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At least 73 records · Page 4

Node-degree aware edge sampling mitigates inflated classification performance in biomedical random walk-based graph representation learning

Motivation: Graph representation learning is a family of related approaches that learn low-dimensional vector representations of nodes and other graph elements called embeddings. Embeddings approximate characteristics of the graph and can be used for a variety of machine-learning tasks such as novel edge prediction. For many biomedical applications, partial knowledge exists about positive edges that represent relationships between pairs of entities, but little to no knowledge is available about negative edges that represent the explicit lack of a relationship between two nodes. For this reason, classification procedures are forced to assume that the vast majority of unlabeled edges are negative. Existing approaches to sampling negative edges for training and evaluating classifiers do so by uniformly sampling pairs of nodes. Results: We show here that this sampling strategy typically leads to sets of positive and negative examples with imbalanced node degree distributions. Using representative heterogeneous biomedical knowledge graph and random walk-based graph machine learning, we show that this strategy substantially impacts classification performance. If users of graph machine-learning models apply the models to prioritize examples that are drawn from approximately the same distribution as the positive examples are, then performance of models as estimated in the validation phase may be artificially inflated. We present a degree-aware node sampling approach that mitigates this effect and is simple to implement. Availability and implementation: Our code and data are publicly available at https://github.com/monarch-initiative/negativeExampleSelection.

59 BASIC BIOLOGICAL SCIENCES↗

Simulations of the mean solar magnetic field during sunspot cycle 21

Regarding new bipolar magnetic regions as sources of flux, the evolution of the photospheric magnetic field during 1976-1984 was computed and the corresponding evolution of the mean line-of-sight field as seen from earth was derived. A good, but imperfect, agreement was obtained between the observed mean field and the field computed for a nominal choice of flux transport parameters. The response of the computed mean field to variations in the transport parameters and the source properties was determined. The results suggest that the mean-field evolution is a random-walk process with dissipation. New eruptions of flux produce the random walk, and together differential rotation, meridional flow, and diffusion provide the dissipation. The net effect of each new source depends on its strength and orientation and on the time elapsed before the next eruption.

Sheeley, N. R., Jr.↗

A finite difference informed random walker (FDiRW) solver for strongly inhomogeneous diffusion problems

In nature, many complex multi-physics coupling problems exhibit strong diffusivity inhomogeneity. For instance, in the context of radionuclide absorption by porous wasteform materials within a flowing waste stream, the difference of species’ diffusivity in solid and liquid phases spans by 3~8 orders of magnitude. To solve the diffusion equations with strongly inhomogeneous diffusivity, traditional discretization-based methods, such as the Finite Difference Method (FDM), require infinitesimally small time steps (<10 -10 ) as high spatial resolutions are employed in most microstructure evolution processes, leading to prohibitively high computational costs. Here, this work developed an integrated numerical approach (FDiRW: Finite Difference informed Random Walk) to tackle this challenge. The idea is that utilizing the Random Walk concept, the fast diffusion is modeled as a superposition of point source’s solution for a concentration distribution while FDM is used to obtain the point source’s solution at each node. A mesh-coarsening algorithm is developed to generate an exclusive coarse mesh for FDiRW approach to maximize its efficiency. The effectiveness of the coarse mesh-based FDiRW approach is validated by benchmarking Finite Difference solutions. Numerical results demonstrated that FDiRW achieves a remarkable 1000x computational efficiency improvement over FDM while preserving desired accuracy for a medium-sized model of 192 × 192 × 192 grids. Finally, as models scale up, a floating-point operations (PLOPs) analysis of the FDiRW algorithm reveals that its computational complexity grows quadratically in terms of the number of nodes employed in computation.

36 MATERIALS SCIENCE↗

Migration of lymphocytes on fibronectin-coated surfaces: temporal evolution of migratory parameters

Lymphocytes typically interact with implanted biomaterials through adsorbed exogenous proteins. To provide a more complete characterization of these interactions, analysis of lymphocyte migration on adsorbed extracellular matrix proteins must accompany the commonly performed adhesion studies. We report here a comparison of the migratory and adhesion behavior of Jurkat cells (a T lymphoblastoid cell line) on tissue culture treated and untreated polystyrene surfaces coated with various concentrations of fibronectin. The average speed of cell locomotion showed a biphasic response to substrate adhesiveness for cells migrating on untreated polystyrene and a monotonic decrease for cells migrating on tissue culture-treated polystyrene. A modified approach to the persistent random walk model was implemented to determine the time dependence of cell migration parameters. The random motility coefficient showed significant increases with time when cells migrated on tissue culture-treated polystyrene surfaces, while it remained relatively constant for experiments with untreated polystyrene plates. Finally, a cell migration computer model was developed to verify our modified persistent random walk analysis. Simulation results suggest that our experimental data were consistent with temporally increasing random motility coefficients.

NASA Program Fundamental Space Biology↗

The interplanetary magnetic field and energetic electrons from Jupiter

The reported four-month 'season' for observation of Jovian electron events at AU is shown to be a plausible consequence of field-line random walk in the solar wind. Values of the field-line random-walk coefficient deduced earlier in connection with observations of solar protons, photospheric supergranulation, and the interplanetary magnetic-field power spectrum, lead to an approximate value for the spread of Jovian electrons at 1 AU, which corresponds to an approximate four-month duration of events. This model is consistent with a point source at Jupiter.

Jokipii, J. R.↗

Variance reduction in Monte Carlo analysis of rarefied gas diffusion

The present analysis uses the Monte Carlo method to solve the problem of rarefied diffusion between parallel walls. The diffusing molecules are evaporated or emitted from one of two parallel walls and diffused through another molecular species. The analysis treats the diffusing molecule as undergoing a Markov random walk and the local macroscopic properties are found as the expected value of the random variable, the random walk payoff. By biasing the transition probabilities and changing the collision payoffs the expected Markov walk payoff is retained but its variance is reduced so that the M. C. result has a much smaller error.

Perlmutter, M.↗

Variance reduction in Monte Carlo analysis of rarefied gas diffusion.

The problem of rarefied diffusion between parallel walls is solved using the Monte Carlo method. The diffusing molecules are evaporated or emitted from one of the two parallel walls and diffuse through another molecular species. The Monte Carlo analysis treats the diffusing molecule as undergoing a Markov random walk, and the local macroscopic properties are found as the expected value of the random variable, the random walk payoff. By biasing the transition probabilities and changing the collision payoffs, the expected Markov walk payoff is retained but its variance is reduced so that the Monte Carlo result has a much smaller error.

Perlmutter, M.↗

Intrepid MCMC: Metropolis-Hastings with exploration

In engineering examples, one often encounters the need to sample from unnormalized distributions with complex shapes that may also be implicitly defined through a physical or numerical simulation model, making it computationally expensive to evaluate the associated density function. For such cases, MCMC has proven to be an invaluable tool. Random-walk Metropolis Methods (also known as Metropolis-Hastings (MH)), in particular, are highly popular for their simplicity, flexibility, and ease of implementation. However, most MH algorithms suffer from significant limitations when attempting to sample from distributions with multiple modes (particularly disconnected ones). Here, in this paper, we present Intrepid MCMC - a novel MH scheme that utilizes a simple coordinate transformation to significantly improve the mode-finding ability and convergence rate to the target distribution of random-walk Markov chains while retaining most of the simplicity of the vanilla MH paradigm. Through multiple examples, we showcase the improvement in the performance of Intrepid MCMC over vanilla MH for a wide variety of target distribution shapes. We also provide an analysis of the mixing behavior of the Intrepid Markov chain, as well as the efficiency of our algorithm for increasing dimensions. A thorough discussion is presented on the practical implementation of the Intrepid MCMC algorithm. Finally, its utility is highlighted through a Bayesian parameter inference problem for a two-degree-of-freedom oscillator under free vibration.

97 - MATHEMATICS AND COMPUTING↗

Neutron Next-Event Estimators Kinematics (Rev.2)

This paper reviews the kinematics of neutron elastic and inelastic scattering with moving and stationary targets for contributions to Neutron Next-Event Estimators (NEEs). NEEs are often used for simulating the response of detectors in locations that have few random walk particles. Contributions to NEEs from collisions differ from sampling the outgoing particle state in standard random walk collisions as the location of the estimator is fixed, thus fixing the scattering angle between the incoming and outgoing directions. To calculate contributions to NEEs, the outgoing energies and probabilities of scatter toward the estimator must be calculated. This paper presents the most general case that encompasses elastic and inelastic scattering with both moving and stationary targets. The moving target case is required for elastic scattering with thermal motion due to the free gas thermal treatment approximation. The stationary target equations are presented for comparison with equations presented in canonical Monte Carlo texts.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Random root movements in weightlessness

The dynamics of root growth was studied in weightlessness. In the absence of the gravitropic reference direction during weightlessness, root movements could be controlled by spontaneous growth processes, without any corrective growth induced by the gravitropic system. If truly random of nature, the bending behavior should follow so-called 'random walk' mathematics during weightlessness. Predictions from this hypothesis were critically tested. In a Spacelab ESA-experiment, denoted RANDOM and carried out during the IML-2 Shuttle flight in July 1994, the growth of garden cress (Lepidium sativum) roots was followed by time lapse photography at 1-h intervals. The growth pattern was recorded for about 20 h. Root growth was significantly smaller in weightlessness as compared to gravity (control) conditions. It was found that the roots performed spontaneous movements in weightlessness. The average direction of deviation of the plants consistently stayed equal to zero, despite these spontaneous movements. The average squared deviation increased linearly with time as predicted theoretically (but only for 8-10 h). Autocorrelation calculations showed that bendings of the roots, as determined from the 1-h photographs, were uncorrelated after about a 2-h interval. It is concluded that random processes play an important role in root growth. Predictions from a random walk hypothesis as to the growth dynamics could explain parts of the growth patterns recorded. This test of the hypothesis required microgravity conditions as provided for in a space experiment.

STS-65 Shuttle Project↗

Quiet-time electron increases, a measure of conditions in the outer solar system

One possible explanation for quiet-time electron increases, increases in the intensity of 3-12 MeV interplanetary electrons that have been reported by McDonald, Cline and Simnett, is discussed. It is argued that the electrons in quiet-time increases are galactic in origin, but that the observed increases are not the result of any variation in the modulation of these particles in the inner solar system. It is suggested instead that quiet-time increases may occur when more electrons than normal penetrate a modulating region that lies far beyond the orbit of earth. The number of electrons penetrating this region may increase when field lines that have experienced an unusually large random walk in the photosphere are carried by the solar wind out to the region. As evidence for this increased random walk, it is shown that five solar rotations before most of the quiet-time increases there is an extended period when the amplitude of the diurnal anisotropy, as is measured by the Deep River neutron monitor, is relatively low. Five rotations delay time implies that the proposed modulating region lies at approximately 30 AU from the Sun, assuming that the average solar wind speed is constant over this distance at approximately 400 km/sec.

Fisk, L. A.↗

Quiet-time electron increases - A measure of conditions in the outer solar system.

Discussion of a possible explanation for the increases in the intensity range of 3- to 12-MeV interplanetary electrons that McDonald et al. (1972) have labeled as 'quiet-time electron increases.' It is argued that the electrons in quiet-time increases are galactic in origin but that the observed increases are not the result of any variation in the modulation of these particles in the inner solar system. It is suggested instead that quiet-time increases may occur when more electrons than normal penetrate a modulating region that lies far beyond the orbit of the earth. The number of electrons penetrating this region may increase when field lines that have experienced an unusually large random walk in the photosphere are carried by the solar wind out to the region. As evidence of this increased random walk, it is shown that five solar rotations before most of the quiet-time increases occur there is an extended period when the amplitude of the diurnal anisotropy (measured by the Deep River neutron monitor) is relatively low. A delay time of five rotations implies that the proposed modulating region lies at about 30 AU from the sun if the average solar-wind speed is assumed to be constant at about 400 km/sec over this distance. The implications for the correlation between periods of low-amplitude diurnal anisotropy and quiet-time increases on interplanetary conditions out to about 30 AU and some possible models for the proposed modulating region are also considered.

Fisk, L. A.↗

A chaotic attractor in timing noise from the Vela pulsar?

Fourteen years of timing residual data from the Vela pulsar have been analyzed in order to determine if a chaotic dynamical process is the origin of timing noise. Using the correlation sum technique, a dimension of about 1.5 is obtained. This low dimension indicates underlying structure in the phase residuals which may be evidence for a chaotic attractor. It is therefore possible that nonlinear dynamics intrinsic to the spin-down may be the cause of the timing noise in the Vela pulsar. However, it has been found that the stimulated random walks in frequency and frequency derivative often used to model pulsar timing noise also have low fractal dimension, using the same analysis technique. Recent work suggesting that random processes with steep power spectra can mimic strange attractors seems to be confirmed in the case of these random walks. It appears that the correlation sum estimator for dimension is unable to distinguish between chaotic and random processes.

Harding, Alice K.↗

Multiscale Modeling of Ablation and Pyrolysis in PICA-Like materials

During atmospheric entry of planetary probes, the thermal protection system (TIPS) of the probe is exposed to high temperatures under low pressures. In these conditions, carbonous fibrous TIPS materials may undergo oxidation leading to mass loss and wall recession called ablation. This work aims to improve the understanding of material/environment interactions through a study of the coupling between oxygen transport in the Knudsen regime, heterogeneous oxidation of carbon, and surface recession. A 3D Random Walk Monte Carlo simulation tool is used for this study. The fibrous architecture of a model material, consisting of high porosity random array of carbon fibers, is numerically represented on a 3D Cartesian grid. Mass transport in the Knudsen regime from the boundary layer to the surface, and inside this porous material is simulated by random walk. A reaction probability is used to simulate the heterogeneous oxidation reaction. The surface recession of the fibers is followed by front tracking using a simplified marching cube approach. The output data of the simulations are ablation velocity and dynamic evolution of the material porosity. A parametric study is carried out to analyze the material behavior as a function of Knudsen number for the porous media (length of the mean free path compared to the mean pore diameter) and the intrinsic reactivity of the carbon fibers. The model is applied to Stardust mission reentry conditions and explains the unexpected behavior of the TIPS material that underwent mass loss in volume.

Lachaud, Jean↗

Monte Carlo lattice models for adsorbed polymer conformation

The adhesion between a polymer film and a metal surface is of great technological interest. However, the prediction of adhesion and wear properties of polymer coated metals is quite difficult because a fundamental understanding of the polymer surface interaction does not yet exist. A computer model for the conformation of a polymer molecule adsorbed on a surface is discussed. The chain conformation is assumed to be described by a partially directed random walk on a three dimensional simple cubic lattice. An attractive surface potential is incorporated into the model through the use of a random walk step probability distribution that is anisotropic in the direction normal to the attractive surface. The effects of variations in potential characteristics are qualitatively included by varying both the degree of anisotropy of the step distribution and the range of the anisotropy. Polymer conformation is characterized by the average end to end distance, average radius of gyration, and average number of chain segments adsorbed on the surface.

Good, B. S.↗

Low pressure radon diffusion - A laboratory study and its implications for lunar venting

Results of a study of radon migration through columns of fine particulate materials, at total pressures of 0.02-0.2 torr, are reported. Materials studied were: NBS Glass Spheres (SRM 1003), Emerson & Cuming Eccospheres (IG-101), activated coconut charcoal, Lipaci obsidian, and W-1 Standard Diabase. Rates of diffusion were used to derive heats of adsorption for radon on the materials tested. The most reliable values found clustered around 8-9 kcal/mole. These high heats of adsorption, if typical for most materials, combined with low percentages of radon emanation by lunar soils found by other researchers, imply that random walk diffusion will not be an important mechanism for redistributing the radon and the radon daughters produced in the lunar regolith. In particular, since random walk migration is not a sufficient mechanism to account for localized high concentrations of radon-222 and its daughter polonium-210 observed by the Apollo 15 and 16 command modules, an alternative mechanism is proposed, in which radon would be swept to the surface by other gases during intermittent venting events.

Friesen, L. J.↗

The noise of BL Lacertae

Results are presented from an intensive optical and IR monitoring program of the flux and polarization characteristics of BL Lac. It is found that the polarization variations increase in amplitude with increasing time interval, and that the path traced out by the polarization vector in the Q-U plane is a random walk. In view of earlier measurements of BL Lac, the polarization fluctuations can be represented at low frequencies by the flat power spectrum of white noise, up to a frequency of 0.05 cycles/day. Above this frequency, the spectrum steepens to that of a random walk. A model for BL Lac suggested by the polarimetric noise can be constructed from independent sources of light with randomly oriented, strong polarization. Small random differences in spectral index from source to source could also explain the variable wavelength dependence of polarization.

Moore, R. L.↗

Self-Supervised Dynamical Systems

Some progress has been made in a continuing effort to develop mathematical models of the behaviors of multi-agent systems known in biology, economics, and sociology (e.g., systems ranging from single or a few biomolecules to many interacting higher organisms). Living systems can be characterized by nonlinear evolution of probability distributions over different possible choices of the next steps in their motions. One of the main challenges in mathematical modeling of living systems is to distinguish between random walks of purely physical origin (for instance, Brownian motions) and those of biological origin. Following a line of reasoning from prior research, it has been assumed, in the present development, that a biological random walk can be represented by a nonlinear mathematical model that represents coupled mental and motor dynamics incorporating the psychological concept of reflection or self-image. The nonlinear dynamics impart the lifelike ability to behave in ways and to exhibit patterns that depart from thermodynamic equilibrium. Reflection or self-image has traditionally been recognized as a basic element of intelligence. The nonlinear mathematical models of the present development are denoted self-supervised dynamical systems. They include (1) equations of classical dynamics, including random components caused by uncertainties in initial conditions and by Langevin forces, coupled with (2) the corresponding Liouville or Fokker-Planck equations that describe the evolutions of probability densities that represent the uncertainties. The coupling is effected by fictitious information-based forces, denoted supervising forces, composed of probability densities and functionals thereof. The equations of classical mechanics represent motor dynamics that is, dynamics in the traditional sense, signifying Newton s equations of motion. The evolution of the probability densities represents mental dynamics or self-image. Then the interaction between the physical and metal aspects of a monad is implemented by feedback from mental to motor dynamics, as represented by the aforementioned fictitious forces. This feedback is what makes the evolution of probability densities nonlinear. The deviation from linear evolution can be characterized, in a sense, as an expression of free will. It has been demonstrated that probability densities can approach prescribed attractors while exhibiting such patterns as shock waves, solitons, and chaos in probability space. The concept of self-supervised dynamical systems has been considered for application to diverse phenomena, including information-based neural networks, cooperation, competition, deception, games, and control of chaos. In addition, a formal similarity between the mathematical structures of self-supervised dynamical systems and of quantum-mechanical systems has been investigated.

Zak, Michail↗