Strong Equivalence Research Articles

Two equivalent n-norms on the space of p-summable sequences

We prove the (strong) equivalence between two known n-norms on the space lp of p-summable sequences (of real numbers). The first n-norm is derived from Gahler’s formula [3], while the second is due to Gunawan [7]. The equivalence is proved by using the properties of the volume of n-dimensional parallelepipeds in lp.

The dynamical phase transitions of stellar systems and the corresponding kinematics

External fields in Migromian dynamics (MD or MOND, Milgrom 1983) break the Strong Equivalence Principle (SEP) and change the dynamics of self-bound stellar systems moving in space-varying background gravitational fields. We study two kinds of re-virialisation of the stellar systems: the violent phase transition and the adiabatic phase transition for systems moving on radial orbits, where the external field evolves from strong to weak and whose corresponding dynamics changes from Newtonian to Milgromian. We find that the time scale for the phase tranformation from Newtonian to Milgromian gravity lies only within one to a few crossing times for low density globular clusters with masses ranging from $10^4\msun$ to $10^6\msun$. Thus a globular cluster can appear frozen in the Newtonian regime despite being in the Milgromian regime for not longer than a few crossing times. We also study the kinematics and anisotropy profiles of the systems. The velocity dispersions of the systems are larger after the phase transitions, especially for the outer regions of the stellar systems. Moreover, the isotropic systems become radially anisotropic, especially for the outer parts, after the process caused by the dynamical phase transition. Deeper Milgromian systems have more radially anisotropic velocity dispersion functions. We also find that the final profiles of density, velocity dispersion and anisotropy do not depend on the details of the phase transition. I.e., the mass distribution and kinematics of the end-states of the globular clusters do not depend on the rapidity of the transition from Newtonian to Milgromian gravity. Thus, the transition from the Newtonian to the Milgromian regime naturally induces a significant radially anisotropic velocity distribution in a globular cluster.

Strong Equivalence of Qualitative Optimization Problems

We introduce the framework of qualitative optimization problems (or, simply, optimization problems) to represent preference theories. The formalism uses separate modules to describe the space of outcomes to be compared (the generator) and the preferences on outcomes (the selector). We consider two types of optimization problems. They differ in the way the generator, which we model by a propositional theory, is interpreted: by the standard propositional logic semantics, and by the equilibrium-model (answer-set) semantics. Under the latter interpretation of generators, optimization problems directly generalize answer-set optimization programs proposed previously. We study strong equivalence of optimization problems, which guarantees their interchangeability within any larger context. We characterize several versions of strong equivalence obtained by restricting the class of optimization problems that can be used as extensions and establish the complexity of associated reasoning tasks. Understanding strong equivalence is essential for modular representation of optimization problems and rewriting techniques to simplify them without changing their inherent properties.

On the universality of free fall, the equivalence principle, and the gravitational redshift

Through the contributions of Galileo, Newton, and Einstein, we recall the universality of free fall (UFF), the weak equivalence principle (WEP), and the strong equivalence principle (SEP), in order to stress that general relativity requires all test masses to be equally accelerated in a gravitational field; that is, it requires UFF and WEP to hold. The possibility of testing this crucial fact with null, highly sensitive experiments makes these the most powerful tests of the theory. Following Schiff, we derive the gravitational redshift from the WEP and special relativity and show that, as long as clocks are affected by a gravitating body like normal matter, measurement of the redshift is a test of UFF/WEP but cannot compete with direct null tests. A new measurement of the gravitational redshift based on free-falling cold atoms and an absolute gravimeter is not competitive either. Finally, we compare UFF/WEP experiments using macroscopic masses as test bodies in one case and cold atoms in the other. We conclude that there is no difference in the nature of the test and that the merit of any such experiment rests on the accuracy it can achieve and on the physical differences between the elements it can test, macroscopic proof masses being superior in both respects.

Abstract Preference Frameworks — a Unifying Perspective on Separability and Strong Equivalence

We introduce abstract preference frameworks to study general properties common across a variety of preference formalisms. In particular, we study strong equivalence in preference formalisms and their separability. We identify abstract postulates on preference frameworks, satisfied by most of the currently studied preference formalisms, that lead to characterizations of both properties of interest.

The Spectrum of Strong Behavioral Equivalences for Nondeterministic and Probabilistic Processes

We present a spectrum of trace-based, testing, and bisimulation equivalences for nondeterministic and probabilistic processes whose activities are all observable. For every equivalence under study, we examine the discriminating power of three variants stemming from three approaches that differ for the way probabilities of events are compared when nondeterministic choices are resolved via deterministic schedulers. We show that the first approach - which compares two resolutions relatively to the probability distributions of all considered events - results in a fragment of the spectrum compatible with the spectrum of behavioral equivalences for fully probabilistic processes. In contrast, the second approach - which compares the probabilities of the events of a resolution with the probabilities of the same events in possibly different resolutions - gives rise to another fragment composed of coarser equivalences that exhibits several analogies with the spectrum of behavioral equivalences for fully nondeterministic processes. Finally, the third approach - which only compares the extremal probabilities of each event stemming from the different resolutions - yields even coarser equivalences that, however, give rise to a hierarchy similar to that stemming from the second approach.

Model-based recasting in answer-set programming

As is well known, answer-set programs do not satisfy the replacement property in general, i.e., programs and that are equivalent may cease to be so when they are put in the context of some other program , i.e., and may have different (sets of) answer sets. Lifschitz, Pearce, and Valverde (2001) thus introduced strong equivalence for context-independent equivalence, and proved that such equivalence holds between given programs and iff and are equivalent theories in the monotonic logic of here-and-there. In this article, we consider a related question: given a program , does there exist some program from a certain class of programs such that and are equivalent under a given notion of equivalence? Furthermore, if the answer to this question is positive, how can we recast as an equivalent program from (i.e., construct such a )? In particular, we consider classes of programs that emerge by (dis)allowing disjunction and/or negation, and as equivalence notions we consider strong, uniform, and ordinary equivalence. Based on general model-theoretic properties and a novel form of canonical programs, we develop semantic characterisations for the existence of such a program , determine the computational complexity of checking existence, and provide (local) rewriting rules for recasting.

Can MOND type hypotheses be tested in a free fall laboratory environment?

The extremely small accelerations of objects required for the onset of modified Newtonian dynamics, or modified Newtonian dynamics (MOND), makes testing the hypothesis in conventional terrestrial laboratories virtually impossible. This is due to the large background acceleration of Earth, which is transmitted to the acceleration of test objects within an apparatus. We show, however, that it may be possible to test MOND-type hypotheses with experiments using a conventional apparatus capable of tracking very small accelerations of its components but performed in locally inertial frames such as artificial satellites and other freely falling laboratories. For example, experiments involving an optical interferometer or a torsion balance in these laboratories would show nonlinear dynamics and displacement amplitudes larger than expected. These experiments may also be able to test potential violations of the strong equivalence principle by MOND and to distinguish between its two possible interpretations (modified inertia and modified gravity).

Equivalence Principle, Higgs Boson and Cosmology

We discuss here possible tests for Palatini f(R)-theories together with their implications for different formulations of the Equivalence Principle. We shall show that Palatini f(R)-theories obey the Weak Equivalence Principle and violate the Strong Equivalence Principle. The violations of the Strong Equivalence Principle vanish in vacuum (and purely electromagnetic) solutions as well as on short time scales with respect to the age of the universe. However, we suggest that a framework based on Palatini f(R)-theories is more general than standard General Relativity (GR) and it sheds light on the interpretation of data and results in a way which is more model independent than standard GR itself.

Geometric BWT: Compressed Text Indexing via Sparse Suffixes and Range Searching

We introduce a new variant of the popular Burrows-Wheeler transform (BWT), called Geometric Burrows-Wheeler Transform (GBWT), which converts a text into a set of points in 2-dimensional geometry. We also introduce a reverse transform, called Points2Text, which converts a set of points into text. Using these two transforms, we show strong equivalence between data structural problems in geometric range searching and text pattern matching. This allows us to apply the lower bounds known in the field of orthogonal range searching to the problems in compressed text indexing. In addition, we give the first succinct (compact) index for I/O-efficient pattern matching in external memory, and show how this index can be further improved to achieve higher-order entropy compressed space.

The Scale of Positive and Negative Experience (SPANE): Psychometric Properties and Normative Data in a Large Chinese Sample

BackgroundThe Scale of Positive and Negative Experience (SPANE) is a new instrument that assesses subjective feelings of well-being and ill-being and overcome several limitations of previous popular instruments. The current study examined the scale's psychometric properties with a large Chinese sample.Principal FindingsData were collected form 21,322 full-time workers from the power industry. The psychometric properties were assessed in term of internal consistency reliability, factorial validity, convergent validity, and measurement invariance across gender, age, marital status, education level, and income level. The results demonstrate that the SPANE has high internal consistency reliability, a correlated two-factor structure (with the uniqueness of three general and specific items of positive and negative feelings allowed to correlate with each other), strict equivalence across gender, age and marital status, and strong equivalence across education and income. Furthermore, the SPANE converges well with two measures of life satisfaction.ConclusionThe Chinese version of the SPANE behaves consistently with the original and can be used in future studies of emotional well-being. The scale norms are presented in terms of percentile rankings, and implications and directions for future research are discussed.

Path Methods for Strong Shift Equivalence of Positive Matrices

In the early 1990’s, Kim and Roush developed path methods for establishing strong shift equivalence (SSE) of positive matrices over a dense subring \(\mathcal{U}\) of ℝ. This paper gives a detailed, unified and generalized presentation of these path methods. New arguments which address arbitrary dense subrings \(\mathcal{U}\) of ℝ are used to show that for any dense subring \(\mathcal{U}\) of ℝ, positive matrices over \(\mathcal{U}\) which have just one nonzero eigenvalue and which are strong shift equivalent over \(\mathcal{U}\) must be strong shift equivalent over \(\mathcal{U}_{+}\). In addition, we show matrices on a path of positive shift equivalent real matrices are SSE over ℝ+; positive rational matrices which are SSE over ℝ+ must be SSE over ℚ+; and for any dense subring \(\mathcal{U}\) of ℝ, within the set of positive matrices over \(\mathcal{U}\) which are conjugate over \(\mathcal{U}\) to a given matrix, there are only finitely many SSE-\(\mathcal{U}_{+}\) classes.

Prediction of polydisperse hard-sphere mixture behavior using tridisperse systems

How many state-variables are needed to predict the equation of state and the jamming density of polydisperse mixtures in glassy, non-equilibrium compressed states? We propose to define equivalent and maximally equivalent systems as those that match three and five moments of a given polydisperse size distribution, respectively. Fluids can be represented well by an equivalent system with only s = 2 components (bidisperse). As little as s = 3 components (tridisperse) are enough to achieve a maximally equivalent system. Those match macroscopic properties in glassy states, but also the volume fraction of rattlers, suggesting strong microstructural equivalency too. For many soft and granular systems, tridisperse, maximally equivalent systems allow for a closed analytical treatment and well-controlled industrial applications, while our proposal waits for experimental validation.

Ideal-related $K$-theory for Leavitt path algebras and graph $C^*$-algebras

We introduce a notion of ideal-related K-theory for rings, and use it to prove that if two complex Leavitt path algebras are equivalent (respectively, isomorphic), then the ideal-related K-theories (respectively, the unital ideal-related K-theories) of the corresponding graph C*-algebras are isomorphic. This has consequences for the Morita equivalence conjecture and isomorphism conjecture for graph algebras, and allows us to prove that when E and F belong to specific collections of graphs whose C*-algebras are classified by ideal-related K-theory, equivalence (respectively, isomorphism) of the Leavitt path algebras implies strong equivalence (respectively, isomorphism) of the graph C*-algebras. We state a number of corollaries that describe various classes of graphs where these implications hold. In addition, we conclude with a classification of Leavitt path algebras of amplified graphs similar to the existing classification for graph C*-algebras of amplified graphs.

LES and acoustic analysis of thermo-acoustic instabilities in a partially premixed model combustor

Numerical simulations were performed using Large Eddy Simulation (LES) and acoustic analysis tools to study thermo-acoustic instabilities in a methane/air academic burner installed at the University of Twente (The Netherlands). It operates under fuel-lean partially premixed conditions at atmospheric pressure, and was built to study thermo-acoustic instabilities in conditions representative of gas turbine Lean Premixed systems: gaseous fuel is injected upstream of the combustor and has a limited time to mix with air. Even though the objective is to burn in a premixed mode, the actual regime corresponds to a partially premixed flame where strong equivalence ratio variations are created especially during combustion instabilities. Capturing these modes with LES is a challenge: here, simulations for both stable and unstable regimes are performed. In the unstable case, the limit cycle oscillations (LCO) are characterized and compared to experimental results. Reasonable agreement is found between simulations and experiments.

A uniform treatment of the orbital effects due to a violation of the strong equivalence principle in the gravitational Stark-like limit

We consider a binary system made of self-gravitating bodies embedded in a constant and uniform external field g. We analytically work out several orbital effects induced by a putative violation of the Strong Equivalence Principle (SEP) due to g. In our calculation, we do not assume e ∼ 0, where e is the binary’s orbit eccentricity. Moreover, we do not a priori choose any specific preferred spatial orientation for the fixed direction of g. Our results do not depend on any particular SEP-violating theoretical scheme. They can be applied to general astronomical and astrophysical binary systems immersed in an external constant and uniform polarizing field.

Results on Embeddings Between State-Based and Event-Based Systems

Kripke Structures (KSs) and Labelled Transition Systems (LTSs) are the two most prominent semantic models used in concurrency theory. Both models are commonly believed to be equi-expressive. One can find manyad hoc embeddings of one of these models into the other. We build upon the seminal work of De Nicola and Vaandrager that firmly established the correspondence between stuttering equivalence in KSs and divergence-sensitive branching bisimulation in LTSs. We show that their embeddings can also be used for a range of other equivalences of interest, such as strong bisimilarity, simulation equivalence and trace equivalence. Furthermore, we extend the results by De Nicola and Vaandrager by showing that there are additional translations that allow one to use minimization techniques in one semantic domain to obtain minimal representatives in the other semantic domain for these equivalences.

Measurement equivalence and mean comparisons of a safety climate measure across construction trades

The use of safety climate measures for needs assessment and interventions has become increasingly popular. However, no research to date has examined whether the meaning and level of safety climate may differ across different groups of interest. This study used multi-group confirmatory factor analyses to investigate the measurement equivalence of a multidimensional safety climate measure across ten construction trade groups (N=4725). In addition, observed mean differences in safety climate perceptions between trades were examined. Results revealed strong measurement equivalence of the safety climate measure across the construction trade groups. Further, significant mean differences were found between the ten trade groups on all four safety climate scales.

Factorial Validity and Invariance of the GHQ-12 Among Clinical and Nonclinical Samples

The purpose of this study was to examine the internal reliability, factorial validity, and measurement invariance of a Brazilian-Portuguese version of the General Health Questionnaire-12 (GHQ-12) across clinical and nonclinical groups. The clinical sample consisted of 228 chronic hemodialysis patients (41.7% female), with a mean age of 48.23 (SD = 16.02) years, whereas the nonclinical sample comprised 350 university students (59.1% female), with a mean age of 21.15 (SD = 2.04) years. Initial model fit comparison of 16 factor structures reported in the literature, through confirmatory factor analysis (CFA), provided mixed results. Additional revisions based on CFA modification indices demonstrated that a reduced (8-item) one-factor model with three error covariances provided the best fit to the data in both samples (comparative fit index > .98 and root mean square error of approximation < .05) and acceptable internal reliability estimates (>.70). Pearson's correlations between the original and the reduced scale was .96 for both samples. Multigroup analysis supported partial strong measurement equivalence across groups. Latent mean differences showed an expected higher factor mean for the clinical sample. Overall results demonstrated that the 8-item one-factor of the GHQ-12 showed good psychometric properties in both samples and provided preliminary support for meaningful comparisons of factor means across clinical and nonclinical groups.

Fuzzy Equilibrium Logic

In this article, we introduce fuzzy equilibrium logic as a generalization of both Pearce equilibrium logic and fuzzy answer set programming. The resulting framework combines the capability of equilibrium logic to declaratively specify search problems, with the capability of fuzzy logics to model continuous domains. We show that our fuzzy equilibrium logic is a proper generalization of both Pearce equilibrium logic and fuzzy answer set programming, and we locate the computational complexity of the main reasoning tasks at the second level of the polynomial hierarchy. We then provide a reduction from the problem of finding fuzzy equilibrium logic models to the problem of solving a particular bilevel mixed integer program (biMIP), allowing us to implement reasoners by reusing existing work from the operations research community. To illustrate the usefulness of our framework from a theoretical perspective, we show that a well-known characterization of strong equivalence in Pearce equilibrium logic generalizes to our setting, yielding a practical method to verify whether two fuzzy answer set programs are strongly equivalent. Finally, to illustrate its application potential, we show how fuzzy equilibrium logic can be used to find strong Nash equilibria, even when players have a continuum of strategies at their disposal. As a second application example, we show how to find abductive explanations from Łukasiewicz logic theories.