We derive new bounds for the generalization error of kernel machines, such as support vector machines and related regularization networks by obtaining new bounds on their covering numbers. The proofs make use of a viewpoint that is apparently novel in the eld of statistical learning theory. The hypothesis class is described in terms of a linear operator mapping from a possibly innnite dimension...

We study the time evolution of R\'enyi entropy in a system two coupled Brownian SYK clusters evolving from an initial product state. The one cluster grows linearly and then saturates to coarse grained entropy. This Page curve is obtained by different methods, path integral saddle point analysis operator dynamics analysis. Using character dynamics, we derive master equation which controls gives ...

Driver fatigue has become one of the major causes of traffic accidents, and is a complicated physiological process. However, there is no effective method to detect driving fatigue. Electroencephalography (EEG) signals are complex, unstable, and non-linear; non-linear analysis methods, such as entropy, maybe more appropriate. This study evaluates a combined entropy-based processing method of EEG...

As an important tool of information fusion, Dempster-Shafer evidence theory is widely applied in handling the uncertain information in fault diagnosis. However, an incorrect result may be obtained if the combined evidence is highly conflicting, which may leads to failure in locating the fault. To deal with the problem, an improved evidential-Induced Ordered Weighted Averaging (IOWA) sensor data...

Some of the important inequalities associated with quantum entropy are immediate algebraic consequences of the Hansen-Pedersen-Jensen inequality. A general argument is given in terms of the matrix perspective of an operator convex function. A matrix analogue of Maréchal’s extended perspectives provides additional inequalities, including a p + q ≤ 1 result of Lieb.

We derive a high-resolution formula for the L-quantization errors of Riemann-Liouville processes and the sharp Kolmogorov entropy asymptotics for related Sobolev balls. We describe a quantization procedure which leads to asymptotically optimal functional quantizers. Regular variation of the eigenvalues of the covariance operator plays a crucial role.

The ordered weighted averaging (OWA) operator by Yager has received more and more attention since its appearance. One key point in the OWA operator is to determine its associated weights. Among numerous methods that have appeared in the literature, we notice the maximum entropy OWA (MEOWA) weights that are determined by taking into account two appealing measures characterizing the OWA weights. ...

Molecular dynamics (MD) simulations of 5 ns on protein-DNA complexes of catabolite-activator protein (CAP), lambda-repressor, and their corresponding uncomplexed protein and DNA, are reported. These cases represent two extremes of DNA bending, with CAP DNA bent severely and the lambda-operator nearly straight when complexed with protein. The calculations were performed using the AMBER suite of ...

Let U denote the unit ball of the Cameron-Martin space of a Gaussian measure on a Hilbert space. The sharp asymptotics for the Kolmogorov (metric) entropy numbers of U is derived. The condition imposed is regular variation of the eigenvalues of the covariance operator. A consequence is a precise link including constants to the functional quantiza-tion problem.

We prove Hausdorff-Young inequality for the Fourier transform connected with Riemann-Liouville operator. We use this inequality to establish the uncertainty principle in terms of entropy. Next, we show that we can derive the Heisenberg-Pauli-Weyl inequality for the precedent Fourier transform.