Related papers: How sharp are PV measures?
Joint, or simultaneous, measurements of non-commuting observables are possible within quantum mechanics, if one accepts an increase in the variances of the jointly measured observables. In this paper, we discuss joint measurements of a spin…
We analytically study proximity and distance properties of various kernels and similarity measures on graphs. This helps to understand the mathematical nature of such measures and can potentially be useful for recommending the adoption of…
A marked metric measure space (mmm-space) is a triple (X,r,mu), where (X,r) is a complete and separable metric space and mu is a probability measure on XxI for some Polish space I of possible marks. We study the space of all (equivalence…
The problem of interpretability of machine learning architecture in particle physics has no agreed-upon definition, much less any proposed solution. We present a first modest step toward these goals by proposing a definition and…
Calibration of a PMT matrix is crucial for the treatment of the data obtained with Cherenkov tracking detector. Furthermore, due to high variability of the aerosol abundance in the atmosphere depending on season, weather etc. A constant…
Magnetic Bright Points (MBPs) are among the smallest observable objects on the solar photosphere. A combination of G-band observations and numerical simulations is used to determine their area distribution. An automatic detection algorithm,…
We show that the metrisability of an oriented projective surface is equivalent to the existence of pseudo-holomorphic curves. A projective structure $\mathfrak{p}$ and a volume form $\sigma$ on an oriented surface $M$ equip the total space…
We prove that the previously established inequality of different metrics for algebraic polynomials is sharp in the sense of order.
Kernels of $\alpha$-permanental processes of the form \[ v(x,y)=u(x,y)+f(y),\qquad x,y\in S, \] in which $u(x,y)$ is symmetric, and $f$ is an excessive function for the Borel right process with potential densities $u(x,y)$, are considered.…
Kernel matrices are of central importance to many applied fields. In this manuscript, we focus on spectral properties of kernel matrices in the so-called ``flat limit'', which occurs when points are close together relative to the scale of…
Reverberation mapping (RM) has long been a powerful tool for measuring the masses of supermassive black holes (SMBHs) at the centers of active galactic nuclei (AGNs), but the precision of these mass measurements depends on the so-called…
We present the development and performance of an optically detected magnetic resonance (ODMR) spectrometer. The spectrometer represents advances over similar instruments in three areas: i) the exciting light is a tunable laser source which…
We consider the Poisson algebra S(M) of smooth functions on T^*M which are fiberwise polynomial. In the case where M is locally projectively (resp. conformally) flat, we seek the star-products on S(M) which are SL(n+1,R) (resp.…
Polarizations of electromagnetic waves from distant galaxies are known to be correlated with the source orientations. These quantities have been used to search for signals of cosmological birefringence. We review and classify transformation…
The numerical calculation of optical properties (extinction, absorption, scattering and polarisation efficiencies) is often time-consuming for non-spherical and inhomogeneous particles. Where possible analytical methods are therefore to be…
We consider smoothed versions of geometric range spaces, so an element of the ground set (e.g. a point) can be contained in a range with a non-binary value in $[0,1]$. Similar notions have been considered for kernels; we extend them to more…
We briefly summarize the kernel regression approach, as used recently in materials modelling, to fitting functions, particularly potential energy surfaces, and highlight how the linear algebra framework can be used to both predict and train…
We study sphericalization, which is a mapping that conformally deforms the metric and the measure of an unbounded metric measure space so that the deformed space is bounded. The goal of this paper is to study sharp conditions on the…
It is shown that mean value of any observable with bounded spectrum can be uniquely determined from binary statistics of the measurement performed on {\it single} qubit ancilla coupled to a given system. The observable structure is fully…
Three notions of complementarity - operational, probabilistic, and value complementarity - are reanalysed with respect to the question of joint measurements and compared with reference to some examples of canonically conjugate observables.…