Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2507.20371

Hypo-paradoxical Linkages: Linkages That Should Move-But Don't

Nir Shvalb·Oded Medina
View original source ↗Read source document ↗Export metadata ↓

Abstract

While paradoxical linkages famously violate the Chebyshev-Grubler-Kutzbach criterion by exhibiting unexpected mobility, we identify an opposing phenomenon: a class of linkages that appear mobile according to the same criterion, yet are in fact rigid. We refer to these as hypo-paradoxical linkages, and proceed to analyze and illustrate their behavior. We use the same tools to further explain the unexpected positive mobility of Bennet mechanism.

Explore related subjects

physics.soc-phcs.RO

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Nir Shvalb, Oded Medina. 2025-09-27. Hypo-paradoxical Linkages: Linkages That Should Move-But Don't. https://arxiv.org/abs/2507.20371

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Allocation condensation under asymptotically complete mixing

We study a fixed network on which new mass is allocated in proportion to a power of each node's stock and then redistributed. Transport retains a fraction of both old and new mass at each node and divides the rest according to fixed background shares. We show that a small amount of retention can sustain concentration on networks where complete redistribution would leave every node's share of new mass vanishing as the network grows. A node receiving most new mass may retain little relative to the network total, yet much more than redistribution alone would supply. For a power above one, the allocation rule amplifies this relative stock advantage at the next step. We identify retention rates tending to zero with network size that allow widely spread and concentrated stationary allocations to coexist on the same network. One of them stays close to the allocation under complete redistribution. Each node can also dominate a separate concentrated allocation, receiving a share of new mass tending to one. The stocks supporting these allocations attract nearby trajectories, although every stationary stock approaches the same background, with even its largest share tending to zero. These allocations continue to coexist under specified changes in transport that preserve the background. Redistribution can therefore spread the stock widely without spreading new allocations in the same way.

physics.soc-ph↗
arXiv2026

Glassy dynamics of metropolitan human mobility frozen near the gravitational equilibrium

This research establishes a connection between macroscopic urban commuting flows and thermal equilibrium. Using mobility data from around 30 million records across six Japanese cities over one year, we introduce the Gravity-based Home Swapping Model (GHSM). This model applies Metropolis dynamics to urban commuting by treating individuals as interacting particles. Within this framework, total commuting time dictates the system energy, and temperature controls how strongly mobility responds to cost savings. Consequently, urban commuting can be analyzed through an evaluable free energy and simulated similarly to physical systems of matter. The maximumentropy doubly constrained gravity model serves as the stationary state. We find that the residential dynamics exhibit glassy characteristics. Through calibration to observed data, we reveal that the system demonstrates signatures of kinetically constrained models, specifically ageing, hysteresis, and freezing near equilibrium. Simulations initialized from arbitrary states converge to empirical origin-destination matrices. This demonstrates that minimal physical mechanisms can reconstruct complex urban realities.

physics.soc-ph↗
arXiv2026

Human-Agent Interaction in Synthetic Social Networks: A Framework for Studying Online Polarization

Online social networks have dramatically altered the landscape of public discourse, creating both opportunities for enhanced civic participation and risks of deepening social divisions. Prevalent approaches to studying online polarization have been limited by a methodological disconnect: mathematical models excel at formal analysis but lack linguistic realism, while language model-based simulations capture natural discourse but often sacrifice analytical precision. This paper introduces an innovative computational framework that synthesizes these approaches by embedding formal opinion dynamics principles within LLM-based artificial agents, enabling both rigorous mathematical analysis and naturalistic social interactions. We validate our framework through comprehensive offline testing and experimental evaluation with 122 human participants engaging in a controlled social network environment. The results demonstrate our ability to systematically investigate polarization mechanisms while preserving ecological validity. Our findings reveal how polarized environments shape user perceptions and behavior: participants exposed to polarized discussions showed markedly increased sensitivity to emotional content and group affiliations, while perceiving reduced uncertainty in the agents' positions. By combining mathematical precision with natural language capabilities, our framework opens new avenues for investigating social media phenomena through controlled experimentation. This methodological advancement allows researchers to bridge the gap between theoretical models and empirical observations, offering unprecedented opportunities to study the causal mechanisms underlying online opinion dynamics.

physics.soc-ph↗