Computational Geometry Research Articles

Computational Investigation of the Operating Mechanism of the Ranque-Hilsch Vortex Tube

Abstract The Ranque-Hilsch vortex tube is a device that splits an incoming flow into two outgoing streams, but with the peculiar property that one stream exits at a lower total temperature than the incoming flow and the other at a higher total temperature. This temperature separation is accomplished without any moving parts, electronics or external power supplied to the device. Despite the passage of nearly a century since the effect's discovery, there remains a dearth of understanding regarding the mechanism responsible for the phenomenon. In fact, the literature contains competing theories with little evidence providing support. A promising technique to discern the responsible mechanisms for the energy transfer from the ultimately cold stream to the ultimately hot stream is to computationally define a stream tube that propagates upstream from the exits such that the stream tube interface separates the hot flow from the cold flow. In this paper, we apply this method to a three-dimensional, full-volume analysis of the flow within a vortex tube using a computational simulation that was thoroughly validated against experiments on a physical replica of the computational geometry. In this novel study, the integral form of the energy equation was used to quantify all forms of the energy transfer within the vortex tube. The results demonstrate that the phenomenon of temperature separation is attributable primarily to viscous work in the radial direction due to the circumferential flow, with a lesser contribution from heat transfer in the radial direction.

Geometry, Topology and p-Adic Numbers in Geospatial Data Modelling, Management and Processing: Review and Future Approaches

Abstract. Geometry and topology are both central concepts in geospatial data modelling and management. While geometry is the central concept for computational geometry applications, e.g. to intersect surfaces and solids in 3D space, topology is helpful for many application classes starting from city modelling to subsurface modelling and indoor navigation. Furthermore, p-adic numbers are useful for describing hierarchical processes on topological models. In this paper we first shortly review geometry- and topology-based approaches used for geospatial applications. We then describe our approach on turning geometry “upside down” focusing on topology during the whole process of distributed geospatial computing, data modelling, data management, and simulation. Furthermore, the way to use p-adic numbers for the description of hierarchical processes on topological models is shown for the example of simulation and the idea of p-adic analysis in distributed simulations is presented in the context of topological city and building models. The approach opens new insights such as topological relationships, components, and efficiently studying of the approximate behaviour of processes in the built environment using distributed computational systems. Finally, exemplary applications are presented to underline the importance of this new approach.

A novel real-time tension distribution method for cable-driven parallel robots

Abstract The tension distribution problem of cable-driven parallel robots is inevitable in real-time control. Currently, iterative algorithms or geometric algorithms are commonly used to solve this problem. Iterative algorithms are difficult to improve in real-time performance, and the tension obtained by geometric algorithms may not be continuous. In this paper, a novel tension distribution method for four-cable, 3-DOF cable-driven parallel robots is proposed based on the wave equation. The tension calculated by this method is continuous and differentiable, without the need for iterative computation or geometric centroid calculations, thus exhibiting good real-time performance. Furthermore, the feasibility and rationality of this algorithm are theoretically proven. Finally, the real-time performance and continuity of cable tension are analyzed through a specific numerical example.

Realizations of Multiassociahedra via Rigidity

AbstractLet $$\Delta _{k}(n)$$ Δ k ( n ) denote the simplicial complex of $$(k+1)$$ ( k + 1 ) -crossing-free subsets of edges in $${\left( {\begin{array}{c}[n]\\ 2\end{array}}\right) }$$ [ n ] 2 . Here $$k,n\in \mathbb {N}$$ k , n ∈ N and $$n\ge 2k+1$$ n ≥ 2 k + 1 . Jonsson (2003) proved that [neglecting the short edges that cannot be part of any $$(k+1)$$ ( k + 1 ) -crossing], $$\Delta _{k}(n)$$ Δ k ( n ) is a shellable sphere of dimension $$k(n-2k-1)-1$$ k ( n - 2 k - 1 ) - 1 , and conjectured it to be polytopal. The same result and question arose in the work of Knutson and Miller (Adv Math 184(1):161-176, 2004) on subword complexes. Despite considerable effort, the only values of (k, n) for which the conjecture is known to hold are $$n\le 2k+3$$ n ≤ 2 k + 3 (Pilaud and Santos, Eur J Comb. 33(4):632–662, 2012. https://doi.org/10.1016/j.ejc.2011.12.003) and (2, 8) (Bokowski and Pilaud, On symmetric realizations of the simplicial complex of 3-crossing-free sets of diagonals of the octagon. In: Proceedings of the 21st annual Canadian conference on computational geometry, 2009). Using ideas from rigidity theory and choosing points along the moment curve we realize $$\Delta _{k}(n)$$ Δ k ( n ) as a polytope for $$(k,n)\in \{(2,9), (2,10) , (3,10)\}$$ ( k , n ) ∈ { ( 2 , 9 ) , ( 2 , 10 ) , ( 3 , 10 ) } . We also realize it as a simplicial fan for all $$n\le 13$$ n ≤ 13 and arbitrary k, except the pairs (3, 12) and (3, 13). Finally, we also show that for $$k\ge 3$$ k ≥ 3 and $$n\ge 2k+6$$ n ≥ 2 k + 6 no choice of points can realize $$\Delta _{k}(n)$$ Δ k ( n ) via bar-and-joint rigidity with points along the moment curve or, more generally, via cofactor rigidity with arbitrary points in convex position.

Algorithm XXXX: The Delaunay Density Diagnostic

Accurate approximation of a real-valued function depends on two aspects of the available data: the density of inputs within the domain of interest and the variation of the outputs over that domain. There are few methods for assessing whether the density of inputs is sufficient to identify the relevant variations in outputs—i.e., the “geometric scale” of the function—despite the fact that sampling density is closely tied to the success or failure of an approximation method. In this paper, we introduce a general purpose, computational approach to detecting the geometric scale of real-valued functions over a fixed domain using a deterministic interpolation technique from computational geometry. The algorithm is intended to work on scalar data in moderate dimensions (2-10). Our algorithm is based on the observation that a sequence of piecewise linear interpolants will converge to a continuous function at a quadratic rate (in \(L^{2}\) norm) if and only if the data are sampled densely enough to distinguish the feature from noise (assuming sufficiently regular sampling). We present numerical experiments demonstrating how our method can identify feature scale, estimate uncertainty in feature scale, and assess the sampling density for fixed (i.e. static) datasets of input–output pairs. We include analytical results in support of our numerical findings and have released lightweight code that can be adapted for use in a variety of data science settings.

Filling the Holes on 3D Heritage Object Surface Based on Automatic Segmentation Algorithm

ABSTRACTReconstructing and processing 3D objects are activities in the research field of computer graphics, image processing and computer vision. The 3D objects are processed based on geometric modelling (a branch of applied mathematics and computational geometry) or machine learning algorithms based on image processing. The computation of geometrical objects includes processing the curves and surfaces, subdivision, simplification, meshing, holes filling or reconstructing the 3D surface's objects on both point cloud data and triangular mesh. While the machine learning methods are developed using deep learning models. With the support of 3D laser scan devices and LiDAR techniques, the obtained dataset is close to the original shape of the real objects. Besides, photography and its application based on modern techniques in recent years help us collect data and process the 3D models more precisely. This article proposes a new method for filling holes on the 3D object's surface based on automatic segmentation. Instead of filling the hole directly as the existing methods, we now subdivide the hole before filling it. The hole is first determined and segmented automatically based on the computation of its local curvature. It is then filled on each part of the hole to match its local curvature shape. The method can work on both 3D point cloud surfaces and triangular mesh surfaces. Compared to the state‐of‐the‐art (SOTA) methods, our proposed method obtained higher accuracy of the reconstructed 3D objects.

Algorithmic Coverage Quantification and Visualization in Range-Free Sensor Networks

This study introduces a novel method that addresses the challenge of visualizing and quantifying detection coverage areas in wireless sensor networks. The method involves projecting a network of range-free sensors and pre-existing transmitters, located within a predefined area of interest, onto a global coordinate system. Detection areas are defined as those covered by the sensing range of at least three sensors. Pre-existing transmitters located within the detection range of the sensors are assumed to degrade the networks’ performance by causing coverage gaps. Interactive satellite maps facilitate the dynamic exploration of coverage via the calculation and visualization of the resulting detection areas. The algorithmic structure of the proposed tool is explained in detail, and four example scenarios demonstrate the tool’s capabilities, as well as its flexibility, adaptability, and effectiveness in identifying the triangulated detection areas. Designed primarily as a geometry calculation and visualization tool that allows for the adjustment of sensor parameters such as locations, ranges, and angular ranges of detection, the proposed tool has the potential to enhance decision-making in sensor network configuration, prior to final sensor placement, across a wide range of applications.

Comments on wormholes and factorization

In AdS/CFT partition functions of decoupled copies of the CFT factorize. In bulk computations of such quantities contributions from spacetime wormholes which link separate asymptotic boundaries threaten to spoil this property, leading to a “factorization puzzle.” Certain simple models like JT gravity have wormholes, but bulk computations in them correspond to averages over an ensemble of boundary systems. These averages need not factorize. We can formulate a toy version of the factorization puzzle in such models by focusing on a specific member of the ensemble where partition functions will again factorize.As Coleman and Giddings-Strominger pointed out in the 1980s, fixed members of ensembles are described in the bulk by “α-states” in a many-universe Hilbert space. In this paper we analyze in detail the bulk mechanism for factorization in such α-states in the topological model introduced by Marolf and Maxfield (the “MM model”) and in JT gravity. In these models geometric calculations in α states are poorly controlled. We circumvent this complication by working in approximate α states where bulk calculations just involve the simplest topologies: disks and cylinders.One of our main results is an effective description of the factorization mechanism. In this effective description the many-universe contributions from the full α state are replaced by a small number of effective boundaries. Our motivation in constructing this effective description, and more generally in studying these simple ensemble models, is that the lessons learned might have wider applicability. In fact the effective description lines up with a recent discussion of the SYK model with fixed couplings [1]. We conclude with some discussion about the possible applicability of this effective model in more general contexts.

Design of Gearings from Involute-Bevel Gears

The article presents formulas for determining the dimensions of involute-bevel gears and the gearings composed of them. It examines the most general cases of gearings formation, consisting of two involute-bevel gears with crossing axes (hyperboloid gearings), with intersecting axes (bevel gearings), and with parallel axes (cylindrical gearings). Gearings composed of involute-bevel gears have design, technological, and operational advantages compared to gearings composed of conventional cylindrical and bevel gears. The use of involute-bevel gearings with crossing axes allows for achieving the required contact character of the teeth from localized contact to linear contact, reducing sensitivity to manufacturing and assembly errors, and increasing the load capacity of the gearing compared to helical gearings from cylindrical gears. Bevel gearings with involute-bevel gears allow for the creation of gearings with any desired small shaft angles, which is difficult to achieve with conventional bevel gears. The use of internal meshing bevel gearings with modified tooth profiles in planetary reducers allows for gearings comparable to harmonic drives in terms of power and kinematic characteristics, but with a higher operational life. The use of involute-bevel gears in cylindrical gearings improves the smoothness of the mechanism and allows for adjusting the center distance and backlash in the meshing, making them suitable for backlash-free drives. By combining the taper angles of the gears and the inclination of the teeth, it is possible to create a one-way rotation mechanism - a freewheel mechanism. Modern CAD systems do not take into account the geometry features of gearings composed of involute-bevel gears, which limits their application in technology. The article proposes an algorithm for calculating the main geometric parameters of gearings composed of involute-bevel gears with arbitrary axis placement in space. Examples of geometric calculations of various types of gearings based on the proposed algorithm are provided.

(G4-SEOPTIM): A GEANT4 application for shielded enclosure, designing and shielding optimizing: The case of a new Moroccan shielded enclosure

PurposeThis study aims to develop and validate a Geant4 simulation application using the latest G4RadioactiveDecayPhysics v5.1 library to optimize the shielding design of a Moroccan shielded enclosure. The goal is to ensure effective radiation protection by comparing simulation results with initial geometric calculations based on the attenuation law (Beer-Lambert Law) and implementing design optimizations to enhance safety and reduce costs. MethodsThe study began with a prototype design based on linear attenuation calculations, which were costly and offered limited patient safety. Using the Geant4 Monte Carlo toolkit, we simulated the decay of a Fluorine-18 source within the shielded enclosure to evaluate dose rate distributions. The simulation's accuracy was validated through comparison with experimental measurements, and the results informed the geometric optimization of the shielding enclosure. ResultsThe Geant4 simulations demonstrated that the current shielding design effectively reduces radiation doses to acceptable levels. However, the simulations also identified opportunities for further optimization of the enclosure's geometry, allowing for more precise and efficient use of shielding materials while maintaining safety standards. ConclusionThe study confirms the utility of Geant4 for optimizing radiation shielding designs. While the initial dimensions provided adequate protection, the simulation enabled more precise geometric optimization. This approach not only enhances radiation protection but also informs the design and construction of more efficient and cost-effective shielding enclosures. The adjustments made to the enclosure's faces significantly improved radiation protection, reducing the dose rate surrounding the shielded enclosure to acceptable levels.

Knowledge-based planning, multicriteria optimization, and plan scorecards: A winning combination

Background and purposeThe ESTRO 2023 Physics Workshop hosted the Fully-Automated Radiotherapy Treatment Planning (Auto-RTP) Challenge, where participants were provided with CT images from 16 prostate cancer patients (6 prostate only, 6 prostate + nodes, and 4 prostate bed + nodes) across 3 challenge phases with the goal of automatically generating treatment plans with minimal user intervention. Here, we present our team’s winning approach developed to swiftly adapt to both different contouring guidelines and treatment prescriptions than those used in our clinic. Materials and methodsOur planning pipeline comprises two main components: 1) auto-contouring and 2) auto-planning engines, both internally developed and activated via DICOM operations. The auto-contouring engine employs 3D U-Net models trained on a dataset of 600 prostate cancer patients for normal tissues, 253 cases for pelvic lymph node, and 32 cases for prostate bed. The auto-planning engine, utilizing the Eclipse Scripting Application Programming Interface, automates target volume definition, field geometry, planning parameters, optimization, and dose calculation. RapidPlan models, combined with multicriteria optimization and scorecards defined on challenge scoring criteria, were employed to ensure plans met challenge objectives. We report leaderboard scores (0–100, where 100 is a perfect score) which combine organ-at-risk and target dose-metrics on the provided cases. ResultsOur team secured 1st place across all three challenge phases, achieving leaderboard scores of 79.9, 77.3, and 78.5 outperforming 2nd place scores by margins of 6.4, 0.4, and 2.9 points for each phase, respectively. Highest plan scores were for prostate only cases, with an average score exceeding 90. Upon challenge completion, a “Plan Only” phase was opened where organizers provided contours for planning. Our current score of 90.0 places us at the top of the “Plan Only” leaderboard. ConclusionsOur automated pipeline demonstrates adaptability to diverse guidelines, indicating progress towards fully automated radiotherapy planning. Future studies are needed to assess the clinical acceptability and integration of automatically generated plans.

Synthesis, Characterization, Crystal structure determination and DFT study of a six coordinated Cu (II) complex of a phosphorous based tris-(2-pyridinylamino) phosphene sulphide ligand and its acid catalysed hydrolysis

One mono nuclear copper(II) complex (Cu-TPPS-OOCCH3 with structural formula C17H19CuN6O3PS) is synthesized using a novel tripodal tetradentate ligand, tris-(2-pyridinylamino)phosphene sulphide (TPPS), which has three pyridinylamino groups attached to a phosphorus atom connected to a sulphur atom (PS). The equatorial positions of the complex are occupied by three amino N-atoms of three aminopyridyl groups and one O-atom of the acetate group. The apical position is occupied by other O-atom of acetate group and one secondary N-atom of the tripodal ligand. The complex has been synthesized and purified as green solid and characterized by various spectroscopic techniques and the structure has been determined by X-ray single crystal diffraction study. The geometry optimizations and calculations of energies of the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) of the compounds are performed by using the hybrid B3LYP density functional theory (DFT) along with the def2TZVP basis set.

Cryogenic thermosiphon used for indirect cooling of superconducting magnets

A thermosiphon is a thermodynamic phenomenon that facilitates the circulation of cryogen within a cooling system, relying solely on gravitational forces and phase change. This mechanism leverages the variations in the density of the cryogenic fluid throughout the entire cooling loop, creating a pressure gradient. This gradient serves as the primary driving force for the circulation of the cryogen. To negate the necessity of a circulation pump, it is crucial to determine the geometry of the cooling loop, the configuration of the thermosiphon, its height, and the vertical placement of the cryogen phase separator. This paper introduces a simplified computational model and the geometric calculations of the cryogenic thermosiphon for two distinct configurations of the indirect cooling loop for superconducting magnets.

Elastic-Degenerate String Matching with 1 Error or Mismatch

An elastic-degenerate (ED) string is a sequence of n finite sets of strings of total length N, introduced to represent a set of related DNA sequences, also known as a pangenome. The ED string matching (EDSM) problem consists in reporting all occurrences of a pattern of length m in an ED text. The EDSM problem has recently received some attention by the combinatorial pattern matching community, culminating in an O~(nmω-1)+O(N)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {\ ilde{O}}(nm^{\\omega -1})+\\mathcal {O}(N)$$\\end{document}-time algorithm [Bernardini et al., SIAM J. Comput. 2022], where ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega $$\\end{document} denotes the matrix multiplication exponent and the O~(·)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {\ ilde{O}}(\\cdot )$$\\end{document} notation suppresses polylog factors. In the k-EDSM problem, the approximate version of EDSM, we are asked to report all pattern occurrences with at most k errors. k-EDSM can be solved in O(k2mG+kN)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {O}(k^2mG+kN)$$\\end{document} time, under edit distance, or O(kmG+kN)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {O}(kmG+kN)$$\\end{document} time, under Hamming distance, where G denotes the total number of strings in the ED text [Bernardini et al., Theor. Comput. Sci. 2020]. Unfortunately, G is only bounded by N, and so even for k=1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k=1$$\\end{document}, the existing algorithms run in Ω(mN)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varOmega (mN)$$\\end{document} time in the worst case. In this paper we make progress in this direction. We show that 1-EDSM can be solved in O((nm2+N)logm)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {O}((nm^2 + N)\\log m)$$\\end{document} or O(nm3+N)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {O}(nm^3 + N)$$\\end{document} time under edit distance. For the decision version of the problem, we present a faster O(nm2logm+Nloglogm)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {O}(nm^2\\sqrt{\\log m} + N\\log \\log m)$$\\end{document}-time algorithm. We also show that 1-EDSM can be solved in O(nm2+Nlogm)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {O}(nm^2 + N\\log m)$$\\end{document} time under Hamming distance. Our algorithms for edit distance rely on non-trivial reductions from 1-EDSM to special instances of classic computational geometry problems (2d rectangle stabbing or 2d range emptiness), which we show how to solve efficiently. In order to obtain an even faster algorithm for Hamming distance, we rely on employing and adapting the k-errata trees for indexing with errors [Cole et al., STOC 2004]. This is an extended version of a paper presented at LATIN 2022.

Synthesis, crystal structure, spectroscopic, electronic and vibrational properties of N′-[(E)-3-pyridinylmethylene]nicotinohydrazide trihydrate: Experimental and computational study

N′-[(E)-3-pyridinylmethylene]nicotinohydrazide trihydrate (C12H10N4O·3(H2O)) was synthesized and its structure was determined by single crystal X-ray diffraction method. X-ray analysis showed that the compound crystalized in the triclinic system P-1 with a = 7.1134 (3) Å, b = 10.0208 (4) Å, c = 10.3601 (4) Å, α = 96.386 (3)°, β = 96.995 (3)°, γ = 101.219 (4)°, V = 712.05 (5) Å3 and Z = 2 and exhibits that the title compound (I) consists of N′-[(E)-3-pyridinylmethylene]nicotinohydrazide (II) (C12H10N4O), and three water molecules of crystallization. The two water molecules are attached to the third water molecule through intermolecular two OH…O hydrogen bonds. At the same time, this water molecule is linked to the NH amide group of the hydrazone by an intermolecular NH…O hydrogen bond. Hirshfeld surface (HS) analyses were carried out are to visualise the intermolecular interactions in the crystals of Compound I. The geometric optimization of the titled compound has been carried out by different computational methods such as by Hatree Fock (HF) and Density Functional Theory (DFT) methods with the 6–311++G (d,p) basis set. The vibrational frequency, dipole moment (μ), polarizability (α), hyperpolarizability (β), and electronic properties including the highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO–LUMO) of the compound have been calculated at the level of both theories. In the results of crystal analysis and geometry calculations of the compound I, it was observed that intermolecular hydrogen bonds, N2H2A…O3, O3H31…O2 and O3H32…O4, were formed. The energy band gap (Eg = ELUMO-EHOMO) values were also obtained by using ELUMO and EHOMO at the level of both theories. The value of equilibrium (ground state) dipole moment of the studied molecule was calculated to be 8.31 Debye in B3LYP and 7.55 Debye in HF. The calculated hyperpolarizability values at the B3LYP/6–311++G(d,p) of the compound are 2.53 × 10−30 esu and this value corresponds to 6.79 times the hyperpolarizability value of urea.

An automated convergence diagnostic for phylogenetic MCMC analyses.

Assessing convergence of Markov chain Monte Carlo (MCMC) based analyses is crucial but challenging, especially so in high dimensional and complex spaces such as the space of phylogenetic trees (treespace). In practice, it is assumed that the target distribution is the unique stationary distribution of the MCMC and convergence is achieved when samples appear to be stationary. Here we leverage recent advances in computational geometry of the treespace and introduce a method that combines classical statistical techniques and algorithms with geometric properties of the treespace to automatically evaluate and assess practical convergence of phylogenetic MCMC analyses. Our method monitors convergence across multiple MCMC chains and achieves high accuracy in detecting both practical convergence and convergence issues within treespace. Furthermore, our approach is developed to allow for real-time evaluation during the MCMC algorithm run, eliminating any of the chain post-processing steps that are currently required. Our tool therefore improves reliability and efficiency of MCMC based phylogenetic inference methods and makes analyses easier to reproduce and compare. We demonstrate the efficacy of our diagnostic via a well-calibrated simulation study and provide examples of its performance on real data sets. Although our method performs well in practice, a significant part of the underlying treespace probability theory is still missing, which creates an excellent opportunity for future mathematical research in this area. The open source package for the phylogenetic inference framework BEAST2, called ASM, that implements these methods, making them accessible through a user-friendly GUI, is available from https://github.com/rbouckaert/asm/. The open source Python package, called tetres, that provides an interface for these methods enabling their applications beyond BEAST2 can be accessed at https://github.com/bioDS/tetres/.

Fast super robust nonadiabatic geometric quantum computation

Nonadiabatic geometric quantum computation (NGQC) provides a method for implementing fast and robust quantum gates. To enhance the robustness of NGQC against control errors, many solutions have been proposed by previous researchers. However, these solutions often lead to longer operation times for quantum gates. To simultaneously enhance quantum gate robustness against control errors and reduce operation times to mitigate decoherence effects, we introduce fast super robust NGQC (FSR-NGQC). This approach achieves faster speeds when operating small-angle rotation gates. Through numerical calculations, we have demonstrated the performance of our scheme in a decoherence environment. The results show that our scheme achieves higher fidelity, thus enabling fast and robust geometric quantum computing.

A short proof for the parameter continuation theorem

The Parameter Continuation Theorem is the theoretical foundation for polynomial homotopy continuation, which is one of the main tools in computational algebraic geometry. In this note, we give a short proof using Gröbner bases. Our approach gives a method for computing discriminants.

Learning Oriented Object Detection via Naive Geometric Computing.

Detecting oriented objects along with estimating their rotation information is one crucial step for image analysis, especially for remote sensing images. Despite that many methods proposed recently have achieved remarkable performance, most of them directly learn to predict object directions under the supervision of only one (e.g., the rotation angle) or a few (e.g., several coordinates) groundtruth (GT) values individually. Oriented object detection would be more accurate and robust if extra constraints, with respect to proposal and rotation information regression, are adopted for joint supervision during training. To this end, we propose a mechanism that simultaneously learns the regression of horizontal proposals, oriented proposals, and rotation angles of objects in a consistent manner, via naive geometric computing, as one additional steady constraint. An oriented center prior guided label assignment strategy is proposed for further enhancing the quality of proposals, yielding better performance. Extensive experiments on six datasets demonstrate the model equipped with our idea significantly outperforms the baseline by a large margin and several new state-of-the-art results are achieved without any extra computational burden during inference. Our proposed idea is simple and intuitive that can be readily implemented. Source codes are publicly available at: https://github.com/wangWilson/CGCDet.git.

The Hampered [formula omitted]-Median Problem with Neighbourhoods

This paper deals with facility location problems in a continuous space with neighbours and barriers. Each one of these two elements, neighbours and barriers, makes the problems harder than their standard counterparts. Combining all together results in a new challenging problem that, as far as we know, has not been addressed before, but has applications for inspection and surveillance activities and the delivery industry assuming uniformly distributed demand in some regions. Specifically, we analyse the k-Median problem with neighbours and polygonal barriers in two different situations. None of these problems can be seen as a simple incremental contribution since in both cases the tools required to analyse and solve them go beyond any standard overlapping of techniques used in the separated problems. As a first building block, we deal with the problem assuming that the neighbourhoods are not visible from one another and therefore there are no rectilinear paths that join two of them without crossing barriers. Under this hypothesis, we derive a valid mixed-integer linear formulation. Removing that hypothesis leads to a more general and realistic problem, but at the price of making it more challenging. Adapting the elements of the first formulation, we also develop another valid mixed-integer bilinear formulation. Both formulations rely on tools borrowed from computational geometry that allow to handle polygonal barriers and neighbours that are second-order cone (SOC) representable, which we preprocess and strengthen with valid inequalities. These mathematical programming formulations are also instrumental to derive an adapted matheuristic algorithm that provides good quality solutions for both problems in short computing time. The paper also reports extensive computational experience, counting 2400 experiments, showing that our exact and heuristic approaches are useful: the exact approach can solve optimally instances with up to 50 neighbourhoods and different number of barriers within one hour of CPU time, whereas the matheuristic approach always returns good feasible solutions in less than 300 s.