Numerical Methods for Computing Discontinuous Solutions of a Class of Hamilton-Jacobi Equations Using a Level Set Method (Free Boundary Problems)

In this article, we first introduce aLax-Friedrichs type finite difference method to compute the $\mathrm{L}$-solution, following its original definition recently proposed by the second author in[12] using level sets. We then generalize our numerical methods to compute the proper viscosity solution proposed in [11] for a more general class of HJ equations that includes conservation laws. We couple our numerical methods with a singular diffusive term of essential importance. With this singular viscosity, our numerical methods do not require the divergence structure of equations and do apply to more general equations developing shocks other than conservation laws. These numerical methods are generalized to higher order accuracy using WENO Local Lax-Friedrichs methods [17]. We verify that our numerical solutions approximate the proper viscosity solutions of [11] and, in particular, the entropy solutions in case of conservation laws

Probability Distribution Function of the Order Parameter: Mixing Fields and Universality

We briefly review the use of the order parameter probability distribution function as a useful tool to obtain the critical properties of statistical mechanical models using computer Monte Carlo simulations. Some simple discrete spin magnetic systems on a lattice, such as Ising, general spin-$S$ Blume-Capel and Baxter-Wu, $Q$-state Potts, among other models, will be considered as examples. The importance and the necessity of the role of mixing fields in asymmetric magnetic models will be discussed in more detail, as well as the corresponding distributions of the extensive conjugate variables.Comment: 14 pages, 13 figures, accepted for publication (Computer Physics Communications

Phase Structure of Kerr-AdS Black Hole

We study the critical phenomena of Kerr-AdS black hole. Phase structures are observed at different temperatures, $T_{L}$, $T_{c1}$ and $T_{c2}$ with various features. We discuss the thermal stability considering the isothermal compressibility and how phase transitions related to each other. The asymptotic value of the angular momentum also has an implication on separating stable and unstable part. Near critical temperature $T_{c1}$, the order parameter is determined to calculate the critical exponents. All the critical exponents ($\alpha$,$\beta$,$\gamma$,$\delta$)=(0,1/2,1,3) are identical to that of mean field systems. We plot the phase diagram near this critical point, and discuss the scaling symmetry of the free energy.Comment: 21 pages, 6 figures, contents revise

The dynamic crossover in water does not require bulk water

Many of the anomalous properties of water may be explained by invoking a second critical point that terminates the coexistence line between the low- and high-density amorphous states in the liquid. Direct experimental evidence of this point, and the associated polyamorphic liquid–liquid transition, is elusive as it is necessary for liquid water to be cooled below its homogeneous-nucleation temperature. To avoid crystallization, water in the eutectic LiCl solution has been studied but then it is generally considered that “bulk” water cannot be present. However, recent computational and experimental studies observe cooperative hydration in which case it is possible that sufficient hydrogen-bonded water is present for the essential characteristics of water to be preserved. For femtosecond optical Kerr-effect and nuclear magnetic resonance measurements, we observe in each case a fractional Stokes–Einstein relation with evidence of the dynamic crossover appearing near 220 K and 250 K respectively. Spectra obtained in the glass state also confirm the complex nature of the hydrogen-bonding modes reported for neat room-temperature water and support predictions of anomalous diffusion due to “worm-hole” structure

Using noble gases to compare parameterizations of air‐water gas exchange and to constrain oxygen losses by ebullition in a shallow aquatic environment

Author Posting. © American Geophysical Union, 2018. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research: Biogeosciences 123 (2018): 2711-2726, doi:10.1029/2018JG004441.Accurate determination of air‐water gas exchange fluxes is critically important for calculating ecosystem metabolism rates from dissolved oxygen in shallow aquatic environments. We present a unique data set of the noble gases neon, argon, krypton, and xenon in a salt marsh pond to demonstrate how the dissolved noble gases can be used to quantify gas transfer processes and evaluate gas exchange parameterizations in shallow, near‐shore environments. These noble gases are sensitive to a variety of physical processes, including bubbling. We thus additionally use this data set to demonstrate how dissolved noble gases can be used to assess the contribution of bubbling from the sediments (ebullition) to gas fluxes. We find that while literature gas exchange parameterizations do well in modeling more soluble gases, ebullition must be accounted for in order to correctly calculate fluxes of the lighter noble gases. In particular, for neon and argon, the ebullition flux is larger than the differences in the diffusive gas exchange flux estimated by four different wind speed‐based parameterizations for gas exchange. We present an application of noble gas derived ebullition rates to improve estimates of oxygen metabolic fluxes in this shallow pond environment. Up to 21% of daily net oxygen production by photosynthesis may be lost from the pond via ebullition during some periods of biologically and physically produced supersaturation. Ebullition could be an important flux of oxygen and other gases that is measurable with noble gases in other shallow aquatic environments.NSF. Grant Numbers 1233678, 1238212, DEB 1354494; Woods Hole Oceanographic Institution (WHOI); National Defense Science and Engineering Graduate Fellowship; Northeast Climate Science Center Grant Number: DOI G12AC000012019-03-0

Is automatic imitation a specialized form of stimulus–response compatibility? Dissociating imitative and spatial compatibilities

In recent years research on automatic imitation has received considerable attention because it represents an experimental platform for investigating a number of inter-related theories suggesting that the perception of action automatically activates corresponding motor programs. A key debate within this research centers on whether automatic imitation is any different than other long-term S-R associations, such as spatial stimulus-response compatibility. One approach to resolving this issue is to examine whether automatic imitation shows similar response characteristics as other classes of stimulus-response compatibility. This hypothesis was tested by comparing imitative and spatial compatibility effects with a two alternative forced-choice stimulus-response compatibility paradigm and two tasks: one that involved selecting a response to the stimulus (S-R) and one that involved selecting a response to the opposite stimulus (OS-R), i.e., the one not presented. The stimulus for both tasks was a left or right hand with either the index or middle finger tapping down. Speeded responses were performed with the index or middle finger of the right hand in response to the finger identity or the left-right spatial position of the fingers. Based on previous research and a connectionist model, we predicted standard compatibility effects for both spatial and imitative compatibility in the S-R task, and a reverse compatibility effect for spatial compatibility but not for imitative compatibility in the OS-R task. The results from the mean response times, mean percentage of errors, and response time distributions all converged to support these predictions. A second noteworthy result was that the recoding of the finger identity in the OS-R task required significantly more time than the recoding of the left-right spatial position, but the encoding time for the two stimuli in the S-R task was equivalent. In sum, this evidence suggests that the processing of spatial and imitative compatibility is dissociable with regard to two different processes in dual processing models of stimulus-response compatibility

How instructions modify perception: An fMRI study investigating brain areas involved in attributing human agency

Behavioural studies suggest that the processing of movement stimuli is influenced by beliefs about the agency behind these actions. The current study examined how activity in social and action related brain areas differs when participants were instructed that identicalmovement stimuli were either human or computer generated.Participants viewed a series of point-light animation figures derived frommotion-capture recordings of amoving actor, while functional magnetic resonance imaging (fMRI) was used to monitor patterns of neural activity. The stimuli were scrambled to produce a range of stimulus realism categories; furthermore, before each trial participants were told that they were about to view either a recording of human movement or a computersimulated pattern of movement. Behavioural results suggested that agency instructions influenced participants' perceptions of the stimuli. The fMRI analysis indicated different functions within the paracingulate cortex: ventral paracingulate cortex was more active for human compared to computer agency instructed trials across all stimulus types, whereas dorsal paracingulate cortex was activated more highly in conflicting conditions (human instruction, lowrealismor vice versa). These findings support the hypothesis that ventral paracingulate encodes stimuli deemed to be of human origin,whereas dorsal paracingulate cortex is involvedmore in the ascertainment of human or intentional agency during the observation of ambiguous stimuli. Our results highlight the importance of prior instructions or beliefs on movement processing and the role of the paracingulate cortex in integrating prior knowledge with bottom-up stimuli

Multiomics modeling of the immunome, transcriptome, microbiome, proteome and metabolome adaptations during human pregnancy.

MotivationMultiple biological clocks govern a healthy pregnancy. These biological mechanisms produce immunologic, metabolomic, proteomic, genomic and microbiomic adaptations during the course of pregnancy. Modeling the chronology of these adaptations during full-term pregnancy provides the frameworks for future studies examining deviations implicated in pregnancy-related pathologies including preterm birth and preeclampsia.ResultsWe performed a multiomics analysis of 51 samples from 17 pregnant women, delivering at term. The datasets included measurements from the immunome, transcriptome, microbiome, proteome and metabolome of samples obtained simultaneously from the same patients. Multivariate predictive modeling using the Elastic Net (EN) algorithm was used to measure the ability of each dataset to predict gestational age. Using stacked generalization, these datasets were combined into a single model. This model not only significantly increased predictive power by combining all datasets, but also revealed novel interactions between different biological modalities. Future work includes expansion of the cohort to preterm-enriched populations and in vivo analysis of immune-modulating interventions based on the mechanisms identified.Availability and implementationDatasets and scripts for reproduction of results are available through: https://nalab.stanford.edu/multiomics-pregnancy/.Supplementary informationSupplementary data are available at Bioinformatics online