Related papers: A Class of Random Binary Waveforms With Impulse-Li…
We propose a class of continuous-time Markov counting processes for analyzing correlated binary data and establish a correspondence between these models and sums of exchangeable Bernoulli random variables. Our approach generalizes many…
The amount of randomness in a signal generated by physical or non-physical process can reveal important information about that process. For example, the presence of randomness in ECG signals may indicate a cardiac disease. On the hand, the…
The autocorrelation function and the run structure are two basic notions for binary sequences, and have been used as two independent postulates to test randomness of binary sequences ever since Golomb 1955. In this paper, we prove for…
We suggest to construct infinite stochastic binary sequences by associating one of the two symbols of the sequence with the renewal times of an underlying renewal process. Focusing on stationary binary sequences corresponding to delayed…
This paper presents a framework for binary autoregressive time series in which each observation is a Bernoulli variable whose success probability evolves with past outcomes and probabilities, in the spirit of GARCH-type dynamics,…
Binary data are highly common in many applications, however it is usually modelled with the assumption that the data are independently and identically distributed. This is typically not the case in many real-world examples and such the…
Bernoulli sieve is a recursive construction of a random composition (ordered partition) of integer $n$. This composition can be induced by sampling from a random discrete distribution which has frequencies equal to the sizes of component…
A very simple event frequency approximation algorithm that is sensitive to event timeliness is suggested. The algorithm iteratively updates categorical click-distribution, producing (path of) a random walk on a standard $n$-dimensional…
We consider a pair of causally independent processes, modelled as the tensor product of two channels, acting on a possibly correlated input to produce random outputs X and Y. We show that, assuming the processes produce a sufficient amount…
A transformed auto-correlation method is presented here, where a received signal is transformed based on a priori reflecting model, and then the transformed signal is cross-correlated to its original one. If the model is correct, after…
We consider a random trial-based telegraph process, which describes a motion on the real line with two constant velocities along opposite directions. At each epoch of the underlying counting process the new velocity is determined by the…
Discovering causal relations among observed variables in a given data set is a main topic in studies of statistics and artificial intelligence. Recently, some techniques to discover an identifiable causal structure have been explored based…
The paper studies discrete time processes and their predictability and randomness in deterministic pathwise setting, without using probabilistic assumptions on the ensemble. We suggest some approaches to quantification of randomness based…
In the simple case of a Bernoulli shift on two symbols, zero and one, by permuting the symbols, it is obvious that any two equal entropy shifts are isomorphic. We show that the isomorphism can be realized by a factor that maps a binary…
We propose a new method to construct a stationary process and random field with a given decreasing covariance function and any one-dimensional marginal distribution. The result is a new class of stationary processes and random fields. The…
We study the effective SNR behavior of various enumerative amplitude shaping algorithms. We show that their relative behavior can be explained via the temporal autocorrelation function or via the energy dispersion index.
We report upon a novel principle for realization of a fast nondeterministic random number generator whose randomness relies on intrinsic randomness of the quantum physical processes of photonic emission in semiconductors and subsequent…
We experimentally demonstrate an all-optical random number generator based on spontaneous symmetry breaking in a coherently-driven Kerr resonator. Random bit sequences are generated by repeatedly tuning a control parameter across a…
Binary concepts are empirically used by humans to generalize efficiently. And they are based on Bernoulli distribution which is the building block of information. These concepts span both low-level and high-level features such as "large vs…
We consider pattern formation in periodically forced binary systems. In particular we focus on systems in which the two species are differentially forced, one being accelerated with respect to the other. Using a continuum model consisting…