10,403 research outputs found
Two applications of elementary knot theory to Lie algebras and Vassiliev invariants
Using elementary equalities between various cables of the unknot and the Hopf
link, we prove the Wheels and Wheeling conjectures of [Bar-Natan, Garoufalidis,
Rozansky and Thurston, arXiv:q-alg/9703025] and [Deligne, letter to Bar-Natan,
January 1996, http://www.ma.huji.ac.il/~drorbn/Deligne/], which give,
respectively, the exact Kontsevich integral of the unknot and a map
intertwining two natural products on a space of diagrams. It turns out that the
Wheeling map is given by the Kontsevich integral of a cut Hopf link (a bead on
a wire), and its intertwining property is analogous to the computation of 1+1=2
on an abacus. The Wheels conjecture is proved from the fact that the k-fold
connected cover of the unknot is the unknot for all k. Along the way, we find a
formula for the invariant of the general (k,l) cable of a knot. Our results can
also be interpreted as a new proof of the multiplicativity of the
Duflo-Kirillov map S(g)-->U(g) for metrized Lie (super-)algebras g.Comment: Published by Geometry and Topology at
http://www.maths.warwick.ac.uk/gt/GTVol7/paper1.abs.htm
Laplace Approximated EM Microarray Analysis: An Empirical Bayes Approach for Comparative Microarray Experiments
A two-groups mixed-effects model for the comparison of (normalized)
microarray data from two treatment groups is considered. Most competing
parametric methods that have appeared in the literature are obtained as special
cases or by minor modification of the proposed model. Approximate maximum
likelihood fitting is accomplished via a fast and scalable algorithm, which we
call LEMMA (Laplace approximated EM Microarray Analysis). The posterior odds of
treatment gene interactions, derived from the model, involve shrinkage
estimates of both the interactions and of the gene specific error variances.
Genes are classified as being associated with treatment based on the posterior
odds and the local false discovery rate (f.d.r.) with a fixed cutoff. Our
model-based approach also allows one to declare the non-null status of a gene
by controlling the false discovery rate (FDR). It is shown in a detailed
simulation study that the approach outperforms well-known competitors. We also
apply the proposed methodology to two previously analyzed microarray examples.
Extensions of the proposed method to paired treatments and multiple treatments
are also discussed.Comment: Published in at http://dx.doi.org/10.1214/10-STS339 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Diffusion-limited reaction for the one-dimensional trap system
We have previously discussed the one-dimensional multitrap system of finite
range and found the somewhat unexpected result that the larger is the number of
imperfect traps the higher is the transmission through them. We discuss in this
work the effect of a small number of such traps arrayed along either a constant
or a variable finite spatial section. It is shown that under specific
conditions, to be described in the following, the remarked high transmission
may be obtained for this case also. Thus, compared to the theoretical large
number of traps case these results may be experimentally applied to real
phenomenaComment: 18 pages, 8 PS Figures; 3 former figures were removed, a new section
added and the representation is improve
Dynamic Windows Scheduling with Reallocation
We consider the Windows Scheduling problem. The problem is a restricted
version of Unit-Fractions Bin Packing, and it is also called Inventory
Replenishment in the context of Supply Chain. In brief, the problem is to
schedule the use of communication channels to clients. Each client ci is
characterized by an active cycle and a window wi. During the period of time
that any given client ci is active, there must be at least one transmission
from ci scheduled in any wi consecutive time slots, but at most one
transmission can be carried out in each channel per time slot. The goal is to
minimize the number of channels used. We extend previous online models, where
decisions are permanent, assuming that clients may be reallocated at some cost.
We assume that such cost is a constant amount paid per reallocation. That is,
we aim to minimize also the number of reallocations. We present three online
reallocation algorithms for Windows Scheduling. We evaluate experimentally
these protocols showing that, in practice, all three achieve constant amortized
reallocations with close to optimal channel usage. Our simulations also expose
interesting trade-offs between reallocations and channel usage. We introduce a
new objective function for WS with reallocations, that can be also applied to
models where reallocations are not possible. We analyze this metric for one of
the algorithms which, to the best of our knowledge, is the first online WS
protocol with theoretical guarantees that applies to scenarios where clients
may leave and the analysis is against current load rather than peak load. Using
previous results, we also observe bounds on channel usage for one of the
algorithms.Comment: 6 figure
Combined High Power and High Frequency Operation of InGaAsP/InP Lasers at 1.3μm
A simultaneous operation of a semiconductor laser at high power and high speed was demonstrated in a buried crescent laser on a P-InP substrate. In a cavity length of 300μm, a
maximum CW power of 130mW at room temperature was obtained in a junction-up mounting configuration. A 3dB bandwidth in excess of 12GHz at an output power of 52mW was observed
Monolithic integration of a very low threshold GaInAsP laser and metal-insulator-semiconductor field-effect transistor on semi-insulating InP
Monolithic integration of 1.3-µm groove lasers and metal-insulator-semiconductor field-effect transistors (MISFET) is achieved by a simple single liquid phase epitaxy (LPE) growth process. Laser thresholds as low as 14 mA for 300-µm cavity length are obtained. MIS depletion mode FET's with n channels on LPE grown InP layer show typical transconductance of 5–10 mmho. Laser modulation by the FET current is demonstrated at up to twice the threshold current
Multi-layer atom chips for versatile atom micro manipulation
We employ a combination of optical UV- and electron-beam-lithography to
create an atom chip combining sub-micron wire structures with larger
conventional wires on a single substrate. The new multi-layer fabrication
enables crossed wire configurations, greatly enhancing the flexibility in
designing potentials for ultra cold quantum gases and Bose-Einstein
condensates. Large current densities of >6 x 10^7 A/cm^2 and high voltages of
up to 65 V across 0.3 micron gaps are supported by even the smallest wire
structures. We experimentally demonstrate the flexibility of the next
generation atom chip by producing Bose-Einstein condensates in magnetic traps
created by a combination of wires involving all different fabrication methods
and structure sizes.Comment: 4 pages, 5 figure
Damping of bulk excitations over an elongated BEC - the role of radial modes
We report the measurement of Beliaev damping of bulk excitations in cigar
shaped Bose Einstein condensates of atomic vapor. By using post selection,
excitation line shapes of the total population are compared with those of the
undamped excitations. We find that the damping depends on the initial
excitation energy of the decaying quasi particle, as well as on the excitation
momentum. We model the condensate as an infinite cylinder and calculate the
damping rates of the different radial modes. The derived damping rates are in
good agreement with the experimentally measured ones. The damping rates
strongly depend on the destructive interference between pathways for damping,
due to the quantum many-body nature of both excitation and damping products.Comment: 5 pages, 4 figure
Atom Chips: Fabrication and Thermal Properties
Neutral atoms can be trapped and manipulated with surface mounted microscopic
current carrying and charged structures. We present a lithographic fabrication
process for such atom chips based on evaporated metal films. The size limit of
this process is below 1m. At room temperature, thin wires can carry more
than 10A/cm current density and voltages of more than 500V. Extensive
test measurements for different substrates and metal thicknesses (up to 5
m) are compared to models for the heating characteristics of the
microscopic wires. Among the materials tested, we find that Si is the best
suited substrate for atom chips
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