Improved bounds and new techniques for Davenport-Schinzel sequences and their generalizations

Let lambda_s(n) denote the maximum length of a Davenport-Schinzel sequence of order s on n symbols. For s=3 it is known that lambda_3(n) = Theta(n alpha(n)) (Hart and Sharir, 1986). For general s>=4 there are almost-tight upper and lower bounds, both of the form n * 2^poly(alpha(n)) (Agarwal, Sharir, and Shor, 1989). Our first result is an improvement of the upper-bound technique of Agarwal et al. We obtain improved upper bounds for s>=6, which are tight for even s up to lower-order terms in the exponent. More importantly, we also present a new technique for deriving upper bounds for lambda_s(n). With this new technique we: (1) re-derive the upper bound of lambda_3(n) <= 2n alpha(n) + O(n sqrt alpha(n)) (first shown by Klazar, 1999); (2) re-derive our own new upper bounds for general s; and (3) obtain improved upper bounds for the generalized Davenport-Schinzel sequences considered by Adamec, Klazar, and Valtr (1992). Regarding lower bounds, we show that lambda_3(n) >= 2n alpha(n) - O(n), and therefore, the coefficient 2 is tight. We also present a simpler version of the construction of Agarwal, Sharir, and Shor that achieves the known lower bounds for even s>=4.Comment: To appear in Journal of the ACM. 48 pages, 3 figure

A Terrestrial Multiple-Receiver Radio Link Experiment at 10.7 GHz - Comparisons of Results with Parabolic Equation Calculations

This work presents the results of a terrestrial multiple-receiver radio link experiment at 10.7 GHz. Results are shown in the form of the power levels recorded at several antennas attached to a receiving mast. Comparisons of the measurement data with theoretical predictions using a parabolic equation technique show that, due to the complex propagation environment of the troposphere in terms of the refractive index of air, closer agreement between measurements and simulations can be achieved during periods of standard refractive conditions

The effects of attentional focus instructions on the performance of a persistent form-based skill in gymnastics

External relative to internal focus instructions have been shown to be more effective for enhancing optimal performance across various motor tasks that do not rely on movement quality or movement form. The aim of this study was to examine the effects of an external versus an internal focus of attention on the motor performance of a gymnastic skill that requires static strength and movement form. Participants with previous experience in aerobic gymnastics were asked to perform an L-support task for 4 seconds in three attentional focus conditions: internal focus, external focus, and control, with the order counter-balanced across focus conditions. Two pieces of yellow tape (2×9 cm) were attached to the gymnasts’ feet on the inner side of the navicular bones. Two pieces of red tape (2×9 cm) were wrapped around the distal phalanx of the big toes of the right and left foot. All participants performed four trials in the external focus (focus on keeping red tape below the yellow tape), internal focus (focus on pointing your toes), and control (no-focus) conditions. The results showed that execution faults were smaller in the external focus condition compared to the internal focus and control conditions. No difference was found between the internal focus and control condition. The findings of this study indicate that the external focus is more beneficial than the internal focus and no-focus control condition for enhancing the performance of a static gymnastic skill that requires static strength and movement form

Every Large Point Set contains Many Collinear Points or an Empty Pentagon

We prove the following generalised empty pentagon theorem: for every integer $\ell \geq 2$, every sufficiently large set of points in the plane contains $\ell$ collinear points or an empty pentagon. As an application, we settle the next open case of the "big line or big clique" conjecture of K\'ara, P\'or, and Wood [\emph{Discrete Comput. Geom.} 34(3):497--506, 2005]

Awareness about developmental coordination disorder

Data availability statement: The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author.The present paper is designed to promote awareness of DCD outside the academic world. With a prevalence of 5–6% it is one of the most common disorders of child development. It is therefore surprising that so little is known about it among professionals in child healthcare and education. Parents have expressed frustration about this lack of awareness, including the general public. The general aim of this paper was to describe those critical aspects of DCD that will promote awareness.Research Foundation Flanders (FWO: 1232221N). This research of PW is supported by the Czech Science Foundation (GACR EXPRO scheme: 21-15728X). The authors are part of the “DCD Big Ideas Group” consisting of 25 key researchers in the field of DCD (from early-career to established) working to develop a clear vision for the future of research on DCD. BS and HB were supported by a grant (TRIAL) from the Dutch Research Council (NWO), grant number NWA.1160.18.249

Planar Point Sets Determine Many Pairwise Crossing Segments

We show that any set of $n$ points in general position in the plane determines $n^{1-o(1)}$ pairwise crossing segments. The best previously known lower bound, $\Omega\left(\sqrt n\right)$, was proved more than 25 years ago by Aronov, Erd\H os, Goddard, Kleitman, Klugerman, Pach, and Schulman. Our proof is fully constructive, and extends to dense geometric graphs.Comment: A preliminary version to appear in the proceedings of STOC 201

Awareness about developmental coordination disorder

The present paper is designed to promote awareness of DCD outside the academic world. With a prevalence of 5–6% it is one of the most common disorders of child development. It is therefore surprising that so little is known about it among professionals in child healthcare and education. Parents have expressed frustration about this lack of awareness, including the general public. The general aim of this paper was to describe those critical aspects of DCD that will promote awareness

Atomic force microscopy analysis of nanoparticles in non-ideal conditions

Nanoparticles are often measured using atomic force microscopy or other scanning probe microscopy methods. For isolated nanoparticles on flat substrates, this is a relatively easy task. However, in real situations, we often need to analyze nanoparticles on rough substrates or nanoparticles that are not isolated. In this article, we present a simple model for realistic simulations of nanoparticle deposition and we employ this model for modeling nanoparticles on rough substrates. Different modeling conditions (coverage, relaxation after deposition) and convolution with different tip shapes are used to obtain a wide spectrum of virtual AFM nanoparticle images similar to those known from practice. Statistical parameters of nanoparticles are then analyzed using different data processing algorithms in order to show their systematic errors and to estimate uncertainties for atomic force microscopy analysis of nanoparticles under non-ideal conditions. It is shown that the elimination of user influence on the data processing algorithm is a key step for obtaining accurate results while analyzing nanoparticles measured in non-ideal conditions