We present how a probabilistic model can describe the asymptotic behavior of the iterations, with applications for ODE and approach of some problems in mechanics in $\mathbb{R}^d$.
Paulina Gil-Kulik, Alicja Petniak, Natalia Kluz
et al.
Colorectal cancer (CRC) is the second most common cause of cancer-related death globally. Because of a tendency to be an asymptomatic primary tumor and therefore resulting in late detection, most CRC patients are diagnosed in the advanced stage. Several miRNAs have the potential to become novel noninvasive biomarkers measured as diagnostic and prognostic indicators of CRC to guide surgical therapies and promote the understanding of the carcinogenesis of CRC. Since the change of miR-3613-3p was associated with several types of cancer other than colorectal cancer, there is a lack of functional evidence and the results are inconsistent. We conducted a pilot microarray study in which we noted a decreased expression of miR-3613-3p in colorectal cancer cells, then we confirmed the expression of miR-3613-3p by qPCR on a group of 83 patients, including 65 patients with colorectal cancer, 5 with a benign tumor and 13 from the control group. We noted that in both malignant and benign tumors, miR-3613-3p is downgraded relative to the surrounding tissue. As a result of the study, we also observed colorectal tumor tissue and surrounding tissue in patients with colorectal cancer who received radiotherapy before surgery, which showed a significantly higher expression of miR-3613-3p compared to patients who did not receive radiotherapy. In addition, we noted that the tissue surrounding the tumor in patients with distant metastases showed a significantly higher expression of miR-3613-3p compared to patients without distant metastases. The increased expression of miR-3613-3p in patients after radiotherapy suggests the possibility of using this miR as a therapeutic target for CRC, but this requires confirmation in further studies.
A conjecture of Arnold, Kozlov and Neishtadt on the exponentially small measure of the non-torus set in analytic systems with two degrees of freedom is discussed.
We show that directional closing in the sense of Guillon-Kari-Zinoviadis and Franks-Kra is not closed under conjugacy. This implies that being polygonal in the sense of Franks-Kra is not closed under conjugacy.
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A necessary and sufficient condition is given for the existence of an embedding of an irreducible subshift of finite type into the Fibonacci-Dyck shift
The aim of this survey is to present some aspects of multifractal analysis around the recently developed subject of multiple ergodic averages. Related topics include dimensions of measures, oriented walks, Riesz products etc.
In this short note, I explain how the non-degeneracy condition of the KAM can be bypassed. The first version of the note has been submitted for publication back in 2010 and this version in 2012.
We expose some selected topics concerning the instability of the action variables in a priori unstable Hamiltonian systems, and outline a new strategy that may allow to apply these methods to a priori stable systems.
We describe some relations between the properties of the Cauchy problem for an ODE and the properties of the Cauchy problem for the associated continuity equation in the class of measures.
I introduce Banach spaces on which it is possible to precisely characterize the spectrum of the transfer operator associated to a piecewise expanding map with Hölder weight.
We investigate an analogue of the L^2-Betti numbers for amenable linear subshifts. The role of the von Neumann dimension shall be played by the topological entropy.