Extremal Results for Directed Tree Connectivity

Odontopleura (Trilobita, Silurian), and a method of constrained congruency analysis

Journal of Paleontology ◽

10.1017/s0022336000042645 ◽

1990 ◽

Vol 64 (4) ◽

pp. 600-614 ◽

Cited By ~ 13

Author(s):

Jonathan M. Adrain ◽

Brian D. E. Chatterton

Keyword(s):

Cladistic Analysis ◽

Canadian Arctic ◽

Wide Distribution ◽

Parsimony Analysis ◽

Directed Tree ◽

Shelf Slope ◽

Major Species ◽

Species Groups ◽

The Universe ◽

A New Species

Odontopleura (Odontopleura) arctica, a new species of odontopleurine trilobite, is described from the Canadian Arctic. A method of cladistic analysis is detailed. Parsimony analysis should be performed treating all characters as unordered. The universe of directed trees implied by the resulting rootless network(s) can then be examined and a preferred tree selected by a criterion of congruency. Namely, the most parsimonious directed tree that accommodates the most congruent arrangement of character-states should be taken as the preferred cladogram. Since this is essentially a general congruency method operating within the constraints of parsimony, it is termed “constrained congruency.” The method is applied to the genus Odontopleura, resulting in the recognition of two major species groups, the nominate subgenus and Sinespinaspis n. subgen. Odontopleura (Ivanopleura) dufrenoyi Barrande is tentatively included in the genus, but considered too poorly known for cladistic analysis. Species assigned to Odontopleura (Odontopleura) include Odontopleura ovata Emmrich, Odontopleura brevigena Chatterton and Perry, Odontopleura (Odontopleura) arctica n. sp., and Diacanthaspis serotina Apollonov. Species assigned to Sinespinaspis n. subgen. include Taemasaspis llandoveryana Šnajdr, Odontopleura greenwoodi Chatterton and Perry, Odontopleura maccallai Chatterton and Perry, and Odontopleura nehedensis Chatterton and Perry. Odontopleura bombini Chatterton and Perry is tentatively placed in synonymy with Odontopleura nehedensis. The genus had a wide distribution throughout the Early and Middle Silurian, due to preferences for deep-water, distal shelf or shelf-slope transition zone habitats.

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Falsification of Hybrid Systems Using Adaptive Probabilistic Search

ACM Transactions on Modeling and Computer Simulation ◽

10.1145/3459605 ◽

2021 ◽

Vol 31 (3) ◽

pp. 1-22

Author(s):

Gidon Ernst ◽

Sean Sedwards ◽

Zhenya Zhang ◽

Ichiro Hasuo

Keyword(s):

Hybrid Systems ◽

Input Signal ◽

Tree Search ◽

Single Trial ◽

Decision Point ◽

Directed Tree ◽

Probabilistic Choice ◽

Original Algorithm ◽

Fine Grained ◽

Probabilistic Search

We present and analyse an algorithm that quickly finds falsifying inputs for hybrid systems. Our method is based on a probabilistically directed tree search, whose distribution adapts to consider an increasingly fine-grained discretization of the input space. In experiments with standard benchmarks, our algorithm shows comparable or better performance to existing techniques, yet it does not build an explicit model of a system. Instead, at each decision point within a single trial, it makes an uninformed probabilistic choice between simple strategies to extend the input signal by means of exploration or exploitation. Key to our approach is the way input signal space is decomposed into levels, such that coarse segments are more probable than fine segments. We perform experiments to demonstrate how and why our approach works, finding that a fully randomized exploration strategy performs as well as our original algorithm that exploits robustness. We propose this strategy as a new baseline for falsification and conclude that more discriminative benchmarks are required.

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Distributed Function Computation Over a Rooted Directed Tree

IEEE Transactions on Information Theory ◽

10.1109/tit.2016.2530398 ◽

2016 ◽

Vol 62 (12) ◽

pp. 7135-7152 ◽

Cited By ~ 7

Author(s):

Milad Sefidgaran ◽

Aslan Tchamkerten

Keyword(s):

Directed Tree ◽

Function Computation ◽

Distributed Function Computation

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Introducing Directed Tree Width

Electronic Notes in Discrete Mathematics ◽

10.1016/s1571-0653(05)80061-7 ◽

1999 ◽

Vol 3 ◽

pp. 222-229 ◽

Cited By ~ 26

Author(s):

B. Reed

Keyword(s):

Directed Tree ◽

Tree Width

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Consistent Allocation of Emission Responsibility in Fossil Fuel Supply Chains

Management Science ◽

10.1287/mnsc.2020.3874 ◽

2021 ◽

Author(s):

Sanjith Gopalakrishnan ◽

Daniel Granot ◽

Frieda Granot

Keyword(s):

Supply Chain ◽

Supply Chains ◽

Fossil Fuel ◽

Subgame Perfect Equilibrium ◽

Polynomial Time Algorithm ◽

Noncooperative Game ◽

Theoretic Model ◽

Directed Tree ◽

Implementation Framework ◽

Fuel Supply

Since 2016, Canada’s federal government has pledged to factor in upstream emissions during the environmental impact assessment of fossil fuel energy projects. The upstream emissions attributable to a proposed project could be compared against a rejection threshold—a maximum permissible level of emissions—or the firm could be mandated to offset the attributed emissions. We adopt a cooperative game-theoretic model and propose the nucleolus mechanism to apportion upstream emission responsibilities in a fossil fuel supply chain, represented by a directed tree, wherein the nodes correspond to various entities in the supply chain such as extractors, distributors, refineries, and end consumers. The nucleolus allocation avoids the distortionary effects of double counting and exhibits a certain consistency property that is especially important in a regulatory context wherein fossil fuel supply chains span multiple legal jurisdictions. We develop a polynomial-time algorithm to compute the nucleolus and further prove that it arises as the unique subgame perfect equilibrium allocation of a noncooperative game induced by two easily stated and verifiable policies, thereby providing an implementation framework. We then demonstrate the strong Nash stability of the nucleolus mechanism subject to the two policies, study its sensitivity to parameter changes, and characterize it on the basis of fairness considerations. Furthermore, under the common assumption that the emissions allocated to a firm and the resulting financial penalties do not impact the revenues from the firm’s core operations, we also provide lower-bound guarantees on the welfare gains it delivers to firms in the fossil fuel supply chain and on the incentives it offers such firms to adopt emission abatement technologies. Finally, we contextualize our discussion with a case study on a proposed expansion of the Trans Mountain pipeline in Western Canada. This paper was accepted by Chung Piaw Teo, optimization.

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