When Can You Fold a Map?

We explore the following problem: given a collection of creases on a piece of paper, each assigned a folding direction of mountain or valley, is there a flat folding by a sequence of simple folds? There are several models of simple folds; the simplest one-layer simple fold rotates a portion of paper about a crease in the paper by +-180 degrees. We first consider the analogous questions in one dimension lower -- bending a segment into a flat object -- which lead to interesting problems on strings. We develop efficient algorithms for the recognition of simply foldable 1D crease patterns, and reconstruction of a sequence of simple folds. Indeed, we prove that a 1D crease pattern is flat-foldable by any means precisely if it is by a sequence of one-layer simple folds. Next we explore simple foldability in two dimensions, and find a surprising contrast: ``map'' folding and variants are polynomial, but slight generalizations are NP-complete. Specifically, we develop a linear-time algorithm for deciding foldability of an orthogonal crease pattern on a rectangular piece of paper, and prove that it is (weakly) NP-complete to decide foldability of (1) an orthogonal crease pattern on a orthogonal piece of paper, (2) a crease pattern of axis-parallel and diagonal (45-degree) creases on a square piece of paper, and (3) crease patterns without a mountain/valley assignment.Comment: 24 pages, 19 figures. Version 3 includes several improvements thanks to referees, including formal definitions of simple folds, more figures, table summarizing results, new open problems, and additional reference

Effects of poloidal sheared flow and active feedback on tokamak edge fluctuations

The influence of sheared poloidal flow and of a phase sensitive feedback source on the various edge instabilities of tokamaks are investigated. The conditions for stabilization of the rippling mode, for the drift dissipative mode and for the radiative condensation instability are obtained from detailed numerical solutions and from approximate analytic solutions of the relevant eigenmode equations

A Mathematical Model for the Dynamics and Synchronization of Cows

We formulate a mathematical model for daily activities of a cow (eating, lying down, and standing) in terms of a piecewise affine dynamical system. We analyze the properties of this bovine dynamical system representing the single animal and develop an exact integrative form as a discrete-time mapping. We then couple multiple cow "oscillators" together to study synchrony and cooperation in cattle herds. We comment on the relevant biology and discuss extensions of our model. With this abstract approach, we not only investigate equations with interesting dynamics but also develop interesting biological predictions. In particular, our model illustrates that it is possible for cows to synchronize \emph{less} when the coupling is increased.Comment: to appear in Physica

Phosphoenolpyruvate carboxylase dentified as a key enzyme in erythrocytic Plasmodium falciparum carbon metabolism

Phospoenolpyruvate carboxylase (PEPC) is absent from humans but encoded in thePlasmodium falciparum genome, suggesting that PEPC has a parasite-specific function. To investigate its importance in P. falciparum, we generated a pepc null mutant (D10Δpepc), which was only achievable when malate, a reduction product of oxaloacetate, was added to the growth medium. D10Δpepc had a severe growth defect in vitro, which was partially reversed by addition of malate or fumarate, suggesting that pepc may be essential in vivo. Targeted metabolomics using 13C-U-D-glucose and 13C-bicarbonate showed that the conversion of glycolytically-derived PEP into malate, fumarate, aspartate and citrate was abolished in D10Δpepc and that pentose phosphate pathway metabolites and glycerol 3-phosphate were present at increased levels. In contrast, metabolism of the carbon skeleton of 13C,15N-U-glutamine was similar in both parasite lines, although the flux was lower in D10Δpepc; it also confirmed the operation of a complete forward TCA cycle in the wild type parasite. Overall, these data confirm the CO2 fixing activity of PEPC and suggest that it provides metabolites essential for TCA cycle anaplerosis and the maintenance of cytosolic and mitochondrial redox balance. Moreover, these findings imply that PEPC may be an exploitable target for future drug discovery

Chimera-like states in modular neural networks

Chimera states, namely the coexistence of coherent and incoherent behavior, were previously analyzed in complex networks. However, they have not been extensively studied in modular networks. Here, we consider a neural network inspired by the connectome of the C. elegans soil worm, organized into six interconnected communities, where neurons obey chaotic bursting dynamics. Neurons are assumed to be connected with electrical synapses within their communities and with chemical synapses across them. As our numerical simulations reveal, the coaction of these two types of coupling can shape the dynamics in such a way that chimera-like states can happen. They consist of a fraction of synchronized neurons which belong to the larger communities, and a fraction of desynchronized neurons which are part of smaller communities. In addition to the Kuramoto order parameter ?, we also employ other measures of coherence, such as the chimera-like ? and metastability ? indices, which quantify the degree of synchronization among communities and along time, respectively. We perform the same analysis for networks that share common features with the C. elegans neural network. Similar results suggest that under certain assumptions, chimera-like states are prominent phenomena in modular networks, and might provide insight for the behavior of more complex modular networks

Centrifugal melt spinning of polyvinylpyrrolidone (PVP)/triacontene copolymer fibres

Polyvinylpyrrolidone/1-triacontene (PVP/TA) copolymer fibre webs produced by centrifugal melt spinning were studied to determine the influence of jet rotation speed on morphology and internal structure as well as their potential utility as adsorbent capture media for disperse dye effluents. Fibres were produced at 72 C with jet head rotation speeds from 7000 to 15,000 r min-1. The fibres were characterised by means of SEM, XRD and DSC. Adsorption behaviour was investigated by means of an isothermal bottle point adsorption study using a commercial disperse dye, Dianix AC-E. Through centrifugal spinning nanofibers and microfibers could be produced with individual fibres as fine as 200–300 nm and mean fibre diameters of ca. 1–2 lm. The PVP/TA fibres were mechanically brittle with characteristic brittle tensile fracture regions observed at the fibre ends. DSC and XRD analyses suggested that this brittleness was linked to the graft chain crystallisation where the PVP/TA was in the form of a radial brush copolymer. In this structure, the triacontene branches interlock and form small lateral crystals around an amorphous backbone. As an adsorbent, the PVP/TA fibres were found to adsorb 35.4 mg g-1 compared to a benchmark figure of 30.0 mg g-1 for a granular-activated carbon adsorbent under the same application conditions. PVP/TA is highly hydrophobic and adsorbs disperse dyes through the strong ‘‘hydrophobic bonding’’ interaction. Such fibrous assemblies may have applications in the targeted adsorption and separation of non-polar species from aqueous or polar environments