398 research outputs found
(R)-Doxylaminium (R,R)-tartrate
In the title compound (systematic name: (R)-dimethyl{2-[1-phenyl-1-(pyridin-2-yl)ethoxy]ethyl}azanium (R,R)-3-carboxy-2,3-dihydroxypropanoate), C17H23N2O+·C4H5O6
−, the doxylaminium cation is protonated at the N atom. The tartrate monoanions are linked by short, almost linear O—H⋯O hydrogen bonds into chains extended along [100]. These chains are interlinked by anion–pyridine O—H⋯N hydrogen bonds into a two-dimensional grid structure. WeakC—H⋯O interactions also play a role in the crystal packing. An intramolecular hydroxy–carboxylate O—H⋯O hydrogen bond influences the conformation of the anion: the hydrogen-bonded fragment is almost planar, the maximum deviation from the mean plane being 0.059 (14) Å. In the cation, the aromatic rings are almost perpendicular [dihedral angle = 84.94 (8)°] and the conformation of the O—C—C—N chain is gauche(−), the dihedral angle is −76.6 (2)°. The absolute configuration was assigned on the basis of known chirality of the parent compound
Notes on bordered Floer homology
This is a survey of bordered Heegaard Floer homology, an extension of the
Heegaard Floer invariant HF-hat to 3-manifolds with boundary. Emphasis is
placed on how bordered Heegaard Floer homology can be used for computations.Comment: 73 pages, 29 figures. Based on lectures at the Contact and Symplectic
Topology Summer School in Budapest, July 2012. v2: Fixed many small typo
Entropy and Quantum Kolmogorov Complexity: A Quantum Brudno's Theorem
In classical information theory, entropy rate and Kolmogorov complexity per
symbol are related by a theorem of Brudno. In this paper, we prove a quantum
version of this theorem, connecting the von Neumann entropy rate and two
notions of quantum Kolmogorov complexity, both based on the shortest qubit
descriptions of qubit strings that, run by a universal quantum Turing machine,
reproduce them as outputs.Comment: 26 pages, no figures. Reference to publication added: published in
the Communications in Mathematical Physics
(http://www.springerlink.com/content/1432-0916/
The road to deterministic matrices with the restricted isometry property
The restricted isometry property (RIP) is a well-known matrix condition that
provides state-of-the-art reconstruction guarantees for compressed sensing.
While random matrices are known to satisfy this property with high probability,
deterministic constructions have found less success. In this paper, we consider
various techniques for demonstrating RIP deterministically, some popular and
some novel, and we evaluate their performance. In evaluating some techniques,
we apply random matrix theory and inadvertently find a simple alternative proof
that certain random matrices are RIP. Later, we propose a particular class of
matrices as candidates for being RIP, namely, equiangular tight frames (ETFs).
Using the known correspondence between real ETFs and strongly regular graphs,
we investigate certain combinatorial implications of a real ETF being RIP.
Specifically, we give probabilistic intuition for a new bound on the clique
number of Paley graphs of prime order, and we conjecture that the corresponding
ETFs are RIP in a manner similar to random matrices.Comment: 24 page
Dynamical stability of infinite homogeneous self-gravitating systems: application of the Nyquist method
We complete classical investigations concerning the dynamical stability of an
infinite homogeneous gaseous medium described by the Euler-Poisson system or an
infinite homogeneous stellar system described by the Vlasov-Poisson system
(Jeans problem). To determine the stability of an infinite homogeneous stellar
system with respect to a perturbation of wavenumber k, we apply the Nyquist
method. We first consider the case of single-humped distributions and show
that, for infinite homogeneous systems, the onset of instability is the same in
a stellar system and in the corresponding barotropic gas, contrary to the case
of inhomogeneous systems. We show that this result is true for any symmetric
single-humped velocity distribution, not only for the Maxwellian. If we
specialize on isothermal and polytropic distributions, analytical expressions
for the growth rate, damping rate and pulsation period of the perturbation can
be given. Then, we consider the Vlasov stability of symmetric and asymmetric
double-humped distributions (two-stream stellar systems) and determine the
stability diagrams depending on the degree of asymmetry. We compare these
results with the Euler stability of two self-gravitating gaseous streams.
Finally, we determine the corresponding stability diagrams in the case of
plasmas and compare the results with self-gravitating systems
A Fresh Variational-Analysis Look at the Positive Semidefinite Matrices World
International audienceEngineering sciences and applications of mathematics show unambiguously that positive semidefiniteness of matrices is the most important generalization of non-negative real num- bers. This notion of non-negativity for matrices has been well-studied in the literature; it has been the subject of review papers and entire chapters of books. This paper reviews some of the nice, useful properties of positive (semi)definite matrices, and insists in particular on (i) characterizations of positive (semi)definiteness and (ii) the geometrical properties of the set of positive semidefinite matrices. Some properties that turn out to be less well-known have here a special treatment. The use of these properties in optimization, as well as various references to applications, are spread all the way through. The "raison d'être" of this paper is essentially pedagogical; it adopts the viewpoint of variational analysis, shedding new light on the topic. Important, fruitful, and subtle, the positive semidefinite world is a good place to start with this domain of applied mathematics
Towards Machine Wald
The past century has seen a steady increase in the need of estimating and
predicting complex systems and making (possibly critical) decisions with
limited information. Although computers have made possible the numerical
evaluation of sophisticated statistical models, these models are still designed
\emph{by humans} because there is currently no known recipe or algorithm for
dividing the design of a statistical model into a sequence of arithmetic
operations. Indeed enabling computers to \emph{think} as \emph{humans} have the
ability to do when faced with uncertainty is challenging in several major ways:
(1) Finding optimal statistical models remains to be formulated as a well posed
problem when information on the system of interest is incomplete and comes in
the form of a complex combination of sample data, partial knowledge of
constitutive relations and a limited description of the distribution of input
random variables. (2) The space of admissible scenarios along with the space of
relevant information, assumptions, and/or beliefs, tend to be infinite
dimensional, whereas calculus on a computer is necessarily discrete and finite.
With this purpose, this paper explores the foundations of a rigorous framework
for the scientific computation of optimal statistical estimators/models and
reviews their connections with Decision Theory, Machine Learning, Bayesian
Inference, Stochastic Optimization, Robust Optimization, Optimal Uncertainty
Quantification and Information Based Complexity.Comment: 37 page
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