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At least 397 records · Page 22

Rapid data-driven model reduction of nonlinear dynamical systems including chemical reaction networks using ℓ 1 -regularization

We develop a new data-driven paradigm for efficient model reduction of a broad class of nonlinear dynamical systems. Our model reduction method directly enables the interpretation of key components of the dynamical system, unlike traditional projection-based model reduction methods that focus on reducing computational complexity more than interpretability. Our method is not application specific and is simple to implement on nonlinear dynamical systems arising from a variety of different fields. It requires minimal parameterization using a single parameter to trade-off between model complexity and estimation error. We use a data-driven paradigm to formulate model reduction as an efficient convex optimization problem that scales polynomially in the original size of the complex system, enabling systems with as many as thousands of components to be reduced in a matter of minutes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Regularities of femtosecond filamentation in the case of superposition of Gaussian and annular laser beams

The self-action of high-power femtosecond laser beams with a radiation wavelength of 800 nm (formed by superposition of Gaussian and annular beams) in air is theoretically modelled. A detailed analysis of self-focusing and filamentation of this radiation is performed based on the numerical solution of the spectral equation of the unidirectional propagation of a wave packet with allowance for the nonlinearity of the medium, and by tracing averaged diffraction-optical rays. It is shown that, in terms of the diffraction-beam optics, the outer annulus forms a waveguide, which facilitates self-trapping of the central part of the combined beam, supplying the light energy to the filament. The spatial stability of this waveguide depends on the energy stored in the annulus and on the distance from the latter to the beam axis.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Regularity of mappings inverse to Sobolev mappings

For homeomorphisms {phi}:{Omega}{yields}{Omega}' on Euclidean domains in R{sup n}, n{>=}2, necessary and sufficient conditions ensuring that the inverse mapping belongs to a Sobolev class are investigated. The result obtained is used to describe a new two-index scale of homeomorphisms in some Sobolev class such that their inverses also form a two-index scale of mappings, in another Sobolev class. This scale involves quasiconformal mappings and also homeomorphisms in the Sobolev class W{sup 1}{sub n-1} such that rankD{phi}(x){<=}n-2 almost everywhere on the zero set of the Jacobian det D{phi}(x). Bibliography: 65 titles.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Communities and regularities in the behavior of investment fund managers

We analyze a large microlevel dataset on the full daily portfolio holdings and exposures of 22 complex investment funds to shed light on the behavior of professional investment fund managers. We introduce a set of quantitative attributes that capture essential distinctive features of manager allocation strategies and behaviors. These characteristics include turnover, attitude toward hedging, portfolio concentration, and reaction to external events, such as changes in market conditions and flows of funds. We find the existence and stability of three main investment attitude profiles: conservative, reactive, and proactive. The conservative profile shows low turnover and resilience against external shocks; the reactive one is more prone to respond to market condition changes; and members of the proactive profile frequently adjust their portfolio allocations, but their behavior is less affected by market conditions. We find that exogenous shocks temporarily alter this configuration, but communities return to their original state once these external shocks have been absorbed and their effects vanish.

99 GENERAL AND MISCELLANEOUS↗

REGULARITY OF THE NORTH–SOUTH ASYMMETRY OF SOLAR ACTIVITY: REVISITED

Extended time series of Solar Activity Indices (ESAI) extended the Greenwich series of sunspot area from the year 1874 back to 1821. The ESAI's yearly sunspot area in the northern and southern hemispheres from 1821 to 2013 is utilized to investigate characteristics of the north–south hemispherical asymmetry of sunspot activity. Periodical behavior of about 12 solar cycles is also confirmed from the ESAI data set to exist in dominant hemispheres, linear regression lines of yearly asymmetry values, and cumulative counts of yearly sunspot areas in the hemispheres for solar cycles. The period is also inferred to appear in both the cumulative difference in the yearly sunspot areas in the hemispheres over the entire time interval and in its statistical Student's t-test. The hemispherical bias of sunspot activity should be regarded as an impossible stochastic phenomenon over a long time period.

79 ASTRONOMY AND ASTROPHYSICS↗

BAYESIAN CONFIDENCE LIMITS OF ELECTRON SPECTRA OBTAINED THROUGH REGULARIZED INVERSION OF SOLAR HARD X-RAY SPECTRA

Many astrophysical observations are characterized by a single, non-repeatable measurement of a source brightness or intensity, from which we are to construct estimates for the true intensity and its uncertainty. For example, the hard X-ray count spectrum from transient events such as solar flares can be observed only once, and from this single spectrum one must determine the best estimate of the underlying source spectrum I({epsilon}), and hence the form of the responsible electron spectrum F(E). Including statistical uncertainties on the measured count spectrum yields a 'confidence strip' that delineates the boundaries of electron spectra that are consistent with the observed photon spectrum. In this short article, we point out that the expectation values of the source brightness and its variance in a given photon energy bin are in general not (as has been assumed in prior works) equal to n, the number of counts observed in that energy bin. Rather, they depend both on n and on prior knowledge of the overall photon spectrum. Using Bayesian statistics, we provide an explicit procedure and formulas for determining the 'confidence strip' (Bayesian credible region) for F(E), thus providing rigorous bounds on the intensity and shape of the accelerated electron spectrum.

79 ASTRONOMY AND ASTROPHYSICS↗

Two regimes in the regularity of sunspot number

Sunspot numbers WN display quasi-periodical variations that undergo regime changes. These irregularities could indicate a chaotic system and be measured by Lyapunov exponents. We define a functional λ (an 'irregularity index') that is close to the (maximal) Lyapunov exponent for dynamical systems and well defined for series with a random component: this allows one to work with sunspot numbers. We compute λ for the daily WN from 1850 to 2012 within 4 yr sliding windows: λ exhibit sharp maxima at solar minima and secondary maxima at solar maxima. This pattern is reflected in the ratio R of the amplitudes of the main versus secondary peaks. Two regimes have alternated in the past 150 yr, R1 from 1850 to 1915 (large λ and R values) and R2 from 1935 to 2005 (shrinking difference between main and secondary maxima, R values between 1 and 2). We build an autoregressive model consisting of Poisson noise plus an 11 yr cycle and compute its irregularity index. The transition from R1 to R2 can be reproduced by strengthening the autocorrelation a of the model series. The features of the two regimes are stable for model and WN with respect to embedding dimension and delay. Near the time of the last solar minimum (∼2008), the irregularity index exhibits a peak similar to the peaks observed before 1915. This might signal a regime change back from R2 to R1 and the onset of a significant decrease of solar activity.

79 ASTRONOMY AND ASTROPHYSICS↗

Regularity underlying complexity: a redshift-independent description of the continuous variation of galaxy-scale molecular gas properties in the mass-star formation rate plane

Star-forming galaxies (SFGs) display a continuous specific star formation rate (sSFR) distribution, which can be approximated by two log-normal functions: one encompassing the galaxy main sequence (MS), and the other a rarer, starbursting population. Starburst (SB) sSFRs can be regarded as the outcome of a physical process (plausibly merging) taking the mathematical form of a log-normal boosting kernel that enhances star formation activity. We explore the utility of splitting the star-forming population into MS and SB galaxies—an approach we term the '2-Star Formation Mode' framework—for understanding their molecular gas properties. Star formation efficiency (SFE) and gas fraction variations among SFGs take a simple redshift-independent form, once these quantities are normalized to the corresponding values for average MS galaxies. SFE enhancements during SB episodes scale supra-linearly with the SFR increase, as expected for mergers. Consequently, galaxies separate more clearly into loci for SBs and normal galaxies in the Schmidt-Kennicutt plane than in (s)SFR versus M {sub *} space. SBs with large deviations (>10 fold) from the MS, e.g., local ULIRGs, are not average SBs, but are much rarer events whose progenitors had larger gas fractions than typical MS galaxies. Statistically, gas fractions in SBs are reduced two- to threefold compared to their direct MS progenitors, as expected for short-lived SFR boosts where internal gas reservoirs are depleted more quickly than gas is re-accreted from the cosmic web. We predict variations of the conversion factor α{sub CO} in the SFR-M {sub *} plane and we show that the higher sSFR of distant galaxies is directly related to their larger gas fractions.

79 ASTRONOMY AND ASTROPHYSICS↗

A fast map-making preconditioner for regular scanning patterns

High-resolution Maximum Likelihood map-making of the Cosmic Microwave Background is usually performed using Conjugate Gradients with a preconditioner that ignores noise correlations. We here present a new preconditioner that approximates the map noise covariance as circulant, and show that this results in a speedup of up to 400% for a realistic scanning pattern from the Atacama Cosmology Telescope. The improvement is especially large for polarized maps.

79 ASTRONOMY AND ASTROPHYSICS↗

Regular and in-plane skyrmions and antiskyrmions from boundary instabilities

We formulate a theory of skyrmion and antiskyrmion generation using magnetic field and charge current pulses. We show that the topological defect can be created at an edge of a system with Dzyaloshinskii-Moriya interaction (DMI) as well as at a boundary between regions with different DMI. We consider both perpendicular and in-plane (also known as magnetic bimerons) versions of skyrmions and antiskyrmions. We show that the magnetization twist in the vicinity of an edge or a boundary is described by a kink solution, the presence of which can instigate the generation of topological defects. We study the collective excitations of magnetization analytically and numerically, and demonstrate that under application of magnetic field and charge current pulses the magnon modes localized near boundaries can develop instabilities leading to the formation of skyrmions or antiskyrmions. As a result, due to the skyrmion and antiskyrmion Hall effects, a properly chosen current direction can push the topological defects away from the boundary, thus facilitating their generation.

36 MATERIALS SCIENCE↗

Nuclear properties with semilocal momentum-space regularized chiral interactions beyond N 2 LO

We present a comprehensive investigation of few-nucleon systems as well as light and medium-mass nuclei up to A = 48 using the current Low Energy Nuclear Physics International Collaboration two-nucleon interactions in combination with the third-order (N 2 LO) three-nucleon forces. To address the systematic overbinding of nuclei starting from A ≈ 10 found in our earlier study utilizing the N 2 LO two- and three-nucleon forces, we take into account higher-order corrections to the two-nucleon potentials up through fifth order in chiral effective field theory. Here, the resulting Hamiltonian can be completely determined using the A = 3 binding energies and selected nucleon-deuteron cross sections as input. It is then shown to predict other nucleon-deuteron scattering observables and spectra of light p-shell nuclei, for which a detailed correlated truncation error analysis is performed, in agreement with experimental data. Moreover, the predicted ground state energies of nuclei in the oxygen isotopic chain from 14 O to 26 O as well as 40 Ca and 48 Ca show a remarkably good agreement with experimental values, given that the Hamiltonian is fixed completely from the A ≤ 3 data, once the fourth-order (N 3 LO) corrections to the two-nucleon interactions are taken into account. On the other hand, the charge radii are found to be underpredicted by ≈10% for the oxygen isotopes and by almost 20% for 40 Ca and 48 Ca.

20 ≤ A ≤ 38↗