Homotopy Type Theory in Lean

We discuss the homotopy type theory library in the Lean proof assistant. The library is especially geared toward synthetic homotopy theory. Of particular interest is the use of just a few primitive notions of higher inductive types, namely quotients and truncations, and the use of cubical methods.Comment: 17 pages, accepted for ITP 201

Interleaving and lock-step semantics for analysis and verification of GPU kernels

Graphics Processing Units (GPUs) from leading vendors employ predicated (or guarded) execution to eliminate branching and increase performance. Similarly, a recent GPU verification technique uses predication to reduce verification of GPU kernels (the massively parallel programs that run on GPUs) to verification of a sequential program. Prior work on the formal semantics of lock-step predicated execution for kernels focused on structured programs, where control is organised using if- and while-statements. We provide lock-step execution semantics for GPU kernels that are represented by arbitrary reducible control flow graphs. We present a traditional interleaving semantics and a novel lock-step semantics based on predication, and show that for terminating kernels either both semantics compute identical results or both behave erroneously. The method allows reducing GPU kernel verification to the verification of a sequential, lock-step program to be applied to GPU kernels with arbitrary reducible control flow. We have implemented the method in the GPUVerify tool, and present an evaluation using a set of 163 open source and commercial GPU kernels. Among these kernels, 42 exhibit unstructured control flow which our novel lock-step predication technique can handle fully automatically. This generality comes at a modest price: verification across our benchmark set was on average 2.25 times slower than using an existing approach that specifically targets structured kernels

Delocalization in harmonic chains with long-range correlated random masses

We study the nature of collective excitations in harmonic chains with masses exhibiting long-range correlated disorder with power spectrum proportional to $1/k^{\alpha}$, where $k$ is the wave-vector of the modulations on the random masses landscape. Using a transfer matrix method and exact diagonalization, we compute the localization length and participation ratio of eigenmodes within the band of allowed energies. We find extended vibrational modes in the low-energy region for $\alpha > 1$. In order to study the time evolution of an initially localized energy input, we calculate the second moment $M_2(t)$ of the energy spatial distribution. We show that $M_2(t)$, besides being dependent of the specific initial excitation and exhibiting an anomalous diffusion for weakly correlated disorder, assumes a ballistic spread in the regime $\alpha>1$ due to the presence of extended vibrational modes.Comment: 6 pages, 9 figure

Influência das variáveis meteorológicas na temperatura da superfície da Caatinga em Petrolina, PE.

A análise da temperatura de um organismo compreende a principal variável utilizada para a compreensão de sua termorregulação. Esta por sua vez, pode variar em função de elementos meteorológicos e principalmente da disponibilidade hídrica do local, sendo um indicador do grau de estresse hídrico da vegetação. O objetivo deste trabalho foi analisar a influencia de variáveis ambientais nos valores da temperatura da superfície da caatinga em Petrolina, PE. Para tanto, realizou-se um experimento em uma área de caatinga preservada pertencente à Embrapa Semiárido, Petrolina ? PE. As medições foram realizadas durante o ano de 2012 por meio de uma torre micrometeorológica de 16m de altura equipada com um sistema de aquisição de dados datalogger. Para determinação da temperatura da superfície utilizou-se o termômetro infravermelho (SI111) instalado a 13,9 metros de altura da superfície do solo. Concomitantemente, foram realizadas medidas dos elementos meteorológicos: temperatura do ar, déficit de pressão de vapor, radiação solar e umidade relativa do ar. Procedeu-se realizando correlações para analisar a influencia de cada variável nos valores médios da temperatura da superfície por meio de regressões e do coeficiente de determinação. Com os resultados observou-se que as variáveis que melhor representaram a temperatura da superfície foram a temperatura do ar e o déficit de pressão de vapor com r² iguais a 0,856 e 0,6327. Essas informações podem ser utilizadas para melhor compreender as respostas dessa área de Caatinga às condições do ambiente, bem como para subsidiar estudos de fluxos de carbono e modelagem climática no Bioma Caatinga

Diagnóstico do espaço turístico e das propostas de gestão no município de Cachoeiras de Macacu.

bitstream/CNPS-2010/14742/1/bpd135-2009-planejamento-espaco-turistico.pd

Observation of Replica Symmetry Breaking in the 1D Anderson Localization Regime in an Erbium-Doped Random Fiber Laser

The analogue of the paramagnetic to spin-glass phase transition in disordered magnetic systems, leading to the phenomenon of replica symmetry breaking, has been recently demonstrated in a two-dimensional random laser consisting of an organic-based amorphous solid-state thin film. We report here the first demonstration of replica symmetry breaking in a one-dimensional photonic system consisting of an erbium-doped random fiber laser operating in the continuous-wave regime based on a unique random fiber grating system, which plays the role of the random scatterers and operates in the Anderson localization regime. The clear transition from a photonic paramagnetic to a photonic spin glass phase, characterized by the probability distribution function of the Parisi overlap, was verified and characterized. In this unique system, the radiation field interacts only with the gain medium, and the fiber grating, which provides the disordered feedback mechanism, does not interfere with the pump