An Approach of Statistical Corrections to Interactions in Hadron Resonance Gas

We propose a new model for hadrons with quantum mechanical attractive and repulsive interactions sensitive to some spatial correlation length parameter inspired by the Beth-Uhlenbeck quantum mechanical nonideal gas model (Uhlenbeck and Beth, 1937). We confront the thermodynamics calculated using our model with a corresponding recent lattice data at four different values of the baryon chemical potential, μ b = 0 , 170 , 340 , 425 MeV over temperatures ranging from 130 MeV to 200 MeV and for five values for the correlation length ranging from 0 to 0.2 fm. For equilibrium temperatures up to the vicinity of the chiral phase transition temperature ≃160 MeV, a decent fitting between the model and the lattice data is observed for different values of r , especially at μ b , r = 170 , 0.05 , 340 , 0.1 , and 340 , 0.15 , where μ b is in MeV and r is in fm. For the vanishing chemical potential, the uncorrelated model r = 0 , which corresponds to the ideal hadron resonance gas model, seems to offer the best fit. The quantum hadron correlations seem to be more probable at nonvanishing chemical potentials, especially within the range μ b ∈ 170 , 340 MeV .

Spatial correlations constrain cellular lifespan and pattern formation in corneal epithelium homeostasis

Homeostasis in adult tissues relies on the replication dynamics of stem cells, their progenitors and the spatial balance between them. This spatial and kinetic coordination is crucial to the successful maintenance of tissue size and its replenishment with new cells. However, our understanding of the role of cellular replicative lifespan and spatial correlation between cells in shaping tissue integrity is still lacking. We developed a mathematical model for the stochastic spatial dynamics that underlie the rejuvenation of corneal epithelium. Our model takes into account different spatial correlations between cell replication and cell removal. We derive the tradeoffs between replicative lifespan, spatial correlation length, and tissue rejuvenation dynamics. We determine the conditions that allow homeostasis and are consistent with biological timescales, pattern formation, and mutants phenotypes. Our results can be extended to any cellular system in which spatial homeostasis is maintained through cell replication.

An Analytical Random Field Solution for the Reliability of Axially Loaded Piles in the Ultimate Limit State Considering the Effect of Soil Sampling

The present work is concerned with the effect of soil spatial variability on estimating the ultimate soil resistance of floating axially loaded piles from point measurements of soil properties along the pile. The ultimate limit state is considered. In particular, closed form formulae for (i) determining the optimal sampling depth for minimizing statistical uncertainty and (ii) the optimal—minimum required—safety factor for a desired failure probability level are derived. A dimensionless parameter, the cohesion-to-friction parameter Λ, is introduced which quantifies the weight of soil’s cohesion contribution relative to that of soil’s friction in the linear trend of the ultimate soil strength. The analysis shows that the probability of failure profile with the sampling depth attains a minimum, designating the optimal sampling point. This depends on the scaled spatial correlation length of the soil Θ (i.e., the spatial correlation length of soil over the length of the pile) and the parameter Λ, but not on the coefficient of variance of the ultimate soil strength (covu) or the safety factor. Furthermore, it was found that the optimal depth is always at the lower half of the pile, approaching the mid-point or the bottom end of the pile for Λ>>1 or Λ<<1, respectively. In addition, it was found that for large Θ, the optimal depth tends to be closer to the mid-point of the pile, while for small Θ, the optimal sampling depth arises closer to the bottom end. The practical usefulness of the results is related to a suitable choice of the safety factor. Inverting the probability of failure formula at its minimum value, an optimal safety factor is obtained as a function of the desired (acceptable) probability of failure, and the parameters Θ, Λ and covu. The optimal safety factor is the minimum value required for a desired level of the probability of failure.

The topological origin of anomalous transport: Persistence of β in the face of varying correlation length.

&lt;p&gt;Traditional concepts for flow in porous media assume that the heterogenous distribution of hydraulic conductivity is the source for the contaminant temporal and spatial heavy tail, a process known as anomalous or non-Fickian transport; this anomalous transport behavior can be captured by the &amp;#946; parameter in the continues time random walk (CTRW) framework. In previous studies we showed that there is a functional form relating the &amp;#946; parameter to the permeability variance&lt;sup&gt;1&lt;/sup&gt; and fracture alignment in fracture fields&lt;sup&gt;2&lt;/sup&gt;. Moreover, we showed that this variance is strongly influencing the reaction pattern during transport&lt;sup&gt;3&lt;/sup&gt;.&amp;#160; This study shows that as the spatial correlation length, between these heterogenous distribution of hydraulic conductivities, increase, the anomaly of the flow reduces, yet the &amp;#946; value is unchanged suggesting that there is a topological component to the flow field, captured by the &amp;#946;&lt;sup&gt;4&lt;/sup&gt;. This finding is verified by an analysis on the flow field, showing that the changes in the conductivity values have little effect on the flow field morphology, which points to the topological component in the flow.&lt;/p&gt;&lt;ol&gt;&lt;li&gt;Y. Edery, A. Guadagnini, H. Scher and B. Berkowitz, Water Resources Research &lt;strong&gt;50&lt;/strong&gt; (2), 1490-1505 (2014).&lt;/li&gt; &lt;li&gt;Y. Edery, S. Geiger and B. Berkowitz, Water Resources Research &lt;strong&gt;52&lt;/strong&gt; (7), 5634-5643 (2016).&lt;/li&gt; &lt;li&gt;Y. Edery, G. M. Porta, A. Guadagnini, H. Scher and B. Berkowitz, Transport in Porous Media &lt;strong&gt;115&lt;/strong&gt; (2), 291-310 (2016).&lt;/li&gt; &lt;li&gt;Y. Edery, arXiv preprint arXiv:1906.07061 (2019).&lt;/li&gt; &lt;/ol&gt;

Convolutional Network Analysis of Optical Micrographs

We provide an in-depth convolutional neural network (CNN) analysis of optical responses of liquid crystals (LCs) when exposed to different chemical environments. Our aim is to identify informative features that can be used to construct automated LC-based chemical sensors and that can shed some light on the underlying phenomena that governs and distinguishes LC responses. Previous work demonstrated that, by using features extracted from AlexNet, micrographs of different LC responses can be classified with an accuracy of 99%. Reaching such high levels of accuracy, however, required use of a large number of features (on the order of thousands), which was computationally intensive and which clouded the physical interpretability of the dominant features. To address these issues, here we report a study of the effectiveness of using features extracted from color images using VGG16, which is a more compact CNN than Alexnet. Our analysis reveals that features extracted from the first and second convolutional layers of VGG16 are sufficient to achieve a perfect classification accuracy on the same dataset used by Cao and coworkers, while reducing the number of features to less than a hundred. The number of features is further reduced to ten via recursive feature elimination with minimal loss in classification accuracy (5-10%). This feature reduction procedure reveals that differences in spatial color patterns are developed within seconds in the LC response. The results thus reveal that hue histograms provide an informative set of features that can be used to characterize LC micrographs of the sensor response. We also hypothesize that differences in spatial correlation length of LC textures detected by VGG16 with DMMP and water likely reflect differences in the anchoring energy of the LC on the surface of the sensor. This latter proposal hints at fresh approaches for the design of LC-based sensors based on characterization of spontaneous fluctuations in orientation (as opposed to changes in time-average orientation)

Convolutional Network Analysis of Optical Micrographs

We provide an in-depth convolutional neural network (CNN) analysis of optical responses of liquid crystals (LCs) when exposed to different chemical environments. Our aim is to identify informative features that can be used to construct automated LC-based chemical sensors and that can shed some light on the underlying phenomena that governs and distinguishes LC responses. Previous work demonstrated that, by using features extracted from AlexNet, micrographs of different LC responses can be classified with an accuracy of 99%. Reaching such high levels of accuracy, however, required use of a large number of features (on the order of thousands), which was computationally intensive and which clouded the physical interpretability of the dominant features. To address these issues, here we report a study of the effectiveness of using features extracted from color images using VGG16, which is a more compact CNN than Alexnet. Our analysis reveals that features extracted from the first and second convolutional layers of VGG16 are sufficient to achieve a perfect classification accuracy on the same dataset used by Cao and coworkers, while reducing the number of features to less than a hundred. The number of features is further reduced to ten via recursive feature elimination with minimal loss in classification accuracy (5-10%). This feature reduction procedure reveals that differences in spatial color patterns are developed within seconds in the LC response. The results thus reveal that hue histograms provide an informative set of features that can be used to characterize LC micrographs of the sensor response. We also hypothesize that differences in spatial correlation length of LC textures detected by VGG16 with DMMP and water likely reflect differences in the anchoring energy of the LC on the surface of the sensor. This latter proposal hints at fresh approaches for the design of LC-based sensors based on characterization of spontaneous fluctuations in orientation (as opposed to changes in time-average orientation)

The role of replication-removal spatial correlations and cellular replicative lifespan in corneal epithelium homeostasis

Homeostasis in adult tissues relies on the replication dynamics of stem cells, their progenitors and the spatial balance between them. This spatial and kinetic coordination is crucial to the successful maintenance of tissue size and its replenishment with new cells. However, our understanding of the role of cellular replicative lifespan and spatial correlation between cells in shaping tissue integrity is still lacking. We developed a mathematical model for the stochastic spatial dynamics that underlie the rejuvenation of corneal epithelium. Our model takes into account different spatial correlations between cell replication and cell removal. We derive the tradeoffs between replicative lifespan, spatial correlation length, and tissue rejuvenation dynamics. We determine the conditions that allow homeostasis and are consistent with biological timescales, pattern formation, and mutants phenotypes. Our results can be extended to any cellular system in which spatial homeostasis is maintained through cell replication.

Convolutional Network Analysis of Optical Micrographs

We provide an in-depth convolutional neural network (CNN) analysis of optical responses of liquid crystals (LCs) when exposed to different chemical environments. Our aim is to identify informative features that can be used to construct automated LC-based chemical sensors and that can shed some light on the underlying phenomena that governs and distinguishes LC responses. Previous work demonstrated that, by using features extracted from AlexNet, micrographs of different LC responses can be classified with an accuracy of 99%. Reaching such high levels of accuracy, however, required use of a large number of features (on the order of thousands), which was computationally intensive and which clouded the physical interpretability of the dominant features. To address these issues, here we report a study of the effectiveness of using features extracted from color images using VGG16, which is a more compact CNN than Alexnet. Our analysis reveals that features extracted from the first and second convolutional layers of VGG16 are sufficient to achieve a perfect classification accuracy on the same dataset used by Cao and coworkers, while reducing the number of features to less than a hundred. The number of features is further reduced to ten via recursive feature elimination with minimal loss in classification accuracy (5-10%). This feature reduction procedure reveals that differences in spatial color patterns are developed within seconds in the LC response. The results thus reveal that hue histograms provide an informative set of features that can be used to characterize LC micrographs of the sensor response. We also hypothesize that differences in spatial correlation length of LC textures detected by VGG16 with DMMP and water likely reflect differences in the anchoring energy of the LC on the surface of the sensor. This latter proposal hints at fresh approaches for the design of LC-based sensors based on characterization of spontaneous fluctuations in orientation (as opposed to changes in time-average orientation)