Discrete and Continuous Time Modulated Random Walks with Heavy-Tailed Increments

We consider a modulated process S which, conditional on a background process X, has independent increments. Assuming that S drifts to −∞ and that its increments (jumps) are heavy-tailed (in a sense made precise in the paper), we exhibit natural conditions under which the asymptotics of the tail distribution of the overall maximum of S can be computed. We present results in discrete and in continuous time. In particular, in the absence of modulation, the process S in continuous time reduces to a Lévy process with heavy-tailed Lévy measure. A central point of the paper is that we make full use of the so-called “principle of a single big jump” in order to obtain both upper and lower bounds. Thus, the proofs are entirely probabilistic. The paper is motivated by queueing and Lévy stochastic networks.     

Synthesis and X-ray crystal structures of six [TeL4][MF6] salts, where L is ethylene- or trimethylene-thiourea, and M is Si, Ge or Sn. Five Te(II) complexes with a novel type of structure linked together by unusual N–HF hydrogen bonds

The complexes [Te(etu)₄][SiF₆] (1), [Te(etu)₄][SiF₆] · H₂O (2), [Te(trtu)₄][SiF₆] (3), [Te(etu)₄][GeF₆] · H₂O (4), [Te(trtu)₄][GeF₆] (5) and [Te(etu)₄][SnF₆] (6) (etu = ethylenethiourea, trtu = trimethylenethiourea) have been prepared and their crystal structures determined by X-ray crystallographic methods. The crystals of 1, 3 and 5 are tetragonal; space groups P4cc (No. 103) with Z = 4 for 1, P4nc (No. 104) with Z = 2 for 3, and I4 (No. 79) with Z = 2 for 5. The crystals of 2, 4 and 6 are orthorhombic, space group Pccn (No. 56) with Z = 8 for 2 and 4 and Z = 4 for 6; those of 2 and 4 being isomorphous. The cations contain square planar or slightly distorted square planar TeS₄ coordination groups. In 1, 3 and 5 the Te atoms are located on fourfold rotation axes; the cations have fourfold rotational symmetry and the four thiourea ligands extend to the same side of the TeS₄ plane. These are the first examples of [TeL₄]²⁺ conformers of this type. In 2 and 4 the Te atoms lie on general positions; the cations are distorted versions of those in 1, and also in these the four ligands extend to the same side of the TeS₄ plane. In 6 the Te atoms are located on twofold rotation axes, the conformation of the cations corresponds to the point group C₂ with two neighbouring ligands extending to one side of the coordination plane and the remaining two to the opposite side. In 1–5 each of the four ligands forms a N–HF bond to the same F atom in the counter ion. The crystals of 1–5 are red, and those of 6 are yellow. The red colour is attributed to interactions of Te and S lone electron pairs caused by ligand TeS₄/TeSC tilt angles markedly different from 90°.     

Regulation of plastic from a circular economy perspective

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Element-Substituted Acylphosphines

Abstract

Element-substituted acylphosphines are stable in form 2 R¹P(ER_n)COR² (A), when E=Ge, Sn, Sb, P, T1 and in form R¹ P=C(OER_n)R² by NMR data. The reaction     

On Transience Conditions for Markov Chains

Siberian Mathematical Journal -     

Cell shape and spreading of stromal (mesenchymal) stem cells cultured on fibronectin coated gold and hydroxyapatite surfaces

In order to identify the cellular mechanisms leading to the biocompatibility of hydroxyapatite implants, we studied the interaction of human bone marrow derived stromal (mesenchymal) stem cells (hMSCs) with fibronectin-coated gold (Au) and hydroxyapatite (HA) surfaces. The adsorption of fibronectin was monitored by Quartz Crystal Microbalance with Dissipation (QCM-D) at two different concentrations, 20 μg/ml and 200 μg/ml, and the fibronectin adsorption experiments were complemented with antibody measurements. The QCM-D results show that the surface mass uptake is largest on the Au surfaces, while the number of polyclonal and monoclonal antibodies directed against the cell-binding domain (CB-domain) on the fibronectin (Fn) is significantly larger on the (HA) surfaces. Moreover, a higher number of antibodies bound to the fibronectin coatings formed from the highest bulk fibronection concentration. In subsequent cell studies with hMSC's we studied the cell spreading, cytoskeletal organization and cell morphology on the respective surfaces. When the cells were adsorbed on the uncoated substrates, a diffuse cell actin cytoskeleton was revealed, and the cells had a highly elongated shape. On the fibronectin coated surfaces the cells adapted to a more polygonal shape with a well-defined actin cytoskeleton, while a larger cell area and roundness values were observed for cells cultured on the coated surfaces. Among the coated surfaces a slightly larger cell area and roundness values was observed on HA as compared to Au. Moreover, the results revealed that the morphology of cells cultured on fibronectin coated HA surfaces were less irregular. In summary we find that fibronectin adsorbs in a more activated state on the HA surfaces, resulting in a slightly different cellular response as compared to the fibronectin coated Au surfaces.     

On the limit law of a random walk conditioned to reach a high level

We consider a random walk with a negative drift and with a jump distribution which under Cramér’s change of measure belongs to the domain of attraction of a spectrally positive stable law. If conditioned to reach a high level and suitably scaled, this random walk converges in law to a nondecreasing Markov process which can be interpreted as a spectrally positive Lévy process conditioned not to overshoot level 1.