Point Configurations Research Articles

Sweeps, Polytopes, Oriented Matroids, and Allowable Graphs of Permutations

A sweep of a point configuration is any ordered partition induced by a linear functional. Posets of sweeps of planar point configurations were formalized and abstracted by Goodman and Pollack under the theory of allowable sequences of permutations. We introduce two generalizations that model posets of sweeps of higher dimensional configurations. Sweeps of a point configuration are in bijection with faces of an associated sweep polytope. Mimicking the fact that sweep polytopes are projections of permutahedra, we define sweep oriented matroids as strong maps of the braid oriented matroid. Allowable sequences are then the sweep oriented matroids of rank 2, and many of their properties extend to higher rank. We show strong ties between sweep oriented matroids and both modular hyperplanes and Dilworth truncations from (unoriented) matroid theory. Pseudo-sweeps are a generalization of sweeps in which the sweeping hyperplane is allowed to slightly change direction, and that can be extended to arbitrary oriented matroids in terms of cellular strings. We prove that for sweepable oriented matroids, sweep oriented matroids provide a sphere that is a deformation retract of the poset of pseudo-sweeps. This generalizes a property of sweep polytopes (which can be interpreted as monotone path polytopes of zonotopes), and solves a special case of the strong Generalized Baues Problem for cellular strings. A second generalization are allowable graphs of permutations: symmetric sets of permutations pairwise connected by allowable sequences. They have the structure of acycloids and include sweep oriented matroids.

Determinantal Varieties From Point Configurations on Hypersurfaces

Abstract We consider the scheme $X_{r,d,n}$ parameterizing $n$ ordered points in projective space $\mathbb {P}^{r}$ that lie on a common hypersurface of degree $d$. We show that this scheme has a determinantal structure, and we prove that it is irreducible, Cohen–Macaulay, and normal. Moreover, we give an algebraic and geometric description of the singular locus of $X_{r,d,n}$ in terms of Castelnuovo–Mumford regularity and $d$-normality. This yields a characterization of the singular locus of $X_{2,d,n}$ and $X_{3,2,n}$.

Lower Bound for the Green Energy of Point Configurations in Harmonic Manifolds

In this paper, we get the sharpest known to date lower bounds for the minimal Green energy of the compact harmonic manifolds of any dimension. Our proof generalizes previous ad-hoc arguments for the most basic harmonic manifold, i.e. the sphere, extending it to the general case and remarkably simplifying both the conceptual approach and the computations.

Tritium removal from JET-ILW after T and D–T experimental campaigns

After the second Deuterium–Tritium Campaign (DTE2) in the JET tokamak with the ITER-Like Wall (ILW) and full tritium campaigns that preceded and followed after the DTE2, a sequence of fuel recovery methods was applied to promote tritium removal from wall components. The sequence started with several days of baking of the main chamber walls at 240 °C and at 320 °C. Subsequently, baking was superimposed with Ion-Cyclotron Wall Conditioning (ICWC) and Glow Discharge Conditioning (GDC) cleaning cycles in deuterium. Diverted plasma operation in deuterium with different strike point configurations, including a Raised Inner Strike Point (RISP) configuration, and with different plasma heating—Ion Cyclotron Resonance Frequency (ICRF) and Neutral Beam Injection (NBI)—concluded the cleaning sequence. Tritium content in plasma and in the pumped gas was monitored throughout the experiment. The applied fuel recovery methods allowed reducing the residual tritium content in deuterium NBI-heated plasmas to about 0.1% as deduced from neutron rate measurements. This value is well below the requirement of 1% set by the maximum 14 MeV fusion neutron budget allocated in the ensuing deuterium plasma campaign. The quantified tritium removal over the course of the experiment was 13.4±0.7×1022 atoms or 0.67±0.03 g with ∼58% attributed to baking, ∼12.5% to ICWC, ∼26% to GDC, and ∼3.5% to first low power RISP plasmas. The experimentally estimated amount of removed tritium is in good agreement with long-term tritium accounting by the JET tritium reprocessing plant, in which the unaccounted amount was reduced by 0.71 g after the cleaning experiment.

New variants of perfect non-crossing matchings

Given a set of points in the plane, we are interested in matching them with straight line segments. We focus on perfect (all points are matched) non-crossing (no two edges intersect) matchings. Apart from the well known MinMax variation, where the length of the longest edge is minimized, we extend work by looking into different optimization variants such as MaxMin, MinMin, and MaxMax. We consider both the monochromatic and bichromatic versions of these problems and by employing diverse techniques we provide efficient algorithms for various input point configurations.

The VC-Dimension and Point Configurations in $${\mathbb F}_q^2$$

The VC-Dimension and Point Configurations in $${\mathbb F}_q^2$$

A Methodology of Traffic Simulation, a Preliminary Work for VANET Technology

Urban regions across the globe continue to grapple with a substantial problem of traffic congestion, which has adverse effects on both the environment and the overall well-being of citizens. Intelligent Transport Systems (ITS) are essential for dealing with and reducing congestion by employing diverse technological solutions. ITS represents a powerful toolbox of technologies and strategies for managing and alleviating traffic congestion in modern cities. Taking into consideration that their real implementation is very expensive, a preliminary simulation work is required. This paper aims to propose a way for conducting a traffic simulation for an intersection, using real data. It provides a comprehensive description of the necessary steps to take in order to carry out this simulation and conduct subsequent analyses. The simulators used for this purpose are SUMO and VEINS. The findings presented here demonstrate that the configuration of a crucial point in the road network has specific impacts on vehicular traffic and should be taken into account when making decisions about altering or establishing the topology of key points in the road network within a city.

Simulasi Setting WLC berdasarkan kebijakan VLAN pada Client yang terhubung ke AP di Gedung Gamma (Administrasi) Sekolah Vokasi IPB

IPB University Vocational School has several buildings including the Gamma Building as an administrative center. In the Gamma Building several access points were installed to support administrative activities. The gamma building consists of 4 floors where each floor has different needs. The 1st floor is for student administration activities, the 2nd floor is for financial administration, data and leadership rooms, the 3rd floor is lecturer meeting rooms and leadership rooms and the 4th floor is lecturer meeting rooms and lecturer rooms. Management is required to set the AP point configuration based on the SSID, so WLC is used to set the SSID based on the VLAN created. The methods used in making this simulation are observation, design and testing. Observations were carried out to see the need for access points in the gamma building and what SSIDs would be created, including VLAN 10 SSID for leadership, VLAN 20 SSID for lecturers, VLAN 30 SSID for students, VLAN 40 SSID for staff and VLAN 50 SSID for guests. Design is the process of making a network topology in a Cisco packet tracer simulation based on observations. Tests are carried out whether the SSID is obtained by each client based on a certain VLAN. Obtained from the results of SSID testing on each floor based on the provisions where on the 1st floor all SSID, on the 2nd floor Leaders, Lecturers and staff, on the 3rd floor Leaders, lecturers and guests and on the 4th floor leaders and lecturers. Each client gets its SSID based on the VLAN that is set.

Landscape complexity beyond invariance and the elastic manifold

AbstractThis paper characterizes the annealed, topological complexity (both of total critical points and of local minima) of the elastic manifold. This classical model of a disordered elastic system captures point configurations with self‐interactions in a random medium. We establish the simple versus glassy phase diagram in the model parameters, with these phases separated by a physical boundary known as the Larkin mass, confirming formulas of Fyodorov and Le Doussal. One essential, dynamical, step of the proof also applies to a general signal‐to‐noise model of soft spins in an anisotropic well, for which we prove a negative‐second‐moment threshold distinguishing positive from zero complexity. A universal near‐critical behavior appears within this phase portrait, namely quadratic near‐critical vanishing of the complexity of total critical points, and cubic near‐critical vanishing of the complexity of local minima. These two models serve as a paradigm of complexity calculations for Gaussian landscapes exhibiting few distributional symmetries, that is, beyond the invariant setting. The two main inputs for the proof are determinant asymptotics for non‐invariant random matrices from our companion paper (Ben Arous, Bourgade, McKenna 2022), and the atypical convexity and integrability of the limiting variational problems.

An ElectroThermal Digital Twin for Design and Management of Radiation Heating in Industrial Processes

The design and management of thermoforming systems based on radiation heat transfer require the development of a mathematical model that can be used at all stages of the system's life cycle. For this reason, in this paper, we present a digital twin based on a hybrid ElectroThermal model that can integrate mathematical equations and data acquired in the field. The model's validity is verified with experiments performed on a test bench. The presented model is modular and can be easily used to represent new configurations of the heating elements for simulation and design. Thanks to the low computational complexity of the proposed Digital Twin, it enables the development of advanced control strategies and the analysis and optimization of the main geometric parameters of the system. In addition, it can support the identification of the best configuration and choice of measurement points.

Exploring the rigidity of planar configurations of points and rods

Exploring the rigidity of planar configurations of points and rods

Self-Dual Matroids from Canonical Curves

Self-dual configurations of 2n points in a projective space of dimension n – 1 were studied by Coble, Dolgachev–Ortland, and Eisenbud–Popescu. We examine the self-dual matroids and self-dual valuated matroids defined by such configurations, with a focus on those arising from hyperplane sections of canonical curves. These objects are parametrized by the self-dual Grassmannian and its tropicalization. We tabulate all self-dual matroids up to rank 5 and investigate their realization spaces. Following Bath, Mukai, and Petrakiev, we explore algorithms for recovering a curve from the configuration. A detailed analysis is given for self-dual matroids arising from graph curves.

𝑘-chain configurations of points over 𝑝-adic rings

This paper uses exponential sum methods to detect the presence of k k -chains of points whose endpoints belong to proper subsets of finite p p -adic rings.

Reworking Geometric Morphometrics into a Methodology of Transformation Grids

AbstractToday’s typical application of geometric morphometrics to a quantitative comparison of organismal anatomies begins by standardizing samples of homologously labelled point configurations for location, orientation, and scale, and then renders the ensuing comparisons graphically by thin-plate spline as applied to group averages, principal components, regression predictions, or canonical variates. The scale-standardization step has recently come under criticism as unnecessary and indeed inappropriate, at least for growth studies. This essay argues for a similar rethinking of the centering and rotation, and then the replacement of the thin-plate spline interpolant of the resulting configurations by a different strategy that leaves unexplained residuals at every landmark individually in order to simplify the interpretation of the displayed grid as a whole, the “transformation grid” that has been highlighted as the true underlying topic ever since D’Arcy Thompson’s celebrated exposition of 1917. For analyses of comparisons involving gradients at large geometric scale, this paper argues for replacement of all three of the Procrustes conventions by a version of my two-point registration of 1986 [originally Galton’s of 1907 (Nature 76:617–618, 1907)]. The choice of the two points interacts with another non-Procrustes concern, interpretability of the grid lines of a coordinate system deformed according to a fitted polynomial trend rather than an interpolating thin-plate spline. The paper works two examples using previously published midsagittal cranial data; there result new findings pertinent to the interpretation of both of these classic data sets. A concluding discussion suggests that the current toolkit of geometric morphometrics, centered on Procrustes shape coordinates and thin-plate splines, is too restricted to suit many of the interpretive purposes of evolutionary and developmental biology.

Mathematical Models of the Phase Voltages of High-, Medium- and Low-Voltage Busbars in a Substation during a Phase-to-Ground Fault on High-Voltage Busbars

The electrical energy supply of industrial equipment is provided by electrical power stations with high- (HT), medium- (MV) and low-voltage (LV) busbars. Consumers are connected to either MV or LV busbars. In this paper, a real power station was considered, through which the gasoline extraction from the well gas installation is powered. Electric consumers (electric motors) supplied by a MV busbar have active power of 13.54 MW, and those fed by a LV busbar have active power of 6.4 MW. Since electrical consumers operate in explosive environments, the design and operating conditions are more severe than in the case of electrical installations operating in non-explosive environments. The case of a single phase-to-ground fault occurring on the HV transmission lines feeding the power station has been analysed. First, the mathematical models for the calculation of the phase voltages, the dissymmetry and asymmetry coefficients, the reduction coefficient of the plus sequence component, and the effective values of the phase voltages were established. The influence of the source impedance (the equivalent impedance of the HV transmission lines) and of the neutral point configuration of the HV/MV medium-voltage transformer on the calculated quantities was analysed. Then, the results obtained using the established mathematical models were compared with those obtained experimentally by provoking a single-phase-to-ground fault near the HV busbars of the real power station. This study has shown that the de-symmetrisation of the phase voltages of the MV and LV busbars is lower when using the Y/Δ connection for the HV/MV transformer. As a result, it is recommended the Y/Δ connection be used for this transformer, instead of the Y0/Δ connection.

Aging mechanisms of nanoceria and pathways for preserving optimum morphology

Thermal aging can modify the unique properties of a nanomaterial via structural change. Mechanistic understanding of the aging process, including accelerated aging under high-temperature operating conditions, is a first step towards property preservation via controlling, limiting, or suppressing aging-related processes. Here, we use molecular dynamics to simulate thermal aging of ceria nanocubes and nanorods, which transform into nanopolyhedra; comparisons with experimental TEM images are presented alongside. We find that morphology changes proceed via the turbulent mobility of CexOy surface clusters from one part of the nanoceria to another. For nanorods and nanocubes, catalytically important {100} and {110} surfaces are eroded, whereas the relative area of {111} surfaces increase. Detailed analysis of the simulations reveals that atoms in the CexOy clusters do not all move simultaneously. Rather, (-O-Ce-O-Ce-O-)n ‘chains’ (subsets of the larger CexOy clusters) move with collective motion, while the atoms inside the chains move in a ‘worm-like’ fashion. This reduces the activation energy barrier associated with all the atoms in the chain simultaneously moving into an activated (saddle point) configuration. We predict gadolinium-doped ceria nanocubes, charge-compensated by oxygen vacancies, age faster than undoped and fully oxidised ceria nanocubes. In particular, dopants that increase catalytic activity, may also accelerate aging by introducing oxygen vacancies that break the (-O-Ce-O-Ce-O-)n chains into smaller chains with reduced activation energies. Accordingly, we advocate that when doping is used to confer catalytic activity, experiment should also target the collective motion of surface (-O-Ce-O-Ce-O-)n chains to maximise thermal stability.

Metrological assessment of a robotic total station for use in post-earthquake emergency conditions

Abstract. The paper provides synthetic indications regarding the measuring performances of procedures for using a robotic total station (RTS) in emergency situations, such as the survey of the structural conditions of buildings and the assessment of the safety level for rescue operations after the occurrence of an earthquake. Particular attention is paid to operative aspects that could impact on the performance of the system in this situation; specifically considered is the effect of the layout of the measurement setup and of the number of monitoring points, depending on the geometry of the site and of the considered buildings, because the criticality of emergency conditions imposes geometrical solutions which are far from having optimal solutions. The analysis is carried out with reference to two different buildings, which have different characteristics from the point of view of height and distance from the instrument, and that implies different geometrical constraints for the instrument during the acquisition of the monitoring points. The methodology allows the evaluation of the repeatability, reproducibility, and detection limit of a RTS, in field conditions, referring to a 1-year observation period, with reference to different quantities, like positions of the monitoring points and the inclination of walls and façades. In particular, the analysis of the geometrical characteristics of reduced configurations of the monitoring points has highlighted interesting aspects in view of defining a simplified procedure, which is also suitable for speeding up the acquisition of reliable data in emergency conditions.

Application of mesh adaptive technology combined with adaptive time stepping technology under strong earthquake liquefaction

Mesh distortion caused by large deformations is a major problem that disrupts finite element (FE) analysis computations. For example, the traditional updating Lagrangian approach updates the spatial configuration of the node points, yet strong earthquakes exacerbate this issue. To address the problem, an arbitrary Lagrangian Euler (ALE) method has been developed based on the updated Lagrangian method and solid‒fluid two-phase mixing theory. This adaptive mesh technique reshapes the deformed mesh at each computational step and projects variables onto a new configuration. However, the constant modification of the mesh to avoid distortion increases the overall analysis time. To solve this problem, an adaptive time stepping methodology is introduced, which evaluates the mixed error through five control parameters and adjusts the calculation step size in real time. This method considers the effect of the time step on the required amount of time and the calculation accuracy and dynamically adjusts the time step to optimize the associated tradeoff between the two. Two FE examples demonstrate the effectiveness of the method. The results show that partitioning the time increment significantly influences the mesh distortion and calculation time and that the ALE method can maintain a nondistorted mesh. The method is optimized for accuracy and calculation time. Various working conditions and models affect the method differently, particularly regarding acceleration properties. Small excitations perform better than large excitation, and the maximum computation time can be reduced by more than 80% through adaptive solver optimization.

Energy-saving access point configurations in WLANs: a swarm intelligent approach

Energy-saving access point configurations in WLANs: a swarm intelligent approach

Iterated and mixed discriminants

Classical work by Salmon and Bromwich classified singular intersections of two quadric surfaces. The basic idea of these results was already pursued by Cayley in connection with tangent intersections of conics in the plane and used by Schäfli for the study of hyperdeterminants. More recently, the problem has been revisited with similar tools in the context of geometric modeling and a generalization to the case of two higher dimensional quadric hypersurfaces was given by Ottaviani. We propose and study a generalization of this question for systems of Laurent polynomials with support on a fixed point configuration. In the non-defective case, the closure of the locus of coefficients giving a non-degenerate multiple root of the system is defined by a polynomial called the mixed discriminant . We define a related polynomial called the multivariate iterated discriminant , generalizing the classical Schäfli method for hyperdeterminants. This iterated discriminant is easier to compute and we prove that it is always divisible by the mixed discriminant. We show that tangent intersections can be computed via iteration if and only if the singular locus of a corresponding dual variety has sufficiently high codimension. We also study when point configurations corresponding to Segre–Veronese varieties and to the lattice points of planar smooth polygons, have their iterated discriminant equal to their mixed discriminant.