Nonlinear structures and thermodynamic instabilities in a one-dimensional lattice system

The equilibrium states of the discrete Peyrard-Bishop Hamiltonian with one end fixed are computed exactly from the two-dimensional nonlinear Morse map. These exact nonlinear structures are interpreted as domain walls (DW), interpolating between bound and unbound segments of the chain. The free energy of the DWs is calculated to leading order beyond the Gaussian approximation. Thermodynamic instabilities (e.g. DNA unzipping and/or thermal denaturation) can be understood in terms of DW formation.Comment: 4 pages, 5 figures, to appear in Phys. Rev. Let

Aggregation of Markov flows I : theory

A Markov flow is a stationary measure, with the associated flows and mean first passage times, for a continuous-time regular jump homogeneous semi-Markov process on a discrete state-space. Nodes in the state-space can be eliminated to produce a smaller Markov flow which is a factor of the original one. Some improvements to elimination methods of Wales are given. The main contribution of the paper is to present an alternative, namely a method to aggregate groups of nodes to produce a factor. The method can be iterated to make hierarchical aggregation schemes. The potential benefits are efficient computation, including recomputation to take into account local changes, and insights into the macroscopic behaviour

Generalized Grad-Shafranov equation for non-axisymmetric MHD equilibria

The structure of static MHD equilibria that admit continuous families of Euclidean symmetries is well understood. Such field configurations are governed by the classical Grad-Shafranov equation, which is a single elliptic PDE in two space dimensions. By revealing a hidden symmetry, we show that in fact all smooth solutions of the equilibrium equations with non-vanishing pressure gradients away from the magnetic axis satisfy a generalization of the Grad-Shafranov equation. In contrast to solutions of the classical Grad-Shafranov equation, solutions of the generalized equation are not automatically equilibria, but instead only satisfy force balance averaged over the one-parameter hidden symmetry. We then explain how the generalized Grad-Shafranov equation can be used to reformulate the problem of finding exact three-dimensional smooth solutions of the equilibrium equations as finding an optimal volume-preserving symmetry

Some mathematics for quasi-symmetry

The concept of quasi-symmetry was introduced in (Booozer, 1983) and then distilled into a design principle for stellarators by N¨uhrenberg & Zille (1988). In its strongest sense it means integrability of first-order guiding-centre motion. An excellent survey of the subject was provided by Helander (2014), assuming magnetohydrostatic (MHS) fields, that is, magnetohydrodynamic equilibrium with isotropic pressure and no mean flow. A fundamental step was made by Burby & Qin (2013), who stated necessary and sufficient local conditions for integrability of guiding-centre motion in terms of a continuous symmetry of three differential forms derived from the magnetic field and made clear that quasi-symmetry can be separated from the issue of whether the magnetic field is MHS or not. Perturbative calculations of Garren & Boozer (1991), however, make it look very likely that the only possibility for exact quasi-symmetry for MHS fields with bounded magnetic surfaces is axisymmetry. Our paper gives first steps to deciding whether or not this is true. In this paper we prove many consequences of quasi-symmetry and thereby restrictions on possible quasi-symmetric fields. In the case of a quasi-symmetric MHS field we derive a generalisation of the axisymmetric Grad-Shafranov equation. Burby & Qin (2013) built in an assumption that a quasi-symmetry must be a circleaction. Here we relax this requirement, though prove that under some mild conditions it is actually a circle-action. We write many equations using differential forms. For those unfamiliar with differential forms, (Arnol’d, 1978, chap. 7) is a classic and there is a tutorial (MacKay, 2019) specifically for plasma physicists. Throughout the paper we will assume enough smoothness that the equations we write make sense, at least in a weak sense

Clustering of solutions in the random satisfiability problem

Using elementary rigorous methods we prove the existence of a clustered phase in the random $K$-SAT problem, for $K\geq 8$. In this phase the solutions are grouped into clusters which are far away from each other. The results are in agreement with previous predictions of the cavity method and give a rigorous confirmation to one of its main building blocks. It can be generalized to other systems of both physical and computational interest.Comment: 4 pages, 1 figur

Finding the complement of the invariant manifolds transverse to a given foliation for a 3D flow

A method is presented to establish regions of phase space for 3D vector fields through which pass no co-oriented invariant 2D submanifolds transverse to a given oriented 1D foliation. Refinements are given for the cases of volume-preserving or Cartan-Arnol’d Hamiltonian flows and for boundaryless submanifolds

LPP3 mediates self-generation of chemotactic LPA gradients by melanoma cells

Melanoma cells steer out of tumours using self-generated lysophosphatidic acid (LPA) gradients. The cells break down LPA, which is present at high levels around the tumours, creating a dynamic gradient that is low in the tumour and high outside. They then also migrate up this gradient, creating a complex and evolving outward chemotactic stimulus. Here we introduce a new assay for self-generated chemotaxis, and show that raising LPA levels causes a delay in migration rather than loss of chemotactic efficiency. Knockdown of the lipid phosphatase LPP3 - but not its homologues LPP1 or LPP2 - diminishes the cell's ability to break down LPA. This is specific for chemotactically active LPAs, such as the 18:1 and 20:4 species. Inhibition of autotaxin-mediated LPA production does not diminish outward chemotaxis, but loss of LPP3-mediated LPA breakdown blocks it. Similarly, in both 2D and 3D invasion assays, knockdown of LPP3 diminishes melanoma cells' ability to invade. Our results demonstrate that LPP3 is the key enzyme in melanoma cells' breakdown of LPA, and confirm the importance of attractant breakdown in LPA-mediated cell steering

Institutional Learning and Change: an introduction

Originally published by the International Service for National Agricultural Research as: Watts, J. R. Mackay, D. Horton, A. Hall, B. Douthwaite, R. Chambers and A. Acosta. (2003). Institutional learning and change: An introduction. ISNAR Discussion Paper No.03-10, The Hague: International Service for National Agricultural ResearchThroughout the world, the pace of environmental, social and technological change is accelerating, and this in turn has major implications for the poor and their development prospects. Traditional transfer-of-technology approaches to agricultural research can no longer keep pace with the complex, diverse, risk-prone and dynamic realities of poor farmers. If agricultural research organizations are to be more successful in reducing poverty and increasing the sustainability of agricultural production systems, they must become less isolated, more interconnected and more responsive. In so doing, they must transform themselves into learning organizations, more in touch with field realities and better able to learn and to change. Recent research on the poverty alleviating impacts of technology associated with the Consultative Group on International Agricultural Research (CGIAR) has identified institutional learning and change (ILAC) as a key area for intervention if research is to be more efficient and effective in serving the poor

Approximate symmetries of guiding-centre motion

In a strong, inhomogeneous magnetic field, charged particle dynamics may be studied in the guiding-centre approximation, which is known to be Hamiltonian. When the magnetic field is quasisymmetric, the first-order guiding-centre Hamiltonian structure admits a continuous symmetry, and therefore a conserved quantity in addition to the energy. Since the first-order guiding-centre system is only an approximation, it is also interesting to consider approximate symmetries of the guiding-centre Hamiltonian structure. We find that any approximate spatial symmetry coincides with quasisymmetry at first order. For approximate phase-space symmetries, we derive weaker conditions than quasisymmetry. The latter include "weak quasisymmetry" as a subcase, recently proposed by Rodriguez et al. Our results, however, show that weak quasisymmetry is necessarily non-spatial at first order. Finally, if the magnetic field is constrained to satisfy magnetohydrostatic force balance then an approximate symmetry must agree with quasisymmetry to first order

Structure-activity relationships and molecular modeling of sphingosine kinase inhibitors

The design, synthesis, and evaluation of the potency of new isoform-selective inhibitors of sphingosine kinases 1 and 2 (SK1 and SK2), the enzyme that catalyzes the phosphorylation of d-erythro-sphingosine to produce the key signaling lipid, sphingosine 1-phosphate, are described. Recently, we reported that 1-(4-octylphenethyl)piperidin-4-ol (RB-005) is a selective inhibitor of SK1. Here we report the synthesis of 43 new analogues of RB-005, in which the lipophilic tail, polar headgroup, and linker region were modified to extend the structure-activity relationship profile for this lead compound, which we explain using modeling studies with the recently published crystal structure of SK1. We provide a basis for the key residues targeted by our profiled series and provide further evidence for the ability to discriminate between the two isoforms using pharmacological intervention