Related papers: Reply to R. Blumenfeld on "Explicit analytical sol…
A highly accurate but overconfident model is ill-suited for deployment in critical applications such as healthcare and autonomous driving. The classification outcome should reflect a high uncertainty on ambiguous in-distribution samples…
We prove a formula, first obtained by Kleban, Simmons and Ziff using conformal field theory methods, for the (renormalized) density of a critical percolation cluster in the upper half-plane "anchored" to a point on the real line. The proof…
This paper has been withdrawn by the author; a revised version is part of the author's phd-thesis "Quasi-logarithmic structures" (Zurich, 2007).
In this paper, we show that the stability analysis in the paper A note on stability of fractional logistic maps, Appl. Math. Lett. 125 (2022) 107787 is incorrect and repeat a proof of a theorem on the convergence of a convolution of the…
The question raised by [Bastin and Martin 2003 J. Phys. B: At. Mol. Opt. Phys. 36, 4201] is examined and used to explain in more detail a key point of our calculations. They have sought to rebut criticisms raised by us of certain techniques…
We consider the problem of embedding one i.i.d.\ collection of Bernoulli random variables indexed by $\mathbb{Z}^d$ into an independent copy in an injective $M$-Lipschitz manner. For the case $d=1$, it was shown by Basu and Sly (PTRF, 2014)…
We report a recent developement on the theory of upper conical densities. More precicely, we look at what can be said in this respect for other measures than just the Hausdorff measure. We illustrate the methods involved by proving a result…
In the paper "The relativistic Doppler effect: when a zero-frequency shift or a red shift exists for sources approaching the observer, Ann. Phys. (Berlin) 523, No. 3, 239-246 (2011), DOI 10.1002/andp.201000099 by C. Wang the use of an…
Recent dispersive techniques developed by us are applied to discuss three problems: 1. A long standing discrepan-cy between the measurements of $R(s)$ for $\sqrt{s} = (5\div 7.5)GeV$ by Crystal Ball and MARK I has been analyzed and its…
The Kepler conjecture asserts that no packing of congruent balls in three-dimensional Euclidean space has density greater than that of the face-centered cubic packing. The original proof, announced in 1998 and published in 2006, is long and…
This manuscript, a revised version of arXiv:0811.3168v1, was inadvertently submitted as a separate paper. It can now be accessed, including some final corrections for the published version, as arXiv:0811.3168v2.
Benenti et al. recently submitted a Comment (arXiv:0912.3667) on our work "Coherent Ratchets in Driven Bose-Einstein condensates". We show that the main claim of the Comment is wrong, and correct some other misunderstandings presented…
We give sufficient conditions for the number rigidity of a translation invariant or periodic point process on $\mathbb{R}^d$, where $d=1,2$. That is, the probability distribution of the number of particles in a bounded domain $\Lambda…
We prove the tightness of radially-symmetric solutions to 2D aggregation-diffusion equations, where the pairwise attraction force is possibly degenerate at large distance. We first reduce the problem into the finiteness of a time integral…
Recently we have reanalyzed the consistency of the solutions of the space fractional Schr\"odinger equation found in a piecewise manner, and showed that an exact and a proper treatment of the relevant integrals prove that they are…
Bernstein-von Mises results (BvM) establish that the Laplace approximation is asymptotically correct in the large-data limit. However, these results are inappropriate for computational purposes since they only hold over most, and not all,…
In Chib (1995), a method for approximating marginal densities in a Bayesian setting is proposed, with one proeminent application being the estimation of the number of components in a normal mixture. As pointed out in Neal (1999) and…
This is a Reply to the Comment (cond-mat/9812331) by Kravchenko et al. on our earlier work (cond-mat/9812216).
In a recent letter (PRL 95, 190601 (2005)), T.M. Rocha Filho and coworkers address the very interesting issue of the entropic form to be used for Hamiltonians with long-range interactions. In our opinion the letter misses several points…
In this paper the random packing fraction of hard disks in a plane is analyzed, following a geometric probabilistic approach. First, the random close packing (RCP) of equally sized disks is modelled. Subsequently, following the same…