742 research outputs found
Introducing CMS: A Contest Management System
No full textWe present Contest Management System (CMS), the free and open source grading system that will be used in IOI 2012. CMS has been designed and developed from scratch, with the aim of providing a grading system that naturally adapts to the needs of an IOI-like competition, including the team selection processes. Particular care has been taken to make CMS secure, robust, developed for the community, extensible, easily adaptable and usable.We present Contest Management System (CMS), the free and open source grading system that will be used in IOI 2012. CMS has been designed and developed from scratch, with the aim of providing a grading system that naturally adapts to the needs of an IOI-like competition, including the team selection processes. Particular care has been taken to make CMS secure, robust, developed for the community, extensible, easily adaptable and usable
Some sphere theorems in linear potential theory
No full textIn this paper we analyze the capacitary potential due to a charged body in order to deduce sharp analytic and geometric inequalities, whose equality cases are saturated by domains with spherical symmetry. In particular, for a regular bounded domain Ω ⊂ Rn, n ≥ 3, we prove that if the mean curvature H of the boundary obeys the condition (Formula Presented) then Ω is a round ball.SCOPUS: ar.jDecretOANoAutActifinfo:eu-repo/semantics/publishe
On the Distributional Hessian of the Distance Function
No full textWe describe the precise structure of the distributional Hessian of the distance
function from a point of a Riemannian manifold. At the same time we discuss some geometrical properties of the cut locus of a point, and compare some different weak notions of the Hessian and Laplacian
CMS: a Growing Grading System
No full textWe give an update on CMS, the free and open source grading system used in IOI 2012, 2013 and 2014. In particular, we focus on the new features and development practices; on what we learned by running dozens of contests with CMS; on the community of users and developers that has started to grow around it
Comparison of cell-cycle phase perturbations induced by the DNA-minor-groove alkylator tallimustine and by melphalan in the SW626 cell line
No full textIntracellular glutathione heterogeneity in L1210 murine leukemia sublines made resistant to DNA-interacting anti-neoplastic agents
No full textModerate Salinity Stress Affects Expression of Main Sugar Metabolism and Transport Genes and Soluble Carbohydrate Content in Ripe Fig Fruits (<i>Ficus carica</i> L. cv. Dottato)
No full textFig trees (Ficus carica L.) are commonly grown in the Mediterranean area, where salinity is an increasing problem in coastal areas. Young, fruiting plants of cv. Dottato were subjected to moderate salt stress (100 mM NaCl added to irrigation water) for 48 days before fruit sampling. To clarify the effect of salinity stress, we investigated changes in the transcription of the main sugar metabolism-related genes involved in the synthesis, accumulation and transport of soluble carbohydrates in ripe fruits by quantitative real-time PCR as well as the content of soluble sugars by quantitative 1H nuclear magnetic resonance spectroscopy. A general increase in the transcript levels of genes involved in the transport of soluble carbohydrates was observed. Alkaline-neutral and Acid Invertases transcripts, related to the synthesis of glucose and fructose, were up-regulated in ripe fruits of NaCl-stressed plants without a change in the content of D-glucose and D-fructose. The increases in sucrose and D-sorbitol contents were likely the result of the up-regulation of the transcription of Sucrose-Synthase- and Sorbitol-Dehydrogenase-encoding genes
The antitumour activity of alkylating agents is not correlated with the levels of glutathione, glutathione transferase and O-6-alkylguanine-DNA-alkyltransferase of human tumour xenografts
No full textFourth-order geometric flows and integral piching of the curvature
No full textGeometric flows have recently become a very important tool for
studying the topology of smooth manifolds admitting Riemannian metrics
satisfying certain hypotheses. A geometric flow is the evolution of
the Riemannian metric of a smooth manifold according to a
differential rule of the form , where at each time
is a positively defined tensor (such that
on a fixed differentiable manifold and is a smooth
differential operator depending on itself and on its space
derivatives, hopefully chosen in order to have the effect of
increasing the ``regularity'' of the Riemannian manifold. Once the
metric has been ``enhanced'' by the flow, one can study it more easily
and obtain topological results that, since the flow is smooth, must
also hold for the initial differentiable manifold.
The study of a geometric flow usually goes through some recurrent
steps:
1. The very first point is to show that, given the initial metric,
there is a (usually unique) smooth solution of the flow for at
least a short interval of time.
2. The maximal time for the existence of a smooth solution can be
finite or infinite: in the first case a singularity of the flow
develops, so its nature must be investigated in order to possibly
exclude it by a contradiction argument, or to classify it to get
topological information on the manifold, or finally to fully
understand its structure and possibly perform a smooth topological
``surgery'' in order to continue the flow after the singular
time. A very remarkable example of this last situation (which by
far is the most difficult case to deal with) is the success in the
study of Hamilton's Ricci flow, that is, the flow , on the --manifolds due to Perelman, leading
to the proof of the Poincaré conjecture.
In our work we will deal only with the first situation: assuming
that the flow of is defined in the maximal time interval
with and that at time a singularity
develops, we will try to exclude this scenario by a contradiction
argument (just to mention, another recent great success of the
application of Ricci flow to geometric problems, the proof of the
differentiable sphere theorem by Brendle and Schoen follows this
line). In this respect, a fundamental point of this program is to
show that the Riemann curvature tensor must be unbounded as .
3. After obtaining the above result, the idea is to perform a
blow--up analysis: we take and dilate the metric
so that the rescaled sequence of manifolds have uniformly
bounded curvatures; then, we prove that they stay within a
precompact class and take a limit of such sequence. At this point,
one has to study the properties of such possible limit manifold
(this may require a full classification result) in order to
proceed in one of the ways described above.
4. In our case, we actually want to find a contradiction in this
procedure by studying the limit manifold. This would imply that
the flow cannot actually be singular in finite time and the
maximal time of smooth existence has to be .
5. Then, once we know that the flow is defined for all times, we
prove again that there is a limit manifold as and
we study its properties. For example, if the limit manifold turns
out to have constant positive sectional curvature, it must be the
quotient of the standard sphere. Hence, the initial manifold too
is topologically a quotient of the sphere, concluding the
geometric program.
Among the geometric flows, a special class is given by the ones
arising as gradients of geometric functionals of the metric and the
curvature. In such cases, because of the variational structure of the
flow, the natural energy (the value of the functional) is decreasing
in time and one can take advantage of this fact to carry out some of
the arguments mentioned above.
Our work, which fits in this context, is based upon the PhD thesis of
Vincent Bour, who studied a class of geometric gradient flows of the
fourth order. To briefly describe it, we recall that the Riemann
curvature tensor of a Riemannian manifold can be
orthogonally decomposed as
Riem_g = W_g + Z_g + S_g
with
S_g = R_g / (2n(n-1)) g . g
Z_g = 1 / (n-2) ( Ric_g - R_g / n * g ) . g
where is the Ricci tensor, the scalar curvature and the
remaining Weyl curvature is a fully traceless tensor (the
operation indicates the Kulkarni--Nomizu product, see the next
chapter for all the definitions).
Then, we define for
F^\lambda (g) = (1-\lambda) \int_{M^n} \abs{W_g}^2 \, dv_g + \lambda \int_{M^n} \abs{Z_g}^2 \, dv_g \]
and consider the gradient flow
\partial_t g(t) = -2 \nabla \F^\lambda(g(t)) . (1)
We will follow the steps outlined above in order to prove that if we
consider a compact manifold with an initial smooth metric
such that has positive scalar curvature and initial
energy \F^\lambda(g_0) sufficiently low, the flow (1) exists for all
times and converges in the topology to a smooth metric
on of positive constant sectional curvature. Thanks to
the Uniformization Theorem, we have that is diffeomorphic to a
quotient of the --sphere, thus, it can only be either the
--sphere or the dimensional real projective space
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