Paper List
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Translating Measures onto Mechanisms: The Cognitive Relevance of Higher-Order Information
This review addresses the core challenge of translating abstract higher-order information theory metrics (e.g., synergy, redundancy) into defensible, ...
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Emergent Bayesian Behaviour and Optimal Cue Combination in LLMs
This paper addresses the critical gap in understanding whether LLMs spontaneously develop human-like Bayesian strategies for processing uncertain info...
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Vessel Network Topology in Molecular Communication: Insights from Experiments and Theory
This work addresses the critical lack of experimentally validated channel models for molecular communication within complex vessel networks, which is ...
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Modulation of DNA rheology by a transcription factor that forms aging microgels
This work addresses the fundamental question of how the transcription factor NANOG, essential for embryonic stem cell pluripotency, physically regulat...
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Imperfect molecular detection renormalizes apparent kinetic rates in stochastic gene regulatory networks
This paper addresses the core challenge of distinguishing genuine stochastic dynamics of gene regulatory networks from artifacts introduced by imperfe...
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PanFoMa: A Lightweight Foundation Model and Benchmark for Pan-Cancer
This paper addresses the dual challenge of achieving computational efficiency without sacrificing accuracy in whole-transcriptome single-cell represen...
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Beyond Bayesian Inference: The Correlation Integral Likelihood Framework and Gradient Flow Methods for Deterministic Sampling
This paper addresses the core challenge of calibrating complex biological models (e.g., PDEs, agent-based models) with incomplete, noisy, or heterogen...
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Contrastive Deep Learning for Variant Detection in Wastewater Genomic Sequencing
This paper addresses the core challenge of detecting viral variants in wastewater sequencing data without reference genomes or labeled annotations, ov...
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.