645 research outputs found
Spectral Orbits and Peak-to-Average Power Ratio of Boolean Functions with respect to the {I,H,N}^n Transform
We enumerate the inequivalent self-dual additive codes over GF(4) of
blocklength n, thereby extending the sequence A090899 in The On-Line
Encyclopedia of Integer Sequences from n = 9 to n = 12. These codes have a
well-known interpretation as quantum codes. They can also be represented by
graphs, where a simple graph operation generates the orbits of equivalent
codes. We highlight the regularity and structure of some graphs that correspond
to codes with high distance. The codes can also be interpreted as quadratic
Boolean functions, where inequivalence takes on a spectral meaning. In this
context we define PAR_IHN, peak-to-average power ratio with respect to the
{I,H,N}^n transform set. We prove that PAR_IHN of a Boolean function is
equivalent to the the size of the maximum independent set over the associated
orbit of graphs. Finally we propose a construction technique to generate
Boolean functions with low PAR_IHN and algebraic degree higher than 2.Comment: Presented at Sequences and Their Applications, SETA'04, Seoul, South
Korea, October 2004. 17 pages, 10 figure
Spinning around or stagnation - what do osteoblasts and chondroblasts really like?
<p>Abstract</p> <p>Objective</p> <p>The influcence of cytomechanical forces in cellular migration, proliferation and differentation of mesenchymal stem cells (MSCs) is still poorly understood in detail.</p> <p>Methods</p> <p>Human MSCs were isolated and cultivated onto the surface of a 3 Ă 3 mm porcine collagen I/III carrier. After incubation, cell cultures were transfered to the different cutures systems: regular static tissue flasks (group I), spinner flasks (group II) and rotating wall vessels (group III). Following standard protocols cells were stimulated lineage specific towards the osteogenic and chondrogenic lines. To evaluate the effects of applied cytomechanical forces towards cellular differentiation distinct parameters were measured (morphology, antigen and antigen expression) after a total cultivation period of 21 days in vitro.</p> <p>Results</p> <p>Depending on the cultivation technique we found significant differences in both gen and protein expression.</p> <p>Conclusion</p> <p>Cytomechanical forces with rotational components strongly influence the osteogenic and chondrogenic differentiation.</p
An open platform for Aerosol InfraRed Spectroscopy analysis â AIRSpec
AIRSpec is a platform consisting of several chemometric packages developed
for analysis of Fourier transform infrared (FTIR) spectra of atmospheric
aerosols. The packages are accessible through a browser-based interface,
which also generates the necessary input files based on user interactions for
provenance management and subsequent use with a command-line interface. The
current implementation includes the task of baseline correction, organic
functional group (FG) analysis, and multivariate calibration for any analyte
with absorption in the mid-infrared. The baseline correction package uses
smoothing splines to correct the drift of the baseline of ambient aerosol
spectra given the variability in both environmental mixture composition and
substrates. The FGÂ analysis is performed by fitting individual Gaussian line
shapes for alcohol (aCOH), carboxylic acid (COOH), alkane (aCH), carbonyl (CO),
primary amine (aNH2), and ammonium (ammNH) for each spectrum.
The multivariate calibration model uses the
spectra to estimate the concentration of relevant target variables (e.g.,
organic or elemental carbon) measured with different reference instruments.
In each of these analyses, AIRSpec receives spectra and user choices on
parameters for model computation; input files with parameters that can later
be used with a command-line interface for batch computation are returned
together with diagnostic figures and tables in text format. AIRSpec is built
using the open-source software consisting of R and Shiny and is released
under the GNU Public License v3. Users can download, modify, and extend the
package, or access its functionality through the web application
(http://airspec.epfl.ch, last access: 3 April 2019) hosted at the Ăcole polytechnique
fédérale de Lausanne (EPFL). AIRSpec provides a unified framework by
which different chemometric techniques can be shared and accessed, and its
underlying suite of packages provides the basic functionality for extending
the platform with new types of analyses. For example, basic functionality
includes operations for populating and accessing spectra residing in
in-memory arrays or relational databases, input and output of spectra and
results of computation, and user interface development. Moreover, AIRSpec
facilitates the exploratory work, can be used by FTIR spectra acquired with
different methods, and can be extended easily with new chemometric packages
when they become available. Therefore AIRSpec provides a framework for
centralizing and disseminating such algorithms. This paper describes the
modular architecture and provides examples of the implemented packages using
the spectra of aerosol samples collected on PM2.5 polytetrafluoroethylene (Teflon) filters.</p
On Exceptional Vertex Operator (Super) Algebras
We consider exceptional vertex operator algebras and vertex operator
superalgebras with the property that particular Casimir vectors constructed
from the primary vectors of lowest conformal weight are Virasoro descendents of
the vacuum. We show that the genus one partition function and characters for
simple ordinary modules must satisfy modular linear differential equations. We
show the rationality of the central charge and module lowest weights,
modularity of solutions, the dimension of each graded space is a rational
function of the central charge and that the lowest weight primaries generate
the algebra. We also discuss conditions on the reducibility of the lowest
weight primary vectors as a module for the automorphism group. Finally we
analyse solutions for exceptional vertex operator algebras with primary vectors
of lowest weight up to 9 and for vertex operator superalgebras with primary
vectors of lowest weight up to 17/2. Most solutions can be identified with
simple ordinary modules for known algebras but there are also four conjectured
algebras generated by weight two primaries and three conjectured extremal
vertex operator algebras generated by primaries of weight 3, 4 and 6
respectively.Comment: 37 page
Equivalence of Approaches to Relational Quantum Dynamics in Relativistic Settings
We have previously shown that three approaches to relational quantum dynamicsârelational Dirac observables, the Page-Wootters formalism and quantum deparametrizationsâare equivalent. Here we show that this âtrinityâ of relational quantum dynamics holds in relativistic settings per frequency superselection sector. Time according to a clock subsystem is defined via a positive operator-valued measure (POVM) that is covariant with respect to the group generated by its (quadratic) Hamiltonian. This differs from the usual choice of a self-adjoint clock observable conjugate to the clock momentum. It also resolves KuchaĆ's criticism that the Page-Wootters formalism yields incorrect localization probabilities for the relativistic particle when conditioning on a Minkowski time operator. We show that conditioning instead on the covariant clock POVM results in a Newton-Wigner type localization probability commonly used in relativistic quantum mechanics. By establishing the equivalence mentioned above, we also assign a consistent conditional-probability interpretation to relational observables and deparametrizations. Finally, we expand a recent method of changing temporal reference frames, and show how to transform states and observables frequency-sector-wise. We use this method to discuss an indirect clock self-reference effect and explore the state and temporal frame-dependence of the task of comparing and synchronizing different quantum clocks
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Imaging stress and magnetism at high pressures using a nanoscale quantum sensor.
Pressure alters the physical, chemical, and electronic properties of matter. The diamond anvil cell enables tabletop experiments to investigate a diverse landscape of high-pressure phenomena. Here, we introduce and use a nanoscale sensing platform that integrates nitrogen-vacancy (NV) color centers directly into the culet of diamond anvils. We demonstrate the versatility of this platform by performing diffraction-limited imaging of both stress fields and magnetism as a function of pressure and temperature. We quantify all normal and shear stress components and demonstrate vector magnetic field imaging, enabling measurement of the pressure-driven [Formula: see text] phase transition in iron and the complex pressure-temperature phase diagram of gadolinium. A complementary NV-sensing modality using noise spectroscopy enables the characterization of phase transitions even in the absence of static magnetic signatures
Three-dimensional AdS gravity and extremal CFTs at c=8m
We note that Witten's proposed duality between extremal c=24k CFTs and
three-dimensional anti-de Sitter gravity may possibly be extended to central
charges that are multiples of 8, for which extremal self-dual CFTs are known to
exist up to c=40. All CFTs of this type with central charge 24 or higher,
provided that they exist, have the required mass gap and may serve as candidate
duals to three-dimensional gravity at the corresponding values of the
cosmological constant. Here, we compute the genus one partition function of
these theories up to c=88, we give exact and approximate formulas for the
degeneracies of states, and we determine the genus two partition functions of
the theories up to c=40.Comment: 17 pages, harvmac; v2: references added, version accepted in JHE
Equivalence of Approaches to Relational Quantum Dynamics in Relativistic Settings
We have previously shown that three approaches to relational quantum dynamicsârelational Dirac observables, the Page-Wootters formalism and quantum deparametrizationsâare equivalent. Here we show that this âtrinityâ of relational quantum dynamics holds in relativistic settings per frequency superselection sector. Time according to a clock subsystem is defined via a positive operator-valued measure (POVM) that is covariant with respect to the group generated by its (quadratic) Hamiltonian. This differs from the usual choice of a self-adjoint clock observable conjugate to the clock momentum. It also resolves KuchaĆ\u27s criticism that the Page-Wootters formalism yields incorrect localization probabilities for the relativistic particle when conditioning on a Minkowski time operator. We show that conditioning instead on the covariant clock POVM results in a Newton-Wigner type localization probability commonly used in relativistic quantum mechanics. By establishing the equivalence mentioned above, we also assign a consistent conditional-probability interpretation to relational observables and deparametrizations. Finally, we expand a recent method of changing temporal reference frames, and show how to transform states and observables frequency-sector-wise. We use this method to discuss an indirect clock self-reference effect and explore the state and temporal frame-dependence of the task of comparing and synchronizing different quantum clocks
Trinity of relational quantum dynamics
The problem of time in quantum gravity calls for a relational solution. Using quantum reduction maps, we establish a previously unknown equivalence between three approaches to relational quantum dynamics: (1) relational observables in the clock-neutral picture of Dirac quantization, (2) Page and Woottersâ (PW) Schrödinger picture formalism, and (3) the relational Heisenberg picture obtained via symmetry reduction. Constituting three faces of the same dynamics, we call this equivalence the trinity. In the process, we develop a quantization procedure for relational Dirac observables using covariant positive operator-valued measures which encompass nonideal clocks and resolve the nonmonotonicity issue of realistic quantum clocks reported by Unruh and Wald. The quantum reduction maps reveal this procedure as the quantum analog of gauge-invariantly extending gauge-fixed quantities. We establish algebraic properties of these relational observables. We extend a recent âclock-neutralâ approach to changing temporal reference frames, transforming relational observables and states, and demonstrate a clock dependent temporal nonlocality effect. We show that KuchaĆâs criticism, alleging that the conditional probabilities of the PW formalism violate the constraint, is incorrect. They are a quantum analog of a gauge-fixed description of a gauge-invariant quantity and equivalent to the manifestly gauge-invariant evaluation of relational observables in the physical inner product. The trinity furthermore resolves a previously reported normalization ambiguity and clarifies the role of entanglement in the PW formalism. The trinity finally permits us to resolve KuchaĆâs criticism that the PW formalism yields wrong propagators by showing how conditional probabilities of relational observables give the correct transition probabilities. Unlike previous proposals, our resolution does not invoke approximations, ideal clocks or ancilla systems, is manifestly gauge invariant, and easily extends to an arbitrary number of conditionings
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