Related papers: Closed-Form Bounds for the Rice $Ie$-Function
Another approach to constructing an upper bound for the Riemann-Farey sum is described.
In this paper, tight upper and lower bounds are derived on the weighted sum of minimum mean-squared errors for additive Gaussian noise channels. The bounds are obtained by constraining the input distribution to be close to a Gaussian…
\citet{farrell2021deep} establish non-asymptotic high-probability bounds for general deep feedforward neural network (with rectified linear unit activation function) estimators, with \citet[Theorem 1]{farrell2021deep} achieving a suboptimal…
We provide an upper bound as a random variable for the functions of estimators in high dimensions. This upper bound may help establish the rate of convergence of functions in high dimensions. The upper bound random variable may converge…
Lattice reduction-aided decoding features reduced decoding complexity and near-optimum performance in multi-input multi-output communications. In this paper, a quantitative analysis of lattice reduction-aided decoding is presented. To this…
A closed-form expression for Wigner-Yanase skew information in mixed-state quantum systems is derived. It is shown that limit values of the mixing coefficients exist such that Wigner-Yanase information is equal to Helstrom information. The…
The intuitive sphere-packing argument is used to obtain analytically-tractable closed-form approximations for achievable information rates of coded modulation transmission systems, for which only analytically-intractable expressions are…
This article revisits the problem of Bayesian shape-restricted inference in the light of a recently developed approximate Gaussian process that admits an equivalent formulation of the shape constraints in terms of the basis coefficients. We…
The paper provides bounds for the ropelength of a link in terms of the crossing numbers of its split components. As in earlier papers, the bounds grow with the square of the crossing number; however, the constant involved is a substantial…
An approach to constructing an upper bound for the Riemann-Farey sum is described.
In this paper we discuss a closed-form approximation of the likelihood functions of an arbitrary diffusion process. The approximation is based on an exponential ansatz of the transition probability for a finite time step $\Delta t$, and a…
An extension of the estimates for the squeezing function of strictly pseudoconvex domains obtained recently by J. E. Forn\ae ss and E. Wold in \cite{FW1} is applied to derive a sharp boundary behaviour of invariant metrics and Bergman…
We obtain explicit bounds on the truncation error of the cumulant series of a bounded complex function of a random vector with independent components. The bounds are based on multidimensional differences. This extends the theory of the…
The diameter of a graph is among its most basic parameters. Since a few years, it moreover became a key issue to compute it for massive graphs in the context of complex network analysis. However, known algorithms, including the ones…
Rice's theorem shows that nontrivial extensional properties of partial recursive functions are undecidable. For finite weighted Boolean optimization/CSP-style slices, a Rice-style structural analogue holds for tractability classification:…
Recently, Gilmer proved the first constant lower bound for the union-closed sets conjecture via an information-theoretic argument. The heart of the argument is an entropic inequality involving the OR function of two i.i.d.\ binary vectors,…
We derive Berry-Esseen approximation bounds for general functionals of independent random variables, based on chaos expansions methods. Our results apply to $U$-statistics satisfying the weak assumption of decomposability in the Hoeffding…
Reconfigurable intelligent surfaces (RISs) allow controlling the propagation environment in wireless networks by tuning multiple reflecting elements. RISs have been traditionally realized through single connected architectures,…
This paper provides inference methods for best linear approximations to functions which are known to lie within a band. It extends the partial identification literature by allowing the upper and lower functions defining the band to be any…
We shall consider a result of Fel'dman, where a sharp Baker-type lower bound is obtained for linear forms in the values of some E-functions. Fel'dman's proof is based on an explicit construction of Pad\'e approximations of the first kind…