Singular Regions Research Articles

Analytic amplitudes for a pair of Higgs bosons in association with three partons

The pair production of Higgs bosons at the LHC can give information about the triple Higgs boson coupling. We perform an analytic one-loop calculation of the amplitudes for a pair of Higgs bosons in association with three partons, retaining the exact dependence on the quark mass circulating in the loop. These amplitudes constitute the real radiation corrections in the calculation of Higgs boson pair production at next-to-leading order in the strong coupling. The results of an analytic generalised-unitarity computation are simplified via analytic reconstruction in spinor variables. Compact ansätze for kinematic pole residues are iteratively fitted via p-adic evaluations near said poles and subtracted until no pole remains. A new ansatz construction is introduced to minimally parametrise coefficients of amplitudes with multiple massive external legs. The simplified expressions are faster to evaluate than automatic codes and can lead to more stable results near singular regions.

Research on Obstacle-Avoidance Trajectory Planning for Drill and Anchor Materials Handling by a Mechanical Arm on a Coal Mine Drilling and Anchoring Robot.

At present, China's coal mine permanent tunneling support commonly uses mechanized drilling and anchoring equipment; there are low support efficiency, labor intensity, and other issues. In order to further improve the support efficiency and liberate productivity, this paper further researches the trajectory planning of the drilling and anchoring materials of the robotic arm for the drilling machine "grasping-carrying-loading-unloading" on the basis of the drilling and anchoring robotic system designed by the team in the previous stage. Firstly, the kinematic model of the robotic arm with material was established by improving the D-H parameter method. Then, the working space of the robotic arm with the material was analyzed using the Monte Carlo method. The singular bit-shaped region of the robotic arm was restricted, and obstacles were removed from the working space. The inverse kinematics was utilized to solve the feasible domain of the robotic arm with material. Secondly, in order to avoid blind searching, the guidance of the Bi-RRT algorithm was improved by adding the target guidance factor, and the two-way tree connection strategy for determining the feasible domain was combined with the Bi-RRT algorithm's feasible domain judgment bi-directional tree connection strategy to improve the convergence speed of the Bi-RRT algorithm. Then, in order to adapt to the dynamic environment and avoid the global planning algorithm from falling into the local minima, on the basis of the above planning methods, an improved Bi-RRT trajectory planning algorithm incorporating the artificial potential field was proposed, which takes the planned paths as the guiding potential field of the artificial potential field to make full use of the global information and avoid falling into the local minimization. Finally, a simulation environment was built in a ROS environment to compare and analyze the planning effect of different algorithms. The simulation results showed that the improved Bi-RRT trajectory planning algorithm incorporating the artificial potential field improved the optimization speed by 69.8% and shortened the trajectory length by 46.6% compared with the traditional RRT algorithm.

Illegal Marriages

Pope Innocent III has drawn constant scholarly attention in the realm of medieval history. Not only was his papacy fundamental in the shaping of the modern-day Roman Catholic Church, but his time as Roman Pontiff is also considered the apogee of the medieval papacy. He expanded papal influence into realms previously dreamt of by Church reformers and exerted it over secular rulers. An often-contested topic of Innocent’s historiography is the motivations and justifications for his actions. Are we to view them through the lens of reform or the mind of a pragmatist? This paper contributes to this debate by analyzing Innocent’s letters and actions pertaining to the consanguineous marriages of Alfonso IX with Berenguela in the Iberian Peninsula and Otto IV with Beatrix in the German lands. By comparing the actions and justifications of Pope Innocent III in the Iberian Peninsula and the German lands—an area on the periphery of Europe and one central in it—this paper seeks to uncover, firstly, whether Innocent acted similarly in comparable situations from both areas and, secondly, whether Church reform or pragmatism influenced his arguments and measures. This paper finds that Innocent acted in a reformist manner (disregarding temporal outcomes in favor of spiritual strictness) in the Iberian Peninsula while he focused on temporal matters through a pragmatic approach in the German lands due to the severe threat the German Empire posed to Church independence and the ongoing Reconquista in Iberia. Utilizing a comparatist approach to this topic allows for conclusions to be made from his actions in different regions rather than a case study in a singular region.

Parallel isogeometric boundary element analysis with T-splines on CUDA

We present a framework for parallel isogeometric boundary element analysis (BEA) of elastic solids on CUDA. To deal with traction discontinuities, we propose a BEA model that supports multiple nodes and semi-discontinuous elements. The multiplicity of a node is defined by the number of regions containing any element influenced by the node. A region is a group of connected elements delimited by a closed crease curve. The default shape function of an element is determined by a linear operator applied to a set of basis functions. A BEA model is supposed to be generated from a watertight boundary representation of a solid. In this paper, we employ bicubic analysis-suitable T-splines. In this case, the shape of an element is defined by its Bézier extraction operator applied to the tensor product of Bernstein polynomials of degree 3. We describe the data structures of the BEA model and the main algorithms of the analysis pipeline on CUDA. In particular, we describe two strategies for parallel assembling of the linear system of equations. We also introduce a novel approach for inside integration based on the subdivision of the singular region in triangles with constant aspect ratio. In the T-splines context, we extend the Bézier extraction to handle unstructured T-meshes with crease edges. Moreover, we propose a scheme for embedding the influence of linked tangency handles on the shape of an element directly into the Bézier extraction operator. Such an embedding enables the removal of the corresponding nodes from the BEA model and the application of an alternative collocation method we discuss in the paper. We present several experiments to evaluate the accuracy and efficiency of the proposed framework. The results demonstrate that the GPU can be advantageously employed for parallelizing T-spline-based isogeometric analysis using boundary elements, achieving a speedup of up to 29x compared to the sequential code on a current laptop. We make the BEA code available in a prototype in MATLAB with a graphical interface that allows users to apply boundary conditions and visualize analysis results on the boundary.

Spectral signatures of solvent-extracted macromolecules in Indian coals of different rank: Insights from fluorescence excitation-emission matrix

Solvent-extracted fractions of six Indian coal samples of different ranks were investigated using multiple geochemical, petrological and spectroscopic proxies and an attempt was made to indicate possible fingerprint regions for different polycyclic aromatic hydrocarbons (PAH) with the help of excitation-emission matrix (EEM). In this study, for the very first time, the influence of rank and maturation of organic matter in the characterisation of coal solvent-extracts from Indian coals were perceived from the viewpoint of fluorescence EEM. Vitrinite reflectance (VRo) values were used to determine the general ranks of the original coal samples viz. lignite, subbituminous, bituminous and anthracite. Different fluorescence peak regions corresponding to different fused aromatic ring (FAR) systems were delineated using the EEM and their indicative depositional environments could be inferred. Our observations indicate that solvent-extracted fractions of low rank coals comprise of a larger number of shorter carbon chains compared to the other samples. For the low rank coal samples, the solvent-extracts show a strong humic influence and the presence of smaller PAH rings while for the medium rank coals, the extracted fractions tend to show a more bimodal distribution of PAHs, possibly comprising of different sized PAHs. Higher fluorescence sensitivity and quick response of smaller PAHs impart a singular centralised region in the EEM for the low rank coal samples while interference in the fluorescence of differently sized PAHs indicate a multimodal distribution of the fluorophores in the medium rank coals. The high rank coal used in this study shows a bimodal distribution with very low intensity of the peaks, indicating the low abundance of extractable macromolecules, possibly as a result of deformation.

Singular value decomposition for single-phase flow and cluster identification in heterogeneous pore networks

Pore networks play a key role in understanding and quantifying flow and transport processes in complex porous media. Realistic pore-spaces may be characterized by singular regions, that is, isolated subnetworks that do not connect inlet and outlet, resulting from unconnected porosity or multiphase configurations. The robust identification of these features is critical for the characterization of network topology and for the solution of the set of linear equations of flow and transport. We propose a robust method based on singular value decomposition to solve for network flow and locate isolated subnetworks simultaneously. The performance of the method is demonstrated for pore networks of different complexity.

Cosmological singularities, holographic complexity and entanglement

We study holographic volume complexity for various families of holographic cosmologies with Kasner-like singularities, in particular with AdS, hyperscaling violating and Lifshitz asymptotics. We find through extensive numerical studies that the complexity surface always bends in the direction away from the singularity and transitions from spacelike near the boundary to lightlike in the interior. As the boundary anchoring time slice approaches the singularity, the transition to lightlike is more rapid, with the spacelike part shrinking. The complexity functional has vanishing contributions from the lightlike region so in the vicinity of the singularity, complexity is vanishingly small, indicating a dual Kasner state of vanishingly low complexity, suggesting an extreme thinning of the effective degrees of freedom dual to the near singularity region. We also develop further previous studies on extremal surfaces for holographic entanglement entropy, and find that in the IR limit they reveal similar behaviour as complexity.

Existence of singular isoperimetric regions in 8-dimensional manifolds

It is well known that isoperimetric regions in a smooth compact (n+1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(n+1)$$\\end{document}-manifold are themselves smooth, up to a closed set of codimension at most 8. In this note, we construct an 8-dimensional compact smooth manifold whose unique isoperimetric region with half volume that of the manifold exhibits two isolated singularities. This stands in contrast with the situation in which a manifold is a space form, where isoperimetric regions are smooth in every dimension.

χ(2) and χ(3) enhancement by arylamine substituents in aromatic conjugated polyenyne polymers

In this work, we have determined the χ(1), χ(2), and χ(3) NLO properties of NH2substituted aromatic polyenynes in ortho, meta, and para positions. It is worth noting that Mednis-Genkin’s approximation takes into account the intraband contribution with a derivate of the dipole valence-conduction band moment transition, unlike, for example, Ward’s summation-over-sates (SOS) methodology, which considers the difference of these states. Indeed, we have selected these polymers because of the high asymmetry in their molecular wavefunction. In this way, the calculated χ(3) values of the para-NH2 substituted aromatic polyenyne with a higher degree of polymerization are near 1 X 10−7 esu. For its part, the ortho polymer has higher values, of the order of 1 X 10−6 esu, due to its high transition dipole moment. We have also found that the energy band distribution in the para position of these polymers produces van Hove points, which have a negligible proportion of the NLO properties, compared with singularity regions 1 and 2, which have a contribution of 100 %. These regions are due to the wavefunction coefficients’ first and second-order derivatives. Besides, without considering border effects nor correlation effects, and only the variation of excitation energy, we have calculated that the quaternary monomeric oligomers of these polymers have almost similar values of χ(2) and χ(3). Then, it implies building a methodology to synthesize the polymers to avoid canceling the NLO-χ(2) and -χ(3) values.

A Bohmian trajectory analysis of singular wave functions

The Schrödinger equation admits smooth and finite solutions that spontaneously evolve into a singularity, even for a free particle. This blowup is generally ascribed to the intrinsic dispersive character of the associated time evolution. We resort to the notion of quantum Bohmian trajectories to relate this singular behavior to local phase variations, which generate an underlying velocity field responsible for driving the quantum flux toward the singular region.

A new third-order EXP-WENO scheme for Hamilton–Jacobi equations

The authors of this research paper have introduced a new method for solving Hamilton–Jacobi (HJ) equations called third-order weighted essentially nonoscillatory (WENO) method. This method uses exponential polynomials to construct numerical fluxes and smoothness indicators, which helps distinguish between singular and smooth regions more efficiently. The smoothness indicators are created using a finite difference operator that eliminates exponential polynomials. The numerical flux is constructed using an interpolation method based on exponential polynomials, which results in better outcomes around steep gradients. The new method maintains a high level of accuracy (i.e. three) in smooth regions, even near critical points. The authors have presented some numerical results to demonstrate the effectiveness of the new method and compared it with other WENO methods.

Isolated disclination in an orthotropic von Kármán elastic plate

We investigate geometry and mechanics of the buckled orthotropic von Kármán elastic plate, with free boundary condition, in the presence of an isolated positive, or negative, disclination. The buckled shape of an isotropic elastic plate is cone-like for a positive disclination and saddle-like for a negative disclination. In either case, with increasing orthotropy, the shape of the buckled plate becomes more tent-like. The Gaussian curvature accordingly spreads along the ridge of the tent. The stress fields too remain focused in the neighbourhood of the defect point and the ridge, indicating that most of the stretching energy is accommodated in these singular regions.

Accurate Detection and Smoothness-Oriented Avoidance Method of Singularity in 5-Axis CNC Machining

As an inherent flaw in the kinematic chain mechanism of 5-axis machine tools, singularity can induce dramatic changes in machine axes motion and unfavorable fluctuations in feedrate. For effective singularity avoidance, it is desirable to first achieve accurate and efficient singularity detection and then eliminate the singularity without impairing tool orientation smoothness. This paper presents a novel approach for accurately detecting and smoothly avoiding the singularity in 5-axis CNC machining. In the detection method, two exclusion criteria are presented to efficiently exclude most non-singular segments of the tool orientation spline, and a curve intersection-based algorithm is thus developed to accurately identify the singular segments. In the singularity avoidance method, a concept of admissible tool orientation annulus (ATOA) is introduced, which serves to confine the range and magnitude of the tool orientation spline’s adjustments, and a local adjustment algorithm is then developed to enable the escape of the tool orientation from the singular region with controllable direction and deviation, while maintaining its continuity and smoothness. The effectiveness of singularity avoidance and the kinematic performance of the tool orientation modified by our method, are comparable to a state-of-the-art singularity avoidance algorithm. Finally, the conducted experiments validate the proposed method.

Equilibrium spherical shell of condensed matter around a scalar naked singularity

From a observational point of view, the central regions of scalar naked singularities possess a very special spacetime geometry, which in turn leads to existence of unusual orbital motion near the centers. We consider naked singularities in the model of static, spherically symmetric, asymptotically flat configurations of a self-gravitating scalar field minimally coupled to gravity. In this case, the effective potential of test particles orbiting around a scalar naked singularity has a minimum even at zero specific angular momentum. This means that the baryonic matter, captured by the naked singularity in the region of gravitational potential well near the center, will eventually be concentrated in some spherical shell, which will be in hydrostatic equilibrium after cooling. We find the conditions of hydrostatic equilibrium of the shell for the polytropic equation of state. In order to show the observational consequences of the possible existence of such configurations as real astrophysical objects, in particular in relation to tidal disruption events, we consider a simple illustrative example.

Singularity avoidance method for dual-arm closed-chain system based on damped least squares

When two manipulators cooperate to clamp a rigid object, a closed chain with both ends fixed is formed. The singularity of a single manipulator causes the closed chain to be at a singularity, which results in uncertainty in the velocity mapping between the terminal and joint space. This study proposes a closed-chain singularity processing method for dual-arm collaboration, adopting the Jacobian pseudoinverse method based on damped least squares to obtain an approximate solution. During the solution process, the adaptive damping factor is improved by cubic polynomials, and the optimal damping factor is determined by quadratic sequence programming. Furthermore, this study analyzes the kinematic constraints of the closed-chain system and constructs a closed-chain Jacobian to judge whether the system is in a singular region. Finally, the effectiveness of the proposed method is verified through simulations.

Colour evolution and infrared physics

We give a complete account of how soft gluon, massless quark, evolution equations in colour space originate, from a factorization into a hard cross section density operator and a soft function encoding measurements and the projection on definite colours. We detail this formalism up to the two loop level and we demonstrate how the evolution kernels relate to infrared subtractions, and how the resolution of infrared singular regions conspires with the structure of observables the algorithm should be able to predict. The latter allows us to address evolution in different kinematic variables, including energy ordering and angular cutoffs in non-global observables. The soft factor and its evolution resembles a hadronization model including effects such as colour reconnection, and could give insight into the structure of power corrections in observables which require soft gluon evolution.

The role of pain modulation pathway and related brain regions in pain.

Pain is a multifaceted process that encompasses unpleasant sensory and emotional experiences. The essence of the pain process is aversion, or perceived negative emotion. Central sensitization plays a significant role in initiating and perpetuating of chronic pain. Melzack proposed the concept of the "pain matrix", in which brain regions associated with pain form an interconnected network, rather than being controlled by a singular brain region. This review aims to investigate distinct brain regions involved in pain and their interconnections. In addition, it also sheds light on the reciprocal connectivity between the ascending and descending pathways that participate in pain modulation. We review the involvement of various brain areas during pain and focus on understanding the connections among them, which can contribute to a better understanding of pain mechanisms and provide opportunities for further research on therapies for improved pain management.

Comparative genomics of rainbow trout (Oncorhynchus mykiss): Is the genetic architecture of migratory behavior conserved among populations?

Rainbow trout (Oncorhynchus mykiss) are a partially migratory species wherein some individuals undergo long-distance anadromous migrations, and others stay as residents in their native freshwater streams. The decision to migrate is known to be highly heritable, and yet, the underlying genes and alleles associated with migration are not fully characterized. Here we used a pooled approach of whole-genome sequence data from migratory and resident trout of two native populations-Sashin Creek, Alaska and Little Sheep Creek, Oregon-to obtain a genome-wide perspective of the genetic architecture of resident and migratory life history. We calculated estimates of genetic differentiation, genetic diversity, and selection between the two phenotypes to locate regions of interest and then compared these associations between populations. We identified numerous genes and alleles associated with life history development in the Sashin Creek population with a notable area on chromosome 8 that may play a critical role in the development of the migratory phenotype. However, very few alleles appeared to be associated with life history development in the Little Sheep Creek system, suggesting population-specific genetic effects are likely important in the development of anadromy. Our results indicate that a migratory life history is not controlled by a singular gene or region but supports the idea that there are many independent ways for a migratory phenotype to emerge in a population. Therefore, conserving and promoting genetic diversity in migratory individuals is paramount to conserving these populations. Ultimately, our data add to a growing body of literature that suggests that population-specific genetic effects, likely mediated through environmental variation, contribute to life history development in rainbow trout.

Locally finite two-loop QCD amplitudes from IR universality for electroweak production

We describe the implementation of infrared subtractions for two-loop QCD corrections to quark-antiquark annihilation to electroweak final states. The subtractions are given as form-factor integrands whose integrals are known. The resulting subtracted amplitudes are amenable to efficient numerical integration. Our procedure is based on the universality of infrared singularities and requires a relatively limited set of subtractions, whose number grows as the number of two-loop diagrams, rather than with the number of singular regions of integration.

Core Promoter Regions of Antisense and Long Intergenic Non-Coding RNAs.

RNA polymerase II (POL II) is responsible for the transcription of messenger RNAs (mRNAs) and long non-coding RNAs (lncRNAs). Previously, we have shown the evolutionary invariance of the structural features of DNA in the POL II core promoters of the precursors of mRNAs. In this work, we have analyzed the POL II core promoters of the precursors of lncRNAs in Homo sapiens and Mus musculus genomes. Structural analysis of nucleotide sequences in positions -50, +30 bp in relation to the TSS have shown the extremely heterogeneous 3D structure that includes two singular regions - hexanucleotide "INR" around the TSS and octanucleotide "TATA-box" at around ~-28 bp upstream. Thus, the 3D structure of core promoters of lncRNA resembles the architecture of the core promoters of mRNAs; however, textual analysis revealed differences between promoters of lncRNAs and promoters of mRNAs, which lies in their textual characteristics; namely, the informational entropy at each position of the nucleotide text of lncRNA core promoters (by the exception of singular regions) is significantly higher than that of the mRNA core promoters. Another distinguishing feature of lncRNA is the extremely rare occurrence in the TATA box of octanucleotides with the consensus sequence. These textual differences can significantly affect the efficiency of the transcription of lncRNAs.