Measuring the convergence of Monte Carlo free energy calculations

The nonequilibrium work fluctuation theorem provides the way for calculations of (equilibrium) free energy based on work measurements of nonequilibrium, finite-time processes and their reversed counterparts by applying Bennett's acceptance ratio method. A nice property of this method is that each free energy estimate readily yields an estimate of the asymptotic mean square error. Assuming convergence, it is easy to specify the uncertainty of the results. However, sample sizes have often to be balanced with respect to experimental or computational limitations and the question arises whether available samples of work values are sufficiently large in order to ensure convergence. Here, we propose a convergence measure for the two-sided free energy estimator and characterize some of its properties, explain how it works, and test its statistical behavior. In total, we derive a convergence criterion for Bennett's acceptance ratio method.Comment: 14 pages, 17 figure

Using bijective maps to improve free energy estimates

We derive a fluctuation theorem for generalized work distributions, related to bijective mappings of the phase spaces of two physical systems, and use it to derive a two-sided constraint maximum likelihood estimator of their free energy difference which uses samples from the equilibrium configurations of both systems. As an application, we evaluate the chemical potential of a dense Lennard-Jones fluid and study the construction and performance of suitable maps.Comment: 17 pages, 11 figure

Results of evaluating the performance of empirical estimators of natural mortality rate

Natural mortality rate, M, of fish is a highly influential stock assessment parameter. The M parameter is also difficult to estimate directly and reliably. Various empirical estimators have been developed to estimate M indirectly, based on relationships established between M and predictor variables such as growth parameters, lifespan and water temperature (e.g., Beverton and Holt, 1959; Alverson and Carney, 1975; Pauly, 1980; Hoenig, 1983). Despite the importance of these estimators, there is no consensus in the literature on how well they work in terms of prediction error or how their performance may be ranked. Then et al. (2015) evaluated estimators based on various combinations of maximum age (tmax), von Bertalanffy growth parameters (K) and asymptotic length (L∞), and water temperature (T), by seeing how well they reproduce independent, direct estimates of M for more than 200 unique fish species. They also considered the possibility of combining different estimators using a weighting scheme to improve estimation of M. This report documents additional analyses and results to supplement the results in the journal article. The estimators, evaluation criteria, and other important details are given in the journal article

Simulations to Compare the Performance of Two Length-based Estimators of Total Mortality Rate

Mean length-based methods to estimate instantaneous total mortality rates, Z, are important assessment tools for data-poor stocks. One commonly used method was developed by Beverton and Holt (1956). The behavior of this method, especially in relation to bias, has been fairly well characterized. Another method by Ehrhardt and Ault (1992) was proposed to correct the Beverton-Holt (BH) method for applications to length frequency distributions that are truncated at the upper end. The Ehrhardt-Ault (EA) method has zero bias at equilibrium when there is no variability in length at age but the reliability of the method has not been demonstrated under conditions of reasonable magnitude of growth variability. It is also unclear how one would determine the best input value for the upper length truncation parameter. This report presents additional simulation results to supplement the results in Then et al. (2015). The estimators, evaluation criteria, simulation procedures, and conditions simulated are given in Then et al. (2015)

Investigation of ConViT on COVID-19 Lung Image Classification and the Effects of Image Resolution and Number of Attention Heads

COVID-19 has been one of the popular foci in the research community since its first outbreak in China, 2019. Radiological patterns such as ground glass opacity (GGO) and consolidations are often found in CT scan images of moderate to severe COVID-19 patients. Therefore, a deep learning model can be trained to distinguish COVID-19 patients using their CT scan images. Convolutional Neural Networks (CNNs) has been a popular choice for this type of classification task. Another potential method is the use of vision transformer with convolution, resulting in Convolutional Vision Transformer (ConViT), to possibly produce on par performance using less computational resources. In this study, ConViT is applied to diagnose COVID-19 cases from lung CT scan images. Particularly, we investigated the relationship of the input image pixel resolutions and the number of attention heads used in ConViT and their effects on the model’s performance. Specifically, we used 512x512, 224x224 and 128x128 pixels resolution to train the model with 4 (tiny), 9 (small) and 16 (base) number of attention heads used. An open access dataset consisting  of 2282 COVID-19 CT images and 9776 Normal CT images from Iran is used in this study. By using 128x128 image pixels resolution, training using 16 attention heads, the ConViT model has achieved an accuracy of 98.01%, sensitivity of 90.83%, specificity of 99.69%, positive predictive value (PPV) of 95.58%, negative predictive value (NPV) of 97.89% and F1-score of 94.55%. The model has also achieved improved performance over other recent studies that used the same dataset. In conclusion, this study has shown that the ConViT model can play a meaningful role to complement RT-PCR test on COVID-19 close contacts and patients

Occurrence of periodic Lam\'e functions at bifurcations in chaotic Hamiltonian systems

We investigate cascades of isochronous pitchfork bifurcations of straight-line librating orbits in some two-dimensional Hamiltonian systems with mixed phase space. We show that the new bifurcated orbits, which are responsible for the onset of chaos, are given analytically by the periodic solutions of the Lam\'e equation as classified in 1940 by Ince. In Hamiltonians with C_${2v}$ symmetry, they occur alternatingly as Lam\'e functions of period 2K and 4K, respectively, where 4K is the period of the Jacobi elliptic function appearing in the Lam\'e equation. We also show that the two pairs of orbits created at period-doubling bifurcations of touch-and-go type are given by two different linear combinations of algebraic Lam\'e functions with period 8K.Comment: LaTeX2e, 22 pages, 14 figures. Version 3: final form of paper, accepted by J. Phys. A. Changes in Table 2; new reference [25]; name of bifurcations "touch-and-go" replaced by "island-chain

Investigation of ConViT on COVID-19 Lung Image Classification and the Effects of Image Resolution and Number of Attention Heads

COVID-19 has been one of the popular foci in the research community since its first outbreak in China, 2019. Radiological patterns such as ground glass opacity (GGO) and consolidations are often found in CT scan images of moderate to severe COVID-19 patients. Therefore, a deep learning model can be trained to distinguish COVID-19 patients using their CT scan images. Convolutional Neural Networks (CNNs) has been a popular choice for this type of classification task. Another potential method is the use of vision transformer with convolution, resulting in Convolutional Vision Transformer (ConViT), to possibly produce on par performance using less computational resources. In this study, ConViT is applied to diagnose COVID-19 cases from lung CT scan images. Particularly, we investigated the relationship of the input image pixel resolutions and the number of attention heads used in ConViT and their effects on the model’s performance. Specifically, we used 512x512, 224x224 and 128x128 pixels resolution to train the model with 4 (tiny), 9 (small) and 16 (base) number of attention heads used. An open access dataset consisting  of 2282 COVID-19 CT images and 9776 Normal CT images from Iran is used in this study. By using 128x128 image pixels resolution, training using 16 attention heads, the ConViT model has achieved an accuracy of 98.01%, sensitivity of 90.83%, specificity of 99.69%, positive predictive value (PPV) of 95.58%, negative predictive value (NPV) of 97.89% and F1-score of 94.55%. The model has also achieved improved performance over other recent studies that used the same dataset. In conclusion, this study has shown that the ConViT model can play a meaningful role to complement RT-PCR test on COVID-19 close contacts and patients

Can one hear the shape of the Universe?

It is shown that the recent observations of NASA's explorer mission "Wilkinson Microwave Anisotropy Probe" (WMAP) hint that our Universe may possess a non-trivial topology. As an example we discuss the Picard space which is stretched out into an infinitely long horn but with finite volume.Comment: 4 page