Ramsey numbers of ordered graphs

An ordered graph is a pair $\mathcal{G}=(G,\prec)$ where $G$ is a graph and $\prec$ is a total ordering of its vertices. The ordered Ramsey number $\overline{R}(\mathcal{G})$ is the minimum number $N$ such that every ordered complete graph with $N$ vertices and with edges colored by two colors contains a monochromatic copy of $\mathcal{G}$. In contrast with the case of unordered graphs, we show that there are arbitrarily large ordered matchings $\mathcal{M}_n$ on $n$ vertices for which $\overline{R}(\mathcal{M}_n)$ is superpolynomial in $n$. This implies that ordered Ramsey numbers of the same graph can grow superpolynomially in the size of the graph in one ordering and remain linear in another ordering. We also prove that the ordered Ramsey number $\overline{R}(\mathcal{G})$ is polynomial in the number of vertices of $\mathcal{G}$ if the bandwidth of $\mathcal{G}$ is constant or if $\mathcal{G}$ is an ordered graph of constant degeneracy and constant interval chromatic number. The first result gives a positive answer to a question of Conlon, Fox, Lee, and Sudakov. For a few special classes of ordered paths, stars or matchings, we give asymptotically tight bounds on their ordered Ramsey numbers. For so-called monotone cycles we compute their ordered Ramsey numbers exactly. This result implies exact formulas for geometric Ramsey numbers of cycles introduced by K\'arolyi, Pach, T\'oth, and Valtr.Comment: 29 pages, 13 figures, to appear in Electronic Journal of Combinatoric

Stationary-state electronic distribution in quantum dots

We wish to draw an attention to a non-gibbsian behavior of zero-dimensional semiconductor nanostructures, which appears to be manifested in experiments by an effect of incomplete depopulation from electronic excited states or by an effect of up-conversion of electronic level occupation after preparing the system in the ground state of electronic excitation. In the present work the effect is interpreted with help of electron-LO-phonon interaction, which is supposed to play a role in these structures in the form of multiple-scattering of electron on the optical phonons. Quantum kinetic equation describing the process of electronic ralaxation with the inclusion of electronic multiple scattering on phonons is considered. The multiple electron scattering interpretation of the effect is supported by pointing out a considerable degree of agreement between the theoretical picture presented and a rather extensive amount of existing experimental data.Comment: 8 pages, 3 figure

On the relationship between {1 1 2¯ 2} and {1 1 2¯ 6} conjugate twins and double extension twins in rolled pure Mg

This is an Accepted Manuscript of an article published by Taylor & Francis Group in Philosophical Magazine on February 2017, available online at: http://www.tandfonline.com/10.1080/14786435.2017.1290846The paper presents a new type of twin-like objects observed in rolled pure magnesium. They have {11¯26} and {11¯22} habit planes and their misorientations to the matrix are close to 56° and 63° about ¿10¯10¿ axis, respectively. The ad hoc performed theoretical analysis and atomic simulations allow to interpret the objects as {10¯12}-{10¯12} double twins formed by the simultaneous action of two twinning shears with completely re-twinned volume of primary twin. The observed inclinations from the ideal misorientations for such double twins can be explained by the compliance of the strain invariant condition in the twin boundary. It seems plausible that, once the double twin is formed, its twin boundaries are hard to move by glide of twinning disconnections. If so, these twins represent obstacles for the motion of crystal dislocations increasing the hardness of the metal.Peer ReviewedPostprint (author's final draft

ARRIVAL: Next Stop in CLS

We study the computational complexity of ARRIVAL, a zero-player game on $n$-vertex switch graphs introduced by Dohrau, G\"{a}rtner, Kohler, Matou\v{s}ek, and Welzl. They showed that the problem of deciding termination of this game is contained in $\text{NP} \cap \text{coNP}$. Karthik C. S. recently introduced a search variant of ARRIVAL and showed that it is in the complexity class PLS. In this work, we significantly improve the known upper bounds for both the decision and the search variants of ARRIVAL. First, we resolve a question suggested by Dohrau et al. and show that the decision variant of ARRIVAL is in $\text{UP} \cap \text{coUP}$. Second, we prove that the search variant of ARRIVAL is contained in CLS. Third, we give a randomized $\mathcal{O}(1.4143^n)$-time algorithm to solve both variants. Our main technical contributions are (a) an efficiently verifiable characterization of the unique witness for termination of the ARRIVAL game, and (b) an efficient way of sampling from the state space of the game. We show that the problem of finding the unique witness is contained in CLS, whereas it was previously conjectured to be FPSPACE-complete. The efficient sampling procedure yields the first algorithm for the problem that has expected runtime $\mathcal{O}(c^n)$ with $c<2$.Comment: 13 pages, 6 figure

On Average-Case Hardness in TFNP from One-Way Functions

The complexity class TFNP consists of all NP search problems that are total in the sense that a solution is guaranteed to exist for all instances. Over the years, this class has proved to illuminate surprising connections among several diverse subfields of mathematics like combinatorics, computational topology, and algorithmic game theory. More recently, we are starting to better understand its interplay with cryptography. We know that certain cryptographic primitives (e.g. one-way permutations, collision-resistant hash functions, or indistinguishability obfuscation) imply average-case hardness in TFNP and its important subclasses. However, its relationship with the most basic cryptographic primitive -- i.e., one-way functions (OWFs) -- still remains unresolved. Under an additional complexity theoretic assumption, OWFs imply hardness in TFNP (Hubacek, Naor, and Yogev, ITCS 2017). It is also known that average-case hardness in most structured subclasses of TFNP does not imply any form of cryptographic hardness in a black-box way (Rosen, Segev, and Shahaf, TCC 2017) and, thus, one-way functions might be sufficient. Specifically, no negative result which would rule out basing average-case hardness in TFNP solely on OWFs is currently known. In this work, we further explore the interplay between TFNP and OWFs and give the first negative results. As our main result, we show that there cannot exist constructions of average-case (and, in fact, even worst-case) hard TFNP problem from OWFs with a certain type of simple black-box security reductions. The class of reductions we rule out is, however, rich enough to capture many of the currently known cryptographic hardness results for TFNP. Our results are established using the framework of black-box separations (Impagliazzo and Rudich, STOC 1989) and involve a novel application of the reconstruction paradigm (Gennaro and Trevisan, FOCS 2000)

ANALYSIS OF NEUTRON FIELDS GENERATED IN SPALLATION TARGETS OF B-URAN EXPERIMENTAL ASSEMBLY USING MONTE CARLO METHOD

The aim of this paper is to introduce experimental assembly B-URAN and the results of Monte Carlo simulations of neutron fields, which will be generated by using various spallation targets. This experimental assembly was constructed in Joint Institute of Nuclear Research in Dubna, Russian Federation, in order to study accelerator driven systems fundamental characteristics. Beam of 660 MeV protons should be used for that purpose. The MCNP model of such set-up has been developed at Brno University of Technology, Czech Republic. The goal is to get data needed for prediction of reaction rates in detectors placed in B-URAN experimental channels. Such data will be experimentally validated later. Furthermore, simulations of radiation exposure around this xperimental assembly were performed

Analysis of fast neutron transport in chloride salts using Monte Carlo method

The aim of this paper is to present results of fast neutron behavior analysis within the chloride salts environment using simulations based on Monte Carlo method (MCNP 6.2). Three non-fueled salts (NaCl, KCl, MgCl2) and two salts containing fissile material (UCl3, ThCl4) were studied. Results of this theoretical study will be used for design of an experimental assembly, which will serve to achieve goals of the international research project ADAR (Accelerator Driven Advanced Reactor). One of the project objectives is to investigate chloride salts as potential coolant and a dissolved fuel carrier of advanced nuclear reactor cooled by molten salts and driven by an accelerator