Area-preserving diffeomorphism of the hyperbolic plane and K-surfaces in Anti-de Sitter space

We prove that any weakly acausal curve $\Gamma$ in the boundary of Anti-de Sitter (2+1)-space is the asymptotic boundary of two spacelike $K$-surfaces, one of which is past-convex and the other future-convex, for every $K\in(-\infty,-1)$. The curve $\Gamma$ is the graph of a quasisymmetric homeomorphism of the circle if and only if the $K$-surfaces have bounded principal curvatures. Moreover in this case a uniqueness result holds. The proofs rely on a well-known correspondence between spacelike surfaces in Anti-de Sitter space and area-preserving diffeomorphisms of the hyperbolic plane. In fact, an important ingredient is a representation formula, which reconstructs a spacelike surface from the associated area-preserving diffeomorphism. Using this correspondence we then deduce that, for any fixed $\theta\in(0,\pi)$, every quasisymmetric homeomorphism of the circle admits a unique extension which is a $\theta$-landslide of the hyperbolic plane. These extensions are quasiconformal.Comment: 47 pages, 18 figures. More details added to Remark 4.14, Remark 6.2 and Theorem 7.8 Step 2. Several references added and typos corrected. Final version. To appear in Journal of Topolog

Predicting Ecologically Important Vegetation Variables from Remotely Sensed Optical/Radar Data Using Neural Networks

A number of satellite sensor systems will collect large data sets of the Earth's surface during NASA's Earth Observing System (EOS) era. Efforts are being made to develop efficient algorithms that can incorporate a wide variety of spectral data and ancillary data in order to extract vegetation variables required for global and regional studies of ecosystem processes, biosphere-atmosphere interactions, and carbon dynamics. These variables are, for the most part, continuous (e.g. biomass, leaf area index, fraction of vegetation cover, vegetation height, vegetation age, spectral albedo, absorbed photosynthetic active radiation, photosynthetic efficiency, etc.) and estimates may be made using remotely sensed data (e.g. nadir and directional optical wavelengths, multifrequency radar backscatter) and any other readily available ancillary data (e.g., topography, sun angle, ground data, etc.). Using these types of data, neural networks can: 1) provide accurate initial models for extracting vegetation variables when an adequate amount of data is available; 2) provide a performance standard for evaluating existing physically-based models; 3) invert multivariate, physically based models; 4) in a variable selection process, identify those independent variables which best infer the vegetation variable(s) of interest; and 5) incorporate new data sources that would be difficult or impossible to use with conventional techniques. In addition, neural networks employ a more powerful and adaptive nonlinear equation form as compared to traditional linear, index transformations, and simple nonlinear analyses. These neural networks attributes are discussed in the context of the authors' investigations of extracting vegetation variables of ecological interest

A strategy planner for NASA robotics applications

Automatic strategy or task planning is an important element of robotics systems. A strategy planner under development at Goddard Space Flight Center automatically produces robot plans for assembly, disassembly, or repair of NASA spacecraft from computer aided design descriptions of the individual parts of the spacecraft

Elliptic hypergeometry of supersymmetric dualities II. Orthogonal groups, knots, and vortices

We consider Seiberg electric-magnetic dualities for 4d $\mathcal{N}=1$ SYM theories with SO(N) gauge group. For all such known theories we construct superconformal indices (SCIs) in terms of elliptic hypergeometric integrals. Equalities of these indices for dual theories lead both to proven earlier special function identities and new conjectural relations for integrals. In particular, we describe a number of new elliptic beta integrals associated with the s-confining theories with the spinor matter fields. Reductions of some dualities from SP(2N) to SO(2N) or SO(2N+1) gauge groups are described. Interrelation of SCIs and the Witten anomaly is briefly discussed. Possible applications of the elliptic hypergeometric integrals to a two-parameter deformation of 2d conformal field theory and related matrix models are indicated. Connections of the reduced SCIs with the state integrals of the knot theory, generalized AGT duality for (3+3)d theories, and a 2d vortex partition function are described.Comment: Latex, 58 pages; paper shortened, to appear in Commun. Math. Phy

Ursinus College Bulletin Vol. 5, No. 6

A digitized copy of the March 1889 Ursinus College Bulletin.https://digitalcommons.ursinus.edu/ucbulletin/1027/thumbnail.jp

The recovery of dialogue

The cultural richness that once made Leonardo’s "Paragone" possible quickly waned in the wake of the 18th century separation of natural science and fine art into competing systems of knowledge, leaving architects to contend with ‘gaps’ and fragments of unity. Arguably these gaps are the cause of much uncertainty in a discipline that, weakened through autonomy is enriched by engagement and multidisciplinary praxis. If traditional architectural treatises that once took art and science to be intertwined skills held together by a higher order of design intelligence are difficult to conceive in our present culture, what valid mode of discourse remains to assist architects [to] think through the future continuity of art and science? This paper does not support the view that systematic methods are easily transposed onto architecture in order to reduce its unpredictable phenomena to stable predictable facts. Contemporary thought is sufficiently mature to realise that the generalisation of specialist knowledge, instrumentality and expertise always leaves something out. The ongoing challenge to architecture today is therefore how to re-articulate the relational space between art and science in a way that enhances their symbiosis within design. Symbolism, metaphor, analogy and geometrical abstraction once supplied architecture and creative discourse with intermediate links and devices, but what other tactics are available to the architect today? The primary objective of the paper is to recover traditional "dialogue" as a legitimate and meaningful mode in this regard. Secondly, the paper critically differentiates dialogue from its more contemporary version, "collaboration", with which it is often confused. The question at stake is whether the now ubiquitous notion of collaborative practice can actually fulfil the purposes of mediation and enrichment associated with dialogical intelligence, or is it yet another functional adjunct for streamlining technique and labour?La recuperación del diálogo: La riqueza cultural que en otra época hizo posible el Paragone de Leonardo declinó rápidamente a partir del siglo XVIII, como resultado de la separación de las ciencias naturales y las bellas artes en dos sistemas rivales de conocimiento, enfrentando a los arquitectos a lagunas y fragmentos de unidad. Podría decirse que estas lagunas son la causa de mucha incertidumbre en una disciplina que se debilita con la autonomía pero se enriquece con la participación y la práctica multidisciplinaria. Ya que los tratados tradicionales de arquitectura, que solían considerar al arte y la ciencia como disciplinas entrelazadas y unidas por un orden supremo de inteligencia diseñadora, son difíciles de concebir en nuestra cultura actual, ¿qué modo de discurso válido permanece para ayudar a los arquitectos a pensar detenidamente sobre la continuidad futura del arte y de la ciencia? Este ensayo no sustenta la opinión de que los métodos sistemáticos se puedan trasponer fácilmente a la arquitectura con la finalidad de reducir sus fenómenos impredecibles a hechos estables y predecibles. El pensamiento contemporáneo es suficientemente maduro para comprender que la generalización del conocimiento especializado, la instrumentalidad y la pericia siempre excluye algo. Por lo tanto, el reto permanente para la arquitectura hoy es cómo articular de nuevo el espacio relacional entre el arte y la ciencia de una manera que incremente su simbiosis dentro del diseño. El simbolismo, la metáfora, la analogía y la abstracción geométrica suministraron en el pasado conexiones y recursos intermedios a la arquitectura y al discurso creativo, pero ¿de qué otras tácticas dispone el arquitecto actual? El objetivo principal de este ensayo es recuperar el "diálogo" tradicional como modo legítimo y significativo en este aspecto. En segundo lugar, el ensayo distingue críticamente entre el diálogo y su versión más contemporánea, la "colaboración", con la cual se confunde frecuentemente. La pregunta decisiva es si el concepto ahora tan ubicuo de práctica colaborativa puede satisfacer el propósito de mediación y enriquecimiento asociado con la inteligencia dialógica, o si se trata de otro apéndice funcional más para racionalizar la técnica y el trabajo

Crises of the political and Human Rights: critical perspectives on the common world

ABSTRACT: The current political order is marked by large, interconnected spaces, that come to expose more than ever the fragilities of a post-Westphalian sovereignty paradigm, anchored in the national imaginary (Rocha-Cunha 2020). Political and economic cleavages, vulnerable democracies, and social polarizations present in today’s globalized world place human rights at the centre of the academic debate of the political realm. Under this prism, in this volume we hope to contribute to a re-evaluation of the current political crises and the need for human rights-centred political alternatives. The chapters that com prise this book are structured around a transdisciplinary meth odological framework, that reflects the evolving and complex affirmations of human rights quest in an ongoing scholarly dis cussion. All the chapters take a critical analysis approach to a wide range of theoretical frameworks and political and institutional settings. All chapters involve problems that are simultaneously situated upstream and downstream of the themes explored here. In effect, they start from the observation that the political models, both internal and international, bear the brunt of the difficulties of the modern paradigms of politics and rights, of the reductionist anthropology and scientism that marked the birth of our world. Humanist and nihilistic values have emerged from these difficulties, which have brought to the present day productivism, possessive individu alism, complex exclusions around the regulation and redistribution of goods and authoritarian forms of exercising power. We can thus define two major critical lines in the present moment.info:eu-repo/semantics/publishedVersio

Semiclassical chaos, the uncertainty principle, and quantum dissipation

Article on semiclassical chaos, the uncertainty principle, and quantum dissipation