3,141 research outputs found
A note on Reeb dynamics on the tight 3-sphere
We show that a nondegenerate tight contact form on the 3-sphere has exactly
two simple closed Reeb orbits if and only if the differential in linearized
contact homology vanishes. Moreover, in this case the Floquet multipliers and
Conley-Zehnder indices of the two Reeb orbits agree with those of a suitable
irrational ellipsoid in 4-space.Comment: 20 pages, no figure
Review of the outcome of two workshops on electronics for LHC experiments
Two Workshops were organized since September 1995 by the CERN LHC Electronics Review Board, LERB. Radiation-hard processes, opto-electronics, trigger and event building systems, electronics for calorimeters, muon detectors and trackers, were discussed in detail. During the first Workshop a variety of designs were presented in the light of the major requirements set by the detector collaborations. The second Workshop held in Hungary last September confirmed that a number of technological choices had been made. Some of the more salient designs are presented
The Omega Counter, a Frequency Counter Based on the Linear Regression
This article introduces the {\Omega} counter, a frequency counter -- or a
frequency-to-digital converter, in a different jargon -- based on the Linear
Regression (LR) algorithm on time stamps. We discuss the noise of the
electronics. We derive the statistical properties of the {\Omega} counter on
rigorous mathematical basis, including the weighted measure and the frequency
response. We describe an implementation based on a SoC, under test in our
laboratory, and we compare the {\Omega} counter to the traditional {\Pi} and
{\Lambda} counters. The LR exhibits optimum rejection of white phase noise,
superior to that of the {\Pi} and {\Lambda} counters. White noise is the major
practical problem of wideband digital electronics, both in the instrument
internal circuits and in the fast processes which we may want to measure. The
{\Omega} counter finds a natural application in the measurement of the
Parabolic Variance, described in the companion article arXiv:1506.00687
[physics.data-an].Comment: 8 pages, 6 figure, 2 table
The Parabolic variance (PVAR), a wavelet variance based on least-square fit
This article introduces the Parabolic Variance (PVAR), a wavelet variance
similar to the Allan variance, based on the Linear Regression (LR) of phase
data. The companion article arXiv:1506.05009 [physics.ins-det] details the
frequency counter, which implements the LR estimate.
The PVAR combines the advantages of AVAR and MVAR. PVAR is good for long-term
analysis because the wavelet spans over , the same of the AVAR wavelet;
and good for short-term analysis because the response to white and flicker PM
is and , same as the MVAR.
After setting the theoretical framework, we study the degrees of freedom and
the confidence interval for the most common noise types. Then, we focus on the
detection of a weak noise process at the transition - or corner - where a
faster process rolls off. This new perspective raises the question of which
variance detects the weak process with the shortest data record. Our
simulations show that PVAR is a fortunate tradeoff. PVAR is superior to MVAR in
all cases, exhibits the best ability to divide between fast noise phenomena (up
to flicker FM), and is almost as good as AVAR for the detection of random walk
and drift
An exact sequence for contact- and symplectic homology
A symplectic manifold with contact type boundary induces
a linearization of the contact homology of with corresponding linearized
contact homology . We establish a Gysin-type exact sequence in which the
symplectic homology of maps to , which in turn maps to
, by a map of degree -2, which then maps to . Furthermore, we
give a description of the degree -2 map in terms of rational holomorphic curves
with constrained asymptotic markers, in the symplectization of .Comment: Final version. Changes for v2: Proof of main theorem supplemented
with detailed discussion of continuation maps. Description of degree -2 map
rewritten with emphasis on asymptotic markers. Sec. 5.2 rewritten with
emphasis on 0-dim. moduli spaces. Transversality discussion reorganized for
clarity (now Remark 9). Various other minor modification
Spt5 Cooperates with Human Immunodeficiency Virus Type 1 Tat by Preventing Premature RNA Release at Terminator Sequences
The human immunodeficiency virus type 1 (HIV-1) Tat protein activates transcription elongation by stimulating the Tat-activated kinase (TAK/p-TEFb), a protein kinase composed of CDK9 and its cyclin partner, cyclin T1. CDK9 is able to hyperphosphorylate the carboxyl-terminal domain (CTD) of the large subunit of RNA polymerase during elongation. In addition to TAK, the transcription elongation factor Spt5 is required for the efficient activation of transcriptional elongation by Tat. To study the role of Spt5 in HIV transcription in more detail, we have developed a three-stage Tat-dependent transcription assay that permits the isolation of active preinitiation complexes, early-stage elongation complexes, and Tat-activated elongation complexes. Spt5 is recruited in the transcription complex shortly after initiation. After recruitment of Tat during elongation through the transactivation response element RNA, CDK9 is activated and induces hyperphosphorylation of Spt5 in parallel to the hyperphosphorylation of the CTD of RNA polymerase II. However, immunodepletion experiments demonstrate that Spt5 is not required for Tat-dependent activation of the kinase. Chase experiments using the Spt5-depleted extracts demonstrate that Spt5 is not required for early elongation. However, Spt5 plays an important role in late elongation by preventing the premature dissociation of RNA from the transcription complex at terminator sequences and reducing the amount of polymerase pausing at arrest sites, including bent DNA sequences. This novel biochemical function of Spt5 is analogous to the function of NusG, an elongation factor found in Escherichia coli that enhances RNA polymerase stability on templates and shows sequence similarity to Spt5
Weak and strong fillability of higher dimensional contact manifolds
For contact manifolds in dimension three, the notions of weak and strong
symplectic fillability and tightness are all known to be inequivalent. We
extend these facts to higher dimensions: in particular, we define a natural
generalization of weak fillings and prove that it is indeed weaker (at least in
dimension five),while also being obstructed by all known manifestations of
"overtwistedness". We also find the first examples of contact manifolds in all
dimensions that are not symplectically fillable but also cannot be called
overtwisted in any reasonable sense. These depend on a higher-dimensional
analogue of Giroux torsion, which we define via the existence in all dimensions
of exact symplectic manifolds with disconnected contact boundary.Comment: 68 pages, 5 figures. v2: Some attributions clarified, and other minor
edits. v3: exposition improved using referee's comments. Published by Invent.
Mat
Fine frequency shift of sigle vortex entrance and exit in superconducting loops
The heat capacity of an array of independent aluminum rings has been
measured under an external magnetic field using highly sensitive
ac-calorimetry based on a silicon membrane sensor. Each superconducting vortex
entrance induces a phase transition and a heat capacity jump and hence
oscillates with . This oscillatory and non-stationary behaviour
measured versus the magnetic field has been studied using the Wigner-Ville
distribution (a time-frequency representation). It is found that the
periodicity of the heat capacity oscillations varies significantly with the
magnetic field; the evolution of the period also depends on the sweeping
direction of the field. This can be attributed to a different behavior between
expulsion and penetration of vortices into the rings. A variation of more than
15% of the periodicity of the heat capacity jumps is observed as the magnetic
field is varied. A description of this phenomenon is given using an analytical
solution of the Ginzburg-Landau equations of superconductivity
The Minimal Length of a Lagrangian Cobordism between Legendrians
To investigate the rigidity and flexibility of Lagrangian cobordisms between
Legendrian submanifolds, we investigate the minimal length of such a cobordism,
which is a -dimensional measurement of the non-cylindrical portion of the
cobordism. Our primary tool is a set of real-valued capacities for a Legendrian
submanifold, which are derived from a filtered version of Legendrian Contact
Homology. Relationships between capacities of Legendrians at the ends of a
Lagrangian cobordism yield lower bounds on the length of the cobordism. We
apply the capacities to Lagrangian cobordisms realizing vertical dilations
(which may be arbitrarily short) and contractions (whose lengths are bounded
below). We also study the interaction between length and the linking of
multiple cobordisms as well as the lengths of cobordisms derived from
non-trivial loops of Legendrian isotopies.Comment: 33 pages, 9 figures. v2: Minor corrections in response to referee
comments. More general statement in Proposition 3.3 and some reorganization
at the end of Section
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