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 × 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 – 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 FG 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 École 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 dynamics—relational Dirac observables, the Page-Wootters formalism and quantum deparametrizations—are equivalent. Here we show that this “trinity” 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 Kuchař'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

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 dynamics—relational Dirac observables, the Page-Wootters formalism and quantum deparametrizations—are equivalent. Here we show that this “trinity” 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 Kuchař\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