Choice Of Coordinates Research Articles

Neoliberalism and the Complexities of Conceptualizing Community School Policy for Racial Equity

Full-service community schools are increasingly adopted as educational policy nationwide to transform educational institutions into community hubs, addressing racial and social disparities and countering deficit narratives related to marginalized youth and families. As the movement toward community schooling as an educational policy gains momentum, more research is needed to understand the complex process of conceptualizing such an initiative for racial equity. Spanning from the early planning stages to 3 years into the implementation of community schooling, this paper uncovers the tensions that emerge as school and district leaderships’ interpretation of the purpose of community schooling and root cause of racial inequity unveil conflicting conceptualizations of the community school initiative: community schooling rooted in neoliberal ideals of efficiency, coordination, and service choice, on one hand, and those rooted in more transformative approach with systemic reflection and change in classrooms, schools, and other institutions on the other.

Quantum scalar field on fuzzy de Sitter space. Part I. Field modes and vacua

We study a scalar field on a noncommutative model of spacetime, the fuzzy de Sitter space, which is based on the algebra of the de Sitter group SO(1, d) and its unitary irreducible representations. We solve the Klein-Gordon equation in d = 2, 4 and show, using a specific choice of coordinates and operator ordering, that all commutative field modes can be promoted to solutions of the fuzzy Klein-Gordon equation. To explore completeness of this set of modes, we specify a Hilbert space representation and study the matrix elements (integral kernels) of a scalar field: in this way the complete set of solutions of the fuzzy Klein-Gordon equation is found. The space of noncommutative solutions has more degrees of freedom than the commutative one, whenever spacetime dimension is d > 2. In four dimensions, the new non-geometric, internal modes are parametrised by S2 × W, where W is a discrete matrix space. Our results pave the way to analysis of quantum field theory on the fuzzy de Sitter space.

General mass formulas for charged Kerr-AdS black holes

It is well-known that the mass of a non-asymptotically flat spacetime cannot be uniquely defined. Some mass formulas for the Kerr-AdS black hole have been found and used in studying black hole thermodynamics. However, the derivations usually need a background subtraction to eliminate the divergence at infinity. It is also unknown whether the mass depends on the choice of coordinates. In this paper, we provide a more straightforward derivation for the mass formula, only demanding that the first law of black hole thermodynamics and Smarr formula are satisfied. We first make use of the Iyer-Wald formalism to derive a first law which avoids the divergence at infinity. Then we apply this formula to charged Kerr-AdS black hole expressed in the coordinates rotating at infinity. However, the first law associated with the timelike Killing vector field ∂∂t is not integrable. Then, by making use of the gauge freedom of t, we find a favorite parameter t′ which just makes the mass integrable. Applying the scaling argument, we show that the mass satisfies the Smarr formula and takes the form M/Ξ3/2. Moreover, applying the conformal method with ∂∂t′ , we obtain the same mass. By applying the first law to the coordinates which is not rotating at infinity, we find a preferred time T that makes the first law integrable and the mass is just the familiar mass M/Ξ2 in the literature. This mass is also confirmed by the conformal method. We find that the two mass formulas correspond to different families of observers and the preferred Killing times. So our work clarifies the ambiguities of mass in Kerr-AdS spacetimes.

Re-evaluating the cosmological redshift: Insights into inhomogeneities and irreversible processes

Understanding the expansion of the Universe remains a profound challenge in fundamental physics. The complexity of solving general relativity equations in the presence of intricate, inhomogeneous flows has compelled cosmological models to rely on perturbation theory in a homogeneous Friedmann-Lemaître-Robertson-Walker background. This approach accounts for a redshift of light encompassing contributions from both the cosmological background expansion along the photon's trajectory and Doppler effects at emission due to peculiar motions. However, this computation of the redshift is not covariant, as it hinges on specific coordinate choices that may distort physical interpretations of the relativity of motion. In this study we show that peculiar motions, when tracing the dynamics along time-like geodesics, must contribute to the redshift of light through a local volume expansion factor, in addition to the background expansion. By employing a covariant approach to redshift calculation, we address the central question of whether the cosmological principle alone guarantees that the averaged local volume expansion factor matches the background expansion. We establish that this holds true only in scenarios characterised by a reversible evolution of the Universe, where inhomogeneous expansion and compression modes compensate for one another. In the presence of irreversible processes, such as the dissipation of large-scale compression modes through matter virialisation and associated entropy production, the averaged expansion factor becomes dominated by expansion in voids that can no longer be compensated for by compression in virialised structures. Furthermore, for a universe in which a substantial portion of its mass has undergone virialisation, adhering to the background evolution on average leads to significant violations of the second law of thermodynamics. Our approach shows that entropy production due to irreversible processes during the formation of structures plays the same role as an effective, time-dependent cosmological constant (i.e. dynamical dark energy) without the need to invoke new unknown physics. Our findings underscore the imperative need to re-evaluate the influence of inhomogeneities and irreversible processes on cosmological models, shedding new light on the intricate dynamics of our Universe.

Riemann-Hilbert problems, Toeplitz operators and ergosurfaces

The Riemann-Hilbert approach, in conjunction with the canonical Wiener-Hopf factorisation of certain matrix functions called monodromy matrices, enables one to obtain explicit solutions to the non-linear field equations of some gravitational theories. These solutions are encoded in the elements of a matrix M depending on the Weyl coordinates ρ and v, determined by that factorisation. We address here, for the first time, the underlying question of what happens when a canonical Wiener-Hopf factorisation does not exist, using the close connection of Wiener-Hopf factorisation with Toeplitz operators to study this question. For the case of rational monodromy matrices, we prove that the non-existence of a canonical Wiener-Hopf factorisation determines curves in the (ρ, v) plane on which some elements of M(ρ, v) tend to infinity, but where the space-time metric may still be well behaved. In the case of uncharged rotating black holes in four space-time dimensions and, for certain choices of coordinates, in five space-time dimensions, we show that these curves correspond to their ergosurfaces.

Derivation of the Invariant Free-Energy Landscape Based on Langevin Dynamics.

A conventionally defined free-energy landscape (FEL) exhibits unphysical dependence on the choice of reaction coordinates and hence lacks universal predictive ability. We here show that three physically plausible requirements uniquely determine the FEL formula for a given reaction coordinate. Our FEL is expressed solely in terms of quantities obtained through time-series data analysis, namely, the probability distribution and the diffusion matrix. It is free from any unphysical coordinate dependence and coincides with the conventional FEL in special cases. The uniqueness and robustness of the formula strongly suggest that our FEL has universal predictive power.

Nonlinear ion acoustic waves in dense magnetoplasmas: Analyzing interaction solutions of the KdV equation using Wronskian formalism for electron trapping with Landau diamagnetism and thermal excitations

Nonlinear ion acoustic waves in the presence of electron trapping with Landau quantization and thermal excitations induced smearing effects of the Fermi step function are investigated using the two-fluid theory in the vicinity of white dwarfs. In spite of the fact that the Kortweg de Vries (KdV) equation is derived within the confines of small amplitude approximation used in the reductive perturbation theory (RPT), it is found to admit solutions that exhibit outstanding capability of wave enhancement and have applications in the nonlinear wave propagation. It is found that enhancing the quantizing magnetic field and the electron thermal effects modify the spatial scale of the formation of the novel nonlinear structures reported for our model. Interestingly, it is found that, unlike the solitary and periodic structures, the choice of space and time coordinates affects the structure of these solutions. Interaction of these solutions with a stable nonlinear structure are also studied.

The dependent coordinates in the linearization of constrained multibody systems: Handling and elimination

In this paper, the handling of the dependent coordinates in the linearization of constrained multibody systems is clarified. To this end, a brief but comprehensive overview of linearization approaches used in the field of Multibody System Dynamics is presented. These procedures are illustrated by using a common notation and classified into four groups, depending on the initial form of the nonlinear equations of motion and the selection of the generalized coordinates (a redundant or a minimal set). The handling of the dependent coordinates in each of the procedures is discussed. The linearized equations of motion of constrained multibody systems are of great importance in several applications, such as linear stability and modal analyses, the design of linear state feedback controllers or the building of state and input estimators, like Kalman filters. When modeling a constrained multibody system, a number of coordinates greater than the number of degrees of freedom of the system is usually used. While some linearization approaches make use of the complete set of coordinates, several procedures are based on a coordinate partition in terms of independent and dependent coordinates to reduce the number of linearized equations of motion. In this latter scenario, the role of the dependent coordinates in the linearization is important and, in a general case, these dependent coordinates cannot be ignored to obtain the correct linearized equations of motion. This aspect, which may seem obvious, is not straightforward and is addressed in this work. The importance of considering the set of dependent coordinates in the linearization is demonstrated with a well-acknowledged bicycle benchmark multibody model and an electric kickscooter multibody model with rear and front suspensions. To this end, the Jacobian matrix and the linear stability results of these case studies are computed by considering different choices of independent and dependent coordinates.

Light-cone gauge in non-relativistic AdS5×S5 string theory

We discuss the non-relativistic limit of string theory in AdS5×S5 for different choices of embedding coordinates. We show that, if we consider Cartesian coordinates, the action of fluctuations around the twisted BMN-like string found in arXiv:2109.13240 in uniform light-cone gauge becomes the one of free fields at large string tension and large AdS5 radius.

Spatially homogeneous teleparallel spacetimes with four-dimensional groups of motions

In this paper, we study metric teleparallel geometries, which can either be defined through a Lorentzian metric and flat, metric-compatible affine connection, or a tetrad and a flat Lorentz spin connection, which are invariant under the transitive action of a four-dimensional Lie group on their spatial equal-time hypersurfaces. There are three such group actions, and their corresponding spatial hypersurfaces belong to the Bianchi types II, III and IX, respectively. For each of these three symmetry groups, we determine the most general teleparallel geometry, and find that it is parametrized by six functions of time, one of which can be eliminated by the choice of the time coordinate. We further show that these geometries are unique up to global Lorentz transformations, coordinate transformations and changes of the choice of the parameter functions.

On the Global Convergence of Randomized Coordinate Gradient Descent for Nonconvex Optimization

In this work, we analyze the global convergence property of a coordinate gradient descent with random choice of coordinates and stepsizes for nonconvex optimization problems. Under generic assumptions, we prove that the algorithm iterate will almost surely escape strict saddle points of the objective function. As a result, the algorithm is guaranteed to converge to local minima if all saddle points are strict. Our proof is based on viewing the coordinate descent algorithm as a nonlinear random dynamical system and a quantitative finite block analysis of its linearization around saddle points.

Four-dimensional SO(3)-spherically symmetric Berwald Finsler spaces

We locally classify all [Formula: see text]-invariant four-dimensional pseudo-Finsler Berwald structures. These are Finslerian geometries which are closest to (spatially, or [Formula: see text])-spherically symmetric pseudo-Riemannian ones — and serve as ansatz to find solutions of Finsler gravity equations which generalize the Einstein equations. We find that there exist five classes of non-pseudo-Riemannian (i.e. non-quadratic in the velocities) [Formula: see text]-spherically symmetric pseudo-Finsler Berwald functions, which have either a heavily constrained dependence on the velocities, or, up to a suitable choice of the tangent bundle coordinates, no dependence at all on the “time” and “radial” coordinates.

CLASSIFICATION OF EXPENDITURES ON INNOVATION ACTIVITIES OF INDUSTRIAL ENTERPRISES

Modern trends in economic development, such as globalisation of markets, intensification of competition, changes in consumer demand, shortening of life cycles of goods and technologies, increasing requirements for their quality, and rising costs of used resources, require leaders and managers to find effective methods of managing the company's activities. Ensuring the competitiveness of enterprises in such conditions is impossible without the introduction of the latest management concepts, which requires changes and development of functional management, one of which is the management of costs based on the definition of new criteria for their classification. Classification of costs for management purposes should meet the main requirement – it should be based on characteristics that allow differentiation of costs for their management in various aspects. It creates conditions for determining the level of costs according to the scope of their management, organisation of planning, accounting, control and analysis. The purpose of the article is to consider the accounting, analytical and management tasks of cost classification in industrial enterprises and its improvement. Methodology. The methodological basis of the thesis is a set of methods and principles of scientific knowledge, general and special methods and techniques used in research. The theoretical basis of the study is the scientific work of domestic and foreign scientists on issues of cost management, organisation of information systems, management accounting of costs, methods of cost management. The legal basis of the study consisted of the current legislative and regulatory documents regulating the formation of costs of enterprises in Ukraine. The information base included official statistical data, reporting and accounting information of enterprises, Internet resources and publications, as well as the results of own research. In order to achieve the set goal, the methods of system approach (to study and characterise the theoretical basis of cost classification) and structural-logical analysis (to determine the criteria for classification of costs of an industrial enterprise) were used when writing the article. Practical implications. The obtained results and the developed recommendations constitute a methodological basis for the improvement of the management of costs for the innovative activity of industrial enterprises based on the definition of new criteria for their classification. The most practical results are: the study of the similarities and differences in the approaches to cost classification of industrial enterprises, the definition of the objectives of cost classification, the consideration of cost classification by cost items, the need to distinguish additional features of cost classification. Value/originality. The classification of costs for the innovative activity of an industrial enterprise has been improved and extended with additional criterion features (possibility of management, accounting and reporting, the principle of accepted obligations, the place of formation, according to the stability factor), due to the need to determine the relationship between the size of the enterprise 's costs and the possibilities of exercising managerial influence on them by managers of different levels, which makes it possible to optimise the composition and structure of costs, which are reflected in various methods of cost management and are the basis for their choice of coordination.

Stability of hairy black holes in shift-symmetric scalar-tensor theories via the effective field theory approach

Shift-symmetric Horndeski theories admit an interesting class of Schwarzschild-de Sitter black hole solutions exhibiting time-dependent scalar hair. The properties of these solutions may be studied via a bottom-up effective field theory (EFT) based on the background symmetries. This is in part possible by making use of a convenient coordinate choice — Lemaître-type coordinates — in which the profile of the Horndeski scalar field is linear in the relevant time coordinate. We construct this EFT, and use it to understand the stability of hairy black holes in shift-symmetric Horndeski theories, providing a set of constraints that the otherwise-free functions appearing in the Horndeski Lagrangian must satisfy in order to admit stable black hole solutions. The EFT is analyzed in the decoupling limit to understand potential sources of instability. We also perform a complete analysis of the EFT with odd-parity linear perturbations around general spherically symmetric space-time.

Parameterizations of immiscible two-phase flow in porous media

A fundamental variable characterizing immiscible two-phase flow in porous media is the wetting saturation, which is the ratio between the pore volume filled with wetting fluid and the total pore volume. More generally, this variable comes from a specific choice of coordinates on some underlying space, the domain of variables that can be used to express the volumetric flow rate. The underlying mathematical structure allows for the introduction of other variables containing the same information, but which are more convenient from a theoretical point of view. We introduce along these lines polar coordinates on this underlying space, where the angle plays a role similar to the wetting saturation. We derive relations between these new variables based on the Euler homogeneity theorem. We formulate these relations in a coordinate-free fashion using differential forms. Finally, we discuss and interpret the co-moving velocity in terms of this coordinate-free representation.

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.

Lessons learned through weighted ensemble simulations of a (surprisingly) challenging protein-ligand unbinding system.

A major challenge in applying the weighted ensemble enhanced sampling strategy to simulate a rare-event process of interest is to identify an effective progress coordinate. Furthermore, the algorithm for the resampling procedure of the strategy can impact both the number and diversity of representative pathways generated. Here, I will share lessons learned from the application of atomistic, weighted ensemble simulations to a surprisingly challenging protein-ligand unbinding process that features a highly-charged ligand. These lessons include key considerations regarding the choice of progress coordinate and resampling algorithm, including binless resamplers.

Anomaly detection under coordinate transformations

There is a growing need for machine learning-based anomaly detection strategies to broaden the search for Beyond-the-Standard-Model (BSM) physics at the Large Hadron Collider (LHC) and elsewhere. The first step of any anomaly detection approach is to specify observables and then use them to decide on a set of anomalous events. One common choice is to select events that have low probability density. It is a well-known fact that probability densities are not invariant under coordinate transformations, so the sensitivity can depend on the initial choice of coordinates. The broader machine learning community has recently connected coordinate sensitivity with anomaly detection and our goal is to bring awareness of this issue to the growing high energy physics literature on anomaly detection. In addition to analytical explanations, we provide numerical examples from simple random variables and from the LHC Olympics Dataset that show how using probability density as an anomaly score can lead to events being classified as anomalous or not depending on the coordinate frame.

Equivariant Filters are Equivariant

Observers for systems with Lie group symmetries are an active area of research that is seeing significant impact in a number of practical domains, including aerospace, robotics, and mechatronics. This paper builds on the theory of the recently proposed Equivariant Filter (EqF), which is a general observer design for systems on homogeneous spaces that takes advantage of symmetries to yield significant performance advantages. It is shown that the EqF error dynamics are invariant to transformation of the input signal and equivariant as a parametrised vector field. The main theorem shows that two EqF's with different choices of local coordinates and origins and with equivalent noise modelling yield identical performance. In other words, the EqF is intrinsic to the system equations and symmetry. This is verified in a simulation of a 2D robot localisation problem, which also shows how the ability to choose an origin for the EqF can yield practical performance advantages by mitigating floating point precision errors.

A local normal form for Hamiltonian actions of compact semisimple Poisson–Lie groups

The main contribution of this manuscript is a local normal form for Hamiltonian actions of Poisson-Lie groups $K$ on a symplectic manifold equipped with an $AN$-valued moment map, where $AN$ is the dual Poisson-Lie group of $K$. Our proof uses the delinearization theorem of Alekseev which relates a classical Hamiltonian action of $K$ with $\mathfrak{k}^*$-valued moment map to a Hamiltonian action with an $AN$-valued moment map, via a deformation of symplectic structures. We obtain our main result by proving a ``delinearization commutes with symplectic quotients'' theorem which is also of independent interest, and then putting this together with the local normal form theorem for classical Hamiltonian actions wtih $\mathfrak{k}^*$-valued moment maps. A key ingredient for our main result is the delinearization $\mathcal{D}(\omega_{can})$ of the canonical symplectic structure on $T^*K$, so we additionally take some steps toward explicit computations of $\mathcal{D}(\omega_{can})$. In particular, in the case $K=SU(2)$, we obtain explicit formulas for the matrix coefficients of $\mathcal{D}(\omega_{can})$ with respect to a natural choice of coordinates on $T^*SU(2)$.