Paper List
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A Theoretical Framework for the Formation of Large Animal Groups: Topological Coordination, Subgroup Merging, and Velocity Inheritance
This paper addresses the core problem of how large, coordinated animal groups form in nature, challenging the classical view of gradual aggregation by...
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CONFIDE: Hallucination Assessment for Reliable Biomolecular Structure Prediction and Design
This paper addresses the critical limitation of current protein structure prediction models (like AlphaFold3) where high-confidence scores (pLDDT) can...
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Generative design and validation of therapeutic peptides for glioblastoma based on a potential target ATP5A
This paper addresses the critical bottleneck in therapeutic peptide design: how to efficiently optimize lead peptides with geometric constraints while...
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Pharmacophore-based design by learning on voxel grids
This paper addresses the computational bottleneck and limited novelty in conventional pharmacophore-based virtual screening by introducing a voxel cap...
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Human-Centred Evaluation of Text-to-Image Generation Models for Self-expression of Mental Distress: A Dataset Based on GPT-4o
This paper addresses the critical gap in evaluating how AI-generated images can effectively support cross-cultural mental distress communication, part...
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ANNE Apnea Paper
This paper addresses the core challenge of achieving accurate, event-level sleep apnea detection and characterization using a non-intrusive, multimoda...
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DeeDeeExperiment: Building an infrastructure for integrating and managing omics data analysis results in R/Bioconductor
This paper addresses the critical bottleneck of managing and organizing the growing volume of differential expression and functional enrichment analys...
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Cross-Species Antimicrobial Resistance Prediction from Genomic Foundation Models
This paper addresses the core challenge of predicting antimicrobial resistance across phylogenetically distinct bacterial species, where traditional m...
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.