Complete Description In Terms Research Articles

Chow rings of stacks of prestable curves II

Abstract We continue the study of the Chow ring of the moduli stack 𝔐 g , n {\mathfrak{M}_{g,n}} of prestable curves begun in [Y. Bae and J. Schmitt, Chow rings of stacks of prestable curves I, Forum Math. Sigma 10 2022, Paper No. e28]. In genus 0, we show that the Chow ring of 𝔐 0 , n {\mathfrak{M}_{0,n}} coincides with the tautological ring and give a complete description in terms of (additive) generators and relations. This generalizes earlier results by Keel and by Kontsevich and Manin for the spaces of stable curves. Our argument uses the boundary stratification of the moduli stack together with the study of the first higher Chow groups of the strata, in particular providing a new proof of the results of Kontsevich and Manin.

Reflections on the past and future of language testing and assessment: An emerging scholar’s perspective

In its 40th year, Language Testing journal has served as the flagship journal for scholars, researchers, and practitioners in the field of language testing and assessment. This viewpoint piece, written from the perspective of an emerging scholar, discusses two possible future trends based on evidence going back to the very first issue of this journal. First, this paper outlines past efforts to describe and define the construct of second language communication, noting that much work has yet to be done for a more complete description in terms of interactional competence and nonverbal behavior. The second trend highlights the growing movement in applied linguistics toward research transparency through Open Science practices, including replication studies, the sharing of data and materials, and preregistration. This paper outlines work to date in Language Testing that encourages open practices and emphasizes the importance of these practices in assessment research.

Three dimensional rendering of auditory neuronal responses: A novel illustration of receptive field across frequency, intensity & time domains

BackgroundNeural coding of sound information is often studied through frequency tuning curve (FTC), spectro-temporal receptive field (STRF), post-stimulus time histogram (PSTH), and other methods such as rate functions. These methods, despite providing a robust characterization of auditory responses in their specific domains, lack a complete description in terms of three sound fundamentals: frequency, amplitude, and time. New MethodUsing the techniques of electrophysiology, neural signal processing and medical image processing, a standalone method is created to illustrate the neural processing of three sound fundamentals in one representation. ResultsThe new method comprehensively showed frequency tuning, intensity tuning, time tuning as well as a novel representation of frequency and time dependent intensity coding. It provides most of the necessary parameters that are used to quantify neural response properties, such as minimum threshold (MT), frequency tuning, latency, best frequency (BF), characteristic frequency (CF), bandwidth (BW), etc. Comparison with Existing MethodsOur method shows neural responses as a function of all three sound fundamentals in a single representation that was not possible in previous methods. It covers many functions of conventional methods and allow extracting novel information such as the intensity coding as the function of the spectrotemporal response area of auditory neurons. ConclusionThis method can be used as a standalone package to study auditory neural responses and evaluate the performance of different hearing related devices such as cochlear implants and hearing aids in animal models as well as study and compare auditory processing in aged and hearing impaired animal models.

A Thermodynamically Consistent Port-Hamiltonian Model for Dielectric Elastomer Membrane Actuators and Generators

Abstract This paper presents a port-Hamiltonian modeling formulation for a Dielectric Elastomer membrane. The model relates electrical and mechanical inputs to corresponding conjugate outputs, allowing to simulate the membrane transducer in actuation and energy harvesting application. Starting from a nonlinear, physics-based model developed in the authors’ previous works, a suitable function is initially proposed to quantify the overall electro-mechanical energy in the system. Subsequently, a complete description in terms of Hamiltonian, dissipation function, and system matrices is provided. The port-Hamiltonian formalism permits to assess the thermodynamic consistency of the model, making it a reliable tool for the prediction of energetic performance in dynamic applications. Furthermore, it opens up the possibility of applying powerful nonlinear analysis and design tools.

Mityagin's extension problem. Progress report

Given a compact set K⊂Rd, let E(K) denote the space of Whitney jets on K. The compact set K is said to have the extension property if there exists a continuous linear extension operator W:E(K)⟶C∞(Rd). In 1961 B.S. Mityagin posed a problem to give a characterization of the extension property in geometric terms. We show that there is no such complete description in terms of densities of Hausdorff contents or related characteristics. Also the extension property cannot be characterized in terms of growth of Markov's factors for the set.

The combinatorial game theory of well-tempered scoring games

The general behavior of combinatorial scoring games is not well-understood. In this paper, we focus on a special class of “well-tempered” scoring games. By analogy with Grossman and Siegel’s notion of even- and odd-tempered normal play games, we declare a dicot scoring game to be even-tempered if all its options are odd-tempered, and odd-tempered if it is not atomic and all its options are even-tempered. Games of either sort are called well-tempered. These show up naturally when analyzing one of the “knot games” introduced by Henrich et al. We consider disjunctive sums of well-tempered scoring games, and develop a theory for them analogous to the standard theory of disjunctive sums of normal play partizan games. We isolate a special class of inversive well-tempered games which behave like normal play partizan games or like the “Milnor games” considered by Milnor and Hanner. In particular, inversive games (modulo equivalence) form a partially ordered abelian group, and there is an effective description of the partial order. Moreover, the full monoid of well-tempered scoring games (modulo equivalence) admits a complete description in terms of the group of inversive games. We also describe several examples of well-tempered scoring games and provide dictionaries listing the values of some small positions in two of these games.

Generalized continuous and left-continuous t-norms arising from algebraic semantics for fuzzy logics

This paper focuses on the issue of how generalizations of continuous and left-continuous t-norms over linearly ordered sets should be from a logical point of view. Taking into account recent results in the scope of algebraic semantics for fuzzy logics over chains with a monoidal residuated operation, we advocate linearly ordered BL-algebras and MTL-algebras as adequate generalizations of continuous and left-continuous t-norms respectively. In both cases, the underlying basic structure is that of linearly ordered residuated lattices. Although the residuation property is equivalent to left-continuity in t-norms, continuous t-norms have received much more attention due to their simpler structure. We review their complete description in terms of ordinal sums and discuss the problem of describing the structure of their generalization to BL-chains. In particular we show the good behavior of BL-algebras over a finite or complete chain, and discuss the partial knowledge of rational BL-chains. Then we move to the general non-continuous case corresponding to left-continuous t-norms and MTL-chains. The unsolved problem of describing the structure of left-continuous t-norms is presented together with a fistful of construction-decomposition techniques that apply to some distinguished families of t-norms and, finally, we discuss the situation in the general study of MTL-chains as a natural generalization of left-continuous t-norms.

Nonperturbative renormalization for 2PI effective action techniques

Nonperturbative approximation schemes based on two-particle irreducible (2PI) effective actions provide an important means for our current understanding of (non-)equilibrium quantum field theory. A remarkable property is their renormalizability, since these approximations involve selective summations to infinite perturbative orders. In this paper, we show how to renormalize all n-point functions of the theory, which are given by derivatives of the 2PI-resummed effective action Γ [ ϕ] for scalar fields ϕ. This provides a complete description in terms of the generating functional for renormalized proper vertices, which extends previous prescriptions in the literature on the renormalization for 2PI effective actions. The importance of the 2PI-resummed generating functional for proper vertices stems from the fact that the latter respect all symmetry properties of the theory and, in particular, Goldstone’s theorem in the phase with spontaneous symmetry breaking. This is important in view of the application of these techniques to gauge theories, where Ward identities play a crucial role.

Fluctuations and correlations in an individual-based model of biological coevolution

We extend our study of a simple model of biological coevolution to its statistical properties. Starting with a complete description in terms of a master equation, we provide its relation to the deterministic evolution equations used in previous investigations. The stationary states of the mutationless model are generally well approximated by Gaussian distributions, so that the fluctuations and correlations of the populations can be computed analytically. Several specific cases are studied by Monte Carlo simulations, and there is an excellent agreement between the data and the theoretical predictions.

The thermodynamics of mixtures and the corresponding mixing rules in the SAFT-VR approach for potentials of variable range

The statistical associating fluid theory (SAFT) has been extended recently to describe the thermodynamic properties of chain molecules formed from monomeric segments interacting with attractive potentials of variable range (VR) (Gil-Villegas, A., Galindo, A., Whitehead, P. J., Mills, S. J., Jackson, G., and Burgess, A. N., 1997, J. chem. Phys., 106, 4168). The SAFTVR approach is based on an accurate and compact representation of the free energy of chain molecules in terms of the contact value of the radial distribution function of the monomer reference system. This paper takes advantage of the SAFT-VR approach to focus on the nature of the expressions for mixtures of non-conformal molecules. A number of mixing rules are proposed, from the usual van der Waals one-fluid prescription to a complete description in terms of the pair distribution functions of the pair interactions that goes beyond the one-fluid level. As a first test of the adequacy of the theory for mixtures the SAFT-VR prediction is compared w...

The thermodynamics of mixtures and the corresponding mixing rules in the SAFT-VR approach for potentials of variable range

The statistical associating fluid theory (SAFT) has been extended recently to describe the thermodynamic properties of chain molecules formed from monomeric segments interacting with attractive potentials of variable range (VR) (Gil-Villegas, A., Galindo, A., Whitehead, P. J., Mills, S. J., Jackson, G., and Burgess, A. N., 1997, J. chem. Phys., 106, 4168). The SAFTVR approach is based on an accurate and compact representation of the free energy of chain molecules in terms of the contact value of the radial distribution function of the monomer reference system. This paper takes advantage of the SAFT-VR approach to focus on the nature of the expressions for mixtures of non-conformal molecules. A number of mixing rules are proposed, from the usual van der Waals one-fluid prescription to a complete description in terms of the pair distribution functions of the pair interactions that goes beyond the one-fluid level. As a first test of the adequacy of the theory for mixtures the SAFT-VR prediction is compared with Gibbs ensemble simulation data for the vapour-liquid and liquid-liquid equilibria of two prototype mixtures containing square-well molecules.

On the dimension of product measures

In recent papers on fractals attention has shifted from sets to measures [1, 5, 10]. Thus it seems interesting to know whether results for the dimension of sets remain valid for the dimension of measures. In the present paper we derive estimates for the dimension of product measures. Falconer [3] summarizes known results for sets and Tricot [8] gives a complete description in terms of Hausdorff and packing dimension. Let dim and Dim denote Hausdorff and packing dimension. If then

Un théorème de Ray-Knight lié au supremum des temps locaux browniens

Let α denote the first hitting time of 1 by the supremum, over nonnegative values of the space variable, of the Brownian local times. We give a complete description in terms of Bessel processes for the law of the process (in the space variable) of the Brownian local times at time α. The proofs rely on stochastic calculus, excursion theory and especially the Ray-Knight Theorems on Brownian local times. This result is applied to give a different proof of Borodin's result concerning the law of the supremum of Brownian local times taken at an independent exponential time.

Restricted ramification for imaginary quadratic number fields and a multiplicator free group

Let K be an imaginary quadratic number field with unit group EK and let t' be a rational prime such that t' IEK . Let S be any finite set of finite primes of K and let K( {, S) denote the maximal e-extension of K (inside a fixed algebraic closure of K) which is nonramified at the finite primes of K outside S. We show that the finitely generated pro-e-group Q(t, S) = Gal(K(t, S)/K) has the property that a complete set of defining relations for Q(t, S) as a pro-{-group can be obtained by lifting the nontrivial abelian or torsion relations in the maximal abelian quotient group U(t, S)ab. In addition we use the key idea of the proof to derive some interesting results on towers of fields over K with restricted ramification. Introduction. If L/K is a Galois extension of fields and E is a Galois extension of K containing L, then E is said to be a central extension of L/K if Gal(E/L) is a subgroup of the centre of Gal(E/K). The study of central extensions of Galois extensions of number fields leads to several arithmetic applications (see [4, Chapter 3]) many of which stem from an early paper of Frohlich [2]. In particular a theorem of Frohlich [4, Theorem 4.11] gives a complete description in terms of topological generators and relations of the Galois group of the maximal tl-extension of Q (t1any prime, Q the field of rational numbers) which is nilpotent of class two with ramification restricted to a finite set of primes. This, in turn, leads to another result of Frohlich [4, Theorem 5.2] which characterizes, in rational terms, all abelian e-extensions L of Q for which edoes not divide the narrow class number of L. Taking the previous discussion as motivation we see that it is important to consider the pro-e-group Q(e, S) = Gal(K(t1, S)/K), where S is a finite set of finite primes of the number field K, and K(t1, S) is the maximal tl-extension of K (inside a fixed algebraic closure of K) which is nonramified at the finite primes of K outside S. The main difficulty in describing Q(t, S) is the determination of a complete set of defining relations for Q(t, S) as a pro-tl-group. When K = Q Frohlich shows that a complete set of defining relations can be obtained by lifting the nontrivial abelian or torsion relations of the maximal abelian quotient group Q(t, S)ab. We explain this idea more precisely in ?1. Our main result shows that Q(e, S) also has the lifting property when K is an imaginary quadratic number field, S is any finite set as above and 1 + I EKI, where EK Received by the editors December 27, 1983 and, in revised form, August 17, 1984. 1980 Mathematics Subject Classification. Primary 12A65. ' This represents part of the author's Ph.D. dissertation written under the direction of Professor Stephen V. Ullom at the University of Illinois at Urbana. ?1985 American Mathematical Society 0002-9947/85 $1.00 + $.25 per page

Solvable classes of pseudoprenex formulas

For constructive (intuitionistic) predicate calculus without functional symbols and equality a complete description is derived, in terms of prefixes and signatures, of reduction classes and of classes of pseudoprenex formulas, i.e., formulas representable in form , where is a quantifier-free formula and is a finite sequence of quantifier complexes and expressions ⌈⌈. The operation plays a fundamental role in the construction of solvable classes. From any pseudoprenex formulaA this operation constructs, preserving signature, a formula list Г such thatA is decidable in the constructive calculus if and only if some formula from Г is decidable in classical calculus. In the paper conditions are formulated sufficient for the carrying out of quantifier ∀ from a disjunction and the permutations of quantifiers ∀ and ∃ to preserve decidability in the constructive calculus. A signature-preserving method for the elimination of positive occurrences of equality is described as well. This method and the conditions mentioned play an important role in the construction of reduction classes. Also examined is the problem of recognition of refutability of pseudoprenex formulas on completely finite Kripke models, i.e., on those Kripke models in which both the set of “time instants” and also the union of objective domains are finite. A complete description in terms of prefixes and signatures is given for classes of pseudoprenex formulas for which the problem of recognition of refutability on completely finite Kripke models is solvable. This description differs essentially from the description of solvable pseudoprenex formulas for constructive predicate calculus.

Topography and microstructure

Three levels of description of the geometric state are considered in discussing the “three-dimensional topography” of a microstructure. The first level is simply a list of the features that exist in the structure; the second associates with each member of this list, numbers that describe its extent or configuration; the third is a complete description in terms of the distribution of features in space. Experimentally, most of the metric properties may be estimated from counting measurements made upon a representative microsection; whereas the topological properties require a serial sectioning analysis. The counting measurements are then combined with some elementary statistical analysis in order to describe anisotropies, gradients, and spatial relationships between microstructural features.