相关论文: A Measure of data-collapse for scaling
Scaling describes how a given quantity $Y$ that characterizes a system varies with its size $P$. For most complex systems it is of the form $Y\sim P^\beta$ with a nontrivial value of the exponent $\beta$, usually determined by regression…
A microcanonical finite-size scaling ansatz is discussed. It exploits the existence of a well-defined transition point for systems of finite size in the microcanonical ensemble. The best data collapse obtained for small systems yields…
We propose a treatment of the subleading corrections to finite-size scaling that preserves the notion of data collapse. This approach is used to extend and improve the usual Binder cumulant analysis. As a demonstration, we present results…
Using single cluster flip Monte Carlo simulations we accurately determine new finite size scaling functions which are expressed only in terms the variable $x = \xi_L / L$, where $\xi_L$ is the correlation length in a finite system of size…
Empirical determination of the scaling properties and exponents of time series presents a formidable challenge in testing, and developing, a theoretical understanding of turbulence and other out-of-equilibrium phenomena. We discuss the…
Collapse models are phenomenological models introduced to solve the measurement problem in quantum mechanics. They modify the Schr\"odinger equation by adding non-linear and stochastic terms, which induce the wavefunction collapse in space.…
A long-standing quantum-mechanical puzzle is whether the collapse of the wave function is a real physical process or simply an epiphenomenon. This puzzle lies at the heart of the measurement problem. One way to choose between the…
Collapse, or a gravitational-like phase transition is studied in a microcanonical ensemble of particles with an attractive $1/r^{\alpha}$ potential. A mean field continuous integral equation is used to determine a saddle-point density…
Preprocessing data is an important step before any data analysis. In this paper, we focus on one particular aspect, namely scaling or normalization. We analyze various scaling methods in common use and study their effects on different…
One of the most impressive features of continuous phase transitions is the concept of universality, that allows to group the great variety of different critical phenomena into a small number of universality classes. All systems belonging to…
We introduce collapsed compilation, a novel approximate inference algorithm for discrete probabilistic graphical models. It is a collapsed sampling algorithm that incrementally selects which variable to sample next based on the partial…
Monte-Carlo simulations are routinely used for estimating the scaling exponents of complex systems. However, due to finite-size effects, determining the exponent values is often difficult and not reliable. Here we present a novel technique…
Complex interactions leading to phase transitions continue to hold a due interest in the scientific community. We charactersize a phase transition in a coupled oscillators model where interactions are not local in nature. At a first order…
Monte-Carlo simulations are routinely used for estimating the scaling exponents of complex systems. However, due to finite-size effects, determining the exponent values is often difficult and not reliable. Here we present a novel technique…
In real-world applications, observations are often constrained to a small fraction of a system. Such spatial subsampling can be caused by the inaccessibility or the sheer size of the system, and cannot be overcome by longer sampling.…
Data assimilation refers to the process of obtaining an estimate of a system's state using a model for the system's time evolution and a time series of measurements that are possibly noisy and incomplete. However, for practical reasons, the…
Data collapse enables comparison of measurement data measured in different laboratories on different samples. In the case of energy losses in Soft Magnetic Materials (SMM) the data collapse is possible to achieved only if the measurement…
Dimension reduction of data sets is a standard problem in the realm of machine learning and knowledge reasoning. They affect patterns in and dependencies on data dimensions and ultimately influence any decision-making processes. Therefore,…
In the era of proliferation of large language and image generation models, the phenomenon of "model collapse" refers to the situation whereby as a model is trained recursively on data generated from previous generations of itself over time,…
This work introduces a method to select linear functional measurements of a vector-valued time series optimized for forecasting distant time-horizons. By formulating and solving the problem of sequential linear measurement design as an…