Paper List
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SSDLabeler: Realistic semi-synthetic data generation for multi-label artifact classification in EEG
This paper addresses the core challenge of training robust multi-label EEG artifact classifiers by overcoming the scarcity and limited diversity of ma...
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Decoding Selective Auditory Attention to Musical Elements in Ecologically Valid Music Listening
This paper addresses the core challenge of objectively quantifying listeners' selective attention to specific musical components (e.g., vocals, drums,...
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Physics-Guided Surrogate Modeling for Machine Learning–Driven DLD Design Optimization
This paper addresses the core bottleneck of translating microfluidic DLD devices from research prototypes to clinical applications by replacing weeks-...
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Mechanistic Interpretability of Antibody Language Models Using SAEs
This work addresses the core challenge of achieving both interpretability and controllable generation in domain-specific protein language models, spec...
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The Effective Reproduction Number in the Kermack-McKendrick model with age of infection and reinfection
This paper addresses the challenge of accurately estimating the time-varying effective reproduction number ℛ(t) in epidemics by incorporating two crit...
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Fluctuating Environments Favor Extreme Dormancy Strategies and Penalize Intermediate Ones
This paper addresses the core challenge of determining how organisms should tune dormancy duration to match the temporal autocorrelation of their envi...
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Covering Relations in the Poset of Combinatorial Neural Codes
This work addresses the core challenge of navigating the complex poset structure of neural codes to systematically test the conjecture linking convex ...
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Revealing stimulus-dependent dynamics through statistical complexity
This paper addresses the core challenge of detecting stimulus-specific patterns in neural population dynamics that remain hidden to traditional variab...
Covering Relations in the Poset of Combinatorial Neural Codes
Pacific Northwest National Laboratory | Florida Atlantic University
The 30-Second View
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.
Innovation (TL;DR)
- 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.
Key conclusions
- 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.
Abstract: 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.