Another way to look at counterfactuals

Counterfactuals such as If the world did not exist, we would not notice it have been a challenge for philosophers and linguists since antiquity. There is no generally accepted semantic analysis. The prevalent view, developed in varying forms by Robert Stalnaker, David Lewis, and others, enriches the idea of strict implication by the idea of a “minimal revision” of the actual world. Objections mainly address problems of maximal similarity between worlds. In this paper, I will raise several problems of a different nature and draw attention to several phenomena that are relevant for counterfactuality but rarely discussed in that context. An alternative analysis that is very close to the linguistic facts is proposed. A core notion is the “situation talked about”: it makes little sense to discuss whether an assertion is true or false unless it is clear which situation is talked about. In counterfactuals, this situation is marked as not belonging to the actual world. Typically, this is done in the form of the finite verb in the main clause. The if-clause is optional and has only a supportive role: it provides information about the world to which the situation talked about belongs. Counterfactuals only speak about some nonactual world, of which we only know what results from the protasis. In order to judge them as true or false, an additional assumption is required: they are warranted according to the same criteria that warrant the corresponding indicative assertion. Overall similarity between worlds is irrelevant.

Wave Asymptotics for Waveguides and Manifolds with Infinite Cylindrical Ends

We describe wave decay rates associated to embedded resonances and spectral thresholds for waveguides and manifolds with infinite cylindrical ends. We show that if the cut-off resolvent is polynomially bounded at high energies, as is the case in certain favorable geometries, then there is an associated asymptotic expansion, up to a $O(t^{-k_0})$ remainder, of solutions of the wave equation on compact sets as $t \to \infty $. In the most general such case we have $k_0=1$, and under an additional assumption on the infinite ends we have $k_0 = \infty $. If we localize the solutions to the wave equation in frequency as well as in space, then our results hold for quite general waveguides and manifolds with infinite cylindrical ends. To treat problems with and without boundary in a unified way, we introduce a black box framework analogous to the Euclidean one of Sjöstrand and Zworski. We study the resolvent, generalized eigenfunctions, spectral measure, and spectral thresholds in this framework, providing a new approach to some mostly well-known results in the scattering theory of manifolds with cylindrical ends.

$$L_2$$-norm sampling discretization and recovery of functions from RKHS with finite trace

In this paper we study $$L_2$$ L 2 -norm sampling discretization and sampling recovery of complex-valued functions in RKHS on $$D \subset \mathbb {R}^d$$ D ⊂ R d based on random function samples. We only assume the finite trace of the kernel (Hilbert–Schmidt embedding into $$L_2$$ L 2 ) and provide several concrete estimates with precise constants for the corresponding worst-case errors. In general, our analysis does not need any additional assumptions and also includes the case of non-Mercer kernels and also non-separable RKHS. The fail probability is controlled and decays polynomially in n, the number of samples. Under the mild additional assumption of separability we observe improved rates of convergence related to the decay of the singular values. Our main tool is a spectral norm concentration inequality for infinite complex random matrices with independent rows complementing earlier results by Rudelson, Mendelson, Pajor, Oliveira and Rauhut.

Wpływy obce w tekstach czasopism luksusowych w języku rosyjskim, polskim i hiszpańskim (na przykładzie Cosmopolitan)

The focus of this paper is the impact of English observed in the language of an international magazine Cosmopolitan. The research was conducted taking into account three language versions of the monthly magazine: Russian, Polish and Spanish. Factual material was excerpted from the periodicals published in 2017–2021. Taking up this topic stems from the need to fill the gap in research on the language of luxury magazines, which have a great influence on forming the canons of linguistic norms and the linguistic awareness of their readers. The aim of the study is to analyze the collected Anglicisms (mainly loanwoard) in terms of their function, way of adaptation and presentation in the text space. Determining the reasons for the popularity of foreign forms in a given language space is also an important point of analysis. An additional assumption of the publication is to indicate the connections between the use of borrowings and the ideological concept of the magazine with cosmopolitanism.

Complex Phase Retrieval from Subgaussian Measurements

Phase retrieval refers to the problem of reconstructing an unknown vector $$x_0 \in {\mathbb {C}}^n$$ x 0 ∈ C n or $$x_0 \in {\mathbb {R}}^n $$ x 0 ∈ R n from m measurements of the form $$y_i = \big \vert \langle \xi ^{\left( i\right) }, x_0 \rangle \big \vert ^2 $$ y i = | ⟨ ξ i , x 0 ⟩ | 2 , where $$ \left\{ \xi ^{\left( i\right) } \right\} ^m_{i=1} \subset {\mathbb {C}}^m $$ ξ i i = 1 m ⊂ C m are known measurement vectors. While Gaussian measurements allow for recovery of arbitrary signals provided the number of measurements scales at least linearly in the number of dimensions, it has been shown that ambiguities may arise for certain other classes of measurements $$ \left\{ \xi ^{\left( i\right) } \right\} ^{m}_{i=1}$$ ξ i i = 1 m such as Bernoulli measurements or Fourier measurements. In this paper, we will prove that even when a subgaussian vector $$ \xi ^{\left( i\right) } \in {\mathbb {C}}^m $$ ξ i ∈ C m does not fulfill a small-ball probability assumption, the PhaseLift method is still able to reconstruct a large class of signals $$x_0 \in {\mathbb {R}}^n$$ x 0 ∈ R n from the measurements. This extends recent work by Krahmer and Liu from the real-valued to the complex-valued case. However, our proof strategy is quite different and we expect some of the new proof ideas to be useful in several other measurement scenarios as well. We then extend our results $$x_0 \in {\mathbb {C}}^n $$ x 0 ∈ C n up to an additional assumption which, as we show, is necessary.

A non-local expanding flow of convex closed curves in the plane

This paper presents a new non-local expanding flow for convex closed curves in the Euclidean plane which increases both the perimeter of the evolving curves and the enclosed area. But the flow expands the evolving curves to a finite circle smoothly if they do not develop singularity during the evolving process. In addition, it is shown that an additional assumption about the initial curve will ensure that the flow exists on the time interval [Formula: see text]. Meanwhile, a numerical experiment reveals that this flow may blow up for some initial convex curves.

Quantum prescriptions are more ontologically distinct than they are operationally distinguishable

Based on an intuitive generalization of the Leibniz principle of `the identity of indiscernibles', we introduce a novel ontological notion of classicality, called bounded ontological distinctness. Formulated as a principle, bounded ontological distinctness equates the distinguishability of a set of operational physical entities to the distinctness of their ontological counterparts. Employing three instances of two-dimensional quantum preparations, we demonstrate the violation of bounded ontological distinctness or excess ontological distinctness of quantum preparations, without invoking any additional assumptions. Moreover, our methodology enables the inference of tight lower bounds on the extent of excess ontological distinctness of quantum preparations. Similarly, we demonstrate excess ontological distinctness of quantum transformations, using three two-dimensional unitary transformations. However, to demonstrate excess ontological distinctness of quantum measurements, an additional assumption such as outcome determinism or bounded ontological distinctness of preparations is required. Moreover, we show that quantum violations of other well-known ontological principles implicate quantum excess ontological distinctness. Finally, to showcase the operational vitality of excess ontological distinctness, we introduce two distinct classes of communication tasks powered by excess ontological distinctness.

Remarks on input-to-state stability of collocated systems with saturated feedback

We investigate input-to-state stability (ISS) of infinite-dimensional collocated control systems subject to saturated feedback. Here, the unsaturated closed loop is dissipative and uniformly globally asymptotically stable. Under an additional assumption on the linear system, we show ISS for the saturated one. We discuss the sharpness of the conditions in light of existing results in the literature.

Regularity of Lagrangian flows over RCD*(K, N) spaces

The aim of this note is to provide regularity results for Regular Lagrangian flows of Sobolev vector fields over compact metric measure spaces verifying the Riemannian curvature dimension condition. We first prove, borrowing some ideas already present in the literature, that flows generated by vector fields with bounded symmetric derivative are Lipschitz, providing the natural extension of the standard Cauchy–Lipschitz theorem to this setting. Then we prove a Lusin-type regularity result in the Sobolev case (under the additional assumption that the m.m.s. is Ahlfors regular) therefore extending the already known Euclidean result.

A model for suspension of clusters of particle pairs

In this paper, we consider N clusters of pairs of particles sedimenting in a viscous fluid. The particles are assumed to be rigid spheres and inertia of both particles and fluid are neglected. The distance between each two particles forming the cluster is comparable to their radii 1/N while the minimal distance between the pairs is of order N−1/2. We show that, at the mesoscopic level, the dynamics are modelled using a transport-Stokes equation describing the time evolution of the position x and orientation ξ of the clusters. Under the additional assumption that the minimal distance is of order N−1/3, we investigate the case where the orientation of each cluster is initially correlated to its position. In this case, a local existence and uniqueness result for the limit model is provided.