2,755 research outputs found
Phase retrieval with polarization
In many areas of imaging science, it is difficult to measure the phase of
linear measurements. As such, one often wishes to reconstruct a signal from
intensity measurements, that is, perform phase retrieval. In this paper, we
provide a novel measurement design which is inspired by interferometry and
exploits certain properties of expander graphs. We also give an efficient phase
retrieval procedure, and use recent results in spectral graph theory to produce
a stable performance guarantee which rivals the guarantee for PhaseLift in
[Candes et al. 2011]. We use numerical simulations to illustrate the
performance of our phase retrieval procedure, and we compare reconstruction
error and runtime with a common alternating-projections-type procedure
Enumeration of chord diagrams on many intervals and their non-orientable analogs
Two types of connected chord diagrams with chord endpoints lying in a
collection of ordered and oriented real segments are considered here: the real
segments may contain additional bivalent vertices in one model but not in the
other. In the former case, we record in a generating function the number of
fatgraph boundary cycles containing a fixed number of bivalent vertices while
in the latter, we instead record the number of boundary cycles of each fixed
length. Second order, non-linear, algebraic partial differential equations are
derived which are satisfied by these generating functions in each case giving
efficient enumerative schemes. Moreover, these generating functions provide
multi-parameter families of solutions to the KP hierarchy. For each model,
there is furthermore a non-orientable analog, and each such model likewise has
its own associated differential equation. The enumerative problems we solve are
interpreted in terms of certain polygon gluings. As specific applications, we
discuss models of several interacting RNA molecules. We also study a matrix
integral which computes numbers of chord diagrams in both orientable and
non-orientable cases in the model with bivalent vertices, and the large-N limit
is computed using techniques of free probability.Comment: 23 pages, 7 figures; revised and extended versio
Prediction of physical-chemical and fire hazard characteristics by carbon chain rules. 2. Carboxylic acids
Investigation of the dependence of physico-chemical and fire hazard properties from the chemical structure of carboxylic acids is carried out. Forecasting of the boiling temperature, the flash point, the temperature and the concentration flammability limits, the heats of combustion and vaporization is performed by the carbon chain rules (CCR). The following empirical equations for the calculation of physico-chemical and fire hazard indices from the conventional carbon chain and from the number of carbon atoms are proposed for the convenience of practical application of the CCR. A comparative analysis of the proposed methods for the flash point calculating and the already known methods of GOST 12.1.044-89, Mendeleev and ACD/Lab 2014 is carried out. It is shown, basically, that the new methods give more accurate calculation results than the comparison design procedures. © Siberian Federal University. All rights reserve
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Asymmetric jump beta estimation with implications for portfolio risk management
We evaluate the impact of extreme market shifts on equity portfolios and study the differ-ence in negative and positive reactions to market jumps with implications for portfolio riskmanagement. Employing high-frequency data for the constituents of the S&P500 index overthe period 2 January 2003 to 30 December 2017, we investigate to what extent the portfolioexposure to the downside and upside jumps can be mitigated. We contrast the risk exposureof individual stocks with those of the portfolios as the number of holdings increases. Varyingthe jump identification threshold, we show that the number of holdings required to stabiliseportfolios’ sensitivities to negative jumps is higher than when positive jumps are consideredand that the asymmetry is more prominent for more extreme events. Ignoring this asymme-try results in under-diversification of portfolios and increases exposure to sudden extremenegative market shifts
On Possible Measurement of Gravitational Interaction Parameters on Board a Satellite
The recently suggested SEE (Satellite Energy Exchange) method of measuring
the gravitational constant , possible equivalence principle violation
(measured by the E\"{o}tv\"{o}s parameter ) and the hypothetic 5th force
parameters and on board a drag-free Earth's satellite is
discussed and further developed. Various particle trajectories near a heavy
ball are numerically simulated. Some basic sources of error are analysed. The
measurement procedure is modelled by noise insertion to a ``true''
trajectory. It is concluded that the present knowledge of (for
m) and can be improved by at least two orders of
magnitude.Comment: (only two misprints on title page) 7 page
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