Paper List
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Exactly Solvable Population Model with Square-Root Growth Noise and Cell-Size Regulation
This paper addresses the fundamental gap in understanding how microscopic growth fluctuations, specifically those with size-dependent (square-root) no...
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Assessment of Simulation-based Inference Methods for Stochastic Compartmental Models
This paper addresses the core challenge of performing accurate Bayesian parameter inference for stochastic epidemic models when the likelihood functio...
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Realistic Transition Paths for Large Biomolecular Systems: A Langevin Bridge Approach
This paper addresses the core challenge of generating physically realistic and computationally efficient transition paths between distinct protein con...
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MoRSAIK: Sequence Motif Reactor Simulation, Analysis and Inference Kit in Python
This work addresses the computational bottleneck in simulating prebiotic RNA reactor dynamics by developing a Python package that tracks sequence moti...
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The BEAT-CF Causal Model: A model for guiding the design of trials and observational analyses of cystic fibrosis exacerbations
This paper addresses the critical gap in cystic fibrosis exacerbation management by providing a formal causal framework that integrates expert knowled...
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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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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...
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.