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Uniqueness and minimal obstructions for tree-depth

Michael D. Barrus, John Sinkovic
2016 Discrete Mathematics  
The tree-depth of G is the smallest value of k for which a k-ranking of G exists. The graph G is k-critical if it has tree-depth k and every proper minor of G has smaller tree-depth.  ...  Generalizing a previously known construction for trees, we exhibit an inductive construction that uses 1-unique k-critical graphs to generate large classes of critical graphs having a given tree-depth.  ...  Proof. eny rnking of G in whih single vertex hs rnk I is lso rnking for G − eF Theorem 3.5. Every 1-unique graph with tree-depth k has a k-critical spanning subgraph.  ... 
doi:10.1016/j.disc.2015.09.027 fatcat:qivi4kfy4zhardj2tf74kfnxcq

Minimal obstructions for tree-depth: A non-1-unique example [article]

Michael D. Barrus, John Sinkovic
2016 arXiv   pre-print
Sinkovic, Uniqueness and minimal obstructions for tree-depth, Discrete Math 339 (2) (2015) 606-613], a graph G is 1-unique if for every vertex v in G, there exists an optimal ranking of G in which v is  ...  The tree-depth of G is the smallest value of k for which a k-ranking of G exists. The graph G is k-critical if it has tree-depth k and every proper minor of G has smaller tree-depth.  ...  For any positive integer a, the graph K a K 2 has tree-depth ⌈3a/2⌉. Proof. The claim is easily verified for a ∈ {1, 2}, so suppose a ≥ 3.  ... 
arXiv:1604.00550v1 fatcat:7tnbcm4fo5gtnbneehcy5ze7lq

Assessing the effect of snow/water obstructions on the measurement of tree seedlings in a large-scale temperate forest inventory

C. W. Woodall, J. A. Westfall, K. Zhu, D. J. Johnson
2013 Forestry (London)  
Given the statistically significant effect of snow/water on seedling abundance estimates, tree regeneration assessments should not include observations obstructed by snow/water depths that exceed minimum  ...  National-scale forest inventories have endeavoured to include holistic measurements of forest health inclusive of attributes such as downed dead wood and tree regeneration that occur in the forest understory  ...  To evaluate the effect of measurement obstructions, depth differences for each plot were used to sequentially incorporate obstructed plots into the sample.  ... 
doi:10.1093/forestry/cpt013 fatcat:nio6myqt4bhf3gmtdn54qz3suu

SAT Backdoors: Depth Beats Size [article]

Jan Dreier, Sebastian Ordyniak, Stefan Szeider
2022 arXiv   pre-print
We base our FPT approximation algorithm on a sophisticated notion of obstructions, extending Mählmann et al.'s obstruction trees in various ways, including the addition of separator obstructions.  ...  This leads to a linear-time algorithm for deciding the satisfiability of formulas of bounded backdoor depth into these classes.  ...  [19] , who introduce obstruction trees for backdoor depth.  ... 
arXiv:2202.08326v1 fatcat:gspo7uttfjfitklditl4frka3q

Forbidden graphs for tree-depth

Zdeněk Dvořák, Archontia C. Giannopoulou, Dimitrios M. Thilikos
2012 European journal of combinatorics (Print)  
We determine these sets for k ≤ 3 for each relation and prove a structural lemma for creating obstructions from simpler ones.  ...  Finally, we prove that each obstruction of G k has at most 2 2 k−1 vertices.  ...  Acknowledgements The first author was supported by the ERC starting grant CCOSA (grant agreement no. 259385), and by the Institute for Theoretical Computer Science (ITI), project 1M0021620808 of the Ministry  ... 
doi:10.1016/j.ejc.2011.09.014 fatcat:4yqltkwhznew3fgs23lx7bjkpe

Study of Attenuation in Vegetation Media and Prediction Model at Microwave Frequencies

Mahmoud Elshayeb
2018 Science Journal of Circuits Systems and Signal Processing  
Also, path geometry and tree geometry are among other parameters under consideration.  ...  This paper presents the First report of an ongoing to study the effects of trees on radio signals at microwave frequencies.  ...  conducted on a grove of trees at mill metric frequencies (9.5GHz -57.6GHz) over a depth of less than 200m for in-leaf and out-of-leaf.  ... 
doi:10.11648/j.cssp.20180701.11 fatcat:ii4sgout2zedneyaiyduq4vjfa

Hydraulic Research for Lateral Plant Obstruction in an Open Channel

Tomasz Tymiński, Krzysztof Wolski, Maciej Gruszczyński, Jianxin Xia, Huatang Ren, Nijun Yao
2019 Journal of Ecological Engineering  
The coefficient of water discharge for the fascine overfall case assumed for the plant obstruction was determined as well.  ...  The plant element was formed by natural deciduous and coniferous tree branches filling the space between tree trunks set in chequered pattern.  ...  For this type of plant obstruction described above, the coefficient of local resistances ζ was determined.  ... 
doi:10.12911/22998993/99786 fatcat:in5grutyq5dvhkvjlrrkustxly

Analysis of Q-learning with random exploration for selection of auxiliary objectives in random local search

Maxim Buzdalov, Arina Buzdalova
2015 2015 IEEE Congress on Evolutionary Computation (CEC)  
For the evolutionary algorithm, we consider the Random Local Search. In our setting, ONEMAX problem should be solved in the presence of the obstructive ZEROMAX objective.  ...  We perform theoretical analysis for a previously proposed method of enhancing performance of an evolutionary algorithm with reinforcement learning.  ...  Proof: Let us define the E(root) for the optimal δbounded strategy for a truncated algorithm tree of depth D as E low (D).  ... 
doi:10.1109/cec.2015.7257102 dblp:conf/cec/BuzdalovB15 fatcat:ulu4g4omxzg45dqexn6crg24cy

Assistance of CT/MR images to plan for one-stage stent placement in biliary obstructions

Vasileios Souftas, Antonios Kozadinos, Michalis Mantatzis, Panos Prassopoulos
2009 Diagnostic and Interventional Radiology  
an indication for percutaneous external biliary drainage or stenting.  ...  Axial CT or MR images, which were obtained during deep expiration, were used to establish the entrance site on the patient's skin, the direction of needle insertion, and the depth of the puncture.  ...  This anatomic information is important for a success-ful and uncomplicated percutaneous puncture of the biliary tree.  ... 
doi:10.4261/1305-3825.dir.1758-08.2 pmid:20658449 fatcat:iahkysmhwvcynpfijgewlyogoq

Staging of cholangiocarcinoma: the role of endoscopy

E.A.J. Rauws, J.J. Kloek, D.J. Gouma, T.M. Van Gulik
2008 HPB  
Endoscopic retrograde cholangiopancreaticography (ERCP) often only shows the ducts below the obstruction, and visualization of an obstructed part of the biliary tree is often not possible.  ...  The main question for staging is resectability, which is reliant on vascular, longitudinal, and metastatic spread.  ...  Endoscopic retrograde cholangiopancreaticography (ERCP) often only shows the ducts below the obstruction, and visualization of an obstructed part of the biliary tree is often not possible.  ... 
doi:10.1080/13651820801992591 pmid:18773066 pmcid:PMC2504387 fatcat:lhv4q7va75clrp3i6vgeqmakfe

Page 165 of Johns Hopkins University Studies in Historical and Political Science Vol. 20, Issue 4 [page]

1902 Johns Hopkins University Studies in Historical and Political Science  
From Florence to the foot of Bee Tree Shoals (30 miles).— The obstructions here found are the Bee Tree and Colbert Shoals which begin about twenty-two miles below Florence and extend a distance of eight  ...  From the foot of Bee Tree Shoals to Paducah, Kentucky.— Along this section of the river comparatively little has been expended owing to the attention attracted to the more serious obstructions above.  ... 

Effect of Floodplain Obstructions on the Discharge Conveyance Capacity of Compound Channels

Saad Mulahasan, Thorsten Stoesser, Richard McSherry
2017 Journal of irrigation and drainage engineering  
channel for a given flow rate.  ...  It was shown that the obstruction configuration significantly influences the flow velocity in the main channel, and in the case of one-line obstructions the floodplain velocity is higher than for an unobstructed  ...  The mean increase in the water depth is 15.88%, 15.13% and 13.1% for dense, medium and sparse obstruction densities respectively.  ... 
doi:10.1061/(asce)ir.1943-4774.0001240 fatcat:5hrkdlgf4ng6znxths465wyllm

Page 13 of The New England Journal of Medicine Vol. 254, Issue 5 [page]

1956 The New England Journal of Medicine  
Excessive tracheobronchial secretions, tracheobronchitis and contamination by resistant bacteria all create respira- tory obstruction at a deeper level of the tracheobron- chial tree that cannot be completely  ...  was not were directly from dry nurse or doctor usually turned on the suction pump introduced the catheter through the tracheotomy and advanced the catheter to varying depths of the tra cheobronchial tree  ... 

Collateral pulmonary respiration of Van Allen. A forgotten essential physiological mechanism for the clearance of bronchiolar blocks

A M Gardner
1983 Bristol medico-chirurgical journal (1963)  
Coughing and muco-ciliary clearance are the most important mechanisms in clearing obstructions in the bronchial tree, but they do not themselves explain how the smaller airways can be unblocked for terminal  ...  Lobar emphysema followed valvular obstruction of lobar bronchi, but no emphysema resulted from this type of obstruction in the primary intra-lobar divisions of the bronchial tree.5 Van Allen extended his  ...  important mechanisms in clearing obstructions in the bronchial tree, but they do not themselves explain how the smaller airways can be unblocked for terminal bronchioles have only cuboidal epithelium and  ... 
pmid:6616291 pmcid:PMC5077046 fatcat:ls5zxzmfozga3dww5xseqmth54

Page 152 of JAMA Otolaryngology - Head & Neck Surgery Vol. 54, Issue 2 [page]

1951 JAMA Otolaryngology - Head & Neck Surgery  
Mechanical Obstruction of the Airway.—This occurs from vocal-cord spasm and obstruction of the tracheobronchial tree by secretion.  ...  Respiration may become irreg:lar in rate, depth, and rhythm. Periods of apnea then intervene.  ... 
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