Related papers: Scaled Relative Graphs in Normed Spaces
The Random Geometric Graph (RGG) is a random graph model for network data with an underlying spatial representation. Geometry endows RGGs with a rich dependence structure and often leads to desirable properties of real-world networks such…
We construct explicit generating sets S_n and \tilde S_n of the for the alternating and the symmetric groups, which turn the Cayley graphs C(Alt(n), S_n) and C(Sym(n), \tilde S_n) into a family of bounded degree expanders for all n. This…
The selfadjoint extensions of a closed linear relation $R$ from a Hilbert space ${\mathfrak H}_1$ to a Hilbert space ${\mathfrak H}_2$ are considered in the Hilbert space ${\mathfrak H}_1\oplus{\mathfrak H}_2$ that contains the graph of…
We study Smale skew product endomorphisms (introduced in [27]) now over countable graph directed Markov systems, and we prove the exact dimensionality of conditional measures in fibers, and then the global exact dimensionality of the…
Recently there has been increased interest in fitting generative graph models to real-world networks. In particular, Bl\"asius et al. have proposed a framework for systematic evaluation of the expressivity of random graph models. We extend…
Scaled Relative Graphs (SRGs) provide an intuitive graphical frequency-domain method for the analysis of Nonlinear (NL) systems, generalizing the Nyquist diagram. In this paper, we develop a method for computing $L_2$-gain bounds for Lur'e…
A spectral theory of linear operators on rigged Hilbert spaces (Gelfand triplets) is developed under the assumptions that a linear operator $T$ on a Hilbert space $\mathcal{H}$ is a perturbation of a selfadjoint operator, and the spectral…
We extend the notion of regularized integrals introduced by Li-Zhou that aims to assign finite values to divergent integrals on configuration spaces of Riemann surfaces. We then give cohomological formulations for the extended notion using…
We present an extended version of Riemannian geometry suitable for the description of current formulations of double field theory (DFT). This framework is based on graded manifolds and it yields extended notions of symmetries, dynamical…
This thesis focuses on theoretical and algorithmic tools for determining the numbers of induced subgraphs in strongly regular graphs, SRGs, and on further applications of such numbers. We consider in more detail a restricted class of these…
Graph rigidity theory studies the capability of a graph embedded in the Euclidean space to constrain its global geometric shape via local constraints among nodes and edges, and has been widely exploited in network localization and formation…
We introduce and study a mathematical framework for a broad class of regularization functionals for ill-posed inverse problems: Regularization Graphs. Regularization graphs allow to construct functionals using as building blocks linear…
We construct series expansions for the scaling variables (which transform multiplicatively under a renormalization group (RG) transformation) in examples where the RG flows, going from an unstable (Wilson's) fixed point to a stable…
We consider the distributed compression of Soft Random Geometric Graphs (SRGGs) above the connectivity threshold. We establish the Slepian-Wolf rate region for the SRGG in the setting where there are a finite number of encoders compressing…
The use of data-random graphs in statistical testing of spatial patterns is introduced recently. In this approach, a random directed graph is constructed from the data using the relative positions of the points from various classes.…
Stochastic variance reduced gradient (SVRG) is an accelerated version of stochastic gradient descent based on variance reduction, and is promising for solving large-scale inverse problems. In this work, we analyze SVRG and a regularized…
In some scientific fields, a scaling is able to modify the topology of an observed object. Our goal in the present work is to introduce a new formalism adapted to the mathematical representation of this kind of phenomenon. To this end, we…
The usual Laurent expansion of the analytic tensors on the complex plane is generalized to any closed and orientable Riemann surface represented as an affine algebraic curve. As an application, the operator formalism for the $b-c$ systems…
This work will appear as a chapter in a forthcoming volume titled "Topics in Probabilistic Graph Theory". A theory of scaling limits for random graphs has been developed in recent years. This theory gives access to the large-scale geometric…
Strongly walk regular graphs (SWRGs or $s$-SWRGs) form a natural generalization of strongly regular graphs (SRGs) where paths of length~2 are replaced by paths of length~$s$. They can be constructed as coset graphs of the duals of…