Finite-sample properties of estimators for first and second order autoregressive processes

Statistical Inference for Stochastic Processes - The class of autoregressive (AR) processes is extensively used to model temporal dependence in observed time series. Such models are easily...     

Markov shifts and topological entropy of families of homoclinic tangles

The existence of a homoclinic orbit in dynamical systems implies chaotic behaviour with positive entropy. In this work, we determine explicitly the Markov shifts associated to certain Smale horseshoe homoclinic orbits which allow us to compute a lower bound for the topological entropy that such a system can have. It is done associating a heteroclinic orbit which belongs to the same isotopy class and then determining the Markov partition of the dynamical core of an end periodic mapping.     

Base-Pairing Properties of Double-Headed Nucleotides

Nucleotides that contain two nucleobases (double-headed nucleotides) have the potential to condense the information of two separate nucleotides into one. This presupposes that both bases must successfully pair with a cognate strand. Here, double-headed nucleotides that feature cytosine, guanine, thymine, adenine, hypoxanthine, and diaminopurine linked to the C2′-position of an arabinose scaffold were developed and examined in full detail. These monomeric units were efficiently prepared by convergent synthesis and incorporated into DNA oligonucleotides by means of the automated phosphoramidite method. Their pairing efficiency was assessed by UV-based melting-temperature analysis in several contexts and extensive molecular dynamics studies. Altogether, the results show that these double-headed nucleotides have a well-defined structure and invariably behave as functional dinucleotide mimics in DNA duplexes.     

Bridging the Green Gap: Metal–Organic Framework Heteromultilayers Assembled from Porphyrinic Linkers Identified by Using Computational Screening

In organic photovoltaics, porphyrins (PPs) are among the most promising compounds owing to their large absorption cross-section, wide spectral range, and stability. Nevertheless, a precise adjustment of absorption band positions to reach a full coverage of the so-called green gap has not been achieved yet. We demonstrate that a tuning of the PP Q- and Soret bands can be carried out by using a computational approach for which substitution patterns are optimized in silico. The most promising candidate structures were then synthesized. The experimental UV/Vis data for the solvated compounds were in excellent agreement with the theoretical predictions. By attaching further functionalities, which allow the use of PP chromophores as linkers for the assembly of metal-organic frameworks (MOFs), we were able to exploit packing effects resulting in pronounced redshifts, which allowed further optimization of the photophysical properties of PP assemblies. Finally, we use a layer-by-layer method to assemble the PP linkers into surface-mounted MOFs (SURMOFs), thus obtaining high optical quality, homogeneous and crystalline multilayer films. Experimental results are in full accord with the calculations, demonstrating the huge potential of computational screening methods in tailoring MOF and SURMOF photophysical properties.     

Solar Thermal Energy Storage in a Photochromic Macrocycle

The conversion and efficient storage of solar energy is recognized to hold significant potential with regard to future energy solutions. Molecular solar thermal batteries based on photochromic systems exemplify one possible technology able to harness and apply this potential. Herein is described the synthesis of a macrocycle based on a dimer of the dihydroazulene/vinylheptafulvene (DHA/VHF) photo/thermal couple. By taking advantage of conformational strain, this DHA–DHA macrocycle presents an improved ability to absorb and store incident light energy in chemical bonds (VHF–VHF). A stepwise energy release over two sequential ring‐closing reactions (VHF→DHA) combines the advantages of an initially fast discharge, hypothetically addressing immediate energy consumption needs, followed by a slow process for consistent, long‐term use. This exemplifies another step forward in the molecular engineering and design of functional organic materials towards solar thermal energy storage and release.     

Sufficient Conditions for a Digraph to be Supereulerian

A (di)graph is supereulerian if it contains a spanning eulerian sub(di)graph. This property is a relaxation of hamiltonicity. Inspired by this analogy with hamiltonian cycles and by similar results in supereulerian graph theory, we analyze a number of sufficient Ore type conditions for a digraph to be supereulerian. Furthermore, we study the following conjecture due to Thomassé and the first author: if the arc‐connectivity of a digraph is not smaller than its independence number, then the digraph is supereulerian. As a support for this conjecture we prove it for digraphs that are semicomplete multipartite or quasitransitive and verify the analogous statement for undirected graphs.