3,423 research outputs found
Large Pseudo-Counts and -Norm Penalties Are Necessary for the Mean-Field Inference of Ising and Potts Models
Mean field (MF) approximation offers a simple, fast way to infer direct
interactions between elements in a network of correlated variables, a common,
computationally challenging problem with practical applications in fields
ranging from physics and biology to the social sciences. However, MF methods
achieve their best performance with strong regularization, well beyond Bayesian
expectations, an empirical fact that is poorly understood. In this work, we
study the influence of pseudo-count and -norm regularization schemes on
the quality of inferred Ising or Potts interaction networks from correlation
data within the MF approximation. We argue, based on the analysis of small
systems, that the optimal value of the regularization strength remains finite
even if the sampling noise tends to zero, in order to correct for systematic
biases introduced by the MF approximation. Our claim is corroborated by
extensive numerical studies of diverse model systems and by the analytical
study of the -component spin model, for large but finite . Additionally
we find that pseudo-count regularization is robust against sampling noise, and
often outperforms -norm regularization, particularly when the underlying
network of interactions is strongly heterogeneous. Much better performances are
generally obtained for the Ising model than for the Potts model, for which only
couplings incoming onto medium-frequency symbols are reliably inferred.Comment: 25 pages, 17 figure
How to enhance crop production and nitrogen fluxes? A result-oriented scheme to evaluate best agri-environmental measures in Veneto Region, Italy
The cost-effectiveness of adopting agri-environmental measures (AEMs) in Europe, which combine agricultural productions with reduced N losses, is debated due to poorly targeted site-specific funding that is allocated regardless of local variability. An integrated DAYCENT model-GIS platform was developed combining pedo-climatic and agricultural systems information. The aim was to evaluate best strategies to improve N fluxes of agro-ecosystems within a perspective of sustainable intensification. Indicators of agronomic efficiency and environmental quality were considered. The results showed that agronomic benefits were observed with a continuous soil cover (conservation agriculture and cover crops), which enhanced nitrogen use efficiency (+17%) and crop yields (+34%), although in some cases these might be overestimated due to modelling limitations. An overall environmental improvement was found with continuous soil cover and long-term change from mineral to organic inputs (NLeach 45 Mg ha 121), which were effective in the sandy soils of western and eastern Veneto with low SOM, improving the soil-water balance and nutrients availability over time. Results suggest that AEM subsidies should be allocated at a site-specific level that includes pedo-climatic variability, following a result-oriented approach
Exponentially hard problems are sometimes polynomial, a large deviation analysis of search algorithms for the random Satisfiability problem, and its application to stop-and-restart resolutions
A large deviation analysis of the solving complexity of random
3-Satisfiability instances slightly below threshold is presented. While finding
a solution for such instances demands an exponential effort with high
probability, we show that an exponentially small fraction of resolutions
require a computation scaling linearly in the size of the instance only. This
exponentially small probability of easy resolutions is analytically calculated,
and the corresponding exponent shown to be smaller (in absolute value) than the
growth exponent of the typical resolution time. Our study therefore gives some
theoretical basis to heuristic stop-and-restart solving procedures, and
suggests a natural cut-off (the size of the instance) for the restart.Comment: Revtex file, 4 figure
Beyond inverse Ising model: structure of the analytical solution for a class of inverse problems
I consider the problem of deriving couplings of a statistical model from
measured correlations, a task which generalizes the well-known inverse Ising
problem. After reminding that such problem can be mapped on the one of
expressing the entropy of a system as a function of its corresponding
observables, I show the conditions under which this can be done without
resorting to iterative algorithms. I find that inverse problems are local (the
inverse Fisher information is sparse) whenever the corresponding models have a
factorized form, and the entropy can be split in a sum of small cluster
contributions. I illustrate these ideas through two examples (the Ising model
on a tree and the one-dimensional periodic chain with arbitrary order
interaction) and support the results with numerical simulations. The extension
of these methods to more general scenarios is finally discussed.Comment: 15 pages, 6 figure
The dependence of traction evolution on the earthquake source time function adopted in kinematic rupture models
We compute the temporal evolution of traction by
solving the elasto-dynamic equation and by using the slip
velocity history as a boundary condition on the fault plane.
We use different source time functions to derive a suite of
kinematic source models to image the spatial distribution of
dynamic and breakdown stress drop, strength excess and
critical slip weakening distance (Dc). Our results show that
the source time functions, adopted in kinematic source
models, affect the inferred dynamic parameters. The critical
slip weakening distance, characterizing the constitutive
relation, ranges between 30% and 80% of the total slip. The
ratio between Dc and total slip depends on the adopted
source time functions and, in these applications, is nearly
constant over the fault. We propose that source time
functions compatible with earthquake dynamics should be
used to infer the traction time history
Dependence of slip weakening distance (Dc) on final slip during dynamic rupture of earthquakes
In this study we aim to understand the dependence of the critical slip weakening distance (Dc) on the final slip (Dtot) during the propagation of a dynamic rupture and the consistency of their inferred correlation. To achieve this goal we have performed a series of numerical tests suitably designed to validate the adopted numerical procedure and to verify the actual capability in measuring Dc. We have retrieved two kinematic rupture histories from spontaneous dynamic rupture models governed by a slip weakening law in which a constant Dc distribution on the fault plane as well as a constant Dc / Dtot ratio are assumed, respectively. The slip velocity and the shear traction time histories represent the synthetic “real” target data which we aim to reproduce. We use a 3-D traction-at-split nodes numerical procedure to image the dynamic traction evolution by assuming our modeled slip velocity as a boundary condition on the fault plane. We assume a regularized Yoffe function as source time function in our modeling attempts and we measure the critical slip weakening distance from the inferred traction versus slip curves at each point on the fault. We compare the inferred values with those of the target dynamic models. Our numerical tests show that fitting the slip velocity functions of the target models at each point on the fault plane is not enough to retrieve good traction evolution curves and to obtain reliable measures of Dc. We find that the estimation of Dc is very sensitive to any small variation of the slip velocity function. An artificial correlation between Dc/Dtot is obtained when a fixed shape of slip velocity is assumed on the fault (i.e., constant rise time and constant time for positive acceleration) which differs from that of the target model. We point out that the estimation of fracture energy (breakdown work) on the fault is not affected by biases in measuring Dc
Protein-Mediated DNA Loops: Effects of Protein Bridge Size and Kinks
This paper focuses on the probability that a portion of DNA closes on itself
through thermal fluctuations. We investigate the dependence of this probability
upon the size r of a protein bridge and/or the presence of a kink at half DNA
length. The DNA is modeled by the Worm-Like Chain model, and the probability of
loop formation is calculated in two ways: exact numerical evaluation of the
constrained path integral and the extension of the Shimada and Yamakawa saddle
point approximation. For example, we find that the looping free energy of a 100
base pairs DNA decreases from 24 kT to 13 kT when the loop is closed by a
protein of r = 10 nm length. It further decreases to 5 kT when the loop has a
kink of 120 degrees at half-length.Comment: corrected typos and figures, references updated; 13 pages, 7 figures,
accepted for publication in Phys. Rev.
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