H.Wanhong

It appears that we require a universal language capable of articulating both the structural outcomes of various generative systems and the processes by which such structures are produced.

Among existing paradigms, the framework of dynamical systems is arguably one of the most powerful. Nevertheless, at the level of structure generation, it typically manifests as linear or quasi-linear evolution within a continuous or discrete state space. As a result, it provides a rather unnatural representation for structures exhibiting fractal, hierarchical, or self-similar organization. Moreover, dynamical systems generally presuppose a fixed spatiotemporal background, rather than constructing the spatiotemporal dimensions from the generative process itself. From an ontological standpoint, they lack an account of “structure generation” as a mode of existence.

In contrast, generative grammar offers a distinct perspective: centered on symbolic rewriting rules, it effectively characterizes the hierarchical generation of structure. However, its symbolic alphabet is typically discrete and finite, rendering it cumbersome when applied to the generation of continuous or smooth geometric structures. To extend its applicability to such cases, one must treat sub-continuous geometric configurations as “words” or primitive units, giving rise to frameworks commonly referred to as geometric grammars.

Beyond these established frameworks, the intersection of Group Field Theory (GFT) and condensed matter theory appears to offer a particularly promising avenue. GFT provides a formalism for describing the generation of discrete structures without positing concrete entities as ontological primitives. Instead, it takes abstract algebraic structures—groups—as the fundamental ontology, and, crucially, it does not presuppose any pre-existing spatiotemporal background.

Complementarily, condensed matter theory supplies a mechanism for the emergent transition from discrete to continuous spacetime. Through the introduction of condensate states and mean-field approximations, GFT can, in the macroscopic limit, manifest continuous and smooth spacetime geometries.

The combination of abstract ontological commitment (eschewing predefined concrete entities), background independence, and the capacity to model both discrete and continuous structures renders Group Field Theory, in conjunction with condensed matter theory, a compelling candidate for a general framework of structural generation.

Wanhong Huang, Group Field Theory of Universal Grammar Symmetry Breaking and Language System Emergence, 2025, 10.17605/OSF.IO/N8Y9B

In physics, a symmetry transformation refers to an operation that does not alter the properties or fundamental laws of a system [1]. Based on this notion of “preservation,” we may introduce the concept of symmetry into formal language systems to analyze the stability and transformation of syntax and semantics.
This work presents a preliminary discussion, attempting to explore syntactic and semantic symmetries within the framework of formal language theory.

Parallel MRI reconstruction relies heavily on knowing the sensitivity of each coil. ESPIRiT offers a data-driven way to learn these sensitivities, directly from acquired k-space data. Let’s break down the ideas step by step.

1. The Key Idea: Coupling Between Coils

In multi-coil MRI, the signals from different coils are correlated. ESPIRiT leverages these correlations to learn coil sensitivities.

• Each coil is a sensor providing a different view of the same underlying image.
• Instead of assuming a coil model, ESPIRiT observes the data to learn how coils are coupled.

2. Capturing Local Correlations: k-Space Patches

To extract these couplings:

1. Take small patches in $k$-space across all coils.
2. Flatten and stack them into a matrix $A$, where each row represents one patch.
3. Solve for the null-space vector $h$, which acts as a convolution kernel in k-space:

$$
(A∗h)≈0
$$

• $h$ also represents a constraint that all valid k-space patches satisfy.
• Intuitively, $h$ is the “language” of coil relationships—any valid $k$-space data should approximately satisfy it.

[Paper Note] Spiking neural P systems: main ideas and results (1)

Title: spiking neural P systems: main ideas and results

Authors: Alberto Leporati, Giancarlo Mauri, Claudio Zandron

Citation: Leporati, A., Mauri, G., & Zandron, C. (2022). Spiking neural P systems: main ideas and results. Natural Computing: An International Journal, 21(4), 629–649.

Background

Spiking neural P system is a distributed language processing system.

Membrane system also called P system.

Original definition of P system:

• A membrane structure
  • Composed by several cell-mem-branes, hierarchically embedded in a main membrane called the skin membrane.
  • Membranes delimit regions.
  • Membrane can contains objects.
  • Objects evolve according rules.
• Development of P systems
  • Tissue P systems
    • substituting tree-like hierarchy into undirected graph.
  • Spiking neural P systems
    • Neurons are nodes.
    • Arrows are synapse-like.

Paper Information

Title: An electronic neuromorphic system for real-time detection of high frequency oscillations (HFO) in intracranial EEG [1]

Authors: Mohammadali Sharifshazileh, Karla Burelo, Johannes Sarnthein, Giacomo Indiveri

Year: 2021

DOI: 10.1038/s41467-021-23342-2

Citation: Sharifshazileh, M., Burelo, K., Sarnthein, J.et al.An electronic neuromorphic system for real-time detection of high frequency oscillations (HFO) in intracranial EEG.Nat Commun12**, 3095 (2021). https://doi.org/10.1038/s41467-021-23342-2

Brief Introduction

High Frequency Oscillations (HFO) phenomenon in the context of EEG signal processing tasks refers to the observation of EEG at $80$-$500$ Hz from brain activity [1].HFO has shown a correlation with seizures in epileptic disorders, and has been utilized in several applications as a detection of epileptogenic zone as a kind of biomarkers.

In biological neural networks, the membrane potential of nerve cells changes over time and generates action potentials (spikes) under certain conditions. These spikes propagate through the synapse to the postsynaptic neuron. Artificial neural networks that simulate such behavior are also known as Spiking Neural Network (SNN).

Title: The Grammar of the Ising Model: A New Complexity Hierarchy

Authors: Tobias Reinhart, Gemma De las Cuevas

Citation: Tobias Reinhart, & Gemma De las Cuevas (2022). The Grammar of the Ising Model: A New Complexity Hierarchy.

To explore the complexity of the Ising model, an effective approach is to analyze the complexity of its Ground State Energy (GSE) problem. Specifically, the GSE problem is defined as follows: given an interaction graph and a specific energy value, determine whether there exists an Ising spin configuration such that the system’s energy is lower than the given value.

The decidability of the GSE problem fundamentally depends on the planarity of the interaction graph of Ising sites, which divides the complexity of the Ising model into two categories. However, this classification method only considers the planarity of the interaction graph, which has certain limitations. To address this, Tobias Reinhart and colleagues, in their study, proposed an analysis method for the Ising model based on formal language modeling, from the perspectives of formal languages, generative grammars, and computational complexity theory. By associating the language of the Ising model with its position in the Chomsky hierarchy, they classified the complexity of the Ising model. Additionally, the study provided detailed discussions and proofs of related theorems and the complexity of seven Ising models as learning cases.

The ising model energy is defined as:
$$
E(\sigma) = -\sum_{ij}J_{ij}\sigma_i\sigma_j - \sum_{i} H_i\sigma_i
$$
In which, $\sigma_i = {0, 1}$ in this work.

Let $\mathcal S$ is the set of all possible configuration. $|\mathcal S| = 2^n$,

where $n$ is the number of sites, and is equal to the length of $\sigma$.

In maximum entropy principle, we expect to maximize the entropy $S(p)=-\sum_\sigma p(\sigma)logp(\sigma)$, in the constraints that

$\langle \sigma_i \sigma_j\rangle^{emp} = \langle \sigma_i \sigma_j\rangle$, $\langle \sigma_i\rangle^{emp}=\langle \sigma_i\rangle$ and $\sum_\sigma p(\sigma) = 1$.

Combine to the Lagrange function:

$\mathcal L(p;J;H)=S(p) -\lambda((\sum_\sigma p(\sigma))-1)-\sum_{ij}J_{ij}(\langle \sigma_i \sigma_j\rangle -\langle \sigma_i \sigma_j\rangle^{emp})-\sum_{j}H_{i}(\langle \sigma_i \rangle -\langle \sigma_i\rangle^{emp})$​

Thank you for visiting this site ^_^.

I am currently an independent researcher conducting interdisciplinary studies across the social sciences, nomological sciences,natural sciences, and engineering.

My work includes, for example, applying natural language processing techniques to electroencephalogram (EEG) analysis, exploring modern nomology and the philosophy of law, and developing field-Theoretic models of structural emergence and dynamics.

My major interests are in domain of philosophy, linguistics (especially computational linguistics), neuroscience and social and nomological sciences.

More specifically, my research interests involve following keywords:

• Field-Theoretic Physics, Statistical Physics, and Dynamical Systems
• Philosophy
• Social and Nomological Sciences
• Statistical Learning and Deep Learning
• Emerging Computer Architectures
• Emerging Computing Paradigms (e.g., neuromorphic computing)
• Computational Linguistics
• Programming Language Theory and Programming Language Processing Systems
• Optimization Algorithms
• Bio-signal Processing

I am engaged in interdisciplinary research and study across the social sciences, nomological sciences, natural sciences, and engineering to better understand human beings and the world. My interests also include developing applications in healthcare, communication enhancement, well-being, policymaking, nomological development, and related fields.

This website aims to share some of my research discoveries and personal reflections.
Thank you again for taking the time to browse this site.

Best wishes,
Wanhong HUANG
November 7, 2025

Email: huangwanhong.g.official@gmail.com