Multiple Singularities Research Articles

"Measuring hunger": psychometric scales of food insecurity and indigenous peoples in Brazil

The Brazilian Food Insecurity Scale (EBIA) was validated for the Brazilian context in 2004. Since then, the scale has evaluated and measured the experience of food insecurity in rural and urban households, initially in the Brazilian National Household Sample Survey and later in the Brazilian National Survey of Demographic and Health. However, indigenous peoples have not been examined specifically in these surveys, despite recognition of their food and nutritional vulnerability. In this scenario, we analyze and discuss the application of the EBIA among indigenous peoples in Brazil, based on a set of fundamental questions for understanding and measuring their experience with food insecurity and "hunger". We conduct a sociopolitical and ethnographic analysis of a set of official documents and significant articles on the use of psychometric scales of food insecurity among Brazilian indigenous peoples, compared to international studies on the validation and application of scales in other sociocultural contexts. The initiatives with adaptation and application of the EBIA to indigenous peoples in Brazil indicate that understanding and measuring food insecurity in these peoples poses a major challenge. Particularly complex is the proposal to guarantee comparability of different contexts while taking into account the multiple local singularities. We propose that ethnographic studies should serve as specific components of future initiatives on this topic and that they should cover aspects such as the seasonality of indigenous peoples' food production, different processes of food monetization, and the dynamics of their food systems.

Energy Spectrum of Linear Internal Wave Field in the Vicinity of Continental Slope

The purpose of the research was to investigate two-dimensional modeling of efficiency of mixing, resulting from the reflection of a linear internal wave field (IWF) off a continental slope. Efficiency of deep ocean mixing was associated with the energy balance of the radiating IWF into an interior of the ocean in the vicinity of a sloping bottom topography. Since waves are generated not only at the fundamental frequency but also at all of its harmonics ωn = nω less than buoyancy frequency N and greater than Coriolis frequency f, our analysis includes, in general, an infinite number of discrete internal wave modes n satisfying the dispersion relationship for internal waves. However, since we are interested only in the radiating part of the field, the mode numbers are limited. Due to multiple singularities of order two caused by resonance in the vicinity of critical slope, the energy is visualized in Lδ -norm with δ > 2. Research results include the visualization of the effects of the continental slope and the Earth’s rotation on resulting energy in the vicinity of the slope.

Investigations on the turbulence resistant characteristics of Custom Designed Beams embedded with multiple phase singularities

Investigation on the propagation of an optical beam carrying phase singularities through atmospheric turbulence attracts researcher involved in the laser projection applications. In this paper, a group of Custom Designed Beams (CDB) are designed by radially encoding the multiple singular phases at the predefined locations to study the turbulence resistant property of these beams. Generation and propagation of these CDB are investigated in free space and the presence of atmospheric turbulence. The CDB are generated by a computer-generated hologram employing on the phase-only SLM. The ensquared energy of the CDB are calculated numerically and validated with the experimental results in free-space. Also, the effect of atmospheric turbulence on the propagation of the CDB is comprehensively investigated with the help of two types of turbulence simulators, atmospheric turbulence simulator and the turbulence cell, in the laboratory. A MATLAB based modified offline video processing method is used to compute all the relevant performance parameters. The effectiveness of these beams is determined by analyzing the beam deformation/spreading as beam spreading ratio and sensitiveness towards intensity fluctuation as scintillation index with reference to the conventional Gaussian beam. It is also reported that the CDB having multiple phase singularities at predefined configuration shows a significant decrease in the percentage of intensity fluctuations as compared to the Gaussian beam. Out of all the analyzed beams, the CDB of cases C14 and C15 show a significant reduction in scintillation index by 20–30% with more energy intact at the center. Thus, CDB of cases C14 and C15 would be proposed as the preferred design for laser projection applications.

Birational Superrigidity and K-Stability of Singular Fano Complete Intersections

Abstract We introduce an inductive argument for proving birational superrigidity and $K$-stability of singular Fano complete intersections of index one, using the same types of information from lower dimensions. In particular, we prove that a hypersurface in $\mathbb{P}^{n+1}$ of degree $n+1$ with only ordinary singularities of multiplicity at most $n-5$ is birationally superrigid and $K$-stable if $n\gg 0$. As part of the argument, we also establish an adjunction-type result for local volumes of singularities.

Interview with Ph.D. Berenice McCarthy on Application of the Model 4 MAT and the search for revolutionary conceptions about teaching

The interview with the Ph.D. Berenice McCarthy, founder of About Learning, addresses the methodological understanding of the Model 4 MAT and its application in the construction of teaching climates for educational justice, difference and inclusion. It is conceived as a key didactic device for overcoming the pragmatic obstacle of Inclusive Education, especially, it appeals to the organization of learning experiences in accordance with human nature, conceiving that human beings are multifaceted, complex and unique. For this reason the Ph.D. McCarthy states that learning arises from the integration of feeling, thinking, reflecting and acting. In short, it provides a new analytical-methodological framework for planning teaching focused on the multiplicity of differences present in the school space. In this framework, the whole must be conceived in terms of multiple singularities.

Patchwise Mapping Method for Solving Elliptic Boundary Value Problems Containing Multiple Singularities

In the paper [1], the geometrical mapping techniques based on Non-Uniform Rational B-Spline (NURBS) were introduced to solve an elliptic boundary value problem containing a singularity. In the mapping techniques, the inverse function of the NURBS geometrical mapping generates singular functions as well as smooth functions by an unconventional choice of control points. It means that the push-forward of the NURBS geometrical mapping that generates singular functions, becomes a piecewise smooth function. However, the mapping method proposed is not able to catch singularities emerging at multiple locations in a domain. Thus, we design the geometrical mapping that generates singular functions for each singular zone in the physical domain. In the design of the geometrical mapping, we should consider the design of control points on the interface between/among patches so that global basis functions are in C0 space. Also, we modify the B-spline functions whose supports include the interface between/among them. We put the idea in practice by solving elliptic boundary value problems containing multiple singularities.

Multiple Singularities of the Equilibrium Free Energy in a One-Dimensional Model of Soft Rods.

There is a misconception, widely shared among physicists, that the equilibrium free energy of a one-dimensional classical model with strictly finite-ranged interactions, and at nonzero temperatures, cannot show any singularities as a function of the coupling constants. In this Letter, we discuss an instructive counterexample. We consider thin rigid linear rods of equal length 2ℓ whose centers lie on a one-dimensional lattice, of lattice spacing a. The interaction between rods is a soft-core interaction, having a finite energy U per overlap of rods. We show that the equilibrium free energy per rod F[(ℓ/a),β], at inverse temperature β, has an infinite number of singularities, as a function of ℓ/a.

On the Usage of Different Coordinate Systems for 3D Plots of Functions of Two Real Variables

Students learning towards a degree in a STEM related domain learn quite early a course in Advanced Calculus, i.e. a course where the main object of study are multivariate functions. It happens that students do not see the connection between the properties of the function such as continuity or differentiability and the 3-dimensional graphical representation. In particular, difficulties appear in classroom for functions having different limits at a point, according to the path approaching the point. One of the ways for this analysis is to use different coordinate systems to study the behavior of the function. Constraints exist on the hardware, the software and on the numerical approximation methods, which may lead to completely different graphs for the same function, when using two different coordinate systems. In this contribution we analyze the different types of graphs created with a CAS such as MATLAB 14 and Maple 2017 for different coordinate systems, in terms of properties of the 2-variable function under study. We prove that when the function is continuous, the 3D graphical representation does not depend on the coordinate system in use. However, when the function is discontinuous,the graphical representation depends strongly on the coordinate system and on the type of discontinuity (point singularity, line singularity, multiple singularity, etc.). Moreover, without a suitable analysis prior to plotting, the 3D graph may be uncorrect. The software shows a strange behavior around the singular points. It happens also that a line singularity is replaced either by a point singularity or by no singularity. We analyse the software behavior using numerical analysis of the meshing algorithm.

On the Neumann problem of Hardy-Sobolev critical equations with the multiple singularities

Let $N ≥ 3$ and $Ω \subset \mathbb{R}^N$ be a $C^2$ bounded domain. We study the existence of positive solution $u ∈ H^1(Ω)$ of$\begin{align*}\left\{\begin{array}{l}-\Delta u + \lambda u = \frac{|u|^{2^*(s)-2}u}{|x-x_1|^s} + \tau \frac{|u|^{2^*(s)-2}u}{|x-x_2|^s}\text{ in }\Omega\\\frac{\partial u}{\partial \nu} = 0 \text{ on }\partial\Omega,\end{array}\right.\end{align*}$where $τ = 1$ or $-1$, $0 < s <2$, $2^*(s) = \frac{2(N-s)}{N-2}$ and $x_1, x_2 ∈ \overline{Ω}$ with $x_1 ≠ x_2$. First, we show the existence of positive solutions to the equation provided the positive $λ$ is small enough. In case that one of the singularities locates on the boundary and the mean curvature of the boundary at this singularity is positive, the existence of positive solutions is obtained for any $λ > 0$ and some $s$ depending on $τ$ and $N$. Furthermore, we extend the existence theory of solutions to the equations for the case of the multiple singularities.

Generalized motorcycle graphs for imperfect quad-dominant meshes

We introduce a practical pipeline to create UV T-layouts for real-world quad dominant semi-regular meshes. Our algorithm creates large rectangular patches by relaxing the notion of motorcycle graphs and making it insensitive to local irregularities in the mesh structure such as non-quad elements, redundant irregular vertices, T-junctions, and others. Each surface patch, which can contain multiple singularities and/or polygonal elements, is mapped to an axis-aligned rectangle, leading to a simple and efficient UV layout, which is ideal for texture mapping (allowing for mipmapping and artifact-free bilinear interpolation). We demonstrate that our algorithm is an ideal solution for both recent semi-regular, quad-dominant meshing methods, and for the low-poly meshes typically used in games and movies.

Black hole and cosmos with multiple horizons and multiple singularities in vector-tensor theories

A stationary and spherically symmetric black hole (For example, Reissner-Nordstrom black hole or Kerr-Newman black hole) has at most one singularity and two horizons. One horizon is the outer event horizon and the other is the inner Cauchy horizon. Can we construct static and spherically symmetric black hole solutions with N horizons and M singularities? De Sitter cosmos has only one apparent horizon. Can we construct cosmos solutions with N horizons? In this article, we present the static and spherically symmetric black hole and cosmos solutions with N horizons and M singularities in the vector-tensor theories. Following these motivations, we also construct the black hole solutions with a firewall. The deviation of these black hole solutions from the usual ones can be potentially tested by future measurements of gravitational waves.

Gaussian beams with multiple polarization singularities

In recent years, alongside light beams with phase singularities (so-called optical vortices), polarization vortices (including beams with radial and azimuthal polarization) have also been studied. In this work, we analyze paraxial Gaussian beams that have an array of arbitrarily located polarization singularities. A closed analytical expression to describe their complex amplitude is derived. A particular case of singularities localized at the vertices of a regular polygonal is discussed. If the beam has one or two singularities, these points will have radial polarization. If, however, there are four singularities, two of them will be characterized by azimuthal polarization. As the beam propagates, the polarization singularities found in the initial plane are shown to reoccur only in a discrete set of planes, unlike phase singularities, which occur at any transverse plane. In the case of two singularities, radial polarization in the initial plane is found to convert into azimuthal polarization in the far-field. The research findings may find uses in optical data transmission.

Interview with Ph.D. Thomas Armstrong on Neurodiversity and Construction of a Talent Pedagogy: critical axes for a new Inclusive Education

interview with the Ph.D. Thomas Armstrong, author of the famous book The power of and director of the American Institute for Learning and Human Development, delves into the emerging understanding of the field of knowledge of neurodiversity, trying to establish significant analytical and methodological links in relation to the dimension didactic of Inclusive Education. central premise of neurodiversity - a concept that emerged in the early 2000s - provides a new framework for the understanding of human nature, through which neurological differences based on genetics in a person should be considered as variations normal in human functioning as well as in the diversity of gender, ethnicity, cultural origin, etc., states the Ph.D. Armstrong. In relation to the education of educators, it is recommended to apprehend to recognize the positive attributes present in the multiple singularities of the human being, to structure the educational and formative processes from the confluence of their interests, motivations and interests. Finally, he explains how Inclusive Education is linked to neurodiversity, arguing that, the neurodiversity paradigm helps to support inclusion in the classroom, because we begin to see that everyone has differences in the ways in which they attend, learn, they behave, they think and they feel. In short, the interview provides new keys to operationalize the understanding of the whole conceived as multiple singularities.

A limit theorem for a class of stationary increments Lévy moving average process with multiple singularities

In this paper we present some new limit theorems for power variations of stationary increment Lévy driven moving average processes. Recently, such asymptotic results have been investigated in [Ann. Probab. 45(6B) (2017), 4477–4528, Festschrift for Bernt Øksendal, Stochastics 81(1) (2017), 360–383] under the assumption that the kernel function potentially exhibits a singular behaviour at 0. The aim of this work is to demonstrate how some of the results change when the kernel function has multiple singularity points. Our paper is also related to the article [Stoch. Process. Appl. 125(2) (2014), 653–677] that studied the same mathematical question for the class of Brownian semi-stationary models.

New conformal mapping for adaptive resolving of the complex singularities of Stokes wave.

A new highly efficient method is developed for computation of travelling periodic waves (Stokes waves) on the free surface of deep water. A convergence of numerical approximation is determined by the complex singularities above the free surface for the analytical continuation of the travelling wave into the complex plane. An auxiliary conformal mapping is introduced which moves singularities away from the free surface thus dramatically speeding up numerical convergence by adapting the numerical grid for resolving singularities while being consistent with the fluid dynamics. The efficiency of that conformal mapping is demonstrated for the Stokes wave approaching the limiting Stokes wave (the wave of the greatest height) which significantly expands the family of numerically accessible solutions. It allows us to provide a detailed study of the oscillatory approach of these solutions to the limiting wave. Generalizations of the conformal mapping to resolve multiple singularities are also introduced.

Singularities of plane rational curves via projections

We consider the parameterization f=(f0:f1:f2) of a plane rational curve C of degree n, and we study the singularities of C via such parameterization. We use the projection from the rational normal curve Cn⊂Pn to C and its interplay with the secant varieties to Cn. In particular, we define via f certain 0-dimensional schemes Xk⊂Pk, 2≤k≤(n−1), which encode all information on the singularities of multiplicity ≥k of C (e.g. using X2 we can give a criterion to determine whether C is a cuspidal curve or has only ordinary singularities). We give a series of algorithms which allow one to obtain information about the singularities from such schemes.

Backlash characterization and position control of a robotic catheter manipulator using experimentally-based kinematic model

This paper deals with the problem of position control of a robot-assisted catheter manipulator for intracardiac interventions. Kinematic controllers based on the Jacobian inverse are not suitable for the catheter because of multiple singularities in the workspace and significant backlash of the system. To tackle these issues, first, the backlash of the system in axial translation and twist motion due to the interaction of the catheter with the veins through which it passes, are characterized. The effects of variations in clinical settings on the backlash parameters are identified through extensive experiments simulating the clinical procedure. Next, to properly compensate for the backlash behavior of the catheter distal shaft, an inverse kinematic model is proposed based on experimental data. A position controller is developed and implemented using the experimentally-based inverse kinematics and the identified inverse backlash model for the twist and axial motion. The results of experiments performed using a robotic catheter manipulation system show that with a proper choice of controller gains, the proposed scheme is able to guide the catheter tip to the goal with the desired behavior. The tracking performance of the controller has also been evaluated under the dynamic external force simulating the blood drag force. The empirical results demonstrate the improved performance of the proposed approach against the existing kinematic-based and uncompensated control schemes.

Heuristic computational intelligence approach to solve nonlinear multiple singularity problem of sixth Painlev́e equation

The present study investigate the numerical solution of nonlinear singular system represented with sixth Painleve equation by the strength of artificial intelligence using feed-forward artificial neural networks (ANNs) optimized with genetic algorithms (GAs), interior point technique (IPT), sequential quadratic programming (SQP), and their hybrids. The ANN provided a compatible method for finding nature-inspired mathematical model based on unsupervised error for sixth Painleve equation and adaptation of weights of these networks is carried out globally by the competency of GA aided with IPT or SQP algorithms. Moreover, a hybrid approach has been adopted for better proposed numerical results. An extensive statistical analysis has been performed through several independent runs of algorithms to validate the accuracy, convergence, and exactness of the proposed scheme.

A note on Sobolev isometric immersions below W2,2 regularity

This paper aims to investigate the Hessian of second order Sobolev isometric immersions below the natural W2,2 setting. We show that the Hessian of each coordinate function of a W2,p, p<2, isometric immersion satisfies a low rank property in the almost everywhere sense, in particular, its Gaussian curvature vanishes almost everywhere. Meanwhile, we provide an example of a W2,p, p<2, isometric immersion from a bounded domain of R2 into R3 that has multiple singularities.

Existence and nonexistence results for critical biharmonic systems involving multiple singularities

In this paper, a system of biharmonic equations is investigated, which involves critical Sobolev nonlinearities and multiple singular points. By variational methods and analytical techniques, the best Soblev constant corresponding to the system is investigated, and the existence (nonexistence) of ground state solutions to the system is established.