Scalar Derivatives Research Articles

Only the (informationally) stronger survive: A probe recognition study with scale-mates and antonyms

Speakers often use scalar words such as warm in a pragmatically strengthened way that results in the conveyed meaning being warm but not hot. In these inferences, known as scalar implicatures, meaning alternatives have been postulated to play a crucial role. Upon encountering warm, the informationally stronger alternative hot has been shown to be active in online sentence processing. Antonyms (cool) have also been shown to be activated in the same way even though they are standardly assumed to not be involved in scalar implicature derivation. In the current study, we focus on the question of whether both strong scalar alternatives and antonyms are represented in the final mental model of the discourse following scalar implicature derivation. We ran two probe recognition experiments, testing strong scalars and antonyms. We found an interference effect for strong scalars, indicating their representation, but not one for antonyms. Thus, we provide evidence that only the strong scalars survive in the eventual representation of the pragmatic meaning of a sentence.

Watch your tune! On the role of intonation for scalar diversity

Recent research has highlighted that lexical scales vary in their likelihood of giving rise to a scalar inference—a finding labeled scalar diversity. The current paper examines the role of intonation for this phenomenon, which has thus far primarily been studied using written materials. A specific focus in this regard was on the so-called rise-fall-rise contour, which has been argued to (i) convey uncertainty, which could have an influence on scalar inference calculation, and (ii) be sensitive to properties of lexical scales, which could interact with factors driving scalar diversity. Experiment 1 combined production with an inference task to assess the likelihood of different intonational contours, as well as how a given contour affects scalar inference rates. Production of the rise-fall-rise varied across lexical scales, as expected, and led to an increase in scalar inference derivation relative to a fall. The latter finding was further confirmed in Experiment 2, which explicitly manipulated intonational contours in the inference task. The results, thus, show the importance of taking intonation into account when studying scalar diversity and scalar inference more generally, and they also have implications for theories of the rise-fall-rise contour. Additionally, the experiments revealed a contour that is prosodically similar to the so-called Contradiction Contour, but appears to serve a different pragmatic function.

Pragmatic competence and pragmatic tolerance in foreign language acquisition—revisiting the case of scalar implicatures

AbstractPrevious L2 studies used binary Truth-Value-Judgment (TVJ) tasks to investigate L1–L2 differences in scalar implicature derivation (some X implicates some but not all X). They examined participants’ judgments of sentences with weak scalar expressions (“Timothy ate some of the pretzels”) when stronger ones are true (“Timothy ate all of the pretzels”). Some studies indicate adult L2 learners are less likely than L1 users to accept such statements while others found the opposite, concluding that implicature derivation is “costly” for L2 learners, rendering them less pragmatically competent than L1 users. Importantly, related L1 research suggests that TVJ tasks only capture sensitivity to under-informativeness. This sensitivity might be completely overridden by metalinguistic attitudes in binary tasks, whereas graded tasks reveal nuanced judgment patterns. Exploring L2 response behaviors, we tested English L1 speakers and competent German L2 English learners using binary and graded tasks. In both tasks, we found evidence of pragmatic responding with no evidence of differences between groups. Bayes factor analyses of the graded data favored H0 over the hypotheses that L2 learners provide fewer or more rejections to under-informative input than L1 learners. We explore implications for L2 learners’ pragmatic abilities, differences with previous studies, and the role of TVJ tasks in under-informative contexts.

Starting inflation from inhomogeneous initial conditions with momentum

We investigate the circumstances under which cosmic inflation can arise from very inhomogeneous initial conditions using numerical relativity simulations. Previous studies have not considered cases with non-zero momentum density due to technical challenges with solving the coupled Einstein constraint equations. Here we address these, introducing and comparing several different ways of constructing cosmological initial conditions with inhomogeneous scalar field and time derivative profiles. We evolve such initial conditions with large inhomogeneities in both single- and two-field inflationary models. We study cases where the initial gradient and kinetic energy are much larger than the inflationary energy scale, and black holes can form, as well as cases where the initial scalar potential energy is comparable, as in scenarios where inflation occurs at nearly Planckian densities, finding large-field inflation to be generally robust. We consider examples of initial conditions where a large scalar field velocity towards non-inflationary values would prevent inflation from occurring in the homogeneous case, finding that the addition of large gradients in the scalar field can actually dilute this effect, with the increased expansion and non-vanishing restoring force leading to inflation.

Fractional gradient descent algorithms for systems with outliers: A matrix fractional derivative or a scalar fractional derivative

Two gradient descent based fractional methods are proposed for systems with outliers in this paper. The outliers in the collected data usually causes biased estimates, resulting in a poor identification model. Tradition fractional gradient descent (FGD) algorithm has an assumption that the fractional derivative is a scalar, which leads to slow convergence rates, especially for systems with an ill-conditioned matrix. The proposed algorithms in this paper have several advantages over the traditional identification methods: (1) can get unbiased estimates; (2) have faster convergence rates; (3) enrich the FGD estimation framework. Simulation examples demonstrate the effectiveness of the proposed algorithms.

A closer look at the sources of variability in scalar implicature derivation: a review

For more than 20 years, studies in experimental pragmatics have provided invaluable insights into the cognitive processes involved in deriving scalar implicatures and achieving inferential comprehension. However, the reports have always contained a notable degree of variability that remained inadequately discussed in the literature. For instance, upon closer inspection of the experimental record, one can always find a group of individuals who tend to be largely pragmatic, overwhelmingly logical, or sometimes mixed not showing a clear preference. There also exist newly-devised paradigms that prompt a radically different type of response than other paradigms, and thus new evidence casting doubt on long-established findings in the field. More recent research on scalar diversity further suggests that differences in the semantic structure of scalar words can lead to differing rates of scalar implicatures and can modulate the time invested in pragmatic processing. Indeed, one can contend that the current empirical landscape on scalar implicatures can be characterized as having three primary sources of variability: inter-individual, methodological, and linguistic. What factor or factors are behind these patterns of variability, and how can we interpret them in light of a pragmatic theory? This paper has a 2-fold objective: one is to review the previous experimental record on scalar implicatures from variability-based lenses, and the other to discuss the factor(s) that could account for this observed variability in the literature. Avenues for future research are provided.

An energy-preserving computational approach for the semilinear space fractional damped Klein–Gordon equation with a generalized scalar potential

Naturally preserving dissipative or conservative structures of a given continuous system in discrete analogs is of high demand when designing numerical schemes for dissipative or Hamiltonian partial differential equations. Armed with this fact, the proposed computational study focuses on the issue of considering energy-preserving discrete numerical schemes for the Riesz space-fractional Klein-Gordon equation with a generalized scalar potential. For the sake of more clearness, a combined numerical scheme that owes energy-preserving properties is a target to be achieved here. This is done by adapting Galerkin spectral approximation based on Legendre polynomials for Riesz space Laplacian operator side by side to invoke a Cranck–Nickolson scheme in time direction after making order reduction of the original system and a special second-order approximation of the scalar potential derivative. The numerical properties (stability, uniqueness, and convergence) of the scheme are well investigated. Numerical simulations also show that the proposed scheme can inherit the physical properties as the original problem and the numerical solution is stable and convergent to the exact solution.

A robust physics-based method to filter coherent wavepackets from high-speed schlieren images

A complete understanding of jet dynamics is greatly enabled by the accurate separation of acoustically efficient wavepackets from their higher-energy convecting turbulent counterparts. Momentum potential theory (MPT) has proven highly effective in filtering the desired acoustic component irrespective of operating conditions or nozzle complexity. However, MPT is a data-intensive method predicated on the knowledge of fluctuation quantities in the entire flow field; as such, it has to date been applied only to numerically obtained data. This work develops an approach to extend its application to extract coherent wavepacket data from high-speed schlieren images. Pixel intensities from the schlieren image are mapped to a scaled surrogate for the line-of-sight integrated density gradient. The linear relation between the irrotational scalar MPT potential and time derivatives of density fluctuations is then exploited to perform the filtering. The effectiveness of the procedure is demonstrated using experimental as well as numerical schlieren images representing a wide range of imperfectly expanded free and impinging jet configurations. When combined with spectral proper orthogonal decomposition (SPOD), the method yields modes that accurately capture (i) the Mach wave radiation from a military-style jet, (ii) the mode shapes of the feedback tones in an impinging jet and (iii) the screech signature in twin rectangular jets, without recourse to user adjusted parameters. This technique can greatly enhance the use of high-speed diagnostics for real-time monitoring of the near-field acoustic content for potential feedback control. Additionally, the general nature of the approach allows a straightforward application to other flows, such as cavity and airfoil flow-acoustic interactions.

Strong gravity effects of charged Q-clouds and inflating black holes

In this paper, we re-examine charged Q-clouds around spherically symmetric, static black holes. In particular, we demonstrate that for fixed coupling constants two different branches of charged scalar clouds exist around Schwarzschild black holes. This had not been noticed previously. We find that the new solutions possess a ‛hard wall’ at maximal possible gauge coupling. This wall separates the interior (containing the black hole horizon), in which the scalar field is trapped in the ‛false vacuum’, from the ‛true vacuum’ exterior. When taking back-reaction onto the space-time into account, we find that at maximal possible back-reaction, the black hole solutions corresponding to these two branches either become extremal black holes with diverging scalar field derivative on the horizon or inflating black holes with a second, ‛cosmological’ horizon which—outside this second horizon—correspond to extremal Reissner–Nordström black holes.

The Role of Executive Function and Theory of Mind in Pragmatic Computations.

In sentences such as "Some dogs are mammals," the literal semantic meaning ("Some and possibly all dogs are mammals") conflicts with the pragmatic meaning ("Not all dogs are mammals," known as a scalar implicature). Prior work has shown that adults vary widely in the extent to which they adopt the semantic or pragmatic meaning of such utterances, yet the underlying reason for this variation is unknown. Drawing on theoretical models of scalar implicature derivation, we explore the hypothesis that the cognitive abilities of executive function (EF) and theory of mind (ToM) contribute to this observed variation. In Experiment 1, we show that individuals with better ToM are more likely to compute a scalar implicature and adopt the pragmatic meaning of an utterance; however, EF makes no unique contribution to scalar implicature comprehension after accounting for ToM. In Experiment 2, we replicate this finding and assess whether it generalizes to the comprehension of other pragmatic phenomena such as indirect requests (e.g., "It's hot in here" uttered to ask for something to be done) and metaphor (e.g., "to harvest courage"). This is the first evidence that differences in ToM are associated with pragmatic competence in neurotypical adults across distinct pragmatic phenomena.

Parameterization of Microsomal and Cytosolic Scaling Factors: Methodological and Biological Considerations for Scalar Derivation and Validation.

Mathematical models that can predict the kinetics of compounds have been increasingly adopted for drug development and risk assessment. Data for these models may be generated from in vitro experimental systems containing enzymes contributing to metabolic clearance, such as subcellular tissue fractions including microsomes and cytosol. Extrapolation from these systems is facilitated by common scaling factors, known as microsomal protein per gram (MPPG) and cytosolic protein per gram (CPPG). Historically, parameterization of MPPG and CPPG has employed the use of recovery factors, commonly benchmarked to cytochromes P450 which work well in some contexts, but could be problematic for other enzymes. Here, we propose absolute quantification of protein content and supplementary assays to evaluate microsomal/cytosolic purity that should be employed. Examples include calculation of microsomal latency by mannose-6-phosphatase activity and immunoblotting of subcellular fractions with fraction-specific markers. Further considerations include tissue source, as disease states can affect enzyme expression and activity, and the methodology used for scalar parameterization. Regional- and organ-specific expression of enzymes, in addition to differences in organ physiology, is another important consideration. Because most efforts have focused on the liver that is, for the most part, homogeneous, derived scalars may not capture the heterogeneity of other major tissues contributing to xenobiotic metabolism including the kidneys and small intestine. Better understanding of these scalars, and how to appropriately derive them from extrahepatic tissues can provide support to the inferences made with physiologically based pharmacokinetic modeling, increase its accuracy in characterizing in vivo drug pharmacokinetics, and improve confidence in go-no-go decisions for clinical trials.

Memory Load Effect in the Real-Time Processing of Scalar Implicatures.

This study examines effects of memory load on the processing of scalar implicature via a dual-task paradigm using reading span and self-paced reading. Results indicate that participants showed online sensitivity to underinformative sentences (e.g., Some birds have wings and beaks) at the end of the sentence. This online sensitivity disappeared when participants were under increased memory load. Moreover, participants in the memory-load condition did not show sensitivity to semantically false sentences (e.g., All books have pictures and drawings). These results pose important conceptual and methodological questions of (1) whether the processing cost associated with scalar implicatures can be attributed to general proposition evaluation rather than scalar implicature derivation per se (Bale et al. in Semant Linguist Theory 20:525-543, 2010), and (2) to what degree memory load affects implicature computation only. I conclude with a discussion of these two issues for future research.

A Method for a Direct Measure of Entrainment and Detrainment

AbstractThe entrainment and detrainment rates are important quantities characterizing airmass exchange between clouds and the environment. One of the challenges in calculating the rates is the need to know the velocity vector of the cloud interface in relation to that of the cloud-free air; however, the interface is not well resolved in most cloud model simulations and so the precise value of the vector is not known. Here a new method is described to approximately calculate mass fluxes across the cloud surface in well-resolved simulations of cumulus convection. The method does away with the need to calculate a cloud interface velocity and instead uses gradients of a defined cloud scalar across the cloud interface. As a result, the entrainment and detrainment rates are expressed as an integration over a small region around the cloud interface. The integrand is composed of the total derivative of the cloud scalar. The new method is applied to large-eddy simulations (LES) of a shallow cumulus case and a deep convection case. Compared to a previous method, the approach described here gives 1.5–2 times smaller exchange rates and shows less noise. The smaller exchange rates are explained as the result of differences in how the two methods correct for the advective contribution to variations of cloud volume. Derived two-dimensional distributions of the exchange rates agree well for both methods. Spatial correlation coefficients are about 0.69–0.88 for entrainment and 0.55–0.78 for detrainment.

A diffusion tensor imaging study to compare normative fractional anisotropy values with patients suffering from Parkinson’s disease in the brain grey and white matter

Diffusion tensor imaging (DTI) appears as a sensitive method to study Parkinson’s disease (PD) pathophysiology and severity. Fractional anisotropy (FA) value is one of the scalar derivatives of DTI used to find out anisotropy within a voxel in a tissue and used for determining white matter integrity in aging and neurodegenerative diseases. We studied DTI derived FA in early PD subjects as their routine MRI scans were normal. 40 patients with early PD and 40 healthy controls were employed to evaluate changes in microstructural white and grey matter in the brain’s using DTI derived FA values. Comparison of FA values in the brain’s white and grey matter of patients with PD and age matched controls at the corpus callosum, centrum semiovale, pons, putamen, caudate nucleus, substantia nigra, cerebral peduncles and cerebellar peduncles, was done using a region of interest (ROI) technique, with b-value 1000s/mm2 and TE = 100 milliseconds using 1.5 T MRI system. PD patients showed differences in FA values in both the grey and white matter areas of the brain’s compared to healthy controls. Our study revealed the presence of damage in the substantia nigra, corpus callosum, putamen and cerebral peduncles mainly in the PD group. Our findings indicate that DTI and region of interest (ROI) methods can be used in patients with early PD to study microstructural alterations mainly in the substantia nigra, putamen and corpus callosum.

СІТКОВІ ПАТЕРНИ, ЯК МАТЕМАТИЧНА МОДЕЛЬ БАГАТОЕЛЕМЕНТНИХ ВИМІРЮВАЧІВ

Computer modeling of measuring devices that contains matrix of electrodes are examined. Method of local weighted approximation is applied. Special location of the measurement nodes that forms a matrix structure (grid pattern) is applied for quadratic basis. It is shown that in this case either calculation of scalar or estimation of scalar derivatives in the central pattern node can be produced uniformly by prior finding of resolvent. Examples of usages of given method for finding the minimum of a function of two variables are considered. The possibility of using considered method for finding minimums of functions with discontinuities derivatives is specified.

Unification of dark energy and dark matter from diffusive cosmology

Generalized ideas of unified dark matter and dark energy in the context of dynamical space time theories with a diffusive transfer of energy are studied. The dynamical space-time theories are introduced a vector field whose equation of motion guarantees a conservation of a certain Energy Momentum tensor, which may be related, but in general is not the same as the gravitational Energy Momentum tensor. This particular energy momentum tensor is built from a general combination of scalar fields derivatives as the kinetic terms, and possibly potentials for the scalar field. By demanding that the dynamical space vector field be the gradient of a scalar the dynamical space time theory becomes a theory for diffusive interacting dark energy and dark matter. These generalizations produce non-conserved energy momentum tensors instead of conserved energy momentum tensors which leads at the end to a formulation for interacting DE-DM. We solved analytically the theories and we show that the $\Lambda$CDM is a fixed point of these theories at large times. A particular case has asymptotic correspondence to previously studied non-Lagrangian formulations of diffusive exchange between dark energy dark matter.

Scalar and vector division and derivatives vectors

The work is devoted to the operations of differentiation in the space of vector fields and smooth functions. In mechanics, it is widely used derivative of a scalar function of the vector. To some extent, like it is determined by the derivative of the vector to another vector. However, formally interpreting the derivative as division differentials are entered in consideration of scalar and vector derived vector on another vector, which may have application to the solution of problems of mechanics. The definition of a derivative of a scalar vector field on another vector field. We prove a theorem on the representation of the scalar derivative in the form of a combination of partial derivatives. As a typical particular case is considered a scalar derivative in the radius vector, generating formalism linking it with the operator nabla. It is noted that in solving some problems in the mechanics to simplify the calculation coordinate system is chosen so that at least some vectors direction coincides with one of the coordinate axes. If it concerns the vector for derivation to be performed, in such cases, the formula for the three-dimensional case can not be used because some of this vector differentials are equal to zero. This circumstance makes it necessary to prove two theorems for the two-dimensional and one-dimensional case. The definition of a vector derivative of a vector field on another vector field. We prove a theorem on the representation of the derivative vector as a combination of partial derivatives. As a typical particular case considered vector derivative of the radius vector, generating formalism linking it with the operator nabla. We prove similar theorems for two-dimensional and one-dimensional case. We give examples of applications of these results to problems of mechanics.

Compressible turbulent mixing: Effects of compressibility.

We studied by numerical simulations the effects of compressibility on passive scalar transport in stationary compressible turbulence. The turbulent Mach number varied from zero to unity. The difference in driven forcing was the magnitude ratio of compressive to solenoidal modes. In the inertial range, the scalar spectrum followed the k^{-5/3} scaling and suffered negligible influence from the compressibility. The growth of the Mach number showed (1) a first reduction and second enhancement in the transfer of scalar flux; (2) an increase in the skewness and flatness of the scalar derivative and a decrease in the mixed skewness and flatness of the velocity-scalar derivatives; (3) a first stronger and second weaker intermittency of scalar relative to that of velocity; and (4) an increase in the intermittency parameter which measures the intermittency of scalar in the dissipative range. Furthermore, the growth of the compressive mode of forcing indicated (1) a decrease in the intermittency parameter and (2) less efficiency in enhancing scalar mixing. The visualization of scalar dissipation showed that, in the solenoidal-forced flow, the field was filled with the small-scale, highly convoluted structures, while in the compressive-forced flow, the field was exhibited as the regions dominated by the large-scale motions of rarefaction and compression.

Non-minimal derivative coupling gravity in cosmology

We give a brief review of the non-minimal derivative coupling (NMDC) scalar field theory in which there is non-minimal coupling between the scalar field derivative term and the Einstein tensor. We assume that the expansion is of power-law type or super-acceleration type for small redshift. The Lagrangian includes the NMDC term, a free kinetic term, a cosmological constant term and a barotropic matter term. For a value of the coupling constant that is compatible with inflation, we use the combined WMAP9 (WMAP9+eCMB+BAO+ $H_0$) dataset, the PLANCK+WP dataset, and the PLANCK $TT,TE,EE$+lowP+Lensing+ext datasets to find the value of the cosmological constant in the model. Modeling the expansion with power-law gives a negative cosmological constants while the phantom power-law (super-acceleration) expansion gives positive cosmological constant with large error bar. The value obtained is of the same order as in the $\Lambda$CDM model, since at late times the NMDC effect is tiny due to small curvature.

Kerr-dS/AdS null tetrads in modified teleparallel gravity theories and thermodynamics

We apply a diagonal axially symmetric tetrad to the field equations of the lowest order of \(f(T)\), “where \(T\) is the teleparallel torsion scalar”, and get an exact vacuum solution which describes Kerr-dS/AdS spacetime. We rewrite the tetrad field of the derived solution in a null tetrad form and multiply it by a boost local Lorentz transformation, which contains unknown function of generalized coordinates, and get a new tetrad field. An exact vacuum solutions, which represents Kerr-dS/AdS spacetime, are derived under the following constraints: (i) The scalar torsion, \(T ={T^{\alpha}}_{\mu \nu}{S_{\alpha}}^{\mu \nu}=T_{0}\), where \(T_{0}\) is constant. (ii) The total derivative term is constant. (iii) The combination of the scalar torsion and the total derivative term is constant. We show that all the derived solutions coincide with general relativity solution when the constants of the torsion scalar, the total derivative term and the combination of the torsion scalar and total derivative term are vanishing. When the rotation parameter vanishing, the solution in the lower order of \(f(T)\) approaches asymptotically de Sitter spacetime, and show the existence of the Nariai spacetime as a background solution. The scalar torsion of Nariai spacetime is vanishing naturally without any constraint. Considering the perturbation around the Nariai spacetime up to the first order, we show the behavior of black hole horizon. We investigate that the anti-evaporation does not exist on the classical level. Finally, we used the total derivative term and the Euclidean continuation method to calculate the energy of Kerr-dS/AdS, entropy and temperature. The mass of a Kerr-dS/AdS black hole is interpreted, in terms of thermodynamic potentials, as being the enthalpy, with the pressure given by the cosmological constant.