Strong Equivalence Research Articles

Probing dipole radiation from binary neutron stars with ground-based laser-interferometer and atom-interferometer gravitational-wave observatories

Atom-interferometer gravitational-wave (GW) observatory, as a new design of ground-based GW detector for the near future, is sensitive at a relatively low frequency for GW observations. Taking the proposed atom interferometer Zhaoshan Long-baseline Atom Interferometer Gravitation Antenna (ZAIGA), and its illustrative upgrade (Z+) as examples, we investigate how the atom interferometer will complement ground-based laser interferometers in testing the gravitational dipole radiation from binary neutron star (BNS) mergers. A test of such kind is important for a better understanding of the strong equivalence principle laying at the heart of Einstein's general relativity. To obtain a statistically sound result, we sample BNS systems according to their merger rate and population, from which we study the expected bounds on the parameterized dipole radiation parameter $B$. Extracting BNS parameters and the dipole radiation from the combination of ground-based laser interferometers and the atom-interferometer ZAIGA/Z+, we are entitled to obtain tighter bounds on $B$ by a few times to a few orders of magnitude, compared to ground-based laser interferometers alone, ultimately reaching the levels of $|B| \lesssim 10^{-9}$ (with ZAIGA) and $|B| \lesssim 10^{-10}$ (with Z+).

Here and There with Arithmetic

AbstarctIn the theory of answer set programming, two groups of rules are called strongly equivalent if, informally speaking, they have the same meaning in any context. The relationship between strong equivalence and the propositional logic of here-and-there allows us to establish strong equivalence by deriving rules of each group from rules of the other. In the process, rules are rewritten as propositional formulas. We extend this method of proving strong equivalence to an answer set programming language that includes operations on integers. The formula representing a rule in this language is a first-order formula that may contain comparison symbols among its predicate constants, and symbols for arithmetic operations among its function constants. The paper is under consideration for acceptance in TPLP.

Exact and approximate role assignment for multi-layer networks

Abstract The concept of role equivalence has been applied in social network analysis for decades. Early definitions recognized two social actors as role equivalent, if they have identical relationships to the same other actors. Although this rather strong equivalence requirement has been relaxed in different ways, it is often challenging to detect interesting, non-trivial role equivalences, especially for social networks derived from empirical data. Multi-layer networks (MLNs) are increasingly gaining popularity for modelling collective adaptive systems, for example, engineered cyber-physical systems or animal collectives. Multiplex networks, a special case of MLNs, transparently and compactly describe such complex interactions (social, biological, transportation), where nodes can be connected by links of different types. In this work, we first propose a novel notion of exact and approximate role equivalence for multiplex MLNs. Then, we implement and experimentally evaluate the algorithm on a suite of real-world case studies. Results demonstrate that our notion of approximate role assignment not only obtains non-trivial partitions over nodes and layers as well, but it provides a fine-grained hierarchy of role equivalences, which is impossible to obtain by (combining) the existing role detection techniques. We demonstrate the latter by interpreting in detail the case study of Florence families, a classical benchmark from literature.

Erratum: Neutron star sensitivities in Hořava gravity after GW170817 [Phys. Rev. D 100 , 084053 (2019)

Hořava gravity breaks boost invariance in the gravitational sector by introducing a preferred time foliation. The dynamics of this preferred slicing is governed, in the low-energy limit suitable for most astrophysical applications, by three dimensionless parameters α, β and λ. The first two of these parameters are tightly bound by Solar System and gravitational-wave propagation experiments, but λ remains relatively unconstrained (0≤λ≲0.01–0.1). We restrict here to the parameter-space region defined by α=β=0 (with λ kept generic), which in a previous paper we showed to be the only one where black hole solutions are nonpathological at the universal horizon, and we focus on possible violations of the strong equivalence principle in systems involving neutron stars. We compute neutron star “sensitivities,” which parametrize violations of the strong equivalence principle at the leading post-Newtonian order, and find that they vanish identically, like in the black hole case, for α=β=0 and generic λ≠0. This implies that no violations of the strong equivalence principle (neither in the conservative sector nor in gravitational-wave fluxes) can occur at the leading post-Newtonian order in binaries of compact objects, and that data from binary pulsars and gravitational interferometers are unlikely to further constrain λ.

Strong Morita equivalence for inclusions of $C^*$-algebras induced by twisted actions of a countable discrete group

We consider two twisted actions of a countable discrete group on $\sigma$-unital $C^*$-algebras. Then by taking the reduced crossed products, we get two inclusions of $C^*$-algebras. We suppose that they are strongly Morita equivalent as inclusions of $C^*$-algebras. Also, we suppose that one of the inclusions of $C^*$-algebras is irreducible, that is, the relative commutant of one of the $\sigma$-unital $C^*$-algebra in the multiplier $C^*$-algebra of the reduced twisted crossed product is trivial. We show that the two actions are then strongly Morita equivalent up to some automorphism of the group.

New binary pulsar constraints on Einstein-æther theory after GW170817

The timing of millisecond pulsars has long been used as an exquisitely precise tool for testing the building blocks of general relativity, including the strong equivalence principle and Lorentz symmetry. Observations of binary systems involving at least 1 ms pulsar have been used to place bounds on the parameters of Einstein-æther theory, a gravitational theory that violates Lorentz symmetry at low energies via a preferred and dynamical time threading of the spacetime manifold. However, these studies did not cover the region of parameter space that is still viable after the recent bounds on the speed of gravitational waves from GW170817/GRB170817A. The restricted coverage was due to limitations in the methods used to compute the pulsar ‘sensitivities’, which parameterize violations of the strong-equivalence principle in these systems. We extend here the calculation of pulsar sensitivities to the parameter space of Einstein-æther theory that remains viable after GW170817/GRB170817A. We show that observations of the damping of the period of quasi-circular binary pulsars and of the triple system PSR J0337+1715 further constrain the viable parameter space by about an order of magnitude over previous constraints.

Strong Equivalence of TAG and CCG

Tree-adjoining grammar (TAG) and combinatory categorial grammar (CCG) are two well-established mildly context-sensitive grammar formalisms that are known to have the same expressive power on strings (i.e., generate the same class of string languages). It is demonstrated that their expressive power on trees also essentially coincides. In fact, CCG without lexicon entries for the empty string and only first-order rules of degree at most 2 are sufficient for its full expressive power.

Morita equivalence of pseudogroups

We take advantage of the correspondence between pseudogroups and inverse quantal frames, and of the recent description of Morita equivalence for inverse quantal frames in terms of biprincipal bisheaves, to define Morita equivalence for pseudogroups and to investigate its applications. In particular, two pseudogroups are Morita equivalent if and only if their corresponding localic étale groupoids are. We explore the clear analogies between our definition of Morita equivalence for pseudogroups and the usual notion of strong Morita equivalence for C⁎-algebras and these lead to a number of concrete results.

Some Results and Examples on The Relation of Leray Equivalent and (Strong) Shift Equivalent

Using the concept of Leray functor and the way it is used to define the Cohomological Conley index, we define Leray equivalent, Leray shift equivalent, Leray elementary strong shift equivalent and Leray strong shift equivalent. We established their relationship with shift equivalent, strong shift equivalent and elementary strong shift equivalent. Then, we show that in the setting of Artinian and Noetherian module Leray equivalent implies strong shift equivalent.

Erratum: “Testing the Strong Equivalence Principle: Detection of the External Field Effect in Rotationally Supported Galaxies” (2020, ApJ, 904, 51)

Erratum: “Testing the Strong Equivalence Principle: Detection of the External Field Effect in Rotationally Supported Galaxies” (2020, ApJ, 904, 51)

Exploring the Role of Cultural Schemata in Bridging the Gap between People

This study aims to investigate the hypothesis proposing "Cultural schemata to bridge the gap between the people of different origins". The researchers have adopted the quantitative and qualitative methods as well as the questionnaire (50) and interview (10) as the tools for collecting data relevant to the study. It is an attempt to bring to the light the importance of cultural schemata in bridging the gap between the people. The sample of this study is comprised of (50) + (10) people who did not share the same cultural background and they were descended from different cultural background. The marks obtained from the questionnaire and interviews were compared. The results have revealed that the cultural schemata play a great role in bridging the gap between the people positively. Accordingly, the results have shown that there are strong equivalences among the people who descended from different cultural background. As a result, more space should be given to those people to bridge the gap between themselves and others in terms of social interaction, transferring the meaning of lexicons of concerned people’s language, strengthening the relationship and knowledge of the world.

On the dimension group of unimodular $${\mathcal {S}}$$-adic subshifts

Dimension groups are complete invariants of strong orbit equivalence for minimal Cantor systems. This paper studies a natural family of minimal Cantor systems having a finitely generated dimension group, namely the primitive unimodular proper $${\mathcal {S}}$$ S -adic subshifts. They are generated by iterating sequences of substitutions. Proper substitutions are such that the images of letters start with a same letter, and similarly end with a same letter. This family includes various classes of subshifts such as Brun subshifts or dendric subshifts, that in turn include Arnoux–Rauzy subshifts and natural coding of interval exchange transformations. We compute their dimension group and investigate the relation between the triviality of the infinitesimal subgroup and rational independence of letter measures. We also introduce the notion of balanced functions and provide a topological characterization of balancedness for primitive unimodular proper S-adic subshifts.

Constraints on Galileons from the positions of supermassive black holes

Galileons are scalar field theories which obey the Galileon symmetry $\varphi \to \varphi + b + c_\mu x^\mu$ and are capable of self-acceleration if they have an inverted sign for the kinetic term. These theories violate the Strong Equivalence Principle, such that black holes (BHs) do not couple to the Galileon field, whereas non-relativistic objects experience a fifth force with strength $\Delta G / G_{\rm N}$ relative to gravity. For galaxies falling down a gradient in the Galileon field, this results in an offset between the centre of the galaxy and its host supermassive BH. We reconstruct the local gravitational and Galileon fields through a suite of constrained N-body simulations (which we dub CSiBORG) and develop a Monte Carlo-based forward model for these offsets on a galaxy-by-galaxy basis. Using the measured offset between the optical centre and active galactic nucleus of 1916 galaxies from the literature, propagating uncertainties in the input quantities and marginalising over an empirical noise model describing astrophysical and observational noise, we constrain the Galileon coupling to be $\Delta G / G_{\rm N} < 0.16$ at $1\sigma$ confidence for Galileons with crossover scale $r_{\rm C} \gtrsim H_0^{-1}$.

Strong equivalence between metrics of Wasserstein type

The sliced Wasserstein metric Wp and more recently max-sliced Wasserstein metric W‾p have attracted abundant attention in data sciences and machine learning due to their advantages to tackle the curse of dimensionality, see e.g. [15], [6]. A question of particular importance is the strong equivalence between these projected Wasserstein metrics and the (classical) Wasserstein metric Wp. Recently, Paty and Cuturi have proved in [14] the strong equivalence of W‾2 and W2. We show that the strong equivalence also holds for p=1, while the sliced Wasserstein metric does not share this nice property.

Coactions of a finite-dimensional $C^*$-Hopf algebra on unital $C^*$-algebras, unital inclusions of unital $C^*$-algebras and strong Morita equivalence

Let $A$ and $B$ be unital $C^*$-algebras and let $H$ be a finite dimensional $C^*$-Hopf algebra. Let $H^0$ be its dual $C^*$-Hopf algebra. Let $(\rho, u)$ and $(\sigma, v)$ be twisted coactions of $H^0$ on $A$ and $B$, respectively. In this paper, we shall show the following theorem: We suppose that the unital inclusions $A\subset A\rtimes_{\rho, u}H$ and $B\subset B\rtimes_{\sigma, v}H$ are strongly Morita equivalent. If $A'\cap (A\rtimes_{\rho, u}H)=\BC1$, then there is a $C^*$-Hopf algebra automorphism $\lambda^0$ of $H^0$ such that the twisted coaction $(\rho, u)$ is strongly Morita equivalent to the twisted coaction $((\id_B \otimes\lambda^0 )\circ\sigma \, , \, (\id_B \otimes\lambda^0 \otimes\lambda^0 )(v))$ induced by $(\sigma, v)$ and $\lambda^0$.

The Nature and Origin of Inertia

This paper aims to present a new theory that explains the mechanism of inertia at providing a satisfying explanation for the yet unknown mechanism for inertia. By considering the vacuum as a liquid with a measurable density, hydrodynamics laws are used to describe the behaviour of the vacuum when it is dragged by moving body. The inertia is the result of the initial resistance between the moving bodies against the static vacuum. The moving body drags the resisting vacuum during acceleration, till the point that the vacuum travels with the moving body and has the same velocity. When the body decelerates, the vacuum continues to flow and to push the body at the same direction of the original flow till its complete stop. Formulations based on Planck theory derived to prove its equivalence to Newton inertia law. Formulation based on hydrodynamics is derived to confirm the theory that the force exerted by the vacuum on static body in gravity and on moving body in inertia is equivalent to Newton law. The strong equivalence principle is reaffirmed and, consequently, Einstein’s equations are preserved.

Modified gravity and the black hole mass gap

We pioneer the black hole mass gap as a powerful new tool for constraining modified gravity theories. These theories predict fifth forces that alter the structure and evolution of population-III stars, exacerbating the pair-instability. This results in the formation of lighter astrophysical black holes and lowers both the upper and lower edges of the mass gap. These effects are explored using detailed numerical simulations to derive quantitative predictions that can be used as theoretical inputs for Bayesian data analysis. We discuss detection strategies in light of current and upcoming data as well as complications that may arise due to environmental screening. To demonstrate the constraining power of the mass gap, we present a novel test of the strong equivalence principle where we apply our results to an analysis of the first ten LIGO/Virgo binary black hole merger events to obtain a 7% bound on the relative difference between the gravitational constant experienced by baryonic matter, and that experienced by black holes, $\mathrm{\ensuremath{\Delta}}G/G$. The recent GW190521 event resulting from two black holes with masses in the canonical mass gap can be explained by modified gravity if the event originated from an unscreened galaxy where the strength of gravity is either enhanced or reduced by $\ensuremath{\sim}30%$ relative to its strength in the Solar System.

Balanced strong shift equivalence, balanced in-splits, and eventual conjugacy

AbstractWe introduce the notion of balanced strong shift equivalence between square non-negative integer matrices, and show that two finite graphs with no sinks are one-sided eventually conjugate if and only if their adjacency matrices are conjugate to balanced strong shift equivalent matrices. Moreover, we show that such graphs are eventually conjugate if and only if one can be reached by the other via a sequence of out-splits and balanced in-splits, the latter move being a variation of the classical in-split move introduced by Williams in his study of shifts of finite type. We also relate one-sided eventual conjugacies to certain block maps on the finite paths of the graphs. These characterizations emphasize that eventual conjugacy is the one-sided analog of two-sided conjugacy.

Two dogmas of dynamicism

I critically discuss two dogmas of the "dynamical approach" to spacetime in general relativity, as advanced by Harvey Brown [Physical Relativity (2005) Oxford:Oxford University Press] and collaborators. The first dogma is that positing a "spacetime geometry" has no implications for the behavior of matter. The second dogma is that postulating the "Strong Equivalence Principle" suffices to ensure that matter is "adapted" to spacetime geometry. I conclude by discussing "spacetime functionalism". The discussion is presented in reaction to and sympathy with recent work by James Read ["Explanation, geometry, and conspiracy in relativity theory"(20??) Thinking about Spacetime. Boston: Birkauser].

The linear time-branching time spectrum of equivalences for stochastic systems with non-determinism

This paper studies the linear time-branching time spectrum of equivalences for a subclass of interactive Markov chains (IMCs) that are not subject to any further synchronization. This subclass of IMCs is known as closed IMCs. We define several variants of trace equivalence by performing button pushing experiments on stochastic trace machines. We establish the relation between these equivalences and also compare them with bisimulation for closed IMCs. Next, we define several variants of stutter trace equivalence for closed IMCs. We perform button pushing experiments with stutter insensitive stochastic trace machines to obtain these equivalences. We investigate the relationship among these stutter trace equivalences and also compare them with weak bisimulation for closed IMCs. We discuss the relation between several strong and weak trace equivalences defined in this paper. Next, we use these results to sketch the linear time-branching time spectrum of equivalences for IMCs. Finally, we prove that maximum and minimum probabilities of satisfying properties specified using metric temporal logic (MTL) formulas are preserved under some of these trace and stutter trace equivalences.