Related papers: Statistical properties of the truncated state with…
In this paper we study the one dimensional random geometric graph when the location of the nodes are independent and exponentially distributed. We derive exact results and the limit theorems for the connectivity and other properties…
Restricted Boltzmann machines (RBMs) are a class of neural networks that have been successfully employed as a variational ansatz for quantum many-body wave functions. Here, we develop an analytic method to study quantum many-body spin…
In truncated partial-wave analysis, one fits observables that are bilinear in the amplitudes rather than the amplitudes themselves. Truncation is therefore not merely a restriction of the amplitude basis, but of the bilinear interference…
Truncated convex models (TCM) are a special case of pairwise random fields that have been widely used in computer vision. However, by restricting the order of the potentials to be at most two, they fail to capture useful image statistics.…
Observations or measurements taken of a quantum system (a small number of fundamental particles) are inherently random. If the state of the system depends on unknown parameters, then the distribution of the outcome depends on these…
We provide an efficient algorithm for the classical problem, going back to Galton, Pearson, and Fisher, of estimating, with arbitrary accuracy the parameters of a multivariate normal distribution from truncated samples. Truncated samples…
Truncated conditional expectation functions are objects of interest in a wide range of economic applications, including income inequality measurement, financial risk management, and impact evaluation. They typically involve truncating the…
We introduce the concept of selective quantum state tomography or SQST, a tomographic scheme that enables a user to estimate arbitrary elements of an unknown quantum state using a fixed measurement record. We demonstrate how this may be…
It is well known that kernel ridge regression (KRR) is a popular nonparametric regression estimator. Nonetheless, in the presence of a large data set with size $n\gg 1,$ the KRR estimator has the drawback to require an intensive…
We study the almost sure convergence of randomly truncated stochastic algorithms. We present a new convergence theorem which extends the already known results by making vanish the classical condition on the noise terms. The aim of this work…
Measurements with randomly chosen settings determine many important properties of quantum states without the need for a shared reference frame or calibration. They naturally emerge in the context of quantum communication and quantum…
We abstract the concept of a randomized controlled trial (RCT) as a triple (beta,b,s), where beta is the primary efficacy parameter, b the estimate and s the standard error (s>0). The parameter beta is either a difference of means, a log…
Random numbers are a basic ingredient of simulation algorithms and cryptography, and play a significant part in computer simulation and information processing. One prominent feature of a squeezed light is its lower fluctuation and more…
Within Bayesian state estimation, considerable effort has been devoted to incorporating constraints into state estimation for process optimization, state monitoring, fault detection and control. Nonetheless, in the domain of state-space…
In this paper, we have established a new framework of truncated inverse sampling for estimating mean values of non-negative random variables such as binomial, Poisson, hyper-geometrical, and bounded variables. We have derived explicit…
The accurate and reliable description of measurement devices is a central problem in both observing uniquely non-classical behaviors and realizing quantum technologies from powerful computing to precision metrology. To date quantum…
We address the important question of the extent to which random variables and vectors with truncated power tails retain the characteristic features of random variables and vectors with power tails. We define two truncation regimes, soft…
Distributional linear quadratic regulator (LQR) is a new framework that integrates the distributional reinforcement learning and classical LQR, which offers a new way to study the random return instead of the expected cost. Unlike iterative…
Randomness is an indispensable resource in modern science and information technology. Fortunately, an experimentally simple procedure exists to generate randomness with well-characterized devices: measuring a quantum system in a basis…
The study of properties of randomly chosen quantum states has in recent years led to many insights into quantum entanglement. In this work, we study private quantum states from this point of view. Private quantum states are bipartite…