153,886 research outputs found
์ํ๊ณ์์์ ๊ฒฝ์ ๊ด์ ์ผ๋ก ๊ทธ๋ํ์ ์ ํฅ๊ทธ๋ํ์ ๊ตฌ์กฐ ์ฐ๊ตฌ
ํ์๋
ผ๋ฌธ(๋ฐ์ฌ) -- ์์ธ๋ํ๊ต๋ํ์ : ์ฌ๋ฒ๋ํ ์ํ๊ต์ก๊ณผ, 2023. 2. ๊น์๋ น.In this thesis, we study m-step competition graphs, (1, 2)-step competition graphs, phylogeny graphs, and competition-common enemy graphs (CCE graphs), which are primary variants of competition graphs. Cohen [11] introduced the notion of competition graph while studying predator-prey concepts in ecological food webs.An ecosystem is a biological community of interacting species and their physical environment. For each species in an ecosystem, there can be m conditions of the good environment by regarding lower and upper bounds on numerous dimensions such as soil, climate, temperature, etc, which may be represented by an m-dimensional rectangle, so-called an ecological niche. An elemental ecological truth is that two species compete if and only if their ecological niches overlap. Biologists often describe competitive relations among species cohabiting in a community by a food web that is a digraph whose vertices are the species and an arc goes from a predator to a prey. In this context, Cohen [11] defined the competition graph of a digraph as follows. The competition graph C(D) of a digraph D is defined to be a simple graph whose vertex set is the same as V (D) and which has an edge joining two distinct vertices u and v if and only if there are arcs (u, w) and (v, w) for some vertex w in D. Since Cohen introduced this definition, its variants such as m-step competition graphs, (i, j)-step competition graphs, phylogeny graphs, CCE graphs, p-competition graphs, and niche graphs have been introduced and studied.
As part of these studies, we show that the connected triangle-free m-step competition graph on n vertices is a tree and completely characterize the digraphs of order n whose m-step competition graphs are star graphs for positive integers 2 โค m < n.
We completely identify (1,2)-step competition graphs C_{1,2}(D) of orientations D of a complete k-partite graph for some k โฅ 3 when each partite set of D forms a clique in C_{1,2}(D). In addition, we show that the diameter of each component of C_{1,2}(D) is at most three and provide a sharp upper bound on the domination number of C_{1,2}(D) and give a sufficient condition for C_{1,2}(D) being an interval graph.
On the other hand, we study on phylogeny graphs and CCE graphs of degreebounded acyclic digraphs. An acyclic digraph in which every vertex has indegree at most i and outdegree at most j is called an (i, j) digraph for some positive integers i and j. If each vertex of a (not necessarily acyclic) digraph D has indegree at most i and outdegree at most j, then D is called an hi, ji digraph. We give a sufficient condition on the size of hole of an underlying graph of an (i, 2) digraph D for the phylogeny graph of D being a chordal graph where D is an (i, 2) digraph. Moreover, we go further to completely characterize phylogeny graphs of (i, j) digraphs by listing the forbidden induced subgraphs.
We completely identify the graphs with the least components among the CCE graphs of (2, 2) digraphs containing at most one cycle and exactly two isolated vertices, and their digraphs. Finally, we gives a sufficient condition for CCE graphs
being interval graphs.์ด ๋
ผ๋ฌธ์์ ๊ฒฝ์๊ทธ๋ํ์ ์ฃผ์ ๋ณ์ด๋ค ์ค m-step ๊ฒฝ์๊ทธ๋ํ, (1, 2)-step ๊ฒฝ์ ๊ทธ๋ํ, ๊ณํต ๊ทธ๋ํ, ๊ฒฝ์๊ณต์ ๊ทธ๋ํ์ ๋ํ ์ฐ๊ตฌ ๊ฒฐ๊ณผ๋ฅผ ์ข
ํฉํ๋ค. Cohen [11]์ ๋จน์ด์ฌ์ฌ์์ ํฌ์์-ํผ์์ ๊ฐ๋
์ ์ฐ๊ตฌํ๋ฉด์ ๊ฒฝ์๊ทธ๋ํ ๊ฐ๋
์ ๊ณ ์ํ๋ค. ์ํ๊ณ๋ ์ํธ์์ฉํ๋ ์ข
๋ค๊ณผ ๊ทธ๋ค์ ๋ฌผ๋ฆฌ์ ํ๊ฒฝ์ ์๋ฌผํ์ ์ฒด๊ณ์ด๋ค. ์ํ๊ณ์ ๊ฐ ์ข
์ ๋ํด์, ํ ์, ๊ธฐํ, ์จ๋ ๋ฑ๊ณผ ๊ฐ์ ๋ค์ํ ์ฐจ์์ ํ๊ณ ๋ฐ ์๊ณ๋ฅผ ๊ณ ๋ คํ์ฌ ์ข์ ํ๊ฒฝ์ m๊ฐ์ ์กฐ๊ฑด๋ค๋ก ๋ํ๋ผ ์ ์๋๋ฐ ์ด๋ฅผ ์ํ์ ์ง์(ecological niche)๋ผ๊ณ ํ๋ค. ์ํํ์ ๊ธฐ๋ณธ๊ฐ์ ์ ๋ ์ข
์ด ์ํ์ ์ง์๊ฐ ๊ฒน์น๋ฉด ๊ฒฝ์ํ๊ณ (compete), ๊ฒฝ์ํ๋ ๋ ์ข
์ ์ํ์ ์ง์๊ฐ ๊ฒน์น๋ค๋ ๊ฒ์ด๋ค. ํํ ์๋ฌผํ์๋ค์ ํ ์ฒด์ ์์ ์์ํ๋ ์ข
๋ค์ ๊ฒฝ์์ ๊ด๊ณ๋ฅผ ๊ฐ ์ข
์ ๊ผญ์ง์ ์ผ๋ก, ํฌ์์์์ ํผ์์์๊ฒ๋ ์ ํฅ๋ณ(arc)์ ๊ทธ์ด์ ๋จน์ด์ฌ์ฌ๋ก ํํํ๋ค. ์ด๋ฌํ ๋งฅ๋ฝ์์ Cohen [11]์ ๋ค์๊ณผ ๊ฐ์ด ์ ํฅ๊ทธ๋ํ์ ๊ฒฝ์ ๊ทธ๋ํ๋ฅผ ์ ์ํ๋ค. ์ ํฅ๊ทธ๋ํ(digraph) D์ ๊ฒฝ์๊ทธ๋ํ(competition graph) C(D) ๋ V (D)๋ฅผ ๊ผญ์ง์ ์งํฉ์ผ๋ก ํ๊ณ ๋ ๊ผญ์ง์ u, v๋ฅผ ์ ๋์ ์ผ๋ก ๊ฐ๋ ๋ณ์ด ์กด์ฌํ๋ค๋ ๊ฒ๊ณผ ๊ผญ์ง์ w๊ฐ ์กด์ฌํ์ฌ (u, w),(v, w)๊ฐ ๋ชจ๋ D์์ ์ ํฅ๋ณ์ด ๋๋ ๊ฒ์ด ๋์น์ธ ๊ทธ๋ํ๋ฅผ ์๋ฏธํ๋ค. Cohen์ด ๊ฒฝ์๊ทธ๋ํ์ ์ ์๋ฅผ ๋์
ํ ์ดํ๋ก ๊ทธ ๋ณ์ด๋ค๋ก m-step ๊ฒฝ์๊ทธ๋ํ(m-step competition graph), (i, j)-step ๊ฒฝ์๊ทธ๋ํ((i, j)-step competition graph), ๊ณํต๊ทธ๋ํ(phylogeny graph), ๊ฒฝ์๊ณต์ ๊ทธ๋ํ(competition-common enemy graph), p-๊ฒฝ์๊ทธ๋ํ(p-competition graph), ๊ทธ๋ฆฌ๊ณ ์ง์๊ทธ๋ํ(niche graph)๊ฐ ๋์
๋์๊ณ ์ฐ๊ตฌ๋๊ณ ์๋ค.
์ด ๋
ผ๋ฌธ์ ์ฐ๊ตฌ ๊ฒฐ๊ณผ๋ค์ ์ผ๋ถ๋ ๋ค์๊ณผ ๊ฐ๋ค. ์ผ๊ฐํ์ด ์์ด ์ฐ๊ฒฐ๋ m-step ๊ฒฝ์ ๊ทธ๋ํ๋ ํธ๋ฆฌ(tree)์์ ๋ณด์์ผ๋ฉฐ 2 โค m < n์ ๋ง์กฑํ๋ ์ ์ m, n์ ๋ํ์ฌ ๊ผญ์ง์ ์ ๊ฐ์๊ฐ n๊ฐ์ด๊ณ m-step ๊ฒฝ์๊ทธ๋ํ๊ฐ ๋ณ๊ทธ๋ํ(star graph)๊ฐ ๋๋ ์ ํฅ๊ทธ๋ํ๋ฅผ ์๋ฒฝํ๊ฒ ํน์งํ ํ์๋ค.
k โฅ 3์ด๊ณ ๋ฐฉํฅ์ง์ด์ง ์์ k-๋ถํ ๊ทธ๋ํ(oriented complete k-partite graph)์ (1, 2)-step ๊ฒฝ์๊ทธ๋ํ C_{1,2}(D)์์ ๊ฐ ๋ถํ ์ด ์์ ๋ถ๋ถ ๊ทธ๋ํ๋ฅผ ์ด๋ฃฐ ๋, C_{1,2}(D)์ ๋ชจ๋ ํน์งํ ํ์๋ค. ๋ํ, C_{1,2}(D)์ ๊ฐ ์ฑ๋ถ(component)์ ์ง๋ฆ(diameter)์ ๊ธธ์ด๊ฐ ์ต๋ 3์ด๋ฉฐ C_{1,2}(D)์ ์ง๋ฐฐ์(domination number)์ ๋ํ ์๊ณ์ ์ต๋๊ฐ์ ๊ตฌํ๊ณ ๊ตฌ๊ฐ๊ทธ๋ํ(interval graph)๊ฐ ๋๊ธฐ ์ํ ์ถฉ๋ถ ์กฐ๊ฑด์ ๊ตฌํ์๋ค.
์ฐจ์๊ฐ ์ ํ๋ ์ ํฅํ๋ก๋ฅผ ๊ฐ์ง ์๋ ์ ํฅ๊ทธ๋ํ(degree-bounded acyclic digraph)์ ๊ณํต๊ทธ๋ํ์ ๊ฒฝ์๊ณต์ ๊ทธ๋ํ์ ๋ํด์๋ ์ฐ๊ตฌํ์๋ค. ์์ ์ ์๋ค i, j์ ๋ํ์ฌ (i, j) ์ ํฅ๊ทธ๋ํ๋ ๊ฐ ๊ผญ์ง์ ์ ๋ด์ฐจ์๋ ์ต๋ i, ์ธ์ฐจ์๋ ์ต๋ j์ธ ์ ํฅํ๋ก ๊ฐ์ง ์๋ ์ ํฅ๊ทธ๋ํ์ด๋ค. ๋ง์ฝ ์ ํฅ๊ทธ๋ํ D์ ๊ฐ ๊ผญ์ง์ ์ด ๋ด์ฐจ์๊ฐ ์ต๋ i, ์ธ์ฐจ์๊ฐ ์ต๋ j ์ธ ๊ฒฝ์ฐ์ D๋ฅผ hi, ji ์ ํฅ๊ทธ๋ํ๋ผ ํ๋ค.
D๊ฐ (i, 2) ์ ํฅ๊ทธ๋ํ์ผ ๋, D์ ๊ณํต๊ทธ๋ํ๊ฐ ํ๊ทธ๋ํ(chordal graph)๊ฐ ๋๊ธฐ ์ํ D์ ๋ฐฉํฅ์ ๊ณ ๋ คํ์ง ์๊ณ ์ป์ด์ง๋ ๊ทธ๋ํ(underlying graph)์์ ๊ธธ์ด๊ฐ 4์ด์์ธ ํ๋ก(hole)์ ๊ธธ์ด์ ๋ํ ์ถฉ๋ถ์กฐ๊ฑด์ ๊ตฌํ์๋ค. ๊ฒ๋ค๊ฐ (i, j) ์ ํฅ๊ทธ๋ํ์ ๊ณํต๊ทธ๋ํ์์ ๋์ฌ ์ ์๋ ์์ฑ ๋ถ๋ถ ๊ทธ๋ํ(forbidden induced subgraph)๋ฅผ ํน์งํ ํ์๋ค.
(2, 2) ์ ํฅ๊ทธ๋ํ D์ ๊ฒฝ์๊ณต์ ๊ทธ๋ํ CCE(D)๊ฐ 2๊ฐ์ ๊ณ ๋ฆฝ์ (isolated vertex)๊ณผ ์ต๋ 1๊ฐ์ ํ๋ก๋ฅผ ๊ฐ์ผ๋ฉด์ ๊ฐ์ฅ ์ ์ ์ฑ๋ถ์ ๊ฐ๋ ๊ฒฝ์ฐ์ผ ๋์ ๊ตฌ์กฐ๋ฅผ ๊ท๋ช
ํ๋ค. ๋ง์ง๋ง์ผ๋ก, CCE(D)๊ฐ ๊ตฌ๊ฐ๊ทธ๋ํ๊ฐ ๋๊ธฐ ์ํ ์ฑ๋ถ์ ๊ฐ์์ ๋ํ ์ถฉ๋ถ์กฐ๊ฑด์ ๊ตฌํ์๋ค.1 Introduction 1
1.1 Graph theory terminology and basic concepts 1
1.2 Competition graphs and its variants 6
1.2.1 A brief background of competition graphs 6
1.2.2 Variants of competition graphs 8
1.2.3 m-step competition graphs 10
1.2.4 (1, 2)-step competition graphs 13
1.2.5 Phylogeny graphs 14
1.2.6 CCE graphs 16
1.3 A preview of the thesis 17
2 Digraphs whose m-step competition graphs are trees 19
2.1 The triangle-free m-step competition graphs 23
2.2 Digraphs whose m-step competition graphs are trees 29
2.3 The digraphs whose m-step competition graphs are star graphs 38
3 On (1, 2)-step competition graphs of multipartite tournaments 47
3.1 Preliminaries 48
3.2 C1,2(D) with a non-clique partite set of D 51
3.3 C1,2(D) without a non-clique partite set of D 66
3.4 C1,2(D) as a complete graph 74
3.5 Diameters and domination numbers of C1,2(D) 79
3.6 Disconnected (1, 2)-step competition graphs 82
3.7 Interval (1, 2)-step competition graphs 84
4 The forbidden induced subgraphs of (i, j) phylogeny graphs 90
4.1 A necessary condition for an (i, 2) phylogeny graph being chordal 91
4.2 Forbidden subgraphs for phylogeny graphs of degree bounded digraphs 99
5 On CCE graphs of (2, 2) digraphs 122
5.1 CCE graphs of h2, 2i digraphs 128
5.2 CCE graphs of (2, 2) digraphs 134
Abstract (in Korean) 168
Acknowledgement (in Korean) 170๋ฐ
Efficient computation of partition of unity interpolants through a block-based searching technique
In this paper we propose a new efficient interpolation tool, extremely
suitable for large scattered data sets. The partition of unity method is used
and performed by blending Radial Basis Functions (RBFs) as local approximants
and using locally supported weight functions. In particular we present a new
space-partitioning data structure based on a partition of the underlying
generic domain in blocks. This approach allows us to examine only a reduced
number of blocks in the search process of the nearest neighbour points, leading
to an optimized searching routine. Complexity analysis and numerical
experiments in two- and three-dimensional interpolation support our findings.
Some applications to geometric modelling are also considered. Moreover, the
associated software package written in \textsc{Matlab} is here discussed and
made available to the scientific community
Spatial patterns in mesic savannas: the local facilitation limit and the role of demographic stochasticity
We propose a model equation for the dynamics of tree density in mesic
savannas. It considers long-range competition among trees and the effect of
fire acting as a local facilitation mechanism. Despite short-range facilitation
is taken to the local-range limit, the standard full spectrum of spatial
structures obtained in general vegetation models is recovered. Long-range
competition is thus the key ingredient for the development of patterns. The
long time coexistence between trees and grass, and how fires affect the
survival of trees as well as the maintenance of the patterns is studied. The
influence of demographic noise is analyzed. The stochastic system, under the
parameter constraints typical of mesic savannas, shows irregular patterns
characteristics of realistic situations. The coexistence of trees and grass
still remains at reasonable noise intensities.Comment: 12 pages, 7 figure
Structure and Problem Hardness: Goal Asymmetry and DPLL Proofs in<br> SAT-Based Planning
In Verification and in (optimal) AI Planning, a successful method is to
formulate the application as boolean satisfiability (SAT), and solve it with
state-of-the-art DPLL-based procedures. There is a lack of understanding of why
this works so well. Focussing on the Planning context, we identify a form of
problem structure concerned with the symmetrical or asymmetrical nature of the
cost of achieving the individual planning goals. We quantify this sort of
structure with a simple numeric parameter called AsymRatio, ranging between 0
and 1. We run experiments in 10 benchmark domains from the International
Planning Competitions since 2000; we show that AsymRatio is a good indicator of
SAT solver performance in 8 of these domains. We then examine carefully crafted
synthetic planning domains that allow control of the amount of structure, and
that are clean enough for a rigorous analysis of the combinatorial search
space. The domains are parameterized by size, and by the amount of structure.
The CNFs we examine are unsatisfiable, encoding one planning step less than the
length of the optimal plan. We prove upper and lower bounds on the size of the
best possible DPLL refutations, under different settings of the amount of
structure, as a function of size. We also identify the best possible sets of
branching variables (backdoors). With minimum AsymRatio, we prove exponential
lower bounds, and identify minimal backdoors of size linear in the number of
variables. With maximum AsymRatio, we identify logarithmic DPLL refutations
(and backdoors), showing a doubly exponential gap between the two structural
extreme cases. The reasons for this behavior -- the proof arguments --
illuminate the prototypical patterns of structure causing the empirical
behavior observed in the competition benchmarks
Cross-Device Tracking: Matching Devices and Cookies
The number of computers, tablets and smartphones is increasing rapidly, which
entails the ownership and use of multiple devices to perform online tasks. As
people move across devices to complete these tasks, their identities becomes
fragmented. Understanding the usage and transition between those devices is
essential to develop efficient applications in a multi-device world. In this
paper we present a solution to deal with the cross-device identification of
users based on semi-supervised machine learning methods to identify which
cookies belong to an individual using a device. The method proposed in this
paper scored third in the ICDM 2015 Drawbridge Cross-Device Connections
challenge proving its good performance
Smart matching
One of the most annoying aspects in the formalization of mathematics is the
need of transforming notions to match a given, existing result. This kind of
transformations, often based on a conspicuous background knowledge in the given
scientific domain (mostly expressed in the form of equalities or isomorphisms),
are usually implicit in the mathematical discourse, and it would be highly
desirable to obtain a similar behavior in interactive provers. The paper
describes the superposition-based implementation of this feature inside the
Matita interactive theorem prover, focusing in particular on the so called
smart application tactic, supporting smart matching between a goal and a given
result.Comment: To appear in The 9th International Conference on Mathematical
Knowledge Management: MKM 201
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