451 research outputs found
Computations and parameterizations of the nonlinear energy transfer in a gravity-wave spectrum. Part II: Parameterizations of the nonlinear energy transfer for application in wave models
Four different parameterizations of the nonlinear energy transfer Snl in a surface wave spectrum are in investigated. Two parameterizations are based on a relatively small number of parameters and are useful primarily for application in parametrical or hybrid wave models. In the first parameterization, shape-distortion parameters are introduced to relate the distribution Snl for different values of the peak-enhancement parameter γ. The second parameterization is based on an EOF expansion of a set of Snl computed for a number of different spectral distributions. The remaining two parameterizations represent operator forms that contain the same number of free parameters as used to describe he wave spectrum. Such parameterizations with a matched number of input and output parameters are required for numerical stability in high-resolution discrete spectral models. A cubic, fourth-order diffusion-operator expression derived by a local-interaction expansion is found to be useful for understanding many of the properties of Snl, but is regarded as too inaccurate in detail for application in most wave models. The best results are achieved with a discrete-interaction operator parameterization, in which a single interaction configuration, together with its mirror image (representing a two-dimensional continuum of interactions with respect to a variable reference wavenumber scale and direction) is used to simulate the net effect of the full five-dimensional interaction continuum
On Resource-bounded versions of the van Lambalgen theorem
The van Lambalgen theorem is a surprising result in algorithmic information
theory concerning the symmetry of relative randomness. It establishes that for
any pair of infinite sequences and , is Martin-L\"of random and
is Martin-L\"of random relative to if and only if the interleaved sequence
is Martin-L\"of random. This implies that is relative random
to if and only if is random relative to \cite{vanLambalgen},
\cite{Nies09}, \cite{HirschfeldtBook}. This paper studies the validity of this
phenomenon for different notions of time-bounded relative randomness.
We prove the classical van Lambalgen theorem using martingales and Kolmogorov
compressibility. We establish the failure of relative randomness in these
settings, for both time-bounded martingales and time-bounded Kolmogorov
complexity. We adapt our classical proofs when applicable to the time-bounded
setting, and construct counterexamples when they fail. The mode of failure of
the theorem may depend on the notion of time-bounded randomness
Polynomial Time Algorithms for Branching Markov Decision Processes and Probabilistic Min(Max) Polynomial Bellman Equations
We show that one can approximate the least fixed point solution for a
multivariate system of monotone probabilistic max(min) polynomial equations,
referred to as maxPPSs (and minPPSs, respectively), in time polynomial in both
the encoding size of the system of equations and in log(1/epsilon), where
epsilon > 0 is the desired additive error bound of the solution. (The model of
computation is the standard Turing machine model.) We establish this result
using a generalization of Newton's method which applies to maxPPSs and minPPSs,
even though the underlying functions are only piecewise-differentiable. This
generalizes our recent work which provided a P-time algorithm for purely
probabilistic PPSs.
These equations form the Bellman optimality equations for several important
classes of infinite-state Markov Decision Processes (MDPs). Thus, as a
corollary, we obtain the first polynomial time algorithms for computing to
within arbitrary desired precision the optimal value vector for several classes
of infinite-state MDPs which arise as extensions of classic, and heavily
studied, purely stochastic processes. These include both the problem of
maximizing and mininizing the termination (extinction) probability of
multi-type branching MDPs, stochastic context-free MDPs, and 1-exit Recursive
MDPs.
Furthermore, we also show that we can compute in P-time an epsilon-optimal
policy for both maximizing and minimizing branching, context-free, and
1-exit-Recursive MDPs, for any given desired epsilon > 0. This is despite the
fact that actually computing optimal strategies is Sqrt-Sum-hard and
PosSLP-hard in this setting.
We also derive, as an easy consequence of these results, an FNP upper bound
on the complexity of computing the value (within arbitrary desired precision)
of branching simple stochastic games (BSSGs)
Growing Sugarcane for Energy Use
The increase in energy demand throughout the world, and the rise of greenhouse gas emissions has lead to the exploration of new energy sources. Sugarcane is already being used as a source of energy and is a growing industry. Sugarcane is currently being used to create ethanol and has the potential to be a competitive alternative to fossil fuels if other by-products of the plant are utilized
Second harmonic light scattering induced by defects in the twist-bend nematic phase of liquid crystal dimers
The nematic twist-bend (NTB) phase, exhibited by certain thermotropic liquid crystalline (LC) dimers, represents a new orientationally ordered mesophase -- the first distinct nematic variant discovered in many years. The NTB phase is distinguished by a heliconical winding of the average molecular long axis (director) with a remarkably short (nanoscale) pitch and, in systems of achiral dimers, with an equal probability to form right- and left-handed domains. The NTB structure thus provides another fascinating example of spontaneous chiral symmetry breaking in nature. The order parameter driving the formation of the heliconical state has been theoretically conjectured to be a polarization field, deriving from the bent conformation of the dimers, that rotates helically with the same nanoscale pitch as the director field. It therefore presents a significant challenge for experimental detection. Here we report a second harmonic light scattering (SHLS) study on two achiral, NTB-forming LCs, which is sensitive to the polarization field due to micron-scale distortion of the helical structure associated with naturally-occurring textural defects. These defects are parabolic focal conics of smectic-like ``pseudo-layers", defined by planes of equivalent phase in a coarse-grained description of the NTB state. Our SHLS data are explained by a coarse-grained free energy density that combines a Landau-deGennes expansion of the polarization field, the elastic energy of a nematic, and a linear coupling between the two
Light scattering study of the “pseudo-layer” compression elastic constant in a twist-bend nematic liquid crystal
The nematic twist-bend (TB) phase, exhibited by certain achiral thermotropic liquid crystalline (LC) dimers, features a nanometer-scale, heliconical rotation of the average molecular long axis (director) with equally probable left- and right-handed domains. On meso to macroscopic scales, the TB phase may be considered as a stack of equivalent slabs or “pseudo-layers”, each one helical pitch in thickness. The long wavelength fluctuation modes should then be analogous to those of a smectic-A phase, and in particular the hydrodynamic mode combining “layer” compression and bending ought to be characterized by an effective layer compression elastic constant Beff and average director splay constant Keff1. The magnitude of Keff1 is expected to be similar to the splay constant of an ordinary nematic LC, but due to the absence of a true mass density wave, Beff could differ substantially from the typical value of ∼10⁶ Pa in a conventional smectic-A. Here we report the results of a dynamic light scattering study, which confirms the “pseudo-layer” structure of the TB phase with Beff in the range 10³–10⁴ Pa. We show additionally that the temperature dependence of Beff at the TB to nematic transition is accurately described by a coarse-grained free energy density, which is based on a Landau-deGennes expansion in terms of a heli-polar order parameter that characterizes the TB state and is linearly coupled to bend distortion of the director
The Complexity of Nash Equilibria in Simple Stochastic Multiplayer Games
We analyse the computational complexity of finding Nash equilibria in simple
stochastic multiplayer games. We show that restricting the search space to
equilibria whose payoffs fall into a certain interval may lead to
undecidability. In particular, we prove that the following problem is
undecidable: Given a game G, does there exist a pure-strategy Nash equilibrium
of G where player 0 wins with probability 1. Moreover, this problem remains
undecidable if it is restricted to strategies with (unbounded) finite memory.
However, if mixed strategies are allowed, decidability remains an open problem.
One way to obtain a provably decidable variant of the problem is restricting
the strategies to be positional or stationary. For the complexity of these two
problems, we obtain a common lower bound of NP and upper bounds of NP and
PSPACE respectively.Comment: 23 pages; revised versio
The Search for Higher in Houston
It is a great pleasure to be invited to join the chorus on this auspicious
occasion to celebrate Professor K. Alex Mueller's 90th birthday by Professors
Annette Bussman-Holder, Hugo Keller, and Antonio Bianconi. As a student in high
temperature superconductivity, I am forever grateful to Professor Alex Mueller
and Dr. Georg Bednorz "for their important breakthrough in the discovery of
superconductivity in the ceramic materials" in 1986 as described in the
citation of their 1987 Nobel Prize in Physics. It is this breakthrough
discovery that has ushered in the explosion of research activities in high
temperature superconductivity (HTS) and has provided immense excitement in HTS
science and technology in the ensuing decades till now. Alex has not been
resting on his laurels and has continued to search for the origin of the
unusual high temperature superconductivity in cuprates.Comment: Dedicated to Alex Mueller, whose "important breakthrough in the
discovery of superconductivity in ceramic materials" in 1986 has changed the
world of superconductivit
Population assessment of future trajectories in coronary heart disease mortality.
Background:
Coronary heart disease (CHD) mortality rates have been decreasing in Iceland since the 1980s, largely
reflecting improvements in cardiovascular risk factors. The purpose of this study was to predict future CHD mortality in
Iceland based on potential risk factor trends.
Methods and findings:
The previously validated IMPACT model was used to predict changes in CHD mortality between 2010 and 2040 among the projected population of Iceland aged 25–74. Calculations were based on combining: i) data on population numbers and projections (Statistics Iceland), ii) population risk factor levels and projections (Refine Reykjavik study), and iii) effectiveness of specific risk factor reductions (published meta-analyses). Projections for three contrasting
scenarios were compared: 1) If the historical risk factor trends of past 30 years were to continue, the declining death rates of past decades would level off, reflecting population ageing. 2) If recent trends in risk factors (past 5 years) continue, this would result in a death rate increasing from 49 to 70 per 100,000. This would reflect a recent plateau in previously falling cholesterol levels and recent rapid increases in obesity and diabetes prevalence. 3) Assuming that in 2040 the entire population enjoys optimal risk factor levels observed in low risk cohorts, this would prevent almost all premature CHD deaths before 2040.
Conclusions:
The potential increase in CHD deaths with recent trends in risk factor levels is alarming both for Iceland and
probably for comparable Western populations. However, our results show considerable room for reducing CHD mortality.
Achieving the best case scenario could eradicate premature CHD deaths by 2040. Public health policy interventions based
on these predictions may provide a cost effective means of reducing CHD mortality in the future
Hybrid Synthetic Receptors on MOSFET Devices for Detection of Prostate Specific Antigen in Human Plasma
The study reports the use of extended gate field-effect transistors (FET) for the label-free and sensitive detection of prostate cancer (PCa) biomarkers in human plasma. The approach integrates for the first time hybrid synthetic receptors comprising of highly selective aptamer-lined pockets (apta-MIP) with FETs for sensitive detection of prostate specific antigen (PSA) at clinically relevant concentrations. The hybrid synthetic receptors were constructed by immobilizing an aptamer–PSA complex on gold and subjecting it to 13 cycles of dopamine electropolymerization. The polymerization resulted in the creation of highly selective polymeric cavities that retained the ability to recognize PSA post removal of the protein. The hybrid synthetic receptors were subsequently used in an extended gate FET setup for electrochemical detection of PSA. The sensor was reported to have a limit of detection of 0.1 pg/mL with a linear detection range from 0.1 pg/mL to 1 ng/mL PSA. Detection of 1–10 pg/mL PSA was also achieved in diluted human plasma. The present apta-MIP sensor developed in conjunction with FET devices demonstrates the potential for clinical application of synthetic hybrid receptors for the detection of clinically relevant biomarkers in complex samples
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