Related papers: One dimensional directed polymer "memory model"
A simple model of a circularly closed dsDNA in a poor solvent is considered as an example of a semi-flexible polymer with self-attraction. To find the ground states, the conformational energy is computed as a sum of the bending and…
The equilibrium statistical mechanics of classical directed polymers in 2 dimensions is well known to be equivalent to the imaginary-time quantum dynamics of a 1+1-dimensional many-particle system, with polymer configurations corresponding…
We consider disordered systems of directed polymer type, for which disorder is so-called marginally relevant. These include the usual (short-range) directed polymer model in dimension (2+1), the long-range directed polymer model with Cauchy…
A model for studying the ultrametricity of the energy landscape in a disordered heteropolymer is presented. It is treated as a simplified model of a protein molecule in which amino acid residues are modeled as point masses. Pairwise…
We study the memorization and generalization capabilities of Diffusion Models (DMs) when data lies on a structured latent manifold. Specifically, we consider a set of $P$ data points in $N$ dimensions confined to a latent subspace of…
It is a well-known open problem in the literature on random polymers to show that a directed polymer in random environment localizes around a favorite path at low temperature. A precise statement of this conjecture is formulated and proved…
We study the depinning phase transition of a directed polymer in a $d$-dimensional space by a periodic potential localized on a straight line. We give exact formulas in all dimensions for the critical pinning we need to localize the…
We consider the unbinding of a directed polymer in a random media from a wall in $d=1+1$ dimensions and a simple one-dimensional model for DNA unzipping. Using the replica trick we show that the restricted partition functions of these…
Commonly used linear and nonlinear constitutive material models in deformation simulation contain many simplifications and only cover a tiny part of possible material behavior. In this work we propose a framework for learning customized…
The statistical mechanics of polymer loops entangled in the two-dimensional array of randomly distributed obstacles of infinite length is discussed. The area of the loop projected to the plane perpendicular to the obstacles is used as a…
In this paper, we propose a novel transfer learning approach called multi-modal cascade model with feature transfer for polymer property prediction.Polymers are characterized by a composite of data in several different formats, including…
The adsorption of an ideal heteropolymer loop at a potential point well is investigated within the frameworks of a standard random matrix theory. On the basis of semi-analytical/semi-numerical approach the histogram of transition points for…
We study analytically a model of a two dimensional, partially directed, flexible or semiflexible polymer, attached to an attractive wall which is perpendicular to the preferred direction. In addition, the polymer is stretched by an…
We investigate by atomistic simulations the memory behavior a model glass subjected to random driving protocols. The training consists of a random walk of forward and/or backward shearing sequences bounded by a maximal shear strain of…
A fundamental theory is presented for the mechanical response of polymer networks undergoing large deformation which seamlessly integrates statistical mechanical principles with macroscopic thermodynamic constitutive theory. Our formulation…
Polymers, composed of repeating structural units called monomers, are fundamental materials in daily life and industry. Accurate property prediction for polymers is essential for their design, development, and application. However, existing…
We introduce a simple geometric model for a double-stranded and double-helical polymer. We study the statistical mechanics of such polymers using both analytical techniques and simulation. Our model has a single energy-scale which…
Attractor networks are an influential theory for memory storage in brain systems. This theory has recently been challenged by the observation of strong temporal variability in neuronal recordings during memory tasks. In this work, we study…
We study directed polymers subject to a quenched random potential in d transversal dimensions. This system is closely related to the Kardar-Parisi-Zhang equation of nonlinear stochastic growth. By a careful analysis of the perturbation…
Adaptive response to a varying environment is a common feature of biological organisms. Reproducing such features in electronic systems and circuits is of great importance for a variety of applications. Here, we consider memory models…