Related papers: Sorting by Resetting
We provide a novel computer-assisted technique for systematically analyzing first-order methods for optimization. In contrast with previous works, the approach is particularly suited for handling sublinear convergence rates and stochastic…
The prospect of assistive robots aiding in object organization has always been compelling. In an image-goal setting, the robot rearranges the current scene to match the single image captured from the goal scene. The key to an image-goal…
Sorted data is usually easier to compress than unsorted permutations of the same data. This motivates a simple compression scheme: specify the sorted permutation of the data along with a representation of the sorted data compressed…
It is well known that the mathematically accurate description of ordering and related symmetry breaking in statistical systems requires to consider the thermodynamic limit. But the order does not appear from nowhere, and yet before the…
In the unidimensional unfolding model, given m objects in general position there arise 1+m(m-1)/2 rankings. The set of rankings is called the ranking pattern of the m given objects. By changing these m objects, we can generate various…
Due to the lack of long-range order, it remains challenging to characterize the structure of disordered solids and understand the nature of the glass transition. Here we propose a new structural order parameter by taking into account…
We introduce an auxiliary technique, called residual nudging, to the particle filter to enhance its performance in cases that it performs poorly. The main idea of residual nudging is to monitor, and if necessary, adjust the residual norm of…
We study the dynamics of a Brownian motion with a diffusion coefficient which evolves stochastically. We first study this process in arbitrary dimensions and find the scaling form and the corresponding scaling function of the position…
Stochastic resetting breaks detailed balance and drives the formation of nonequilibrium steady states . Here, we consider a chain of diffusive processes $x_i(t)$ that interact unilaterally: at random time intervals, the process $x_n$…
Many of the large structures of the cell, such as the cytoskeleton, are assembled and maintained far from equilibrium. We study the stabilities of various structures for a simple model of such a far-from-equilibrium organized assembly in…
The last decade has seen a revolution in the theory and application of machine learning and pattern recognition. Through these advancements, variable ranking has emerged as an active and growing research area and it is now beginning to be…
Link-based data structures, such as linked lists and binary search trees, have many well-known rearrangement steps allowing for efficient implementations of insertion, deletion, and other operations. We describe a rearrangement primitive…
We study the space requirements of a sorting algorithm where only items that at the end will be adjacent are kept together. This is equivalent to the following combinatorial problem: Consider a string of fixed length n that starts as a…
Self-organizing systems demonstrate how simple local rules can generate complex stochastic patterns. Many natural systems rely on such dynamics, making self-organization central to understanding natural complexity. A fundamental challenge…
Non-equilibrium systems display memory, a dependence not merely on their present environment but on previously applied fields. Multistable systems such as spin glasses, martensites and granular matter have exponentially many microstates…
The partition problem is a well-known basic NP-complete problem. We mainly consider the optimization version of it in this paper. The problem has been investigated from various perspectives for a long time and can be solved efficiently in…
Recent experiments have implemented resetting by means of an external trap, whereby a system relaxes to the minimum of the trap and is reset in a finite time. In this work, we set up and analyse the thermodynamics of such a protocol. We…
The lattice of partitions of a set and its d-divisible generalization have been much studied for their combinatorial, topological, and representation-theoretic properties. An ordered set partition is a set partition where the subsets are…
The transport of interacting Brownian particles in a periodic asymmetric (ratchet) substrate is studied numerically. In a zero-temperature regime, the system behaves as a reversible step motor, undergoing multiple sign reversals of the…
The model of binary aggregation with constant kernel is subjected to stochastic resetting: aggregates of any size explode into monomers at independent stochastic times. These resetting times are Poisson distributed, and the rate of the…