Chaos edges of zz-logistic maps: Connection between the relaxation and sensitivity entropic indices

Chaos thresholds of the $z$-logistic maps $x_{t+1}=1-a|x_t|^z$ $(z>1; t=0,1,2,...)$ are numerically analysed at accumulation points of cycles 2, 3 and 5. We verify that the nonextensive $q$-generalization of a Pesin-like identity is preserved through averaging over the entire phase space. More precisely, we computationally verify $\lim_{t \to\infty}< S_{q_{sen}^{av}} >(t)/t= \lim_{t \to\infty}(t)/t \equiv \lambda_{q_{sen}^{av}}^{av}$, where the entropy $S_{q} \equiv (1- \sum_i p_i^q)/ (q-1)$ ($S_1=-\sum_ip_i \ln p_i$), the sensitivity to the initial conditions $\xi \equiv \lim_{\Delta x(0) \to 0} \Delta x(t)/\Delta x(0)$, and $\ln_q x \equiv (x^{1-q}-1)/ (1-q)$ ($\ln_1 x=\ln x$). The entropic index $q_{sen}^{av}0$ depend on both $z$ and the cycle. We also study the relaxation that occurs if we start with an ensemble of initial conditions homogeneously occupying the entire phase space. The associated Lebesgue measure asymptotically decreases as $1/t^{1/(q_{rel}-1)}$ ($q_{rel}>1$). These results led to (i) the first illustration of the connection (conjectured by one of us) between sensitivity and relaxation entropic indices, namely $q_{rel}-1 \simeq A (1-q_{sen}^{av})^\alpha$, where the positive numbers $(A,\alpha)$ depend on the cycle; (ii) an unexpected and new scaling, namely $q_{sen}^{av}(cycle n)=2.5 q_{sen}^{av}(cycle 2)+ \epsilon$ ($\epsilon=-0.03$ for $n=3$, and $\epsilon = 0.03$ for $n=5$).Comment: 5 pages, 5 figure

Generalized entropy arising from a distribution of q-indices

It is by now well known that the Boltzmann-Gibbs (BG) entropy $S_{BG}=-k\sum_{i=1}^W p_i \ln p_i$ can be usefully generalized into the entropy $S_q=k (1-\sum_{i=1}^Wp_i^{q}) / (q-1)$ ($q\in \mathcal{R}; S_1=S_{BG}$). Microscopic dynamics determines, given classes of initial conditions, the occupation of the accessible phase space (or of a symmetry-determined nonzero-measure part of it), which in turn appears to determine the entropic form to be used. This occupation might be a uniform one (the usual {\it equal probability hypothesis} of BG statistical mechanics), which corresponds to $q=1$; it might be a free-scale occupancy, which appears to correspond to $q \ne 1$. Since occupancies of phase space more complex than these are surely possible in both natural and artificial systems, the task of further generalizing the entropy appears as a desirable one, and has in fact been already undertaken in the literature. To illustrate the approach, we introduce here a quite general entropy based on a distribution of $q$-indices thus generalizing $S_q$. We establish some general mathematical properties for the new entropic functional and explore some examples. We also exhibit a procedure for finding, given any entropic functional, the $q$-indices distribution that produces it. Finally, on the road to establishing a quite general statistical mechanics, we briefly address possible generalized constraints under which the present entropy could be extremized, in order to produce canonical-ensemble-like stationary-state distributions for Hamiltonian systems.Comment: 14 pages including 3 figure

B cells in the formation of Tertiary Lymphoid Organs in autoimmunity, transplantation and tumorigenesis.

TLS develop in target organs of autoimmune diseases, transplantation and cancer. • TLS can function as germinal centres supporting B-cell selection/differentiation. • TLS can be destructive or have beneficial effects at the site of inflammation/disease. • Therapeutic targeting of TLS results in beneficial effects in patients, though inhibition may lead to immune suppression while stimulation may lead to autoimmunity. Tertiary lymphoid organs named also tertiary lymphoid structures (TLS) often occur at sites of autoimmune inflammation, organ transplantation and cancer. Although the mechanisms for their formation/function are not entirely understood, it is known that TLS can display features of active germinal centres supporting the proliferation and differentiation of (auto)-reactive B cells. In this Review, we discuss current knowledge on TLS-associated B cells with particular reference on how within diseased tissues these structures are linked to either deleterious or protective outcomes in patients and the potential for therapeutic targeting of TLS through novel drugs

The Edge of Quantum Chaos

We identify a border between regular and chaotic quantum dynamics. The border is characterized by a power law decrease in the overlap between a state evolved under chaotic dynamics and the same state evolved under a slightly perturbed dynamics. For example, the overlap decay for the quantum kicked top is well fitted with $[1+(q-1) (t/\tau)^2]^{1/(1-q)}$ (with the nonextensive entropic index $q$ and $\tau$ depending on perturbation strength) in the region preceding the emergence of quantum interference effects. This region corresponds to the edge of chaos for the classical map from which the quantum chaotic dynamics is derived.Comment: 4 pages, 4 figures, revised version in press PR

Desempenho agro-econômico do feijoeiro comum semeado em duas época da safrinha no médio-norte matogrossense.

Esse trabalho objetivou determinar e analisar os indicadores agro-econômicos de nove cultivares do feijoeiro comum, semeadas na safrinha do ano agrícola de 2010-11 em duas épocas distintas (15/02/2011 e 25/02/2011) dentro do município de Sinop (MT).CONAFE

Desempenho agro-econômico do consórcio entre feijão-comum e Brachiaria ruziziensis implantado simultâneamente na safrinha do médio-norte matogrossense.

Esse trabalho objetivou analisar o desempenho agro-econômico de oito consórcios entre feijão-comum e Brachiaria ruziziensis implantados simultaneamente na safrinha do médio-norte matogrossense, submetidos ou não, á dose reduzida de graminicida.CONAFE

Earlinet validation of CATS L2 product

The Cloud-Aerosol Transport System (CATS) onboard the International Space Station (ISS), is a lidar system providing vertically resolved aerosol and cloud profiles since February 2015. In this study, the CATS aerosol product is validated against the aerosol profiles provided by the European Aerosol Research Lidar Network (EARLINET). This validation activity is based on collocated CATS-EARLINET measurements and the comparison of the particle backscatter coefficient at 1064nm.Peer ReviewedPostprint (published version

Effect of Inoculation with Rhizobacteria and Arbuscular Mycorrhizal Fungi on Growth and Yield of Capsicum chinense Jacquin

We evaluated the effect of two rhizobacteria (Azotobacter chroococcum and Azospirillum brasilense) and a commercial product containing multiple strains of arbuscular mycorrhizal fungi (AMF) and an NPK fertiliser on the growth and yield of habanero chilli (Capsicum chinense Jacquin). All treatments were applied as single or combined inoculants, under nursery and field conditions, in a completely randomised design. The biofertilisers were applied to the roots by coating or dipping, with the inoculants in a solid or liquid support, respectively. At 30 days after inoculation, populations of 2.5×106 to 1.3×106 cfu g soil−1 of A. brasilense and 10.3×105 to 2.6×105 of A. chroococcum were detected in the rhizosphere of the crop. The prevalence of colonisation of plants inoculated with AMF ranged from 35 to 57%, with the greatest values recorded for the treatment involving single biofertilisation by root coating. In the nursery phase, single biofertilisation promoted a higher growth and nutrient content in the crop than combined biofertilisation. However, in the field phase the combined biofertilisation increased the nutrient content of the plant leaves, which was significantly greater than observed in the NPK treatment. The highest yields were recorded for the treatments involving a single inoculation of A. chroococcum and for those with the multi-strain of AMF, with average values of 2.5 and 2.3 kg plant−1 respectively, compared with 1.0 kg plant−1 obtained with the treatment in which NPK fertiliser was applied

Pyothorax and pulmonary lymphomatoid granulomatosis in a cat

A 7-year-old female neutered British Short Hair cat was presented for further investigation and treatment of pleural effusion due to a possible pyothorax. Cytology and culture of the fluid identified pyothorax and a large mass/consolidated right caudal lung lobe was found on x-ray, ultrasound and CT scan. Lung lobectomy was performed and a diagnosis of pulmonary lymphomatoid granulomatosis (PLG) was confirmed by histopathology and immunohistochemistry. Despite medical treatment the patient was euthanized due to progression of the disease and deterioration of her clinical signs. This is the second case of PLG reported in a cat and the first case of PLG with concurrent pyothorax. PLG, despite being very rare, should be added to the list of differential diagnoses for pyothorax and solitary lung masses in cats.Non