相关论文: Optimal Metastability-Containing Sorting Networks

We study a large class of reversible Markov chains with discrete state space and transition matrix $P_N$. We define the notion of a set of {\it metastable points} as a subset of the state space $\G_N$ such that (i) this set is reached from…

This paper focuses on a networked state estimation problem for a spatially large linear system with a distributed array of sensors, each of which offers partial state measurements, and the transmission is lossy. We propose a measurement…

Clusters of solid-state quantum devices have long-living metastable states of local energy minima which may be used to store quantum information. The low to vanishing rate of dissipation fulfils the prerequisite to maintain quantum…

Sorting is a foundational primitive in modern data processing, influencing the execution speed of high-performance data pipelines. However, the algorithmic landscape is currently bifurcated by a pervasive "Stability Tax": practitioners must…

Sorting and ranking supervision is a method for training neural networks end-to-end based on ordering constraints. That is, the ground truth order of sets of samples is known, while their absolute values remain unsupervised. For that, we…

In this paper we optimize constellation sets to be used for channels affected by phase noise. The main objective is to maximize the achievable mutual information of the constellation under a given power constraint. The mutual information…

Decentralized optimization is typically studied under the assumption of noise-free transmission. However, real-world scenarios often involve the presence of noise due to factors such as additive white Gaussian noise channels or…

The overdamped motion of a Brownian particle in randomly switching piece-wise metastable linear potential shows noise enhanced stability (NES): the noise stabilizes the metastable system and the system remains in this state for a longer…

Often it is desirable to stabilize a system around an optimal state. This can be effectively accomplished using feedback control, where the system deviation from the desired state is measured in order to determine the magnitude of the…

Zeroth-order (ZO) optimization has emerged as a promising alternative to gradient-based backpropagation methods, particularly for black-box optimization and large language model (LLM) fine-tuning. However, ZO methods often suffer from slow…

We study the long-time effect of noise on pattern formation for the aggregation model. We consider aggregation kernels that generate patterns consisting of two delta-concentrations. Without noise, there is a one-parameter family of…

Pre-fault tolerant quantum computers have already demonstrated the ability to estimate observable values accurately, at a scale beyond brute-force classical computation. This has been enabled by error mitigation techniques that often rely…

Metadamping is the phenomenon of either enhanced or diminished intrinsic dissipation in a material stemming from the material's internal structural dynamics. It has been previously shown that a locally resonant elastic metamaterial may be…

Dynamical stabilizer codes may offer a practical route to large-scale quantum computation. Such codes are defined by a schedule of error-detecting measurements, which allows for flexibility in their construction. In this work, we ask how…

Metric data structures (distance oracles, distance labeling schemes, routing schemes) and low-distortion embeddings provide a powerful algorithmic methodology, which has been successfully applied for approximation algorithms \cite{llr},…

We present a general method to derive the metastable behavior of weakly mixing Markov chains. This approach is based on properties of the resolvent equations and can be applied to metastable dynamics which do not satisfy the mixing…

Algorithmic stability is a central concept in statistics and learning theory that measures how sensitive an algorithm's output is to small changes in the training data. Stability plays a crucial role in understanding generalization,…

The vast majority of the literature on learning dynamical systems or stochastic processes from time series has focused on stable or ergodic systems, for both Bayesian and frequentist inference procedures. However, most real-world systems…

In this letter we study metamaterials made out of resonant electric wires arranged on a spatial scale much smaller than the free space wavelength and we show that they present a hybridization band that is insensible to positional disorder.…

Synchronous Counting is the task of reaching agreement on a common round counter in a synchronous system of $n$ nodes with up to $t$ Byzantine faults in a self-stabilizing manner. That is, after transient faults may have arbitrarily…