Linear orthogonality preservers of Hilbert bundles

Due to the corresponding fact concerning Hilbert spaces, it is natural to ask if the linearity and the orthogonality structure of a Hilbert $C^*$-module determine its $C^*$-algebra-valued inner product. We verify this in the case when the $C^*$-algebra is commutative (or equivalently, we consider a Hilbert bundle over a locally compact Hausdorff space). More precisely, a $\mathbb{C}$-linear map $\theta$ (not assumed to be bounded) between two Hilbert $C^*$-modules is said to be "orthogonality preserving" if \left =0 whenever \left =0. We prove that if $\theta$ is an orthogonality preserving map from a full Hilbert $C_0(\Omega)$-module $E$ into another Hilbert $C_0(\Omega)$-module $F$ that satisfies a weaker notion of $C_0(\Omega)$-linearity (known as "localness"), then $\theta$ is bounded and there exists $\phi\in C_b(\Omega)_+$ such that \left\ =\ \phi\cdot\left, \quad \forall x,y \in E. On the other hand, if $F$ is a full Hilbert $C^*$-module over another commutative $C^*$-algebra $C_0(\Delta)$, we show that a "bi-orthogonality preserving" bijective map $\theta$ with some "local-type property" will be bounded and satisfy \left\ =\ \phi\cdot\left\circ\sigma, \quad \forall x,y \in E where $\phi\in C_b(\Omega)_+$ and $\sigma: \Delta \rightarrow \Omega$ is a homeomorphism

Linear orthogonality preservers of Hilbert C∗C^*-modules over general C∗C^*-algebras

As a partial generalisation of the Uhlhorn theorem to Hilbert $C^*$-modules, we show in this article that the module structure and the orthogonality structure of a Hilbert $C^*$-module determine its Hilbert $C^*$-module structure. In fact, we have a more general result as follows. Let $A$ be a $C^*$-algebra, $E$ and $F$ be Hilbert $A$-modules, and $I_E$ be the ideal of $A$ generated by $\{\langle x,y\rangle_A: x,y\in E\}$. If $\Phi : E\to F$ is an $A$-module map, not assumed to be bounded but satisfying $$\langle \Phi(x),\Phi(y)\rangle_A\ =\ 0\quad\text{whenever}\quad\langle x,y\rangle_A\ =\ 0,$$ then there exists a unique central positive multiplier $u\in M(I_E)$ such that $$\langle \Phi(x), \Phi(y)\rangle_A\ =\ u \langle x, y\rangle_A\qquad (x,y\in E).$$ As a consequence, $\Phi$ is automatically bounded, the induced map $\Phi_0: E\to \overline{\Phi(E)}$ is adjointable, and $\overline{Eu^{1/2}}$ is isomorphic to $\overline{\Phi(E)}$ as Hilbert $A$-modules. If, in addition, $\Phi$ is bijective, then $E$ is isomorphic to $F$.Comment: 15 page

On the decomposition into Discrete, type II and type III C∗C^*-algebras

We obtained a "decomposition scheme" of C*-algebras. We show that the classes of discrete C*-algebras (as defined by Peligard and Zsido), type II C*-algebras and type III C*-algebras (both defined by Cuntz and Pedersen) form a good framework to "classify" C*-algebras. In particular, we found that these classes are closed under strong Morita equivalence, hereditary C*-subalgebras as well as taking "essential extension" and "normal quotient". Furthermore, there exist the largest discrete finite ideal $A_{d,1}$, the largest discrete essentially infinite ideal $A_{d,\infty}$, the largest type II finite ideal $A_{II,1}$, the largest type II essentially infinite ideal $A_{II,\infty}$, and the largest type III ideal $A_{III}$ of any C*-algebra $A$ such that $A_{d,1} + A_{d,\infty} + A_{II,1} + A_{II,\infty} + A_{III}$ is an essential ideal of $A$. This "decomposition" extends the corresponding one for $W^*$-algebras. We also give a closer look at C*-algebras with Hausdorff primitive spectrum, AW*-algebras as well as local multiplier algebras of C*-algebras. We find that these algebras can be decomposed into continuous fields of prime C*-algebras over a locally compact Hausdorff space, with each fiber being non-zero and of one of the five types mentioned above.Comment: 41 pages; we added a lot of details and some new result

Climate Change and Crop Yield Distribution: Some New Evidence From Panel Data Models

This study examines the impact of climate on the yields of seven major crops in Taiwan based on pooled panel data for 15 prefectures over the 1977-1996 period. Unit-root tests and maximum likelihood methods involving a panel data model are explored to obtain reliable estimates. The results suggest that climate has different impacts on different crops and a gradual increase in crop yield variation is expected as global warming prevails. Policy measures to counteract yield variability should therefore be carefully evaluated to protect farmers from exposure to these long-lasting and increasingly climate-related risks.Yield response, Climate change, Panel data, Unit-root test

Threshold Effects in Cigarette Addiction: An Application of the Threshold Model in Dynamic Panels

We adopt the threshold model of myopic cigarette addiction to US state-level panel data. The threshold model is used to identify the structural effects of cigarette demand determinants across the income stratification. Furthermore, we apply a bootstrap approach to correct for the small-sample bias that arises in the dynamic panel threshold model with fixed effects. Our empirical results indicate that there exists the heterogeneity of smoking dynamics across consumers.Cigarettes demand, price elasticity, threshold regression model, dynamic panel model, bias correction, bootstrap

A QHD-capable parallel H.264 decoder

Video coding follows the trend of demanding higher performance every new generation, and therefore could utilize many-cores. A complete parallelization of H.264, which is the most advanced video coding standard, was found to be difficult due to the complexity of the standard. In this paper a parallel implementation of a complete H.264 decoder is presented. Our parallelization strategy exploits function-level as well as data-level parallelism. Function-level parallelism is used to pipeline the H.264 decoding stages. Data-level parallelism is exploited within the two most time consuming stages, the entropy decoding stage and the macroblock decoding stage. The parallelization strategy has been implemented and optimized on three platforms with very different memory architectures, namely an 8-core SMP, a 64-core cc-NUMA, and an 18-core Cell platform. Evaluations have been performed using 4kx2k QHD sequences. On the SMP platform a maximum speedup of 4.5x is achieved. The SMP-implementation is reasonably performance portable as it achieves a speedup of 26.6x on the cc-NUMA system. However, to obtain the highest performance (speedup of 33.4x and throughput of 200 QHD frames per second), several cc-NUMA specific optimizations are necessary such as optimizing the page placement and statically assigning threads to cores. Finally, on the Cell platform a near ideal speedup of 16.5x is achieved by completely hiding the communication latency.EC/FP7/248647/EU/ENabling technologies for a programmable many-CORE/ENCOR