grids. • Efficiency speedups of several orders of magnitude are achieved. [ABSTRACT FROM AUTHOR]

• Algebraic invariance property of a polyhedron from which system trajectories converge in finite-time to a bounded polyhedron. • Synthesis of static and dynamic output feedback control laws with structural constraints such as controller decentralization. • Bilinear optimization for solving an associated constrained control problem under persistent bounded disturbances. • Numerical analysis compared with existing techniques show the efficiency of control synthesis with bilinear optimization. In this work, we use the Δ -Invariance property of polyhedral sets to design a stabilizing Static Output Feedback (SOF) for linear discrete-time systems subject to persistent disturbances, assuring the states and control constraints fulfillment. We deduce new algebraic conditions to guarantee that any trajectory emanating from the Δ -Invariant polyhedron remains in it and converges in finite-time to another polyhedral set around the origin, where the trajectory remains ultimately bounded. Thus, the proposed SOF solution for the constrained control problem also requires determining the Δ -invariant and the ultimately bounded polyhedra. Therefore, the proposal considers a bilinear optimization problem whose objective function weighs the two associated polyhedral sets' size and whose constraints are formed by the invariance relation. Moreover, an efficient non-linear optimization solver is used to tackle the present bilinearities. Numerical examples showcase the effectiveness and potential of our proposal. [ABSTRACT FROM AUTHOR]

The integer linear programming approach to structural learning of decomposable graphical models led us earlier to the concept of a chordal graph polytope. An open mathematical question motivated by this research is what is the minimal set of linear inequalities defining this polytope, i.e. what are its facet-defining inequalities, and we came up in 2016 with a specific conjecture that it is the collection of so-called clutter inequalities. In this theoretical paper we give an implicit characterization of the minimal set of inequalities. Specifically, we introduce a dual polyhedron (to the chordal graph polytope) defined by trivial equality constraints, simple monotonicity inequalities and certain inequalities assigned to incomplete chordal graphs. Our main result is that the vertices of this polyhedron yield the facet-defining inequalities for the chordal graph polytope. We also show that the original conjecture is equivalent to the condition that all vertices of the dual polyhedron are zero-one vectors. Using that result we disprove the original conjecture: we find a vector in the dual polyhedron which is not in the convex hull of zero-one vectors from the dual polyhedron. [ABSTRACT FROM AUTHOR]

A recent study conducted at Yunnan Normal University in Kunming, China, has found that a chiral metal-organic polyhedron (MOP) can be used as a stationary phase for gas chromatographic separations. The MOP coated capillary column demonstrated efficient separation of various compounds, including enantiomers and isomers, with high selectivity. The researchers concluded that the chiral MOP shows great potential as a novel type of stationary phase for gas chromatography. This research has been peer-reviewed and published in the Microchemical Journal. [Extracted from the article]

For Takagi–Sugeno (T–S) fuzzy systems, relaxed stability conditions are obtained by more effectively enveloping the trajectory of the membership functions (MFs) in a unified space of MF. Considering an open-loop T–S fuzzy system, the system premise variables operation domain can be divided into a series of subdomains. Based on an MF unified space extremum calculation technique, the MFs extremum values in each premise variable corresponding to the unified space subdomain are calculated. With these extremes, a tight local convex polyhedron enveloping the MF trajectory is constructed in each subdomain. Thus, linear matrix inequality (LMI) stability conditions are derived via a piecewise Lyapunov function. Then, a state-feedback local controller is designed to close the system loop. From a geometric viewpoint, MF extremum enveloping and piecewise linear-approximation methods are both utilized to achieve relaxed stability and robustness conditions. Finally, several examples are adopted to illustrate the metrics of the proposed approaches. [ABSTRACT FROM AUTHOR]

La- and Nb-doped BaTi 2 O 5 (BT 2) spherical glasses were prepared by a containerless aerodynamic levitation method and their glass-forming regions were established. It is found that La-doping on the Ba-site (network-modifier) and Nb-doping on the Ti-site (network-former) show distinct difference in the glass-forming region: less than 10 % La can replace Ba whereas 40 % Nb can incorporate into BT 2 glass. The distinction in glass-forming ability induced by La- and Nb-doping is discussed mainly from the structural arrangement of the glass. Raman spectroscopy analysis shows that La-doping elongates the short Ti–O bonds in the distorted [TiO 5 polyhedra and thus relaxes the network. Nb-doping introduces [NbO 6 polyhedra into BT 2 and there exists a critical doping level (20 %), below which incorporation of Nb into BT 2 relaxes the [TiO n polyhedra by shortening the long Ti–O bond and above which [NbO 6 starts to participate in the network skeleton construction resulting in a dramatic change in the glass structure, which is supported by the dramatic change in the exothermic peak on the DTA curves. This work triggers the speculation that the network-modifiers in BT 2 glass possess a very important role in the structure of network-former skeleton than those in glasses based on traditional network-former oxides such as SiO 2 , GeO 2 and B 2 O 3 , which may provide a useful strategy for modifying the properties of these novel glasses by chemical doping. [ABSTRACT FROM AUTHOR]

The article discusses the law of polyhedra and its continued relevance in the modern world. The author suggests that in order understand the dependence on, and importance of, the law of polyhedra in daily living, it is necessary to search deeper into the ways in which the abstractions of geometry describe the world. Topics include an idea by philosopher and mathematician Plato that five three-dimensional (3D) geometric shapes, called polyhedra, represented the essence of the cosmos, an overview of mathematician Warren Hirsch's law of polyhedra, first proposed in 1957, and the relevance of Hirsch's law to every day life, such as situations in which more than four things can vary independently. INSETS: EDGES, CORNERS AND FACES;2000 YEARS OF ALGORITHMS;STRAIGHT DOWN THE LINE.

A convex polyhedron classifier that encloses the minority class using a combination of hyperplanes is potentially effective in imbalanced classification. To construct an easy-to-use convex polyhedron classifier, this paper first presents a theoretical foundation for determining whether a point is within the convex hull of a finite point set. This foundation corresponds to a geometric method in which the result is expressed as a separating hyperplane. If the given point and the given convex hull are located on either side of the learned hyperplane, this indicates that the point is outside of the convex hull. Otherwise, the conclusion that the point is within the convex hull can be obtained. As a generalization of the geometric method, a convex polyhedron classifier is further proposed for binary classification. If two finite point sets are polyhedrally separable, a series of hyperplanes can be learned as a combined (piecewise linear) classifier, which surrounds a point set that is inside using a convex polyhedron and excludes the other point set that is outside. Experimental results on twelve real-world datasets show that the proposed classifier is generally better than the other two piecewise linear classifiers. Moreover, a comparison with several types of support vector machines confirms its competitiveness. [ABSTRACT FROM AUTHOR]

The article offers step-by-step instructions for making congruent isosceles or scalene polyhedra triangles.

Highlights • Compared with homogeneous MJSs [1,9,34,38], the considered systems with nonhomogeneous Markov chain in this paper are more general, and the former can be viewed as a special case of the proposed approach. • In order to guarantee the system behaviors stay within a given threshold during a fixed time interval, an observer-based controller is designed and novel sufficient criteria are derived. • A numerical example and a DC motor device are exploited to illustrate the correctness and applicability of the proposed design technique in this paper. Abstract The problem of observer-based finite-time H ∞ control for discrete-time Markov jump systems with time-varying transition probabilities and uncertainties is studied in this paper, in which time-varying transition probabilities are modelled as convex polyhedron, and the parameter uncertainty satisfies norm-bounded. First of all, a Luenberger observer is designed to measure the system state. Then, observer-based controller is constructed to ensure the stochastic finite-time boundedness of the resulting closed-loop system with an H ∞ performance. Furthermore, sufficient conditions are derived in light of linear matrix inequalities. In the end, the flexibility and applicability of the developed methods are demonstrated by two illustrative examples. [ABSTRACT FROM AUTHOR]

Presents an algorithm for the interference detection among solids and surfaces. Occurrence of interference problems; Representation of object as polyhedra or piecewise planar surfaces; Types of interference detection.

The article provides information on the Császá;r polyhedron. Discovered by Hungarian topologist Ákos Császár, the polyhedrons have skeletons which are isomorphic with graphs and sets of vertexes joined by lines. Topologically equivalent to a sphere, a Császár polyhedron is a bizarre solid with a different color map on a torus.

Discusses a method for determining which parts of three-dimensional objects are visible and invisible when the objects are rotated about some axis using a polygon comparison scheme. Classification and variation of the relationship between two polygons; Definition of a rotation table; Means for rapid determination of visible and hidden line relationships.

Focuses on the plaiting of polyhedrons designed by philosopher Plato and the asymmetrical yin-yang-lee. Information on plaiting each Platonic solid from n congruent straight strips devised by Jean J. Pedersen, a mathematics teacher at the University of Santa Clara in California; Application of the plaiting on tetrahedron; Citation to the resemblance of dodecahedron with a sphere as the reason why Plato identified the universe with the shape.

The article offers information on the challenge of making new polyhedra using just isosceles triangles of Congruent Isosceles triangles. Topics discussed include acute isosceles triangle from the regular pentagon MAT; using acute isosceles triangles cut from regular pentagons; and making deltahedra using obtuse isosceles pentagon triangles.

This paper presents the concept of convex lifting, which will be proven to enable significant implementation benefits for the class of piecewise affine controllers. Accordingly, two different algorithms to construct a convex lifting for a given polyhedral/polytopic partition will be presented. These two algorithms rely on either the vertex or the halfspace representation of the related polyhedra. Also, we introduce an algorithm to refine a polyhedral partition, which does not admit a convex lifting, into a convexly liftable one. Furthermore, two different schemes will be put forward to considerably reduce both the memory footprint and the online evaluation effort, which play a key role in implementation of piecewise affine controllers. Finally, these results will be illustrated via numerical examples and a complexity analysis. [ABSTRACT FROM AUTHOR]

This paper presents an efficient algorithm for the sequential positioning, also called nested dissection, of two planes in an arbitrary polyhedron. Two planar interfaces are positioned such that the first plane truncates a given volume from this arbitrary polyhedron and the next plane truncates a second given volume from the residual polyhedron. This is a relevant task in the numerical simulation of three-phase flows when resorting to the geometric Volume-of-Fluid (VoF) method (Hirt and Nichols, 1981) with a Piecewise Linear Interface Calculation (PLIC) (Youngs, 1982). An efficient algorithm for this task significantly speeds up the three-phase PLIC algorithm. The present study describes a method based on a recursive application of the Gaussian divergence theorem, where the fact that the truncated polyhedron shares multiple faces with the original polyhedron can be exploited to reduce the computational effort. A careful choice of the coordinate system origin for the volume computation allows for successive positioning of two planes without reestablishing polyhedron connectivity. Combined with a highly efficient root finding, this results in a significant performance gain in the reconstruction of the three-phase interface configurations. The performance of the new method is assessed in a series of carefully designed numerical experiments. Compared to a conventional decomposition-based approach, the number of iterations and, thus, of the required truncations was reduced by up to an order of magnitude. The PLIC positioning run-time was reduced by about 90% in our reference implementation. Integrated into the multi-phase flow solver Free Surface 3D (FS3D), an overall performance gain of about 20% was achieved. The reference implementation of the efficient sequential PLIC positioning is available as a Fortran module at https://doi.org/10.18419/darus-2488. Allowing for simple integration into existing numerical schemes, the proposed algorithm is self-contained, requiring no external decomposition libraries. • Efficient sequential positioning of PLIC planes for multi-material cells. • Enhancement of the geometric VoF method for three-phase flows. • Numerical assessment with an extensive sample set of input data. • Performance insensitive with respect to volume fractions and normal orientations. • Significant performance gain both stand-alone and within a VoF flow solver. [ABSTRACT FROM AUTHOR]

The VOFTools library includes efficient analytical and geometrical routines for (1) area/volume computation, (2) truncation operations that typically arise in VOF (volume of fluid) methods, (3) area/volume conservation enforcement (VCE) in PLIC (piecewise linear interface calculation) reconstruction and(4) computation of the distance from a given point to the reconstructed interface. The computation of a polyhedron volume uses an efficient formula based on a quadrilateral decomposition and a 2D projection of each polyhedron face. The analytical VCE method is based on coupling an interpolation procedure to bracket the solution with an improved final calculation step based on the above volume computation formula. Although the library was originally created to help develop highly accurate advection and reconstruction schemes in the context of VOF methods, it may have more general applications. To assess the performance of the supplied routines, different tests, which are provided in FORTRAN and C , were implemented for several 2D and 3D geometries. Program summary Program Title: VOFTools Program Files doi: http://dx.doi.org/10.17632/brrgt645bh.1 Licensing provisions: GNU General Public License, version 3 Programming language: FORTRAN and C , with C interfaces Nature of problem: The package of routines includes simple and efficient analytical and geometrical tools for area/volume computation, truncation operations that typically arise in VOF (volume of fluid) methods, area/volume conservation enforcement (VCE) in PLIC (piecewise linear interface calculation) reconstruction and computation of the distance from a given point to the reconstructed interface. Solution method: The volume (area in 2D) computation of a polyhedron (polygon in 2D) uses an efficient formula based on a quadrilateral decomposition and a 2D projection of each polyhedron face. The analytical VCE method is based on coupling an interpolation bracketing procedure with an improved final calculation step based on the above volume computation formula. Also, the exact distance from a given point to a reconstructed polygonal interface is calculated. Restrictions: Convex 2D and 3D polytopes. [ABSTRACT FROM AUTHOR]

The discovery of a formal process model from event logs describing real process executions is a challenging problem that has been studied from several angles. Most of the contributions consider the extraction of a model as a one-class supervised learning problem where only a set of process instances is available. Moreover, the majority of techniques cannot generate complex models, a crucial feature in some areas like manufacturing. In this paper we present a fresh look at process discovery where undesired process behaviors can also be taken into account. This feature may be crucial for deriving process models which are less complex, fitting and precise, but also good on generalizing the right behavior underlying an event log. The technique is based on the theory of convex polyhedra and satisfiability modulo theory (SMT) and can be combined with other process discovery approach as a post processing step to further simplify complex models. We show in detail how to apply the proposed technique in combination with a recent method that uses numerical abstract domains. Experiments performed in a new prototype implementation show the effectiveness of the technique and the ability to be combined with other discovery techniques. [ABSTRACT FROM AUTHOR]

Active-set methods are recognized to often outperform other methods in terms of speed and solution accuracy when solving small-size quadratic programming (QP) problems, making them very attractive in embedded linear model predictive control (MPC) applications. A drawback of active-set methods is the lack of tight bounds on the worst-case number of iterations, a fundamental requirement for their implementation in a real-time system. Extensive simulation campaigns provide an indication of the expected worst-case computation load, but not a complete guarantee. This paper solves such a certification problem by proposing an algorithm to compute the exact bound on the maximum number of iterations and floating point operations required by a state-of-the-art dual active-set QP solver. The algorithm is applicable to a given QP problem whose linear term of the cost function and right-hand side of the constraints depend linearly on a vector of parameters, as in the case of linear MPC. In addition, a new solver is presented that combines explicit and implicit MPC ideas, guaranteeing improvements of the worst-case computation time. The ability of the approach to exactly quantify memory and worst-case computation requirements is tested on a few MPC examples, also highlighting when online optimization should be preferred to explicit MPC. [ABSTRACT FROM PUBLISHER]

The article looks into the role of geometry in fashioning an inclusive mathematics education and the differences made by the ATM MATs, a resource that can be used to create tiling patterns and polyhedra. Topics mentioned include the finite and the infinite, tessellations and polyhedra, and symm-nets, as well as pop up polyhedra, nets and polyhedra, and the infinite sequences of polyhedra. It also discusses the vertex codes produced by the author to support the exploration of tessellations.

In this paper, a displacement based finite element framework for general three-dimensional convex polyhedra is presented. The method is based on a semi-analytical framework, the scaled boundary finite element method. The method relies on the definition of a scaling center from which the entire boundary is visible. The salient feature of the method is that the discretizations are restricted to the surfaces of the polyhedron, thus reducing the dimensionality of the problem by one. Hence, an explicit form of the shape functions inside the polyhedron is not required. Conforming shape functions defined over arbitrary polygon, such as the Wachpress interpolants are used over each surface of the polyhedron. Analytical integration is employed within the polyhedron. The proposed method passes patch test to machine precision. The convergence and the accuracy properties of the method is discussed by solving few benchmark problems in linear elasticity. [ABSTRACT FROM AUTHOR]

Despite the recognition of the enormous potential of periodic trusses for use in a broad range of technologies, there are no widely-accepted descriptors of their structure. The terminology has been based loosely either on geometry of polyhedra or of point lattices: neither of which, on its own, has an appropriate structure to fully define periodic trusses. The present article lays out a system for classification of truss structure types. The system employs concepts from crystallography and geometry to describe nodal locations and connectivity of struts. Through a series of illustrative examples of progressively increasing complexity, a rational taxonomy of truss structure is developed. Its conceptual evolution begins with elementary cubic trusses, increasing in complexity with non-cubic and compound trusses as well as supertrusses, and, finally, with complex trusses. The conventions and terminology adopted to define truss structure yield concise yet unambiguous descriptions of structure types and of specific (finite) trusses. The utility of the taxonomy is demonstrated by bringing into alignment a disparate set of ad hoc and incomplete truss designations previously employed in a broad range of science and engineering fields. Additionally, the merits of a particular compound truss (comprising two interpenetrating elementary trusses) is shown to be superior to the octet truss for applications requiring high stiffness and elastic isotropy. By systematically stepping through and analyzing the finite number of structure types identified through the present classification system, optimal structures for prescribed mechanical and functional requirements are expected to be ascertained in an expeditious manner. [ABSTRACT FROM AUTHOR]

The news correspondents obtained a quote from the research from theUniversity of the Chinese Academy of Sciences, "Herein, we present anovel strategy using a dual recognition by two types of targetedligands, based on photoelectrochemical (PEC) sensing for detection ofSARS-CoV-2 spike protein. According to the news reporters, the research concluded: "The workprovides useful advance for the development of PEC biosensors forsensitive detection of SARS-CoV-2.". [Extracted from the article]

Classical theorems on the complete characterization of stability boundaries provided little information about the existence and types of unstable equilibrium points on a stability boundary. In this technical note, we derive analytical results and sufficient conditions about the existence of all types of unstable equilibrium points in a dynamical system whose stability regions are uniformly bounded. Some applications of these analytical results are illustrated using electric power systems. [ABSTRACT FROM PUBLISHER]

The equations of motion are derived, and the existence of symmetrical radial solutions of the general spatial ( N + 1)-body problem, in which N bodies of identical mass m are found at the initial instant of time at the vertices of polyhedrons known as Platonic bodies ( N = 4, 6, 8, 12, 20) and the ( N + 1)-th body of mass M is found at the geometrical centre of the polyhedron, is proved rigorously, analytically and numerically. It is assumed that all the bodies are attracted according to Newton's law and that the initial velocities of the bodies with mass m are directed along a radius vector. The solutions found are homothetically expanding (contracting) central configurations. A geometrical image of the solutions is presented for a hexahedron, and their evolution is described for all the Platonic bodies. A distinguishing characteristic of the solutions is the value of the rate of expansion (contraction) of a configuration, which depends on the attraction law, the number of vertices in the polyhedron and its configuration. [ABSTRACT FROM AUTHOR]

This note presents an efficient approach for the evaluation of multi-parametric mixed integer quadratic programming (mp-MIQP) solutions, occurring for instance in control problems involving discrete time hybrid systems with quadratic cost. Traditionally, the online evaluation requires a sequential comparison of piecewise quadratic value functions. We introduce a lifted parameter space in which the piecewise quadratic value functions become piecewise affine and can be merged to a single value function defined over a single polyhedral partition without any overlaps. This enables efficient point location approaches using a single binary search tree. Numerical experiments with a power electronics application demonstrate an online speedup up to an order of magnitude. We also show how the achievable online evaluation time can be traded off against the offline computational time. [ABSTRACT FROM PUBLISHER]

We introduce a novel formalism that performs dimensionality reduction and captures topological features (such as the shape of the observed data) to conduct pattern classification. This mission is achieved by: 1) reducing the dimension of the observed variables through a kernelized radial basis function technique and expressing the latent variables probability distribution in terms of the observed variables; 2) disclosing the data manifold as a 3-D polyhedron via the $\alpha $ -shape constructor and extracting topological features; and 3) classifying a data set using a mixture of multinomial distributions. We have applied our methodology to the problem of age-invariant face recognition. Experimental results obtained demonstrate the efficiency of the proposed methodology named nonlinear topological component analysis when compared with some state-of-the-art approaches. [ABSTRACT FROM PUBLISHER]

The atoms in disordered structures such as liquids and glasses are arranged in a complex manner. Their atomic arrangements are often studied using the Voronoi tessellation method. This method divides the space containing atoms into regions called Voronoi polyhedra. Each polyhedron contains one atom. From the structure of the polyhedron, we can know the bond network, or the topology, of the cluster composed of the atoms in the polyhedron and its neighbors. Thus, the topological order can be characterized by identifying the most dominant Voronoi polyhedron. For this purpose, the Voronoi index has long been used. However, it does not specify how polygons are arranged in the polyhedron. Therefore, polyhedra with different graph structures can have the same index. This problem can lead to failure in characterizing the topological order. In addition, the Voronoi index does not tell anything about the chemical arrangement, namely how different types of atoms are arranged in the cluster. To characterize both of the topological and chemical order of disordered structures, a polyhedron-naming system called the polyhedron code has been developed and implemented in the Vorotis software. This paper presents the essential features of Vorotis. Program Title: Vorotis CPC Library link to program files: https://doi.org/10.17632/4548pnvzpy.1 Developer's repository link: https://doi.org/10.5281/zenodo.6069726 Code Ocean capsule: https://doi.org/10.24433/CO.1700993.v1 Licensing provisions: MIT Programming language: Fortran, Csh, Python Nature of problem: Characterizing the arrangement of atoms in substances. Solution method: The polyhedron code is combined with the Voronoi tessellation method. Additional comments including restrictions and unusual features: The current version of Vorotis assumes that every vertex of a Voronoi polyhedron meets three faces. [1] K. Nishio, T. Miyazaki, Sci. Rep. 6 (2016) 23455. [2] K. Nishio, T. Miyazaki, Sci. Rep. 7 (2017) 40269. [3] K. Nishio, T. Miyazaki, Polyhedron and Polychoron Codes for Describing Atomic Arrangements, in Nanoinformatics edited by I. Tanaka (Springer, Singapore, 2018), pp. 97-130. [4] K. Nishio, T. Miyazaki, Phys. Rev. Research 2 (2020) 023193. [5] K. Nishio, A. K. A. Lu, J. Non-Cryst. Solids 576 (2022) 121254. [ABSTRACT FROM AUTHOR]

This paper proposes a higher-order accurate curvature computation method for volume-of-fluid (VOF) interfaces on 3D non-orthogonal structured meshes. Analogous to the height-function (HF) method, a novel approach is introduced to identify columns of control volumes that straddle the interface. This is followed by a volume conserving piecewise-linear interface construction (PLIC). In the interest of efficiency and generality, the latter employs a novel sweep-plane algorithm with bracketing on convex-decomposed control volumes in each column. The emphasis is on the generalisation of a PLIC-based least squares polynomial surface fitting procedure owing to its invariance with respect to local coordinate rotations in 3D. The PLIC representation of the interface is then smoothed by iteratively refining the PLIC facet normals. The interface curvature is finally computed analytically by fitting either second- or fourth-order polynomial surfaces to local stencils of PLIC facets in a least squares manner. Formal second- and fourth-order accuracy of interface curvature is demonstrated by comparing numerical results with a variety of analytical interface definitions. • A novel conservative PLIC procedure for convex-decomposed arbitrary polyhedra. • Second- or fourth-order polynomial surfaces fitted through local PLIC stencils. • Proof of curvature invariance with respect to rotations of the local coordinate system about its z -axis. • Second- and fourth-order accurate curvature computation on 3D non-orthogonal structured grids. [ABSTRACT FROM AUTHOR]

Quantum polyhedra constructed from angular momentum operators are the building blocks of space in its quantum description as advocated by loop quantum gravity. Here we extend previous results on the semiclassical properties of quantum polyhedra. Regarding tetrahedra, we compare the results from a canonical quantization of the classical system with a recent wave-function-based approach to the large-volume sector of the quantum system. Both methods agree in the leading order of the resulting effective operator (given by an harmonic oscillator), while minor differences occur in higher corrections. Perturbative inclusion of such corrections improves the approximation to the eigenstates. Moreover, the comparison of both methods leads also to a full wave function description of the eigenstates of the (square of the) volume operator at negative eigenvalues of large modulus. For the case of general quantum polyhedra described by discrete angular momentum quantum numbers we formulate a set of quantum operators fulfilling in the semiclassical regime the standard commutation relations between momentum and position. Differently from previous formulations, the position variable here is chosen to have dimension of (Planck) length squared which facilitates the identification of quantum corrections. Finally, we provide expressions for the pentahedral volume in terms of Kapovich-Millson variables. [ABSTRACT FROM AUTHOR]

We propose and experimentally demonstrate an approximate universal-not (unot) operation that is robust against operational errors. In our proposal, the unot operation is composed of stochastic unitary operations represented by the vertices of regular polyhedrons. The operation is designed to be robust against random operational errors by increasing the number of unitary operations (i.e., reference axes). Remarkably, no increase in the total number of measurements nor additional resources are required to perform the unot operation. Our method can be applied in general to reduce operational errors to an arbitrary degree of precision when approximating any antiunitary operation in a stochastic manner. [ABSTRACT FROM AUTHOR]

We analyse the geometric properties of an artistic polyhedral structure in several different ways. [ABSTRACT FROM AUTHOR]

The article describes a lampshade that embodies a polyhedron. It cites the defining properties of archimedian polyhedrons, which include all faces are congruent and every vertex is regular. It notes that the lampshade is a rhombic triacontahedron (RT), with 30 identical units, 20 three-petal flowers that are the vertices of a dodecahedron and 12 five-petal flowers that are vertices of an icosahedron.

Abstract: A recently formulated frame-invariant monotonicity criterion and slope limiter for vectors was applied to the Staggered Mesh Godunov-SMG/Q scheme for Lagrangian and ALE hydrodynamics. The VIP (vector-space polygon or polyhedron) was shown to be a natural extension of monotonicity constraints from scalar to vector variables. Taking notice of the fact that gradients of scalars are vectors, we now seek to use this new concept to devise better, and perhaps truly multidimensional, slope limiters for scalar variables. The proposed scheme constitutes a generalization of a 1D monotonic-averaging limiter for scalars, to a VIP type limiter for (vector) gradients of scalars in 2D or 3D. Test cases computed by the SMG/ALE scheme, using the new VIP limiter for gradients, are presented. As we can see from them, the new method, while being robust in strong shock computations, can better preserve gradients of density under advection. [Copyright &y& Elsevier]

This technical note proposes a saturation-based switching anti-windup design for the enlargement of the domain of attraction of the closed-loop system. A widely adopted method of dealing with an m-dimensional saturated linear feedback is to express it as a linear combination of a set of 2^m auxiliary linear feedbacks. For each value of the state, these auxiliary linear feedbacks form a convex polyhedron of 2^m vertices in the input space. We propose to divide this convex polyhedron into several convex sub-polyhedrons, each of which is defined as the convex hull of a subset of the auxiliary feedbacks. Whenever the value of the saturated linear feedback falls into a sub-polyhedron, it can be expressed as a linear combination of a subset of the 2^m auxiliary linear feedbacks that define the sub-polyhedron and thus a less conservative result can be expected. A separate anti-windup gain is designed for each sub-polyhedron by using a common quadratic Lyapunov function and implemented when the value of the saturated linear feedback falls into this sub-polyhedron. Simulation results indicate that such a saturation-based switching anti-windup design has the ability to significantly enlarge the domain of attraction of the closed-loop system. [ABSTRACT FROM PUBLISHER]

Abstract: Multi-objective optimization problems (MOPs) with interval parameters are ubiquitous in real-world applications. Existing evolutionary optimization methods, however, aim to obtain a set of well-converged and evenly-distributed Pareto-optimal solutions. In this paper, we presented a novel evolutionary algorithm (EA) that interacts with a decision maker (DM) during the optimization process to obtain the most preferred solution. The theory of preference polyhedron for the optimization problem with interval parameters was developed first. An interactive evolutionary algorithm (IEA) for MOPs with interval parameters was then proposed based on the theory of preference polyhedron. The algorithm periodically provides a set of non-dominated solutions to the DM; a preference polyhedron is constructed in the objective space by taking the worst solution chosen by the DM as the vertex. The solutions with the same rank are sorted based on the polyhedron constructed. Finally, our method was empirically evaluated on several MOPs with interval parameters where the value functions were used to simulate the DM’s responses. The numerical results indicated that our method is simpler and more efficient than the a posteriori method. [Copyright &y& Elsevier]

We introduce a class of propagation invariant spatiotemporal optical wave packets with spherical harmonic symmetries in their field configurations. The evolution of these light orbitals is considered theoretically in anomalously dispersive media, and their spinning dynamics are analyzed in terms of their corresponding energy flows. Similarly, localized waves generated via spherical superposition from Archimedean and Platonic solids in ...-ѡ space are investigated in this work. [ABSTRACT FROM AUTHOR]

This paper proposes multiplexer-flip-flops (MUX-FFs) to be a high-throughput and low-cost solution for serial link transmitters. We also propose multiplexer-latches (MUX-Latches) that possess the logic function of combinational circuits and storing capacity of sequential circuits. Adopting the pipeline with MUX-FFs, which are composed of cascaded latches and MUX-Latches, many latch gates for sequencing can be removed. Analysis and simulation results show that an 8-to-1 serializer in the pipeline topology with MUX-FFs reduces 52% gate-count compared to that in the traditional pipeline topology. To verify the functions of the proposed design, two chips are implemented with the proposed 4-to-1 MUX-FF and 8-to-1 serializer with MUX-FFs in 90 nm CMOS technology. The measured results show that the MUX-FF and the proposed serializer with MUX-FFs are almost bit-error-free (with BER <; 10-12 ), operating at up to 6 Gbits/s and 12 Gbit/s, respectively. [ABSTRACT FROM PUBLISHER]

We analyze the structure and stability of singular singly quantized vortices in a rotating spin-1 Bose-Einstein condensate. We show that the singular vortex can be energetically stable in both the ferromagnetic and polar phases despite the existence of a lower-energy nonsingular coreless vortex in the ferromagnetic phase. The spin-1 system exhibits an energetic hierarchy of length scales resulting from different interaction strengths, and we find that the vortex cores deform to a larger size determined by the characteristic length scale of the spin-dependent interaction: We show that in the ferromagnetic phase the resulting stable core structure, despite apparent cothplexity, can be identified as a single polar core with an axially symmetric density profile which is nonvanishing everywhere. In the polar phase, the energetically favored core deformation leads to a splitting of a singly quantized vortex into a pair of half-quantum vortices that preserves the topology of the vortex outside the extended core region, but breaks the axial symmetry of the core. The resulting half-quantum vortices exhibit nonvanishing ferromagnetic cores. [ABSTRACT FROM AUTHOR]

Abstract: It will be shown that probabilities of infinite-valued events represented by formulas in Łukasiewicz propositional logic are in one-to-one correspondence with tight probability measures over rational polyhedra in the unit hypercube. This result generalizes a recent work on rational measures of polyhedra and provides an elementary geometric approach to reasoning under uncertainty with states in Łukasiewicz logic. [Copyright &y& Elsevier]