11,413 research outputs found
Optimal Flood Control
A mathematical model for optimal control of the water levels in a chain of
reservoirs is studied. Some remarks regarding sensitivity with respect to the time horizon, terminal cost and forecast of inflow are made
Subvarieties of generic hypersurfaces in any variety
Let W be a projective variety of dimension n+1, L a free line bundle on W, X
in a hypersurface of degree d which is generic among those given by
sums of monomials from , and let be a generically finite map
from a smooth m-fold Y. We suppose that f is r-filling, i.e. upon deforming X
in , f deforms in a family such that the corresponding deformations
of dominate . Under these hypotheses we give a lower bound for the
dimension of a certain linear system on the Cartesian product having
certain vanishing order on a diagonal locus as well as on a double point locus.
This yields as one application a lower bound on the dimension of the linear
system |K_{Y} - (d - n + m)f^*L - f^*K_{W}| which generalizes results of Ein
and Xu (and in weaker form, Voisin). As another perhaps more surprising
application, we conclude a lower bound on the number of quadrics containing
certain projective images of Y.Comment: We made some improvements in the introduction and definitions. In an
effort to clarify the arguments we separated the 1-filling case from the
r-filling case and we gave a more detailed proof of the key lemma. The
article will appear in the Math. Proc. Cambridge Philos. So
FROST -- Fast row-stochastic optimization with uncoordinated step-sizes
In this paper, we discuss distributed optimization over directed graphs,
where doubly-stochastic weights cannot be constructed. Most of the existing
algorithms overcome this issue by applying push-sum consensus, which utilizes
column-stochastic weights. The formulation of column-stochastic weights
requires each agent to know (at least) its out-degree, which may be impractical
in e.g., broadcast-based communication protocols. In contrast, we describe
FROST (Fast Row-stochastic-Optimization with uncoordinated STep-sizes), an
optimization algorithm applicable to directed graphs that does not require the
knowledge of out-degrees; the implementation of which is straightforward as
each agent locally assigns weights to the incoming information and locally
chooses a suitable step-size. We show that FROST converges linearly to the
optimal solution for smooth and strongly-convex functions given that the
largest step-size is positive and sufficiently small.Comment: Submitted for journal publication, currently under revie
Pair density waves and vortices in an elongated two-component Fermi gas
We study the vortex structures of a two-component Fermi gas experiencing a
uniform effective magnetic field in an anisotropic trap that interpolates
between quasi-one dimensional (1D) and quasi-two dimensional (2D). At a fixed
chemical potential, reducing the anisotropy (or equivalently increasing the
attractive interactions or increasing the magnetic field) leads to
instabilities towards pair density waves, and vortex lattices. Reducing the
chemical potential stabilizes the system. We calculate the phase diagram, and
explore the density and pair density. The structures are similar to those
predicted for superfluid Bose gases. We further calculate the paired fraction,
showing how it depends on chemical potential and anisotropy.Comment: 6 pages, 3 figure
Spectroscopic Evidence for the Specific Na+ and K+ Interactions with the Hydrogen-bonded Water Molecules at the Electrolyte Aqueous Solution Surfaces
Sum frequency generation vibrational spectra of the water molecules at the
NaF and KF aqueous solution surfaces showed significantly different spectral
features and different concentration dependence. This result is the first
direct observation of the cation effects of the simple alkali cations, which
have been believed to be depleted from the aqueous surface, on the hydrogen
bonding structure of the water molecules at the electrolyte solution surfaces.
These observations may provide important clue to understand the fundamental
phenomenon of ions at the air/water interface.Comment: 15 pages, 2 figure
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