Monotone Grid Drawings of Planar Graphs

A monotone drawing of a planar graph $G$ is a planar straight-line drawing of $G$ where a monotone path exists between every pair of vertices of $G$ in some direction. Recently monotone drawings of planar graphs have been proposed as a new standard for visualizing graphs. A monotone drawing of a planar graph is a monotone grid drawing if every vertex in the drawing is drawn on a grid point. In this paper we study monotone grid drawings of planar graphs in a variable embedding setting. We show that every connected planar graph of $n$ vertices has a monotone grid drawing on a grid of size $O(n)\times O(n^2)$, and such a drawing can be found in O(n) time

Maximizing Maximal Angles for Plane Straight-Line Graphs

Let $G=(S, E)$ be a plane straight-line graph on a finite point set $S\subset\R^2$ in general position. The incident angles of a vertex $p \in S$ of $G$ are the angles between any two edges of $G$ that appear consecutively in the circular order of the edges incident to $p$. A plane straight-line graph is called $\phi$-open if each vertex has an incident angle of size at least $\phi$. In this paper we study the following type of question: What is the maximum angle $\phi$ such that for any finite set $S\subset\R^2$ of points in general position we can find a graph from a certain class of graphs on $S$ that is $\phi$-open? In particular, we consider the classes of triangulations, spanning trees, and paths on $S$ and give tight bounds in most cases.Comment: 15 pages, 14 figures. Apart of minor corrections, some proofs that were omitted in the previous version are now include

Retrieving Layer-Averaged Tropospheric Humidity from Advanced Technology Microwave Sounder Water Vapor Channels

A method is presented to calculate layer-averaged tropospheric humidity (LAH) from the observations of the Advanced Technology Microwave Sounder (ATMS) water vapor channels. The method is based on a linear relation between the satellite brightness temperatures (Tb) and natural logarithm of Jacobian weighted humidity. The empirical coefficients of this linear relation were calculated using different data sets, as well as a fast and a line-by-line radiative transfer (RT) model. It was found that the coefficients do not significantly depend on the data set or the RT model. This Tb to the LAH transformation method can be applied to either original or limb-corrected ATMS Tb's. The method was validated using both simulated and observed ATMS Tb's. The systematic difference between the estimated and calculated LAH values was less than 10% in most cases. We also tested the transformation method using a fixed Jacobian for each channel. The bias generally increases when fixed Jacobians are used, but there is still a satisfactory agreement between estimated and calculated LAH values. In addition, the spatial distribution of the bias was investigated using the European Center for Medium-Range Weather Forecasting (ECMWF) Interim Reanalysis (ERA-interim) and collocated ATMS observations. The bias did not indicate any significant regional dependence when actual Jacobians were used, but in the case of fixed Jacobians, the bias generally increased from middle latitude toward the poles

Bounded-Angle Spanning Tree: Modeling Networks with Angular Constraints

We introduce a new structure for a set of points in the plane and an angle $\alpha$, which is similar in flavor to a bounded-degree MST. We name this structure $\alpha$-MST. Let $P$ be a set of points in the plane and let $0 < \alpha \le 2\pi$ be an angle. An $\alpha$-ST of $P$ is a spanning tree of the complete Euclidean graph induced by $P$, with the additional property that for each point $p \in P$, the smallest angle around $p$ containing all the edges adjacent to $p$ is at most $\alpha$. An $\alpha$-MST of $P$ is then an $\alpha$-ST of $P$ of minimum weight. For $\alpha < \pi/3$, an $\alpha$-ST does not always exist, and, for $\alpha \ge \pi/3$, it always exists. In this paper, we study the problem of computing an $\alpha$-MST for several common values of $\alpha$. Motivated by wireless networks, we formulate the problem in terms of directional antennas. With each point $p \in P$, we associate a wedge $W_p$ of angle $\alpha$ and apex $p$. The goal is to assign an orientation and a radius $r_p$ to each wedge $W_p$, such that the resulting graph is connected and its MST is an $\alpha$-MST. (We draw an edge between $p$ and $q$ if $p \in W_q$, $q \in W_p$, and $|pq| \le r_p, r_q$.) Unsurprisingly, the problem of computing an $\alpha$-MST is NP-hard, at least for $\alpha=\pi$ and $\alpha=2\pi/3$. We present constant-factor approximation algorithms for $\alpha = \pi/2, 2\pi/3, \pi$. One of our major results is a surprising theorem for $\alpha = 2\pi/3$, which, besides being interesting from a geometric point of view, has important applications. For example, the theorem guarantees that given any set $P$ of $3n$ points in the plane and any partitioning of the points into $n$ triplets, one can orient the wedges of each triplet {\em independently}, such that the graph induced by $P$ is connected. We apply the theorem to the {\em antenna conversion} problem

Circadian Rhythmicity by Autocatalysis

The temperature compensated in vitro oscillation of cyanobacterial KaiC phosphorylation, the first example of a thermodynamically closed system showing circadian rhythmicity, only involves the three Kai proteins (KaiA, KaiB, and KaiC) and ATP. In this paper, we describe a model in which the KaiA- and KaiB-assisted autocatalytic phosphorylation and dephosphorylation of KaiC are the source for circadian rhythmicity. This model, based upon autocatalysis instead of transcription-translation negative feedback, shows temperature-compensated circadian limit-cycle oscillations with KaiC phosphorylation profiles and has period lengths and rate constant values that are consistent with experimental observations

Vibrational Enhancement of the Effective Donor - Acceptor Coupling

The paper deals with a simple three sites model for charge transfer phenomena in an one-dimensional donor (D) - bridge (B) - acceptor (A) system coupled with vibrational dynamics of the B site. It is found that in a certain range of parameters the vibrational coupling leads to an enhancement of the effective donor - acceptor electronic coupling as a result of the formation of the polaron on the B site. This enhancement of the charge transfer efficiency is maximum at the resonance, where the effective energy of the fluctuating B site coincides with the donor (acceptor) energy.Comment: 5 pages, 3 figure

Genome-Wide Requirements for Resistance to Functionally Distinct DNA-Damaging Agents

The mechanistic and therapeutic differences in the cellular response to DNA-damaging compounds are not completely understood, despite intense study. To expand our knowledge of DNA damage, we assayed the effects of 12 closely related DNA-damaging agents on the complete pool of ~4,700 barcoded homozygous deletion strains of Saccharomyces cerevisiae. In our protocol, deletion strains are pooled together and grown competitively in the presence of compound. Relative strain sensitivity is determined by hybridization of PCR-amplified barcodes to an oligonucleotide array carrying the barcode complements. These screens identified genes in well-characterized DNA-damage-response pathways as well as genes whose role in the DNA-damage response had not been previously established. High-throughput individual growth analysis was used to independently confirm microarray results. Each compound produced a unique genome-wide profile. Analysis of these data allowed us to determine the relative importance of DNA-repair modules for resistance to each of the 12 profiled compounds. Clustering the data for 12 distinct compounds uncovered both known and novel functional interactions that comprise the DNA-damage response and allowed us to define the genetic determinants required for repair of interstrand cross-links. Further genetic analysis allowed determination of epistasis for one of these functional groups

Star Routing: Between Vehicle Routing and Vertex Cover

We consider an optimization problem posed by an actual newspaper company, which consists of computing a minimum length route for a delivery truck, such that the driver only stops at street crossings, each time delivering copies to all customers adjacent to the crossing. This can be modeled as an abstract problem that takes an unweighted simple graph $G = (V, E)$ and a subset of edges $X$ and asks for a shortest cycle, not necessarily simple, such that every edge of $X$ has an endpoint in the cycle. We show that the decision version of the problem is strongly NP-complete, even if $G$ is a grid graph. Regarding approximate solutions, we show that the general case of the problem is APX-hard, and thus no PTAS is possible unless P $=$ NP. Despite the hardness of approximation, we show that given any $\alpha$-approximation algorithm for metric TSP, we can build a $3\alpha$-approximation algorithm for our optimization problem, yielding a concrete $9/2$-approximation algorithm. The grid case is of particular importance, because it models a city map or some part of it. A usual scenario is having some neighborhood full of customers, which translates as an instance of the abstract problem where almost every edge of $G$ is in $X$. We model this property as $|E - X| = o(|E|)$, and for these instances we give a $(3/2 + \varepsilon)$-approximation algorithm, for any $\varepsilon > 0$, provided that the grid is sufficiently big.Comment: Accepted to the 12th Annual International Conference on Combinatorial Optimization and Applications (COCOA'18