Quasiperiodic graphs: structural design, scaling and entropic properties

A novel class of graphs, here named quasiperiodic, are constructed via application of the Horizontal Visibility algorithm to the time series generated along the quasiperiodic route to chaos. We show how the hierarchy of mode-locked regions represented by the Farey tree is inherited by their associated graphs. We are able to establish, via Renormalization Group (RG) theory, the architecture of the quasiperiodic graphs produced by irrational winding numbers with pure periodic continued fraction. And finally, we demonstrate that the RG fixed-point degree distributions are recovered via optimization of a suitably defined graph entropy

New invariants for entangled states

We propose new algebraic invariants that distinguish and classify entangled states. Considering qubits as well as higher spin systems, we obtained complete entanglement classifications for cases that were either unsolved or only conjectured in the literature.Comment: published versio

Vector valued Macdonald polynomials

This paper defines and investigates nonsymmetric Macdonald polynomials with values in an irreducible module of the Hecke algebra of type $A_{N-1}$. These polynomials appear as simultaneous eigenfunctions of Cherednik operators. Several objects and properties are analyzed, such as the canonical bilinear form which pairs polynomials with those arising from reciprocals of the original parameters, and the symmetrization of the Macdonald polynomials. The main tool of the study is the Yang-Baxter graph. We show that these Macdonald polynomials can be easily computed following this graph. We give also an interpretation of the symmetrization and the bilinear forms applied to the Macdonald polynomials in terms of the Yang-Baxter graph.Comment: 85 pages, 5 figure

Why one-size-fits-all vaso-modulatory interventions fail to control glioma invasion: in silico insights

There is an ongoing debate on the therapeutic potential of vaso-modulatory interventions against glioma invasion. Prominent vasculature-targeting therapies involve functional tumour-associated blood vessel deterioration and normalisation. The former aims at tumour infarction and nutrient deprivation medi- ated by vascular targeting agents that induce occlusion/collapse of tumour blood vessels. In contrast, the therapeutic intention of normalising the abnormal structure and function of tumour vascular net- works, e.g. via alleviating stress-induced vaso-occlusion, is to improve chemo-, immuno- and radiation therapy efficacy. Although both strategies have shown therapeutic potential, it remains unclear why they often fail to control glioma invasion into the surrounding healthy brain tissue. To shed light on this issue, we propose a mathematical model of glioma invasion focusing on the interplay between the mi- gration/proliferation dichotomy (Go-or-Grow) of glioma cells and modulations of the functional tumour vasculature. Vaso-modulatory interventions are modelled by varying the degree of vaso-occlusion. We discovered the existence of a critical cell proliferation/diffusion ratio that separates glioma invasion re- sponses to vaso-modulatory interventions into two distinct regimes. While for tumours, belonging to one regime, vascular modulations reduce the tumour front speed and increase the infiltration width, for those in the other regime the invasion speed increases and infiltration width decreases. We show how these in silico findings can be used to guide individualised approaches of vaso-modulatory treatment strategies and thereby improve success rates

Modeling the chemical impact and the optical emissions produced by lightning-induced electromagnetic fields in the upper atmosphere: the case of halos and elves triggered by different lightning discharges

Halos and elves are Transient Luminous Events (TLEs) produced in the lower ionosphere as a consequence of lightning-driven electromagnetic fields. These events can influence the upper-atmospheric chemistry and produce optical emissions. We have developed different two-dimensional self-consistent models that couple electrodynamical equations with a chemical scheme to simulate halos and elves produced by vertical cloud-to-ground (CG) lightning discharges, Compact Intra-cloud Discharges (CIDs) and Energetic In-cloud Pulses (EIPs). The optical emissions from radiative relaxation of excited states of molecular and atomic nitrogen and oxygen have been calculated. We have upgraded previous local models of halos and elves to calculate for the first time the vibrationally detailed optical spectra of elves triggered by CIDs and EIPs. According to our results, the optical spectra of elves do not depend on the type of parent lightning discharge. Finally, we have quantified the local chemical impact in the upper atmosphere of single halos and elves. In the case of the halo, we follow the cascade of chemical reactions triggered by the lightning-produced electric field during a long-time simulation of up to one second. We obtain a production rate of NO molecules by single halos and elves of 10$^{16}$ and 10$^{14}$ molecules/J, respectively. The results of these local models have been used to estimate the global production of NO by halos and elves in the upper atmopshere at $\sim10^{-7}$ Tg~N/y. This global chemical impact of halos and elves is seven orders of magnitude below the production of NO in the troposphere by lightning discharges