Unifilarisation of stochastic Mealy machines is an instance of coalgebraic determinisation over monads with support structure, producing causal stochastic behaviours rather than Moore-style output distributions.
Sheaf theory: from deep geometry to deep learning , shorttitle =
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SheafStain reinterprets VFM embeddings as sheaf sections within a Schrödinger Bridge, using co-pretrained H&E/IHC backbones to produce spatially and biologically coherent virtual staining evaluated on stitched 1024x1024 outputs for HER2, ER, PR, and Ki-67.
Copositive matrices with nondecreasing off-diagonal entries admit a PSD plus nonnegative decomposition, which implies exactness of a natural relaxation for separable quadratic optimization over the simplex.
Liability clearing in networks is modeled as global sections of a liability sheaf on directed hypergraphs, identified as a finite-limit construction with existence and uniqueness from lattice and metric theorems on payment objects.
A finite sheaf-theoretic framework ranks obstruction measures to identify when an AI agent's theory must deform within its language or extend to a new one, validated on a controlled transition benchmark.
Clef compiler applies fixed-point scaffolding and a functor from compilation poset to target category to preserve dimensional, grade, escape and numeric structure through MLIR lowering while adding compact-closed negative and fractional types.
The brain acts as a homology engine that minimizes topological complexity to convert high-entropy sensory flux into low-entropy invariant cognitive structure via parity between scaffolds and flows.
Sheaf theory and the sheaf Laplacian are proposed as a topological framework for data fusion and consensus in distributed sensing networks.
citing papers explorer
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Bayesian updates from coalgebraic determinisation
Unifilarisation of stochastic Mealy machines is an instance of coalgebraic determinisation over monads with support structure, producing causal stochastic behaviours rather than Moore-style output distributions.
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SheafStain: Sheaf-Theoretic Schr\"odinger Bridge for Spatially and Biologically Coherent Virtual Staining
SheafStain reinterprets VFM embeddings as sheaf sections within a Schrödinger Bridge, using co-pretrained H&E/IHC backbones to produce spatially and biologically coherent virtual staining evaluated on stitched 1024x1024 outputs for HER2, ER, PR, and Ki-67.
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Copositive Matrices with Ordered Off-Diagonal Entries
Copositive matrices with nondecreasing off-diagonal entries admit a PSD plus nonnegative decomposition, which implies exactness of a natural relaxation for separable quadratic optimization over the simplex.
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Clearing in Liability Networks via Sheaves on Directed Hypergraphs
Liability clearing in networks is modeled as global sections of a liability sheaf on directed hypergraphs, identified as a finite-limit construction with existence and uniqueness from lattice and metric theorems on payment objects.
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Sheaf-Theoretic Transport and Obstruction for Detecting Scientific Theory Shift in AI Agents
A finite sheaf-theoretic framework ranks obstruction measures to identify when an AI agent's theory must deform within its language or extend to a new one, validated on a controlled transition benchmark.
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Fixed-Point Scaffolding in the Clef Programming Language
Clef compiler applies fixed-point scaffolding and a functor from compilation poset to target category to preserve dimensional, grade, escape and numeric structure through MLIR lowering while adding compact-closed negative and fractional types.
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The Homological Brain: Parity Principle and Amortized Inference
The brain acts as a homology engine that minimizes topological complexity to convert high-entropy sensory flux into low-entropy invariant cognitive structure via parity between scaffolds and flows.
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The Sheaf Laplacian: A Topological Framework for Data Fusion and Consensus in Distributed Sensing Networks
Sheaf theory and the sheaf Laplacian are proposed as a topological framework for data fusion and consensus in distributed sensing networks.