Local Isometric immersions of pseudo-spherical surfaces and evolution equations

The class of differential equations describing pseudo-spherical surfaces, first introduced by Chern and Tenenblat [3], is characterized by the property that to each solution of a differential equation, within the class, there corresponds a 2-dimensional Riemannian metric of curvature equal to $-1$. The class of differential equations describing pseudo-spherical surfaces carries close ties to the property of complete integrability, as manifested by the existence of infinite hierarchies of conservation laws and associated linear problems. As such, it contains many important known examples of integrable equations, like the sine-Gordon, Liouville and KdV equations. It also gives rise to many new families of integrable equations. The question we address in this paper concerns the local isometric immersion of pseudo-spherical surfaces in ${\bf E}^{3}$ from the perspective of the differential equations that give rise to the metrics. Indeed, a classical theorem in the differential geometry of surfaces states that any pseudo-spherical surface can be locally isometrically immersed in ${\bf E}^{3}$. In the case of the sine-Gordon equation, one can derive an expression for the second fundamental form of the immersion that depends only on a jet of finite order of the solution of the pde. A natural question is to know if this remarkable property extends to equations other than the sine-Gordon equation within the class of differential equations describing pseudo-spherical surfaces. In an earlier paper [11], we have shown that this property fails to hold for all other second order equations, except for those belonging to a very special class of evolution equations. In the present paper, we consider a class of evolution equations for $u(x,t)$ of order $k\geq 3$ describing pseudo-spherical surfaces. We show that whenever an isometric immersion in ${\bf E}^3$ exists, depending on a jet of finite order of $u$, then the coefficients of the second fundamental forms are functions of the independent variables $x$ and $t$ only.Comment: Fields Institute Communications, 2015, Hamiltonian PDEs and Applications, pp.N

Device-independent bounds for Hardy's experiment

In this Letter we compute an analogue of Tsirelson's bound for Hardy's test of nonlocality, that is, the maximum violation of locality constraints allowed by the quantum formalism, irrespective of the dimension of the system. The value is found to be the same as the one achievable already with two-qubit systems, and we show that only a very specific class of states can lead to such maximal value, thus highlighting Hardy's test as a device-independent self-test protocol for such states. By considering realistic constraints in Hardy's test, we also compute device-independent upper bounds on this violation and show that these bounds are saturated by two-qubit systems, thus showing that there is no advantage in using higher-dimensional systems in experimental implementations of such test.Comment: 4 pages, 2 figure

Online and offline representations of biocultural diversity: A political ecology perspective on nature-based tourism and indigenous communities in the Brazilian Pantanal

The concept of biocultural diversity is confronted with contemporary changes that impact on local communities, such as globalization and digital transformations. Engaging the conceptual flexibility of ‘biocultural diversity’, we studied nature-based tourism at the intersection of indigenous communities and the digital realm. We employed a political ecology perspective to examine online and offline representations of biocultural diversity in the Brazilian Pantanal, one of the biggest wetlands in the world, and home to groups of peoples known as the Pantaneiros. Data from interviews with 48 stakeholders in the tourist sector were structured along three ‘myths’—the Uncivilised, Unrestrained, and Unchanged—for which we have also constructed counter narratives. Each myth denoted the primacy of biodiversity, and ignored broader dimensions of the Pantanal as a bioculturally diverse landscape. The relationships of the Pantaneiros with their environment were found to be intricate and had clear repercussions for tourism, but ironically, reference to the Pantaneiro culture in nature-based tourism was superficial. Moreover, thriving on the myths, this form of tourism perpetuates skewed power structures and social inequalities. Lower-class Pantaneiros likely suffer most from this. We recommend stakeholder engagement with a biocultural design that facilitates the integration of other-than-biodiversity values, and that thereby promotes sustainability of the entire social-ecological system

Study of infection by Babesia bovis and Anaplasma marginale in dairy water buffaloes in the state of São Paulo.

The aim of this study was to evaluate the prevalence of infection by Babesia bovis and Anaplasma margina/e in dairy water buffaloes infested by ticks on farms, either in exclusive buffalo herds or in in mixed herds along with cattle

Estudo comparativo entre técnicas de extração de DNA para o futuro diagnóstico do endossimbionte Wolbachia em Haematobia irritans.

Editores técnicos: João de Mendonça Naime, Caue Ribeiro, Maria Alice Martins, Elaine Cristina Paris, Paulino Ribeiro Villas Boas, Ladislau Marcelino Rabello