arXiv research

Introduces intrinsic Hopf-Lax semigroup linking to intrinsic slope.

Survey of intrinsically linked or knotted graphs.

The paper studies properties of intrinsically Lipschitz constants in metric spaces.

We introduce new sufficient conditions for intrinsic knotting and linking. A graph on n vertices with at least 4n-9 edges is intrinsically linked. A graph on n vertices with at least 5n-14 edges is intrinsically knotted. We also classify graphs that are 0, 1, or 2 edges short of being complete partite graphs with respe…

New graph shows edge deletion/contraction doesn't always result in intrinsically linked graphs.

New method estimates intrinsic dimensionality using angles, not distances.

A directed graph $G$ is $\textit{intrinsically linked}$ if every embedding of that graph contains a non-split link $L$, where each component of $L$ is a consistently oriented cycle in $G$. A $\textit{tournament}$ is a directed graph where each pair of vertices is connected by exactly one directed edge. We consider intr…

We classify graphs that are 0, 1, or 2 edges short of being complete partite graphs with respect to intrinsic linking and intrinsic knotting. In addition, we classify intrinsic knotting of graphs on 8 vertices. For graphs in these families, we verify a conjecture presented in Adams' "The Knot Book": If a vertex is remo…

We show that deleting an edge of a 3-cycle in an intrinsically knotted graph gives an intrinsically linked graph.

Investigates intrinsic Lipschitz sections in nonlinear quotient maps.

We prove that a graph is intrinsically linked in an arbitrary 3-manifold M if and only if it is intrinsically linked in S^3. Also, assuming the Poincare Conjecture, we prove that a graph is intrinsically knotted in M if and only if it is intrinsically knotted in S^3.

Recalls intrinsically harmonic forms and open problems.

Criterion for flat circle bundles using intrinsically harmonic forms.

Paper analyzes a new Hopf-Lax semigroup in metric spaces.

Revisits VIC method to correct intrinsic reward bias in stochastic environments.

New research finds six bipartite intrinsically knotted graphs with 23 edges.

We answer the question "Does the Y-triangle move preserve intrinsic knottedness?" in the negative by giving an example of a graph that is obtained from the intrinsically knotted graph K_7 by triangle-Y and Y-triangle moves but is not intrinsically knotted.

Estimates intrinsic dimension of data for GANs.

Study uniformly differentiable graphs in Carnot groups, proving area formulas.

We focus our attention on the notion of intrinsic Lipschitz graphs, inside a special class of metric spaces i.e. the Carnot groups. More precisely, we provide a characterization of locally intrinsic Lipschitz functions in Carnot groups of step 2 in terms of their intrinsic distributional gradients.

New metric measure space theory for Lipschitz constants.

We list more than 200 new examples of minor minimal intrinsically knotted graphs and describe many more that are intrinsically knotted and likely minor minimal.

Johnson, Kidwell, and Michael showed that intrinsically knotted graphs have at least 21 edges. Also it is known that K7 and the thirteen graphs obtained from K7 by rY moves are intrinsically knotted graphs with 21 edges. We prove that these 14 graphs are the only intrinsically knotted graphs with 21 edges.

Study shows stable graphs in Heisenberg group are essentially planes.

The paper studies maps in the Heisenberg group and their images, called Rickman rugs.

This paper introduces a number of new intrinsically 3-linked graphs through five new constructions. We then prove that intrinsic 3-linkedness is not preserved by $\text{Y}\nabla$ moves. We will see that the graph $M$, which is obtained through a $\text{Y}\nabla$ move on $(PG)^*_*(PG)$, is not intrinsically 3-linked.

Market activity scales near a constant of 0.632 in intrinsic time.

The study shows that the second fundamental form is intrinsic under certain conditions in space forms.

Two new minor minimal intrinsically chiral graphs identified.

We examine graphs that contain a non-trivial link in every embedding into real projective space, using a weaker notion of unlink than was used by Flapan, et al. We call such graphs intrinsically linked in projective space. We fully characterize such graphs with connectivity 0,1 and 2. We also show that only one Peterse…

Exploration in sparse reward reinforcement learning remains an open challenge. Many state-of-the-art methods use intrinsic motivation to complement the sparse extrinsic reward signal, giving the agent more opportunities to receive feedback during exploration. Commonly these signals are added as bonus rewards, which res…

New manifolds with negative curvature limit to one with negative curvature.

We define the intrinsic scale at which a network begins to reveal its identity as the scale at which subgraphs in the network (created by a random walk) are distinguishable from similar sized subgraphs in a perturbed copy of the network. We conduct an extensive study of intrinsic scale for several networks, ranging fro…

Characterizes intrinsic Lorentzian spaces using midpoint properties.

A graph is intrinsically knotted if every embedding contains a knotted cycle. It is known that intrinsically knotted graphs have at least 21 edges and that the KS graphs, $K_7$ and the 13 graphs obtained from $K_7$ by $\nabla Y$ moves, are the only minor minimal intrinsically knotted graphs with 21 edges. This set incl…

A Carnot group G is a connected, simply connected, nilpotent Lie group with stratified Lie algebra. Intrinsic regular surfaces in Carnot groups play the same role as C^1 surfaces in Euclidean spaces. As in Euclidean spaces, intrinsic regular surfaces can be locally defined in different ways: e.g. as non critical level …

New infinite family of 2-complexes intrinsically linked in 4D.

This article introduces the problem of finding intrinsic torsion varieties associated to G-structures on a fixed parallelizable Riemannian manifold. As an illustration, the intrinsic torsion varieties of orthogonal almost product structures are analysed on the Iwasawa manifold.

Study on ratio of intrinsic to extrinsic metrics and its relation to surface area.

Analyzes intrinsic time in financial markets, linking it to physical time.

Graphs and their complements are intrinsically knotted.

We classify which complete multipartite graphs are intrinsically chiral.

This paper addresses the following questions pertaining to the intrinsic dimensionality of any given image representation: (i) estimate its intrinsic dimensionality, (ii) develop a deep neural network based non-linear mapping, dubbed DeepMDS, that transforms the ambient representation to the minimal intrinsic space, an…

A graph is called intrinsically knotted if every embedding of the graph contains a knotted cycle. Johnson, Kidwell and Michael, and, independently, Mattman showed that intrinsically knotted graphs have at least 21 edges. Recently Lee, Kim, Lee and Oh, and, independently, Barsotti and Mattman, showed that $K_7$ and the …

Almost perimeter-minimizing boundaries in plentiful groups can be approximated by Lipschitz graphs.

Study of intrinsic sub-Laplacian for hypersurfaces in contact sub-Riemannian manifolds.

The intrinsic entropy model accurately estimates stock market volatility.

Study maps in semidirect products of groups, proving Lipschitz properties without intrinsic dilations.