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We proposed a new criterion \textit{noise-stability}, which revised the classical rigidity theory, for evaluation of MDS algorithms which can truthfully represent the fidelity of global structure reconstruction; then we proved the…
We provide a simple framework for the study of parametric (multiplicative) noise, making use of scale parameters. We show that for a large class of stochastic differential equations increasing the multiplicative noise intensity surprisingly…
We prove algorithmic and hardness results for the problem of finding the largest set of a fixed diameter in the Euclidean space. In particular, we prove that if $A^*$ is the largest subset of diameter $r$ of $n$ points in the Euclidean…
We investigate the stabilization of unstable multidimensional partially observed single-sensor and multi-sensor linear systems driven by unbounded noise and controlled over discrete noiseless channels under fixed-rate information…
A fundamental step in many data-analysis techniques is the construction of an affinity matrix describing similarities between data points. When the data points reside in Euclidean space, a widespread approach is to from an affinity matrix…
Benjamini, Kalai and Schramm showed that a monotone function $f : \{-1,1\}^n \to \{-1,1\}$ is noise stable if and only if it is correlated with a half-space (a set of the form $\{x: \langle x, a\rangle \le b\}$). We study noise stability in…
Max-stable processes provide natural models for the modelling of spatial extreme values observed at a set of spatial sites. Full likelihood inference for max-stable data is, however, complicated by the form of the likelihood function as it…
The results of Raghavendra (2008) show that assuming Khot's Unique Games Conjecture (2002), for every constraint satisfaction problem there exists a generic semi-definite program that achieves the optimal approximation factor. This result…
Stable quantum computation requires noisy results to remain bounded even in the presence of noise fluctuations. Yet non-stationary noise processes lead to drift in the varying characteristics of a quantum device that can greatly influence…
Consider a set $V$ of voters, represented by a multiset in a metric space $(X,d)$. The voters have to reach a decision -- a point in $X$. A choice $p\in X$ is called a $\beta$-plurality point for $V$, if for any other choice $q\in X$ it…
The stable clustering hypothesis is a fundamental assumption about the nonlinear clustering of matter in cosmology. It states that the mean physical separation of particles is a constant on sufficiently small scales. While many authors have…
Levitated nanoparticles provide a controllable and isolated platform for probing fundamental quantum phenomena at the macroscopic scale. In this work, we introduce an optimization method to determine optimal static potentials for the…
We consider estimation models of the form $Y=X^*+N$, where $X^*$ is some $m$-dimensional signal we wish to recover, and $N$ is symmetrically distributed noise that may be unbounded in all but a small $\alpha$ fraction of the entries. We…
We study asymmetric rank-one spiked tensor models in the high-dimensional regime, where the noise entries are independent and identically distributed with zero mean, unit variance, and finite fourth moment. This extends the classical…
To devise efficient solutions for approximating a mean partition in consensus clustering, Dimitriadou et al. [3] presented a necessary condition of optimality for a consensus function based on least square distances. We show that their…
Locating a target is key in many applications, namely in high-stakes real-world scenarios, like detecting humans or obstacles in vehicular networks. In scenarios where precise statistics of the measurement noise are unavailable,…
Quantum machine learning models have the potential to offer speedups and better predictive accuracy compared to their classical counterparts. However, these quantum algorithms, like their classical counterparts, have been shown to also be…
In this paper we study the problem of signal detection in Gaussian noise in a distributed setting where the local machines in the star topology can communicate a single bit of information. We derive a lower bound on the Euclidian norm that…
We analyze the robustness of Grover's quantum search algorithm performed by a quantum register under a possibly time-correlated noise acting locally on the qubits. We model the noise as originating from an arbitrary but fixed unitary…
Parameter estimation is of fundamental importance in areas from atomic spectroscopy and atomic clocks to gravitational wave detection. Entangled probes provide a significant precision gain over classical strategies in the absence of noise.…