5,527 research outputs found
Algebraic methods for dynamic systems
Algebraic methods for application to dynamic control system
Collective Quartics and Dangerous Singlets in Little Higgs
Any extension of the standard model that aims to describe TeV-scale physics
without fine-tuning must have a radiatively-stable Higgs potential. In little
Higgs theories, radiative stability is achieved through so-called collective
symmetry breaking. In this letter, we focus on the necessary conditions for a
little Higgs to have a collective Higgs quartic coupling. In one-Higgs doublet
models, a collective quartic requires an electroweak triplet scalar. In
two-Higgs doublet models, a collective quartic requires a triplet or singlet
scalar. As a corollary of this study, we show that some little Higgs theories
have dangerous singlets, a pathology where collective symmetry breaking does
not suppress quadratically-divergent corrections to the Higgs mass.Comment: 4 pages; v2: clarified the existing literature; v3: version to appear
in JHE
Physical and magnetic properties of Ba(FeRu)As single crystals
Single crystals of Ba(FeRu)As, , have been grown
and characterized by structural, magnetic and transport measurements. These
measurements show that the structural/magnetic phase transition found in pure
BaFeAs at 134 K is suppressed monotonically by Ru doping, but, unlike
doping with TM=Co, Ni, Cu, Rh or Pd, the coupled transition seen in the parent
compound does not detectably split into two separate ones. Superconductivity is
stabilized at low temperatures for and continues through the highest
doping levels we report. The superconducting region is dome like, with maximum
T ( K) found around . A phase diagram of temperature
versus doping, based on electrical transport and magnetization measurements,
has been constructed and compared to those of the
Ba(FeTM)As (TM=Co, Ni, Rh, Pd) series as well as to the
temperature-pressure phase diagram for pure BaFeAs. Suppression of the
structural/magnetic phase transition as well as the appearance of
superconductivity is much more gradual in Ru doping, as compared to Co, Ni, Rh
and Pd doping, and appears to have more in common with BaFeAs tuned
with pressure; by plotting and as a function of changes in unit
cell dimensions, we find that changed in the ratio, rather than changes
in , or V, unify the and phase diagrams for BaFeAs
and Ba(FeRu)As respectively.Comment: 16 pages, 10 figure
Using Frost-damaged Soybeans in Livestock Rations
Soybeans are routinely grown in the upper Midwest as a cash crop. However, late planting coupled with an early freeze can result in frost-damaged or “green beans.” Even after processing, the resulting soybean meal and soy oil are still green due to high chlorophyll concentrations. Since the consumer is reluctant to purchase green soy oil, frost-damaged soybeans (FDS) are of little use to the processing industry and often are docked at local elevators. However, when done properly, FDS can be marketed effectively through livestock. Frost-damaged soybeans, green beans, and immature soybeans are all synonymous terms and will be denoted by FDS in the rest of this article. Raw refers to non-heat treated soybeans
Nearly Optimal Private Convolution
We study computing the convolution of a private input with a public input
, while satisfying the guarantees of -differential
privacy. Convolution is a fundamental operation, intimately related to Fourier
Transforms. In our setting, the private input may represent a time series of
sensitive events or a histogram of a database of confidential personal
information. Convolution then captures important primitives including linear
filtering, which is an essential tool in time series analysis, and aggregation
queries on projections of the data.
We give a nearly optimal algorithm for computing convolutions while
satisfying -differential privacy. Surprisingly, we follow
the simple strategy of adding independent Laplacian noise to each Fourier
coefficient and bounding the privacy loss using the composition theorem of
Dwork, Rothblum, and Vadhan. We derive a closed form expression for the optimal
noise to add to each Fourier coefficient using convex programming duality. Our
algorithm is very efficient -- it is essentially no more computationally
expensive than a Fast Fourier Transform.
To prove near optimality, we use the recent discrepancy lowerbounds of
Muthukrishnan and Nikolov and derive a spectral lower bound using a
characterization of discrepancy in terms of determinants
Thermodynamic phase transitions for Pomeau-Manneville maps
We study phase transitions in the thermodynamic description of
Pomeau-Manneville intermittent maps from the point of view of infinite ergodic
theory, which deals with diverging measure dynamical systems. For such systems,
we use a distributional limit theorem to provide both a powerful tool for
calculating thermodynamic potentials as also an understanding of the dynamic
characteristics at each instability phase. In particular, topological pressure
and Renyi entropy are calculated exactly for such systems. Finally, we show the
connection of the distributional limit theorem with non-Gaussian fluctuations
of the algorithmic complexity proposed by Gaspard and Wang [Proc. Natl. Acad.
Sci. USA 85, 4591 (1988)].Comment: 5 page
Operator renewal theory and mixing rates for dynamical systems with infinite measure
We develop a theory of operator renewal sequences in the context of infinite
ergodic theory. For large classes of dynamical systems preserving an infinite
measure, we determine the asymptotic behaviour of iterates of the
transfer operator. This was previously an intractable problem.
Examples of systems covered by our results include (i) parabolic rational
maps of the complex plane and (ii) (not necessarily Markovian) nonuniformly
expanding interval maps with indifferent fixed points.
In addition, we give a particularly simple proof of pointwise dual ergodicity
(asymptotic behaviour of ) for the class of systems under
consideration.
In certain situations, including Pomeau-Manneville intermittency maps, we
obtain higher order expansions for and rates of mixing. Also, we obtain
error estimates in the associated Dynkin-Lamperti arcsine laws.Comment: Preprint, August 2010. Revised August 2011. After publication, a
minor error was pointed out by Kautzsch et al, arXiv:1404.5857. The updated
version includes minor corrections in Sections 10 and 11, and corresponding
modifications of certain statements in Section 1. All main results are
unaffected. In particular, Sections 2-9 are unchanged from the published
versio
Reference Distorted Prices
I show that when consumers (mis)perceive prices relative to reference prices,
budgets turn out to be soft, prices tend to be lower and the average quality of
goods sold decreases. These observations provide explanations for decentralized
purchase decisions, for people being happy with a purchase even when they have
paid their evaluation, and for why trade might affect high quality local firms
'unfairly'
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