scholarly journals Testing the Agreement of Trees with Internal Labels

2021 ◽  
Author(s):  
David Fernández-Baca ◽  
Lei Liu
Keyword(s):  
Phylogenetic Trees ◽  
Worst Case ◽  
Labeled Trees ◽  
Number Of Children ◽  
Phylogenetic Studies ◽  
Overlapping Sets ◽  
Special Case ◽  
Labeled Tree ◽  
Agreement Problem ◽  
Better Than

Abstract Background: A semi-labeled tree is a tree where all leaves as well as, possibly, some internal nodes are labeledwith taxa. Semi-labeled trees encompass ordinary phylogenetic trees and taxonomies. Suppose we are given a collection P = {T1, T2, . . . , Tk} of semi-labeled trees, called input trees, over partially overlapping sets of taxa. The agreement problem asks whether there exists a tree T , called an agreement tree, whose taxon set is the union of the taxon sets of the input trees such that the restriction of T to the taxon set of Ti is isomorphic to i, for each i ε 1, 2, . . . , k . The agreement problems is a special case of the supertree problem, the problem of synthesizing a collection of phylogenetic trees with partially overlapping taxon sets into a single supertree that represents the information in the input trees. An obstacle to building large phylogenetic supertrees is the limited amount of taxonomic overlap among the phylogenetic studies from which the input trees are obtained. Incorporating taxonomies into supertree analyses can alleviate this issue. Results: We give a O(nk(i∈[k]di + log2(nk))) algorithm for the agreement problem, where n is the total number of distinct taxa in P, k is the number of trees in P, and di is the maximum number of children of a node in Ti. Our computational experience with the algorithm suggests that its performance in practice is much better than its worst-case bound indicates.

scholarly journals Testing the agreement of trees with internal labels

2021 ◽  
Vol 16 (1) ◽  
Author(s):  
David Fernández-Baca ◽  
Lei Liu
Keyword(s):  
Phylogenetic Trees ◽  
Worst Case ◽  
Labeled Trees ◽  
Number Of Children ◽  
Phylogenetic Studies ◽  
Overlapping Sets ◽  
Special Case ◽  
Labeled Tree ◽  
Agreement Problem ◽  
Better Than

Abstract Background A semi-labeled tree is a tree where all leaves as well as, possibly, some internal nodes are labeled with taxa. Semi-labeled trees encompass ordinary phylogenetic trees and taxonomies. Suppose we are given a collection $${\mathcal {P}}= \{{\mathcal {T}}_1, {\mathcal {T}}_2, \ldots , {\mathcal {T}}_k\}$$ P = { T 1 , T 2 , … , T k } of semi-labeled trees, called input trees, over partially overlapping sets of taxa. The agreement problem asks whether there exists a tree $${\mathcal {T}}$$ T , called an agreement tree, whose taxon set is the union of the taxon sets of the input trees such that the restriction of $${\mathcal {T}}$$ T to the taxon set of $${\mathcal {T}}_i$$ T i is isomorphic to $${\mathcal {T}}_i$$ T i , for each $$i \in \{1, 2, \ldots , k\}$$ i ∈ { 1 , 2 , … , k } . The agreement problems is a special case of the supertree problem, the problem of synthesizing a collection of phylogenetic trees with partially overlapping taxon sets into a single supertree that represents the information in the input trees. An obstacle to building large phylogenetic supertrees is the limited amount of taxonomic overlap among the phylogenetic studies from which the input trees are obtained. Incorporating taxonomies into supertree analyses can alleviate this issue. Results We give a $${\mathcal {O}}(n k (\sum _{i \in [k]} d_i + \log ^2(nk)))$$ O ( n k ( ∑ i ∈ [ k ] d i + log 2 ( n k ) ) ) algorithm for the agreement problem, where n is the total number of distinct taxa in $${\mathcal {P}}$$ P , k is the number of trees in $${\mathcal {P}}$$ P , and $$d_i$$ d i is the maximum number of children of a node in $${\mathcal {T}}_i$$ T i . Conclusion Our algorithm can aid in integrating taxonomies into supertree analyses. Our computational experience with the algorithm suggests that its performance in practice is much better than its worst-case bound indicates.

Modeling of Nonlinear Viscoelastic Creep of Polycarbonate

e-Polymers ◽  
2007 ◽  
Vol 7 (1) ◽  
Author(s):  
Wenbo Luo ◽  
Said Jazouli ◽  
Toan Vu-Khanh
Keyword(s):  
Creep Behavior ◽  
Room Temperature ◽  
Multiple Integral ◽  
Model Fit ◽  
Viscoelastic Creep ◽  
Commercial Grade ◽  
Nonlinear Viscoelastic ◽  
Schapery Model ◽  
Special Case ◽  
Better Than

AbstractThe creep behavior of a commercial grade polycarbonate was investigated in this study. 10 different constant stresses ranging from 8 MPa to 50 MPa were applied to the specimen, and the resultant creep strains were measured at room temperature. It was found that the creep could be modeled linearly below 15 MPa, and nonlinearly above 15 MPa. Different nonlinear viscoelastic models have been briefly reviewed and used to fit the test data. It is shown that the Findley model is a special case of the Schapery model, and both the Findley model and the simplified multiple integral representation are suitable for properly describing the creep behavior of the polycarbonate investigated in this paper; however, the Findley model fit the data better than the simplified multiple integral with three terms.

scholarly journals Characterization of Five New Earthworm Mitogenomes (Oligochaeta: Lumbricidae): Mitochondrial Phylogeny of Lumbricidae

Diversity ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 580
Author(s):  
Hongyi Liu ◽  
Yufeng Zhang ◽  
Wei Xu ◽  
Yu Fang ◽  
Honghua Ruan
Keyword(s):  
Phylogenetic Trees ◽  
Mitochondrial Gene ◽  
Morphological Characteristics ◽  
Molecular Techniques ◽  
Phylogenetic Studies ◽  
Octolasion Tyrtaeum ◽  
Eisenia Nordenskioldi ◽  
Novel Strategy

Identification based on conventional morphological characteristics is typically difficult and time-consuming. The development of molecular techniques provides a novel strategy that relies on specific mitochondrial gene fragments to conduct authentication. For this study, five newly sequenced partial mitogenomes of earthworms (Bimastos parvus, Dendrobaena octaedra, Eisenia andrei, Eisenia nordenskioldi, and Octolasion tyrtaeum) with lengths ranging from 14,977 to 15,715 were presented. Each mitogenome possessed a putative control region that resided between tRNA-Arg and tRNA-His. All of the PCGs were under negative selection according to the value of Ka/Ks. The phylogenetic trees supported the classification of Eisenia and Lumbricus; however, the trees based on cox1 did not. Through various comparisons, it was determined that cox1 fragments might be more suitable for molecular identification. These results lay the foundation for further phylogenetic studies on Lumbricidae.

scholarly journals Results on a Super Strong Exponential Time Hypothesis

2020 ◽  
Vol 34 (09) ◽  
pp. 13700-13703
Author(s):  
Nikhil Vyas ◽  
Ryan Williams
Keyword(s):  
Randomized Algorithm ◽  
Time Algorithm ◽  
Critical Threshold ◽  
Polynomial Method ◽  
Variable Ratio ◽  
Sat Solving ◽  
Worst Case ◽  
Exponential Time ◽  
Exponential Time Hypothesis ◽  
Special Case

All known SAT-solving paradigms (backtracking, local search, and the polynomial method) only yield a 2n(1−1/O(k)) time algorithm for solving k-SAT in the worst case, where the big-O constant is independent of k. For this reason, it has been hypothesized that k-SAT cannot be solved in worst-case 2n(1−f(k)/k) time, for any unbounded ƒ : ℕ → ℕ. This hypothesis has been called the “Super-Strong Exponential Time Hypothesis” (Super Strong ETH), modeled after the ETH and the Strong ETH. We prove two results concerning the Super-Strong ETH:1. It has also been hypothesized that k-SAT is hard to solve for randomly chosen instances near the “critical threshold”, where the clause-to-variable ratio is 2k ln 2 −Θ(1). We give a randomized algorithm which refutes the Super-Strong ETH for the case of random k-SAT and planted k-SAT for any clause-to-variable ratio. In particular, given any random k-SAT instance F with n variables and m clauses, our algorithm decides satisfiability for F in 2n(1−Ω( log k)/k) time, with high probability (over the choice of the formula and the randomness of the algorithm). It turns out that a well-known algorithm from the literature on SAT algorithms does the job: the PPZ algorithm of Paturi, Pudlak, and Zane (1998).2. The Unique k-SAT problem is the special case where there is at most one satisfying assignment. It is natural to hypothesize that the worst-case (exponential-time) complexity of Unique k-SAT is substantially less than that of k-SAT. Improving prior reductions, we show the time complexities of Unique k-SAT and k-SAT are very tightly related: if Unique k-SAT is in 2n(1−f(k)/k) time for an unbounded f, then k-SAT is in 2n(1−f(k)(1−ɛ)/k) time for every ɛ > 0. Thus, refuting Super Strong ETH in the unique solution case would refute Super Strong ETH in general.

scholarly journals Managing contamination delay to improve Timing Speculation architectures

2016 ◽  
Vol 2 ◽  
pp. e79 ◽  
Author(s):  
Naga Durga Prasad Avirneni ◽  
Prem Kumar Ramesh ◽  
Arun K. Somani
Keyword(s):  
Performance Improvement ◽  
Short Path ◽  
Performance Enhancement ◽  
Propagation Delay ◽  
Performance Impact ◽  
Worst Case ◽  
Circuit Delay ◽  
Timing Speculation ◽  
Better Than

Timing Speculation (TS) is a widely known method for realizing better-than-worst-case systems. Aggressive clocking, realizable by TS, enable systems to operate beyond specified safe frequency limits to effectively exploit the data dependent circuit delay. However, the range of aggressive clocking for performance enhancement under TS is restricted by short paths. In this paper, we show that increasing the lengths of short paths of the circuit increases the effectiveness of TS, leading to performance improvement. Also, we propose an algorithm to efficiently add delay buffers to selected short paths while keeping down the area penalty. We present our algorithm results for ISCAS-85 suite and show that it is possible to increase the circuit contamination delay by up to 30% without affecting the propagation delay. We also explore the possibility of increasing short path delays further by relaxing the constraint on propagation delay and analyze the performance impact.

scholarly journals The agreement problem for unrooted phylogenetic trees is FPT

2014 ◽  
Vol 18 (3) ◽  
pp. 385-392 ◽  
Author(s):  
Celine Scornavacca ◽  
Leo van Iersel ◽  
Steven Kelk ◽  
David Bryant
Keyword(s):  
Phylogenetic Trees ◽  
Agreement Problem

scholarly journals Hybrid ARIMA and Neural Network Modelling Applied to Telecommunications in Urban Environments in the Amazon Region

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Ramz L. Fraiha Lopes ◽  
Simone G. C. Fraiha ◽  
Vinicius D. Lima ◽  
Herminio S. Gomes ◽  
Gervásio P. S. Cavalcante
Keyword(s):  
Neural Network ◽  
Moving Average ◽  
Urban Environments ◽  
Digital Television ◽  
Network Modelling ◽  
Worst Case ◽  
Autoregressive Integrated Moving Average ◽  
Neural Network Modelling ◽  
Better Than

This study explores the use of a hybrid Autoregressive Integrated Moving Average (ARIMA) and Neural Network modelling for estimates of the electric field along vertical paths (buildings) close to Digital Television (DTV) transmitters. The work was carried out in Belém city, one of the most urbanized cities in the Brazilian Amazon and includes a case study of the application of this modelling within the subscenarios found in Belém. Its results were compared with the ITU recommendations P. 1546-5 and proved to be better in every subscenario analysed. In the worst case, the estimate of the model was approximately 65% better than that of the ITU. We also compared this modelling with a classic modelling technique: the Least Squares (LS) method. In most situations, the hybrid model achieved better results than the LS.

scholarly journals A generalized Robinson-Foulds distance for labeled trees

BMC Genomics ◽  
2020 ◽  
Vol 21 (S10) ◽  
Author(s):  
Samuel Briand ◽  
Christophe Dessimoz ◽  
Nadia El-Mabrouk ◽  
Manuel Lafond ◽  
Gabriela Lobinska
Keyword(s):  
Approximation Algorithm ◽  
Phylogenetic Trees ◽  
Linear Time ◽  
Crucial Aspect ◽  
Labeled Trees ◽  
Link Type

Abstract Background The Robinson-Foulds (RF) distance is a well-established measure between phylogenetic trees. Despite a lack of biological justification, it has the advantages of being a proper metric and being computable in linear time. For phylogenetic applications involving genes, however, a crucial aspect of the trees ignored by the RF metric is the type of the branching event (e.g. speciation, duplication, transfer, etc). Results We extend RF to trees with labeled internal nodes by including a node flip operation, alongside edge contractions and extensions. We explore properties of this extended RF distance in the case of a binary labeling. In particular, we show that contrary to the unlabeled case, an optimal edit path may require contracting “good” edges, i.e. edges shared between the two trees. Conclusions We provide a 2-approximation algorithm which is shown to perform well empirically. Looking ahead, computing distances between labeled trees opens up a variety of new algorithmic directions.Implementation and simulations available at https://github.com/DessimozLab/pylabeledrf.

On the dependence structure of hitting times of univariate processes

1988 ◽  
Vol 25 (02) ◽  
pp. 355-362 ◽  
Author(s):  
Nader Ebrahimi ◽  
T. Ramalingam
Keyword(s):  
Brownian Motion ◽  
Structural Properties ◽  
Hitting Times ◽  
Dependence Structure ◽  
Special Case ◽  
New Better Than Used ◽  
Better Than

Some concepts of dependence have recently been introduced by Ebrahimi (1987) to explore the structural properties of the hitting times of bivariate processes. In this framework, the special case of univariate processes has curious features. New properties are derived for this case. Some applications to sequential inference and inequalities for Brownian motion and new better than used (NBU) processes are also provided.

INFERRING PHYLOGENETIC RELATIONSHIPS AVOIDING FORBIDDEN ROOTED TRIPLETS

2006 ◽  
Vol 04 (01) ◽  
pp. 59-74 ◽  
Author(s):  
YING-JUN HE ◽  
TRINH N. D. HUYNH ◽  
JESPER JANSSON ◽  
WING-KIN SUNG
Keyword(s):  
Approximation Algorithms ◽  
Phylogenetic Tree ◽  
Phylogenetic Trees ◽  
Evolutionary History ◽  
Phylogenetic Network ◽  
Evolutionary Relationships ◽  
Large Set ◽  
Tree Network ◽  
History Of ◽  
Overlapping Sets

To construct a phylogenetic tree or phylogenetic network for describing the evolutionary history of a set of species is a well-studied problem in computational biology. One previously proposed method to infer a phylogenetic tree/network for a large set of species is by merging a collection of known smaller phylogenetic trees on overlapping sets of species so that no (or as little as possible) branching information is lost. However, little work has been done so far on inferring a phylogenetic tree/network from a specified set of trees when in addition, certain evolutionary relationships among the species are known to be highly unlikely. In this paper, we consider the problem of constructing a phylogenetic tree/network which is consistent with all of the rooted triplets in a given set [Formula: see text] and none of the rooted triplets in another given set [Formula: see text]. Although NP-hard in the general case, we provide some efficient exact and approximation algorithms for a number of biologically meaningful variants of the problem.

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