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We present a general framework of examining the validity of weak measurement -- the standard procedure to acquire Aharonov's weak value -- which has been used intensively in recent years for precision measurement, taking advantage of the…
This paper presents two alternative approaches for counting the number of two-row weakly increasing matrices, which are $2\times n$ matrices whose entries are integers from $1$ to $k$ and are weakly increasing along all rows and columns,…
An experimental proposal is presented in which dark port post-selection together with weak measurements are used to enlarge the radiation pressure effect of a single photon on a mechanical oscillator placed in the middle of a Fabry-Perot…
I comment on Zaccone, Phys. Rev. Lett. {\bf 128}, 028002 (2022) highlighting a flaw in the derivation that led to a spurious divergent factor. This renders the derivation of the random close packing density invalid.
We address the problem of modulating a parameter onto a power-limited signal, transmitted over a discrete-time Gaussian channel and estimating this parameter at the receiver. Continuing an earlier work, where the optimal trade-off between…
Weak-head normalization is inconsistent with functional extensionality in the call-by-name $\lambda$-calculus. We explore this problem from a new angle via the conflict between extensionality and effects. Leveraging ideas from work on the…
In functional analysis it is well known that every linear functional defined on the dual of a locally convex vector space which is continuous for the weak topology is the evaluation at a uniquely determined point of the given vector space.…
Weak measurement has garnered widespread interest for its ability to amplify small physical effects at the cost of low detection probabilities. Previous entanglement and recycling techniques enhance postselection efficiency and…
Main theoretical approaches to weak radiative hyperon decays are briefly reviewed. It is emphasized that only approaches with great predictive power should be seriously considered when seeking a resolution of the puzzle presented by…
Linear instrumental variable regressions are widely used to estimate causal effects. Many instruments arise from the use of ``technical'' instruments and more recently from the empirical strategy of ``judge design''. This paper surveys and…
A simple construction of Euclidean invariant and reflection positive measures on the cylindrical compactification is performed under a weaker hypothesis than has recently been obtained. Moreover, the results are extended to the case when…
Statistical paradoxes such as the Hardy paradox and the enhancement of phase estimation via post-selection both draw upon the same non-classical features of quantum statistics described by non-positive quasi-probabilities. In this paper, we…
In this paper, we shall study existence of weak solutions to complex Hessian equations. With appropriate assumptions, it is possible to obtain weak solutions in pluripotential sense.
The technique of almost-balanced weak values amplification (ABWV) was recently proposed [Phys. Rev. Lett. 116: 100803 (2016)]. We demonstrate this technique using a modified Sagnac interferometer, where the counter-propagating beams are…
We present a comprehensive full-sky 3-dimensional analysis of the weak-lensing fields and their corresponding power spectra. Using the formalism of spin-weight spherical harmonics and spherical Bessel functions, we relate the two-point…
Two proofs of a weighted weak-type $\left(1,\ldots,1;\frac{1}{m}\right)$ estimate for multilinear Calder\'on-Zygmund operators are given. The ideas are motivated by different proofs of the classical weak-type $(1,1)$ estimate for…
We address the issue of how to properly treat, and in a more general setting, the concept of a weak value of a weak measurement in quantum mechanics. We show that for this purpose, one must take in account the effects of the measuring…
The "anomalous" values of C. Ferrie and J. Combes in Phys. Rev. Lett. 113, 120404 (2014) say nothing about quantum - or even classical - physics. They are not analogues of the weak values that emerge when we describe the quantum world via…
Weak values as introduced by Aharonov, Albert and Vaidman (AAV) are ensemble average values for the results of weak measurements. They are interesting when the ensemble is preselected on a particular initial state and postselected on a…
We show that there exists, in quantum theory, a close relationship between the weak value and the correlation function, which sheds new lights on the concept of the weak value.