Point Configurations Research Articles

Optimization of Water Quality Monitoring Networks Using Metaheuristic Approaches: Moscow Region Use Case

Currently many countries are struggling to rationalize water quality monitoring stations which is caused by economic demand. Though this process is essential indeed, the exact elements of the system to be optimized without a subsequent quality and accuracy loss still remain obscure. Therefore, accurate historical data on groundwater pollution is required to detect and monitor considerable environmental impacts. To collect such data appropriate sampling and assessment methodologies with an optimum spatial distribution augmented should be exploited. Thus, the configuration of water monitoring sampling points and the number of the points required are now considered as a fundamental optimization challenge. The paper offers and tests metaheuristic approaches for optimization of monitoring procedure and multi-factors assessment of water quality in “New Moscow” area. It is shown that the considered algorithms allow us to reduce the size of the training sample set, so that the number of points for monitoring water quality in the area can be halved. Moreover, reducing the dataset size improved the quality of prediction by 20%. The obtained results convincingly demonstrate that the proposed algorithms dramatically decrease the total cost of analysis without dampening the quality of monitoring and could be recommended for optimization purposes.

Endoscopic Anatomy of the Chorda Tympani: Systematic Dissection, Novel Anatomic Classification, and Surgical Implications.

A transcanal endoscopic approach enables visualization of the variable course of the chorda tympani inside the middle ear. The chorda tympani is the longest intrapetrous branch of the facial nerve. Despite having been investigated in several studies, a description of its tympanic tract from an endoscopic point of view is lacking in the literature. We performed transcanal endoscopic dissections of 44 human cadaveric head and ear specimens. The entry point of the chorda tympani into the middle ear was classified into four categories according to its location, and as covered or dehiscent according to its appearance. The chordal eminence (CE) was defined as absent, shallow, intermediate, prominent, or fused, based on its shape and extension. The relationship of the chorda tympani to adjacent bony and ligamental structures was assessed. The tympanic tract of the chorda tympani was divided into three portions. The periannular segment was dehiscent in 54.5% of specimens, with type II being the most frequent entry point configuration (52.3%). In the interossicular segment, the nerve consistently passed lateral to the incus and medial to the malleus. The course of the intrapetrous segment was independent from the conformation of the tensor fold and supratubal recess. The transcanal endoscopic approach allows a detailed description of tympanic segment of the chorda tympani. Novel anatomic classifications of the chorda tympani and CE are proposed herein to highlight their possible surgical implications during otologic procedures.

The complete classification of empty lattice 4-simplices

An empty simplex is a lattice simplex with only its vertices as lattice points. Their classification in dimension three was completed by G. White in 1964. In 1988, S. Mori, D. R. Morrison, and I. Morrison started the task in dimension four, with their motivation coming from the close relationship between empty simplices and terminal quotient singularities. They conjectured a classification of empty simplices of prime volume, modulo finitely many exceptions. Their conjecture was proved by Sankaran (1990) with a simplified proof by Bober (2009). The same classification was claimed by Barile et al. in 2011 for simplices of non-prime volume, but this statement was proved wrong by Blanco et al. (2016+). In this article, we complete the classification of 4-dimensional empty simplices. In doing so, we correct and complete the classification by Barile et al., and we also compute all the finitely many exceptions, by first proving an upper bound for their volume. The whole classification has: 1) One 3-parameter family, consisting of simplices of width equal to one. 2) Two 2-parameter families (the one in Mori et al., plus a second new one). 3) Forty-six 1-parameter families (the 29 in Mori et al., plus 17 new ones). 4) 2461 individual simplices not belonging to the above families, with (normalized) volumes ranging between 24 and 419. We characterize the infinite families of empty simplices in terms of the lower dimensional point configurations that they project to, with techniques that can potentially be applied to higher dimensions and other classes of lattice polytopes.

Point configurations, phylogenetic trees, and dissimilarity vectors

In 2004, Pachter and Speyer introduced the higher dissimilarity maps for phylogenetic trees and asked two important questions about their relation to the tropical Grassmannian. Multiple authors, using independent methods, answered affirmatively the first of these questions, showing that dissimilarity vectors lie on the tropical Grassmannian, but the second question, whether the set of dissimilarity vectors forms a tropical subvariety, remained opened. We resolve this question by showing that the tropical balancing condition fails. However, by replacing the definition of the dissimilarity map with a weighted variant, we show that weighted dissimilarity vectors form a tropical subvariety of the tropical Grassmannian in exactly the way that Pachter and Speyer envisioned. Moreover, we provide a geometric interpretation in terms of configurations of points on rational normal curves and construct a finite tropical basis that yields an explicit characterization of weighted dissimilarity vectors.

Insights into MnAl-C nano-twin defects by micromagnetic characterization

MnAl-C is a prominent candidate for the replacement of rare earth magnets with a moderate energy density product. Crystallographic defects have a strong effect on magnetization properties. In this work, we show the influence of twinning defects in the nanometer regime on the quality of the magnet. Standard micromagnetic simulations and computations of the saddle point configuration for magnetization reversal highlight the importance of optimizing the fraction of and reducing the width of crystallographic twin defects. Switching field distributions and the maximum possible coercive field for ideal microstructures without defects are estimated using a reduced order micromagnetic model.

On Differences of Multiplicative Functions and Solutions of the Equation $$n-\varphi(n)=c$$

The following general problem is studied: Given a positive integer $$c$$ and two multiplicative functions $$f$$ and $$g$$ , it is required to determine for what values of $$n$$ the equality $$f(n)-g(n)=c$$ holds. It is proved that, under certain constraints on the functions $$f$$ and $$g$$ and the solutions (in particular, under the constraint $$f(n)>g(n)$$ for $$n>1$$ ), this equation has at most $$c^{1-\epsilon}$$ solutions. For the equation $$n-\varphi(n)=c$$ , it is proved that the number of solutions equals $$G(c+1)+O(c^{3/4+o(1)}),$$ where $$G(k)$$ is the number of ways in which $$k$$ can be represented as a sum of two primes. This result is based on an assertion concerning configurations of points and straight lines.

Non-Hermitian topological phases and exceptional lines in topolectrical circuits

We propose a scheme to realize various non-Hermitian topological phases in a topolectrical (TE) circuit network consisting of resistors, inductors, and capacitors. These phases are characterized by topologically protected exceptional points and lines. The positive and negative resistive couplings R g in the circuit provide loss and gain factors which break the Hermiticity of the circuit Laplacian. By controlling R g, the exceptional lines of the circuit can be modulated, e.g. from open curves to closed ellipses in the Brillouin zone. In practice, the topology of the exceptional lines can be detected by the impedance spectra of the circuit. We also considered finite TE systems with open boundary conditions, the admittance spectra of which exhibit highly tunable zero-admittance states demarcated by boundary points (BPs). The phase diagram of the system shows topological phases that are characterized by the number of their BPs. The transition between different phases can be controlled by varying the circuit parameters and tracked via the impedance readout between the terminal nodes. Our TE model offers an accessible and tunable means of realizing different topological phases in a non-Hermitian framework and characterizing them based on their boundary point and exceptional line configurations.

Areas spanned by point configurations in the plane

We consider an over-determined Falconer type problem on ( k + 1 ) (k+1) -point configurations in the plane using the group action framework introduced in by Greenleaf, Iosevich, Liu, and Palsson in [Rev. Mat. Iberoam. 31 (2015), pp. 799–810]. We define the area type of a ( k + 1 ) (k+1) -point configuration in the plane to be the vector in R ( k + 1 2 ) \mathbb {R}^{\binom {k+1}{2}} with entries given by the areas of parallelograms spanned by each pair of points in the configuration. We show that the space of all area types is 2 k − 1 2k-1 dimensional, and prove that a compact set E ⊂ R d E\subset \mathbb {R}^d of sufficiently large Hausdorff dimension determines a positve measure set of area types.

Sharp phase transition for the continuum Widom–Rowlinson model

The Widom–Rowlinson model (or the Area-interaction model) is a Gibbs point process in Rd with the formal Hamiltonian defined as the volume of ∪x∈ωB1(x), where ω is a locally finite configuration of points and B1(x) denotes the unit closed ball centred at x. The model is also tuned by two other parameters: the activity z>0 related to the intensity of the process and the inverse temperature β≥0 related to the strength of the interaction. In the present paper we investigate the phase transition of the model in the point of view of percolation theory and the liquid-gas transition. First, considering the graph connecting points with distance smaller than 2r>0, we show that for any β≥0, there exists 0 z˜ca(β,r)). These results are in the spirit of recent works using the theory of randomised tree algorithms (Probab. Theory Related Fields 173 (2019) 479–490, Ann. of Math. 189 (2019) 75–99, Duminil-Copin, Raoufi and Tassion (2018)). Secondly we study a standard liquid-gas phase transition related to the uniqueness/non-uniqueness of Gibbs states depending on the parameters z, β. Old results (Phys. Rev. Lett. 27 (1971) 1040–1041, J. Chem. Phys. 52 (1970) 1670–1684) claim that a non-uniqueness regime occurs for z=β large enough and it is conjectured that the uniqueness should hold outside such an half line (z=β≥βc>0). We solve partially this conjecture in any dimension by showing that for β large enough the non-uniqueness holds if and only if z=β. We show also that this critical value z=β corresponds to the percolation threshold z˜ca(β,r)=β for β large enough, providing a straight connection between these two notions of phase transition.

Steiner Configurations Ideals: Containment and Colouring

Given a homogeneous ideal I⊆k[x0,…,xn], the Containment problem studies the relation between symbolic and regular powers of I, that is, it asks for which pairs m,r∈N, I(m)⊆Ir holds. In the last years, several conjectures have been posed on this problem, creating an active area of current interests and ongoing investigations. In this paper, we investigated the Stable Harbourne Conjecture and the Stable Harbourne–Huneke Conjecture, and we show that they hold for the defining ideal of a Complement of a Steiner configuration of points in Pkn. We can also show that the ideal of a Complement of a Steiner Configuration of points has expected resurgence, that is, its resurgence is strictly less than its big height, and it also satisfies Chudnovsky and Demailly’s Conjectures. Moreover, given a hypergraph H, we also study the relation between its colourability and the failure of the containment problem for the cover ideal associated to H. We apply these results in the case that H is a Steiner System.

Characterizing the hyperuniformity of ordered and disordered two-phase media.

The hyperuniformity concept provides a unified means to classify all perfect crystals, perfect quasicrystals, and exotic amorphous states of matter according to their capacity to suppress large-scale density fluctuations. While the classification of hyperuniform point configurations has received considerable attention, much less is known about the classification of hyperuniform two-phase heterogeneous media, which include composites, porous media, foams, cellular solids, colloidal suspensions, and polymer blends. The purpose of this article is to begin such a program for certain two-dimensional models of hyperuniform two-phase media by ascertaining their local volume-fraction variances σ_{_{V}}^{2}(R) and the associated hyperuniformity order metrics B[over ¯]_{V}. This is a highly challenging task because the geometries and topologies of the phases are generally much richer and more complex than point-configuration arrangements, and one must ascertain a broadly applicable length scale to make key quantities dimensionless. Therefore, we purposely restrict ourselves to a certain class of two-dimensional periodic cellular networks as well as periodic and disordered or irregular packings of circular disks, some of which maximize their effective transport and elastic properties. Among the cellular networks considered, the honeycomb networks have minimal values of the hyperuniformity order metrics B[over ¯]_{V} across all volume fractions. On the other hand, for all packings of circular disks examined, the triangular-lattice packings have the smallest values of B[over ¯]_{V} for the possible range of volume fractions. Among all structures studied here, the triangular-lattice packing of circular disks have the minimal values of the order metric for almost all volume fractions. Our study provides a theoretical foundation for the establishment of hyperuniformity order metrics for general two-phase media and a basis to discover new hyperuniform two-phase systems with desirable bulk physical properties by inverse design procedures.

Energy and exergy performance comparison of conventional, dew point and new external-cooling indirect evaporative coolers

External-cooling indirect evaporative cooling is an effective energy saving technology, where air–water finned coils are linked with packed cooling tower by water pipes. However, external-cooling indirect evaporative coolers with different configurations and working air sources are incomprehensively analyzed and compared. This study presented an energy and exergy analysis of five external-cooling indirect evaporative coolers, including conventional configuration, dew point configuration, newly patented dew point configuration, and energy recovery forms of the first two. In order to analyze the evaporative cooler and its hybrid system combined with mechanical vapor compression system, the numerical model and experimental correlation are used. The effect of four selected parameters (ambient temperature, ambient humidity ratio, total number of transfer units and fresh air flowrate), and the summer energy saving potential in three different cities are studied. The analysis results show that the new dew point configuration has the best performance under the conditions of high temperature, high humidity, and high fresh air flowrate. This new dew point cooler’s hybrid system achieves the best energy saving rate in humid and arid climates, between 19.1% and 48.5% compared with the pure mechanical vapor compression system. In this study, the advantages and disadvantages of presented designs are established and their application potential under different climates is estimated.

Rational double points on Enriques surfaces

We classify, up to some lattice-theoretic equivalence, all possible configurations of rational double points that can appear on a surface whose minimal resolution is a complex Enriques surface.

Residual vibration reduction in back-and-forth moving systems driven by slider-crank mechanisms working through a dead point configuration

This study proposes an algorithm to construct back-and-forth motion profiles to reduce residual vibrations of 1-dof linear oscillatory systems, driven through a transmission chain made up of a 1-dof linkage mechanism. This set can be advantageous for high transmission ratios, when multistage drive trains are discouraged to prevent a build-up of backlash nonlinearities. We assume that the mechanism: i) is moved by a conventional electric actuator and, ii) is working through a dead point configuration. The solution focuses on the continuity degree Cn of the motion profile to guarantee its feasibility by means of the mentioned actuators. We aim to provide an algorithm to design these profiles. The development meshes several conclusions from other studies: the classical strategies of residual vibration reduction together with an analytical solution, with regard to Cn, of the inverse kinematic problem at a dead point configuration. The development includes an analytical approach to some methods of residual vibration reduction, in addition to numerical simulations. Finally, we present experimental results on a slider-crank mechanism test bed, with a pendulum acting as the oscillatory system.

The Point-Descriptor-Precedence representation for point configurations and movements

ABSTRACT In this paper, we represent (moving) point configurations along a curved directed line qualitatively by means of a system of relational symbols based on two distance descriptors: one representing distance along the curved directed line and the other representing signed orthogonal distance to the curved directed line. The curved directed line represents the direction of the movement of interest. For instance, it could be straight as in the case of driving along a highway or could be curved as in the case of an intersection or a roundabout. Inspired by the Point Calculus, the order between the points on the curved directed line is described by means of a small set of binary relations () acting upon the distance descriptors. We call this representation the Point-Descriptor-Precedence-Static (PDPS) representation at a time point and Point-Descriptor-Precedence-Dynamic (PDPD) representation during a time interval. To illustrate how the proposed approach can be used to represent and analyse curved movements, some basic micro-analysis traffic examples are studied. Finally, we discuss some extensions of our work to highlight the practical benefits of PDP in identifying motion patterns that could be useful in GIS, autonomous vehicles, sports analytics, and gait analysis.

Configurations of the Topological Indices of the Planar Polynomial Differential Systems of Degree (2, m)

Using the Euler–Jacobi formula there is a relation between the singular points of a polynomial vector field and their topological indices. Using this formula we obtain the configuration of the singular points together with their topological indices for the polynomial differential systems \(\dot{x}=P(x,y)\), \(\dot{y} =Q(x,y)\) with degree of P equal to 2 and degree of Q equal to m when these systems have 2m finite singular points.

Configuration optimization of the feature-oriented reference system in large component assembly

Multi-station measurement is a key technology for the high accuracy and efficiency of large component assembly. The unity of measurement coordinate systems (MCSs) and assembly coordinate system (ACS) is achieved by registration of enhanced reference system (ERS) points. As the transformation errors of assembly features are related to the configuration of ERS points, and to minimize them as possible, the feature-oriented reference system is of great importance, and a configuration optimization method is proposed in this paper. The detailed analyses with regard to structures, inspections, and tolerances of assembly features are conducted, and the complex constraints are established. By applying them and considering the direct connections between MCSs, the modified configuration model is built. The proposed optimization method is based on the improved binary particle swarm optimization (IBPSO), which involves a two-stage strategy and a novel mutation. The mutation is developed by using feasible centers to attract and correct infeasible particles, and simultaneously, to maintain the particle diversity. The performed experiments show that the method can effectively output optimal positions of ERS points, and the reference system is eventually hybrid on the premise of meeting accuracy requirements. The increase of ERS points is beneficial, but no further optimization happens when the amount reaches the upper limit. The limits are 12 and 18 when the measurement instruments are located at two and three different stations respectively.

A tabular optimisation technique for steel lazy wave riser

Steel lazy wave riser (SLWR) is derived from the simple catenary riser (SCR) by the installation of buoyancy modules on its section. Infinite SLWR configurations are possible, and this poses difficulties in determining the best configuration. However, it is possible to capture some suitable configurations which satisfy some given design criteria specific to a project. We referred to these as the optimum configurations for the problem. Several advanced optimization tools and techniques for engineering optimization are available. In this paper, we present a 2D tabular optimization method for SLWR, which is an index-based optimization technique. The approach reduces a multidimensional problem to a 2D type providing a significant reduction in the required computational resources. It combines the design variables in pairs and assigns indices to the resulting design points (configurations) for each combination. The optimum design points are then tracked through index matching using techniques such as data sorting and intersection operations. In the application of the technique to SLWR design, we set the number of design variable for the problem to three. This results in three pair of combinations of the design variables. The design variables are the apparent mass ratio, the sag bend elevation, and the arc height. The output variables of interest to be optimized include the SLWR hanging length, the smeared buoyancy section length, the smeared buoyancy thickness, the riser hang-off tension, the stress utilization and fatigue damage around the bends. Selected optimum SLWR configurations from the optimization process are subjected to an irregular wave simulation to demonstrate the suitability of the approach for such optimisation problems.

How to keep a spot cool?

Let \(D\) be a planar domain, let \(a\) be a reference point fixed in \(D\), and let \(b_k\), \(k=1,\ldots,n\), be \(n\) controlling points fixed in \(D\setminus\{a\}\). Suppose further that each \(b_k\) is connected to the boundary \(\partial D\) by an arc \(l_k\). In this paper, we propose the problem of finding a shape of arcs \(l_k\), \(k=1,\ldots,n\), which provides the minimum to the harmonic measure \(\omega(a,\bigcup_{k=1}^n l_k,D\setminus \bigcup_{k=1}^n l_k)\). This problem can also be interpreted as a problem on the minimal temperature at \(a\), in the steady-state regime, when the arcs \(l_k\) are kept at constant temperature \(T_1\) while the boundary \(\partial D\) is kept at constant temperature \(T_0<T_1\). In this paper, we mainly discuss the first non-trivial case of this problem when \(D\) is the unit disk \(\mathbf{D}=\{z\colon|z|<1\}\) with the reference point \(a=0\) and two controlling points \(b_1=ir\), \(b_2=-ir\), \(0<r<1\). It appears, that even in this case our minimization problem is highly nontrivial and the arcs \(l_1\) and \(l_2\) providing minimum for the harmonic measure are not the straight line segments as it could be expected from symmetry properties of the configuration of points under consideration.

Disentanglement approach to quantum spin ground states: field theory and stochastic simulation

While several tools have been developed to study the ground state of many-body quantum spin systems, the limitations of existing techniques call for the exploration of new approaches. In this manuscript we develop an alternative analytical and numerical framework for many-body quantum spin ground states, based on the disentanglement formalism. In this approach, observables are exactly expressed as Gaussian-weighted functional integrals over scalar fields. We identify the leading contribution to these integrals, given by the saddle point of a suitable effective action. Analytically, we develop a field-theoretical expansion of the functional integrals, performed by means of appropriate Feynman rules. The expansion can be truncated to a desired order to obtain analytical approximations to observables. Numerically, we show that the disentanglement approach can be used to compute ground state expectation values from classical stochastic processes. While the associated fluctuations grow exponentially with imaginary time and the system size, this growth can be mitigated by means of an importance sampling scheme based on knowledge of the saddle point configuration. We illustrate the advantages and limitations of our methods by considering the quantum Ising model in 1, 2 and 3 spatial dimensions. Our analytical and numerical approaches are applicable to a broad class of systems, bridging concepts from quantum lattice models, continuum field theory, and classical stochastic processes.