Precise definitions of “weak [quantum] measurements” and “weak value” [of a quantum observable] are offered, which seem to capture the meaning of the often vague ways that these terms are used in the literature. Simple finite dimensional examples are given showing that weak values of an observable are not unique, and in fact arbitrary weak values can be obtained by appropriate weak measurements...

We review and clarify the sufficient conditions for uniquely defining the generalized weak value as the weak limit of a conditioned average using the contextual values formalism introduced in Dressel J, Agarwal S and Jordan A N 2010 Phys. Rev. Lett. 104 240401. We also respond to criticism of our work in [arXiv:1105.4188v1] concerning a proposed counter-example to the uniqueness of the definiti...

In this article we present an analytical calculation of the probability distribution of the magnification of distant sources due to weak gravitational lensing from non-linear scales. We use a realistic description of the non-linear density field, which has already been compared with numerical simulations of structure formation within hierarchical scenarios. Then, we can directly express the pro...

We define and compare a selection of congruence properties of quasivarieties, including the relative congruence meet semi-distributivity, RSD(∧), and the weak extension property, WEP. We prove that if K ⊆ L ⊆ L′ are quasivarieties of finite signature, and L′ is finitely generated while K |= WEP, then K is finitely axiomatizable relative to L. We prove for any quasivariety K that K |= RSD(∧) iff...

This paper presents a machine learning approach to Lip Reading and proposes a novel learning technique called sequential pattern boosting that allows us to efficiently search and combine temporal patterns to form strong spatio-temporal classifiers. Attempts at automatic lip reading need to address the demanding challenge that the problem is inherently temporal in nature. It is crucial to model ...

We analyze the average of weak values over statistical ensembles of pre and post-selected states. The protocol of weak values, proposed by Aharonov et al. [3], is the result of a weak measurement conditional on the outcome of a subsequent strong (projective) measurement. Weak values can be beyond the range of eigenvalues of the measured observable and, in general, can be complex numbers. We sho...

In many practical situations, we are not satisfied with the accuracy of the existing measurements. There are two possible ways to improve the measurement accuracy: • first, instead of a single measurement, we can make repeated measurements; the additional information coming from these additional measurements can improve the accuracy of the result of this series of measurements; • second, we can...

The ratio R T of K + − 12 C to K + − d cross sections has been calculated microscopically using a boson-exchange KN amplitude in which the σ and ω mesons are dressed by the modifications of the Dirac sea in nuclear matter. In spite of the fact that this dressing leads to a scaling of the mesons effective mass in nuclear matter, the effect on the R T ratio is found to be weak.

We characterize regular boundary points for p-harmonic functions using weak barriers. We use this to obtain some consequences on boundary regularity. The results also hold for A-harmonic functions under the usual assumptions on A, and for Cheeger p-harmonic functions in metric spaces.

In this paper we examine weak logics similar to S0.5[ Φ], where Φ ⊆ S0.5. We also examine their versions (one of which is S0.5rte[ Φ]) that are closed under replacement of tautological equivalents (rte). We have that: S0.5rte[ (K), (T)] ( S0.9, S0.5rte[ (X), (T)] ( S1, and in general, if Φ ⊆ E1, then S0.5rte[ Φ] ( S2. In the second part we shall give simplified semantics for these logics, formu...