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A complete foundational discussion of acceleration in context of Special Relativity is presented. Acceleration allows the measurement of a Lorentz-FitzGerald body contraction created. It is argued that in the back scattering of a probing…
Multivariate extreme-value analysis is concerned with the extremes in a multivariate random sample, that is, points of which at least some components have exceptionally large values. Mathematical theory suggests the use of max-stable models…
Several statistics-based detectors, based on unimodal matrix models, for determining the number of sources in a field are designed. A new variance ratio statistic is proposed, and its asymptotic distribution is analyzed. The variance ratio…
The method of maximum entropy is quite a powerful tool to solve the generalized moment problem, which consists of determining the probability density of a random variable X from the knowledge of the expected values of a few functions of the…
We established a new method called Discrete Weierstrass Fourier Transform, a faster and more generalized Discrete Fourier Transform, to approximate discrete data. The theory of this method as well as some experiments are analyzed in this…
Addressing multi-modality constitutes one of the major challenges of sampling. In this reflection paper, we advocate for a more systematic evaluation of samplers towards two sources of difficulty that are mode separation and dimension. For…
We show that Transformers are Maximum Posterior Probability estimators for Mixtures of Gaussian Models. This brings a probabilistic point of view to Transformers and suggests extensions to other probabilistic cases.
We consider the fundamental problem of matching a template to a signal. We do so by M-estimation, which encompasses procedures that are robust to gross errors (i.e., outliers). Using standard results from empirical process theory, we derive…
We investigate sources of error in acceleration statistics from Lagrangian Particle Tracking (LPT) data and demonstrate techniques to eliminate or minimise bias errors introduced during processing. Numerical simulations of particle tracking…
We present a theoretical model to sufficiently investigate the optical rotational Doppler effect based on modal expansion method. We find that the frequency shift content is only determined by the surface of spinning object and the reduced…
In this paper, we introduce a translational force control method with disturbance observer (DOB)-based force disturbance cancellation for precise three-dimensional acceleration control of a multi-rotor UAV. The acceleration control of the…
We study the spin current tensor of a Dirac particle at accelerations close to the upper limit introduced by Caianiello. Continual interchange between particle spin and angular momentum is possible only when the acceleration is…
We study the multi-task learning problem that aims to simultaneously analyze multiple datasets collected from different sources and learn one model for each of them. We propose a family of adaptive methods that automatically utilize…
Experimental observation of Doppler-free signals for weak transitions can be greatly facilitated by an estimate for their expected amplitudes. We derive an analytical model which allows the Doppler-free amplitude to be estimated for small…
An information-spectrum approach is applied to solve the multiterminal source coding problem for correlated general sources, where sources may be nonstationary and/or nonergodic, and the distortion measure is arbitrary and may be…
The electron mass shift in a laser field has long remained an elusive concept. We show that the mass shift can exist in pulses but that it is neither unique nor universal: it can be reduced by pulse shaping. We show also that the detection…
In this review we confront the current theoretical understanding of particle acceleration at relativistic outflows with recent observational results on various source classes thought to involve such outflows, e.g. gamma-ray bursts, active…
The search for a diffuse neutrino flux component from astrophysical sources complements searches for point sources. In 2010 and 2011 many new results have been published on this subject. Realistic models can now be tested with these new…
A model for the diffusion of vector fields driven by external forces is proposed. Using the renormalization group and the $\epsilon$-expansion, the dynamical critical properties of the model with gaussian noise for dimensions below the…
Sudden changes are ubiquitous in nature. Identifying them is of crucial importance for a number of applications in medicine, biology, geophysics, and social sciences. Here we investigate the problem in the quantum domain, considering a…