3,673 research outputs found
The mean, variance and limiting distribution of two statistics sensitive to phylogenetic tree balance
For two decades, the Colless index has been the most frequently used
statistic for assessing the balance of phylogenetic trees. In this article,
this statistic is studied under the Yule and uniform model of phylogenetic
trees. The main tool of analysis is a coupling argument with another well-known
index called the Sackin statistic. Asymptotics for the mean, variance and
covariance of these two statistics are obtained, as well as their limiting
joint distribution for large phylogenies. Under the Yule model, the limiting
distribution arises as a solution of a functional fixed point equation. Under
the uniform model, the limiting distribution is the Airy distribution. The
cornerstone of this study is the fact that the probabilistic models for
phylogenetic trees are strongly related to the random permutation and the
Catalan models for binary search trees.Comment: Published at http://dx.doi.org/10.1214/105051606000000547 in the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org
Creation and Growth of Components in a Random Hypergraph Process
Denote by an -component a connected -uniform hypergraph with
edges and vertices. We prove that the expected number of
creations of -component during a random hypergraph process tends to 1 as
and tend to with the total number of vertices such that
. Under the same conditions, we also show that
the expected number of vertices that ever belong to an -component is
approximately . As an immediate
consequence, it follows that with high probability the largest -component
during the process is of size . Our results
give insight about the size of giant components inside the phase transition of
random hypergraphs.Comment: R\'{e}sum\'{e} \'{e}tend
Fully Analyzing an Algebraic Polya Urn Model
This paper introduces and analyzes a particular class of Polya urns: balls
are of two colors, can only be added (the urns are said to be additive) and at
every step the same constant number of balls is added, thus only the color
compositions varies (the urns are said to be balanced). These properties make
this class of urns ideally suited for analysis from an "analytic combinatorics"
point-of-view, following in the footsteps of Flajolet-Dumas-Puyhaubert, 2006.
Through an algebraic generating function to which we apply a multiple
coalescing saddle-point method, we are able to give precise asymptotic results
for the probability distribution of the composition of the urn, as well as
local limit law and large deviation bounds.Comment: LATIN 2012, Arequipa : Peru (2012
An Interesting Class of Operators with unusual Schatten-von Neumann behavior
We consider the class of integral operators Q_\f on of the form
(Q_\f f)(x)=\int_0^\be\f (\max\{x,y\})f(y)dy. We discuss necessary and
sufficient conditions on to insure that is bounded, compact,
or in the Schatten-von Neumann class \bS_p, . We also give
necessary and sufficient conditions for to be a finite rank
operator. However, there is a kind of cut-off at , and for membership in
\bS_{p}, , the situation is more complicated. Although we give
various necessary conditions and sufficient conditions relating to
Q_{\phi}\in\bS_{p} in that range, we do not have necessary and sufficient
conditions. In the most important case , we have a necessary condition and
a sufficient condition, using and modulus of continuity,
respectively, with a rather small gap in between. A second cut-off occurs at
: if \f is sufficiently smooth and decays reasonably fast, then \qf
belongs to the weak Schatten-von Neumann class \wS{1/2}, but never to
\bS_{1/2} unless \f=0.
We also obtain results for related families of operators acting on
and .
We further study operations acting on bounded linear operators on
related to the class of operators Q_\f. In particular we
study Schur multipliers given by functions of the form and
we study properties of the averaging projection (Hilbert-Schmidt projection)
onto the operators of the form Q_\f.Comment: 87 page
Intrinsic peculiarities of real material realizations of a spin-1/2 kagome lattice
Spin-1/2 magnets with kagome geometry, being for years a generic object of
theoretical investigations, have few real material realizations. Recently, a
DFT-based microscopic model for two such materials, kapellasite Cu3Zn(OH)6Cl2
and haydeeite Cu3Mg(OH)6Cl2, was presented [O. Janson, J. Richter and H.
Rosner, arXiv:0806.1592]. Here, we focus on the intrinsic properties of real
spin-1/2 kagome materials having influence on the magnetic ground state and the
low-temperature excitations. We find that the values of exchange integrals are
strongly dependent on O--H distance inside the hydroxyl groups, present in most
spin-1/2 kagome compounds up to date. Besides the original kagome model,
considering only the nearest neighbour exchange, we emphasize the crucial role
of the exchange along the diagonals of the kagome lattice.Comment: 4 pages, 4 figures. A paper for the proceedings of the HFM 2008
conferenc
Monotone graph limits and quasimonotone graphs
The recent theory of graph limits gives a powerful framework for
understanding the properties of suitable (convergent) sequences of
graphs in terms of a limiting object which may be represented by a symmetric
function on , i.e., a kernel or graphon. In this context it is
natural to wish to relate specific properties of the sequence to specific
properties of the kernel. Here we show that the kernel is monotone (i.e.,
increasing in both variables) if and only if the sequence satisfies a
`quasi-monotonicity' property defined by a certain functional tending to zero.
As a tool we prove an inequality relating the cut and norms of kernels of
the form with and monotone that may be of interest in its
own right; no such inequality holds for general kernels.Comment: 38 page
Environmental effects on progesterone profile measures of dairy cow fertility
Environmental effects on fertility measures early in lactation, such as the interval from calving to first luteal activity (CLA), proportion of samples with luteal activity during the first 60 days after calving (PLA) and interval to first ovulatory oestrus (OOE) were studied. In addition, traditional measurements of fertility, such as pregnancy to first insemination, number of inseminations per service period and interval from first to last insemination were studied as well as associations between the early and late measurements. Data were collected from an experimental herd during 15 years and included 1106 post-partum periods from 191 Swedish Holsteins and 325 Swedish Red and White dairy cows. Individual milk progesterone samples were taken twice a week until cyclicity and thereafter less frequently. First parity cows had 14.8 and 18.1 days longer CLA (LS-means difference) than second parity cows and older cows, respectively. Moreover, CLA was 10.5 days longer for cows that calved during the winter season compared with the summer season and 7.5 days longer for cows in tie-stalls than cows in loose-housing system. Cows treated for mastitis and lameness had 8.4 and 18.0 days longer CLA, respectively, compared with healthy cows. OOE was affected in the same way as CLA by the different environmental factors. PLA was a good indicator of CLA, and there was a high correlation (−0.69) between these two measurements. Treatment for lameness had a significant influence on all late fertility measurements, whereas housing was significant only for pregnancy to first insemination. All fertility traits were unfavourably associated with increased milk production. Regression of late fertility measurements on early fertility measurements had only a minor association with conception at first AI and interval from first to last AI for cows with conventional calving intervals, i.e. a 22 days later, CLA increased the interval from first to last insemination by 3.4 days. Early measurements had repeatabilities of 0.14–0.16, indicating a higher influence by the cow itself compared with late measurements, which had repeatabilities of 0.09–0.10. Our study shows that early fertility measurements have a possibility to be used in breeding for better fertility. To improve the early fertility of the cow, there are a number of important factors that have to be taken into account
Random trees with superexponential branching weights
We study rooted planar random trees with a probability distribution which is
proportional to a product of weight factors associated to the vertices of
the tree and depending only on their individual degrees . We focus on the
case when grows faster than exponentially with . In this case the
measures on trees of finite size converge weakly as tends to infinity
to a measure which is concentrated on a single tree with one vertex of infinite
degree. For explicit weight factors of the form with
we obtain more refined results about the approach to the infinite
volume limit.Comment: 19 page
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