Strong Equivalence Research Articles

On the decomposition into Discrete, Type II and Type III C*-algebras

AbstractWe obtained a “decomposition scheme” of C*-algebras. We show that the classes of discrete C*-algebras (as defined by Peligard and Zsidó), type II C*-algebras and type III C*-algebras (both defined by Cuntz and Pedersen) form a good framework to “classify” C*-algebras. In particular, we found that these classes are closed under strong Morita equivalence, hereditary C*-subalgebras as well as taking “essential extension” and “normal quotient”. Furthermore, there exist the largest discrete finite ideal Ad,1, the largest discrete essentially infinite ideal Ad,∞, the largest type II finite ideal AII,1, the largest type II essentially infinite ideal AII,∞, and the largest type III ideal AIII of any C*-algebra A such that Ad,1 + Ad,∞ + AII,1 + AII,∞ + AIII is an essential ideal of A. This “decomposition” extends the corresponding one for W*-algebras.We also give a closer look at C*-algebras with Hausdorff primitive ideal spaces, AW*-algebras as well as local multiplier algebras of C*-algebras. We find that these algebras can be decomposed into continuous fields of prime C*-algebras over a locally compact Hausdorff space, with each fiber being non-zero and of one of the five types mentioned above.

Confirmation and the ordinal equivalence thesis

According to a widespread but implicit thesis in Bayesian confirmation theory, two confirmation measures are considered equivalent if they are ordinally equivalent --- call this the ``ordinal equivalence thesis'' (OET). I argue that adopting OET has significant costs. First, adopting OET renders one incapable of determining whether a piece of evidence substantially favors one hypothesis over another. Second, OET must be rejected if merely ordinal conclusions are to be drawn from the expected value of a confirmation measure. Furthermore, several arguments and applications of confirmation measures given in the literature already rely on a rejection of OET. I also contrast OET with stronger equivalence theses and show that they do not have the same costs as OET. On the other hand, adopting a thesis stronger than OET has costs of its own, since a rejection of OET ostensibly implies that people's epistemic states have a very fine-grained quantitative structure. However, I suggest that the normative upshot of the paper in fact has a conditional form, and that other Bayesian norms can also fruitfully be construed as having a similar conditional form.

Tests of Gravity Theories Using Supermassive Black Holes

Abstract Scalar-tensor theories of gravity generally violate the strong equivalence principle, namely that compact objects have a suppressed coupling to the scalar force, which causes them to fall slower. A black hole is the extreme example where such a coupling vanishes, i.e., black holes have no scalar hair. We explore observational scenarios for detecting strong equivalence principle violation, focusing on galileon gravity as an example. For galaxies infalling toward galaxy clusters, the supermassive black hole can be offset from the galaxy center away from the direction of the cluster. Well-resolved images of galaxies around nearby clusters can therefore be used to identify the displaced black hole via the star cluster bound to it. We show that this signal is accessible with imaging surveys, both ongoing ones such as the Dark Energy Survey and future ground- and space-based surveys. Already, the observation of the central black hole in M 87 places new constraints on the galileon parameters, which we present here. matter couplings are disfavored for a large region of the parameter space. We also find a novel phenomenon whereby the black hole can escape the galaxy completely in less than one billion years.

Existence of equilibrium on asset markets with a countably infinite number of states

We consider a model with a countably infinite number of states of nature. The agents have equivalent probability beliefs and von Neumann–Morgenstern utilities. The No-Arbitrage Prices in this paper are, up to a scalar, the marginal utilities. We introduce the Beliefs Strong Equivalence and the No Half Line Condition of the same type conditions. Under these conditions, the No Arbitrage price condition is sufficient for the existence of an equilibrium when the commodity space is lp,1≤p<+∞. This No Arbitrage condition is necessary and sufficient for the existence of equilibrium when the total endowment is in l∞. Moreover, it is equivalent to the compactness of the individually rational utility set.

Logical Characterization of Trace Metrics

In this paper we continue our research line on logical characterizations of behavioral metrics obtained from the definition of a metric over the set of logical properties of interest. This time we provide a characterization of both strong and weak trace metric on nondeterministic probabilistic processes, based on a minimal boolean logic L which we prove to be powerful enough to characterize strong and weak probabilistic trace equivalence. Moreover, we also prove that our characterization approach can be restated in terms of a more classic probabilistic L-model checking problem.

Serious limitations of the strong equivalence principle

It is well known that an accelerated charged particle radiates away energy. However, whether an accelerated neutral composite particle radiates away energy is unclear. We study decoherent Larmor radiation from an accelerated neutral composite object. We find that the neutral object’s long wavelength radiation is highly suppressed because radiation from different charges is canceled out. However, the neutral object radiates high energy or short wavelength radiation without any suppression. In that case, radiation from each particle can be treated independently, and it is called the decoherent radiation. We compare a hydrogen atom’s decoherent Larmor radiation with its gravitational radiation while the atom is in a circular orbit around a star. Gravitational radiation is stronger than the electromagnetic radiation if the orbital radius is larger than some critical radius. Since the decoherent radiation is related to the object’s structure, this implies that the strong equivalence principle which states that gravitational motion does not depend on an object’s constitution has severe limitations.

Space tests of the strong equivalence principle: BepiColombo and the Sun–Earth Lagrangian points opportunity

The validity of General Relativity (GR), after 100 years, is supported by solid experimental evidence. However, there is a lot of interest in pushing the limits of precision by other experiments. Here, we focus our attention on the equivalence principle (EP), in particular, the strong form. The results of ground experiments and Lunar Laser Ranging (LLR) have provided the best upper limit on the Nordtvedt parameter [Formula: see text] that models deviations from the strong EP. Its uncertainty is currently [Formula: see text]. In the first part of this paper, we will describe the experiment, to measure [Formula: see text], that will be done by the future mission BepiColombo (BC). The expected precision on [Formula: see text] is [Formula: see text]. In the second part, we will consider the ranging between the Earth and a spacecraft (SC) orbiting near the Sun–Earth Lagrangian points to get an independent measurement of [Formula: see text]. In this case, we forecast a constraint similar to that achieved by LLR.

Therapy workshop: Experience of the senses

IntroductionThe psychoactive substances consumption modifies the users’ sense-perception.ObjectivesDiscuss the therapeutic workshop as a stimulation strategy of the sense organs.MethodologyThe activities were developed at a Center of Psycho-Social Attention for alcohol and other drugs – CPSAad, located in north-eastern Brazil. The therapeutic workshop was divided into six sessions; being worked a sense organ in each meeting. Initially, the sessions were explained and they entered the room in silence. At first, vision and lastly, taste. The taste dynamic session was initiated by the pool where users experienced different flavours and made distinctions between them, including a food without flavour, experiencing feelings of pleasure and displeasure. This dynamic was finalized in the institute's kitchen with different ice cream flavours. The participants freely served themselves, being led to reflections on their choices of pleasure. The sixth session was constituted by listening about all Therapy Workshop Experience of the Senses, on which participants reported emotions and feelings experienced during the sessions, such as: fear, anxiety, craving, denial, pleasure and displeasure.ResultsIt was identified a universe of sensations that can be translated into a sense-perception reframing about themselves and their surroundings.ConclusionThe participants presented a sensory dullness, relating the experienced stimuli to the consumption of psychoactive substances, demonstrating a strong equivalence between the proposed activity and substance dependence. This activity enabled an interdisciplinary approach, through knowledge and interventions exchange.Disclosure of interestThe authors have not supplied their declaration of competing interest.

Accessible single-valued neutrosophic graphs

This paper derived single-valued neutrosophic graphs from single-valued neutrosophic hypergraphs via strong equivalence relation. We show that any weak single-valued neutrosophic graph is a derived single-valued neutrosophic graph and any linear weak single-valued neutrosophic tree is an extendable linear single-valued neutrosophic tree.

Characterizing causal action theories and their implementations in answer set programming

We consider a simple language for writing causal action theories, and postulate several properties for the state transition models of these theories. We then consider some possible embeddings of these causal action theories in some other action formalisms, and their implementations in logic programs with answer set semantics. In particular, we propose to consider what we call permissible translations from these causal action theories to logic programs. We identify two sets of properties, and prove that for each set, there is only one permissible translation, under strong equivalence, that can satisfy all properties in the set. We also show that these two sets of conditions are minimal in that removing any condition from each of them will result in multiple permissible mappings. Furthermore, as it turns out, for one set, the unique permissible translation is essentially the same as Balduccini and Gelfond's translation from Gelfond and Lifschitz's action language B to logic programs. For the other, it is essentially the same as Lifschitz and Turner's translation from the action language C to logic programs. This work provides a new perspective on understanding, evaluating and comparing action languages by using sets of properties instead of examples. The results in this paper provide a characterization of two representative action languages B and C in terms of permissible mappings from our causal action theories to logic programs. It will be interesting to see if other action languages can be similarly characterized, and whether new action formalisms can be defined using different sets of properties.

Infinitary equilibrium logic and strongly equivalent logic programs

Strong equivalence is an important concept in the theory of answer set programming. Informally speaking, two sets of rules are strongly equivalent if they have the same meaning in any context. Equilibrium logic was used to prove that sets of rules expressed as propositional formulas are strongly equivalent if and only if they are equivalent in the logic of here-and-there. We extend this line of work to formulas with infinitely long conjunctions and disjunctions, show that the infinitary logic of here-and-there characterizes strong equivalence of infinitary formulas, and give an axiomatization of that logic. This is useful because of the relationship between infinitary formulas and logic programs with local variables.

On Equivalence and Inconsistency of Answer Set Programs with External Sources

HEX-programs extend of answer-set programs (ASP) with ex-ternal sources. In previous work, notions of equivalence ofASP programs under extensions have been developed. Mostwell-known are strong equivalence, which is given for pro-grams P and Q if P ∪ R and Q ∪ R have the same answersets for arbitrary programs R, and uniform equivalence, whichis given if this is guaranteed for sets R of facts. More fine-grained approaches exist, which restrict the set of atoms inthe added program R. In this paper we provide a characteriza-tion of equivalence of HEX -programs. Since well-known ASPextensions (e.g. constraint ASP) amount to special cases ofHEX , the results are interesting beyond the particular formal-ism. Based on this, we further characterize inconsistency ofprograms wrt. program extensions. We then discuss possibleapplications of the results for algorithms improvements.

The electromagnetic signature of gravitational wave interaction with the quantum vacuum

An analysis of the effects of the passage of a gravitational wave (GW) on the quantum vacuum is made within the context of the Nexus paradigm of quantum gravity. Results indicate that if the quantum vacuum includes electrically charged virtual particle fields, then a GW will induce vacuum polarization. The equations of General Relativity (GR) are then reformulated to include electric charge displacements in the quantum vacuum imposed by an anisotropic stress — momentum tensor. It is then demonstrated that as a result of the spacetime piezoelectric effect, a gravitational wave is associated with a rotating electromagnetic wave and that the converse effect produced by strong electromagnetic fields is responsible for the generation of relativistic jets and gamma ray bursts. Objects with strong electromagnetic fields will apparently violate the strong equivalence principle.

Towards equivalence links between senses in plWordNet and Princeton WordNet

AbstractThe paper focuses on the issue of creating equivalence links in the domain of bilingual computational lexicography. The existing interlingual links between plWordNet and Princeton WordNet synsets (sets of synonymous lexical units – lemma and sense pairs) are re-analysed from the perspective of equivalence types as defined in traditional lexicography and translation. Special attention is paid to cognitive and translational equivalents. A proposal of mapping lexical units is presented. Three types of links are defined: super-strong equivalence, strong equivalence and weak implied equivalence. The strong equivalences have a common set of formal, semantic and usage features, with some of their values slightly loosened for strong equivalence. These will be introduced manually by trained lexicographers. The sense-mapping will partly draw on the results of the existing synset mapping. The lexicographers will analyse lists of pairs of synsets linked by interlingual relations such as synonymy, partial synonymy, hyponymy and hypernymy. They will also consult bilingual dictionaries and check translation probabilities in a parallel corpus. The results of the proposed mapping have great application potential in the area of natural language processing, translation and language learning.

Topological Conjugacy of Topological Markov Shifts and Cuntz–Krieger Algebras

For an irreducible non-permutation matrix A , the triplet (\mathcal{O}_A,\mathcal{D}_A,\rho^A) for the Cuntz–Krieger algebra \mathcal{O}_A , its canonical maximal abelian C^\ast -subalgebra \mathcal{D}_A , and its gauge action \rho^A is called the Cuntz–Krieger triplet. We introduce a notion of strong Morita equivalence in the Cuntz–Krieger triplets, and prove that two Cuntz–Krieger triplets (\mathcal{O}_A,\mathcal{D}_A,\rho^A) and (\mathcal{O}_B,\mathcal{D}_B,\rho^B) are strong Morita equivalent if and only if A and B are strong shift equivalent. We also show that the generalized gauge actions on the stabilized Cuntz–Krieger algebras are cocycle conjugate if the underlying matrices are strong shift equivalent. By clarifying K-theoretic behavior of the cocycle conjugacy, we investigate a relationship between cocycle conjugacy of the gauge actions on the stabilized Cuntz–Krieger algebras and topological conjugacy of the underlying topological Markov shifts.

Limits and limitations of no-regret learning in games

AbstractWe study the limit behavior and performance of no-regret dynamics in general game theoretic settings. We design protocols that achieve both good regret and equilibration guarantees in general games. We also establish a strong equivalence between them and coarse correlated equilibria (CCE). We examine structured game settings where stronger properties can be established for no-regret dynamics and CCE. In congestion games with non-atomic agents (each contributing a fraction of the flow), as we decrease the individual flow of agents, CCE become closely concentrated around the unique equilibrium flow of the non-atomic game. Moreover, we compare best/worst case no-regret learning behavior to best/worst case Nash equilibrium (NE) in small games. We prove analytical bounds on these inefficiency ratios for 2×2 games and unboundedness for larger games. Experimentally, we sample normal form games and compute their measures of inefficiency. We show that the ratio distribution has sharp decay, in the sense that most generated games have small ratios. They also exhibit strong anti-correlation between each other, that is games with large improvements from the best NE to the best CCE present small degradation from the worst NE to the worst CCE.

Spatial correspondence between the specialist galling insect genusKladothrips(Thysanoptera: Tubulifera: Phlaeothripidae) and itsAcaciahost: ecological and evolutionary constraints on host use

Specialised insect–plant associations, and the presence of other organisms that specifically target this interaction, represent relatively ancient ecological interactions. These types of associations are characterised by non-random geographical range correspondence, especially in the presence of narrow resource use. However, empirical studies rarely investigate how spatial relationships between insects and their host plants contribute to phenotypic interactions resulting from host shifting. This is important because geographic range discontinuities highlight biotic or abiotic conditions that might interfere with ecological interactions and how species diversify. In this study, we test the null hypothesis that the geographic range of the galling genus Kladothrips corresponds with their Acacia hosts. We then evaluate whether ecological characteristics of Acacia are related to evolutionary constraints on Kladothrips host use. The results indicated discontinuities between spatial distribution models of Acacia and the hosts that support Kladothrips. Temperature, precipitation and edaphic variables contributed strongly to these differences and reveal Kladothrips gall Acacia hosts present in harsh, arid environments. However, Acacia are distributed throughout all Australia's diverse biomes including mesic, arid and monsoonal regions. Discontinuities in spatial correspondence between Acacia and Kladothrips suggest biotic and abiotic pressures limiting ecological interactions are present in mesic and hydric climates. Acacia hosts observed to support Kladothrips share strong spatial model equivalency, but not necessarily close phylogenetic relatedness. Co-phylogenetic analyses indicated contrasting host use conservatism between Acacia sections. The results of this study support the hypothesis that specialised associations between insects and plants are a function of varying climatic and evolutionary constraints over the geographic range of the host lineage. These findings agree with the premise that ecological constraints underlie evolutionary patterns of host use.

A Mixed-Methods Pilot Study of Student Athlete Engagement in LGBTQ Ally Actions

Reports of sexual prejudice and heterosexism in sports are still pervasive, despite growing acceptance of lesbian, gay, bisexual, transgender, and queer (LGBTQ) persons in the U.S. Yet, few studies have investigated how and why college studentathletes engage in LGBTQ-focused ally actions (e.g., standing up and speaking out against sexual prejudice; showing support at LGBTQ events). This mixed-methods pilot study describes the development and psychometric testing of the Engagement in LGBTQ Ally Actions in Sports Scale, in addition to analyses of two open-ended questions that provided supplementary insight into what it means to collegiate athletes to be an ally to the LGBTQ community. The convenience sample included 159 college student-athletes from two public universities (M age = 20.67 years, SD = 1.56). Findings indicated that the Engagement in LGBTQ Ally Actions in Sports Scale demonstrated strong internal consistency, validity, and equivalence across gender. Qualitative analyses suggested that college ...

Strong shift equivalence and algebraic K-theory

Abstract For a semiring ℛ \mathcal{R} , the relations of shift equivalence over ℛ \mathcal{R} ( SE- ⁢ ℛ \textup{SE-}\mathcal{R} ) and strong shift equivalence over ℛ \mathcal{R} ( SSE- ⁢ ℛ \textup{SSE-}\mathcal{R} ) are natural equivalence relations on square matrices over ℛ \mathcal{R} , important for symbolic dynamics. When ℛ \mathcal{R} is a ring, we prove that the refinement of SE- ⁢ ℛ \textup{SE-}\mathcal{R} by SSE- ⁢ ℛ \textup{SSE-}\mathcal{R} , in the SE- ⁢ ℛ \textup{SE-}\mathcal{R} class of a matrix A, is classified by the quotient N ⁢ K 1 ⁢ ( ℛ ) / E ⁢ ( A , ℛ ) NK_{1}(\mathcal{R})/E(A,\mathcal{R}) of the algebraic K-theory group N ⁢ K 1 ⁢ ( ℛ ) NK_{1}(\mathcal{R}) . Here, E ⁢ ( A , ℛ ) E(A,\mathcal{R}) is a certain stabilizer group, which we prove must vanish if A is nilpotent or invertible. For this, we first show for any square matrix A over ℛ \mathcal{R} that the refinement of its SE- ⁢ ℛ \textup{SE-}\mathcal{R} class into SSE- ⁢ ℛ \textup{SSE-}\mathcal{R} classes corresponds precisely to the refinement of the GL ⁢ ( ℛ ⁢ [ t ] ) \mathrm{GL}(\mathcal{R}[t]) equivalence class of I - t ⁢ A I-tA into El ⁢ ( ℛ ⁢ [ t ] ) \mathrm{El}(\mathcal{R}[t]) equivalence classes. We then show this refinement is in bijective correspondence with N ⁢ K 1 ⁢ ( ℛ ) / E ⁢ ( A , ℛ ) NK_{1}(\mathcal{R})/E(A,\mathcal{R}) . For a general ring ℛ \mathcal{R} and A invertible, the proof that E ⁢ ( A , ℛ ) E(A,\mathcal{R}) is trivial rests on a theorem of Neeman and Ranicki on the K-theory of noncommutative localizations. For ℛ \mathcal{R} commutative, we show ∪ A E ⁢ ( A , ℛ ) = N ⁢ S ⁢ K 1 ⁢ ( ℛ ) \cup_{A}E(A,\mathcal{R})=NSK_{1}(\mathcal{R}) ; the proof rests on Nenashev’s presentation of K 1 K_{1} of an exact category.

Effect of cosmological evolution on Solar System constraints and on the scalarization of neutron stars in massless scalar-tensor theories

Certain scalar-tensor theories of gravity that generalize Jordan-Fierz-Brans-Dicke theory are known to predict non-trivial phenomenology for neutron stars. In these theories, first proposed by Damour and Esposito-Far\`ese, the scalar field has a standard kinetic term, and couples conformally to the matter fields. The weak equivalence principle is therefore satisfied, but scalar effects may arise in strong-field regimes, e.g. allowing for violations of the strong equivalence principle in neutron stars ("spontaneous scalarization") or in sufficiently tight binary neutron-star systems ("dynamical/induced scalarization"). The original scalar-tensor theory proposed by Damour and Esposito-Far\`ese is in tension with solar-system constraints (for couplings that lead to scalarization), if one accounts for cosmological evolution of the scalar field and no mass term is included in the action. We here extend the conformal coupling of that theory, in order to ascertain if, in this way, solar-system tests can be passed, while retaining a non-trivial phenomenology for neutron stars. We find that even with this generalized conformal coupling, it is impossible to construct a theory that passes both Big-Bang nucleosynthesis and solar-system constraints, while simultaneously allowing for scalarization in isolated/binary neutron stars.