Class Constraints Research Articles

Translational symmetries of quadratic Lagrangians

In this paper, we show that a quadratic Lagrangian, with no constraints, containing ordinary time derivatives up to the order [Formula: see text] of [Formula: see text] dynamical variables, has [Formula: see text] symmetries consisting in the translation of the variables with solutions of the equations of motion. We construct explicitly the generators of these transformations and prove that they satisfy the Heisenberg algebra. We also analyze other specific cases which are not included in our previous statement: the Klein–Gordon Lagrangian, [Formula: see text] Fermi oscillators and the Dirac Lagrangian. In the first case, the system is described by an equation involving partial derivatives, the second case is described by Grassmann variables and the third shows both features. Furthermore, the Fermi oscillator and the Dirac field Lagrangians lead to second class constraints. We prove that also in these last two cases there are translational symmetries and we construct the algebra of the generators. For the Klein–Gordon case we find a continuum version of the Heisenberg algebra, whereas in the other cases, the Grassmann generators satisfy, after quantization, the algebra of the Fermi creation and annihilation operators.

Gauge generator for bi-gravity and multi-gravity models

Following the Hamiltonian structure of bi-gravity and multi-gravity models in the full phase space, we have constructed the generating functional of diffeomorphism gauge symmetry. As is expected, this generator is constructed from the first class constraints of the system. We show that this gauge generator works well in giving the gauge transformations of the canonical variables.

Jacobi sigma models

We introduce a two-dimensional sigma model associated with a Jacobi manifold. The model is a generalisation of a Poisson sigma model providing a topological open string theory. In the Hamiltonian approach first class constraints are derived, which generate gauge invariance of the model under diffeomorphisms. The reduced phase space is finite-dimensional. By introducing a metric tensor on the target, a non-topological sigma model is obtained, yielding a Polyakov action with metric and B-field, whose target space is a Jacobi manifold.

Hamiltonian formalism of the ghost free tri(-multi)gravity theory

We study the Hamiltonian structure of tri-gravity and four-gravity in the framework of ADM decomposition of the corresponding metrics. Hence we can deduce the general structure of the constraint system of multi-gravity. We will show it is possible and consistent to assume additional constraints which provide the needed first class constraints for generating diffeomorphism as well as enough second class constraints to omit the ghosts.

Canonical analysis of Brans-Dicke theory addresses Hamiltonian inequivalence between the Jordan and Einstein frames

Jordan and Einstein frame are studied under the light of Hamiltonian formalism. Dirac's constraint theory for Hamiltonian systems is applied to Brans-Dicke theory in the Jordan Frame. In both Jordan and Einstein frame, Brans-Dicke theory has four secondary first class constraints and their constraint algebra is closed. We show, contrary to what is generally believed, the Weyl (conformal) transformation, between the two frames, is not a canonical transformation, in the sense of Hamiltonian formalism. This addresses quantum mechanical inequivalence as well. A canonical transformation is shown.

A Generalized Method for Binary Optimization: Convergence Analysis and Applications.

Binary optimization problems (BOPs) arise naturally in many fields, such as information retrieval, computer vision, and machine learning. Most existing binary optimization methods either use continuous relaxation which can cause large quantization errors, or incorporate a highly specific algorithm that can only be used for particular loss functions. To overcome these difficulties, we propose a novel generalized optimization method, named Alternating Binary Matrix Optimization (ABMO), for solving BOPs. ABMO can handle BOPs with/without orthogonality or linear constraints for a large class of loss functions. ABMO involves rewriting the binary, orthogonality and linear constraints for BOPs as an intersection of two closed sets, then iteratively dividing the original problems into several small optimization problems that can be solved as closed forms. To provide a strict theoretical convergence analysis, we add a sufficiently small perturbation and translate the original problem to an approximated problem whose feasible set is continuous. We not only provide rigorous mathematical proof for the convergence to a stationary and feasible point, but also derive the convergence rate of the proposed algorithm. The promising results obtained from four binary optimization tasks validate the superiority and the generality of ABMO compared with the state-of-the-art methods.

Ferri-chiral compounds with potentially switchable Dresselhaus spin splitting

Spin splitting of energy bands can be induced by relativistic spin-orbit interactions in materials without inversion symmetry. Whereas polar space group symmetries permit Rashba (R-1) spin splitting with helical spin textures in momentum space, which could be reversed upon switching a ferroelectric polarization via applied electric fields, the ordinary Dresselhaus effect (D-1A) is ac-tive only in materials exhibiting nonpolar noncentrosymmetric crystal classes with atoms occupy-ing exclusively non-polar lattice sites. Consequently, the spin-momentum locking induced by D-1A is not electric field-switchable. An alternative type of Dresselhaus symmetry, referred to as D-1B, exhibits crystal class constraints similar to D-1A (all dipoles add up to zero), but unlike D-1A, at least one polar site is occupied. We find that this behavior exists in a class of ferri-chiral crys-tals, which in principle could be reversed upon a change in chirality. Focusing on alkali metal chalcogenides, we identify NaCu5S3 in the nonentiamorphic ferri-chiral structure, which exhibits CuS3 chiral units differing in the magnitude of their Cu displacements. We then synthesize NaCu5S3 (space group P6322) and confirm its ferri-chiral structure with power x-ray diffraction. Our electronic structure calculations demonstrate it exhibits D-1B spin splitting as well as a ferri-chiral phase transition, revealing spin splitting interdependent on chirality. Our electronic struc-ture calculations show that a few percent biaxial tensile strain can reduce (or nearly quench) the switching barrier separating the monodomain ferri-chiral P6322 states. We discuss what type of external stimuli might switch the chirality so as to reverse the (non-helical) Dresselhaus D-1B spin texture, offering an alternative to the traditional reversal of the (helical) Rashba spin texture.

Schwarzian quantum mechanics as a Drinfeld-Sokolov reduction of BF theory

We give an interpretation of the holographic correspondence between two-dimensional BF theory on the punctured disk with gauge group PSL(2, ℝ) and Schwarzian quantum mechanics in terms of a Drinfeld-Sokolov reduction. The latter, in turn, is equivalent to the presence of certain edge states imposing a first class constraint on the model. The constrained path integral localizes over exceptional Virasoro coadjoint orbits. The reduced theory is governed by the Schwarzian action functional generating a Hamiltonian S1-action on the orbits. The partition function is given by a sum over topological sectors (corresponding to the exceptional orbits), each of which is computed by a formal Duistermaat-Heckman integral.

Efficient Generation of Different Topological Representations of Graphs Beyond-Planarity

Beyond-planarity focuses on combinatorial properties of classes of non-planar graphs that allow for representations satisfying certain local geometric or topological constraints on their edge crossings. Beside the study of a specific graph class for its maximum edge density, another parameter that is often considered in the literature is the size of the largest complete or complete bipartite graph belonging to it. Overcoming the limitations of standard combinatorial arguments, we present a technique to systematically generate all non-isomorphic topological representations of complete and complete bipartite graphs, taking into account the constraints of the specific class. As a proof of concept, we apply our technique to various beyond-planarity classes and achieve new tight bounds for the aforementioned parameter.

A Comparison of Label Switching Algorithms in the Context of Growth Mixture Models.

Simulation studies involving mixture models inevitably aggregate parameter estimates and other output across numerous replications. A primary issue that arises in these methodological investigations is label switching. The current study compares several label switching corrections that are commonly used when dealing with mixture models. A growth mixture model is used in this simulation study, and the design crosses three manipulated variables-number of latent classes, latent class probabilities, and class separation, yielding a total of 18 conditions. Within each of these conditions, the accuracy of a priori identifiability constraints, a priori training of the algorithm, and four post hoc algorithms developed by Tueller et al.; Cho; Stephens; and Rodriguez and Walker are tested to determine their classification accuracy. Findings reveal that, of all a priori methods, training of the algorithm leads to the most accurate classification under all conditions. In a case where an a priori algorithm is not selected, Rodriguez and Walker's algorithm is an excellent choice if interested specifically in aggregating class output without consideration as to whether the classes are accurately ordered. Using any of the post hoc algorithms tested yields improvement over baseline accuracy and is most effective under two-class models when class separation is high. This study found that if the class constraint algorithm was used a priori, it should be combined with a post hoc algorithm for accurate classification.

Ireland, Reading and Cultural Nationalism, 1790–1930, Bringing the Nation to Book

Ireland, Reading and Cultural Nationalism, 1790–1930, Bringing the Nation to Book

A Smartphone-Based Adaptive Recognition and Real-Time Monitoring System for Human Activities

Human activity recognition (HAR) using smartphones provides significant healthcare guidance for telemedicine and long-term treatment. Machine learning and deep learning (DL) techniques are widely utilized for the scientific study of the statistical models of human behaviors. However, the performance of existing HAR platforms is limited by complex physical activity. In this article, we proposed an adaptive recognition and real-time monitoring system for human activities (Ada-HAR), which is expected to identify more human motions in dynamic situations. The Ada-HAR framework introduces an unsupervised online learning algorithm that is independent of the number of class constraints. Furthermore, the adopted hierarchical clustering and classification algorithms label and classify 12 activities (five dynamics, six statics, and a series of transitions) autonomously. Finally, practical experiments have been performed to validate the effectiveness and robustness of the proposed algorithms. Compared with the methods mentioned in the literature, the results show that the DL-based classifier obtains a higher recognition rate (95.15%, waist, and 92.20%, pocket). The decision-tree-based classifier is the fastest method for modal evolution. Finally, the Ada-HAR system can monitor human activity in real time, regardless of the direction of the smartphone.

Second class constraints and the consistency of optimal control theory in phase space

As has been shown in the literature (Rothe and Rothe, 2010; Rothe and Scholtz, 2003), the description of a mechanical system in terms of canonical transformations together with the Hamilton–Jacobi equation for the S function is ill-defined when the system has second class constraints. In this case, Carathéodory’s integrability conditions are violated and either the corresponding Hamilton–Jacobi equation cannot be solved or their solutions do not describe the system at all. This can be remedied by enlarging the phase space so that the constraints become first class in the extended space. Another way to approach this problem, is to apply the Rothe–Scholtz method discussed in Rothe and Rothe (2010) and Rothe and Scholtz (2003), so that the constraints themselves become variables of a new canonical transformation. This method works when the elements of the Dirac matrix are constant. On the other hand, it has been shown that optimal control theory can be written in phase space as a mechanical system with second class restrictions (Itami, 2001; Hojman, 0000; Contreras et al., 2017; Contreras and Peña 2018). This implies that the description of control theory can become inconsistent in terms of the Hamilton–Jacobi equation. In this article we will use the description of Rothe–Scholtz to analyse a subclass of LQ linear-quadratic problems whose Dirac matrix is constant and to check if the integrability conditions can be fulfilled so as to not get inconsistencies.

Start-Up Sprint: Providing a Small Group Learning Experience in a Large Group Setting

Entrepreneurial education should reflect the real-world entrepreneurial process by providing for experiential learning. The challenge is reconciling this with the resource constraints that lead to large class settings, even in specialized postgraduate programs. This article offers practical suggestions for creating a highly interactive event as part of a largely lecture-based module. Students participate in a full-day Start-Up Sprint that uses real-world entrepreneurship tools and mimics the intense experience of a start-up event. This experiential exercise is designed to provide students in a large class with the experience and benefits of small group teaching, through a hands-on problem-based learning exercise that is supported by mentoring and live feedback. It provides entrepreneurship teachers of large classes with a way to mitigate the constraints of large classes, faculty time, and physical infrastructure and offer students a meaningful learning experience.

Ghosts in higher derivative Maxwell-Chern-Simon's theory and [formula omitted]-symmetry

Ghost fields in quantum field theory have been a long standing problem. Specifically, theories with higher derivatives involve ghosts that appear in the Hamiltonian in the form of linear momenta term, which is commonly known as the Ostrogradski ghost. Higher derivative theories may involve both types of constraints i.e. first class and second class. Interestingly, these higher derivative theories may have non-Hermitian Hamiltonian respecting PT-symmetries. In this paper, we have considered the PT-symmetric nature of the extended Maxwell-Chern-Simon's theory and employed the second class constraints to remove the linear momenta terms causing the instabilities. We found that the removal is not complete rather conditions arise among the coefficients of the operator Q.

Reductions of topologically massive gravity II. First order realizations of second order Lagrangians

Second order degenerate Clément and Sarıoğlu–Tekin Lagrangians are casted into forms of various first order Lagrangians. The structures of the iterated tangent bundle and acceleration bundle are presented as a suitable geometric framework. Hamiltonian analyses of these equivalent formalisms are performed by means of the Dirac–Bergmann constraint algorithm. All formulations are shown to possess only second class constraints.

Observer and descriptor satisfying incremental quadratic constraint for class of chaotic systems and its applications in a quadrotor chaotic system.

A drone based on four rotors is considered in this research paper. Its chaotic solution is shown bounded in an inscribed sphere whose vertices are tangent to faces of octahedron. Based on concept of constrained optimization; Linear Matrix Inequalities (LMIs) satisfying quadratic constraint increment multiplier matrix σm , state observers and descriptors with estimated parameter is calculated. Moreover, an image file is decrypted by designing description for mentioned chaotic system and then encrypted on its receiver end. Furthermore, an electric circuit is designed for chaotic quadrotor using LTspice and is fitted into wireless flying robot to observe its dynamics in bounded rectangular region.

Canonical quantization of massive symmetric rank-two tensor in string theory

The canonical quantization of a massive symmetric rank-two tensor in string theory, which contains two Stueckelberg fields, was studied. As a preliminary study, we performed a canonical quantization of the Proca model to describe a massive vector particle that shares common properties with the massive symmetric rank-two tensor model. By performing a canonical analysis of the Lagrangian, which describes the symmetric rank-two tensor, obtained by Siegel and Zwiebach (SZ) from string field theory, we deduced that the Lagrangian possesses only first class constraints that generate local gauge transformation. By explicit calculations, we show that the massive symmetric rank-two tensor theory is gauge invariant only in the critical dimension of open bosonic string theory, i.e., d=26. This emphasizes that the origin of local symmetry is the nilpotency of the Becchi-Rouet-Stora-Tyutin (BRST) operator, which is valid only in the critical dimension. For a particular gauge imposed on the Stueckelberg fields, the gauge-invariant Lagrangian of the SZ model reduces to the Fierz-Pauli Lagrangian of a massive spin-two particle. Thus, the Fierz-Pauli Lagrangian is a gauge-fixed version of the gauge-invariant Lagrangian for a massive symmetric rank-two tensor. By noting that the Fierz-Pauli Lagrangian is not suitable for studying massive spin-two particles with small masses, we propose the transverse-traceless (TT) gauge to quantize the SZ model as an alternative gauge condition. In the TT gauge, the two Stueckelberg fields can be decoupled from the symmetric rank-two tensor and integrated trivially. The massive spin-two particle can be described by the SZ model in the TT gauge, where the propagator of the massive spin-two particle has a well-defined massless limit.

Different Sourcing Point of Interest Matching Method Considering Multiple Constraints

Point of interest (POI) matching is critical but is the most technically difficult part of multi-source POI fusion. The accurate matching of POIs from different sources is important for the effective reuse of POI data. However, the existing research on POI matching usually adopts weak constraints, which leads to a low POI matching accuracy. To address the shortcomings of previous studies, this paper proposes a POI matching method with multiple determination constraints. First, according to various attributes (name, class, and spatial location), a new calculation model considering spatial topology, name role labeling, and bottom-up class constraints is established. In addition, the optimal threshold values corresponding to the different attribute constraints are determined. Second, according to the multiattribute constraint values and optimal thresholds, a constraint model with multiple strict determination constraints is proposed. Finally, actual POI data from Baidu Map and Gaode Map in Dongying city is used to validate the method. Comparing to the existing method, the accuracy and recall of the proposed method increase 0.3% and 7.1%, respectively. The experimental results demonstrate that the proposed POI matching method attains a high matching accuracy and high feasibility.

BRST Cohomologies of Mixed and Second Class Constraints

The cohomological resolution of mixed constraints is constructed and shown to give Gupta–Bleuler space of physical states. The differential space and so-called anomalous BRST complex is constructed in detail. Special structures associated with anomaly are demonstrated and proved to be of important significance. Finally, the formalism is applied to a spinorial system with second class constraints. In this case, the Laplace operators are proved to define the (irreducibility) equations for fields carrying arbitrary (high) spin.