Systems of variational inequalities in the context of optimal switching problems and operators of Kolmogorov type

In this paper we study the system $$\begin{aligned}&\min \biggl \{-\mathcal H u_i(x,t)-\psi _i(x,t),u_i(x,t)-\max _{j\ne i}(-c_{i,j}(x,t)+u_j(x,t))\biggr \}=0,\\&u_i(x,T)=g_i(x),\ i\in \{1,\ldots ,d\}, \end{aligned}$$ where \((x,t)\in \mathbb R ^{N}\times [0,T]\) . A special case of this type of system of variational inequalities with terminal data occurs in the context of optimal switching problems. We establish a general comparison principle for viscosity sub- and supersolutions to the system under mild regularity, growth, and structural assumptions on the data, i.e., on the operator \(\mathcal H \) and on continuous functions \(\psi _i\) , \(c_{i,j}\) , and \(g_i\) . A key aspect is that we make no sign assumption on the switching costs \(\{c_{i,j}\}\) and that \(c_{i,j}\) is allowed to depend on \(x\) as well as \(t\) . Using the comparison principle, the existence of a unique viscosity solution \((u_1,\ldots ,u_d)\) to the system is constructed as the limit of an increasing sequence of solutions to associated obstacle problems. Having settled the existence and uniqueness, we subsequently focus on regularity of \((u_1,\ldots ,u_d)\) beyond continuity. In this context, in particular, we assume that \(\mathcal H \) belongs to a class of second-order differential operators of Kolmogorov type of the form: $$\begin{aligned} \mathcal H =\sum _{i,j=1}^m a_{i,j}(x,t)\partial _{x_i x_j}+\sum _{i=1}^m a_i(x,t)\partial _{x_i} +\sum _{i,j=1}^N b_{i,j}x_i\partial _{x_j}+\partial _t, \end{aligned}$$ where \(1\le m\le N\) . The matrix \(\{a_{i,j}(x,t)\}_{i,j=1,\ldots ,m}\) is assumed to be symmetric and uniformly positive definite in \(\mathbb R ^m\) . In particular, uniform ellipticity is only assumed in the first \(m\) coordinate directions, and hence, \(\mathcal H \) may be degenerate.     

A mathematical insight in the epithelial-mesenchymal-like transition in cancer cells and its effect in the invasion of the extracellular matrix

Current biological knowledge supports the existence of a secondary group of cancer cells within the body of the tumour that exhibits stem cell-like properties. These cells are termed cancer stem cells, and as opposed to themore usual differentiated cancer cells, they exhibit highermotility, they are more resilient to therapy, and are able to metastasize to secondary locations within the organism and produce new tumours. The origin of the cancer stem cells is not completely clear; they seem to stem from the differentiated cancer cells via a transition process related to the epithelial-mesenchymal transition that can also be found in normal tissue. In the current work we model and numerically study the transition between these two types of cancer cells, and the resulting “ensemble” invasion of the extracellular matrix. This leads to the derivation and numerical simulation of two systems: an algebraic-elliptic system for the transition and an advection-reaction-diffusion system of Keller-Segel taxis type for the invasion.     

On two-scale convergence and related sequential compactness topics

A general concept of two-scale convergence is introduced and two-scale compactness theorems are stated and proved for some classes of sequences of bounded functions in L ²(Ω) involving no periodicity assumptions. Further, the relation to the classical notion of compensated compactness and the recent concepts of two-scale compensated compactness and unfolding is discussed and a defect measure for two-scale convergence is introduced.     

The SYM integrable super spin chain

Recently it was established that the one-loop planar dilatation generator of super-Yang–Mills theory may be identified, in some restricted cases, with the Hamiltonians of various integrable quantum spin chains. In particular Minahan and Zarembo established that the restriction to scalar operators leads to an integrable vector chain, while recent work in QCD suggested that restricting to twist operators, containing mostly covariant derivatives, yields certain integrable Heisenberg XXX chains with non-compact spin symmetry . Here we unify and generalize these insights and argue that the complete one-loop planar dilatation generator of is described by an integrable super spin chain. We also write down various forms of the associated Bethe ansatz equations, whose solutions are in one-to-one correspondence with the complete set of all one-loop planar anomalous dimensions in the gauge theory. We finally speculate on the non-perturbative extension of these integrable structures, which appears to involve non-local deformations of the conserved charges.     

Single and networked CuO nanowires for highly sensitive p‐type semiconductor gas sensor applications

Development of high‐performance p‐type semiconductor based gas sensors exhibiting fast‐response/recovery times with ultra‐high response are of major importance for gas sensing applications. Recent reports demonstrated the excellent properties of p‐type semiconducting oxide for various practical applications, especially for selective oxidation of volatile organic compounds (VOCs). In this work, sensors based on CuO nanowire (NW) networks have been successfully fabricated via a simple thermal oxidation process on pre‐patterned Au/Cr pads. Our investigation demonstrates high impact of the process temperature on aspect ratio and density of copper oxide NWs. An optimal temperature for growth of thin and densely packed NWs was found to be at 425 °C. The fabricated sensors demonstrated ultra‐high gas response by a factor of 313 to ethanol vapour (100 ppm) at an operating temperature of 250 °C. High stability and repeatability of these sensors indicate the efficiency of p‐type oxide based gas sensors for selective detection of VOCs. A high‐performance nanodevice was fabricated in a FIB‐SEM system using a single CuO NW, demonstrating an ethanol response of 202 and rapid response and recovery of ～198 ms at room temperature. The involved gas sensing mechanism of CuO NW networks has been described. We consider that the presented results will be of a great interest for the development of higher‐performance p‐type semiconductor based sensors and bottom‐up nanotechnologies. (© 2016 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

Synthesis and screening of peptoid arrays on cellulose membranes

Rapid synthesis and screening of compound libraries enables the accelerated identification of novel protein ligands in order to support processes like analysis of protein interactions, drug target discovery or lead structure discovery. SPOT synthesis—a well established method for the rapid preparation of peptide arrays—has recently been extended to the field of nonpeptides. In this contribution we report on the systematic evaluation of the SPOT technique for the assembly of N-alkylglycine (peptoid) library arrays. In the course of this investigation bromoacetic acid 2,4-dinitrophenylester (1a) was identified to be the most suited agent for bromoacetylation in terms of yield and N-selectivity enabling straightforward submonomer synthesis on hydroxy-group rich cellulose membranes. The potential of this method for the rapid identification of novel nonpeptidic protein ligands was demonstrated by synthesis and screening of a library consisting of 8000 peptoids and peptomers (i.e. their hybrids with α-substituted amino acids) allowing the identification of micromolar ligands for the monoclonal antibody Tab-2.     

Linear and Bent Cp*2Si: Reversible Phase Transition of a Key Molecule

The solid-state structure of decamethylsilicocene Cp*₂Si with a bent and a linear molecule in the same unit cell was so far considered an exception in relation to the structures of its all-bent heavier analogues Cp*₂E with E=Ge, Sn, Pb. Here, we present the solution to this conundrum by reporting a low-temperature phase, where all three symmetrically independent molecules are present in a bent formation. This reversible enantiotropic phase transition occurs in the temperature range between 80 K and 130 K and provides a rationale for the unexpected linear molecule based in entropy beyond hand-waving explanations such as electronic reasons or packing effects.     

Accelerator mass spectrometry of small biological samples

Accelerator mass spectrometry (AMS) is an ultra-sensitive technique for isotopic ratio measurements. In the biomedical field, AMS can be used to measure femtomolar concentrations of labeled drugs in body fluids, with direct applications in early drug development such as Microdosing. Likewise, the regenerative properties of cells which are of fundamental significance in stem-cell research can be determined with an accuracy of a few years by AMS analysis of human DNA. However, AMS nominally requires about 1 mg of carbon per sample which is not always available when dealing with specific body substances such as localized, organ-specific DNA samples. Consequently, it is of analytical interest to develop methods for the routine analysis of small samples in the range of a few tens of microg. We have used a 5 MV Pelletron tandem accelerator to study small biological samples using AMS. Different methods are presented and compared. A (12)C-carrier sample preparation method is described which is potentially more sensitive and less susceptible to contamination than the standard procedures.