Steven Rayan
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A Graph-Based Classical and Quantum Approach to Deterministic L-System Inference Open
L-systems can be made to model and create simulations of many biological processes, such as plant development. Finding an L-system for a given process is typically solved by hand, by experts, in a massively time-consuming process. It would…
View article: Reconstructing Biological Pathways by Applying Selective Incremental Learning to (Very) Small Language Models
Reconstructing Biological Pathways by Applying Selective Incremental Learning to (Very) Small Language Models Open
The use of generative artificial intelligence (AI) models is becoming ubiquitous in many fields. Though progress continues to be made, general purpose large language AI models (LLM) show a tendency to deliver creative answers, often called…
View article: GPU-accelerated Modeling of Biological Regulatory Networks
GPU-accelerated Modeling of Biological Regulatory Networks Open
The complex regulatory dynamics of a biological network can be succinctly captured using discrete logic models. Given even sparse time-course data from the system of interest, previous work has shown that global optimization schemes are su…
Identifying Protein Co-regulatory Network Logic by Solving B-SAT Problems through Gate-based Quantum Computing Open
There is growing awareness that the success of pharmacologic interventions on living organisms is significantly impacted by context and timing of exposure. In turn, this complexity has led to an increased focus on regulatory network dynami…
Direct entanglement ansatz learning (DEAL) with ZNE on error-prone superconducting qubits Open
Quantum combinatorial optimization algorithms typically face challenges due to complex optimization landscapes featuring numerous local minima, exponentially scaling latent spaces, and susceptibility to quantum hardware noise. In this stud…
Nakajima quiver bundles Open
We introduce the notion of a Nakajima bundle representation. Given a labelled quiver and a variety or manifold $X$, such a representation involves an assignment of a complex vector bundle on $X$ to each node of the doubled quiver; to the e…
A Graph-Based Classical and Quantum Approach to Deterministic L-System Inference Open
L-systems can be made to model and create simulations of many biological processes, such as plant development. Finding an L-system for a given process is typically solved by hand, by experts, in a massively time-consuming process. It would…
Very stable and wobbly loci for elliptic curves Open
We explore very stable and wobbly bundles, twisted in a particular sense by a line bundle, over complex algebraic curves of genus $1$. We verify that twisted stable bundles on an elliptic curve are not very stable for any positive twist. W…
Asynchronous Telegate and Teledata Protocols for Distributed Quantum Computing Open
The cost of distributed quantum operations such as the telegate and teledata protocols is high due to latencies from distributing entangled photons and classical information. This paper proposes an extension to the telegate and teledata pr…
Asynchronous Telegate and Teledata Protocols for Distributed Quantum Computing Open
The cost of distributed quantum operations such as the telegate and teledata protocols is high due to latencies from distributing entangled photons and classical information. This paper proposes an extension to the telegate and teledata pr…
Moduli stacks of quiver bundles with applications to Higgs bundles Open
We provide a general method for constructing moduli stacks whose points are diagrams of vector bundles over a fixed base, indexed by a fixed simplicial set -- that is, quiver bundles of a fixed shape. We discuss some constraints on the bas…
Topological recursion and variations of spectral curves for twisted Higgs bundles Open
Prior works relating meromorphic Higgs bundles to topological recursion, in particular those of Dumitrescu-Mulase, have considered non-singular models that allow the recursion to be carried out on a smooth Riemann surface. We start from an…
A generalized spectral correspondence Open
We explore a strong categorical correspondence between isomorphism classes of sheaves of arbitrary rank on a given algebraic curve and twisted pairs on another algebraic curve, mostly from a linear-algebraic standpoint. In a particular app…
Kirwan surjectivity and Lefschetz-Sommese theorems for a generalized hyperkähler reduction Open
Let $G$ be a compact Lie group. We study a class of Hamiltonian $(G \times S^{1})$-manifolds decorated with a function $s$ with certain equivariance properties, under conditions on the $G$-action which we call of (semi-)linear type. In thi…
TQFTs and quantum computing Open
Quantum computing is captured in the formalism of the monoidal subcategory of $\textbf{Vect}_{\mathbb C}$ generated by $\mathbb C^2$ -- in particular, quantum circuits are diagrams in $\textbf{Vect}_{\mathbb C}$ -- while topological quantu…
On the hyperbolic Bloch transform Open
Motivated by recent theoretical and experimental developments in the physics of hyperbolic crystals, we study the noncommutative Bloch transform of Fuchsian groups that we call the hyperbolic Bloch transform. First, we prove that the hyper…
Crystallography of hyperbolic lattices Open
Hyperbolic lattices are a revolutionary platform for tabletop simulations of holography and quantum physics in curved space and facilitate efficient quantum error correcting codes. Their underlying geometry is non-Euclidean, and the absenc…
Automorphic Bloch theorems for hyperbolic lattices Open
Significance Recent experiments in circuit quantum electrodynamics and electric circuit networks have demonstrated the coherent propagation of wave-like excitations on hyperbolic lattices. The negative curvature of space that underlies suc…
All 81 crepant resolutions of a finite quotient singularity are hyperpolygon spaces Open
We demonstrate that the linear quotient singularity for the exceptional subgroup G in Sp(4,C) of order 32 is isomorphic to an affine quiver variety for a 5-pointed star-shaped quiver. This allows us to construct uniformly all 81 projective…
Hyperbolic band theory Open
The band theory of solids—including Bloch waves, crystal momentum, and energy bands—is generalized to hyperbolic lattices.
Automorphic Bloch theorems for finite hyperbolic lattices Open
Hyperbolic lattices are a new form of synthetic quantum matter in which particles effectively hop on a discrete tessellation of two-dimensional hyperbolic space, a non-Euclidean space of uniform negative curvature. To describe the single-p…
Toric co-Higgs bundles on toric varieties Open
Starting from the data of a nonsingular complex projective toric variety, we define an associated notion of toric co-Higgs bundle. We provide a Lie-theoretic classification of these objects by studying the interaction between Klyachko's fa…
The Kapustin-Witten equations and nonabelian Hodge theory Open
Arising from a topological twist of $\mathcal{N} = 4$ super Yang-Mills theory are the Kapustin-Witten equations, a family of gauge-theoretic equations on a four-manifold parametrized by $t\in\mathbb{P}^1$. The parameter corresponds to a li…
Homogeneous Higgs and co-Higgs bundles on Hermitian symmetric spaces Open
We define homogeneous principal Higgs and co-Higgs bundles over irreducible Hermitian symmetric spaces of compact type. We provide a classification for each type of object up to isomorphism, which in each case can be interpreted as definin…
Moduli Spaces of Generalized Hyperpolygons Open
We introduce the notion of generalized hyperpolygon, which arises as a representation, in the sense of Nakajima, of a comet-shaped quiver. We identify these representations with rigid geometric figures, namely pairs of polygons: one in the…
Hyperbolic band theory Open
The notions of Bloch wave, crystal momentum, and energy bands are commonly regarded as unique features of crystalline materials with commutative translation symmetries. Motivated by the recent realization of hyperbolic lattices in circuit …
The Calogero-Franc¸oise Integrable System: Algebraic Geometry, Higgs Fields, and the Inverse Problem Open
We review the Calogero-Fran\\c{c}oise integrable system, which is a\ngeneralization of the Camassa-Holm system. We express solutions as (twisted)\nHiggs bundles, in the sense of Hitchin, over the projective line. We use this\npoint of view…