On a Reconstruction Problem for Sequences

AbstractIt is shown that any word of lengthnis uniquely determined by all its[formula]subwords of lengthk, providedk⩾⌊167n⌋+5. This improves the boundk⩾⌊n/2⌋ given in B. Manvelet al.(Discrete Math.94(1991), 209–219)

Switching reconstruction and diophantine equations

AbstractBased on a result of R. P. Stanley (J. Combin. Theory Ser. B 38, 1985, 132–138) we show that for each s ≥ 4 there exists an integer Ns such that any graph with n > Ns vertices is reconstructible from the multiset of graphs obtained by switching of vertex subsets with s vertices, provided n ≠ 0 (mod 4) if s is odd. We also establish an analog of P. J. Kelly's lemma (Pacific J. Math., 1957, 961–968) for the above s-switching reconstruction problem

Reliable Computation of the Zeros of Solutions of Second Order Linear ODEs Using a Fourth Order Method

A fourth order fixed point method to compute the zeros of solutions of second order homogeneous linear ODEs is obtained from the approximate integration of the Riccati equation associated with the ODE. The method requires the evaluation of the logarithmic derivative of the function and also uses the coefficients of the ODE. An algorithm to compute with certainty all the zeros in an interval is given which provides a fast, reliable, and accurate method of computation. The method is illustrated by the computation of the zeros of Gauss hypergeometric functions (including Jacobi polynomials) and confluent hypergeometric functions (Laguerre polynomials, Hermite polynomials, and Bessel functions included) among others. The examples show that typically 4 or 5 iterations per root are enough to provide more than 100 digits of accuracy, without requiring a priori estimations of the roots

Технология бережливого производства и минимизация потерь от аварий

[For the English abstract and full text of the article please see the attached PDF-File (English version follows Russian version)].ABSTRACT In railway sector there are many dangerous destabilizing factors. One of the most common problems is collision of a train with a vehicle which is stuck on or entered out of driver’s negligence into a railway crossing. In the article methods of minimization of losses from this type of accidents are considered. They comprise construction of tunnels and overpasses at the intersections of the railway and the road, use of a 3D-laser radar to warn the locomotive crew about the stuck transport. In addition, it is possible to use web cameras, the image from which, using a router installed within 4-5 km far from the crossing, is transferred to the train driver’s cab on a separate display in advance to see the stuck vehicle and to have time to take emergency braking measures. Keywords: lean manufacturing, safety factors, railway crossing, emergency situation, visual perception, 3D-laser radar, web camera.Текст аннотации на англ. языке и полный текст статьи на англ. языке находится в прилагаемом файле ПДФ (англ. версия следует после русской версии).В железнодорожном деле существует множество опасных дестабилизирующих факторов. Одна из самых распространённых проблем - столкновение поезда с застрявшим или выехавшим по неосторожности водителя на железнодорожный переезд транспортным средством. В статье рассмотрены способы минимизации потерь от такого вида аварий. Ими могут быть постройка тоннелей и путепроводов в местах пересечения железнодорожного полотна и автомобильной дороги, применение 3D-лазерного радара для предупреждения локомотивной бригады о застрявшем транспорте. Кроме того, возможно использование веб-камер, изображение с которых при помощи роутера, установленного за 4-5 км от переезда, передается в кабину машиниста на отдельный дисплей, чтобы заранее увидеть застрявшее транспортное средство и было время принять меры по экстренному торможению

Canadians Should Travel Randomly

We study online algorithms for the Canadian Traveller Problem (CTP) introduced by Papadimitriou and Yannakakis in 1991. In this problem, a traveller knows the entire road network in advance, and wishes to travel as quickly as possible from a source vertex s to a destination vertex t, but discovers online that some roads are blocked (e.g., by snow) once reaching them. It is PSPACE-complete to achieve a bounded competitive ratio for this problem. Furthermore, if at most k roads can be blocked, then the optimal competitive ratio for a deterministic online algorithm is 2k + 1, while the only randomized result known is a lower bound of k + 1. In this paper, we show for the first time that a polynomial time randomized algorithm can beat the best deterministic algorithms, surpassing the 2k + 1 lower bound by an o(1) factor. Moreover, we prove the randomized algorithm achieving a competitive ratio of (1 + [√2 over 2])k + 1 in pseudo-polynomial time. The proposed techniques can also be applied to implicitly represent multiple near-shortest s-t paths.NSC Grant 102-2221-E-007-075-MY3Japan Society for the Promotion of Science (KAKENHI 23240002

Greedy Solution of Ill-Posed Problems: Error Bounds and Exact Inversion

The orthogonal matching pursuit (OMP) is an algorithm to solve sparse approximation problems. Sufficient conditions for exact recovery are known with and without noise. In this paper we investigate the applicability of the OMP for the solution of ill-posed inverse problems in general and in particular for two deconvolution examples from mass spectrometry and digital holography respectively. In sparse approximation problems one often has to deal with the problem of redundancy of a dictionary, i.e. the atoms are not linearly independent. However, one expects them to be approximatively orthogonal and this is quantified by the so-called incoherence. This idea cannot be transfered to ill-posed inverse problems since here the atoms are typically far from orthogonal: The ill-posedness of the operator causes that the correlation of two distinct atoms probably gets huge, i.e. that two atoms can look much alike. Therefore one needs conditions which take the structure of the problem into account and work without the concept of coherence. In this paper we develop results for exact recovery of the support of noisy signals. In the two examples in mass spectrometry and digital holography we show that our results lead to practically relevant estimates such that one may check a priori if the experimental setup guarantees exact deconvolution with OMP. Especially in the example from digital holography our analysis may be regarded as a first step to calculate the resolution power of droplet holography