Variants of Plane Diameter Completion

The {\sc Plane Diameter Completion} problem asks, given a plane graph $G$ and a positive integer $d$, if it is a spanning subgraph of a plane graph $H$ that has diameter at most $d$. We examine two variants of this problem where the input comes with another parameter $k$. In the first variant, called BPDC, $k$ upper bounds the total number of edges to be added and in the second, called BFPDC, $k$ upper bounds the number of additional edges per face. We prove that both problems are {\sf NP}-complete, the first even for 3-connected graphs of face-degree at most 4 and the second even when $k=1$ on 3-connected graphs of face-degree at most 5. In this paper we give parameterized algorithms for both problems that run in $O(n^{3})+2^{2^{O((kd)^2\log d)}}\cdot n$ steps.Comment: Accepted in IPEC 201

Genetic code on the dyadic plane

We introduce the simple parametrization for the space of codons (triples of nucleotides) by 8\times 8 table. This table (which we call the dyadic plane) possesses the natural 2-adic ultrametric. We show that after this parametrization the genetic code will be a locally constant map of the simple form. The local constancy of this map will describe degeneracy of the genetic code. The map of the genetic code defines 2-adic ultrametric on the space of amino acids. We show that hydrophobic amino acids will be clustered in two balls with respect to this ultrametric. Therefore the introduced parametrization of space of codons exhibits the hidden regularity of the genetic code.Comment: Some gap in the construction was fixe

Evaluation of many load tests of passive rock bolts in the Czech Republic

Within the research project "FR-TI4/329 Research and development - creating an application system for the design and analysis of soil and rock anchors including the development of monitoring elements", an extensive stage of field load tests of rock bolts was carried out. The tests were conducted at 14 locations with varied rock composition. Before the initial tests, a loading stand was designed and constructed. A total of 201 pieces of tensile tests of bolts having lengths from 0.5 up to 2.5 m, a diameter of 22-32 mm, were performed. These were fully threaded rods, self-drilling rods, and fiberglass rods. The bolts were clamped into the cement and resin. The loading tests were always performed until material failure of bolts or shear stress failure at the interface cement-rock. At each location, basic geotechnical survey was carried out in the form of core drilling in a length of 3.0 metres with the assessment of the rock mass in situ, and laboratory testing of rock mechanics. Upon the completion of testing protocols, rock mass properties analysis was performed focusing on the evaluation of shear friction at the grouting-rock interface

Design study of Self-Alining Bearingless Planetary (SABP) gear

The feasibility of using the self alining, bearingless planetary (SABP) transmission in an uprated version of the OH-58 helicopter was evaluated, specific performance comparisons of this new transmission with contemporary helicopter transmission systems and with the uprated version of the OH-58 power transmission were made

Nanoscale switching characteristics of nearly tetragonal BiFeO3 thin films

We have investigated the nanoscale switching properties of strain-engineered BiFeO3 thin films deposited on LaAlO3 substrates using a combination of scanning probe techniques. Polarized Raman spectral analysis indicate that the nearly-tetragonal films have monoclinic (Cc) rather than P4mm tetragonal symmetry. Through local switching-spectroscopy measurements and piezoresponse force microscopy we provide clear evidence of ferroelectric switching of the tetragonal phase but the polarization direction, and therefore its switching, deviates strongly from the expected (001) tetragonal axis. We also demonstrate a large and reversible, electrically-driven structural phase transition from the tetragonal to the rhombohedral polymorph in this material which is promising for a plethora of applications.Comment: 10 pages, 6 figure

The Minimum Backlog Problem

We study the minimum backlog problem (MBP). This online problem arises, e.g., in the context of sensor networks. We focus on two main variants of MBP. The discrete MBP is a 2-person game played on a graph $G=(V,E)$. The player is initially located at a vertex of the graph. In each time step, the adversary pours a total of one unit of water into cups that are located on the vertices of the graph, arbitrarily distributing the water among the cups. The player then moves from her current vertex to an adjacent vertex and empties the cup at that vertex. The player's objective is to minimize the backlog, i.e., the maximum amount of water in any cup at any time. The geometric MBP is a continuous-time version of the MBP: the cups are points in the two-dimensional plane, the adversary pours water continuously at a constant rate, and the player moves in the plane with unit speed. Again, the player's objective is to minimize the backlog. We show that the competitive ratio of any algorithm for the MBP has a lower bound of $\Omega(D)$, where $D$ is the diameter of the graph (for the discrete MBP) or the diameter of the point set (for the geometric MBP). Therefore we focus on determining a strategy for the player that guarantees a uniform upper bound on the absolute value of the backlog. For the absolute value of the backlog there is a trivial lower bound of $\Omega(D)$, and the deamortization analysis of Dietz and Sleator gives an upper bound of $O(D\log N)$ for $N$ cups. Our main result is a tight upper bound for the geometric MBP: we show that there is a strategy for the player that guarantees a backlog of $O(D)$, independently of the number of cups.Comment: 1+16 pages, 3 figure