相关论文: Constructing physically intuitive graph invariants

The fundamental challenge in causal induction is to infer the underlying graph structure given observational and/or interventional data. Most existing causal induction algorithms operate by generating candidate graphs and evaluating them…

One of the main questions that arise when studying random and quasi-random structures is which properties P are such that any object that satisfies P "behaves" like a truly random one. In the context of graphs, Chung, Graham, and Wilson…

The analysis of observable phenomena (for instance, in biology or physics) allows the detection of dynamical behaviors and, conversely, starting from a desired behavior allows the design of objects exhibiting that behavior in engineering.…

The invariance of natural objects under perceptual changes is possibly encoded in the brain by symmetries in the graph of synaptic connections. The graph can be established via unsupervised learning in a biologically plausible process…

It is demonstrated that in gate-based quantum computing architectures quantum walk is a natural mathematical description of quantum gates. It originates from field-matter interaction driving the system, but is not attached to specific qubit…

This paper studies how to capture dependency graph structures from real data which may not be Gaussian. Starting from marginal loss functions not necessarily derived from probability distributions, we utilize an additive…

We construct graph-valued analogues of the Kuperberg sl(3) and G2 invariants for virtual knots. The restriction of the sl(3) or G2 invariants for classical knots coincides with the usual Homflypt sl(3) invariant and G2 invariants. For…

We analyze the effect of twists on the electronic structure of configurations of infinite stacks of graphene layers. We focus on three different cases: an infinite stack where each layer is rotated with respect to the previous one by a…

We strengthen and put in a broader perspective previous results of the first two authors on colliding permutations. The key to the present approach is a new non-asymptotic invariant for graphs.

We introduce an elementary quantum system consisting of a set of spins on a graph and a particle hopping between its nodes. The quantum state is build sequentially, applying a unitary transformation that couples neighboring spins and, at a…

We consider the ring I_n of polynomial invariants over weighted graphs on n vertices. Our primary interest is the use of this ring to define and explore algebraic versions of isomorphism problems of graphs, such as Ulam's reconstruction…

Random graphs have proven to be one of the most important and fruitful concepts in modern Combinatorics and Theoretical Computer Science. Besides being a fascinating study subject for their own sake, they serve as essential instruments in…

Quantum knot invariants (like colored HOMFLY-PT or Kauffman polynomials) are a distinguished class of non-perturbative topological invariants. Any known way to construct them (via Chern-Simons theory or quantum R-matrix) starts with a…

We expand on some invariants used for classifying nonselfadjoint operator algebras. Specifically to nonselfadjoint operator algebras which have a conditional expectation onto a commutative diagonal we construct an edge-colored directed…

Natural physical, chemical, and biological dynamical systems are often complex, with heterogeneous components interacting in diverse ways. We show how simple graph neural networks can be designed to jointly learn the interaction rules and…

Quantum computing (QC) is a new computational paradigm whose foundations relate to quantum physics. Notable progress has been made, driving the birth of a series of quantum-based algorithms that take advantage of quantum computational…

This is lecture notes for a course given at the PCMI Summer School "Quantum Field Theory and Manifold Invariants" (July 1 -- July 5, 2019). I describe basics of gauge-theoretic approach to construction of invariants of manifolds. The main…

Virtual knot theory is a generalization (discovered by the author in 1996) of knot theory to the study of all oriented Gauss codes. (Classical knot theory is a study of planar Gauss codes.) Graph theory studies non-planar graphs via…

We address the effects of natural three-qubit interactions on the computational power of one-way quantum computation (\QC). A benefit of using more sophisticated entanglement structures is the ability to construct compact and economic…

We construct quantum K-invariants in non-archimedean analytic geometry. Contrary to the classical approach in algebraic geometry via perfect obstruction theory, we build on our previous works on the foundations of derived non-archimedean…