741 research outputs found
The Fast Multipole Method and Point Dipole Moment Polarizable Force Fields
We present an implementation of the fast multipole method for computing
coulombic electrostatic and polarization forces from polarizable force-fields
based on induced point dipole moments. We demonstrate the expected
scaling of that approach by performing single energy point calculations on
hexamer protein subunits of the mature HIV-1 capsid. We also show the long time
energy conservation in molecular dynamics at the nanosecond scale by performing
simulations of a protein complex embedded in a coarse-grained solvent using a
standard integrator and a multiple time step integrator. Our tests show the
applicability of FMM combined with state-of-the-art chemical models in
molecular dynamical systems.Comment: 11 pages, 8 figures, accepted by J. Chem. Phy
Algorithms for bounding Folkman numbers
For an undirected, simple graph G, we write G -\u3e (a_1,...,a_k)^v (G -\u3e (a_1,...,a_k)^e) if for every vertex (edge) k-coloring, a monochromatic K_(a_i) is forced in some color i in {1,...,k}. The vertex (edge) Folkman number is defined as F_v(a_1,...,a_k;p) = min{|V(G)| : G -\u3e (a_1,...,a_k;p)^v, K_p not in G} F_e(a_1,...,a_k;p) = min{|V(G)| : G -\u3e (a_1,...,a_k;p)^e, K_p not in G} for p \u3e max{a_1,...,a_k}. Folkman showed in 1970 that these numbers always exist for valid values of p. This thesis concerns the computation of a new result in Folkman number theory, namely that F_v(2,2,3;4)=14. Previously, the bounds stood at 10 \u3c= F_v(2,2,3;4) \u3c= 14, proven by Nenov in 2000. To achieve this new result, specialized algorithms were executed on the computers of the Computer Science network in a distributed processing effort. We discuss the mathematics and algorithms used in the computation. We also discuss ongoing research into the computation of the value of F_e(3,3;4). The current bounds stand at 16 \u3c= F_e(3,3;4) \u3c= 3e10^9. This number was once the subject of an Erd s prize---claimed by Spencer in 1988
Alpha- and beta-adrenergic mediation of changes in metabolism and Na/K exchange in rat brown fat
Double- and triple-barreled ion-sensitive microelectrodes were used to measure changes in extracellular K+ and Na+ concentrations ([K+]o, [Na+]o) in brown fat. Redox states of different respiratory enzymes were measured simultaneously in order to correlate ion movements with metabolic activity. Trains of stimuli applied to the efferent nerves evoked two distinct increases in [K+]o. A first, small, rapid increase occurred within 10 s and accompanied a first, rapid membrane depolarization. A second, slow increase of [K+]o occurred several minutes after stimulation and accompanied a second, slow depolarization. A few seconds after stimulation onset, while the membrane was repolarizing and shifts in redox states indicated increases in lipolysis and respiration, [K+]o decreased. The [K+]o decrease was accompanied by an increase in [Na+]o, and could be partly blocked by ouabain. Phentolamine, an alpha-antagonist that blocks the first depolarization, also blocked the first, rapid [K+]o increase and part of the subsequent decrease. Propranolol, a beta-antagonist, had little effect on the first depolarization and the first increase in [K+]o, but blocked part of the subsequent [K+]o decrease and the second, slow [K+]o increase. The changes in [K+]o were almost completely abolished in the presence of both antagonists. It is concluded that brown adipocytes take up K+ and simultaneously lose Na+ in response to the interaction of noradrenaline with alpha- and beta-receptors, and this indicates a very early stimulation of the Na+ pump
A New Estimate of the Hubble Time with Improved Modeling of Gravitational Lenses
This paper examines free-form modeling of gravitational lenses using Bayesian
ensembles of pixelated mass maps. The priors and algorithms from previous work
are clarified and significant technical improvements are made. Lens
reconstruction and Hubble Time recovery are tested using mock data from simple
analytic models and recent galaxy-formation simulations. Finally, using
published data, the Hubble Time is inferred through the simultaneous
reconstruction of eleven time-delay lenses. The result is
H_0^{-1}=13.7^{+1.8}_{-1.0} Gyr.Comment: 24 pages, 9 figures. Accepted to Ap
Computing the Folkman number F_v(2,2,3;4)
We discuss a branch of Ramsey theory concerning vertex Folkman numbers and how computer algorithms have been used to compute a new Folkman number. We write G ! (a1, . . . , ak)v if for every vertex k-coloring of an undirected simple graph G, a monochromatic Kai is forced in color i 2 {1, . . . , k}. The vertex Folkman number is defined as Fv(a1, . . . , ak; p) = min{|V (G)| : G ! (a1, . . . , ak)v ^ Kp 6 G}. Folkman showed in 1970 that this number exists for p \u3e max{a1, . . . , ak}. Let m = 1+Pk i=1(ai−1) and a = max{a1, . . . , ak}, then Fv(a1, . . . , ak; p) = m for p \u3e m, and Fv(a1, . . . , ak; p) = a +m for p = m. For p \u3c m the situation is more difficult and much less is known. We show here that, for a case of p = m−1, Fv(2, 2, 3; 4) = 14
Literature review of the costs of being "not in education, employment or training" at age 16-18
An Optimizing Symbolic Algebra Approach for Generating Fast Multipole Method Operators
We have developed a symbolic algebra approach to automatically produce,
verify, and optimize computer code for the Fast Multipole Method (FMM)
operators. This approach allows for flexibility in choosing a basis set and
kernel, and can generate computer code for any expansion order in multiple
languages. The procedure is implemented in the publicly available Python
program Mosaic. Optimizations performed at the symbolic level through algebraic
manipulations significantly reduce the number of mathematical operations
compared with a straightforward implementation of the equations. We find that
the optimizer is able to eliminate 20-80% of the floating-point operations and
for the expansion orders it changes the observed scaling properties.
We present our approach using three variants of the operators with the
Cartesian basis set for the harmonic potential kernel , including the use
of totally symmetric and traceless multipole tensors.Comment: Updated to final version submitted to Computer Physics
Communications. Accepted on 20 November 201
Gravitational lens recovery with glass: measuring the mass profile and shape of a lens
We use a new non-parametric gravitational modelling tool - glass - to determine what quality of data (strong lensing, stellar kinematics, and/or stellar masses) are required to measure the circularly averaged mass profile of a lens and its shape. glass uses an underconstrained adaptive grid of mass pixels to model the lens, searching through thousands of models to marginalize over model uncertainties. Our key findings are as follows: (i) for pure lens data, multiple sources with wide redshift separation give the strongest constraints as this breaks the well-known mass-sheet or steepness degeneracy; (ii) a single quad with time delays also performs well, giving a good recovery of both the mass profile and its shape; (iii) stellar masses - for lenses where the stars dominate the central potential - can also break the steepness degeneracy, giving a recovery for doubles almost as good as having a quad with time-delay data, or multiple source redshifts; (iv) stellar kinematics provide a robust measure of the mass at the half-light radius of the stars r1/2 that can also break the steepness degeneracy if the Einstein radius rE ≠r1/2; and (v) if rE∼r1/2, then stellar kinematic data can be used to probe the stellar velocity anisotropy β - an interesting quantity in its own right. Where information on the mass distribution from lensing and/or other probes becomes redundant, this opens up the possibility of using strong lensing to constrain cosmological model
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