Estimation of the infinitesimal generator by square-root approximation

For the analysis of molecular processes, the estimation of time-scales, i.e., transition rates, is very important. Estimating the transition rates between molecular conformations is -- from a mathematical point of view -- an invariant subspace projection problem. A certain infinitesimal generator acting on function space is projected to a low-dimensional rate matrix. This projection can be performed in two steps. First, the infinitesimal generator is discretized, then the invariant subspace is approxi-mated and used for the subspace projection. In our approach, the discretization will be based on a Voronoi tessellation of the conformational space. We will show that the discretized infinitesimal generator can simply be approximated by the geometric average of the Boltzmann weights of the Voronoi cells. Thus, there is a direct correla-tion between the potential energy surface of molecular structures and the transition rates of conformational changes. We present results for a 2d-diffusion process and Alanine dipeptide

Efficient Estimation of Transition Rates as Functions of pH

Extracting the kinetic properties of a system whose dynamics depend on the pH of the environment with which it exchanges energy and atoms requires sampling the Grand Canonical Ensemble. As an alternative, we present a novel strategy that requires simulating only the most recurrent Canonical Ensembles that compose the Grand Canonical Ensemble. The simulations are used to estimate the Gran Canonical distribution for a specific pH value by reweighting and to construct the transition rate matrix by discretizing the Fokker-Planck equation by Square Root Approximation and robust Perron Cluster Cluster Analysis. As an application, we have studied the tripeptide Ala-Asp-Ala

Augmented ant colony algorithm for virtual drug discovery

Docking is a fundamental problem in computational biology and drug discovery that seeks to predict a ligand’s binding mode and affinity to a target protein. However, the large search space size and the complexity of the underlying physical interactions make docking a challenging task. Here, we review a docking method, based on the ant colony optimization algorithm, that ranks a set of candidate ligands by solving a minimization problem for each ligand individually. In addition, we propose an augmented version that takes into account all energy functions collectively, allowing only one minimization problem to be solved. The results show that our modification outperforms in accuracy and efficiency

A complete hand-drawn sketch vectorization framework

Vectorizing hand-drawn sketches is a challenging task, which is of paramount importance for creating CAD vectorized versions for the fashion and creative workflows. This paper proposes a complete framework that automatically transforms noisy and complex hand-drawn sketches with different stroke types in a precise, reliable and highly-simplified vectorized model. The proposed framework includes a novel line extraction algorithm based on a multi-resolution application of Pearson's cross correlation and a new unbiased thinning algorithm that can get rid of scribbles and variable-width strokes to obtain clean 1-pixel lines. Other contributions include variants of pruning, merging and edge linking procedures to post-process the obtained paths. Finally, a modification of the original Schneider's vectorization algorithm is designed to obtain fewer control points in the resulting Bezier splines. All the proposed steps of the framework have been extensively tested and compared with state-of-the-art algorithms, showing (both qualitatively and quantitatively) its outperformance

Experimental assessment of hot-work tool steels performances under the creep-fatigue regime

In the present research an innovative testing method, specifially developed to characterize the tool steels under creep-fatigue conditions, was carried out an a TQ1 hot-work tool steel. The experimental campaign consisted of different testing conditions and part of the specimens were nitrided to account for the specific surface state of the tools. Tests were performed on a 10tons MTS fatigue machine equipped with a heating furnace. A creep-fatigue loading type was applied to the specimens, i.e. a cyclic load with a dwell-time, in order to properly reproduce the conditions acting on a hot forging or extrusion tool. Then, under a constant temperature of 520°C, the effects of four different load levels and 2 different values of dwell-times were evaluated. In addition, selected test conditions were replicated with the specimens not nitrided with the aim to evalute and quantify the influence of the superficial treatment. Final results were presented in terms of fatigue curves of the TQ1 and compared to the performances of the H11 tool steel tested in a previous research by the same authors

A Numerical Modelling Approach for Time-Dependent Deformation of Hot Forming Tools under the Creep-Fatigue Regime

The present study was aimed at predicting the time-dependent deformation of tools used in hot forming applications subjected to the creep-fatigue regime. An excessive accumulated plastic deformation is configured as one of the three main causes of premature failure of tools in these critical applications and it is accumulated cycle by cycle without evident marks leading to noncompliant products. With the aim of predicting this accumulated deformation, a novel procedure was developed, presented, and applied to the extrusion process as an example. A time-hardening primary creep law was used and novel regression equations for the law's coefficients were developed to account not only for the induced stress-temperature state but also for the dwell-time value, which is determined by the selected set of process parameters and die design. The procedure was validated against experimental data both on a small-scale extrusion die at different stress, temperature, load states, and for different geometries and on an industrial extrusion die which was discarded due to the excessive plastic deformation after 64 cycles. A numerical-experimental good agreement was achieved

Melanosis of the lower lip subverted by filler injection: a simulator of early mucosal melanoma

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Reweighting methods for Molecular Dynamics

The dynamical response of molecular systems, when the potential energy function is perturbed at a microscopic level, is difficult to predict without a numerical or laboratory experiment. This is due to the non-linearity and high-dimensionality of molecular systems. An efficient investigation of such a behaviour is necessary to better understand the nature of molecules and to improve the predictability of Molecular Dynamics simulations. In this thesis we propose a reweighting scheme for Markov State Models (MSMs), based on the Girsanov theorem, that permits to reduce the computational cost of the analysis when the potential energy function of a molecule is perturbed. The method has been successfully extended and implemented with metadynamics, in order to build the MSM of a molecular system in a significantly shorter computational time compared to a standard unbiased MD simulation. We also propose a new method to discretize the infinitesimal generator into a rate matrix, that could be used to efficiently study Hamiltonian perturbations as well

Tiny Deep Learning Architectures Enabling Sensor-Near Acoustic Data Processing and Defect Localization

The timely diagnosis of defects at their incipient stage of formation is crucial to extending the life-cycle of technical appliances. This is the case of mechanical-related stress, either due to long aging degradation processes (e.g., corrosion) or in-operation forces (e.g., impact events), which might provoke detrimental damage, such as cracks, disbonding or delaminations, most commonly followed by the release of acoustic energy. The localization of these sources can be successfully fulfilled via adoption of acoustic emission (AE)-based inspection techniques through the computation of the time of arrival (ToA), namely the time at which the induced mechanical wave released at the occurrence of the acoustic event arrives to the acquisition unit. However, the accurate estimation of the ToA may be hampered by poor signal-to-noise ratios (SNRs). In these conditions, standard statistical methods typically fail. In this work, two alternative deep learning methods are proposed for ToA retrieval in processing AE signals, namely a dilated convolutional neural network (DilCNN) and a capsule neural network for ToA (CapsToA). These methods have the additional benefit of being portable on resource-constrained microprocessors. Their performance has been extensively studied on both synthetic and experimental data, focusing on the problem of ToA identification for the case of a metallic plate. Results show that the two methods can achieve localization errors which are up to 70% more precise than those yielded by conventional strategies, even when the SNR is severely compromised (i.e., down to 2 dB). Moreover, DilCNN and CapsNet have been implemented in a tiny machine learning environment and then deployed on microcontroller units, showing a negligible loss of performance with respect to offline realizations

A review of Girsanov Reweighting and of Square Root Approximation for building molecular Markov State Models

Dynamical reweighting methods permit to estimate kinetic observables of a stochastic process governed by a target potential $\tilde{V}(x)$ from trajectories that have been generated at a different potential $V(x)$. In this article, we present Girsanov reweighting and Square Root Approximation (SqRA): the first method reweights path probabilities exploiting the Girsanov theorem and can be applied to Markov State Models (MSMs) to reweight transition probabilities; the second method was originally developed to discretize the Fokker-Planck operator into a transition rate matrix, but here we implement it into a reweighting scheme for transition rates. We begin by reviewing the theoretical background of the methods, then present two applications relevant to Molecular Dynamics (MD), highlighting their strengths and weaknesses