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Diffusion models, typically formulated as discretizations of stochastic differential equations (SDEs), have achieved state-of-the-art performance in generative tasks. However, their theoretical analysis often involves complex proofs. In…
In precision frequency transfer systems, stringent requirements are imposed on the phase stability of transmitted signals. Throughout the transmission process, the inherent challenges of long-haul signal propagation inevitably introduce…
We discover restrained numerical instabilities in current training practices of deep networks with stochastic gradient descent (SGD), and its variants. We show numerical error (on the order of the smallest floating point bit and thus the…
The power spectral density in Fourier frequency domain, and the different variants of the Allan deviation (ADEV) in dependence on the averaging time are well established tools to analyse the fluctuation properties and frequency instability…
We investigate the spectral statistics of the difference of two density matrices, each of which is independently obtained by partially tracing a random bipartite pure quantum state. We first show how a closed-form expression for the exact…
An electroencephalogram (EEG) signal is currently accepted as a standard for automatic sleep staging. Lately, Near-human accuracy in automated sleep staging has been achievable by Deep Learning (DL) based approaches, enabling multi-fold…
Wireless Sensor Networks (WSNs) contain numerous sensor nodes having limited power resource, which report sensed data to the Base Station (BS) that requires high energy usage. Many routing protocols have been proposed in this regard…
In equilibrium, the fluctuation-dissipation theorem (FDT) expresses the response of an observable to a small perturbation by a correlation function of this variable with another one that is conjugate to the perturbation with respect to…
Information from frequency bands in biomedical time series provides useful summaries of the observed signal. Many existing methods consider summaries of the time series obtained over a few well-known, pre-defined frequency bands of…
Experimentally, the phase of the amplitude for electron transmission through a quantum dot (transmission phase) shows the same pattern between consecutive resonances. Such universal behavior, found for long sequences of resonances, is…
We consider a model applicable in many communication systems where the sum of n stochastic sinusoidal signals of the same frequency, but with random amplitudes as well as phase angles is present. The exact probability distribution of the…
We analytically derive the bit-string probability distributions of subsystems of random pure states and depolarized random states using the Dirichlet distribution. We identify the exact Beta distribution as the universal statistical law of…
We derive analytically, and validate numerically, the dispersion renormalization and attenuation of acoustic waves propagating through quenched disordered media in the long-wavelength limit. We consider weak spatial fluctuations in elastic…
We propose a novel algorithm for sleep dynamics visualization and automatic annotation by applying diffusion geometry based sensor fusion algorithm to fuse spectral information from two electroencephalograms (EEG). The diffusion geometry…
Two-dimensional electronic spectroscopy (2DES) is a powerful tool for investigating the dynamics of complex systems. However, analyzing the resulting spectra can be challenging, and thus may require the use of theoretical modeling…
In causal inference, measuring treatment heterogeneity is crucial as it provides scientific insights into how treatments influence outcomes and guides personalized decision-making. In this work, we study semi-supervised settings where a…
The variability in EEG signals between different individuals poses a significant challenge when implementing brain-computer interfaces (BCI). Commonly proposed solutions to this problem include deep learning models, due to their increased…
The problem of synthetic speech detection has enjoyed considerable attention, with recent methods achieving low error rates across several established benchmarks. However, to what extent can low error rates on academic benchmarks translate…
Burst suppression is an electroencephalography (EEG) pattern associated with profoundly inactivated brain states characterized by cerebral metabolic depression. Its distinctive feature is alternation between short temporal segments of…
We apply flicker-noise spectroscopy (FNS), a time series analysis method operating on structure functions and power spectrum estimates, to study the clinical electroencephalogram (EEG) signals recorded in children/adolescents (11 to 14…