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Tuberous sclerosis complex is a rare genetic disorder leading to the growth of hamartomas in multiple organs, including cardiac rhabdomyomas. Children with symptomatic cardiac rhabdomyoma require frequent admissions to intensive care units, have major complications, namely, arrhythmias, cardiac outflow tract obstruction and heart failure, affecting the quality of life and taking on high healthcare cost. Currently, there is no standard pharmacological treatment for this condition, and the management includes a conservative approach and supportive care. Everolimus has shown positive effects on subependymal giant cell astrocytomas, renal angiomyolipoma and refractory seizures associated with tuberous sclerosis complex. However, evidence supporting efficacy in symptomatic cardiac rhabdomyoma is limited to case reports. The ORACLE trial is the first randomised clinical trial assessing the efficacy of everolimus as a specific therapy for symptomatic cardiac rhabdomyoma.
ORACLE is a phase II, prospective, randomised, placebo-controlled, double-blind, multicentre protocol trial. A total of 40 children with symptomatic cardiac rhabdomyoma secondary to tuberous sclerosis complex will be randomised to receive oral everolimus or placebo for 3 months. The primary outcome is 50% or more reduction in the tumour size related to baseline. As secondary outcomes we include the presence of arrhythmias, pericardial effusion, intracardiac obstruction, adverse events, progression of tumour reduction and effect on heart failure.
ORACLE protocol addresses a relevant unmet need in children with tuberous sclerosis complex and cardiac rhabdomyoma. The results of the trial will potentially support the first evidence-based therapy for this condition.
We devote this paper to proving non-existence and existence of stable solutions to weighted Lane-Emden equations on the Euclidean space ℝN, N ⩾ 2. We first prove some new Liouville-type theorems for stable solutions which recover and considerably improve upon the known results. In particular, our approach applies to various weighted equations, which naturally appear in many applications, but that are not covered by the existing literature. A typical example is provided by the well-know Matukuma's equation. We also prove an existence result for positive, bounded and stable solutions to a large family of weighted Lane–Emden equations, which indicates that our Liouville-type theorems are somehow sharp.
We consider a possibly anisotropic integrodifferential semilinear equation, driven by a non-decreasing nonlinearity. We prove that if the solution grows less than the order of the operator at infinity, then it must be affine (possibly constant).
We prove pointwise gradient bounds for entire solutions of pde’s of the form
ℒu(x) = ψ(x, u(x), ∇u(x)),
where ℒ is an elliptic operator (possibly singular or degenerate). Thus, we obtain some Liouville type rigidity results. Some classical results of J. Serrin are also recovered as particular cases of our approach.
We consider the functional in a periodic setting. We discuss whether the minimizers or the stable solutions satisfy some symmetry or monotonicity properties, with special emphasis on the autonomous case when F is x-independent. In particular, we give an answer to a question posed by Victor Bangert when F is autonomous in dimension n≤3 and in any dimension for non-zero rotation vectors.
The main goal of this paper is the investigation of a relevant
property which appears in the various definition of deterministic
topological chaos for discrete time dynamical system:
transitivity. Starting from the standard Devaney's notion of topological chaos
based on regularity, transitivity, and sensitivity to the initial
conditions, the critique formulated by Knudsen is taken into
account in order to exclude periodic chaos from this definition.
Transitivity (or some stronger versions of it) turns out to be the
relevant condition of chaos and its role is discussed by a survey
of some important results about it with the presentation of some
new results. In particular, we study topological mixing, strong transitivity,
and full transitivity. Their applications to symbolic dynamics are
investigated with respect to the relationships with the associated
We investigate the relationships among all currently known X-ray structures of crystalline pentacene by calculating their “inherent” structures of minimum potential energy. We are thus able to show that two distinct bulk crystalline phases of pentacene exist, with very subtle but clear di.erences. We then assess the effects of temperature on the crystal structures, by including both inter- molecular and low-frequency intra-molecular phonons in the framework of quasi harmonic lattice dynamics methods. In this way we properly reproduce the experimental thermal expansion, and obtain a reliable description of the phonon dynamics and of its temperature dependence. The calculated phonon frequencies compare well with the experimental Raman spectrum.
The struggle against death is one of the main themes in human history.
Mortality as it declined in recent times, became a central factor behind
population growth. In this context, childhood mortality was the key, not
only because deaths at these young ages often constituted more than half
of all deaths, but also because any decrease in it brought about
fundamental changes in the age structure and the size of the population
and in fertility.
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