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While circular data occur in a wide range of scientific fields, the methodology for distributional modeling and probabilistic forecasting of circular response variables is rather limited. Most of the existing methods are built on the…
The hierarchical and recursive expressive capability of rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. On the other hand, such hierarchical…
In this review we provide an organized summary of the theoretical and computational results which are available for polymers subject to spatial or topological constraints. Because of the interdisciplinary character of the topic, we provide…
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…
By means of sophisticated Monte Carlo methods, we investigate the conformational phase diagram of a simple model for flexible polymers with explicit thickness. The thickness constraint, which is introduced geometrically via the global…
We consider the monomer-dimer model on sequences of random graphs locally convergent to trees. We prove that the monomer density converges almost surely, in the thermodynamic limit, to an analytic function of the monomer activity. We…
We study random labelings of graphs conditioned on a small number (typically one or two) peaks, i.e., local maxima. We show that the boundaries of level sets of a random labeling of a square with a single peak have dimension 2, in a…
Standard statistical mechanical or condensed matter arguments tell us that bulk properties of a physical system do not depend too much on boundary conditions. Random tilings of large regions provide counterexamples to such intuition, as…
The interplay of topological constraints, excluded volume interactions, persistence length and dynamical entanglement length in solutions and melts of linear chains and ring polymers is investigated by means of kinetic Monte Carlo…
The joint probability distribution function (PDF) of the density within multiple concentric spherical cells is considered. It is shown how its cumulant generating function can be obtained at tree order in perturbation theory as the Legendre…
The statistics of equally weighted random paths (ideal polymer) is studied in $2$ and $3$ dimensional percolating clusters. This is equivalent to diffusion in the presence of a trapping environment. The number of $N$ step walks follows a…
Entangled networks of stiff biopolymers exhibit complex dynamic response, emerging from the topological constraints that neighboring filaments impose upon each other. We propose a class of reference models for entanglement dynamics of stiff…
We extend existing renormalization group calculations for the exponents describing scaling of star polymers and polymer networks constituted by chains of different species (the so-called copolymer star exponents). Our four loop results find…
A convenient measure of a map or flow's chaotic action is the topological entropy. In many cases, the entropy has a homological origin: it is forced by the topology of the space. For example, in simple toral maps, the topological entropy is…
We study reversible polymerization of rings. In this stochastic process, two monomers bond and as a consequence, two disjoint rings may merge into a compound ring, or, a single ring may split into two fragment rings. This…
Motivated by recent observations that non-concatenated ring polymers in their dense solution exhibit a glass-like dynamics, we propose a free volume description of the motion of such rings based on the notion of topological volume. We first…
A Flory theory is constructed for a long polymer ring in a melt of unknotted and non-concatenated rings. The theory assumes that the ring forms an effective annealed branched object and computes its primitive path. It is shown that the…
We analyze the structure of two dimensional disordered cellular systems generated by extensive computer simulations. These cellular structures are studied as topological trees rooted on a central cell or as closed shells arranged…
Using a theoretical model we show that ideal ring polymers are stronger depletants than ideal linear polymers of equal radii of gyration, but not of equal hydrodynamic radii. The difference in the depletion-induced force profile is largely…
We deduce a structurally inductive description of the determinantal probability measure associated with Kalai's celebrated enumeration result for higher--dimensional spanning trees of the $n-1$--simplex. As a consequence, we derive the…