The origin of the E+ transition in GaAsN alloys

Optical properties of GaAsN system with nitrogen concentrations in the range of 0.9-3.7% are studied by full-potential LAPW method in a supercell approach. The E+ transition is identified by calculating the imaginary part of the dielectric function. The evolution of the energy of this transition with nitrogen concentration is studied and the origin of this transition is identified by analyzing the contributions to the dielectric function from different band combinations. The L_1c-derived states are shown to play an important role in the formation of the E+ transition, which was also suggested by recent experiments. At the same time the nitrogen-induced modification of the first conduction band of the host compound are also found to contribute significantly to the E+ transition. Further, the study of several model supercells demonstrated the significant influence of the nitrogen potential on the optical properties of the GaAsN system.Comment: 5 pages, 3 figure

Constructing the determinant sphere using a Tate twist

Following an idea of Hopkins, we construct a model of the determinant sphere $S\langle det \rangle$ in the category of $K(n)$-local spectra. To do this, we build a spectrum which we call the Tate sphere $S(1)$. This is a $p$-complete sphere with a natural continuous action of $\mathbb{Z}_p^\times$. The Tate sphere inherits an action of $\mathbb{G}_n$ via the determinant and smashing Morava $E$-theory with $S(1)$ has the effect of twisting the action of $\mathbb{G}_n$. A large part of this paper consists of analyzing continuous $\mathbb{G}_n$-actions and their homotopy fixed points in the setup of Devinatz and Hopkins

Functional Coefficient Estimation with Both Categorical and Continuous Data

We propose a local linear functional coefficient estimator that admits a mix of discrete and contin-uous data for stationary time series. Under weak conditions our estimator is asymptotically normally distributed. A small set of simulation studies is carried out to illustrate the finite sample performance of our estimator. As an application, we estimate a wage determination function that explicitly allows the return to education to depend on other variables. We find evidence of the complex interacting patterns among the regressors in the wage equation, such as increasing returns to education when experience is very low, high return to education for workers with several years of experience, and diminishing returns to education when experience is high. Compared with the commonly used para-metric and semi-parametric methods, our estimator performs better in both goodness-of-fit and in yielding economically interesting interpretation

Media Reporting and Business Cycles: Empirical Evidence based on News Data

Recent literature suggests that news shocks could be an important driver of economic cycles. In this article, we use a direct measure of news sentiment derived from media reports. This allows us to examine whether innovations in the reporting tone correlate with changes in the assessment and expectations of the business situation as reported by firms in the German manufacturing sector. We fi nd that innovations in news reporting affect business expectations, even when conditioning on the current business situation and industrial production. The dynamics of the empirical model con rm theoretical predictions that news innovations affect real variables such as production via changes in expectations. Looking at individual sectors within manufacturing, we fi nd that macroeconomic news is at least as important for business expectations as sector-spefici c news. This is consistent with the existence of information complementarities across sectors

Compressed Membership for NFA (DFA) with Compressed Labels is in NP (P)

In this paper, a compressed membership problem for finite automata, both deterministic and non-deterministic, with compressed transition labels is studied. The compression is represented by straight-line programs (SLPs), i.e. context-free grammars generating exactly one string. A novel technique of dealing with SLPs is introduced: the SLPs are recompressed, so that substrings of the input text are encoded in SLPs labelling the transitions of the NFA (DFA) in the same way, as in the SLP representing the input text. To this end, the SLPs are locally decompressed and then recompressed in a uniform way. Furthermore, such recompression induces only small changes in the automaton, in particular, the size of the automaton remains polynomial. Using this technique it is shown that the compressed membership for NFA with compressed labels is in NP, thus confirming the conjecture of Plandowski and Rytter and extending the partial result of Lohrey and Mathissen; as it is already known, that this problem is NP-hard, we settle its exact computational complexity. Moreover, the same technique applied to the compressed membership for DFA with compressed labels yields that this problem is in P; for this problem, only trivial upper-bound PSPACE was known

Processing Succinct Matrices and Vectors

We study the complexity of algorithmic problems for matrices that are represented by multi-terminal decision diagrams (MTDD). These are a variant of ordered decision diagrams, where the terminal nodes are labeled with arbitrary elements of a semiring (instead of 0 and 1). A simple example shows that the product of two MTDD-represented matrices cannot be represented by an MTDD of polynomial size. To overcome this deficiency, we extended MTDDs to MTDD_+ by allowing componentwise symbolic addition of variables (of the same dimension) in rules. It is shown that accessing an entry, equality checking, matrix multiplication, and other basic matrix operations can be solved in polynomial time for MTDD_+-represented matrices. On the other hand, testing whether the determinant of a MTDD-represented matrix vanishes PSPACE$-complete, and the same problem is NP-complete for MTDD_+-represented diagonal matrices. Computing a specific entry in a product of MTDD-represented matrices is #P-complete.Comment: An extended abstract of this paper will appear in the Proceedings of CSR 201

Implementation of the LDA+U method using the full potential linearized augmented plane wave basis

We provide a straightforward and efficient procedure to combine LDA+U total energy functional with the full potential linearized augmented plane wave method. A detailed derivation of the LDA+U Kohn-Sham type equations is presented for the augmented plane wave basis set, and a simple ``second-variation'' based procedure for self-consistent LDA+U calculations is given. The method is applied to calculate electronic structure and magnetic properties of NiO and Gd. The magnetic moments and band eigenvalues obtained are in very good quantitative agreement with previous full potential LMTO calculations. We point out that LDA+U reduces the total d charge on Ni by 0.1 in NiO