Related papers: Inverse algorithm and triple point diagrams
Brane tilings are efficient mnemonics for Lagrangians of N=2 Chern-Simons-matter theories. Such theories are conjectured to arise on M2-branes probing singular toric Calabi-Yau fourfolds. In this paper, a simple modification of the…
Graphene quantum dots provide a platform for manipulating electron behaviors in two-dimensional (2D) Dirac materials. Most previous works were of the "forward" type in that the objective was to solve various confinement, transport and…
We prove for the first time that, if a linear inverse problem exhibits a group symmetry structure, gradient-based optimizers can be designed to exploit this structure for faster convergence rates. This theoretical finding demonstrates the…
Brane Tilings represent one of the largest classes of superconformal theories with known gravity duals in 3+1 and also 2+1 dimensions. They provide a useful link between a large class of quiver gauge theories and their moduli spaces, which…
We present an algorithm for solving inverse problems on graphs analogous to those arising in diffuse optical tomography for continuous media. In particular, we formulate and analyze a discrete version of the inverse Born series, proving…
We introduce a correspondence between dimer models (and hence superconformal quivers) and the quantum Teichmuller space of the Riemann surfaces associated to them by mirror symmetry. Via the untwisting map, every brane tiling gives rise to…
Symmetry is a fundamental tool in the exploration of a broad range of complex systems. In machine learning symmetry has been explored in both models and data. In this paper we seek to connect the symmetries arising from the architecture of…
In this note, we give a closed formula for the partition function of the dimer model living on a (2 x n) strip of squares or hexagons on the torus for arbitrary even n. The result is derived in two ways, by using a Potts model like…
Dimer models have been used in string theory to construct path algebras with relations that are 3-dimensional Calabi-Yau Algebras. These constructions result in algebras that share some specific properties: they are finitely generated…
In the past three decades, the study of rhombus tilings and domino tilings of various plane regions has been a thriving subfield of enumerative combinatorics. Physicists classify such work as the study of dimer covers of finite graphs. In…
We propose a geometric counterpart of the dimer model on bipartite graphs. A state of our model consists of a choice of a point for each white vertex and hyperplane for each black vertex. This data is subject to certain conditions…
In this paper we develop constructive invertibility conditions for the twisted convolution. Our approach is based on splitting the twisted convolution with rational parameters into a finite number of weighted convolutions, which can be…
Image reconstruction under multiple light scattering is crucial in a number of applications such as diffraction tomography. The reconstruction problem is often formulated as a nonconvex optimization, where a nonlinear measurement model is…
Three-branes at a given toric Calabi-Yau singularity lead to different phases of the conformal field theory related by toric (Seiberg) duality. Using the dimer model/brane tiling description in terms of bipartite graphs on a torus, we find…
Gradient descent optimizations and backpropagation are the most common methods for training neural networks, but they are computationally expensive for real time applications, need high memory resources, and are difficult to converge for…
An infinite class of $4d$ $\mathcal{N}=1$ gauge theories can be engineered on the worldvolume of D3-branes probing toric Calabi-Yau 3-folds. This kind of setup has multiple applications, ranging from the gauge/gravity correspondence to…
We present a geometrical approach for studying dimers. We introduce a connection for dimer problems on bipartite and non-bipartite graphs. In the bipartite case the connection is flat but has non-trivial ${\bf Z}_2$ holonomy round certain…
Brane tilings describe Lagrangians (vector multiplets, chiral multiplets, and the superpotential) of four dimensional $\mathcal{N}=1$ supersymmetric gauge theories. These theories, written in terms of a bipartite graph on a torus,…
Data inconsistency leads to a slow training process when deep neural networks are used for the inverse design of photonic devices, an issue that arises from the fundamental property of non-uniqueness in all inverse scattering problems. Here…
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part (arXiv:2501.15657), we discused…