Related papers: Rank of Stably Dissipative Graphs

We develop a notion of (principal) differential rank for differential-valued fields, in analog of the exponential rank and of the difference rank. We give several characterizations of this rank. We then give a method to define a derivation…

Ranking nodes in networks according to a defined measure of importance is an extensively studied task, with applications in ecology, economic trade networks, and social networks. This paper introduces a method based on a non-linear…

We consider a geometrically finite discrete group of conformal transformations of the sphere. Further we consider distributions which are supported on the limit set and are invariant with conformal weight. We estimate their regularity in…

Conjecturally, almost all graphs are determined by their spectra. This problem has also been studied for variants such as the spectra of the Laplacian and signless Laplacian. Here we consider the problem of determining graphs with Ihara and…

We study some aspects of the global dynamics of an $n$-dimensional Lotka-Volterra system with infinite delay and patch structure, such as extinction, persistence, existence and global attractivity of a positive equilibrium. Both the cases…

A classification of discrete integrable systems on quad-graphs, i.e. on surface cell decompositions with quadrilateral faces, is given. The notion of integrability laid in the basis of the classification is the three-dimensional…

A square matrix $M$ represents a graph $\Gamma$ if its nonzero off-diagonal entries encode the adjacencies of $\Gamma$, subject to a fixed ordering of the vertices. Over the field of two elements, we investigate the distribution of ranks in…

We determine the Waring rank of the fundamental skew invariant of any complex reflection group whose highest degree is a regular number. This includes all irreducible real reflection groups.

We classify graphs and, more generally, finite relational structures that are identified by C2, that is, two-variable first-order logic with counting. Using this classification, we show that it can be decided in almost linear time whether a…

In casual discussion, a stack is often described as a variety (the coarse space) together with stabilizer groups attached to some of its subvarieties. However, this description does not uniquely specify the stack. Our main result shows that…

We prove that the genus of the Turaev surface of a link diagram is determined by a graph whose vertices correspond to the boundary components of the maximal alternating regions of the link diagram. Furthermore, we use these graphs to…

In this paper, we have considered the dense rank for assigning positions to alternatives in weak orders. If we arrange the alternatives in tiers (i.e., indifference classes), the dense rank assigns position 1 to all the alternatives in the…

For $\alpha \in (1,2]$, the $\alpha$-stable graph arises as the universal scaling limit of critical random graphs with i.i.d. degrees having a given $\alpha$-dependent power-law tail behavior. It consists of a sequence of compact measured…

Cross-sectional observations from a dynamical system can be modeled via steady-state distributions of Markov processes. The major challenge is then to determine whether the process parameters can be identified and estimated from the…

We study the algebraic rank of a divisor on a graph, an invariant defined using divisors on algebraic curves dual to the graph. We prove it satisfies the Riemann-Roch formula, a specialization property, and the Clifford inequality. We prove…

Let V be a rank one discrete valuation ring (DVR) on a field F and let L/F be a finite separable algebraic field extension with [L:F] = m. The integral closure of V in L is a Dedekind domain that encodes the following invariants: (i) the…

We introduce a refinement of the persistence diagram, the graded persistence diagram. It is the Mobius inversion of the graded rank function, which is obtained from the rank function using the unary numeral system. Both persistence diagrams…

This text is about geometric structures imposed by robust dynamical behaviour. We explain recent results towards the classification of partially hyperbolic systems in dimension 3 using the theory of foliations and its interaction with…

In this work we show that, using the eigen-decomposition of the adjacency matrix, we can consistently estimate feature maps for latent position graphs with positive definite link function $\kappa$, provided that the latent positions are…

The WL-rank of a graph $\Gamma$ is defined to be the rank of the coherent configuration of $\Gamma$. The WL-dimension of $\Gamma$ is defined to be the smallest positive integer $m$ for which $\Gamma$ is identified by the $m$-dimensional…