arXiv subjects

Ruoshi Yuan

Publications and source records attributed to Ruoshi Yuan.

14 recordsLinked to original sources

arXiv2026

ATLAS: All-round Testing of Long-context Abilities across Scales

Long-context language models now advertise context windows up to millions of tokens, yet evaluations typically report a single length or a narrow task family, masking two failure modes: performance can collapse as length grows, and strong retrieval need not transfer to downstream use. We present ATLAS, a benchmarking framework that redefines long-context evaluation as length-dependent capability profiling. ATLAS contributes three methodological principles:(i) a layered taxonomy separating foundational operations from application workloads so failures can be attributed, (ii) length-aware AUC scoring that integrates score-length curves over a fixed 8K-1M grid, replacing single-point metrics with full degradation profiles, and (iii) ATLAScore, a harmonic-mean aggregate over taxonomy categories that penalizes imbalanced profiles, with end-to-end uncertainty propagation from subset scores through the nonlinear final aggregate. We instantiate the framework across eight capability dimensions with nine auditable components and 6,438 instances, and evaluate 26 models. Gemini-3.1-Pro-Preview leads at 128K, Claude-Opus-4.6 leads at 1M. Rankings reshuffle substantially between ATLASscore@8K-128K and ATLASscore@8K-1M: 7 models move by at least two ranks, and the two taxonomy layers share only 61% of cross-model variance, with individual rank gaps up to 12 positions. These results support reporting long-context quality by capability and length, not by a single headline score.

cs.CL↗

arXiv2017

Potential landscape of high dimensional nonlinear stochastic dynamics with large noise

Quantifying stochastic processes is essential to understand many natural phenomena, particularly in biology, including cell-fate decision in developmental processes as well as genesis and progression of cancers. While various attempts have been made to construct potential landscape in high dimensional systems and to estimate rare transitions, they are practically limited to cases where either noise is small or detailed balance condition holds. A general and practical approach to investigate nonequilibrium systems typically subject to finite or large multiplicative noise and breakdown of detailed balance remains elusive. Here, we formulate a computational framework to address this important problem. The current approach is based on a least action principle to efficiently calculate potential landscapes of systems under arbitrary noise strength and without detailed balance. With the deterministic stability structure preserving A-type stochastic integration, the potential barrier between different (local) stable stables is directly computable. We demonstrate our approach in a numerically accurate manner through solvable examples. We further apply the method to investigate the role of noise on tumor heterogeneity in a 38 dimensional network model for prostate cancer, and provide a new strategy on controlling cell populations by manipulating noise strength.

cond-mat.stat-mech↗

arXiv2016

On Uniqueness of "SDE Decomposition" in A-type Stochastic Integration

An innovative theoretical framework for stochastic dynamics based on a decomposition of a stochastic differential equation (SDE) has been developed with an evident advantage in connecting deterministic and stochastic dynamics, as well as useful applications in physics, engineering, chemistry and biology. It introduces the A-type stochastic integration for SDE beyond traditional Ito's or Stratonovich's interpretation. Serious question on its uniqueness was recently raised. We provide here both mathematical and physical demonstrations that the uniqueness is guaranteed. Such discussion leads to a better understanding on the robustness of the novel framework. We also discuss the limitation of a related approach of obtaining potential function from steady state distribution.

cond-mat.stat-mech↗

arXiv2015

Work Relations Connecting Nonequilibrium Steady States Without Detailed Balance

Bridging equilibrium and nonequilibrium statistical physics attracts sustained interest. Hallmarks of nonequilibrium systems include a breakdown of detailed balance, and an absence of a priori potential function corresponding to the Boltzmann-Gibbs distribution, without which classical equilibrium thermodynamical quantities could not be defined. Here, we construct dynamically the potential function through decomposing the system into a dissipative part and a conservative part, and develop a nonequilibrium theory by defining thermodynamical quantities based on the potential function. Concepts for equilibrium can thus be naturally extended to nonequilibrium steady state. We elucidate this procedure explicitly in a class of time-dependent linear diffusive systems without mathematical ambiguity. We further obtain the exact work distribution for an arbitrary control parameter, and work equalities connecting nonequilibrium steady states. Our results provide a direct generalization on Jarzynski equality and Crooks fluctuation theorem to systems without detailed balance.

cond-mat.stat-mech↗

arXiv2014

Non-equilibrium work relation beyond Boltzmann-Gibbs distribution

The presence of multiplicative noise can alter measurements of forces acting on nanoscopic objects. Taking into account of multiplicative noise, we derive a series of non-equilibrium thermodynamical equalities as generalization of the Jarzynski equality, the detailed fluctuation theorem and the Hatano-Sasa's relation. Our result demonstrates that the Jarzynski equality and the detailed fluctuation theorem remains valid only for systems with the Boltzmann-Gibbs distribution at the equilibrium state, but the Hatano-Sasa's relation is robust with respect to the ambiguity on multiplicative noise.

cond-mat.stat-mech↗

arXiv2014

Summing over trajectories of stochastic dynamics with multiplicative noise

We demonstrate that the conventional path integral formulations generate inconsistent results exemplified by the geometric Brownian motion under the general stochastic interpretation. We thus develop a novel path integral formulation for the overdamped Langevin equation with the multiplicative noise. The present path integral leads to the corresponding Fokker-Planck equation, and naturally gives a normalized transition probability consistently in examples for general stochastic interpretations. Our result can be applied to study the fluctuation theorems and numerical calculations based on the path integral framework.

cond-mat.stat-mech↗

arXiv2013

Lyapunov Functions in Piecewise Linear Systems: From Fixed Point to Limit Cycle

This paper provides a first example of constructing Lyapunov functions in a class of piecewise linear systems with limit cycles. The method of construction helps analyze and control complex oscillating systems through novel geometric means. Special attention is stressed upon a problem not formerly solved: to impose consistent boundary conditions on the Lyapunov function in each linear region. By successfully solving the problem, the authors construct continuous Lyapunov functions in the whole state space. It is further demonstrated that the Lyapunov functions constructed explain for the different bifurcations leading to the emergence of limit cycle oscillation.

nlin.CD↗

arXiv2012

Determine dynamical behaviors by the Lyapunov function in competitive Lotka-Volterra systems

Global dynamical behaviors of the competitive Lotka-Volterra system even in 3-dimension are not fully understood. The Lyapunov function can provide us such knowledge once it is constructed. In this paper, we construct explicitly the Lyapunov function in three examples of the competitive Lotka-Volterra system for the whole state space: (1) the general 2-dimensional case; (2) a 3-dimensional model; (3) the model of May-Leonard. The dynamics of these examples include bistable case and cyclical behavior. The first two examples are the generalized gradient system defined in the Appendixes, while the model of May-Leonard is not. Our method is helpful to understand the limit cycle problems in general 3-dimensional case.

q-bio.PE↗

arXiv2012

Exact Mapping Noisy van der Pol Type Oscillator onto Quasi-symplectic Dynamics

We find exact mappings for a class of limit cycle systems with noise onto quasi-symplectic dynamics, including a van der Pol type oscillator. A dual role potential function is obtained as a component of the quasi-symplectic dynamics. Based on a stochastic interpretation different from the traditional Ito's and Stratonovich's, we show the corresponding steady state distribution is the familiar Boltzmann-Gibbs type for arbitrary noise strength. The result provides a new angle for understanding processes without detailed balance and can be verified by experiments.

cond-mat.stat-mech↗

arXiv2012

Relation of a New Interpretation of Stochastic Differential Equations to Ito Process

Stochastic differential equations (SDE) are widely used in modeling stochastic dynamics in literature. However, SDE alone is not enough to determine a unique process. A specified interpretation for stochastic integration is needed. Different interpretations specify different dynamics. Recently, a new interpretation of SDE is put forward by one of us. This interpretation has a built-in Boltzmann-Gibbs distribution and shows the existence of potential function for general processes, which reveals both local and global dynamics. Despite its powerful property, its relation with classical ones in arbitrary dimension remains obscure. In this paper, we will clarify such connection and derive the concise relation between the new interpretation and Ito process. We point out that the derived relation is experimentally testable.

math-ph↗

arXiv2012

Beyond Itô versus Stratonovich

Recently, a novel framework to handle stochastic processes has emerged from a series of studies in biology, showing situations beyond 'Itô versus Stratonovich'. Its internal consistency can be demonstrated via the zero mass limit of a generalized Klein-Kramers equation. Moreover, the connection to other integrations becomes evident: the obtained Fokker-Planck equation defines a new type of stochastic calculus that in general differs from the α-type interpretation. A unique advantage of this new approach is a natural correspondence between stochastic and deterministic dynamics, which is useful or may even be essential in practice. The core of the framework is a transformation from the usual Langevin equation to a form that contains a potential function with two additional dynamical matrices, which reveals an underlying symplectic structure. The framework has a direct physical meaning and a straightforward experimental realization. A recent experiment has offered a first empirical validation of this new stochastic integration.

cond-mat.stat-mech↗

arXiv2012

Potential Function in a Continuous Dissipative Chaotic System: Decomposition Scheme and Role of Strange Attractor

In this paper, we demonstrate, first in literature known to us, that potential functions can be constructed in continuous dissipative chaotic systems and can be used to reveal their dynamical properties. To attain this aim, a Lorenz-like system is proposed and rigorously proved chaotic for exemplified analysis. We explicitly construct a potential function monotonically decreasing along the system's dynamics, revealing the structure of the chaotic strange attractor. The potential function can have different forms of construction. We also decompose the dynamical system to explain for the different origins of chaotic attractor and strange attractor. Consequently, reasons for the existence of both chaotic nonstrange attractors and nonchaotic strange attractors are clearly discussed within current decomposition framework.

nlin.CD↗

arXiv2012

Zero Mass Limit and Its Experimental Test

J. M. Sancho [Phys. Rev. E 84, 062102 (2011)] analyzed two stochastic interpretations on a recent experiment [Phys. Rev. Lett. 104, 170602 (2010)] of Brownian colloidal particles. The author asserted that the stochastic interpretation "obtained by simply setting the acceleration equal to zero" should not be taken and that the zero-mass limit interpretation of the experimental data would not be physically correct. In this Comment we show that Sancho's analysis is incomplete in that it pre-excludes zero mass limit and hence his assertions are incorrect. Our reasoning will be both mathematical and physical.

physics.data-an↗

arXiv2010

Constructive Proof of Global Lyapunov Function as Potential Function

We provide a constructive proof on the equivalence of two fundamental concepts: the global Lyapunov function in engineering and the potential function in physics, establishing a bridge between these distinct fields. This result suggests new approaches on the significant unsolved problem namely to construct Lyapunov functions for general nonlinear systems through the analogy with existing methods on potential functions. In addition, we show another connection that the Lyapunov equation is a reduced form of the generalized Einstein relation for linear systems.

nlin.CD↗