397 research outputs found
Parameter estimation from an Ornstein-Uhlenbeck process with measurement noise
This article aims to investigate the impact of noise on parameter fitting for
an Ornstein-Uhlenbeck process, focusing on the effects of multiplicative and
thermal noise on the accuracy of signal separation. To address these issues, we
propose algorithms and methods that can effectively distinguish between thermal
and multiplicative noise and improve the precision of parameter estimation for
optimal data analysis. Specifically, we explore the impact of both
multiplicative and thermal noise on the obfuscation of the actual signal and
propose methods to resolve them. Firstly, we present an algorithm that can
effectively separate thermal noise with comparable performance to Hamilton
Monte Carlo (HMC) but with significantly improved speed. Subsequently, we
analyze multiplicative noise and demonstrate that HMC is insufficient for
isolating thermal and multiplicative noise. However, we show that, with
additional knowledge of the ratio between thermal and multiplicative noise, we
can accurately distinguish between the two types of noise when provided with a
sufficiently large sampling rate or an amplitude of multiplicative noise
smaller than thermal noise. This finding results in a situation that initially
seems counterintuitive. When multiplicative noise dominates the noise spectrum,
we can successfully estimate the parameters for such systems after adding
additional white noise to shift the noise balance.Comment: 16 pages, 4 figure
Bond Orientational Order, Molecular Motion and Free Energy of High Density DNA Mesophases
By equilibrating condensed DNA arrays against reservoirs of known osmotic
stress and examining them with several structural probes, it has been possible
to achieve a detailed thermodynamic and structural characterization of the
change between two distinct regions on the liquid crystalline phase digram: a
higher-density hexagonally packed region with long-range bond orientational
order in the plane perpendicular to the average molecular direction; and a
lower-density cholesteric region with fluid-like positional order. X-rays
scattering on highly ordered DNA arrays at high density and with the helical
axis oriented parallel to the incoming beam showed a six-fold azimuthal
modulation of the first order diffraction peak that reflects the macroscopic
bond-orientational order. Transition to the less-dense cholesteric phase
through osmotically controlled swelling shows the loss of this bond
orientational order that had been expected from the change in optical
birefringence patterns and that is consistent with a rapid onset of molecular
positional disorder. This change in motion was previously inferred from
intermolecular force measurements and is now confirmed by NMR.
Controlled reversible swelling and compaction under osmotic stress, spanning a
range of densities between mg/ml to mg/ml, allows
measurement of the free energy changes throughout each phase and at the phase
transition, essential information for theories of liquid-crystalline states.Comment: 14 pages, 3 figures in gif format available at
http://abulafia.mgsl.dcrt.nih.gov/pics.html E-mail: [email protected]
Positional, Reorientational and Bond Orientational Order in DNA Mesophases
We investigate the orientational order of transverse polarization vectors of
long, stiff polymer molecules and their coupling to bond orientational and
positional order in high density mesophases. Homogeneous ordering of transverse
polarization vector promotes distortions in the hexatic phase, whereas
inhomogeneous ordering precipitates crystalization of the 2D sections with
different orientations of the transverse polarization vector on each molecule
in the unit cell. We propose possible scenarios for going from the hexatic
phase, through the distorted hexatic phase to the crystalline phase with an
orthorhombic unit cell observed experimentally for the case of DNA.Comment: 4 pages, 2 figure
Second-Hand Stress: Neurobiological Evidence for a Human Alarm Pheromone
Alarm pheromones are airborne chemical signals, released by an individual into the environment, which transmit warning of danger to conspecifics via olfaction. Using fMRI, we provide the first neurobiological evidence for a human alarm pheromone. Individuals showed activation of the amygdala in response to sweat produced by others during emotional stress, with exercise sweat as a control; behavioral data suggest facilitated evaluation of ambiguous threat
H2O–D2O Condensation in A Supersonic Nozzle
We examined the condensation of H2O, D2O, and four intermediate mixtures (20, 40, 60, and 80 mol % D2O) in a supersonic nozzle. Because the physical and chemical properties of protonated and deuterated water are so similar, this system is ideal for studying the change in condensation behavior as a function of condensible composition. In our experiments dilute mixtures of condensible vapor in N2 are expanded from three different stagnation temperatures resulting in a broad range of onset temperatures (190–238 K) and pressures (27–787 kPa). For a fixed stagnation temperature, the partial pressure required to maintain the onset of condensation at a given location or temperature in the nozzle is consistently higher for H2O than for D2O. In contrast, the supersaturation at fixed onset temperature is usually higher for D2O than for H2O and this difference increases toward lower temperature. The partial pressure at onset for the intermediate mixtures varied linearly between the values observed for the pure components in this ideal system
Small Angle Neutron Scattering from D2O–H2O Nanodroplets and Binary Nucleation Rates in A Supersonic Nozzle
Small angle neutron scattering (SANS) experiments were used to characterize binary nanodroplets composed of D2O and H2O. The droplets were formed by expanding dilute mixtures of condensible vapor in a N2 carrier gas through a supersonic nozzle, while maintaining the onset of condensation at a fixed position in the nozzle. It is remarkable, given the small coherent scattering length density of light water, that even the pure H2O aerosol gave a scattering signal above background. The scattering spectra were analyzed assuming a log-normal distribution of droplets. On average, the geometric radius of the nanodroplets rg was rg=13 (±1) nm, the polydispersity ln σr was ln σr=0.19 (±0.07), and the number density N was N=(2±0.2)⋅1011 cm−3. The aerosol volume fractions derived from the SANS measurements are consistent with those derived from the pressure trace experiments, suggesting that the composition of the droplets was close to that of the initial condensible mixture. A quantitative analysis of the scattering spectra as a function of the isotopic composition gave further evidence that the binary droplets exhibit ideal mixing behavior. Because both the stagnation temperature T0 and the location of onset were fixed, the temperature corresponding to the maximum nucleation rate was constant at TJ max=229 (±1) K. Thus, the experiments let us estimate the isothermal peak nucleation rates as a function of the isotopic composition. The nucleation rates were found to be essentially constant with Jmax equal to (3.6±0.5)⋅1016 cm−3 s−1 at a mean supersaturation of 44 (±3)
The air pressure effect on the homogeneous nucleation of carbon dioxide by molecular simulation
Vapour-liquid equilibria (VLE) and the influence of an inert carrier gas on
homogeneous vapour to liquid nucleation are investigated by molecular
simulation for quaternary mixtures of carbon dioxide, nitrogen, oxygen, and
argon. Canonical ensemble molecular dynamics simulation using the
Yasuoka-Matsumoto method is applied to nucleation in supersaturated vapours
that contain more carbon dioxide than in the saturated state at the dew line.
Established molecular models are employed that are known to accurately
reproduce the VLE of the pure fluids as well as their binary and ternary
mixtures. On the basis of these models, also the quaternary VLE properties of
the bulk fluid are determined with the Grand Equilibrium method.
Simulation results for the carrier gas influence on the nucleation rate are
compared with the classical nucleation theory (CNT) considering the "pressure
effect" [Phys. Rev. Lett. 101: 125703 (2008)]. It is found that the presence of
air as a carrier gas decreases the nucleation rate only slightly and, in
particular, to a significantly lower extent than predicted by CNT. The
nucleation rate of carbon dioxide is generally underestimated by CNT, leading
to a deviation between one and two orders of magnitude for pure carbon dioxide
in the vicinity of the spinodal line and up to three orders of magnitude in
presence of air as a carrier gas. Furthermore, CNT predicts a temperature
dependence of the nucleation rate in the spinodal limit, which cannot be
confirmed by molecular simulation
FixFit: using parameter-compression to solve the inverse problem in overdetermined models
All fields of science depend on mathematical models. One of the fundamental
problems with using complex nonlinear models is that data-driven parameter
estimation often fails because interactions between model parameters lead to
multiple parameter sets fitting the data equally well. Here, we develop a new
method to address this problem, FixFit, which compresses a given mathematical
model's parameters into a latent representation unique to model outputs. We
acquire this representation by training a neural network with a bottleneck
layer on data pairs of model parameters and model outputs. The bottleneck layer
nodes correspond to the unique latent parameters, and their dimensionality
indicates the information content of the model. The trained neural network can
be split at the bottleneck layer into an encoder to characterize the
redundancies and a decoder to uniquely infer latent parameters from
measurements. We demonstrate FixFit in two use cases drawn from classical
physics and neuroscience
Coupling between Smectic and Twist Modes in Polymer Intercalated Smectics
We analyse the elastic energy of an intercalated smectic where
orientationally ordered polymers with an average orientation varying from layer
to layer are intercalated between smectic planes. The lowest order terms in the
coupling between polymer director and smectic layer curvature are added to the
smectic elastic energy. Integration over the smectic degrees of freedom leaves
an effective polymer twist energy that has to be included into the total
polymer elastic energy leading to a fluctuational renormalization of the
intercalated polymer twist modulus. If the polymers are chiral this in its turn
leads to a renormalization of the cholesteric pitch.Comment: 8 pages, 1 fig in ps available from [email protected] Replaced
version also contains title and abstract in the main tex
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