Bell inequalities, counterfactual definiteness and falsifiability

We formally prove the existence of an enduring incongruence pervading a widespread interpretation of the Bell inequality and explain how to rationally avoid it with a natural assumption justified by explicit reference to a mathematical property of Bell’s probabilistic model. Although the amendment does not alter the relevance of the theorem regarding local realism, it brings back Bell theorem from the realm of philosophical discussions about counterfactual conditionals to the concrete experimental arena.

Continuity Editing Basics

Chapter 6 uses text and storyboards to explore the basics of continuity editing, whose goal is to tell a story on film that flows continuously, clearly, and logically in time and space. Continuity editing respects viewers’ natural assumption that time and space are contiguous from shot to shot. Continuity editing helps filmmakers satisfy their viewers’ expectation that people and objects should not seem to jump instantaneously and unrealistically within a setting or to a new place and time. Continuity editing is the standard for film storytelling. Even directors who have a style in which they frequently use jump cuts and cross the axis nevertheless practice continuity editing much of the time. This chapter is an overview of continuity editing’s main principles, and these ideas and the methods used to implement them are interwoven with the storytelling theme throughout this book.

Minimal submanifolds from the abelian Higgs model

Given a Hermitian line bundle $$L\rightarrow M$$ L → M over a closed, oriented Riemannian manifold M, we study the asymptotic behavior, as $$\epsilon \rightarrow 0$$ ϵ → 0 , of couples $$(u_\epsilon ,\nabla _\epsilon )$$ ( u ϵ , ∇ ϵ ) critical for the rescalings $$\begin{aligned} E_\epsilon (u,\nabla )=\int _M\Big (|\nabla u|^2+\epsilon ^2|F_\nabla |^2+\frac{1}{4\epsilon ^2}(1-|u|^2)^2\Big ) \end{aligned}$$ E ϵ ( u , ∇ ) = ∫ M ( | ∇ u | 2 + ϵ 2 | F ∇ | 2 + 1 4 ϵ 2 ( 1 - | u | 2 ) 2 ) of the self-dual Yang–Mills–Higgs energy, where u is a section of L and $$\nabla $$ ∇ is a Hermitian connection on L with curvature $$F_{\nabla }$$ F ∇ . Under the natural assumption $$\limsup _{\epsilon \rightarrow 0}E_\epsilon (u_\epsilon ,\nabla _\epsilon )<\infty $$ lim sup ϵ → 0 E ϵ ( u ϵ , ∇ ϵ ) < ∞ , we show that the energy measures converge subsequentially to (the weight measure $$\mu $$ μ of) a stationary integral $$(n-2)$$ ( n - 2 ) -varifold. Also, we show that the $$(n-2)$$ ( n - 2 ) -currents dual to the curvature forms converge subsequentially to $$2\pi \Gamma $$ 2 π Γ , for an integral $$(n-2)$$ ( n - 2 ) -cycle $$\Gamma $$ Γ with $$|\Gamma |\le \mu $$ | Γ | ≤ μ . Finally, we provide a variational construction of nontrivial critical points $$(u_\epsilon ,\nabla _\epsilon )$$ ( u ϵ , ∇ ϵ ) on arbitrary line bundles, satisfying a uniform energy bound. As a byproduct, we obtain a PDE proof, in codimension two, of Almgren’s existence result for (nontrivial) stationary integral $$(n-2)$$ ( n - 2 ) -varifolds in an arbitrary closed Riemannian manifold.

Asymptotic Behaviors for Delay Lotka–Volterra Model Disturbed by G-Brownian Motion

In this paper, we propose the stochastic Lotka–Volterra model with delay disturbed by G-Brownian motion dx=diagx1,x2,…,xnAxt−τ+bdBt+σxdBt. Under a natural assumption on noise, we study existence and uniqueness of the global positive solution for the system and its asymptotic pathwise moment behavior and prove that the solution does not explode to infinity in a finite time.

An empirical investigation of guilty pleasures

In everyday language, the expression “guilty pleasure” refers to instances where one feels bad about enjoying a particular artwork. Thus, one’s experience of guilty pleasure seems to involve the feeling that one should not enjoy this particular artwork and by implication the belief that there are norms according to which some aesthetic responses are more appropriate than others. One natural assumption would be that these norms are first and foremost aesthetic norms. However, this suggestion runs directly against recent findings in experimental philosophy, according to which most people deny the existence of aesthetic norms. Through three studies, we investigated people's experience of guilty pleasures and the norms that underlie this experience. We tentatively conclude that guilty pleasures are more often connected to one’s personal norms and social expectations than to properly aesthetic norms.

Accreted Globular Clusters in external galaxies: Why adaptive dynamics is not the solution

Many astrophysical and galaxy-scale cosmological problems require a well determined gravitational potential which is often modeled by observers under strong assumptions. Globular clusters (GCs) surrounding galaxies can be used as dynamical tracers of the luminous and dark matter distribution at large (kpc) scales. A natural assumption for modeling the gravitational potential is that GCs accreted in the same dwarf galaxy merger event move at the present time on similar orbits in the host galaxy and should therefore have similar actions. We investigate this idea in one realistic Milky Way like galaxy of the cosmological N-body simulation suite Auriga. We show how the actions of accreted stellar particles in the simulation evolve and that minimizing the standard deviation of GCs in action space, however, cannot constrain the true potential. This approach known as ‘adaptive dynamics’ does therefore not work for accreted GCs.

Regularized Nyström subsampling in regression and ranking problems under general smoothness assumptions

In the supervised learning, the Nyström type subsampling is considered as a tool for reducing the computational complexity of regularized kernel methods in the big data setting. Up to now, the theoretical analysis of this approach has been done almost exclusively in the context of the regression learning and in the case where the smoothness of the target functions is restricted to the Hölder type source conditions. Such conditions do not cover the case of target functions with high and low smoothness, which are also of practical interest. Moreover, in the case of the Hölder source conditions, there is no need to consider a regularization with high enough qualification because order-optimal learning rates are achieved by the simple Tikhonov regularization known also as the kernel ridge regression. At the same time, this learning method does not improve its performance for any smoothness higher than Hölder ones. Therefore, in this paper, our goal is to extend previous analysis of the Nyström type subsampling to the case of the general source conditions, and to the regularization schemes with high enough qualification. We also show that under rather natural assumption, our results can be easily reformulated in the ranking learning setting.

Black holes in the turbulence phase of viscous rip cosmology

We study the phantom fluid in the late universe, thus assuming the equation of state parameter [Formula: see text] to be less than [Formula: see text]. The fluid is assumed to consist of two components, one laminar component [Formula: see text] and one turbulent component [Formula: see text], the latter set proportional to [Formula: see text] as well as to the Hubble parameter, [Formula: see text] with [Formula: see text] a positive constant associated with the turbulence. The effective energy density is taken to be [Formula: see text], and the corresponding effective pressure is [Formula: see text], with [Formula: see text] constant. These basic assumptions lead to a Big Rip universe; the physical quantities diverging during a finite rip time [Formula: see text]. We then consider the mass accretion of a black hole in such a universe. The most natural assumption of setting the rate [Formula: see text] proportional to [Formula: see text] times the sum [Formula: see text] leads to a negative mass accretion, where [Formula: see text] goes to zero linearly in [Formula: see text] near the singularity. The Hubble parameter diverges as [Formula: see text], whereas [Formula: see text] and [Formula: see text] diverge as [Formula: see text]. We also discuss other options and include, for the sake of comparison, some essential properties of mass accretion in the early (inflationary) universe.

Acoustic transmission problems: Wavenumber-explicit bounds and resonance-free regions

We consider the Helmholtz transmission problem with one penetrable star-shaped Lipschitz obstacle. Under a natural assumption about the ratio of the wavenumbers, we prove bounds on the solution in terms of the data, with these bounds explicit in all parameters. In particular, the (weighted) [Formula: see text] norm of the solution is bounded by the [Formula: see text] norm of the source term, independently of the wavenumber. These bounds then imply the existence of a resonance-free strip beneath the real axis. The main novelty is that the only comparable results currently in the literature are for smooth, convex obstacles with strictly positive curvature, while here we assume only Lipschitz regularity and star-shapedness with respect to a point. Furthermore, our bounds are obtained using identities first introduced by Morawetz (essentially integration by parts), whereas the existing bounds use the much-more sophisticated technology of microlocal analysis and propagation of singularities. We also adapt existing results to show that if the assumption on the wavenumbers is lifted, then no bound with polynomial dependence on the wavenumber is possible.