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This paper studies the distributed adaptiveestimation problems for stochastic large regression modelswith an infinite number of parameters. By constructing a re-cursive local cost function, we propose a novel distributedrecursive least…
Sharp asymptotic lower bounds of the expected quadratic variation of discretization error in stochastic integration are given. The theory relies on inequalities for the kurtosis and skewness of a general random variable which are themselves…
Many computer vision and human-computer interaction applications developed in recent years need evaluating complex and continuous mathematical functions as an essential step toward proper operation. However, rigorous evaluation of this kind…
The study of multidimensional stochastic processes involves complex computations in intricate functional spaces. In particular, the diffusion processes, which include the practically important Gauss-Markov processes, are ordinarily defined…
Stochastic volatility models based on Gaussian processes, like fractional Brownian motion, are able to reproduce important stylized facts of financial markets such as rich autocorrelation structures, persistence and roughness of sample…
This paper studies continuous-time Markov decision processes under the risk-sensitive average cost criterion. The state space is a finite set, the action space is a Borel space, the cost and transition rates are bounded, and the…
Approximating significance scans of searches for new particles in high-energy physics experiments as Gaussian fields is a well-established way to estimate the trials factors required to quantify global significances. We propose a novel,…
Hybrid evolution protocols, composed of unitary dynamics and repeated, weak or projective measurements, give rise to new, intriguing quantum phenomena, including entanglement phase transitions and unconventional conformal invariance.…
We study the time evolution of the entanglement entropy in bosonic systems with time-independent, or time-periodic, Hamiltonians. In the first part, we focus on quadratic Hamiltonians and Gaussian initial states. We show that all quadratic…
This paper presents a method to approximately solve stochastic optimal control problems in which the cost function and the system dynamics are polynomial. For stochastic systems with polynomial dynamics, the moments of the state can be…
While general quantum many-body systems require exponential resources to be simulated on a classical computer, systems of non-interacting fermions can be simulated exactly using polynomially scaling resources. Such systems may be of…
We introduce a nonparametric approach for estimating drift and diffusion functions in systems of stochastic differential equations from observations of the state vector. Gaussian processes are used as flexible models for these functions and…
We introduce a complete description of a multi-mode bosonic quantum state in the coherent-state basis (which in this work is denoted as "$K$" function ), which---up to a phase---is the square root of the well-known Husimi "$Q$"…
We present a variational method which uses a quartic exponential function as a trial wave-function to describe time-dependent quantum mechanical systems. We introduce a new physical variable $y$ which is appropriate to describe the shape of…
Using a real-time path integral approach we develop an algorithm to calculate multi-time correlation functions of open few-level quantum systems that is applicable to highly nonequilibrium dynamics. The calculational scheme fully keeps the…
A major challenge in developing quantum computing technologies is to accomplish high precision tasks by utilizing multiplex optimization approaches, on both the physical system and algorithm levels. Loss functions assessing the overall…
This paper investigates the intrinsic formation problem of a multi-agent system using an exogenous system. The problem is formulated as an intrinsic infinite time-horizon linear quadratic optimal control problem, namely, no formation error…
Quadratic bosonic Hamiltonians and their associated unitary transformations form a fundamental class of operations in quantum optics, modelling key processes such as squeezing, displacement, and beam-splitting. Their Heisenberg-picture…
Motivated by the recent developments in artificial intelligence, we introduce linear quadratic deep structured teams in this paper. Two notions of equivariant and partially equivariant systems are defined, and it is shown that such systems…
We study a constrained stochastic control problem with jumps; the jump times of the controlled process are given by a Poisson process. The cost functional comprises quadratic components for an absolutely continuous control and the…