Non-critical Points Research Articles

Multipartite entanglement serves as a faithful detector for quantum phase transitions

We investigate quantum phase transitions (QPTs) in various spin chain systems using the multipartite entanglement measure τSEF based on the monogamy inequality of squared entanglement of formation (EOF). Our results demonstrate that τSEF is more effective and reliable than bipartite entanglement or bipartite correlation measures such as EOF, von Neumann entropy, and quantum discord in characterizing QPTs. τSEF not only detects critical points that may go unnoticed by other detectors but also avoids the issue of singularity at non-critical points encountered by other measures. Furthermore, by applying τSEF , we have obtained the phase diagram for the XY spin chain with three and four interactions and discovered a new quantum phase.

Searching natural neighbors in an accelerated way

Natural neighbor (NaN) is an adaptive neighbor concept for automatically determining k value for k-nearest neighbors, which has been proved effective in clustering analysis, classification, and outlier detection. However, the existing algorithms for searching NaN employ the global search strategy, which increases unnecessary consumption of time on non-critical points. To solve this problem, we propose a novel accelerated algorithm by utilizing a local search strategy, called ASNN. ASNN is based on the fact that if remote points have reverse nearest neighbors, others are likely to have reverse nearest neighbors. Firstly, it extracts the remote points by defining remote radius. Secondly, only the neighbors of remote points are searched, so that ASNN can quickly obtain the natural neighbor eigenvalue (NaNE). Compared to existing algorithms for searching NaNs, ASNN drastically reduces the number of query points and time consumption. The efficiency and effectiveness of ASNN are proved on synthetic and real datasets.

Quantum speed limit and topological quantum phase transition in an extended [formula omitted] model

We explore quantum speed limit time τQSL of a qubit system coupling to a spin chain environment which is described by an extended Ising model associated with non-trivial topological characterization. For an initial pure state, we find that τQSL exhibits a behavior of local maximum around all critical points when the environment spin chain undergoes a topological quantum phase transition driven by external magnetic field λ or the anisotropy γ of nearest-neighbor interaction. And the value of local maximum would increase by strengthening the coupling between the system and environment around the critical points. However, the behavior of τQSL are both driving parameters and critical points dependent when the topological quantum phase transition is driven by the three-site interaction α or its anisotropy δ. Additionally, we also investigate τQSL for arbitrary time-evolution state in the whole dynamics process and find that τQSL exhibits a behavior of oscillation at non-critical points. However, τQSL will decay rapidly to zero around all critical points, and such trend accompany with oscillation behavior at some critical points.

Families of Bianchi modular symbols: critical base-change p-adic L-functions and p-adic Artin formalism

Let K be an imaginary quadratic field. In this article, we study the eigenvariety for mathrm {GL}_2/K, proving an étaleness result for the weight map at non-critical classical points and a smoothness result at base-change classical points. We give three main applications of this; let f be a p-stabilised newform of weight k ge 2 without CM by K. Suppose f has finite slope at p and its base-change f_{/K} to K is p-regular. Then: (1) We construct a two-variable p-adic L-function attached to f_{/K} under assumptions on f that conjecturally always hold, in particular with no non-critical assumption on f/K. (2) We construct three-variable p-adic L-functions over the eigenvariety interpolating the p-adic L-functions of classical base-change Bianchi cusp forms. (3) We prove that these base-change p-adic L-functions satisfy a p-adic Artin formalism result, that is, they factorise in the same way as the classical L-function under Artin formalism.

Towards an adaptable quality monitoring process for self-piercing riveting

In the automotive industry self-piercing riveting (SPR) is a standard joining technology, especially for vehicles with a high mix of materials. The applied quality control system and the underlying quality decisions have hardly changed in the recent years. The commonly used combination of process monitoring and rework strategies leads to a large number of false positives and a high amount of manual work. The collected process data is not used comprehensively and misses the potential to improve the SPR process. This article introduces a quality monitoring method for SPR to show a proof of concept by using machine learning to predict faulty joining points. Based on numerous technical and statistical features extracted from the force-displacement curve of SPR, the trained model categorizes the observations in two rivet head height (RHH) classes. An evolutionary algorithm is used for the feature selection and a random forest model for classification. The resulting accuracy scores up to 84.4% and shows the potential of the developed random forest model. The potential application of this approach in the context of serial body-shop production improves the prediction of joining quality and the process availability significantly. This enables the adaptable rework of non-critical joining points depending on the classified RHH.

Thermodynamic properties of the spin S=3/2 quantum ferromagnetic Blume-Capel model in a transverse crystal field.

The thermodynamic properties of the spin S=3/2 ferromagnetic Ising model in the presence of transverse and longitudinal crystal fields (equivalent to the Blume-Capel model with a transverse crystal field) have been studied by using two different approaches: (i) a zero-temperature mapping of the system onto a spin-1/2 quantum Ising model in longitudinal and transverse fields, together with time-independent quantum perturbation theory; and (ii) a standard mean-field approximation within the framework of the Bogoliubov inequality for the free energy. A very rich phase diagram, with different kinds of multicritical behavior, has been obtained. The results show first- and second-order transition lines, tricritical and tetracritical points, critical end points with a two-phase coexistence, double critical end points, and also double noncritical end points. Additionally, the behavior of the magnetization as a function of temperature, over a wide range of values of both longitudinal and transverse crystal fields, has also been analyzed in detail. While large magnitudes of the longitudinal crystal field select the z-spin components either in their states ±3/2 or ±1/2, it is surprising that a large transverse crystal field induces the spin component in the z direction to values ±1, which are completely different from any expected natural component. This comes indeed as a result of the zero-temperature mapping of the ground state with the superposition of the states 3/2 and -1/2, in one sector of the Hilbert space, and the states -3/2 and 1/2 on the other disjoint sector of the Hilbert space. This superposition for a large transverse crystal field prevails even for finite temperatures, implying that the exact critical points are obtained for the model on the one-dimensional lattice and the two-dimensional square lattice, and quite accurate estimates can be achieved for the three-dimensional simple cubic lattice.

Higher order weighted Sobolev spaces on the real line for strongly degenerate weights. Application to variational problems in elasticity of beams

For one-dimensional interval and integrable weight function w we define via completion a weighted Sobolev space Hμwm,p of arbitrary integer order m. The weights in consideration may suffer strong degeneration so that, in general, functions u from Hμwm,p do not have weak derivatives. This contribution is focussed on studying the continuity properties of functions u at a chosen internal point x0 to which we attribute a notion of criticality of order k and with respect to the weight w. For non-critical points x0 we formulate a local embedding result that guarantees continuity of functions u or their derivatives. Conversely, we employ duality theory to show that criticality of x0 furnishes a smooth approximation of functions in Hμwm,p admitting jump-type discontinuities at x0. The work concludes with demonstration of established results in the context of variational problem in elasticity theory of beams with degenerate width distribution.

¿Emergency ambulances potential source of infections? An assessment of cleaning and disinfection procedures

Objective: evaluate the cleaning and disinfection procedures (CDP) in six ambulances from three different entities in Pereira (Risaralda-Colombia).
 Methods: cross-sectional descriptive study frequencies of presence/absence were calculated from data obtained in the bacterial growth results before and after CDP, taking samples in three different places on the ambulances, being: back door, stretcher and wall next to the patient, before and after said processes. Additionally, surveys were carried out at the domicile of companies providing pre-hospital transport service.
 Results: 77.8% of the samples were positive. The most frequent morphology in the study was gram-positive cocci, which remained in a greater proportion after disinfection. At the microbiologic level, most of these suggested being Staphylococcus aureus-type. By implementing CDP, microbiological isolates were eliminated in 33.3%, being the door the ambulance area, which showed the greatest decrease (50.0%).
 Conclusions: A high prevalence of potentially pathogenic microorganisms exists in non-critical points of emergency ambulances. With CDPs, a decrease in microorganisms is achieved, but not their elimination, leaving in evidence that different factors must be considered in order to improve these CDP.

Vulnerability of the Largest Normalized Residual Statistical Test to Leverage Points

The largest normalized residual statistical test (LNRT) is claimed to have the ability to detect noncritical single or multiple interacting but nonconforming bad data. However, we show in this letter that this claim does not always hold true for bad leverage points. Specifically, we prove that while a single noncritical and nonleverage measurement that is corrupted by a sufficiently large gross error is likely to be detected, the same measurement in a position of leverage and corrupted by the same gross error is unlikely to be detected. Furthermore, we show that multiple noncritical bad leverage points that are topologically adjacent to each other naturally form one or several groups of interacting bad data, which may cause the LNRT to fail. Since leverage points are common in actual power systems, the LNRT is doomed to frequently fail to detect bad data. Simulation results carried out on IEEE 30-bus system validate our theoretical results.

Critical mathcal{N} = (1, 1) general massive supergravity

In this paper we study the supermultiplet structure of mathcal{N} = (1, 1) General Massive Supergravity at non-critical and critical points of its parameter space. To do this, we first linearize the theory around its maximally supersymmetric AdS3 vacuum and obtain the full linearized Lagrangian including fermionic terms. At generic values, linearized modes can be organized as two massless and 2 massive multiplets where supersymmetry relates them in the standard way. At critical points logarithmic modes appear and we find that in three of such points some of the supersymmetry transformations are non-invertible in logarithmic multiplets. However, in the fourth critical point, there is a massive logarithmic multiplet with invertible supersymmetry transformations.

Comparison of Different Training Data Reduction Approaches for Fast Support Vector Machines Based on Principal Component Analysis and Distance Based Measurements

Support vector machine is a supervised learning algorithm, which is recommended for classification and nonlinear function approaches. Support vector machines require remarkable amount of memory with time consuming process for large data sets in the training process. The main reason for this is the solving a constrained quadratic programming problem within the algorithm. In this paper, we proposed three approaches for identifying the non-critical points in training set and remove these non-critical points from the original training set for speeding up the training process of support vector machine. For this purpose, we used principal component analysis, Mahalanobis distance and Euclidean distance based measurements for the elimination of non-critical training instances in the training set. We compared the proposed methods in terms of computational time and classification accuracy between each other and conventional support vector machine. Our experimental results show that principal component analysis and Mahalanobis distance based proposed methods have positive effects on computational time without degrading the classification results than the Euclidean distance based proposed method and conventional support vector machine.

Triangulation of refined families

We prove the global triangulation conjecture for families of refined p -adic representations under a mild condition. That is, for a refined family, the associated family of (\varphi, \Gamma) -modules admits a global triangulation on a Zariski open and dense subspace of the base that contains all regular non-critical points. We also determine a large class of points which belongs to the locus of global triangulation. Furthermore, we prove that all the specializations of a refined family are trianguline. In the case of the Coleman–Mazur eigencurve, our results provide the key ingredient for showing its properness in a subsequent work [15].

Periodic points of birational transformations on projective surfaces

We classify birational maps of projective smooth surfaces whose non-critical periodic points are Zariski dense. In particular, we show that if the first dynamical degree is greater than one, then the periodic points are Zariski dense.

Plateau-Stein manifolds

Abstract We study/construct (proper and non-proper) Morse functions f on complete Riemannian manifolds X such that the hypersurfaces f(x) = t for all −∞ < t < +∞ have positive mean curvatures at all non-critical points x ∈ X of f. We show, for instance, that if X admits no such (not necessarily proper) function, then it contains a (possibly, singular) complete (possibly, compact) minimal hypersurface of finite volume.

Fractional sewage treatment models with impulses at variable times

In this article, two classes of sewage treatment models involving Caputo fractional derivative with impulses at variable times are established. Firstly, some new developed concepts such as critical points and noncritical points, () nonlinear functions sets, and ()-mild solutions are introduced. Secondly, local and global existence of solutions are obtained and other interesting properties such as local stability and periodic oscillatory phenomena of solutions are presented. Finally, a useful wastewater treatment model is given to demonstrate our theory results.

On the infinite fern of Galois representations of unitary type

Soient E un corps de nombres CM, p un nombre premier impair totalement décomposé dans E, et soit X l’espace analytique p-adique paramétrant les classes d’isomorphie de représentations p-adiques semisimples de dimension 3 de Gal (E ¯/E) satisfaisant une condition d’autodualité « de type U(3) ». Nous étudions un analogue de la fougère infinie de Gouvêa-Mazur dans ce contexte et démontrons que l’adhérence Zariski des points modulaires de X a toutes ses composantes irréductibles de dimension au moins 3[E:ℚ]. Au passage, nous prouvons en toute dimension que toute déformation à l’ordre 1 d’une représentation cristalline suffisamment générique de Gal (ℚ ¯ p /ℚ p ) est une combinaison linéaire de déformations triangulines, et que les variétés de Hecke unitaires sont étales sur l’espace des poids aux points classiques non critiques. Enfin, nous obtenons un critère de surjectivité de l’application de localisation en p du groupe de Selmer adjoint ' d’une représentation galoisienne p-adique attachée à une représentation automorphe cuspidale cohomologique de GL n (𝔸 E ) qui est de type U(n) (pour tout n).

The problem of minimizing locally a 𝐶² functional around non-critical points is well-posed

In this paper, we prove the following general result: Let X X be a real Hilbert space and J : X → R J:X\to \textbf {R} a C 1 C^1 functional, with locally Lipschitzian derivative. Then, for each x 0 ∈ X x_0\in X with J ′ ( x 0 ) ≠ 0 J’(x_0)\neq 0 , there exists δ > 0 \delta >0 such that, for every r ∈ ] 0 , δ [ r\in ]0,\delta [ , the restriction of J J to the sphere { x ∈ X : ‖ x − x 0 ‖ = r } \{x\in X : \|x-x_0\|=r\} has a unique global minimum toward which every minimizing sequence strongly converges.

Diagnóstico del estudio ergonómico en la Universidad Militar Nueva Granada

El proyecto “Estudio y análisis ergonómico en las oficinas de la Universidad Militar Nueva Granada en los niveles administrativos (asesor, ejecutivo, profesional, técnico y asistencial)”, esta constituido por cuatro fases: diagnóstico, estudio de condiciones ambientales, estudio antropométrico y diseño del plan de capacitación. En este artículo, Nosotros describimos la primera fase, que consiste en evaluar los aspectos ergonómicos de la Universidad Militar. La recolección de información a través de encuestas y formatos de observación y se realizo un análisis estadísticos de un software comercial. Basado en resultados cuatro puntos críticos fueron identificados, iluminación, seguridad industrial, diseño de puestos de trabajo, así como también la percepción de los empleados frente a la ergonomía. Dos factores no críticos fueron identificados, el ruido y la temperatura. Estos serán sujeto de futuras investigaciones.

Entanglement properties of quantum spin chains

Entanglement are the non-local correlations permitted by quantum theory, believed to play a fundamental role in a quantum computer. We have investigated these correlations in a number of theoretical models for condensed matter systems. Such systems are likely candidates for quantum computing, and experimentally feasible for instance as superconducting qubits. At quantum critical points the ground state of these systems is very complicated, and the entanglement is usually larger than at non-critical points. This entanglement can be used to identify the critical points through what we denote the entanglement signature, even for very small systems. From another perspective, it seems that the entanglement is an essential tool to find an unknown ground state, since this gives rise to a simple decomposition of the state.

The Chang–Refsdal lens revisited

This paper provides a complete theoretical treatment of the point-mass lens perturbed by constant external shear, often called the Chang–Refsdal lens. We show that simple invariants exist for the products of the (complex) positions of the four images, as well as moment sums of their signed magnifications. The image topographies and equations of the caustics and critical curves are also studied. We derive the fully analytic expressions for pre-caustics, which are the loci of non-critical points that map to the caustics under the lens mapping. They constitute boundaries of the region in the image domain that maps on to the interior of the caustics. The areas under the critical curves, caustics and pre-caustics are all evaluated, which enables us to calculate the mean magnification of the source within the caustics. Additionally, the exact analytic expression for the magnification distribution for the source in the triangular caustics is derived, as well as a useful approximate expression. Finally, we find that the Chang–Refsdal lens with additional convergence greater than unity (the ‘overfocusing case’) can exhibit third-order critical behaviour, if the ‘reduced shear’ is exactly equal to , and that the number of images for N-point masses with non-zero constant shear cannot be greater than 5N− 1.