Paper List
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Autonomous Agents Coordinating Distributed Discovery Through Emergent Artifact Exchange
This paper addresses the fundamental limitation of current AI-assisted scientific research by enabling truly autonomous, decentralized investigation w...
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D-MEM: Dopamine-Gated Agentic Memory via Reward Prediction Error Routing
This paper addresses the fundamental scalability bottleneck in LLM agentic memory systems: the O(N²) computational complexity and unbounded API token ...
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Countershading coloration in blue shark skin emerges from hierarchically organized and spatially tuned photonic architectures inside skin denticles
This paper solves the core problem of how blue sharks achieve their striking dorsoventral countershading camouflage, revealing that coloration origina...
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Human-like Object Grouping in Self-supervised Vision Transformers
This paper addresses the core challenge of quantifying how well self-supervised vision models capture human-like object grouping in natural scenes, br...
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Hierarchical pp-Adic Framework for Gene Regulatory Networks: Theory and Stability Analysis
This paper addresses the core challenge of mathematically capturing the inherent hierarchical organization and multi-scale stability of gene regulator...
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Towards unified brain-to-text decoding across speech production and perception
This paper addresses the core challenge of developing a unified brain-to-text decoding framework that works across both speech production and percepti...
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Dual-Laws Model for a theory of artificial consciousness
This paper addresses the core challenge of developing a comprehensive, testable theory of consciousness that bridges biological and artificial systems...
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Pulse desynchronization of neural populations by targeting the centroid of the limit cycle in phase space
This work addresses the core challenge of determining optimal pulse timing and intensity for desynchronizing pathological neural oscillations when the...
Covering Relations in the Poset of Combinatorial Neural Codes
Pacific Northwest National Laboratory | Florida Atlantic University
30秒速读
IN SHORT: This work addresses the core challenge of navigating the complex poset structure of neural codes to systematically test the conjecture linking convex neural codes to representable oriented matroids.
核心创新
- Methodology Provides the first complete characterization of upward covering relations in the poset P_Code of combinatorial neural codes.
- Theory Introduces a constructive method to generate all codes that cover a given neural code, based on the concept of isolated subsets within its intersection completion.
- Methodology Establishes a key lemma (Lemma 3.1) showing that a morphism between codes uniquely extends to a morphism between their intersection completions, preserving surjectivity.
主要结论
- A code C covers a code D in P_Code if and only if its intersection completion C_hat covers D_hat (Lemma 3.3).
- If C covers D, then C_hat is isomorphic to D_hat_[I] for some isolated subset I ⊆ D_hat (Theorem 3.5).
- All codes covering a given code D can be constructed via four explicit types of operations on isolated subsets of D_hat, as defined in Definition 3.9 and Table 1.
摘要: A combinatorial neural code is a subset of the power set 2[n] on [n]={1,…,n}, in which each 1≤i≤n represents a neuron and each element (codeword) represents the co-firing event of some neurons. Consider a space X⊆ℝd, simulating an animal’s environment, and a collection 𝒰={U1,…,Un} of open subsets of X. Each Ui⊆X simulates a place field which is a specific region where a place cell i is active. Then, the code of 𝒰 in X is defined as code(𝒰,X)={σ⊆[n]|⋂i∈σUi∖⋃j∉σUj≠∅}. If a neural code 𝒞=code(𝒰,X) for some X and 𝒰, we say 𝒞 has a realization of open subsets of some space X. Although every combinatorial neural code obviously has a realization by some open subsets, determining whether it has a realization by some open convex subsets remains unsolved. Many studies attempted to tackle this decision problem, but only partial results were achieved. In fact, a previous study showed that the decision problem of convex neural codes is NP-hard. Furthermore, the authors of this study conjectured that every convex neural code can be realized as a minor of a neural code arising from a representable oriented matroid, which can lead to an equivalence between convex and polytope convex neural codes. Even though this conjecture has been confirmed in dimension two, its validity in higher dimensions is still unknown. To advance the investigation of this conjecture, we provide a complete characterization of the covering relations within the poset 𝐏𝐂𝐨𝐝𝐞 of neural codes.