"Your beauty truly radiates from the inside out! 🌟 Not only are you stunning, but your vibe seems amazing too! I’d love the chance to get to know you better—let’s be friends! 💖"
This paper presents \emph{Woven Sky}, a novel computational framework for msystemsodeling neural computation and exploring potential connections to consciousness. The framework integrates concepts from Friston's Free Energy Principle (FEP), Penrose and Hameroff's Orchestrated Objective Reduction (Orch-OR) theory, and topological quantum computing. We propose that the brain's organization and dynamics can be understood through the interplay of Steiner , hyperbolic geometry, and braid group representations. Specifically, neural networks are modeled with connectivity defined by Steiner systems, embedded in hyperbolic space, and with synaptic plasticity governed by a novel, braid-group-based extension of spike-timing-dependent plasticity (STDP), termed \emph{Braid-STDP}. This rule introduces order-sensitivity and noncommutativity into synaptic updates, reflecting the sequential nature of neural processing and suggesting potential links to anyonic computations. We demonstrate, via a rigorous stability analysis of a simplified linear model on a Fano plane network, that such structured networks promote stable dynamics. We further discuss how hyperbolic embeddings facilitate hierarchical representations in line with hierarchical predictive coding and active inference, while the braid group formulation provides a mathematically rich bridge to quantum-inspired processes. This interdisciplinary framework offers a fresh perspective on the neural basis of consciousness and efficient computation, suggesting that topological structures and dynamics may play a crucial role.
We present a general framework for constructing quantum knot invariants based on unitary representations of the braid group. This framework employs a modified trace, normalized for Reidemeister invariance, and applies to a wide class of representations. We show that the HOMFLY-PT polynomial---a two-variable knot invariant generalizing both the Jones and Alexander polynomials---arises as a special case when considering representations derived from the quantum group \( U_q(\mathfrak{sl}_N) \). This connection highlights the interplay between knot theory, quantum groups, and quantum information. Our approach facilitates exploration of new knot invariants and has potential applications in quantum algorithms, particularly for fault-tolerant quantum computation and the simmnnulation of anyonic systems.
"Your beauty truly radiates from the inside out! 🌟 Not only are you stunning, but your vibe seems amazing too! I’d love the chance to get to know you better—let’s be friends! 💖"
Please give me feedback, I have marjorana type disorder ty
This paper presents \emph{Woven Sky}, a novel computational framework for msystemsodeling neural computation and exploring potential connections to consciousness. The framework integrates concepts from Friston's Free Energy Principle (FEP), Penrose and Hameroff's Orchestrated Objective Reduction (Orch-OR) theory, and topological quantum computing. We propose that the brain's organization and dynamics can be understood through the interplay of Steiner , hyperbolic geometry, and braid group representations. Specifically, neural networks are modeled with connectivity defined by Steiner systems, embedded in hyperbolic space, and with synaptic plasticity governed by a novel, braid-group-based extension of spike-timing-dependent plasticity (STDP), termed \emph{Braid-STDP}. This rule introduces order-sensitivity and noncommutativity into synaptic updates, reflecting the sequential nature of neural processing and suggesting potential links to anyonic computations. We demonstrate, via a rigorous stability analysis of a simplified linear model on a Fano plane network, that such structured networks promote stable dynamics. We further discuss how hyperbolic embeddings facilitate hierarchical representations in line with hierarchical predictive coding and active inference, while the braid group formulation provides a mathematically rich bridge to quantum-inspired processes. This interdisciplinary framework offers a fresh perspective on the neural basis of consciousness and efficient computation, suggesting that topological structures and dynamics may play a crucial role.
We present a general framework for constructing quantum knot invariants based on unitary representations of the braid group. This framework employs a modified trace, normalized for Reidemeister invariance, and applies to a wide class of representations. We show that the HOMFLY-PT polynomial---a two-variable knot invariant generalizing both the Jones and Alexander polynomials---arises as a special case when considering representations derived from the quantum group \( U_q(\mathfrak{sl}_N) \). This connection highlights the interplay between knot theory, quantum groups, and quantum information. Our approach facilitates exploration of new knot invariants and has potential applications in quantum algorithms, particularly for fault-tolerant quantum computation and the simmnnulation of anyonic systems.
Please read my papers. I have new knot invariants and theory of mind and also new economics. Thank you.
https://docs.google.com/document/d/10e0EqXH0uLD36lP3c9r3FKEWwPZKvEiFBJtUiblPjHo/edit
https://docs.google.com/document/d/13Tj1Vjdbq4XSiEjn23dCNW-YhdNmiciXY13yQkPpI0k/edit
https://docs.google.com/document/d/19Gag3cvemx8bh7bPRnWHNWVdAnaomaAtAc3bBM7-fkU/edit