4,013 research outputs found
Sufficient Conditions for Tuza's Conjecture on Packing and Covering Triangles
Given a simple graph , a subset of is called a triangle cover if
it intersects each triangle of . Let and denote the
maximum number of pairwise edge-disjoint triangles in and the minimum
cardinality of a triangle cover of , respectively. Tuza conjectured in 1981
that holds for every graph . In this paper, using a
hypergraph approach, we design polynomial-time combinatorial algorithms for
finding small triangle covers. These algorithms imply new sufficient conditions
for Tuza's conjecture on covering and packing triangles. More precisely,
suppose that the set of triangles covers all edges in . We
show that a triangle cover of with cardinality at most can be
found in polynomial time if one of the following conditions is satisfied: (i)
, (ii) , (iii)
.
Keywords: Triangle cover, Triangle packing, Linear 3-uniform hypergraphs,
Combinatorial algorithm
Enumeration of maps with self avoiding loops and the O(n) model on random lattices of all topologies
We compute the generating functions of a O(n) model (loop gas model) on a
random lattice of any topology. On the disc and the cylinder, they were already
known, and here we compute all the other topologies. We find that the
generating functions (and the correlation functions of the lattice) obey the
topological recursion, as usual in matrix models, i.e they are given by the
symplectic invariants of their spectral curve.Comment: pdflatex, 89 pages, 12 labelled figures (15 figures at all), minor
correction
Validating CFD predictions of flow over an escarpment using ground-based and airborne measurement devices
Micrometeorological observations from a tower, an eddy-covariance (EC) station and an unmanned aircraft system (UAS) at the WINSENT test-site are used to validate a computational fluid dynamics (CFD) model, driven by a mesoscale model. The observation site is characterised by a forested escarpment in a complex terrain. A two-day measurement campaign with a flow almost perpendicular to the escarpment is analysed. The first day is dominated by high wind speeds, while, on the second one, calm wind conditions are present. Despite some minor differences, the flow structure, analysed in terms of horizontal wind speeds, wind direction and inclination angles shows similarities for both days. A real-time strategy is used for the CFD validation with the UAS measurement, where the model follows spatially and temporally the aircraft. This strategy has proved to be successful. Stability indices such as the potential temperature and the bulk Richardson number are calculated to diagnose atmospheric boundary layer (ABL) characteristics up to the highest flight level. The calculated bulk Richardson values indicate a dynamically unstable region behind the escarpment and near the ground for both days. At higher altitudes, the ABL is returning to a near neutral state. The same characteristics are found in the model but only for the first day. The second day, where shear instabilities are more dominant, is not well simulated. UAS proves its great value for sensing the flow over complex terrains at high altitudes and we demonstrate the usefulness of UAS for validating and improving models
Numerical Construction of LISS Lyapunov Functions under a Small Gain Condition
In the stability analysis of large-scale interconnected systems it is
frequently desirable to be able to determine a decay point of the gain
operator, i.e., a point whose image under the monotone operator is strictly
smaller than the point itself. The set of such decay points plays a crucial
role in checking, in a semi-global fashion, the local input-to-state stability
of an interconnected system and in the numerical construction of a LISS
Lyapunov function. We provide a homotopy algorithm that computes a decay point
of a monotone op- erator. For this purpose we use a fixed point algorithm and
provide a function whose fixed points correspond to decay points of the
monotone operator. The advantage to an earlier algorithm is demonstrated.
Furthermore an example is given which shows how to analyze a given perturbed
interconnected system.Comment: 30 pages, 7 figures, 4 table
Irreducible triangulations of surfaces with boundary
A triangulation of a surface is irreducible if no edge can be contracted to
produce a triangulation of the same surface. In this paper, we investigate
irreducible triangulations of surfaces with boundary. We prove that the number
of vertices of an irreducible triangulation of a (possibly non-orientable)
surface of genus g>=0 with b>=0 boundaries is O(g+b). So far, the result was
known only for surfaces without boundary (b=0). While our technique yields a
worse constant in the O(.) notation, the present proof is elementary, and
simpler than the previous ones in the case of surfaces without boundary
Mathematical modelling of the interactive dynamics of wild and <i>Microsporidia MB</i>-infected mosquitoes
A recent discovery highlighted that mosquitoes infected with Microsporidia MB are unable to transmit the Plasmodium to humans. Microsporidia MB is a symbiont transmitted vertically and horizontally in the mosquito population, and these transmission routes are known to favor the persistence of the parasite in the mosquito population. Despite the dual transmission, data from field experiments reveal a low prevalence of MB-infected mosquitoes in nature. This study proposes a compartmental model to understand the prevalence of MB-infected mosquitoes. The dynamic of the model is obtained through the computation of the basic reproduction number and the analysis of the stability of the MB-free and coexistence equilibria. The model shows that, in spite of the high vertical transmission efficiency of Microsporidia MB, there can still be a low prevalence of MB-infected mosquitoes. Numerical analysis of the model shows that male-to-female horizontal transmission contributes more than female-to-male horizontal transmission to the spread of MB-infected mosquitoes. Moreover, the female-to-male horizontal transmission contributes to the spread of the symbiont only if there are multiple mating occurrences for male mosquitoes. Furthermore, when fixing the efficiencies of vertical transmission, the parameters having the greater influence on the ratio of MB-positive to wild mosquitoes are identified. In addition, by assuming a similar impact of the temperature on wild and MB-infected mosquitoes, our model shows the seasonal fluctuation of MB-infected mosquitoes. This study serves as a reference for further studies, on the release strategies of MB-infected mosquitoes, to avoid overestimating the MB-infection spread
Ordered Information Systems and Graph Granulation
The concept of an Information System, as used in Rough Set theory, is extended to the case of a partially ordered universe equipped with a set of order preserving attributes. These information systems give rise to partitions of the universe where the set of equivalence classes is partially ordered. Such ordered partitions correspond to relations on the universe which are reflexive and transitive. This correspondence allows the definition of approximation operators for an ordered information system by using the concepts of opening and closing from mathematical morphology. A special case of partial orders are graphs and hypergraphs and these provide motivation for the need to consider approximations on partial orders
A measurement of from the Gross-Llewellyn Smith Sum Rule
We extract a set of values for the Gross-Llewellyn Smith sum rule at
different values of 4-momentum transfer squared (), by combining revised
CCFR neutrino data with data from other neutrino deep-inelastic scattering
experiments for . A comparison with the order
theoretical predictions yields a determination of
at the scale of the Z-boson mass of . This measurement
provides a new and useful test of perturbative QCD at low , because of the
low uncertainties in the higher order calculations.Comment: 4 pages, 4 figure
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