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This paper aims to quantitatively evaluate the performance of ChatGPT, an interactive large language model, on inter-sentential relations such as temporal relations, causal relations, and discourse relations. Given ChatGPT's promising performance across various tasks, we proceed to carry out thorough evaluations on the whole test sets of 11 datasets, including temporal and causal relations, PDTB2.0-based, and dialogue-based discourse relations. To ensure the reliability of our findings, we employ three tailored prompt templates for each task, including the zero-shot prompt template, zero-shot prompt engineering (PE) template, and in-context learning (ICL) prompt template, to establish the initial baseline scores for all popular sentence-pair relation classification tasks for the first time. Through our study, we discover that ChatGPT exhibits exceptional proficiency in detecting and reasoning about causal relations, albeit it may not possess the same level of expertise in identifying the temporal order between two events. While it is capable of identifying the majority of discourse relations with existing explicit discourse connectives, the implicit discourse relation remains a for

In 1998, it was shown that, if flavor SU(3) symmetry [SU(3)$_F$] is assumed in charmless $B \to PP$ decays ($P$ is a light pseudoscalar meson), some reduced matrix elements involving electroweak penguin (EWP) operators are related to those involving tree operators. Similarly, EWP diagrams are related to tree diagrams. These SU(3)$_F$ EWP-tree relations were recently used in global analyses of $B \to PP$ decays. They have also been used over the years in analyses of the $B \to πK$ puzzle, even though the $B \to πK$ amplitudes are related by isospin symmetry [SU(2)$_I$], and not the full SU(3)$_F$. In this paper, we show that, even if only SU(2)$_I$ is assumed, there are still EWP-tree relations. In $ΔS=0$ decays, these relations are similar to those of SU(3)$_F$, and can be used to take into account the EWP contributions in the extraction of the CP phase $α$ from $B \to ππ$ decays. In $ΔS=1$ decays, the SU(2)$_I$ EWP-tree relations are quite different from those of SU(3)$_F$; when these are used to analyze the $B \to πK$ puzzle, one now finds a 4-5$σ$ discrepancy with the Standard Model, much larger than what was previously found. We argue that, if one analyzes a set of hadronic $B$

Let $N$ be a positive integer. In this paper we shall study the special values of multiple polylogarithms at $N$th roots of unity, called multiple polylogarithm values (MPVs) of level $N$. These objects are generalizations of multiple zeta values and alternating Euler sums, which was studied by Euler, and more recently, many mathematicians and theoretical physicists.. Our primary goal in this paper is to investigate the relations among the MPVs of the same weight and level by using the regularized double shuffle relations, regularized distribution relations, lifted versions of such relations from lower weights, and seeded relations which are produced by relations of weight one MPVs. We call relations from the above four families \emph{standard}. Let $d(w,N)$ be the $\Q$-dimension of $\Q$-span of all MPVs of weight $w$ and level $N$. Then we obtain upper bound for $d(w,N)$ by the standard relations which in general are no worse or no better than the one given by Deligne and Goncharov depending on whether $N$ is a prime-power or not, respectively, except for 2- and 3-powers, in which case standard relations seem to be often incomplete whereas Deligne shows that their bound should be

We give a new, conceptual proof of the $\imath$Serre and Serre-Lusztig relations for $\imath$quantum groups. The key to our approach is a new formula for the comultiplication of the $\imath$-divided powers, which allows us to reformulate the relations in terms of the adjoint action. We then obtain a proof using properties of the adjoint representation. The flexibility of this approach allows us to establish a more general family of relations which seem difficult to establish otherwise.

Classical pulsating stars such as Cepheid and RR Lyrae variables exhibit well-defined Period-Luminosity relations at near-infrared wavelengths. Despite their extensive use as stellar standard candles, the effects of metallicity on Period-Luminosity relations for these pulsating variables, and in turn, on possible biases in distance determinations, are not well understood. We present ongoing efforts in determining accurate and precise metallicity coefficients of Period-Luminosity-Metallicity relations for classical pulsators at near-infrared wavelengths. For Cepheids, it is crucial to obtain a homogeneous sample of photometric light curves and high-resolution spectra for a wide range of metallicities to empirically determine metallicity coefficient and reconcile differences with the predictions of the theoretical models. For RR Lyrae variables, using their host globular clusters covering a wide range of metallicities, we determined the most precise metallicity coefficient at near-infrared wavelengths, which is in excellent agreement with the predictions of the horizontal branch evolution and stellar pulsation models.

Human-centered environments are rich with a wide variety of spatial relations between everyday objects. For autonomous robots to operate effectively in such environments, they should be able to reason about these relations and generalize them to objects with different shapes and sizes. For example, having learned to place a toy inside a basket, a robot should be able to generalize this concept using a spoon and a cup. This requires a robot to have the flexibility to learn arbitrary relations in a lifelong manner, making it challenging for an expert to pre-program it with sufficient knowledge to do so beforehand. In this paper, we address the problem of learning spatial relations by introducing a novel method from the perspective of distance metric learning. Our approach enables a robot to reason about the similarity between pairwise spatial relations, thereby enabling it to use its previous knowledge when presented with a new relation to imitate. We show how this makes it possible to learn arbitrary spatial relations from non-expert users using a small number of examples and in an interactive manner. Our extensive evaluation with real-world data demonstrates the effectiveness of ou

This publication presents a relation computation or calculus for international relations using a mathematical modeling. It examined trust for international relations and its calculus, which related to Bayesian inference, Dempster-Shafer theory and subjective logic. Based on an observation in the literature, we found no literature discussing the calculus method for the international relations. To bridge this research gap, we propose a relation algebra method for international relations computation. The proposed method will allow a relation computation which is previously subjective and incomputable. We also present three international relations as case studies to demonstrate the proposed method is a real-world scenario. The method will deliver the relation computation for the international relations that to support decision makers in a government such as foreign ministry, defense ministry, presidential or prime minister office. The Department of Defense (DoD) may use our method to determine a nation that can be identified as a friendly, neutral or hostile nation.

We present Period-Luminosity-Color and Period-Luminosity relations of classical Cepheids constructed for about 1280 Cepheids from the LMC and 2140 from the SMC. High quality BVI observations (120-360 epochs in the I-band and 15-40 in the BV-bands) were collected during the OGLE-II microlensing experiment. The I-band diagrams of the LMC show very small scatter, σ=0.074 mag, indicating that Cepheid variables can potentially be a very good standard candle. We compare relations of fundamental mode Cepheids from the LMC and SMC and we do not find significant differences of slopes of the Period-Luminosity- Color and Period-Luminosity relations in these galaxies. For the first overtone Cepheids a small change of the slope of Period-Luminosity relation is possible. We determine the difference of distance moduli between the SMC and LMC with Cepheid relations and compare the result with difference obtained with other standard candles: RR Lyr and red clump stars. Results are very consistent and indicate that the values of zero points of the fundamental mode Cepheid relations are similar in these galaxies. The mean difference of distance moduli between the SMC and LMC is equal to μ_SMC-μ_LMC=0

By using the Grothendieck-Riemann-Roch theorem we derive cycle relations modulo algebraic equivalence in the Jacobian of a curve. The relations generalize the relations found by Colombo and van Geemen and are analogous to but simpler than the relations recently found by Herbaut. In an appendix due to Zagier it is shown that these sets of relations are equivalent.

We describe in this note a torsor structure arising on the affine scheme defined by a system of rationnal algebraic relations between polyzetas at roots of unity (values of hyperlogarithmic functions on a fixed finite group of complex roots of unity). When this group is reduced to 1, we call these numbers the polyzetas. They generalize the values of the Riemann zeta function at odd positive integers and are also called MZVs, multizetas, multiple harmonic series or Euler/Zagier sums. It is believed that the relations we consider here span all algebraic relations between them. The torsor structure underlying these relations should in that case be se same as Drinfeld's torsor made of the Grothendieck- Teichmueller group acting on associators. The formulas for the general case are derived from the action of the absolute Galois group on the projective line minus finitely many points. It is an easy consequence of the torsor structure that the algebra defined by these relations is a polynomial algebra. This was stated first by J. Ecalle in the polyzetas case.

Pandharipande-Pixton have used the geometry of the moduli space of stable quotients to produce relations between tautological Chow classes on the moduli space $M_g$ of smooth genus g curves. We study a natural extension of their methods to the boundary and more generally to Hassett's moduli spaces $\overline M_{g, w}$ of stable nodal curves with weighted marked points. Algebraic manipulation of these relations brings them into a Faber-Zagier type form. We show that they give Pixton's generalized FZ relations when all weights are one. As a special case, we give a formulation of FZ relations for the n-fold product of the universal curve over $M_g$.

We construct ergodic discrete probability measure preserving equivalence relations $\cR$ that has no proper ergodic normal subequivalence relations and no proper ergodic finite-index subequivalence relations. We show that every treeable equivalence relation satisfying a mild ergodicity condition and cost $>1$ surjects onto every countable group with ergodic kernel. Lastly, we provide a simple characterization of normality for subequivalence relations and an algebraic description of the quotient.

We formulate uncertainty relations for mutually unbiased bases and symmetric informationally complete measurements in terms of the Rényi and Tsallis entropies. For arbitrary number of mutually unbiased bases in a finite-dimensional Hilbert space, we give a family of Tsallis $α$-entropic bounds for $α\in(0;2]$. Relations in a model of detection inefficiences are obtained. In terms of Rényi's entropies, lower bounds are given for $α\in[2;\infty)$. State-dependent and state-independent forms of such bounds are both given. Uncertainty relations in terms of the min-entropy are separately considered. We also obtain lower bounds in term of the so-called symmetrized entropies. The presented results for mutually unbiased bases are extensions of some bounds previously derived in the literature. We further formulate new properties of symmetric informationally complete measurements in a finite-dimensional Hilbert space. For a given state and any SIC-POVM, the index of coincidence of generated probability distribution is exactly calculated. Short notes are made on potential use of this result in entanglement detection. Further, we obtain state-dependent entropic uncertainty relations for a sing

Uncertainty relations for mixed quantum states (precisely, purity-bounded position-momentum relations, developed by Bastiaans and then by Man'ko and Dodonov) are studied in general multi-dimensional case. An expression for family of mixed states at the lower bound of uncertainty relation is obtained. It is shown, that in case of entropy-bounded uncertainty relations, lower-bound state is thermal, and a transition from one-dimensional problem to multi-dimensional one is trivial. Results of numerical calculation of the relation lower bound for different types of generalized purity are presented. Analytical expressions for general purity-bounded relations for highly mixed states are obtained.

Commonsense knowledge relations are crucial for advanced NLU tasks. We examine the learnability of such relations as represented in CONCEPTNET, taking into account their specific properties, which can make relation classification difficult: a given concept pair can be linked by multiple relation types, and relations can have multi-word arguments of diverse semantic types. We explore a neural open world multi-label classification approach that focuses on the evaluation of classification accuracy for individual relations. Based on an in-depth study of the specific properties of the CONCEPTNET resource, we investigate the impact of different relation representations and model variations. Our analysis reveals that the complexity of argument types and relation ambiguity are the most important challenges to address. We design a customized evaluation method to address the incompleteness of the resource that can be expanded in future work.

We explicitly show that the Bern-Carrasco-Johansson color-kinematic duality holds at tree level through at least eight points in Aharony-Bergman-Jafferis-Maldacena theory with gauge group SU(N) x SU(N). At six points we give the explicit form of numerators in terms of amplitudes, displaying the generalized gauge freedom that leads to amplitude relations. However, at eight points no amplitude relations follow from the duality, so the diagram numerators are fixed unique functions of partial amplitudes. We provide the explicit amplitude-numerator decomposition and the numerator relations for eight-point amplitudes.

(Abridged) We examine the X-ray luminosity scaling relations of 31 nearby galaxy clusters from the Representative XMM-Newton Cluster Structure Survey (REXCESS). The objects are selected in X-ray luminosity only, optimally sampling the cluster luminosity function; temperatures range from 2 to 9 keV and there is no bias toward any particular morphological type. Pertinent values are extracted in an aperture corresponding to R_500, estimated using the tight correlation between Y_X and total mass. The data exhibit power law relations between bolometric X-ray luminosity and temperature, Y_X and total mass, all with slopes that are significantly steeper than self-similar expectations. We examine the causes for the steepening, finding that the primary driver appears to be a systematic variation of the gas content with mass. Scatter about the relations is dominated in all cases by the presence of cool cores. The natural logarithmic scatter about the raw X-ray luminosity-temperature relation is about 70%, and about the X-ray luminosity-Y_X relation it is 40%. Cool core and morphologically disturbed systems occupy distinct regions in the residual space with respect to the best fitting mean re

We suggest that the dark side of the universe builds a dark medium modifying the Standard Model particle dispersion relations. We introduce the generic form for the modified dispersion relations and provide explicit models of the dark medium. We use the derived neutrino dispersion relations to show that the size of the corrections are smaller than the SN1987a bounds. We argue that before invoking modifications of Einstein's theory of relativity one should investigate the dark medium effects.