scholarly journals On Grounded L-Graphs and their Relatives

10.37236/8096 ◽  
2019 ◽  
Vol 26 (3) ◽  
Author(s):  
Vít Jelínek ◽  
Martin Töpfer
Keyword(s):  
Horizontal Line ◽  
String Graphs ◽  
Graph Classes ◽  
Tolerance Graphs ◽  
Vertex Ordering ◽  
Forbidden Patterns

We consider the graph classes Grounded-L and Grounded-{𝖫,⅃} corresponding to graphs that admit an intersection representation by 𝖫-shaped curves (or 𝖫-shaped and ⅃-shaped curves, respectively), where additionally the topmost points of each curve are assumed to belong to a common horizontal line. We prove that Grounded-L graphs admit an equivalent characterisation in terms of vertex ordering with forbidden patterns. We also compare these classes to related intersection classes, such as the grounded segment graphs, the monotone 𝖫-graphs (a.k.a. max point-tolerance graphs), or the outer-1-string graphs. We give constructions showing that these classes are all distinct and satisfy only trivial or previously known inclusions.

scholarly journals Graph Classes and Forbidden Patterns on Three Vertices

2021 ◽  
Vol 35 (1) ◽  
pp. 55-90
Author(s):  
Laurent Feuilloley ◽  
Michel Habib
Keyword(s):  
Graph Classes ◽  
Forbidden Patterns

Tolerance Graphs

2004 ◽  
Author(s):  
Martin Charles Golumbic ◽  
Ann N. Trenk
Keyword(s):  
Tolerance Graphs

scholarly journals A Lower Bound for the Query Phase of Contraction Hierarchies and Hub Labels and a Provably Optimal Instance-Based Schema

Algorithms ◽  
2021 ◽  
Vol 14 (6) ◽  
pp. 164
Author(s):  
Tobias Rupp ◽  
Stefan Funke
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Real World ◽  
Road Network ◽  
Upper And Lower Bounds ◽  
Bounded Degree ◽  
Shortest Path Routing ◽  
Graph Classes ◽  
Speed Up ◽  
To Come

We prove a Ω(n) lower bound on the query time for contraction hierarchies (CH) as well as hub labels, two popular speed-up techniques for shortest path routing. Our construction is based on a graph family not too far from subgraphs that occur in real-world road networks, in particular, it is planar and has a bounded degree. Additionally, we borrow ideas from our lower bound proof to come up with instance-based lower bounds for concrete road network instances of moderate size, reaching up to 96% of an upper bound given by a constructed CH. For a variant of our instance-based schema applied to some special graph classes, we can even show matching upper and lower bounds.

scholarly journals A Mutual Capacitance Touch Readout IC with Synchronization in Touch and Mobile Display Driving for High Refresh Rate AMOLED Panels

Micromachines ◽  
2021 ◽  
Vol 12 (8) ◽  
pp. 922
Author(s):  
Seunghoon Ko
Keyword(s):  
System Architecture ◽  
Noise Suppression ◽  
Touch Screen ◽  
Horizontal Line ◽  
Time Sharing ◽  
Refresh Rate ◽  
Front End ◽  
Scan Rate ◽  
Mutual Capacitance ◽  
Analog Voltage

This paper presents a mutual capacitance touch readout IC architecture for 120 Hz high-refresh-rate AMOLED displays. In high-refresh-rate AMOLED panels, whole pixels in a horizontal line should be updated without any time-sharing with each other, leading to an amplified display noise on touch screen panel (TSP) electrodes. The proposed system architecture mitigates severe display noise by synchronizing the driving for the TSP and AMOLED pixel circuits. The proposed differential sensing technique, which is based on noise suppression in reference to mutual capacitance channels, minimizes common-mode display noise. In the front-end circuit, intrinsic circuit offset is cancelled by a chopping scheme, which correlates to the phase of the driving signals in the TSP driver and operating clocks of the front-end. Operating at a 120 Hz scan-rate, it reduces display noise by more than 11.6 dB when compared with the conventional single-ended TSP sensing method. With a built-in 130-nm CMOS, a prototype IC occupies an area of 8.02 mm2 while consuming 6.4-mW power from a 3.3 V analog voltage supply.

scholarly journals Isomorphism, canonization, and definability for graphs of bounded rank width

2021 ◽  
Vol 64 (5) ◽  
pp. 98-105
Author(s):  
Martin Grohe ◽  
Daniel Neuen
Keyword(s):  
Fixed Point ◽  
Complexity Theory ◽  
Polynomial Time ◽  
Graph Isomorphism ◽  
Isomorphism Problem ◽  
Descriptive Complexity ◽  
Graph Isomorphism Problem ◽  
Structural Graph ◽  
Graph Classes ◽  
Bounded Rank

We investigate the interplay between the graph isomorphism problem, logical definability, and structural graph theory on a rich family of dense graph classes: graph classes of bounded rank width. We prove that the combinatorial Weisfeiler-Leman algorithm of dimension (3 k + 4) is a complete isomorphism test for the class of all graphs of rank width at most k. A consequence of our result is the first polynomial time canonization algorithm for graphs of bounded rank width. Our second main result addresses an open problem in descriptive complexity theory: we show that fixed-point logic with counting expresses precisely the polynomial time properties of graphs of bounded rank width.

scholarly journals Unsplit superconducting and time reversal symmetry breaking transitions in Sr2RuO4 under hydrostatic pressure and disorder

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Vadim Grinenko ◽  
Debarchan Das ◽  
Ritu Gupta ◽  
Bastian Zinkl ◽  
Naoki Kikugawa ◽  
...  
Keyword(s):  
Hydrostatic Pressure ◽  
Symmetry Breaking ◽  
Time Reversal ◽  
Order Parameter ◽  
Muon Spin Rotation ◽  
Horizontal Line ◽  
Time Reversal Symmetry ◽  
Zero Field ◽  
Symmetry Protected ◽  
Line Node

AbstractThere is considerable evidence that the superconducting state of Sr2RuO4 breaks time reversal symmetry. In the experiments showing time reversal symmetry breaking, its onset temperature, TTRSB, is generally found to match the critical temperature, Tc, within resolution. In combination with evidence for even parity, this result has led to consideration of a dxz ± idyz order parameter. The degeneracy of the two components of this order parameter is protected by symmetry, yielding TTRSB = Tc, but it has a hard-to-explain horizontal line node at kz = 0. Therefore, s ± id and d ± ig order parameters are also under consideration. These avoid the horizontal line node, but require tuning to obtain TTRSB ≈ Tc. To obtain evidence distinguishing these two possible scenarios (of symmetry-protected versus accidental degeneracy), we employ zero-field muon spin rotation/relaxation to study pure Sr2RuO4 under hydrostatic pressure, and Sr1.98La0.02RuO4 at zero pressure. Both hydrostatic pressure and La substitution alter Tc without lifting the tetragonal lattice symmetry, so if the degeneracy is symmetry-protected, TTRSB should track changes in Tc, while if it is accidental, these transition temperatures should generally separate. We observe TTRSB to track Tc, supporting the hypothesis of dxz ± idyz order.

scholarly journals The definition of an atmospheric database for Aeolus

2011 ◽  
Vol 4 (1) ◽  
pp. 67-88 ◽  
Author(s):  
G. J. Marseille ◽  
K. Houchi ◽  
J. de Kloe ◽  
A. Stoffelen
Keyword(s):  
High Resolution ◽  
Meteorological Data ◽  
Sampling Strategy ◽  
Laser Wavelength ◽  
Geographic Region ◽  
Atmospheric Dynamics ◽  
Specific Humidity ◽  
Small Scale ◽  
Horizontal Line ◽  
Definition Of

Abstract. The definition of an atmospheric database is an important component of simulation studies in preparation of future earth observing remote sensing satellites. The Aeolus mission, formerly denoted Atmospheric Dynamics Mission (ADM) or ADM-Aeolus, is scheduled for launch end of 2013 and aims at measuring profiles of single horizontal line-of-sight (HLOS) wind components from the surface up to about 32 km with a global coverage. The vertical profile resolution is limited but may be changed during in-orbit operation. This provides the opportunity of a targeted sampling strategy, e.g., as a function of geographic region. Optimization of the vertical (and horizontal) sampling strategy requires a characterization of the atmosphere optical and dynamical properties, more in particular the distribution of atmospheric particles and their correlation with the atmospheric dynamics. The Aeolus atmospheric database combines meteorological data from the ECMWF model with atmosphere optical properties data from CALIPSO. An inverse algorithm to retrieve high-resolution particle backscatter from the CALIPSO level-1 attenuated backscatter product is presented. Global weather models tend to underestimate atmospheric wind variability. A procedure is described to ensure compatibility of the characteristics of the database winds with those from high-resolution radiosondes. The result is a high-resolution database of zonal, meridional and vertical wind, temperature, specific humidity and particle and molecular backscatter and extinction at 355 nm laser wavelength. This allows the simulation of small-scale atmospheric processes within the Aeolus observation sampling volume and their impact on the quality of the retrieved HLOS wind profiles. The database extends over four months covering all seasons. This allows a statistical evaluation of the mission components under investigation. The database is currently used for the development of the Aeolus wind processing, the definition of wind calibration strategies and the optimization of the Aeolus sampling strategy.

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