arXiv subjects

Liyu Liu

Publications and source records attributed to Liyu Liu.

At least 19 recordsLinked to original sources

arXiv2026

\c{S}tefan spectral sequence for faithfully flat Hopf Galois extensions is multiplicative

Let $H$ be a Hopf algebra with a bijective antipode over a field $\mathbf k$ and $B/A$ be a flat right $H$-Galois extension. \c{S}tefan constructed a spectral sequence converging to the Hochschild cohomology $\mathrm{HH}^{p+q}(B, N)$ with $\mathrm{E}_2^{p,q} = \mathrm{H}^p(H, \mathrm{HH}^q(A, N))$. We show that when $B/A$ is faithfully flat, the \c{S}tefan spectral sequence is multiplicative. More precisely, a new formalism of functorial multiplicative spectral sequences via lax monoidal functors over monoidal categories is introduced. A functorial multiplicative spectral sequence is constructed for any faithfully flat Hopf Galois extension. Identification with \c{S}tefan's spectral sequence from the $E_2$-page follows from K\"unzer's comparison theorems. Applications include strongly graded algebras, smash products, crossed products, group and Lie algebra extensions, with new multiplicativity results in several cases.

math.RA↗

arXiv2025

Digitization Can Stall Swarm Transport: Commensurability Locking in Quantized-Sensing Chains

We present a minimal model for autonomous robotic swarms in one- and higher-dimensional spaces, where identical, field-driven agents interact pairwise to self-organize spacing and independently follow local gradients sensed through quantized digital sensors. We show that the collective response of a multi-agent train amplifies sensitivity to weak gradients beyond what is achievable by a single agent. We discover a fractional transport phenomenon in which, under a uniform gradient, collective motion freezes abruptly whenever the ratio of intra-agent sensor separation to inter-agent spacing satisfies a number-theoretic commensurability condition. This commensurability locking persists even as the number of agents tends to infinity. We find that this condition is exactly solvable on the rationals -- a dense subset of real numbers -- providing analytic, testable predictions for when transport stalls. Our findings establish a surprising bridge between number theory and emergent transport in swarm robotics, informing design principles with implications for collective migration, analog computation, and even the exploration of number-theoretic structure via physical experimentation.

cond-mat.soft↗

arXiv2025

Intrinsic pressure as a convenient mechanical framework for dry active matter

The identification of local pressure in active matter systems remains a subject of considerable debate. Through theoretical calculations and extensive simulations of various active systems, we demonstrate that intrinsic pressure (defined in the same way as in passive systems) is an ideal candidate for local pressure of dry active matter, while the self-propelling forces on the active particles are considered as effective external forces originating from the environment. Such a framework is universal and especially convenient for analyzing mechanics of dry active systems, and it recovers the conventional scenario of mechanical equilibrium well-known in passive systems. Thus, our work is of fundamental importance to further explore mechanics and thermodynamics of complex active systems.

cond-mat.soft↗

arXiv2025

Active Hyperuniform Networks of Chiral Magnetic Micro-Robotic Spinners

Disorder hyperuniform (DHU) systems possess a hidden long-range order manifested as the complete suppression of normalized large-scale density fluctuations like crystals, which endows them with many unique properties. Here, we demonstrate a new organization mechanism for achieving stable DHU structures in active-particle systems via investigating the self-assembly of robotic spinners with three-fold symmetric magnetic binding sites up to a heretofore experimentally unattained system size, i.e., with $\sim 1000$ robots. The spinners can self-organize into a wide spectrum of actively rotating three-coordinated network structures, among which a set of stable DHU networks robustly emerge. These DHU networks are topological transformations of a honeycomb network by continuously introducing the Stone-Wales defects, which are resulted from the competition between tunable magnetic binding and local twist due to active rotation of the robots. Our results reveal novel mechanisms for emergent DHU states in active systems and achieving novel DHU materials with desirable properties.

cond-mat.soft↗

arXiv2025

Quantum gas microscopy of three-flavor Hubbard systems

Hubbard systems are paradigmatic realizations of strongly correlated many-body systems. Introducing additional species breaks the SU(2) symmetry of the Hubbard model and leads to a wide variety of novel exotic quantum phases. Three-component fermionic systems are at the heart of model systems for quantum chromodynamics where the three components reflect the three flavors. Here, we extend quantum gas microscopy to three-flavor Fermi lattice gases in the Hubbard regime. Relying on site- and flavor-resolved detection, we study the phase diagram of the three-flavor Hubbard model and find signatures of flavor-selective localization and selective pairing at temperatures down to the tunneling energy scale. Our measurements are compared with numerical linked-cluster expansion calculations. Further increase of phase space density may enable the observation of a novel pair Mott phase at half filling, and shows a path towards the study of color superfluidity and other aspects of quantum chromodynamics.

cond-mat.quant-gas↗

arXiv2025

Cup Products on Hochschild Cohomology of Hopf-Galois Extensions.pdf

In this paper, we give an explicit chain map, which induces the algebra isomorphism between the Hochschild cohomology ${\bf HH}^{\bullet}(B)$ and the $H$-invariant subalgebra ${\bf H}^{\bullet}(A, B)^{H}$ under two mild hypotheses, where $H$ is a finite dimensional semisimple Hopf algebra and $B$ is an $H$-Galois extension of $A$. In particular, the smash product $B=A\#H$ always satisfies the mild hypotheses. The isomorphism between ${\bf HH}^{\bullet}(A\#H)$ and ${\bf H}^{\bullet}(A, A\#H)^{H}$ generalizes the classical result of group actions. As an application, Hochschild cohomology and cup product of the smash product of the quantum $(-1)$-plane and Kac--Paljutkin Hopf algebra are computed.

math.RA↗

arXiv2024

Informational Memory Shapes Collective Behavior in Intelligent Swarms

We present an experimental and theoretical study of 2-D swarms in which collective behavior emerges from both direct local mechanical coupling between agents and from the exchange and processing of information between agents. Each agent, an air-table drone endowed with internal memory and a binary decision variable, updates its state by integrating a time series of memories of local past collisions. This internal computation transforms the drone swarm into a dynamical information network in which history-dependent feedback drives spontaneous complete spin polarization, pitchfork bifurcated spin collectives, and chaotic switching between collective states. By tuning the depth of memory and the decision algorithm, we uncover a memory-induced phase transition that breaks spin symmetry at the population level. A minimal theoretical model maps these dynamics onto an effective potential landscape sculpted by informational feedback, revealing how temporally correlated computation can replace instantaneous forces as the driver of collective organization, informed by experiments. These results position physically interacting drone swarms as a model system for exploring the physics of informational drone ensembles whose emergent behavior arises from the interplay between physical interaction and information processing.

physics.soc-ph↗

arXiv2023

Morphological entropy encodes cellular migration strategies on multiple length scales

Cell migration is crucial to many physiological and pathological processes. During migration, a cell adapts its morphology, including the overall morphology and nucleus morphology, in response to various cues in complex microenvironments, e.g. topotaxis and chemotaxis. Thus, cellular morphology dynamics can encode migration strategies based on which various migration mechanisms can be inferred. However, how to decipher cell migration mechanisms encoded in the morphology dynamics remains a challenging problem. Here we introduce a novel universal metric, namely cell morphological entropy (CME), by combining parametric morphological analysis with Shannon entropy. The utility of CME, which accurately quantifies the complex cellular morphology on multiple length scales through the deviation from the perfect circular shape, is demonstrated using a variety of normal and tumorous cell lines in distinct in vitro microenvironments. Our results reveal that 1) the effects of geometric constraints on cell nucleus, 2) the emerging interplays of MCF-10A cells migrating on collagen gel, and 3) the critical transition of tumor spheroid from proliferation to invasion. The analysis indicates that the CME offers a physically interpretable and efficient tool to quantify morphology on multiple length scales in real-time, which provides more insights into cell migration, and further contributing to the understanding of the diverse behavioral modes as well as collective cell motility in more complex microenvironment.

physics.bio-ph↗

arXiv2023

Inertial Spinner Swarm Experiments: Spin Pumping, Entropy Oscillations and Spin Frustration

We present here an inertial active spinning swarm consisting of mixtures of opposite handedness torque driven spinners floating on an air bed with low damping. Depending on the relative spin sign, spinners can act as their own anti-particles and annihilate their spins. Rotational energy can become highly focused, with minority fraction spinners pumped to very high levels of spin angular momentum. Spinner handedness also matters at high spinner densities but not low densities: oscillations in the mixing spatial entropy of spinners over time emerge if there is a net spin imbalance from collective rotations. Geometrically confined spinners can lock themselves into frustrated spin states.

cond-mat.soft↗

arXiv2022

Quantum gas microscopy of a geometrically frustrated Hubbard system

Geometrically frustrated many-particle quantum systems are notoriously hard to study numerically but are of profound interest because of their unusual properties and emergent phenomena. In these systems energetic constraints cannot be minimized simultaneously, leading to large ground-state degeneracy and a variety of exotic quantum phases. Here, we present a platform that enables unprecedentedly detailed experimental exploration of geometrically frustrated electronic systems on lattices with triangular geometry. We demonstrate the first realization of triangular atomic Hubbard systems, directly image Mott insulators in the triangular geometry with single-atom and single-site resolution, and measure antiferromagnetic spin-spin correlations for all nearest neighbors allowing for thermometry. This platform provides a powerful new approach for studying exotic quantum magnetism and direct detection of quantum spin liquid signatures in Hubbard systems.

cond-mat.quant-gas↗

arXiv2022

Site-resolved observables in the doped spin-imbalanced triangular Hubbard model

The suppression of antiferromagnetic ordering in geometrically frustrated Hubbard models leads to a variety of exotic quantum phases including quantum spin liquids and chiral states. Here, we focus on the Hubbard model on one of the simplest frustrated lattice geometries, a triangular lattice. Motivated by the recent realization of ultracold fermionic atoms in triangular optical lattices, we study the properties of the triangular-lattice Hubbard model through a Numerical Linked-Cluster Expansion algorithm. We investigate the Mott insulator transition finding a critical interaction $U_c/t = 7.0(2)$ and use spatial two- and three-point correlation functions to explore doped and imbalanced systems. Our results demonstrate that many interesting features occur at temperatures previously obtained for ultracold fermions in optical lattices and are accessible by upcoming experiments. Our calculations will be helpful for thermometry in ultracold atom quantum simulators and can guide experimental searches for exotic quantum phases in atomic triangular Hubbard quantum simulators.

cond-mat.quant-gas↗

arXiv2021

Batalin--Vilkovisky algebra structures on the Hochschild cohomology of generalized Weyl algebras

This paper is devoted to the calculation of Batalin-Vilkovisky algebra structures on the Hochschild cohomology of skew Calabi-Yau generalized Weyl algebras. We firstly establish a Van den Bergh duality at the level of complex. Then based on the results of Solotar et al., we apply Kowalzig and Krähmer's method to the Hochschild homology of generalized Weyl algebras, and translate the homological information into cohomological one by virtue of the Van den Bergh duality, obtaining the desired Batalin-Vilkovisky algebra structures. Finally, we apply our results to quantum weighted projective lines and Podleś quantum spheres, and the Batalin-Vilkovisky algebra structures for them are described completely.

math.RA↗

arXiv2021

Site-resolved imaging of ultracold fermions in a triangular-lattice quantum gas microscope

Quantum gas microscopes have expanded the capabilities of quantum simulation of Hubbard models by enabling the study of spatial spin and density correlations in square lattices. However, quantum gas microscopes have not been realized for fermionic atoms in frustrated geometries. Here, we demonstrate the single-atom resolved imaging of ultracold fermionic $^{6}$Li atoms in a triangular optical lattice with a lattice constant of 1003 nm. The optical lattice is formed by a recycled narrow-linewidth, high-power laser combined with a light sheet to allow for Raman sideband cooling on the $D_1$ line. We optically resolve single atoms on individual lattice sites using a high-resolution objective to collect scattered photons while cooling them close to the two-dimensional ground vibrational level in each lattice site. By reconstructing the lattice occupation, we measure an imaging fidelity of ~98%. Our new triangular lattice microscope platform for fermions clears the path for studying spin-spin correlations, entanglement and dynamics of geometrically frustrated Hubbard systems which are expected to exhibit exotic emergent phenomena including spin liquids and kinetic frustration.

cond-mat.quant-gas↗

arXiv2020

Shannon Entropy for Time-Varying Persistence of Cell Migration

Cell migration, which can be significantly affected by intracellular signaling pathways (ICSP) and extracellular matrix (ECM), plays a crucial role in many physiological and pathological processes. The efficiency of cell migration, which is typically modeled as a persistent random walk (PRW), depends on two critical motility parameters, i.e., migration speed and persistence. It is generally very challenging to efficiently and accurately extract these key dynamics parameters from noisy experimental data. Here, we employ the normalized Shannon entropy to quantify the deviation of cell migration dynamics from that of diffusive/ballistic motion as well as to derive the persistence of cell migration based on the Fourier power spectrum of migration velocities. Moreover, we introduce the time-varying Shannon entropy based on the wavelet power spectrum of cellular dynamics and demonstrate its superior utility to characterize the time-dependent persistence of cell migration, which is typically resulted from complex and time-varying intra or extra-cellular mechanisms. We employ our approach to analyze trajectory data of in vitro cell migration regulated by distinct intracellular and extracellular mechanisms, exhibiting a rich spectrum of dynamic characteristics. Our analysis indicates that the combination of Shannon entropy and wavelet transform offers a simple and efficient tool to estimate the persistence of cell migration, which may also reflect the real-time effects of ICSP-ECM to some extent.

physics.bio-ph↗

arXiv2020

Deriving Time-varying Cellular Motility Parameters via Wavelet Analysis

Cell migration is an indispensable physiological and pathological process for normal tissue development and cancer metastasis, which is greatly regulated by intracellular signal pathways and extracellular microenvironment (ECM). However, there is a lack of adequate tools to analyze the time-varying cell migration characteristics because of the effects of some factors, i.e., the ECM including the time-dependent local stiffness due to microstructural remodeling by migrating cells. Here, we develop an approach to derive the time-dependent motility parameters from cellular trajectories, based on the time-varying persistent random walk model. In particular, we employ the wavelet denoising and wavelet transform to investigate cell migration velocities and obtain the wavelet power spectrum. The time-dependent motility parameters are subsequently derived via Lorentzian power spectrum. Our analysis shows that the combination of wavelet denoising, wavelet transform and Lorentzian power spectrum provides a powerful tool to derive accurately the time-dependent motility parameters, which reflects the time-varying microenvironment characteristics to some extent.

physics.bio-ph↗

arXiv2019

Modeling cell migration regulated by cell-ECM micromechanical coupling

Cell migration in fibreous extracellular matrix (ECM) is crucial to many physiological and pathological processes such as tissue regeneration, immune response and cancer progression. During migration, individual cells can generate active pulling forces via actin filament contraction, which are transmitted to the ECM fibers through focal adhesion complexes, remodel the ECM, and eventually propagate to and can be sensed by other cells in the system. The microstructure and physical properties of the ECM can also significantly influence cell migration, e.g., via durotaxis and contact guidance. Here, we develop a computational model for cell migration regulated by cell-ECM micro-mechanical coupling. Our model explicitly takes into account a variety of cellular level processes including focal adhesion formation and disassembly, active traction force generation and cell locomotion due to actin filament contraction, transmission and propagation of tensile forces in the ECM, as well as the resulting ECM remodeling. We validate our model by accurately reproducing single-cell dynamics of MCF-10A breast cancer cells migrating on collagen gels and show that the durotaxis and contact guidance effects naturally arise as a consequence of the cell-ECM micro-mechanical interactions considered in the model. Moreover, our model predicts strongly correlated multi-cellular migration dynamics, which are resulted from the ECM-mediated mechanical coupling among the migrating cell and are subsequently verified in {\it in vitro} experiments using MCF-10A cells. Our computational model provides a robust tool to investigate emergent collective dynamics of multi-cellular systems in complex {\it in vivo} micro-environment and can be utilized to design {\it in vitro} micro-environments to guide collective behaviors and self-organization of cells.

q-bio.CB↗

arXiv2019

Biomechanics of Collective Cell Migration in Cancer Progression -- Experimental and Computational Methods

Cell migration is essential for regulating many biological processes in physiological or pathological conditions, including embryonic development and cancer invasion. In vitro and in silico studies suggest that collective cell migration is associated with some biomechanical particularities, such as restructuring of extracellular matrix, stress and force distribution profiles, and reorganization of cytoskeleton. Therefore, the phenomenon could be understood by an in-depth study of cells' behavior determinants, including but not limited to mechanical cues from the environment and from fellow travelers. This review article aims to cover the recent development of experimental and computational methods for studying the biomechanics of collective cell migration during cancer progression and invasion. We also summarized the tested hypotheses regarding the mechanism underlying collective cell migration enabled by these methods. Together, the paper enables a broad overview on the methods and tools currently available to unravel the biophysical mechanisms pertinent to cell collective migration, as well as providing perspectives on future development towards eventually deciphering the key mechanisms behind the most lethal feature of cancer.

q-bio.CB↗

arXiv2018

Nakayama automorphisms of Ore extensions over polynomial algebras

Nakayama automorphisms play an important role in several mathematical branches, which are known to be tough to compute in general. We compute the Nakayama automorphism $ν$ of any Ore extension $R[x; σ, δ]$ over a polynomial algebra $R$ in $n$ variables for an arbitrary $n$. The formula of $ν$ is obtained explicitly. When $σ$ is not the identity map, the invariant $E^G$ is also investigated in term of Zhang's twist, where $G$ is a cyclic group sharing the same order with $σ$.

math.RA↗