332 research outputs found
Optimal life insurance purchase, consumption and investment on a financial market with multi-dimensional diffusive terms
We introduce an extension to Merton’s famous continuous time model of optimal
consumption and investment, in the spirit of previous works by Pliska and Ye, to allow for
a wage earner to have a random lifetime and to use a portion of the income to purchase life
insurance in order to provide for his estate, while investing his savings in a financial market
comprised of one risk-free security and an arbitrary number of risky securities driven by multidimensional
Brownian motion. We then provide a detailed analysis of the optimal consumption,
investment, and insurance purchase strategies for the wage earner whose goal is to maximize
the expected utility obtained from his family consumption, from the size of the estate in the
event of premature death, and from the size of the estate at the time of retirement. We use
dynamic programming methods to obtain explicit solutions for the case of discounted constant
relative risk aversion utility functions and describe new analytical results which are presented
together with the corresponding economic interpretations.We thank the Calouste Gulbenkian Foundation, PRODYN-ESF, POCTI and POSI by FCT and Ministerio da Ciencia, Tecnologia e Ensino Superior, CEMAPRE, LIAAD-INESC Porto LA, Centro de Matematica da Universidade do Minho and Centro de Matematica da Universidade do Porto for their financial support. D. Pinheiro's research was supported by FCT - Fundacao para a Ciencia e Tecnologia program 'Ciencia 2007' and project 'Randomness in Deterministic Dynamical Systems and Applications' (PTDC/MAT/105448/2008). I. Duarte's research was supported by FCT - Fundacao para a Ciencia e Tecnologia grant with reference SFRH/BD/33502/2008
Exploring the Post-translational Enzymology of PaaA by mRNA Display
PaaA is a RiPP enzyme that catalyzes the transformation of two glutamic acid residues within a substrate peptide into the bicyclic core of Pantocin A. Here, for the first time, we use mRNA display techniques to understand RiPP enzyme-substrate interactions to illuminate PaaA substrate recognition. Additionally, our data revealed insights into the enzymatic timing of glutamic acid modification. The technique developed is quite sensitive and a significant advancement over current RiPP studies and opens the door to enzyme modified mRNA display libraries for natural product-like inhibitor pans
Neutrino-Deuteron Scattering in Effective Field Theory at Next-to-Next-to Leading Order
We study the four channels associated with neutrino-deuteron breakup
reactions at next-to-next to leading order in effective field theory. We find
that the total cross-section is indeed converging for neutrino energies up to
20 MeV, and thus our calculations can provide constraints on theoretical
uncertainties for the Sudbury Neutrino Observatory. We stress the importance of
a direct experimental measurement to high precision in at least one channel, in
order to fix an axial two-body counterterm.Comment: 32 pages, 14 figures (eps
The S-Wave Pion-Nucleon Scattering Lengths from Pionic Atoms using Effective Field Theory
The pion-deuteron scattering length is computed to next-to-next-to-leading
order in baryon chiral perturbation theory. A modified power-counting is then
formulated which properly accounts for infrared enhancements engendered by the
large size of the deuteron, as compared to the pion Compton wavelength. We use
the precise experimental value of the real part of the pion-deuteron scattering
length determined from the decay of pionic deuterium, together with constraints
on pion-nucleon scattering lengths from the decay of pionic hydrogen, to
extract the isovector and isoscalar S-wave pion-nucleon scattering lengths, a^-
and a^+, respectively. We find a^-=(0.0918 \pm 0.0013) M_\pi^{-1} and
a^+=(-0.0034 \pm 0.0007) M_\pi^{-1}.Comment: 19 pages LaTeX, 7 eps fig
Deconstructing 1S0 nucleon-nucleon scattering
A distorted-wave method is used to analyse nucleon-nucleon scattering in the
1S0 channel. Effects of one-pion exchange are removed from the empirical phase
shift to all orders by using a modified effective-range expansion. Two-pion
exchange is then subtracted in the distorted-wave Born approximation, with
matrix elements taken between scattering waves for the one-pion exchange
potential. The residual short-range interaction shows a very rapid energy
dependence for kinetic energies above about 100 MeV, suggesting that the
breakdown scale of the corresponding effective theory is only 270MeV. This may
signal the need to include the Delta resonance as an explicit degree of freedom
in order to describe scattering at these energies. An alternative strategy of
keeping the cutoff finite to reduce large, but finite, contributions from the
long-range forces is also discussed.Comment: 10 pages, 2 figures (introduction revised, references added; version
to appear in EPJA
Flexizyme-Enabled Benchtop Biosynthesis of Thiopeptides
Thiopeptides are natural antibiotics that are fashioned from short peptides by multiple layers of post-translational modification. Their biosynthesis, in particular the pyridine synthases that form the macrocyclic antibiotic core, has attracted intensive research but is complicated by the challenges of reconstituting multiple-pathway enzymes. By combining select RiPP enzymes with cell free expression and flexizyme-based codon reprogramming, we have developed a benchtop biosynthesis of thiopeptide scaffolds. This strategy side-steps several challenges related to the investigation of thiopeptide enzymes and allows access to analytical quantities of new thiopeptide analogs. We further demonstrate that this strategy can be used to validate the activity of new pyridine synthases without the need to reconstitute the cognate prior pathway enzymes
Quenched Lattice QCD with Domain Wall Fermions and the Chiral Limit
Quenched QCD simulations on three volumes, , and
and three couplings, , 5.85 and 6.0 using domain
wall fermions provide a consistent picture of quenched QCD. We demonstrate that
the small induced effects of chiral symmetry breaking inherent in this
formulation can be described by a residual mass (\mres) whose size decreases
as the separation between the domain walls () is increased. However, at
stronger couplings much larger values of are required to achieve a given
physical value of \mres. For and , we find
\mres/m_s=0.033(3), while for , and ,
\mres/m_s=0.074(5), where is the strange quark mass. These values are
significantly smaller than those obtained from a more naive determination in
our earlier studies. Important effects of topological near zero modes which
should afflict an accurate quenched calculation are easily visible in both the
chiral condensate and the pion propagator. These effects can be controlled by
working at an appropriately large volume. A non-linear behavior of in
the limit of small quark mass suggests the presence of additional infrared
subtlety in the quenched approximation. Good scaling is seen both in masses and
in over our entire range, with inverse lattice spacing varying between
1 and 2 GeV.Comment: 91 pages, 34 figure
A renormalisation group approach to two-body scattering in the presence of long-range forces
We apply renormalisation-group methods to two-body scattering by a
combination of known long-range and unknown short-range potentials. We impose a
cut-off in the basis of distorted waves of the long-range potential and
identify possible fixed points of the short-range potential as this cut-off is
lowered to zero. The expansions around these fixed points define the power
countings for the corresponding effective field theories. Expansions around
nontrivial fixed points are shown to correspond to distorted-wave versions of
the effective-range expansion. These methods are applied to scattering in the
presence of Coulomb, Yukawa and repulsive inverse-square potentials.Comment: 22 pages (RevTeX), 4 figure
Heat release by controlled continuous-time Markov jump processes
We derive the equations governing the protocols minimizing the heat released
by a continuous-time Markov jump process on a one-dimensional countable state
space during a transition between assigned initial and final probability
distributions in a finite time horizon. In particular, we identify the
hypotheses on the transition rates under which the optimal control strategy and
the probability distribution of the Markov jump problem obey a system of
differential equations of Hamilton-Bellman-Jacobi-type. As the state-space mesh
tends to zero, these equations converge to those satisfied by the diffusion
process minimizing the heat released in the Langevin formulation of the same
problem. We also show that in full analogy with the continuum case, heat
minimization is equivalent to entropy production minimization. Thus, our
results may be interpreted as a refined version of the second law of
thermodynamics.Comment: final version, section 2.1 revised, 26 pages, 3 figure
An optimization principle for deriving nonequilibrium statistical models of Hamiltonian dynamics
A general method for deriving closed reduced models of Hamiltonian dynamical
systems is developed using techniques from optimization and statistical
estimation. As in standard projection operator methods, a set of resolved
variables is selected to capture the slow, macroscopic behavior of the system,
and the family of quasi-equilibrium probability densities on phase space
corresponding to these resolved variables is employed as a statistical model.
The macroscopic dynamics of the mean resolved variables is determined by
optimizing over paths of these probability densities. Specifically, a cost
function is introduced that quantifies the lack-of-fit of such paths to the
underlying microscopic dynamics; it is an ensemble-averaged, squared-norm of
the residual that results from submitting a path of trial densities to the
Liouville equation. The evolution of the macrostate is estimated by minimizing
the time integral of the cost function. The value function for this
optimization satisfies the associated Hamilton-Jacobi equation, and it
determines the optimal relation between the statistical parameters and the
irreversible fluxes of the resolved variables, thereby closing the reduced
dynamics. The resulting equations for the macroscopic variables have the
generic form of governing equations for nonequilibrium thermodynamics, and they
furnish a rational extension of the classical equations of linear irreversible
thermodynamics beyond the near-equilibrium regime. In particular, the value
function is a thermodynamic potential that extends the classical dissipation
function and supplies the nonlinear relation between thermodynamics forces and
fluxes
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