For a quantum channel of additive Gaussian noise with loss, in the general case of n copies input, we show that up to first order perturbation, any non-Gaussian perturbation to the product thermal state input has a less quantum information transmission rate when the input energy tend to infinitive. PACS number(s): 03.67.-a, 42.50.Dv, 89.70.+c

This paper presents the design of an additive fault tolerant control for nonlinear time-invariant singularly perturbed systems against actuator faults based on Lyapunov redesign principle. The overall system is reduced into subsystems with fast and slow dynamic behavior using singular perturbation method. The time scale reduction is carried out when the singular perturbation parameter is set to...

A highly non-gaussian cosmological perturbation with a flat spectrum has unusual stochastic properties. We show that they depend on the size of the box within which the perturbation is defined, but that for a typical observer the parameters defining the perturbation ‘run’ to compensate for any change in the box size. Focusing on the primordial curvature perturbation, we show that an un-correlat...

We present a generalization bound for feedforward neural networks with ReLU activations in terms of the product of the spectral norm of the layers and the Frobenius norm of the weights. The key ingredient is a bound on the changes in the output of a network with respect to perturbation of its weights, thereby bounding the sharpness of the network. We combine this perturbation bound with the PAC...

I recall the well-known sufficient conditions for the bound r < 16ǫ on the spectrum of the primordial tensor perturbation. Two recent papers claim a violation of this bound, without stating explicitely any violation of the sufficient conditions. The following conditions are sufficient for the bound r < 16ǫ on the primordial tensor perturbation. • Inflation is of the slow-roll variety. • The cur...

Karchmer, Kushilevitz and Nisan formulated the formula size problem as an integer programming problem called the rectangle bound and introduced a technique called the LP bound, which gives a formula size lower bound by showing a feasible solution of the dual problem of its LP-relaxation. As extensions of the LP bound, we introduce novel general techniques proving formula size lower bounds, name...

This paper gives normwise and componentwise perturbation analyses for the Q-factor of the QR factorization of the matrix A with full column rank when A suffers from an additive perturbation. Rigorous perturbation bounds are derived on the projections of the perturbation of the Q-factor in the range of A and its orthogonal complement. These bounds overcome a serious shortcoming of the first-orde...

Abstract We derive new concentration bounds for time averages of measurement outcomes in quantum Markov processes. This generalizes well-known classical chains, which provide constraints on finite-time fluctuations time-additive quantities around their averages. employ spectral, perturbation and martingale techniques, together with non-commutative $$L_2$$ <mml:math xmlns:mml="http://www.w3.org/...