Class Constraints Research Articles

Symmetric vs. chiral approaches to massive fields with spin

Abstract Massive higher spin fields are notoriously difficult to introduce interactions when they are described by symmetric (spin)-tensors. An alternative approach is to use chiral description that does not have unphysical longitudinal modes. For low spin fields we show that chiral and symmetric approaches can be related via a family of invertible change of variables (equivalent to parent actions), which should facilitate introduction of consistent interactions in the symmetric approach and help to control parity in the chiral one. We consider some examples of electromagnetic and gravitational interactions and their transmutations when going to the chiral formulation. An interesting feature of the relation is how second class constraints get eliminated while preserving Lorentz invariance.

Canonical analysis of gravity with dynamical determinant of metric-general case

We analyse general form of theory with the dynamical determinant of metric. We show that due to the presence of general function of determinant that multiplies scalar curvature the Hamiltonian constraint is second class constraint that makes consistency of this theory questionable.

Partition refinement of WorldPop population spatial distribution data method: A case study of Zhuhai, China.

Currently, the core idea of the refined method of population spatial distribution is to establish a correlation between the population and auxiliary data at the administrative-unit level and, then, refine it to the grid unit. However, this method ignores the advantages of public population spatial distribution data. Given these problems, this study proposed a partition strategy using the natural break method at the grid-unit level, which adopts the population density to constrain the land class weight and redistributes the population under the dual constraints of land class and area weights. Accordingly, we used the dasymetric method to refine the population distribution data. The study established a partition model for public population spatial distribution data and auxiliary data at the grid-unit level and, then, refined it to smaller grid units. This method effectively utilizes the public population spatial distribution data and solves the problem of the dataset being not sufficiently accurate to describe small-scale regions and low resolutions. Taking the public WorldPop population spatial distribution dataset as an example, the results indicate that the proposed method has higher accuracy than other public datasets and can also describe the actual spatial distribution characteristics of the population accurately and intuitively. Simultaneously, this provides a new concept for research on population spatial distribution refinement methods.

Giddens, Sen and IsiXhosa-Speaking Women Traders: Theoretical Grafting to Enhance Analysis

ABSTRACT Grafting selected elements into a primary theory from another theoretical approach can sometimes enhance the theoretical framework to facilitate more refined data analysis. Because of the possible risks of theoretical fragmentation that may result from incorporating elements of different theories into a single framework, we opted for grafting selected elements of one theory into our primary theory, to carefully retain the logical coherence of the main theory. In this paper, we draw on a study of isiXhosa-speaking women traders in Cape Town’s Langa Township (hereafter referred as Langa) to argue that grafting elements of Sen’s capability approach (CA) into Giddens’s structuration theory (ST) enhanced our theoretical framework. This improved the quality of our analysis and enabled us to generate more nuanced findings. Our qualitative study with 25 African women traders investigated how these women exercised agency in responding to structural constraints and opportunities that affected their trading businesses. We used participant observation and in-depth interviews to collect data. Sen’s CA (grounded in social justice) expanded on Giddens’s notion of structures as constraining and enabling. For this aspect of our theoretical framework, CA informed by Sen’s research on women’s empowerment projects amplified the intersection of gender, class and race constraints that affected the women traders. Furthermore, CA’s emphasis on quality of life and well-being outcomes was useful in helping us assess the transformative capacity of the women traders’ agency. This dimension complemented Giddens’s ST and therefore our theoretical framework was enhanced by grafting in these elements from Sen’s CA.

A STORY TELLING APPROACH FOR TEACHING ENGINEERING COURSES: A MINI-CASE METHOD

Engineering courses should connect theory and practice, promote critical thinking, and engage students. Traditional teaching methods are becoming less appealing, and new strategies such as Problem-Based Learning and Flipped Classrooms have not been widely adopted. Case studies have been tried before, but open-ended ones require a complete overhaul of teaching methods and can end up feeling like projects rather than classroom tools. The mini-case approach is introduced as an in-class teaching tool to better engage students and show them the real-world implications of what they are learning. The mini-case structure includes a story, objective statement, student ideation, synthesis of students' ideas, simplification and working model, solution, conclusion, and discussion. The story is crucial to generating interest and retaining attention. The objective statement summarizes the case study's story, goals, and constraints in a single sentence. Students ideate about how to approach the problem, and their ideas are synthesized into a model that is simplified to fit the class's constraints. The solution is either analytical or numeric, and the case study objective statement is revisited to examine whether the requirements and criteria have been met. Reflection on the process and what the results mean is encouraged. The Mini Applied Case Studies (MACS) framework was developed as a structured approach to problem-solving in engineering courses. In the context of a Dynamics class, the framework was applied to the crank-slider mechanism, a challenging topic that students often struggle to understand. The MACS method successfully engaged students and developed their problem-solving skills. Feedback indicated that students found the method effective and interactive. Further research is needed to determine the full potential of the MACS method in other academic contexts.

On the quantization of FLPR model

In this paper, we quantize the Friedberg–Lee–Pang–Ren (FLPR) model, using an admissible gauge condition, within the framework of modified Faddeev–Jackiw formalism. Further, we deduce the gauge symmetries and establish off-shell nilpotent and absolutely anti-commuting (anti-)BRST symmetries. We also show that the physical states of the theory are annihilated by the first class constraints which is consistent à la Dirac formalism.

Tactical Game-theoretic Decision-making with Homotopy Class Constraints

Tactical Game-theoretic Decision-making with Homotopy Class Constraints

Tetrad Fields, Reference Frames, and the Gravitational Energy–Momentum in the Teleparallel Equivalent of General Relativity

AbstractThe concept and definitions of the energy–momentum and angular momentum of the gravitational field in the teleparallel equivalent of general relativity (TEGR) are reviewed. The importance of these definitions is justified by three major reasons. First, the TEGR is a well established and widely accepted formulation of the gravitational field, whose basic field strength is the torsion tensor of the Weitzenböck connection. Second, in the phase space of the TEGR there exists an algebra of the Poincaré group. Not only the definitions of the gravitational energy–momentum and 4‐angular momentum satisfy this algebra, but also the first class constraints related to these definitions satisfy the algebra. And third, numerous applications of these definitions lead to physically consistent results. These definitions follow from a well established Hamiltonian formulation, and rely on the idea of localization of the gravitational energy. In this review, the concept of localizability of the gravitational energy is revisited, in light of results obtained in recent years. The behavior of free particles is studied in the space–time of plane fronted gravitational waves (pp‐waves). Free particles are here understood as particles that are not subject to external forces other than the gravitational acceleration due to pp‐waves. Since these particles acquire or loose kinetic energy locally, the transfer of energy from or to the gravitational field must also be localized. This theoretical result is considered an important and definite argument in favor of the localization of the gravitational energy–momentum, and by extension, of the gravitational 4‐angular momentum.

Developing a framework for a games-based injury prevention exercise programme for post-primary (12–18 years) physical education class: A Delphi poll study

Despite calls for injury prevention exercise programmes (IPEPs) to move to school settings for the general adolescent population, current research has had mixed outcomes regarding their efficacy in schools as many of the traditional barriers to IPEP implementation still exist, for example, lack of engagement with the programme. A games-based approach may negate some of these barriers as it has been shown to increase participation and adherence to activity. The aim of this study was to achieve consensus on the fundamental framework for the development of a games-based IPEP for physical education (PE) class. Nineteen academic and practitioner experts in the areas of PE, injury prevention and adolescent coaching took part in a four-round Delphi poll, consisting of an opening exploration round followed by three subsequent rounds of questions. Agreement of at least 67% was required for consensus to be deemed achieved on outcomes. Agreement was reached on the key components of an IPEP and potential layouts of the programme. Requirements for an activity/exercise to be deemed games-based and key outcome measures for a games-based IPEP for PE class were established. Finally, PE teacher supports and resources required for implementing a games-based IPEP in PE class were determined, including supports for PE teachers and IPEP location within the class. The recommendations of this study provide a fundamental framework for the development of future games-based IPEPs that could be applied internationally as it provides the flexibility to be adapted to suit various constraints of PE classes across the globe.

Making paths and doing bazaar: Rhythms and techniques of walking‐as‐dwelling

AbstractThis article posits the concept of “walking‐as‐dwelling” as a critical analytical frame to counter the dominant Western conceptualization of walking as an event or novel experience that is set apart from ordinary life. Walking‐as‐dwelling refers to how walking is bound with routines of work, domesticity, and leisure, through which people inhabit and make places. Drawing attention to the situatedness of walking in particular places and subjectivities, the article follows the walking practices of women in the Monday bazaar of Nizamuddin Basti, a low‐income neighborhood in Delhi. It examines how women's walking itineraries, rhythms, and techniques co‐constitute the bazaar as a dynamic spacetime configuration, making and remaking the public and social character of the bazaar. It draws attention to the creative and political potential of ordinary practices of walking through which the Basti's women negotiate constraints of gender and class and, in the process, forge affective ties with the bazaar, perform modes of sociality, and articulate freedom and mobility.

Action for N D0-branes invariant under gauged Galilean transformations

In this short note we formulate an action for N D0-branes that is manifestly invariant under gauged Galilean transformations. We also find its canonical form and determine first class constraints that are generators of gauge transformations.

To Half-Be or Not To Be?

It has recently been argued that half degrees of freedom could emerge in Lorentz and parity invariant field theories, using a non-linear Proca field theory dubbed Proca-Nuevo as a specific example. We provide two proofs, using the Lagrangian and Hamiltonian pictures, that the theory possesses a pair of second class constraints, leaving D − 1 degrees of freedom in D spacetime dimensions, as befits a consistent Proca model. Our proofs are explicit and straightforward in two dimensions and we discuss how they generalize to an arbitrary number of dimensions. We also clarify why local Lorentz and parity invariant field theories cannot hold half degrees of freedom.

Lifelong learning on evolving graphs under the constraints of imbalanced classes and new classes

Lifelong graph learning deals with the problem of continually adapting graph neural network (GNN) models to changes in evolving graphs. We address two critical challenges of lifelong graph learning in this work: dealing with new classes and tackling imbalanced class distributions. The combination of these two challenges is particularly relevant since newly emerging classes typically resemble only a tiny fraction of the data, adding to the already skewed class distribution. We make several contributions: First, we show that the amount of unlabeled data does not influence the results, which is an essential prerequisite for lifelong learning on a sequence of tasks. Second, we experiment with different label rates and show that our methods can perform well with only a tiny fraction of annotated nodes. Third, we propose the gDOC method to detect new classes under the constraint of having an imbalanced class distribution. The critical ingredient is a weighted binary cross-entropy loss function to account for the class imbalance. Moreover, we demonstrate combinations of gDOC with various base GNN models such as GraphSAGE, Simplified Graph Convolution, and Graph Attention Networks. Lastly, our k-neighborhood time difference measure provably normalizes the temporal changes across different graph datasets. With extensive experimentation, we find that the proposed gDOC method is consistently better than a naive adaption of DOC to graphs. Specifically, in experiments using the smallest history size, the out-of-distribution detection score of gDOC is 0.09 compared to 0.01 for DOC. Furthermore, gDOC achieves an Open-F1 score, a combined measure of in-distribution classification and out-of-distribution detection, of 0.33 compared to 0.25 of DOC (32% increase).

Blended Learning Models Using Moodle SPADA Unram to Enhance Student Critical Thinking PPKn Study Program FKIP University of Mataram

This project aims to learn more about the usage of blended learning models using moodle Spada Unram to foster critical thinking among students enrolled in programs at Mataram's PPKn and FKIP universities. This type of investigation is quasi-experimental. There was no requirement for a group control because this study only involved one group and was a group experiment. Students participating in the PPKn FKIP University of Mataram study program may exhibit enhanced critical thinking if blended learning models with moodle Spada Unram are utilized. Students have watched the process of learning. Blended learning is a method of instruction that makes use of technology, specifically the internet and websites, to augment offline or face-to-face learning with online instruction. Due to the convenience of access offered, learning can assist in overcoming educational difficulties such as room class constraints, level presence lecturer class, and level presence student in the classroom.Blended Learning, Moodle, SPADA, UNRAM, and Critical Thinking are described.

Schrödinger from Wheeler–DeWitt: The issues of time and inner product in canonical quantum gravity

The wave-function in quantum gravity is supposed to obey the Wheeler–DeWitt (WDW) equation, however there is neither a satisfactory probability interpretation nor a successful solution to the problem of time in the WDW framework. To gain some insight on these issues we compare quantization of ordinary systems, first in the usual way having the Schrödinger equation and second by promoting them as parametrized theories by introducing embedding coordinate fields, which yields first class constraints and the WDW equation. We observe that the time evolution in the WDW framework can be described with respect to the embedding coordinates, where the WDW equation becomes Schrödinger like, i.e. it involves first order timelike functional derivatives. Moreover, the equivalence with the ordinary quantization procedure determines a suitable Hilbert space with a viable probability interpretation. We then apply the same construction to general relativity by adding embedding fields without any prior coordinate choice. The reparametrized general relativity has two different types of diffeomorphism invariance, which arises from world-volume and target-space reparametrizations. As in the case of ordinary systems, the time evolution can be described with respect to the embedding fields and the WDW equation becomes Schrödinger like; the construction is almost identical to an ordinary parametrized field theory in terms of time evolution and Hilbert space structure. However, this time, the constraint algebra enforces the wave-function to be in a subspace of states annihilated by an operator that can be identified as the Hamiltonian. The implications of these results for the canonical quantization program, and in particular for the minisuperspace quantum cosmology, are discussed.

Gravitational-gauge vector interaction in the Hořava–Lifshitz framework

An anisotropic model describing gravity-vector gauge coupling at all energy scales is presented. The starting point is the 4+1 dimensional non–projectable Hořava–Lifshitz gravity theory subject to a geometrical restriction. Renormalizability arguments require all possible interactions in the potential up to terms with z = 4 spatial derivatives on the geometrical tensor fields: the Riemann and Weyl tensors. The latter being necessary on a 4+1 dimensional formulation. The dimensional reduction to 3+1 dimensions gives rise to a model invariant under foliation-preserving diffeomorphisms (FDiff) and U(1) symmetry groups. The reduced theory on the kinetic conformal point (), propagates the same spectrum of the Einstein–Maxwell theory. Moreover, at low energies, on the IR point α = 0, β = 1, its field equations are exactly the Einstein–Maxwell ones in a particular gauge condition. The Minkowski ground state is stable provided several restrictions on the coupling parameters are satisfied, they are explicitly obtained. The quantum propagators of the physical degrees of freedom are obtained and after an analysis of the first and second class constraints the renormalizability by power counting is proved, provided that the aforementioned restrictions on the coupling parameters are satisfied.

BFV extensions for mechanical systems with Lie-2 symmetry

We consider mechanical systems on ${T}^{*}M$ with possibly irregular and reducible first class constraints linear in the momenta, which thus correspond to singular foliations on $M$. According to a recent result, the latter ones have a Lie-infinity algebroid $(\mathcal{M},Q)$ covering them, where we restrict to the case of Lie-2 algebroids. We propose to consider ${T}^{*}\mathcal{M}$ as a potential Batalin-Fradkin-Vilkovisky (BFV) extended phase space of the constrained system, such that the canonical lift of the nilpotent vector field $Q$ yields automatically a solution to the BFV master equation. We show that in this case, the BFV extension of the Hamiltonian, providing a second corner stone of the BFV formalism, may be obstructed. We identify the corresponding complex governing this second extension problem explicitly (the first extension problem was circumvented by means of the lift of the Lie-2 algebroid structure). We repeatedly come back to the example of angular momenta on ${T}^{*}{\mathbb{R}}^{3}$: in this procedure, the standard free Hamiltonian does not have a BFV extension---while it does so on ${T}^{*}({\mathbb{R}}^{3}\{0})$, with a relatively involved ghost contribution singular at the origin.

Homotopy Method for Optimal Motion Planning With Homotopy Class Constraints

Optimal motion planning is an essential task within the field of control theory. Therein, the key task is to synthesize optimal system trajectories that pass through cluttered environments while respecting given homotopy class constraints, which is critical in many topology-restricted applications such as search and rescue. In this letter, we introduce a novel optimal motion planning technique with 2-dimensional homotopy class constraints for general dynamical systems. We first initialize an optimal system trajectory regardless of obstacles and homotopy class constraints, and design an auxiliary obstacle trajectory for each obstacle such that the system trajectory belongs to the desired homotopy class regarding these auxiliary obstacle trajectories. During the procedure of deforming the auxiliary obstacle trajectory to the original counterparts, we propose a homotopy method based on nonlinear programming (NLP) such that the synthesized optimal system trajectories fulfill the aforementioned homotopy class constraints. The proposed method is validated with numerical results on two classic nonlinear systems with planar static and moving obstacles.

Time Series Analysis of Policy Discourse on Green Consumption in China: Text Mining and Network Analysis

Green consumption in China is a major promotion strategy for achieving sustainable development goals. It should be promoted from a long-term perspective based on cooperation from all levels of society. In addition, constantly revising the policy direction using policy discourse as feedback is necessary. This study analyzes policy discourse on green consumption in China from the long-term and time series perspectives. It employs text mining and network analysis by collecting Chinese online portal data on policy discourse over a period from 2000 to 2020. Using text mining, the study finds that green consumption develops through four stages, namely awareness, practice, diffusion, and social responsibility. From a long-term perspective, policymaking and the preparation of government guidelines take place during the awareness stage, the distribution of action plans and related guidelines from central to local governments takes place in the practice stage, and participation in green consumption in the different classes of society occurs in the diffusion stage. The conscious transition to green consumption by the government, the business sector, and the public can be found in the social responsibility stage. The results of the convergence of iterated correlation analysis reveal that policy discourse on green consumption initially transitions from a specific to a diversified topic. This means that, since there are many complex policy and social issues related to green consumption, it is necessary to select and focus on appropriate topics when setting policy directions. Lastly, core–periphery analysis indicates that growers related to global environmental issues, such as carbon neutrality and climate change, are leading green consumption in China. This confirms that green consumption is a key issue that the government and the public must practice to support the sustainable development of mankind, transcending constraints of time, space, class, and ideology. On the basis of its results, the study proposes a development strategy that can strike a balance between the universality and specificity of green consumption in China.

Double-branch U-Net for multi-scale organ segmentation.

U-Net has achieved great success in the task of medical image segmentation. It encodes and extracts information from several convolution blocks, and then decodes the feature maps to get the segmentation results. Our experiments show that in a multi-scale medical segmentation task, excessive downsampling will cause the model to ignore the small segmentation objects and thus fail to complete the segmentation task. In this work, we propose a more complete method Double-branch U-Net (2BUNet) to solve the multi-scale organ segmentation challenge. Our model is divided into four parts: main branch, tributary branch, information exchange module and classification module. The main advantages of the new model consist of: (1) Extracting information to improve model decoding capabilities using the complete encoding structure. (2) The information exchange module is added to the main branch and tributaries to provide regularization for the model, so as to avoid the large gap between the two paths. (3) Main branch structure for extracting major features of large organ. (4) The tributary structure is used to enlarge the image to extract the microscopic characteristics of small organ. (5) A classification assistant module is proposed to increase the class constraint for the output tensor. The comparative experiments show that our method achieves state-of-the-art performances in real scenes.