Results 41 to 50 of about 5,542 (141)

Loss Behavior in Supervised Learning With Entangled States

Advanced Quantum Technologies, Volume 9, Issue 4, April 2026.
Entanglement in training samples supports quantum supervised learning algorithm in obtaining solutions of low generalization error. Using analytical as well as numerical methods, this work shows that the positive effect of entanglement on model after training has negative consequences for the trainability of the model itself, while showing the ...
Alexander Mandl, Johanna Barzen, Marvin Bechtold, Frank Leymann, Lavinia Stiliadou   +4 more
wiley   +1 more source

Function spaces for decoupling

Journal of the London Mathematical Society, Volume 113, Issue 4, April 2026.
Abstract We introduce new function spaces LW,sq,p(Rn)$\mathcal {L}_{W,s}^{q,p}(\mathbb {R}^{n})$ that yield a natural reformulation of the ℓqLp$\ell ^{q}L^{p}$ decoupling inequalities for the sphere and the light cone. These spaces are invariant under the Euclidean half‐wave propagators, but not under all Fourier integral operators unless p=q$p=q$, in ...
Andrew Hassell, Pierre Portal, Jan Rozendaal, Po‐Lam Yung   +3 more
wiley   +1 more source

A Miyaoka–Yau inequality for hyperplane arrangements in CPn$\mathbb {CP}^n$

Journal of the London Mathematical Society, Volume 113, Issue 4, April 2026.
Abstract Let H$\mathcal {H}$ be a hyperplane arrangement in CPn$\mathbb {CP}^n$. We define a quadratic form Q$Q$ on RH$\mathbb {R}^{\mathcal {H}}$ that is entirely determined by the intersection poset of H$\mathcal {H}$. Using the Bogomolov–Gieseker inequality for parabolic bundles, we show that if a∈RH$\mathbf {a}\in \mathbb {R}^{\mathcal {H}}$ is ...
Martin de Borbon, Dmitri Panov
wiley   +1 more source

A Probabilistic Extension of the Fubini Polynomials

Bulletin of the Malaysian Mathematical Sciences Society
In this paper, we present a probabilistic extension of the Fubini polynomials and numbers associated with a random variable satisfying some appropriate moment conditions. We obtain the exponential generating function and an integral representation for it. The higher order Fubini polynomials and recurrence relations are also derived.
Soni, R., Pathak, A. K., Vellaisamy, P.
openaire   +3 more sources

Approximation of Discontinuous Functions by Positive Linear Operators. A Probabilistic Approach

Mathematical Methods in the Applied Sciences, Volume 49, Issue 5, Page 4184-4197, 30 March 2026.
ABSTRACT We obtain approximation results for general positive linear operators satisfying mild conditions, when acting on discontinuous functions and absolutely continuous functions having discontinuous derivatives. The upper bounds, given in terms of a local first modulus of continuity, are best possible, in the sense that we can construct particular ...
J.A. Adell, P. Garrancho, F.J. Martínez‐Sánchez   +2 more
wiley   +1 more source

On Bounds for Norms of Reparameterized ReLU Artificial Neural Network Parameters: Sums of Fractional Powers of the Lipschitz Norm Control the Network Parameter Vector

Mathematical Methods in the Applied Sciences, Volume 49, Issue 4, Page 2135-2160, 15 March 2026.
ABSTRACT It is an elementary fact in the scientific literature that the Lipschitz norm of the realization function of a feedforward fully connected rectified linear unit (ReLU) artificial neural network (ANN) can, up to a multiplicative constant, be bounded from above by sums of powers of the norm of the ANN parameter vector.
Arnulf Jentzen, Timo Kröger
wiley   +1 more source

Quantitative equidistribution for the solutions of systems of sparse polynomial equations

, 2014
For a system of Laurent polynomials f_1,..., f_n \in C[x_1^{\pm1},..., x_n^{\pm1}] whose coefficients are not too big with respect to its directional resultants, we show that the solutions in the algebraic n-th dimensional complex torus of the system of ...
D'Andrea, Carlos, Galligo, André, Sombra, Martín   +2 more
core   +2 more sources

A standardization procedure to incorporate variance partitioning‐based priors in latent Gaussian models

Scandinavian Journal of Statistics, Volume 53, Issue 1, Page 364-394, March 2026.
ABSTRACT Latent Gaussian models (LGMs) are a subset of Bayesian Hierarchical models where Gaussian priors, conditional on variance parameters, are assigned to all effects in the model. LGMs are employed in many fields for their flexibility and computational efficiency. However, practitioners find prior elicitation on the variance parameters challenging
Luisa Ferrari, Massimo Ventrucci
wiley   +1 more source

Distribution of zeros of random and quantum chaotic sections of positive line bundles

, 1998
We study the limit distribution of zeros of certain sequences of holomorphic sections of high powers $L^N$ of a positive holomorphic Hermitian line bundle $L$ over a compact complex manifold $M$.
Shiffman, Bernard, Zelditch, Steve
core   +2 more sources

From simplex slicing to sharp reverse Hölder inequalities

Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.
Abstract Simplex slicing (Webb, 1996) is a sharp upper bound on the volume of central hyperplane sections of the regular simplex. We extend this to sharp bounds in the probabilistic framework of negative moments, and beyond, of centred log‐concave random variables, establishing a curious phase transition of the extremising distribution for new sharp ...
James Melbourne, Michael Roysdon, Colin Tang, Tomasz Tkocz   +3 more
wiley   +1 more source