Phototauntomerism of o-nitrobenzyl compounds: o-quinonoid aci-nitro species studied by matrix isolation and DFT calculations

Photolyses of 2-nitrobenzyl methyl ether and 2-nitrotoluene with 254 nm light have been investigated in Ar and N2 matrices at 12 K, and have been found to give o-quinonoid aci-nitro species as the primary photoproducts, along with other products. The o-quinonoid species have UV absorptions at relatively long wavelengths (λmax at 385–430 nm) and undergo facile secondary photolysis when irradiated in these absorption bands. By means of this selective photolysis, fairly complete IR spectra of the o-quinonoids have been obtained. Comparison of the matrix IR spectra of these species with simulated spectra computed using density functional theory (DFT) has confirmed the identity of these reactive intermediates. Moreover, detailed analysis of the fit between the computed and experimental IR spectra has allowed the specific stereoisomers generated to be identified with reasonable confidence. Computations have also been made of the relative energies of the starting compounds, intermediate o-quinonoid isomers and the possible secondary products, together with the transition states connecting them. The results of these computations indicate that the observed stereoisomer of each of the o-quinonoid species cannot arise by photoinduced H-atom transfer followed by isomerizations on the electronic ground-state surfaces, since the energy barriers for reversion to starting compounds are substantially lower than those for the necessary isomerizations. It is therefore concluded that H-atom transfer and conformational interconversion occur in an electronic excited state

An Axiomatic Setup for Algorithmic Homological Algebra and an Alternative Approach to Localization

In this paper we develop an axiomatic setup for algorithmic homological algebra of Abelian categories. This is done by exhibiting all existential quantifiers entering the definition of an Abelian category, which for the sake of computability need to be turned into constructive ones. We do this explicitly for the often-studied example Abelian category of finitely presented modules over a so-called computable ring $R$, i.e., a ring with an explicit algorithm to solve one-sided (in)homogeneous linear systems over $R$. For a finitely generated maximal ideal $\mathfrak{m}$ in a commutative ring $R$ we show how solving (in)homogeneous linear systems over $R_{\mathfrak{m}}$ can be reduced to solving associated systems over $R$. Hence, the computability of $R$ implies that of $R_{\mathfrak{m}}$. As a corollary we obtain the computability of the category of finitely presented $R_{\mathfrak{m}}$-modules as an Abelian category, without the need of a Mora-like algorithm. The reduction also yields, as a by-product, a complexity estimation for the ideal membership problem over local polynomial rings. Finally, in the case of localized polynomial rings we demonstrate the computational advantage of our homologically motivated alternative approach in comparison to an existing implementation of Mora's algorithm.Comment: Fixed a typo in the proof of Lemma 4.3 spotted by Sebastian Posu

A probabilistic algorithm to test local algebraic observability in polynomial time

The following questions are often encountered in system and control theory. Given an algebraic model of a physical process, which variables can be, in theory, deduced from the input-output behavior of an experiment? How many of the remaining variables should we assume to be known in order to determine all the others? These questions are parts of the \emph{local algebraic observability} problem which is concerned with the existence of a non trivial Lie subalgebra of the symmetries of the model letting the inputs and the outputs invariant. We present a \emph{probabilistic seminumerical} algorithm that proposes a solution to this problem in \emph{polynomial time}. A bound for the necessary number of arithmetic operations on the rational field is presented. This bound is polynomial in the \emph{complexity of evaluation} of the model and in the number of variables. Furthermore, we show that the \emph{size} of the integers involved in the computations is polynomial in the number of variables and in the degree of the differential system. Last, we estimate the probability of success of our algorithm and we present some benchmarks from our Maple implementation.Comment: 26 pages. A Maple implementation is availabl

Local, hierarchic, and iterative reconstructors for adaptive optics

Adaptive optics systems for future large optical telescopes may require thousands of sensors and actuators. Optimal reconstruction of phase errors using relative measurements requires feedback from every sensor to each actuator, resulting in computational scaling for n actuators of n^2 . The optimum local reconstructor is investigated, wherein each actuator command depends only on sensor information in a neighboring region. The resulting performance degradation on global modes is quantified analytically, and two approaches are considered for recovering "global" performance. Combining local and global estimators in a two-layer hierarchic architecture yields computations scaling with n^4/3 ; extending this approach to multiple layers yields linear scaling. An alternative approach that maintains a local structure is to allow actuator commands to depend on both local sensors and prior local estimates. This iterative approach is equivalent to a temporal low-pass filter on global information and gives a scaling of n^3/2 . The algorithms are simulated by using data from the Palomar Observatory adaptive optics system. The analysis is general enough to also be applicable to active optics or other systems with many sensors and actuators

Sympiler: Transforming Sparse Matrix Codes by Decoupling Symbolic Analysis

Sympiler is a domain-specific code generator that optimizes sparse matrix computations by decoupling the symbolic analysis phase from the numerical manipulation stage in sparse codes. The computation patterns in sparse numerical methods are guided by the input sparsity structure and the sparse algorithm itself. In many real-world simulations, the sparsity pattern changes little or not at all. Sympiler takes advantage of these properties to symbolically analyze sparse codes at compile-time and to apply inspector-guided transformations that enable applying low-level transformations to sparse codes. As a result, the Sympiler-generated code outperforms highly-optimized matrix factorization codes from commonly-used specialized libraries, obtaining average speedups over Eigen and CHOLMOD of 3.8X and 1.5X respectively.Comment: 12 page