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In the study of the conformational behavior of complex systems, such as proteins, several related statistical measures are commonly used to compare two different potential energy functions. Among them, the Pearson's correlation coefficient…
Understanding protein structure is of crucial importance in science, medicine and biotechnology. For about two decades, knowledge based potentials based on pairwise distances -- so-called "potentials of mean force" (PMFs) -- have been…
In spite of decades of research, much remains to be discovered about folding: the detailed structure of the initial (unfolded) state, vestigial folding instructions remaining only in the unfolded state, the interaction of the molecule with…
Calculating free energy differences is a topic of substantial interest and has many applications including molecular docking and hydration, solvation, and binding free energies which is used in computational drug discovery. However, in…
We present several natural notions of distance between spectral density functions of (discrete-time) random processes. They are motivated by certain filtering problems. First we quantify the degradation of performance of a predictor which…
A microscopic theory of the free energy barriers and folding routes for minimally frustrated proteins is presented, greatly expanding on the presentation of the variational approach outlined previously [J. J. Portman, S. Takada, P. G.…
Kinetics of folding of a protein held in a force-clamp are compared to an unconstrained folding. The comparison is made within a simple topology-based dynamical model of ubiquitin. We demonstrate that the experimentally observed variations…
It is well-understood that different algorithms, training processes, and corpora produce different word embeddings. However, less is known about the relation between different embedding spaces, i.e. how far different sets of embeddings…
In this paper we introduce a novel method of deriving a pairwise potential for protein folding. The potential is obtained by optimization procedure, which simultaneously maximizes the energy gap for {\it all} proteins in the database. To…
A theoretical framework is developed to study the dynamics of protein folding. The key insight is that the search for the native protein conformation is influenced by the rate r at which external parameters, such as temperature, chemical…
The energy distance is used to test distributional equality, and as a loss function in machine learning. While $D^2(X, Y)=0$ only when $X\sim Y$, the sensitivity to different moments is of practical importance. This work considers $D^2(X,…
The distance from a given position toward one or more destinations, exits, and way points is a more or less important input variable in most models of pedestrian dynamics. Except for the special case when there are no obstacles in a concave…
Mechanical unfolding of polyproteins by force spectroscopy provides valuable insight into their free energy landscapes. Most phenomenological models of the unfolding process are two-state and/or one dimensional, with the details of the…
Distance queries are a basic tool in data analysis. They are used for detection and localization of change for the purpose of anomaly detection, monitoring, or planning. Distance queries are particularly useful when data sets such as…
Proteins employ the information stored in the genetic code and translated into their sequences to carry out well-defined functions in the cellular environment. The possibility to encode for such functions is controlled by the balance…
The prediction of the three-dimensional native structure of proteins from the knowledge of their amino acid sequence, known as the protein folding problem, is one of the most important yet unsolved issues of modern science. Since the…
Free energy calculation is critical in predictive tasks such as protein folding, docking and design. However, rigorous calculation of free energy change is prohibitively expensive in these practical applications. The minimum potential…
This work addresses the question of whether it is possible to define simple pair-wise interaction terms to approximate free energies of proteins or polymers. Rather than ask how reliable a potential of mean force is, one can ask how…
For many optimization problems it is possible to define a distance metric between problem variables that correlates with the likelihood and strength of interactions between the variables. For example, one may define a metric so that the…
The dynamics of folding of proteins is studied by means of a phenomenological master equation. The energy distribution is taken as a truncated exponential for the misfolded states plus a native state sitting below the continuum. The…