We show a relationship between the non-acyclic Reidemeister torsion and a zero of the acyclic Reidemeister torsion for a lambda-regular SU(2) or SL(2, C)-representation of a knot group. Then we give a method to calculate the non-acyclic Reidemeister torsion of a knot exterior. We calculate a new example and investigate…
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We explore non-acyclic GFlowNets in discrete settings.
problem Training and understanding non-acyclic GFlowNets in discrete environments.
method Relaxing acyclicity assumption, simpler theoretical framework, novel theoretical insights, experimental validation.
result Theoretical and experimental validation of non-acyclic GFlowNets in discrete environments.
Study non-acyclic SL2-representations of twist knots and their L-functions.
problem Characterize SL2-representations of twist knots and their properties.
method Character variety, Reidemeister torsion, Chebyshev polynomials, and L-functions.
result Non-acyclic SL2-representations lie on the line x=y in character variety, and their orders are related to (-3)-Dehn surgery.
New invariant from non-acyclic flat connections.
problem Constructing a higher-loop perturbative invariant.
method Integral of a Chern-Simons volume form over moduli space of flat connections.
result Generalization of Chern-Simons invariant to non-acyclic connections.
We consider the Reidemeister torsion associated with SL(2, C)-representations of a knot group. A bifurcation point in the SL(2, C)-character variety of a knot group is a character which is given by both an abelian SL(2, C)-representation and a non-abelian one. We show that there exist limits of the non-acyclic Reidemei…
Generalizes Hodge correlators using quantum master equation concepts.
problem Developing a mathematical framework for non-acyclic Chern-Simons theory.
method Introduces a DG Lie algebra of uni-trivalent graphs with loops satisfying a Maurer-Cartan equation.
result Arithmetic analogue of effective action and quantum master equation.
Multiplicity of non-acyclic -representations and L-functions of the odd-twisted Whitehead linksmath.GT
Study multiplicity of non-acyclic SL2-representations and L-functions of Whitehead links.
problem Understanding the multiplicity of non-acyclic SL2-representations and their L-functions.
method Geometric interpretation of Reidemeister torsion divisors and application to L-functions.
result Prove multiplicity two for odd-twisted Whitehead links.
Generative Flow Networks solve shortest path problems in graphs.
problem Finding shortest paths in graphs.
method Generative Flow Networks with flow regularization.
result Training a GFlowNet can solve pathfinding problems in arbitrary graphs.
We extend the Chern-Simons perturbative invariant of Axelrod and Singer to non-acyclic connections. We construct a solution of the quantum master equation on the space of functions on the cohomology of the connection. We prove that this solution is well defined up to master homotopy. We discuss also invariants of links…
We introduce non-acyclic -torsion of a 3-manifold with toroidal boundary as an extension of J. Porti's -torsion, and present an explicit formula of the -torsion of a mapping torus for a surface with punctures, by using the higher Teichmüler theory due to V. Fock …
Associated to Legendrian links in the standard contact three-space, Ruling polynomials are Legendrian isotopy invariants, which also compute augmentation numbers, that is, the points-counting of augmentation varieties for Legendrian links (up to a normalized factor) \cite{HR15}. In this article, we generalize this pict…
Adaptive stopping in MCMC using classifier-based dynamics
problem Sampling from complex, unnormalized probability densities
method Training state-dependent neural classifiers
result Significant reduction in average trajectory lengths
EGFs use ergodicity to simplify generative flows for easier training and imitation learning.
problem Challenges in training generative flows, especially in continuous settings and for imitation learning.
method EGFs leverage ergodicity to build simple flows with universality guarantees and tractable FM loss. They introduce a KL-weakFM loss for IL training without a separate reward model.
result EGFs simplify generative flow training and enable effective imitation learning.