Related papers: Some Comments on the Strong Simplex Conjecture
We consider geometrical optimization problems related to optimizing the error probability in the presence of a Gaussian noise. One famous questions in the field is the "weak simplex conjecture". We discuss possible approaches to it, and…
Sensory information propagates through successive processing stages in the brain, where synaptic weight patterns between stations determine how downstream neurons decode information from upstream populations. Although optimized synaptic…
By using the wavelet transformation (WT), we have analyzed the response of an ensemble of $N$ (=1, 10, 100 and 500) Hodgkin-Huxley (HH) neurons to {\it transient} $M$-pulse spike trains ($M=1-3$) with independent Gaussian noises. The…
We study the rate of decay of the probability of error for distinguishing between a sparse signal with noise, modeled as a sparse mixture, from pure noise. This problem has many applications in signal processing, evolutionary biology,…
In this paper, we demonstrate some applications of compressive sensing over networks. We make a connection between compressive sensing and traditional information theoretic techniques in source coding and channel coding. Our results provide…
Methods borrowed from the world of quantum information processing have lately been used to enhance the signal-to-noise ratio of quantum detectors. Here we analyze the use of stabilizer quantum error-correction codes for the purpose of…
The problem of information extraction from discrete stochastic time series, produced with some finite sampling frequency, using flicker-noise spectroscopy, a general framework for information extraction based on the analysis of the…
In this paper we prove strong well-posedness for a system of stochastic differential equations driven by a degenerate diffusion satisfying a weak-type H\"ormander condition, assuming H\"older regularity assumptions on the drift coefficient.…
We consider the problem of signal estimation (denoising) from a statistical mechanical perspective, using a relationship between the minimum mean square error (MMSE), of estimating a signal, and the mutual information between this signal…
Under standard assumptions including stationary and serially uncorrelated Gaussian gravitational wave stochastic background signal and noise distributions, as well as homogenous detector sensitivities, the standard cross-correlation…
In this article, we provide an alternative up-sampling and PSF deconvolution method for the iterative multi-exposure coaddition. Different from the previous works, the new method has a ratio-correction term, which allows the iterations to…
We show that the axiom of choice, a basic yet controversial postulate of set theory, leads to revise the standard understanding of one of the pillars of our best physical theories, namely the no-signaling principle. While it is well known…
We study the statistical decision process of detecting the signal from a `signal+noise' type matrix model with an additive Wigner noise. We propose a hypothesis test based on the linear spectral statistics of the data matrix, which does not…
We present a simple classical (random) signal model reproducing Born's rule. The crucial point of our approach is that the presence of detector's threshold and calibration procedure have to be treated not as simply experimental…
In compressed sensing, we wish to reconstruct a sparse signal $x$ from observed data $y$. In sparse coding, on the other hand, we wish to find a representation of an observed signal $y$ as a sparse linear combination, with coefficients $x$,…
In this work, we show that Spearman's correlation coefficient test about $H_0:\rho_s=0$ found in most statistical software packages is theoretically incorrect and performs poorly when bivariate normality assumptions are not met or the…
Quantum fluctuations yield inevitable noises in quantum detection. We derive an upper bound of signal to noise ratio for arbitrary quantum detection described by trace-class operators with discrete spectra. The bound is independent of…
Consider a waveform channel where the transmitted signal is corrupted by Wiener phase noise and additive white Gaussian noise (AWGN). A discrete-time channel model that takes into account the effect of filtering on the phase noise is…
This paper considers the joint compression and enhancement problem for speech signal in the presence of noise. Recently, the SoundStream codec, which relies on end-to-end joint training of an encoder-decoder pair and a residual vector…
We revisit the fundamental question of simple-versus-simple hypothesis testing with an eye towards computational complexity, as the statistically optimal likelihood ratio test is often computationally intractable in high-dimensional…