Related papers: The L2 strong maximum principle on arbitrary count…
We study heat transport in a pair of strongly coupled spins. In particular, we present a condition for optimal rectification, i.e., flow of heat in one direction and complete isolation in the opposite direction. We show that the…
We study a notion of cross ratios on metric graphs and electrical networks. We show that several known results immediately follow from the basic properties of cross ratios. We show that the projection matrices of Kirchhoff have nice (and…
We introduce an algorithmic model of heat conduction, the thermodynamic graph. The thermodynamic graph is analogous to meshes in the finite difference method in the sense that the calculation of temperature is carried out at the vertices of…
Using the spectral theory of weakly convergent sequences of finite graphs, we prove the uniform existence of the integrated density of states for a large class of infinite graphs.
Assessing homophily in large-scale networks is central to understanding structural regularities in graphs, and thus inform the choice of models (such as graph neural networks) adopted to learn from network data. Evaluation of smoothness…
This work maps deep neural networks to classical Ising spin models, allowing them to be described using statistical thermodynamics. The density of states shows that structures emerge in the weights after they have been trained --…
Explaining the influence of strong coupling in the dynamics of open quantum systems is one of the most challenging issues in the rapidly growing field of quantum thermodynamics. By using a particular definition of heat, we develop a new…
We give a bound for the graph energy with given maximal degree in terms of the second and fourth moments of a graph. In the case in which the graph is $d$-regular we obtain the bound that is given in Van Dam, E. et al. (2014). through…
In this work, we study the propagation of influence and computation in dynamic distributed systems. We focus on broadcasting models under a worst-case dynamicity assumption which have received much attention recently. We drop for the first…
We consider the problem of heat diffusion in branched systems and networks on the basis of a model described in terms of heat equation on metric graphs. Using the explicit analytical solutions of the latter, evolution of the temperature…
The strong maximum principle is proved to hold for weak (in the sense of support functions) sub- and super-solutions to a class of quasi-linear elliptic equations that includes the mean curvature equation for $C^0$ spacelike hypersurfaces…
Stream graphs model highly dynamic networks in which nodes and/or links arrive and/or leave over time. Strongly connected components in stream graphs were defined recently, but no algorithm was provided to compute them. We present here…
We establish a strong law of large numbers under intermediate trimming for a particular example of Birkhoff sums of a non-integrable observable over the doubling map. It has been shown in a previous work by Haynes that there is no strong…
An induced matching in a graph is a set of edges whose endpoints induce a $1$-regular subgraph. Gupta et al. (2012,\cite{Gupta}) showed that every $n$-vertex graph has at most $10^{\frac{n}{5}}\approx 1.5849^n$ maximal induced matchings,…
We study the strong maximum principle for horizontal (p-) mean curvature operator and p-(sub)laplacian operator on subriemannian manifolds including, in particular, Heisenberg groups and Heisenberg cylinders. Under a certain Hormander type…
The study of minimal subgraphs witnessing a connectivity property is an important field in graph theory. The foundation for large flames has been laid by Lov\'asz: Let $ D=(V,E) $ be a finite digraph and let $ r\in V $. The local…
We study the extremal energy problem for complex unit gain graphs whose underlying graph is the dumbbell graph $D_{r,s,\ell}$. Using switching equivalence, we reduce the spectrum to the real parts of the two cycle gains and obtain an…
We present faster algorithms for approximate maximum flow in undirected graphs with good separator structures, such as bounded genus, minor free, and geometric graphs. Given such a graph with $n$ vertices, $m$ edges along with a recursive…
Modeling how networks change under structural perturbations can yield foundational insights into network robustness, which is critical in many real-world applications. The largest connected component is a popular measure of network…
We study the superconducting transition temperature $T_c$ of the bilayer d-p model with $d_{x^2-y^2}$-wavelike attractive interaction based on the formalism first employed by Nozi\`{e}res and Schmitt-Rink. In the strong coupling regime,…