Paper List
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GOPHER: Optimization-based Phenotype Randomization for Genome-Wide Association Studies with Differential Privacy
This paper addresses the core challenge of balancing rigorous privacy protection with data utility when releasing full GWAS summary statistics, overco...
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Real-time Cricket Sorting By Sex A low-cost embedded solution using YOLOv8 and Raspberry Pi
This paper addresses the critical bottleneck in industrial insect farming: the lack of automated, real-time sex sorting systems for Acheta domesticus ...
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Training Dynamics of Learning 3D-Rotational Equivariance
This work addresses the core dilemma of whether to use computationally expensive equivariant architectures or faster symmetry-agnostic models with dat...
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Fast and Accurate Node-Age Estimation Under Fossil Calibration Uncertainty Using the Adjusted Pairwise Likelihood
This paper addresses the dual challenge of computational inefficiency and sensitivity to fossil calibration errors in Bayesian divergence time estimat...
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Few-shot Protein Fitness Prediction via In-context Learning and Test-time Training
This paper addresses the core challenge of accurately predicting protein fitness with only a handful of experimental observations, where data collecti...
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scCluBench: Comprehensive Benchmarking of Clustering Algorithms for Single-Cell RNA Sequencing
This paper addresses the critical gap of fragmented and non-standardized benchmarking in single-cell RNA-seq clustering, which hinders objective compa...
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Simulation and inference methods for non-Markovian stochastic biochemical reaction networks
This paper addresses the computational bottleneck of simulating and performing Bayesian inference for non-Markovian biochemical systems with history-d...
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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...
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.