scholarly journals Generalized Fitch Graphs III: Symmetrized Fitch maps and Sets of Symmetric Binary Relations that are explained by Unrooted Edge-labeled Trees

2021 ◽  
Vol vol. 23 no. 1 (Graph Theory) ◽  
Author(s):  
Marc Hellmuth ◽  
Carsten R. Seemann ◽  
Peter F. Stadler
Keyword(s):  
Natural Generalization ◽  
Formal Models ◽  
Binary Relations ◽  
Transfer Event ◽  
Graph Representations ◽  
Labeled Trees ◽  
Unique Path ◽  
Alternative Characterization ◽  
Np Complete

Binary relations derived from labeled rooted trees play an import role in mathematical biology as formal models of evolutionary relationships. The (symmetrized) Fitch relation formalizes xenology as the pairs of genes separated by at least one horizontal transfer event. As a natural generalization, we consider symmetrized Fitch maps, that is, symmetric maps $\varepsilon$ that assign a subset of colors to each pair of vertices in $X$ and that can be explained by a tree $T$ with edges that are labeled with subsets of colors in the sense that the color $m$ appears in $\varepsilon(x,y)$ if and only if $m$ appears in a label along the unique path between $x$ and $y$ in $T$. We first give an alternative characterization of the monochromatic case and then give a characterization of symmetrized Fitch maps in terms of compatibility of a certain set of quartets. We show that recognition of symmetrized Fitch maps is NP-complete. In the restricted case where $|\varepsilon(x,y)|\leq 1$ the problem becomes polynomial, since such maps coincide with class of monochromatic Fitch maps whose graph-representations form precisely the class of complete multi-partite graphs.

scholarly journals Revisiting the Notion of Extension over Incomplete Abstract Argumentation Frameworks

2020 ◽  
Author(s):  
Bettina Fazzinga ◽  
Sergio Flesca ◽  
Filippo Furfaro
Keyword(s):  
Fundamental Notion ◽  
Beneficial Effects ◽  
Abstract Argumentation ◽  
Verification Problem ◽  
Np Complete ◽  
Definition Of

We revisit the notion of i-extension, i.e., the adaption of the fundamental notion of extension to the case of incomplete Abstract Argumentation Frameworks. We show that the definition of i-extension raises some concerns in the "possible" variant, e.g., it allows even conflicting arguments to be collectively considered as members of an (i-)extension. Thus, we introduce the alternative notion of i*-extension overcoming the highlighted problems, and provide a thorough complexity characterization of the corresponding verification problem. Interestingly, we show that the revisitation not only has beneficial effects for the semantics, but also for the complexity: under various semantics, the verification problem under the possible perspective moves from NP-complete to P.

scholarly journals ON THE PARTITION MONOID AND SOME RELATED SEMIGROUPS

2010 ◽  
Vol 83 (2) ◽  
pp. 273-288 ◽  
Author(s):  
D. G. FITZGERALD ◽  
KWOK WAI LAU
Keyword(s):  
Transformation Semigroup ◽  
Galois Connection ◽  
Inverse Semigroups ◽  
Natural Order ◽  
Binary Relations ◽  
Ideal Lattices ◽  
New Interpretation ◽  
Semigroup Of Transformations ◽  
The Ideal

AbstractThe partition monoid is a salient natural example of a *-regular semigroup. We find a Galois connection between elements of the partition monoid and binary relations, and use it to show that the partition monoid contains copies of the semigroup of transformations and the symmetric and dual-symmetric inverse semigroups on the underlying set. We characterize the divisibility preorders and the natural order on the (straight) partition monoid, using certain graphical structures associated with each element. This gives a simpler characterization of Green’s relations. We also derive a new interpretation of the natural order on the transformation semigroup. The results are also used to describe the ideal lattices of the straight and twisted partition monoids and the Brauer monoid.

Classification Trees as Proxies

2015 ◽  
Vol 2 (2) ◽  
pp. 31-44 ◽  
Author(s):  
Anthony Scime ◽  
Nilay Saiya ◽  
Gregg R. Murray ◽  
Steven J. Jurek
Keyword(s):  
Data Analysis ◽  
Classification Trees ◽  
Original Model ◽  
Classification Model ◽  
Model Based ◽  
Alternative Characterization

In data analysis, when data are unattainable, it is common to select a closely related attribute as a proxy. But sometimes substitution of one attribute for another is not sufficient to satisfy the needs of the analysis. In these cases, a classification model based on one dataset can be investigated as a possible proxy for another closely related domain's dataset. If the model's structure is sufficient to classify data from the related domain, the model can be used as a proxy tree. Such a proxy tree also provides an alternative characterization of the related domain. Just as important, if the original model does not successfully classify the related domain data the domains are not as closely related as believed. This paper presents a methodology for evaluating datasets as proxies along with three cases that demonstrate the methodology and the three types of results.

scholarly journals Structural Transformation, the Mismeasurement of Productivity Growth, and the Cost Disease of Services

2014 ◽  
Vol 104 (11) ◽  
pp. 3635-3667 ◽  
Author(s):  
Alwyn Young
Keyword(s):  
Productivity Growth ◽  
Developed Economies ◽  
Goods And Services ◽  
Employment Share ◽  
Alternative Characterization ◽  
The Difference ◽  
The Cost ◽  
Relative Productivity ◽  
Absolute Advantage

If workers self-select into industries based upon their relative productivity in different tasks, and comparative advantage is aligned with absolute advantage, then the average efficacy of a sector's workforce will be negatively correlated with its employment share. This might explain the difference in the reported productivity growth of contracting goods and expanding services. Instrumenting with defense expenditures, I find the elasticity of worker efficacy with respect to employment shares is substantially negative, albeit estimated imprecisely. The estimates suggest that the view that goods and services have similar productivity growth rates is a plausible alternative characterization of growth in developed economies. (JEL E23, E24, H56, J24, O41, O47)

scholarly journals Sequentially Rationalizable Choice

2007 ◽  
Vol 97 (5) ◽  
pp. 1824-1839 ◽  
Author(s):  
Paola Manzini ◽  
Marco Mariotti
Keyword(s):  
Choice Function ◽  
Binary Relations ◽  
Choice Functions ◽  
Choice Problem ◽  
Full Characterization ◽  
Human Choice ◽  
Fixed Set ◽  
Rationalizable Choice

A sequentially rationalizable choice function is a choice function that can be retrieved by applying sequentially to each choice problem the same fixed set of asymmetric binary relations (rationales) to remove inferior alternatives. These concepts translate into economic language some human choice heuristics studied in psychology and explain cyclical patterns of choice observed in experiments. We study some properties of sequential rationalizability and provide a full characterization of choice functions rationalizable by two and three rationales. (JEL D01).

scholarly journals Alternative characterization of the nematic transition in deposition of rods on two-dimensional lattices

2020 ◽  
Vol 101 (2) ◽  
Author(s):  
E. E. Vogel ◽  
G. Saravia ◽  
A. J. Ramirez-Pastor ◽  
Marcelo Pasinetti
Keyword(s):  
Two Dimensional ◽  
Alternative Characterization

scholarly journals Computing the Interleaving Distance is NP-Hard

2019 ◽  
Vol 20 (5) ◽  
pp. 1237-1271 ◽  
Author(s):  
Håvard Bakke Bjerkevik ◽  
Magnus Bakke Botnan ◽  
Michael Kerber
Keyword(s):  
Computational Complexity ◽  
Complete Characterization ◽  
Np Hard ◽  
Slight Improvement ◽  
Approximation Factor ◽  
Distance Computation ◽  
Persistence Modules ◽  
Np Complete ◽  
Interleaving Distance

Abstract We show that computing the interleaving distance between two multi-graded persistence modules is NP-hard. More precisely, we show that deciding whether two modules are 1-interleaved is NP-complete, already for bigraded, interval decomposable modules. Our proof is based on previous work showing that a constrained matrix invertibility problem can be reduced to the interleaving distance computation of a special type of persistence modules. We show that this matrix invertibility problem is NP-complete. We also give a slight improvement in the above reduction, showing that also the approximation of the interleaving distance is NP-hard for any approximation factor smaller than 3. Additionally, we obtain corresponding hardness results for the case that the modules are indecomposable, and in the setting of one-sided stability. Furthermore, we show that checking for injections (resp. surjections) between persistence modules is NP-hard. In conjunction with earlier results from computational algebra this gives a complete characterization of the computational complexity of one-sided stability. Lastly, we show that it is in general NP-hard to approximate distances induced by noise systems within a factor of 2.

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