Quantum Cluster Variables via Serre Polynomials

For skew-symmetric acyclic quantum cluster algebras, we express the quantum $F$-polynomials and the quantum cluster monomials in terms of Serre polynomials of quiver Grassmannians of rigid modules. As byproducts, we obtain the existence of counting polynomials for these varieties and the positivity conjecture with respect to acyclic seeds. These results complete previous work by Caldero and Reineke and confirm a recent conjecture by Rupel.Comment: minor corrections, reference added, example 4.3 added, 38 page

The effects of maternal social phobia on mother-infant interactions and infant social responsiveness

Background: Social phobia aggregates in families. The genetic contribution to intergenerational transmission is modest, and parenting is considered important. Research on the effects of social phobia on parenting has been subject to problems of small sample size, heterogeneity of samples and lack of specificity of observational frameworks. We addressed these problems in the current study.Methods: We assessed mothers with social phobia (N = 84) and control mothers (N = 89) at 10 weeks in face-to-face interactions with their infants, and during a social challenge, namely, engaging with a stranger. We also assessed mothers with generalised anxiety disorder (GAD) (N = 50). We examined the contribution to infant social responsiveness of early infant characteristics (neonatal irritability), as well as maternal behaviour. Results: Mothers with social phobia were no less sensitive to their infants during face-to-face interactions than control mothers, but when interacting with the stranger they appeared more anxious, engaged less with the stranger themselves, and were less encouraging of the infant's interaction with the stranger; infants of index mothers also showed reduced social responsiveness to the stranger. These differences did not apply to mothers with GAD and their infants. Regression analyses showed that the reduction in social responsiveness in infants of mothers with social phobia was predicted by neonatal irritability and the degree to which the mother encouraged the infant to interact with the stranger.Conclusions: Mothers with social phobia show specific parenting difficulties, and their infants show early signs of reduced social responsiveness that are related to both individual infant differences and a lack of maternal encouragement to engage in social interactions

Efficient algorithms for rigid body integration using optimized splitting methods and exact free rotational motion

Hamiltonian splitting methods are an established technique to derive stable and accurate integration schemes in molecular dynamics, in which additional accuracy can be gained using force gradients. For rigid bodies, a tradition exists in the literature to further split up the kinetic part of the Hamiltonian, which lowers the accuracy. The goal of this note is to comment on the best combination of optimized splitting and gradient methods that avoids splitting the kinetic energy. These schemes are generally applicable, but the optimal scheme depends on the desired level of accuracy. For simulations of liquid water it is found that the velocity Verlet scheme is only optimal for crude simulations with accuracies larger than 1.5%, while surprisingly a modified Verlet scheme (HOA) is optimal up to accuracies of 0.4% and a fourth order gradient scheme (GIER4) is optimal for even higher accuracies.Comment: 2 pages, 1 figure. Added clarifying comments. Accepted for publication in the Journal of Chemical Physic

Probing spin-charge separation in a Tomonaga-Luttinger liquid

In a one-dimensional (1D) system of interacting electrons, excitations of spin and charge travel at different speeds, according to the theory of a Tomonaga-Luttinger Liquid (TLL) at low energies. However, the clear observation of this spin-charge separation is an ongoing challenge experimentally. We have fabricated an electrostatically-gated 1D system in which we observe spin-charge separation and also the predicted power-law suppression of tunnelling into the 1D system. The spin-charge separation persists even beyond the low-energy regime where the TLL approximation should hold. TLL effects should therefore also be important in similar, but shorter, electrostatically gated wires, where interaction effects are being studied extensively worldwide.Comment: 11 pages, 4 PDF figures, uses scicite.sty, Science.bs

Cluster algebras of type A2(1)A_2^{(1)}

In this paper we study cluster algebras \myAA of type $A_2^{(1)}$. We solve the recurrence relations among the cluster variables (which form a T--system of type $A_2^{(1)}$). We solve the recurrence relations among the coefficients of \myAA (which form a Y--system of type $A_2^{(1)}$). In \myAA there is a natural notion of positivity. We find linear bases \BB of \myAA such that positive linear combinations of elements of \BB coincide with the cone of positive elements. We call these bases \emph{atomic bases} of \myAA. These are the analogue of the "canonical bases" found by Sherman and Zelevinsky in type $A_{1}^{(1)}$. Every atomic basis consists of cluster monomials together with extra elements. We provide explicit expressions for the elements of such bases in every cluster. We prove that the elements of \BB are parameterized by \ZZ^3 via their $\mathbf{g}$--vectors in every cluster. We prove that the denominator vector map in every acyclic seed of \myAA restricts to a bijection between \BB and \ZZ^3. In particular this gives an explicit algorithm to determine the "virtual" canonical decomposition of every element of the root lattice of type $A_2^{(1)}$. We find explicit recurrence relations to express every element of \myAA as linear combinations of elements of \BB.Comment: Latex, 40 pages; Published online in Algebras and Representation Theory, springer, 201

Colloid-stabilized emulsions: behaviour as the interfacial tension is reduced

We present confocal microscopy studies of novel particle-stabilized emulsions. The novelty arises because the immiscible fluids have an accessible upper critical solution temperature. The emulsions have been created by beginning with particles dispersed in the single-fluid phase. On cooling, regions of the minority phase nucleate. While coarsening these nuclei become coated with particles due to the associated reduction in interfacial energy. The resulting emulsion is arrested, and the particle-coated interfaces have intriguing properties. Having made use of the binary-fluid phase diagram to create the emulsion we then make use of it to study the properties of the interfaces. As the emulsion is re-heated toward the single-fluid phase the interfacial tension falls and the volume of the dispersed phase drops. Crumpling, fracture or coalescence can follow. The results show that the elasticity of the interfaces has a controlling influence over the emulsion behaviour.Comment: Submitted for the proceedings of the 6th Liquid Matter Conference, held in Utrecht (NL) in July 200

How should we interpret the two transport relaxation times in the cuprates ?

We observe that the appearance of two transport relaxation times in the various transport coefficients of cuprate metals may be understood in terms of scattering processes that discriminate between currents that are even, or odd under the charge conjugation operator. We develop a transport equation that illustrates these ideas and discuss its experimental and theoretical consequences.Comment: 19 pages, RevTeX with 8 postscript figures included. To appear in ``Non Fermi Liquid Physics'', J. Phys:Cond. Matt. (1997

Brief Report: Evidence of Ingroup Bias on the Shooter Task in a Saudi Sample

When predominantly White participants in Western countries are asked to shoot individuals in a computer game who may carry weapons, they show a greater bias to shoot at outgroup members and people stereotyped as dangerous. The goal was to determine the extent to which shooter biases in the Middle East would vary as a function of target ethnicity and culturally appropriate or inappropriate headgear. Within a sample of 37 male Saudi Arabian residents, we examined shooter biases outside of Western nations for the first time. Targets in this task were either White or Middle Eastern in appearance, and wore either American style baseball caps or a Saudi Arabian style shemagh and igal. Our results replicated the bias to shoot racial outgroup members observed in Western samples; we found a bias to shoot White over Middle Eastern targets. Unexpectedly, we also found a bias for Saudi participants to shoot at people wearing culturally appropriate traditional Saudi headgear over Western style baseball caps. To explain this latter finding, we cautiously speculate that relative perceptions of dangerousness in the Middle East may be influenced by media exposure and changing social conditions in the region