相关论文: Majority vote model with ancillary noise in comple…

We study consensus processes on the complete graph of $n$ nodes. Initially, each node supports one from up to n opinions. Nodes randomly and in parallel sample the opinions of constant many nodes. Based on these samples, they use an update…

Reinforcement Learning from AI Feedback (RLAIF) relies on LLM judges as preference measurement instruments, yet these instruments are fundamentally limited by random measurement errors -- stochastic fluctuations that manifest as preference…

We prove an inequality on decision trees on monotonic measures which generalizes the OSSS inequality on product spaces. As an application, we use this inequality to prove a number of new results on lattice spin models and their…

A continuous-time average consensus system is a linear dynamical system defined over a graph, where each node has its own state value that evolves according to a simultaneous linear differential equation. A node is allowed to interact with…

This paper considers a class of non-Markovian discrete-time random processes on a finite state space {1,...,d}. The transition probabilities at each time are influenced by the number of times each state has been visited and by a fixed a…

Discontinuous transitions have received considerable interest due to the uncovering that many phenomena such as catastrophic changes, epidemic outbreaks and synchronization present a behavior signed by abrupt (macroscopic) changes (instead…

The empirical measure of an interacting particle system is a purely atomic random probability measure. In the limit as the number of particles grows to infinity, we show for McKean-Vlasov systems with common noise that this measure becomes…

Using recent mathematical advances, a geometric approach to rare noise-driven transition events in nonequilibrium systems is given, and an algorithm for computing the maximum likelihood transition curve is generalized to the case of…

We present a new theoretical perspective of data noising in recurrent neural network language models (Xie et al., 2017). We show that each variant of data noising is an instance of Bayesian recurrent neural networks with a particular…

The notions of noise sensitivity and stability were recently extended for the voter model. In this model, the vertices of a graph have opinions that are updated by uniformly selecting edges. We further extend stability results to different…

We study a binary dynamical process that is a representation of the voter model with opinion makers. The process models an election with two candidates but can also describe the frequencies of a biallelic gene in a population or atoms with…

In this study, we introduced a probabilistic voter, regarding symbol probabilities in decision process besides majority consensus. Conventional majority voter is independent of functionality of redundant modules. In our study, proposed…

Neural systems process information in a dynamical regime between silence and chaotic dynamics. This has lead to the criticality hypothesis which suggests that neural systems reach such a state by self-organizing towards the critical point…

Disordered mechanical systems with high connectivity represent a limit opposite to the more familiar case of disordered crystals. Individual ions in a crystal are subjected essentially to nearest-neighbor interactions. In contrast, the…

We consider time-continuous Markovian discrete-state dynamics on random networks of interacting agents and study the large population limit. The dynamics are projected onto low-dimensional collective variables given by the shares of each…

We study numerically and analytically first- and second-order phase transitions in neuronal networks stimulated by shot noise (a flow of random spikes bombarding neurons). Using an exactly solvable cortical model of neuronal networks on…

We investigate theoretically the V-I characteristics and voltage noise of superconducting tunnel junctions with small critical current via the matrix-continued-fraction method. Special attention is paid to the large hysteresis in the V-I…

We discuss the complex dynamics of a non-linear random networks model, as a function of the connectivity k between the elements of the network. We show that this class of networks exhibit an order-chaos phase transition for a critical…

We present a stochastic Justh-Krishnaprasad flocking model and study the phase transition of the Vlasov-McKean-Fokker-Planck (VMFP) equation, which can be obtained in the mean-field limit. To describe the alignment, we use order parameters…

This paper summarises a numerical investigation of phase mixing in time-independent Hamiltonian systems that admit a coexistence of regular and chaotic phase space regions, allowing also for low amplitude perturbations idealised as periodic…