Succinct Population Protocols for Presburger Arithmetic

International audienceIn [5], Angluin et al. proved that population protocols compute exactly the predicates definable in Presburger arithmetic (PA), the first-order theory of addition. As part of this result, they presented a procedure that translates any formula $ϕ$ of quantifier-free PA with remainder predicates (which has the same expressive power as full PA) into a population protocol with $2 O(poly(|ϕ|))$ states that computes $ϕ$. More precisely, the number of states of the protocol is exponential in both the bit length of the largest coefficient in the formula, and the number of nodes of its syntax tree. In this paper, we prove that every formula $ϕ$ of quantifier-free PA with remainder predicates is computable by a leaderless population protocol with $O(poly(|ϕ|))$ states. Our proof is based on several new constructions, which may be of independent interest. Given a formula $ϕ$ of quantifier-free PA with remainder predicates, a first construction produces a succinct protocol (with $O(|ϕ| 3)$ leaders) that computes ϕ; this completes the work initiated in [8], where we constructed such protocols for a fragment of PA. For large enough inputs, we can get rid of these leaders. If the input is not large enough, then it is small, and we design another construction producing a succinct protocol with one leader that computes $ϕ$. Our last construction gets rid of this leader for small inputs

Dynamics of a thin liquid film with surface rigidity and spontaneous curvature

The effect of rigid surfaces on the dynamics of thin liquid films which are amenable to the lubrication approximation is considered. It is shown that the Helfrich energy of the layer gives rise to additional terms in the time-evolution equations of the liquid film. The dynamics is found to depend on the absolute value of the spontaneous curvature, irrespective of its sign. Due to the additional terms, a novel finite wavelength instability of flat rigid interfaces can be observed. Furthermore, the dependence of the shape of a droplet on the bending rigidity as well as on the spontaneous curvature is discussed.Comment: 4 pages, 5 figure

Circulation around islands and ridges

The circulation in an ocean basin containing an island is studied under nearly geostrophic, beta plane dynamics. The model is a fluid of uniform density driven by wind forcing or sources and sinks of mass at the upper boundary of the flow. The circulation is studied analytically, numerically, as well as in the laboratory through the device of the “sliced cylinder” model for the ocean circulation. Of particular interest is the estimate of the transport between the island and the oceanic basin\u27s boundary. The model is conceived as relevant to both the wind-driven circulation as well as the circulation of abyssal waters around deep topographic features such as mid-ocean ridge segments. Godfrey\u27s Island Rule for the transport is re-derived in general form and the validity of the original approximation of Godfrey (1989) is examined in a variety of circumstances. In particular, the role of dissipative boundary layers and inertial effects such as vortex shedding are scrutinized to determine their role in determining the net transport around the island. Linear theory in many cases predicts a recirculation on the eastern side of the island, provided the meridional extent of the island is large enough. The existence of the recirculation, containing trapped fluid, is confirmed in both laboratory and numerical experiments and the evolution of the structure of the recirculation is examined as a function of the boundary layer Reynolds number. In both the laboratory and numerical studies, the recirculation predicted by linear theory is joined and then superseded by an inertial recirculation springing from boundary layer separation as the Reynolds number increases past a critical value. Even in the linear limit it is shown that the recirculation region, which is closed in quasi-geostrophic theory, is subject to a small leak due to planetary geostrophic effects, which prediction is confirmed in the laboratory. The original island rule of Godfrey yields an estimate of the transport which is surprisingly robust and generally within 75% of the values measured in our numerical experiments. Agreement is moderately good when island western boundary layer transport is used as a basis for comparison. Several cases are discussed, however, in which the assumptions made by Godfrey are violated. One occurs when the frictional boundary layers of the island and the basin boundary overlap. We derive a threshold width for the gap for the case where the island is close to a northern or southern boundary of the basin and show how the transport is increasingly blocked as the gap is reduced. A second case occurs when the island is thin and zonally elongated so that the dissipative effects on the northern and southern boundaries of the island become important. Here the vorticity balance assumed in the simple Island Rule is fundamentally altered, and we extend the Island Rule to account for the new dissipation

Interface-mediated interactions: Entropic forces of curved membranes

Particles embedded in a fluctuating interface experience forces and torques mediated by the deformations and by the thermal fluctuations of the medium. Considering a system of two cylinders bound to a fluid membrane we show that the entropic contribution enhances the curvature-mediated repulsion between the two cylinders. This is contrary to the usual attractive Casimir force in the absence of curvature-mediated interactions. For a large distance between the cylinders, we retrieve the renormalization of the surface tension of a flat membrane due to thermal fluctuations.Comment: 11 pages, 5 figures; final version, as appeared in Phys. Rev.

Conical defects in growing sheets

A growing or shrinking disc will adopt a conical shape, its intrinsic geometry characterized by a surplus angle $se$ at the apex. If growth is slow, the cone will find its equilibrium. Whereas this is trivial if $se <= 0$, the disc can fold into one of a discrete infinite number of states if $se$ is positive. We construct these states in the regime where bending dominates, determine their energies and how stress is distributed in them. For each state a critical value of $se$ is identified beyond which the cone touches itself. Before this occurs, all states are stable; the ground state has two-fold symmetry.Comment: 4 pages, 4 figures, LaTeX, RevTeX style. New version corresponds to the one published in PR

Contact lines for fluid surface adhesion

When a fluid surface adheres to a substrate, the location of the contact line adjusts in order to minimize the overall energy. This adhesion balance implies boundary conditions which depend on the characteristic surface deformation energies. We develop a general geometrical framework within which these conditions can be systematically derived. We treat both adhesion to a rigid substrate as well as adhesion between two fluid surfaces, and illustrate our general results for several important Hamiltonians involving both curvature and curvature gradients. Some of these have previously been studied using very different techniques, others are to our knowledge new. What becomes clear in our approach is that, except for capillary phenomena, these boundary conditions are not the manifestation of a local force balance, even if the concept of surface stress is properly generalized. Hamiltonians containing higher order surface derivatives are not just sensitive to boundary translations but also notice changes in slope or even curvature. Both the necessity and the functional form of the corresponding additional contributions follow readily from our treatment.Comment: 8 pages, 2 figures, LaTeX, RevTeX styl

Chlorophylls of the c family: absolute configuration and inhibition of NADPH:protochlorophyllide oxidoreductase

AbstractUsing circular dichroism (CD) spectroscopy, the stereochemistry at C-132 of members of the chlorophyll (Chl) c family, namely Chls c1, c2, c3 and [8-vinyl]-protochlorophyllide a (Pchlide a) was determined. By comparison with spectra of known enantiomers, all Chl c members turned out to have the (R) configuration, which is in agreement with considerations drawn from chlorophyll biosynthesis. Except for a double bond in the side chain at C-17, the chemical structure of Chl c1 is identical with Pchlide a, the natural substrate of the light-dependent NADPH:protochlorophyllide oxidoreductase (POR). Thus, lack of binding to the active site due to the wrong configuration at C-132, which had been proposed previously, cannot be an explanation for inactivity of Chl c in this enzymic reaction. Our results show rather that Chl c1 is a competitive inhibitor for this enzyme, tested with Pchlide a and Zn-protopheophorbide a (Zn-Ppheide a) as substrates

Functional interaction between Sequestosome-1/p62 and Autophagy-Linked FYVE-containing protein WDFY3 in human osteoclasts

Peer reviewedPostprin

How to determine local elastic properties of lipid bilayer membranes from atomic-force-microscope measurements: A theoretical analysis

Measurements with an atomic force microscope (AFM) offer a direct way to probe elastic properties of lipid bilayer membranes locally: provided the underlying stress-strain relation is known, material parameters such as surface tension or bending rigidity may be deduced. In a recent experiment a pore-spanning membrane was poked with an AFM tip, yielding a linear behavior of the force-indentation curves. A theoretical model for this case is presented here which describes these curves in the framework of Helfrich theory. The linear behavior of the measurements is reproduced if one neglects the influence of adhesion between tip and membrane. Including it via an adhesion balance changes the situation significantly: force-distance curves cease to be linear, hysteresis and nonzero detachment forces can show up. The characteristics of this rich scenario are discussed in detail in this article.Comment: 14 pages, 9 figures, REVTeX4 style. New version corresponds to the one accepted by PRE. The result section is restructured: a comparison to experimental findings is included; the discussion on the influence of adhesion between AFM tip and membrane is extende