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A widely used strategy to discover and understand language model mechanisms is circuit analysis. A circuit is a minimal subgraph of a model's computation graph that executes a specific task. We identify a gap in existing circuit discovery…
We study in a systematic way a generic nonderivative (massive) deformation of general relativity using the Hamiltonian formalism. The number of propagating degrees of freedom is analyzed in a nonperturbative and background independent way.…
An efficient Monte Carlo algorithm for the simulation of spin models with long-range interactions is discussed. Its central feature is that the number of operations required to flip a spin is independent of the number of interactions…
For a systematic study of charge degrees of freedom in lattices with geometric frustration, we consider spinless fermions on the checkerboard lattice with nearest-neighbor hopping $t$ and nearest-neighbor repulsion $V$ at quarter-filling.…
Many studies simulates the machining process by using a single degree of freedom spring-mass sytem to model the tool stiffness, or the workpiece stiffness, or the unit tool-workpiece stiffness in modelings 2D. Others impose the tool action,…
For the elliptic Gaudin model (a degenerate case of XYZ integrable spin chain) a separation of variables is constructed in the classical case. The corresponding separated coordinates are obtained as the poles of a suitably normalized…
The dynamics of a complex system is usually recorded in the form of time series, which can be studied through its visibility graph from a complex network perspective. We investigate the visibility graphs extracted from fractional Brownian…
Motility is an essential factor for an organism's survival and diversification. With the advent of novel single-cell technologies, analytical frameworks and theoretical methods, we can begin to probe the complex lives of microscopic motile…
In this paper we consider deterministic limits of molecular stochastic systems with finite and infinite degrees of freedom. The method to obtain the deterministic vector field is based on the continuum limit of such microscopic systems…
With image-based high-throughput experiments, new challenges arise in both, the design of experiments and the automated analysis. To be able to handle the massive number of single experiments and the corresponding amount of data, a…
Scale free dynamics are observed in a variety of physical and biological systems. These include neural activity in which evidence for scale freeness has been reported using a range of imaging modalities. Here, we derive the ways in which…
Screw theory provides geometrical insight into the mechanics of rigid bodies. Screw axis is defined as the line coinciding with the joint axis. Line transformations in the form of a screw operator are used to determine the joint axes of a…
The conflict between the physical degrees of freedom of gauge bosons and the Lorentz group irreps naturally used to describe their couplings to matter fields are illustrated and discussed, and applied to issues of linear and angular…
In this paper we present a new mathematical rigorous technique for computing the average free energy of a disordered system with quenched randomness, using the replicas. The basic tool of this technique is a distributional zeta-function, a…
Computational experiments are used to show that grain boundary mobility is independent of driving force in a two-dimensional, square-lattice Ising model with Metropolis kinetics. This is established over the entire Monte Carlo temperature…
In this paper computer simulation results of higher order density correlation for cellular automaton models of traffic flow are presented. The examinations show the jamming transition as a function of both the density and the magnitude of…
The existence of an extra degree of freedom (d.o.f.) in $f(T)$ gravity has been recently proved by means of the Dirac formalism for constrained Hamiltonian systems. We will show a toy model displaying the essential feature of $f(T)$…
How do cells tune emergent properties at the scale of tissues? One class of such emergent behaviors are rigidity transitions, in which a tissue changes from a solid-like to a fluid-like state or vice versa. Here, we introduce a new way for…
The paper analyses stochastic systems describing reacting molecular systems with a combination of two types of state spaces, a finite-dimensional, and an infinite dimenional part. As a typical situation consider the interaction of larger…
We propose a new Monte Carlo method for efficiently sampling trajectories with fixed initial and final conditions in a system with discrete degrees of freedom. The method can be applied to any stochastic process with local interactions,…