376 research outputs found
Improved Bounds for -Identifying Codes of the Hex Grid
For any positive integer , an -identifying code on a graph is a set
such that for every vertex in , the intersection of the
radius- closed neighborhood with is nonempty and pairwise distinct. For
a finite graph, the density of a code is , which naturally extends
to a definition of density in certain infinite graphs which are locally finite.
We find a code of density less than , which is sparser than the prior
best construction which has density approximately .Comment: 12p
Characterizing extremal digraphs for identifying codes and extremal cases of Bondy's theorem on induced subsets
An identifying code of a (di)graph is a dominating subset of the
vertices of such that all distinct vertices of have distinct
(in)neighbourhoods within . In this paper, we classify all finite digraphs
which only admit their whole vertex set in any identifying code. We also
classify all such infinite oriented graphs. Furthermore, by relating this
concept to a well known theorem of A. Bondy on set systems we classify the
extremal cases for this theorem
An improved lower bound for (1,<=2)-identifying codes in the king grid
We call a subset of vertices of a graph a -identifying
code if for all subsets of vertices with size at most , the sets
are distinct. The concept of
identifying codes was introduced in 1998 by Karpovsky, Chakrabarty and Levitin.
Identifying codes have been studied in various grids. In particular, it has
been shown that there exists a -identifying code in the king grid
with density 3/7 and that there are no such identifying codes with density
smaller than 5/12. Using a suitable frame and a discharging procedure, we
improve the lower bound by showing that any -identifying code of
the king grid has density at least 47/111
Communication and trust in the bounded confidence model
The communication process in a situation of emergency is discussed within the
Scheff theory of shame and pride. The communication involves messages from
media and from other persons. Three strategies are considered: selfish (to
contact friends), collective (to join other people) and passive (to do
nothing). We show that the pure selfish strategy cannot be evolutionarily
stable. The main result is that the community structure is statistically
meaningful only if the interpersonal communication is weak.Comment: 6 pages, 5 figures, RevTeX, for ICCCI-201
Improved Parameterized Algorithms for the Kemeny Aggregation Problem
We give improvements over fixed parameter tractable (FPT) algo-rithms to solve the Kemeny aggregation problem, where the task is to summarize a multi-set of preference lists, called votes, over a set of alternatives, called candidates, into a single preference list that has the minimum total τ-distance from the votes. The τ-distance between two preference lists is the number of pairs of candidates that are or-dered differently in the two lists. We study the problem for preference lists that are total orders. We develop algorithms of running times O∗(1.403kt), O∗(5.823kt/m) ≤ O∗(5.823kavg) and O∗(4.829kmax) for the problem, ignoring the polynomial factors in the O ∗ notation, where kt is the optimum total τ-distance, m is the number of votes, and kavg (resp, kmax) is the average (resp, maximum) over pairwise τ-distances of votes. Our algorithms improve the best previously known running times of O∗(1.53kt) and O∗(16kavg) ≤ O∗(16kmax) [4, 5], which also implies an O∗(164kt/m) running time. We also show how to enumerate all optimal solutions in O∗(36kt/m) ≤ O∗(36kavg) time.
A Model for the Development of the Rhizobial and Arbuscular Mycorrhizal Symbioses in Legumes and Its Use to Understand the Roles of Ethylene in the Establishment of these two Symbioses
We propose a model depicting the development of nodulation and arbuscular mycorrhizae. Both processes are dissected into many steps, using Pisum sativum L. nodulation mutants as a guideline. For nodulation, we distinguish two main developmental programs, one epidermal and one cortical. Whereas Nod factors alone affect the cortical program, bacteria are required to trigger the epidermal events. We propose that the two programs of the rhizobial symbiosis evolved separately and that, over time, they came to function together. The distinction between these two programs does not exist for arbuscular mycorrhizae development despite events occurring in both root tissues. Mutations that affect both symbioses are restricted to the epidermal program. We propose here sites of action and potential roles for ethylene during the formation of the two symbioses with a specific hypothesis for nodule organogenesis. Assuming the epidermis does not make ethylene, the microsymbionts probably first encounter a regulatory level of ethylene at the epidermis–outermost cortical cell layer interface. Depending on the hormone concentrations there, infection will either progress or be blocked. In the former case, ethylene affects the cortex cytoskeleton, allowing reorganization that facilitates infection; in the latter case, ethylene acts on several enzymes that interfere with infection thread growth, causing it to abort. Throughout this review, the difficulty of generalizing the roles of ethylene is emphasized and numerous examples are given to demonstrate the diversity that exists in plants
Advances in the Direct Study of Carbon Burning in Massive Stars
The C12+C12 fusion reaction plays a critical role in the evolution of massive stars and also strongly impacts various explosive astrophysical scenarios. The presence of resonances in this reaction at energies around and below the Coulomb barrier makes it impossible to carry out a simple extrapolation down to the Gamow window-the energy regime relevant to carbon burning in massive stars. The C12+C12 system forms a unique laboratory for challenging the contemporary picture of deep sub-barrier fusion (possible sub-barrier hindrance) and its interplay with nuclear structure (sub-barrier resonances). Here, we show that direct measurements of the C12+C12 fusion cross section may be made into the Gamow window using an advanced particle-gamma coincidence technique. The sensitivity of this technique effectively removes ambiguities in existing measurements made with gamma ray or charged-particle detection alone. The present cross-section data span over 8 orders of magnitude and support the fusion-hindrance model at deep sub-barrier energies
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