Peeling from a patterned thin elastic film

Inspired by the observation that many naturally occurring adhesives arise as textured thin films, we consider the displacement controlled peeling of a flexible plate from an incision-patterned thin adhesive elastic layer. We find that crack initiation from an incision on the film occurs at a load much higher than that required to propagate it on a smooth adhesive surface; multiple incisions thus cause the crack to propagate intermittently. Microscopically, this mode of crack initiation and propagation in geometrically confined thin adhesive films is related to the nucleation of cavitation bubbles behind the incision which must grow and coalesce before a viable crack propagates. Our theoretical analysis allows us to rationalize these experimental observations qualitatively and quantitatively and suggests a simple design criterion for increasing the interfacial fracture toughness of adhesive films.Comment: 8 pages, To appear in Proceedings of Royal Society London, Ser.

Sprectral data for Generation of Molecular Complexity from Cyclooctatetraene Using Dienyliron and Olefin Metathesis

Spectral data used in the course of researching Generation of molecular complexity from cyclooctatetraene using dienyliron and olefin metathesis methodology . Transformation of the simple hydrocarbon cyclooctatetraene into a variety of polycyclic skeletons was achieved by sequential coordination to iron, reaction with electrophiles followed by allylated nucleophiles, decomplexation and olefin metathesis

A Trib2-p38 axis controls myeloid leukaemia cell cycle and stress response signalling

Trib2 pseudokinase is involved in the etiology of a number of cancers including leukaemia, melanoma, ovarian, lung and liver cancer. Both high and low Trib2 expression levels correlate with different types of cancer. Elevated Trib2 expression has oncogenic properties in both leukaemia and lung cancer dependent on interactions with proteasome machinery proteins and degradation of transcription factors. Here, we demonstrated that Trib2 deficiency conferred a growth and survival advantage both at steady state and in stress conditions in leukaemia cells. In response to stress, wild type leukaemia cells exited the cell cycle and underwent apoptosis. In contrast, Trib2 deficient leukaemia cells continued to enter mitosis and survive. We showed that Trib2 deficient leukaemia cells had defective MAPK p38 signalling, which associated with a reduced γ-H2Ax and Chk1 stress signalling response, and continued proliferation following stress, associated with inefficient activation of cell cycle inhibitors p21, p16 and p19. Furthermore, Trib2 deficient leukaemia cells were more resistant to chemotherapy than wild type leukaemia cells, having less apoptosis and continued propagation. Trib2 re-expression or pharmacological activation of p38 in Trib2 deficient leukaemia cells sensitised the cells to chemotherapy-induced apoptosis comparable with wild type leukaemia cells. Our data provide evidence for a tumour suppressor role of Trib2 in myeloid leukaemia via activation of p38 stress signalling. This newly identified role indicates that Trib2 may counteract the propagation and chemotherapy resistance of leukaemia cells

Robust Ferroelectric State in Multiferroic Mn1−x_{1-x}Znx_xWO4_4

We report the remarkably robust ferroelectric state in the multiferroic compound Mn$_{1-x}$Zn$_x$WO$_4$. The substitution of the magnetic Mn$^{2+}$ with nonmagnetic Zn$^{2+}$ reduces the magnetic exchange and provides control of the various magnetic and multiferroic states of MnWO$_4$. Only 5 % of Zn substitution results in a complete suppression of the frustrated collinear (paraelectric) low temperature phase. The helical magnetic and ferroelectric phase develops as the ground state. The multiferroic state is stable up to a high level of substitution of more than 50 %. The magnetic, thermodynamic, and dielectric properties as well as the ferroelectric polarization of single crystals of Mn$_{1-x}$Zn$_x$WO$_4$ are studied for different substitutions up to x=0.5. The magnetic phases have been identified in single crystal neutron scattering experiments. The ferroelectric polarization scales with the neutron intensity of the incommensurate peak of the helical phase.Comment: 6 pages, 8 figure

EFX exists for three agents

We study the problem of distributing a set of indivisible items among agents with additive valuations in a $\mathit{fair}$ manner. The fairness notion under consideration is Envy-freeness up to any item (EFX). Despite significant efforts by many researchers for several years, the existence of EFX allocations has not been settled beyond the simple case of two agents. In this paper, we show constructively that an EFX allocation always exists for three agents. Furthermore, we falsify the conjecture by Caragiannis et al. by showing an instance with three agents for which there is a partial EFX allocation (some items are not allocated) with higher Nash welfare than that of any complete EFX allocation

Fair and Efficient Allocations under Subadditive Valuations

We study the problem of allocating a set of indivisible goods among agents with subadditive valuations in a fair and efficient manner. Envy-Freeness up to any good (EFX) is the most compelling notion of fairness in the context of indivisible goods. Although the existence of EFX is not known beyond the simple case of two agents with subadditive valuations, some good approximations of EFX are known to exist, namely $\tfrac{1}{2}$-EFX allocation and EFX allocations with bounded charity. Nash welfare (the geometric mean of agents' valuations) is one of the most commonly used measures of efficiency. In case of additive valuations, an allocation that maximizes Nash welfare also satisfies fairness properties like Envy-Free up to one good (EF1). Although there is substantial work on approximating Nash welfare when agents have additive valuations, very little is known when agents have subadditive valuations. In this paper, we design a polynomial-time algorithm that outputs an allocation that satisfies either of the two approximations of EFX as well as achieves an $\mathcal{O}(n)$ approximation to the Nash welfare. Our result also improves the current best-known approximation of $\mathcal{O}(n \log n)$ and $\mathcal{O}(m)$ to Nash welfare when agents have submodular and subadditive valuations, respectively. Furthermore, our technique also gives an $\mathcal{O}(n)$ approximation to a family of welfare measures, $p$-mean of valuations for $p\in (-\infty, 1]$, thereby also matching asymptotically the current best known approximation ratio for special cases like $p =-\infty$ while also retaining the fairness properties

Ability grouping practices in the primary school: A survey

In 1997, the DfEE suggested that schools should consider 'setting' pupils by ability as it was believed that this would contribute to raising standards. This survey of primary schools aimed to establish the extent to which primary schools, with same and mixed age classes, implement different grouping practices including setting, streaming, within class ability and mixed ability groupings for different curriculum subjects. Schools were asked to complete a questionnaire indicating their grouping practices for each subject in each year group. The findings showed that schools predominantly adopted within class ability groupings, either mixed or ability grouped, for most subjects. Ability grouping (within class and setting) was most common in mathematics, followed by English and science. Its implementation increased as pupils progressed through school. The type of setting adopted, same or cross-age, tended to reflect the nature of the class structures within the school

Transport and bistable kinetics of a Brownian particle in a nonequilibrium environment

A system reservoir model, where the associated reservoir is modulated by an external colored random force, is proposed to study the transport of an overdamped Brownian particle in a periodic potential. We then derive the analytical expression for the average velocity, mobility, and diffusion rate. The bistable kinetics and escape rate from a metastable state in the overdamped region are studied consequently. By numerical simulation we then demonstrate that our analytical escape rate is in good agreement with that of numerical result.Comment: 10 pages, 2 figures, RevTex4, minor correction

Competitive Allocation of a Mixed Manna

We study the fair division problem of allocating a mixed manna under additively separable piecewise linear concave (SPLC) utilities. A mixed manna contains goods that everyone likes and bads that everyone dislikes, as well as items that some like and others dislike. The seminal work of Bogomolnaia et al. [Econometrica'17] argue why allocating a mixed manna is genuinely more complicated than a good or a bad manna, and why competitive equilibrium is the best mechanism. They also provide the existence of equilibrium and establish its peculiar properties (e.g., non-convex and disconnected set of equilibria even under linear utilities), but leave the problem of computing an equilibrium open. This problem remained unresolved even for only bad manna under linear utilities. Our main result is a simplex-like algorithm based on Lemke's scheme for computing a competitive allocation of a mixed manna under SPLC utilities, a strict generalization of linear. Experimental results on randomly generated instances suggest that our algorithm will be fast in practice. The problem is known to be PPAD-hard for the case of good manna, and we also show a similar result for the case of bad manna. Given these PPAD-hardness results, designing such an algorithm is the only non-brute-force (non-enumerative) option known, e.g., the classic Lemke-Howson algorithm (1964) for computing a Nash equilibrium in a 2-player game is still one of the most widely used algorithms in practice. Our algorithm also yields several new structural properties as simple corollaries. We obtain a (constructive) proof of existence for a far more general setting, membership of the problem in PPAD, rational-valued solution, and odd number of solutions property. The last property also settles the conjecture of Bogomolnaia et al. in the affirmative