Weak Version Research Articles

Unweaving the embodied nature of English temporal prepositions

AbstractThe metaphortime is space(Lakoff & Johnson 1999) and the pervasiveness of metaphor and image-schematic structure in human conceptualization (Johnson 1987;Hampe 2005) have been widely accepted among cognitive scientists as constructs that help explain non-spatial and temporal linguistic constructions. However, Conceptual Metaphor Theory (CMT) might not be the whole story. While it is acceptable that moments in time can be construed as being analogous to points in space as in utterances such asatthe cornervs.at2:30, there seems to be much moretemporal cognitionthan previously thought. It turns out that time exhibits its own structure (followingEvans 2004,2013;Galton 2011) that is based on transience. This idea has made some scholars support the weak version of CMT which posits that the temporal meaning of prepositions is represented and processed independently of the corresponding spatial meanings (seeKemmerer 2005for such a view). The present article supports the idea that spatial and temporal structures complement each other in order to achieve temporal conceptions. This is indeed a conceptual pattern showed by the English prepositionatthat makes use of an extrinsic temporal reference to activate its temporal semantics. To analyze the different temporal realizations thatatmay have, the paper aims to identify the topological structure that underlies theconceptual basisof this preposition. This allows us to appreciate how the spatio-conceptual structure ofatpartially structures temporal conceptions. The paper also identifies the nature of the temporal structure that is involved in temporal realizations. The article concludes with some remarks, among them the pivotal role of the schematic temporal structure that is captured by the extrinsic temporal reference, and the role of conceptual metaphor in underdetermining temporal thinking.

Price convergence: Representation and testing

This paper provides a new, unified, and flexible framework to measure and characterize a convergence process in time series. We formally define a general notion of price convergence, which encompasses convergence as steady-state and catching-up, and propose a model to represent a wide range of transition paths. Our framework enables the measurement of such transitional behaviors and the development of testing procedures. In particular, we use existing unit root tests (with and without breaks) to determine whether asymptotic convergence exists and, if so, its starting point and type: as steady-state or catching-up and in its weak or strong version. We illustrate the power and flexibility of the methodology with two different datasets with potential convergence processes: (1) the aggregated price level of the Eurozone's largest economies (Germany, France and Italy) after the introduction of the common currency and, (2) the transatlantic 19th Century wheat prices.

Kernel methods for center manifold approximation and a weak data-based version of the Center Manifold Theorem

For dynamical systems with a non hyperbolic equilibrium, it is possible to significantly simplify the study of stability by means of the center manifold theory. This theory allows to isolate the complicated asymptotic behavior of the system close to the equilibrium point and to obtain meaningful predictions of its behavior by analyzing a reduced order system on the so-called center manifold.Since the center manifold is usually not known, good approximation methods are important as the center manifold theorem states that the stability properties of the origin of the reduced order system are the same as those of the origin of the full order system.In this work, we establish a data-based version of the center manifold theorem that works by considering an approximation in place of an exact manifold. Also the error between the approximated and the original reduced dynamics is quantified.We then use an apposite data-based kernel method to construct a suitable approximation of the manifold close to the equilibrium, which is compatible with our general error theory. The data are collected by repeated numerical simulation of the full system by means of a high-accuracy solver, which generates sets of discrete trajectories that are then used as a training set. The method is tested on different examples which show promising performance and good accuracy.

Stochastic Schrödinger-Lohe model

The Schrödinger-Lohe model consists of wave functions interacting with each other, according to a system of Schrödinger equations with a specific coupling such that all wave functions evolve on the L2 unit ball. This model has been extensively studied over the last decade and it was shown that under suitable assumptions on the initial state, if one waits long enough all the wave functions become arbitrarily close to each other, which we call a synchronization. In this paper, we consider a stochastic perturbation of the Schrödinger-Lohe model and show a weak version of synchronization for this perturbed model in the case of two oscillators.

Precautionary Principle in the Court Settlement of Civil Environmental Cases

In recent years, the precautionary principle has begun to enter legal decision-making in Indonesian civil courts. This introduction is in line with environmental cases that often involve much scientific evidence. This article aims to describe theoretical elaboration and, to a certain extent, legal developments in the application of the precautionary principle in the settlement of civil environmental cases in Indonesia. The precautionary principle provides a framework for environmental decision-making in the event of scientific uncertainty. The theoretical elaboration shows a wide dimension of influence of the precautionary principle on the system of liability and proof. In comparison, the court cases also show the application of the precautionary principle in the liability system and proof despite still in its weak version.

Weighted Envy-freeness in Indivisible Item Allocation

We introduce and analyze new envy-based fairness concepts for agents with weights that quantify their entitlements in the allocation of indivisible items. We propose two variants of weighted envy-freeness up to one item (WEF1): strong , where envy can be eliminated by removing an item from the envied agent’s bundle, and weak , where envy can be eliminated either by removing an item (as in the strong version) or by replicating an item from the envied agent’s bundle in the envying agent’s bundle. We show that for additive valuations, an allocation that is both Pareto optimal and strongly WEF1 always exists and can be computed in pseudo-polynomial time; moreover, an allocation that maximizes the weighted Nash social welfare may not be strongly WEF1, but it always satisfies the weak version of the property. Moreover, we establish that a generalization of the round-robin picking sequence algorithm produces in polynomial time a strongly WEF1 allocation for an arbitrary number of agents; for two agents, we can efficiently achieve both strong WEF1 and Pareto optimality by adapting the adjusted winner procedure. Our work highlights several aspects in which weighted fair division is richer and more challenging than its unweighted counterpart.

How to Be RAD: Repeated Acquisition Design Features that Enhance Internal and External Validity.

The Repeated Acquisition Design (RAD) is a type of single-case research design (SCRD) that involves repeated and rapid measurement of irreversible discrete skills or behaviors through pre-and postintervention probes across different sets of stimuli. Researchers interested in the study of learning in animals and humans have used the RAD because of its sensitivity to detect immediate changes in rate or accuracy. Despite its strengths, critics of the RAD have cautioned against its use due to reasonable threats to internal validity like pretest effects, history, and maturation. Furthermore, many methodologists and researchers have neglected the RAD in their SCRD standards (e.g., What Works Clearinghouse [WWC], 2020; Horner et al., 2005). Unless given guidance to address threats to internal validity, researchers may avoid the design altogether or continue to use a weak version of the RAD. Therefore, we propose a set of 15 quality RAD indicators, comprising foundational elements that should be present in all RAD studies and additional features that enhance causal inference and external validity. We review contemporary RAD use and describe how the additional features strengthen the rigor of RAD studies. We end the article with suggested guidelines for interpreting effects and the strength of the evidence generated by RAD studies. We invite researchers to use these initial guidelines as a jumping off point for a more RAD future.

Pseudo-strongly graded rings associated to Ore sets

Let G be a group, and A a G-graded ring. Motivated by the study of densely group graded algebras, we introduce the concept of a pseudo-strongly graded ring associated to an Ore set in this paper. A pseudo-strongly graded ring is a weak version of a strongly graded ring. It induces an equivalence of certain quotient categories.

A determinant involving Ramanujan sums and So\u2019s conjecture

We compute the determinant of a matrix containing Ramanujan sums associated to the divisors of an integer n, and use this computation to prove a weak version of So’s conjecture on circulant graphs with integral spectrum.

Some Applications of the Poincaré–Bendixson Theorem

AbstractWe consider a $${\mathcal {C}}^1$$ C 1 vector field X defined on an open subset U of the plane with compact closure. If X has no singular points and if U is simply connected, a weak version of the Poincaré–Bendixson theorem says that the limit sets of X in U are empty but that one can define non empty extended limit sets contained in the boundary of U. We give an elementary proof of this result, independent of the classical Poincaré–Bendixson theorem. A trapping triangle $${\mathcal {T}}$$ T based at p, for a $${\mathcal {C}}^1$$ C 1 vector field X defined on an open subset $${\mathcal {U}}$$ U of the plane, is a topological triangle with a corner at a point p located on the boundary $$\partial {\mathcal {U}}$$ ∂ U and a good control of the tranversality of X along the sides. The principal application of the weak Poincaré–Bendixson theorem is that a trapping triangle at p contains a separatrix converging toward the point p. This does not depend on the properties of X along $$\partial {\mathcal {U}}$$ ∂ U . For instance, X could be non differentiable at p, as in the example presented in the last section.

On the canonical bundle formula and log abundance in positive characteristic

We show that a weak version of the canonical bundle formula holds for fibrations of relative dimension one. We provide various applications thereof, for instance, using the recent result of Xu and Zhang, we prove the log non-vanishing conjecture for three-dimensional klt pairs over any algebraically closed field k of characteristic $$p>5$$ , which in turn implies the termination of any sequence of three-dimensional flips in the pseudo-effective case. We also show the log abundance conjecture for threefolds over k when the nef dimension is not maximal, and the base point free theorem for threefolds over $$\mathbb {{\overline{F}}}_p$$ when $$p>2$$ .

Rule of law and state of exception: the genesis of the problem

The purpose of this study was to clarify the correlation between the concepts of the rule of law and the state of exception in the context of the question of the nature of law and its correlation with force. The relevance of the study is explained by the need to reinterpret the idea of the rule of law and its boundaries in the context of modern challenges, in particular in the context of a pandemic. The study is of an interdisciplinary nature, which lies in combining legal, philosophical legal, and historical-philosophical perspectives using methods of philosophical legal reflection, comparison, analysis and synthesis, and historical-philosophical reconstruction. The correlation between the rule of law and the state of exception was clarified in three steps. First, the fundamental idea of the rule of law was explicated, which unites its numerous interpretations: law was considered as the antithesis of the arbitrariness of the powerful. Accordingly, the rule of law turned out to be a requirement immanent to any legal system. At the same time, the internal limitation of the rule of law associated with the statutory nature of the latter was emphasised, which inevitably necessitates striking a balance between the rule of law and justice, and the radicalisation of which brings to life the idea of a state of exception. The second part of this study contains a critical analysis of the theory of the state of exception, which, in contrast to the idea of the rule of law, identifies law and force, and ultimately denies law as such, normalising lawlessness. Finally, in the third step, three approaches to the correlation between the rule of law and the state of exception were analysed: 1) the priority of the state of exception, 2) a weak version of the priority of the rule of law, and 3) a strong version of the priority of the rule of law. It was concluded that the fundamental opposition between the rule of law and the state of exception renders their consistent combination impossible, and the corresponding attempts always turn out to be a compromise not favouring the former. However, according to the authors of this study, it is necessary to recognise the limitations of the law itself, without abandoning the discourse of the rule of law and the fundamental grounds for it

‘Ethnic memories’ from above? The Kosovo myth among the South Slavs and minimalist ethnosymbolism

AbstractThe Kosovo myth is often seen as a critical supporting case for ethnosymbolist theory. Many theorists of nationalism and area scholars see this myth as either the direct continuation or creative reinterpretation of a long‐standing epic and liturgical tradition among the Slavic Orthodox population in the Balkans. Using primary and secondary sources, this article traces how pre‐modern cultural and communicative memories of Kosovo were transformed into a modern nationalist myth of the Serbs and, then, the Yugoslavs. It argues that cultural rupture and change rather than continuity or recurrence characterise the history of these scattered and ambivalent pre‐modern legacies. The evidence shows that the medieval monastic texts and epics referring to the Kosovo battle cannot be considered as the ‘widespread ethnic memories’ necessary in ethnosymbolist theory. However, ethnosymbolist theory is multifaceted. The article's findings about the Kosovo myth suggest that scholars can adopt only a weak minimalist version of ethnosymbolism, which views this approach as a research programme or a focus of study rather than an explanatory theory. This version does not contradict modernist constructivism but aligns with the neo‐Weberian tradition of longue durée research within it.

On the constant scalar curvature Kähler metrics (II)—Existence results

In this paper, we apply our previous estimates in Chen and Cheng [On the constant scalar curvature Kähler metrics (I): a priori estimates, Preprint] to study the existence of cscK metrics on compact Kähler manifolds. First we prove that the properness ofKK-energy in terms ofL1L^1geodesic distanced1d_1in the space of Kähler potentials implies the existence of cscK metrics. We also show that the weak minimizers of theKK-energy in(E1,d1)(\mathcal {E}^1, d_1)are smooth cscK potentials. Finally we show that the non-existence of cscK metric implies the existence of a destabilizedL1L^1geodesic ray where theKK-energy is non-increasing, which is a weak version of a conjecture by Donaldson. The continuity path proposed by Xiuxiong Chen [Ann. Math. Qué. 42 (2018), pp. 69–189] is instrumental in the above proofs.

Testing eigenstate decoherence hypothesis in a model of collisional decoherence

The eigenstate decoherence hypothesis (EDH) asserts that each individual eigenstate of a large closed system is locally classical-like. We test this hypothesis for a heavy particle interacting with a gas of light particles. This system is paradigmatic for studies of the quantum-to-classical transition: the reduced state of the heavy particle is widely believed to rapidly loose any non-classical features due to the interaction with the gas. Yet, we find numerical evidence that the EDH is violated: certain eigenstates of this model are manifestly non-classical. Only the weak version of EDH referring to the majority (instead of the totality) of eigenstates holds.

The reduced Dijkgraaf–Witten invariant of double twist knots in the Bloch group of 𝔽p

In 2004, Neumann showed that the complex hyperbolic volume of a hyperbolic 3-manifold [Formula: see text] can be obtained as the image of the Dijkgraaf–Witten invariant of [Formula: see text] by a certain 3-cocycle. After that, Zickert gave an analogue of Neumann’s work for free fields containing finite fields. The author formulated a geometric method to calculate a weaker version of Zickert’s analogue, called the reduced Dijkgraaf–Witten invariant, for finite fields and gave a formula for twist knot complements and [Formula: see text] in his previous work. In this paper, we show concretely how to calculate the reduced Dijkgraaf–Witten invariants of double twist knot complements and [Formula: see text], and give a formula of them for [Formula: see text].

Does weak quasi-o-minimality behave better than weak o-minimality?

We present a relatively simple description of binary, definable subsets of models of weakly quasi-o-minimal theories. In particular, we closely describe definable linear orders and prove a weak version of the monotonicity theorem. We also prove that weak quasi-o-minimality of a theory with respect to one definable linear order implies weak quasi-o-minimality with respect to any other such order.

Weak modular Zilber–Pink with derivatives

In unpublished notes Pila proposed a Modular Zilber-Pink with Derivatives (MZPD) conjecture, which is a Zilber-Pink type statement for the modular $j$-function and its derivatives. In this article we define D-special varieties, then state and prove two functional (differential) analogues of the MZPD conjecture for those varieties. In particular, we prove a weak version of MZPD. As a special case of our results, we obtain a functional Modular Andr\'e-Oort with Derivatives statement. The main tools used in the paper come from (model theoretic) differential algebra and complex analytic geometry, and the Ax-Schanuel theorem for the $j$-function and its derivatives (established by Pila and Tsimerman) plays a crucial role in our proofs. In the proof of the second Zilber-Pink type theorem we also use an Existential Closedness statement for the differential equation of the $j$-function.

Identification of parameters of Poisson distributions by the extreme order statistics

Let Poisson variables be independent and be also independent such that each We prove that if and have the same distribution, then m = n and = The weak version in term of minimum statistics is also derived.

Catching-up Convergence and its Speed: Representation and Testing

This paper provides a new, unified, and flexible framework to measure and characterize a convergence process. Specifically, we formally define a general notion of asymptotic price convergence, which encompasses convergence as steady-state and catching-up, and propose a model to represent a wide range of transition paths. Our framework enables the econometric measurement of such transitional behaviors and the development of testing procedures. In particular, we use unit root tests (with and without breaks) to determine whether asymptotic convergence exists and, if so, its starting point and its type: as steady-state or catching-up and in its weak or strong version. We apply this methodology to illustrate the convergence process in two very different cases: (1) the aggregated price level of the Eurozone’s largest economies (Germany, France and Italy) and, (2) the transatlantic 19th Century wheat prices.