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We study the constant contributions to the free energies obtained through the topological recursion applied to the complex curves mirror to toric Calabi-Yau threefolds. We show that the recursion reproduces precisely the corresponding…
We consider the problem of exact learning of parameters of a linear RNA energy model from secondary structure data. A necessary and sufficient condition for learnability of parameters is derived, which is based on computing the convex hull…
We have established an RNA Mapping Database (RMDB) to enable a new generation of structural, thermodynamic, and kinetic studies from quantitative single-nucleotide-resolution RNA structure mapping (freely available at…
The spectra of random feature matrices provide essential information on the conditioning of the linear system used in random feature regression problems and are thus connected to the consistency and generalization of random feature models.…
Sequence data, such as DNA, RNA, and protein sequences, exhibit intricate, multi-scale structures that pose significant challenges for conventional analysis methods, particularly those relying on alignment or purely statistical…
Keeping in mind the several models of M(atrix) theory we attempt to understand the possible structure of the topological M(atrix) theory ``underlying'' these approaches. In particular we raise the issue about the nature of the structure of…
Keeping in mind the several models of M(atrix) theory we attempt to understand the possible structure of the topological M(atrix) theory ``underlying'' these approaches. In particular we are motivated by the issue about the nature of the…
RNA is a fundamental class of biomolecules that mediate a large variety of molecular processes within the cell. Computational algorithms can be of great help in the understanding of RNA structure-function relationship. One of the main…
The thermodynamic properties of DNA circular molecules are investigated by a new path integral computational method which treats in the real space the fundamental forces stabilizing the molecule. The base pair and stacking contributions to…
We describe a dynamic programming algorithm for predicting optimal RNA secondary structure, including pseudoknots. The algorithm has a worst case complexity of ${\cal O}(N^6)$ in time and ${\cal O}(N^4)$ in storage. The description of the…
Due to the highly complex chemical structure of biomolecules, the extensive understanding of the electronic information for proteomics can be challenging. Here, we constructed a charge transfer database at residue level derived from…
We introduce a computational topology-based approach with unsupervised machine-learning algorithms to estimate the database size and content of RNA-like graph topologies. Specifically, we apply graph theory enumeration to generate all…
Simple recursion relations for zero energy states of supersymmetric matrix models are derived by using an unconventional reducible representation for the fermionic degrees of freedom.
We suggest that the spectral properties near zero virtuality of three dimensional QCD, follow from a Hermitean random matrix model. The exact spectral density is derived for this family of random matrix models both for even and odd number…
Atomically detailed simulations of RNA folding have proven very challenging in view of the difficulties of developing realistic force fields and the intrinsic computational complexity of sampling rare conformational transitions. To tackle…
Pseudo-hermitian matrices are matrices hermitian with respect to an indefinite metric. They can be thought of as the truncation of pseudo-hermitian operators, defined over some Krein space, together with the associated metric, to a finite…
The aim of this work is to proceed with the development of a model of topological electromagnetism in empty space, proposed by one of us some time ago and based on the existence of a topological structure associated with the radiation…
We view the folding of RNA-sequences as a map that assigns a pattern of base pairings to each sequence, known as secondary structure. These preimages can be constructed as random graphs (i.e. the neutral networks associated to the structure…
A geometric entropy is defined as the Riemannian volume of the parameter space of a statistical manifold associated with a given network. As such it can be a good candidate for measuring networks complexity. Here we investigate its ability…
The full-density-matrix numerical renormalization group (NRG) has evolved as a systematic and transparent setting for the cal- culation of thermodynamical quantities at arbitrary temperatures within the NRG framework. It directly evaluates…