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We have combined infrared (IR) experiments with molecular dynamics (MD) simulations in solution at finite temperature to analyse the vibrational signature of the small floppy peptide Alanine-Leucine. IR spectra computed from first-principles MD simulations exhibit no distinct differences between conformational clusters of -helix or -sheet-like folds with different orientations of the bulky leucine side chain. All computed spectra show two prominent bands, in good agreement with the experiment, that are assigned to the stretch vibrations of the carbonyl and carboxyl group, respectively. Variations in band widths and exact maxima are likely due to small fluctuations in the backbone torsion angles.
This chapter explains the different ways in which Markov State Models (MSMs) can be helpful in structure-based drug design. MSMs are constructed from the time series of molecular dynamics (MD), which can be generated by classical MD simulations. Several features of the MSMs can be utilized for rational drug design. The discretization of a validated MSM is particularly suited to extract meaningful representatives from the conformational ensemble, because the discretization yields a small number of microstates and mirrors the features of the free energy landscape. Long-lived conformations consist of a set of microstates which show high transition rates within the set and low transition rates to microstates outside of the set. The Bayesian agglomerative clustering engine (BACE) algorithm uses the observed transition counts to extract long-lived conformations from an MSM. By iteratively merging microstates according to the Bayes factor and recalculating the Bayes-factor matrix, the algorithm yields an aggregation of the microstates into long-lived conformations.
Metadynamics is a computational method to explore the phase space of a molecular system. Gaussian functions are added along relevant coordinates on the fly during a molecular-dynamics simulation to force the system to escape from minima in the potential energy function. The dynamics in the resulting trajectory are however unphysical and cannot be used directly to estimate dynamical properties of the system. Girsanov reweighting is a recent method used to construct the Markov State Model (MSM) of a system subjected to an external perturbation. With the combination of these two techniques—metadynamics/Girsanov-reweighting—the unphysical dynamics in a metadynamics simulation can be reweighted to obtain the MSM of the unbiased system. We demonstrate the method on a one-dimensional diffusion process, alanine dipeptide, and the hexapeptide Val-Gly-Val-Ala-Pro-Gly (VGVAPG). The results are in excellent agreement with the MSMs obtained from direct unbiased simulations of these systems. We also apply metadynamics/Girsanov-reweighting to a β-hairpin peptide, whose dynamics is too slow to efficiently explore its phase space by direct simulation
A hierarchical mixed-integer linear programming method to solve optimal design problems of energy supply systems efficiently has been proposed. The original problem is solved by dividing it into a relaxed optimal design problem at the upper level and optimal operation problems which are independent of each other at the lower level. In this paper, a method of reducing model by time aggregation is proposed to search design solution candidates efficiently in the relaxed optimal design problem at the upper level. This method is realized only by clustering periods and averaging energy demands for clustered periods, while it guarantees to derive the optimal solution. On one hand, the method may decrease the number of design variables and costraints at the upper level, and thus the computation time at the upper level. On the other hand, it may increase the numbers of generated design solution candidates and solved optimal operation problems, and thus the computation time at both the levels. Though a case study on the optimal design of a cogeneration system, it is clarified how the model reduction is effective to enhance the computation efficiency.
Ahierarchical mixed-integer linear programmingmethod has been proposed to solve optimal design problems of energy supply systems efficiently. In this paper, a method of reducing model by clustering periods is proposed to search design solution candidates efficiently in the relaxed optimal design problem at the upper level. This method is realized only by clustering periods and averaging energy demands for clustered periods, while it guarantees to derive the optimal solution.
Through acase study on the optimaldesign of a cogeneration system, ti is clarified how the model reduction si effective ot enhance the computation efficiency.
Based on about 1 million of pressure measurements around comet 67P/Churyumov-Gerasimenko we reconstruct the gas emission across the entire nucleus. Dust particles are seeded in the gas model and the resulting dust distribution follows a daily pattern which agrees with observations if a uniform dust release across the entire sunlit surface is assumed.
We reconstruct the temporal evolution of surface emissions for the four major gas species H2O, CO2, CO, and O2 emitted during the 2015 apparition of comet 67P/Churyumov-Gerasimenko (67P/C-G). Measurements from the Double Focusing Mass Spectrometer (DFMS) of the Rosetta Orbiter Spectrometer for Ion and Neutral Analysis (ROSINA) and the COmet Pressure Sensor (COPS) are used to determine the gas sources on the surface with an inverse gas model for the entire coma. For all species, peak production rates and integrated production rates per orbit are evaluated separately for the northern and the southern hemisphere. Complemented with the total mass production, this allows us to estimate the dust-to-gas ratio of the
emitted material.
Mathematical models for optimal decisions often require both nonlinear and discrete components. These mixed-integer nonlinear programs (MINLP) may be used to optimize the energy use of large industrial plants, integrate renewable sources into energy networks, design biological and biomedical systems, and address numerous other applications of societal importance. The first MINLP algorithms and software were designed by application engineers. While these efforts initially proved useful, scientists, engineers, and practitioners have realized that a transformational shift in technology will be required for MINLP to achieve its full potential. MINLP has transitioned to a forefront position in computer science, with researchers actively developing MINLP theory, algorithms, and implementations. Even with their concerted effort, algorithms and available software are often unable to solve practically-sized instances of these important models. Current obstacles include characterizing the computability boundary, effectively exploiting known optimization technologies for specialized classes of MINLP, and effectively using logical formulas holistically throughout algorithms.
Deep Learning has received significant attention due to its impressive performance in many state-of-the-art learning tasks. Unfortunately, while very powerful, Deep Learning is not well understood theoretically and in particular only recently results for the complexity of training deep neural networks have been obtained. In this work we show that large classes of deep neural networks with various architectures (e.g., DNNs, CNNs, Binary Neural Networks, and ResNets), activation functions (e.g., ReLUs and leaky ReLUs), and loss functions (e.g., Hinge loss, Euclidean loss, etc) can be trained to near optimality with desired target accuracy using linear programming in time that is exponential in the input data and parameter space dimension and polynomial in the size of the data set; improvements of the dependence in the input dimension are known to be unlikely assuming P≠NP, and improving the dependence on the parameter space dimension remains open. In particular, we obtain polynomial time algorithms for training for a given fixed network architecture. Our work applies more broadly to empirical risk minimization problems which allows us to generalize various previous results and obtain new complexity results for previously unstudied architectures in the proper learning setting.