92 research outputs found
Store Edge Networked Data (SEND): A Data and Performance Driven Edge Storage Framework
The number of devices that the edge of the Internet accommodates and the volume of the data these devices generate are expected to grow dramatically in the years to come. As a result, managing and processing such massive data amounts at the edge becomes a vital issue. This paper proposes "Store Edge Networked Data" (SEND), a novel framework for in-network storage management realized through data repositories deployed at the network edge. SEND considers different criteria (e.g., data popularity, data proximity from processing functions at the edge) to intelligently place different categories of raw and processed data at the edge based on system-wide identifiers of the data context, called labels. We implement a data repository prototype on top of the Google file system, which we evaluate based on real-world datasets of images and Internet of Things device measurements. To scale up our experiments, we perform a network simulation study based on synthetic and real-world datasets evaluating the performance and trade-offs of the SEND design as a whole. Our results demonstrate that SEND achieves data insertion times of 0.06ms-0.9ms, data lookup times of 0.5ms-5.3ms, and on-time completion of up to 92% of user requests for the retrieval of raw and processed data
Damage in porous media due to salt crystallization
We investigate the origins of salt damage in sandstones for the two most
common salts: sodium chloride and sulfate. The results show that the observed
difference in damage between the two salts is directly related to the kinetics
of crystallization and the interfacial properties of the salt solutions and
crystals with respect to the stone. We show that, for sodium sulfate, the
existence of hydrated and anhydrous crystals and specifically their dissolution
and crystallization kinetics are responsible for the damage. Using magnetic
resonance imaging and optical microscopy we show that when water imbibes sodium
sulfate contaminated sandstones, followed by drying at room temperature, large
damage occurs in regions where pores are fully filled with salts. After partial
dissolution, anhydrous sodium sulfate salt present in these regions gives rise
to a very rapid growth of the hydrated phase of sulfate in the form of clusters
that form on or close to the remaining anhydrous microcrystals. The rapid
growth of these clusters generates stresses in excess of the tensile strength
of the stone leading to the damage. Sodium chloride only forms anhydrous
crystals that consequently do not cause damage in the experiments
Special biconformal changes of K\"ahler surface metrics
The term "special biconformal change" refers, basically, to the situation
where a given nontrivial real-holomorphic vector field on a complex manifold is
a gradient relative to two K\"ahler metrics, and, simultaneously, an
eigenvector of one of the metrics treated, with the aid of the other, as an
endomorphism of the tangent bundle. A special biconformal change is called
nontrivial if the two metrics are not each other's constant multiples. For
instance, according to a 1995 result of LeBrun, a nontrivial special
biconformal change exists for the conformally-Einstein K\"ahler metric on the
two-point blow-up of the complex projective plane, recently discovered by Chen,
LeBrun and Weber; the real-holomorphic vector field involved is the gradient of
its scalar curvature. The present paper establishes the existence of nontrivial
special biconformal changes for some canonical metrics on Del Pezzo surfaces,
viz. K\"ahler-Einstein metrics (when a nontrivial holomorphic vector field
exists), non-Einstein K\"ahler-Ricci solitons, and K\"ahler metrics admitting
nonconstant Killing potentials with geodesic gradients.Comment: 16 page
Gauge Theoretic Invariants of, Dehn Surgeries on Knots
New methods for computing a variety of gauge theoretic invariants for
homology 3-spheres are developed. These invariants include the Chern-Simons
invariants, the spectral flow of the odd signature operator, and the rho
invariants of irreducible SU(2) representations. These quantities are
calculated for flat SU(2) connections on homology 3-spheres obtained by 1/k
Dehn surgery on (2,q) torus knots. The methods are then applied to compute the
SU(3) gauge theoretic Casson invariant (introduced in [H U Boden and C M
Herald, The SU(3) Casson invariant for integral homology 3--spheres, J. Diff.
Geom. 50 (1998) 147-206]) for Dehn surgeries on (2,q) torus knots for q=3,5,7
and 9.Comment: Version 3: minor corrections from version 2. Published by Geometry
and Topology at http://www.maths.warwick.ac.uk/gt/GTVol5/paper6.abs.htm
Nonrelativistic hydrogen type stability problems on nonparabolic 3-manifolds
We extend classical Euclidean stability theorems corresponding to the
nonrelativistic Hamiltonians of ions with one electron to the setting of non
parabolic Riemannian 3-manifolds.Comment: 20 pages; to appear in Annales Henri Poincar
Scattering theory for lattice operators in dimension
This paper analyzes the scattering theory for periodic tight-binding
Hamiltonians perturbed by a finite range impurity. The classical energy
gradient flow is used to construct a conjugate (or dilation) operator to the
unperturbed Hamiltonian. For dimension the wave operator is given by
an explicit formula in terms of this dilation operator, the free resolvent and
the perturbation. From this formula the scattering and time delay operators can
be read off. Using the index theorem approach, a Levinson theorem is proved
which also holds in presence of embedded eigenvalues and threshold
singularities.Comment: Minor errors and misprints corrected; new result on absense of
embedded eigenvalues for potential scattering; to appear in RM
High density QCD on a Lefschetz thimble?
It is sometimes speculated that the sign problem that afflicts many quantum
field theories might be reduced or even eliminated by choosing an alternative
domain of integration within a complexified extension of the path integral (in
the spirit of the stationary phase integration method). In this paper we start
to explore this possibility somewhat systematically. A first inspection reveals
the presence of many difficulties but - quite surprisingly - most of them have
an interesting solution. In particular, it is possible to regularize the
lattice theory on a Lefschetz thimble, where the imaginary part of the action
is constant and disappears from all observables. This regularization can be
justified in terms of symmetries and perturbation theory. Moreover, it is
possible to design a Monte Carlo algorithm that samples the configurations in
the thimble. This is done by simulating, effectively, a five dimensional
system. We describe the algorithm in detail and analyze its expected cost and
stability. Unfortunately, the measure term also produces a phase which is not
constant and it is currently very expensive to compute. This residual sign
problem is expected to be much milder, as the dominant part of the integral is
not affected, but we have still no convincing evidence of this. However, the
main goal of this paper is to introduce a new approach to the sign problem,
that seems to offer much room for improvements. An appealing feature of this
approach is its generality. It is illustrated first in the simple case of a
scalar field theory with chemical potential, and then extended to the more
challenging case of QCD at finite baryonic density.Comment: Misleading footnote 1 corrected: locality deserves better
investigations. Formula (31) corrected (we thank Giovanni Eruzzi for this
observation). Note different title in journal versio
Bifurcation of critical points for continuous families of C^2 functionals of Fredholm type
Given a continuous family of C^2 functionals of Fredholm type, we show that the non-vanishing of the spectral flow for the family of Hessians along a known (trivial) branch of critical points not only entails bifurcation of nontrivial critical points but also allows to estimate the number of bifurcation points along the branch. We use this result for several parameter bifurcation, estimating the number of connected components of the complement of the set of bifurcation points and apply our results to bifurcation of periodic orbits of Hamiltonian systems. By means of a comparison principle for the spectral flow, we obtain lower bounds for the number of bifurcation points of periodic orbits on a given interval in terms of the coefficients of the linearization
Klein-Gordon Solutions on Non-Globally Hyperbolic Standard Static Spacetimes
We construct a class of solutions to the Cauchy problem of the Klein-Gordon
equation on any standard static spacetime. Specifically, we have constructed
solutions to the Cauchy problem based on any self-adjoint extension (satisfying
a technical condition: "acceptability") of (some variant of) the
Laplace-Beltrami operator defined on test functions in an -space of the
static hypersurface. The proof of the existence of this construction completes
and extends work originally done by Wald. Further results include the
uniqueness of these solutions, their support properties, the construction of
the space of solutions and the energy and symplectic form on this space, an
analysis of certain symmetries on the space of solutions and of various
examples of this method, including the construction of a non-bounded below
acceptable self-adjoint extension generating the dynamics
General Spectral Flow Formula for Fixed Maximal Domain
We consider a continuous curve of linear elliptic formally self-adjoint
differential operators of first order with smooth coefficients over a compact
Riemannian manifold with boundary together with a continuous curve of global
elliptic boundary value problems. We express the spectral flow of the resulting
continuous family of (unbounded) self-adjoint Fredholm operators in terms of
the Maslov index of two related curves of Lagrangian spaces. One curve is given
by the varying domains, the other by the Cauchy data spaces. We provide
rigorous definitions of the underlying concepts of spectral theory and
symplectic analysis and give a full (and surprisingly short) proof of our
General Spectral Flow Formula for the case of fixed maximal domain. As a side
result, we establish local stability of weak inner unique continuation property
(UCP) and explain its role for parameter dependent spectral theory.Comment: 22 page
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