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Random number generators (RNG) based on quantum mechanics are captivating due to their security and unpredictability compared to conventional generators, such as pseudo-random number generators and hardware-random number generators. This…
The hyperbolic Anosov C-systems have a countable set of everywhere dense periodic trajectories which have been recently used to generate pseudorandom numbers. The asymptotic distribution of periodic trajectories of C-systems with periods…
The traditional method to generate pulses in the range of some nanoseconds with high amplitudes, is the using of the avalanche-effect of transistors. However the problem with this method is the poor possibility for parameterizing. That was…
Choose a random degree d poly f with coefficients in a finite field F. We estimate the ultimate period of f under compositional iteration. We also determine the joint distribution of the small cycle lengths in the graph with edges (x,f(x)),…
Elliptic curve cryptography has received great attention in recent years due to its high resistance against modern cryptanalysis. The aim of this article is to present efficient generators to generate substitution boxes (S-boxes) and pseudo…
This work introduces a method for constructing polyphase alternating codes in which the length of a code transmission cycle can be $p^m$ or $p-1$, where $p$ is a prime number and $m$ is a positive integer. The relevant properties leading to…
Even if the output of a Random Number Generator (RNG) is perfectly uniformly distributed, it may be correlated to pre-existing information and therefore be predictable. Statistical tests are thus not sufficient to guarantee that an RNG is…
We describe an optoelectronic system for simultaneously generating parallel, independent streams of random bits using spectrally separated noise signals obtained from a single optical source. Using a pair of non-overlapping spectral filters…
Discrete-time models are very convenient to simulate a nonlinear system on a computer. In order to build the discrete-time simulation models for the nonlinear feedback systems (which is a very important class of systems in many…
We propose a new approach to nondeterministic random number generation. In theory, the randomness originated from the uncorrelated nature of consecutive laser pulses with Poissonian photon number distribution and that of the consecutive…
We consider a class of reflected backward doubly stochastic differential equations with time delayed generator (in short RBDSDE with time delayed generator), in this case generator at time $t$ can depend on the values of a solution in the…
For random maps, the expected value of the order (i.e. the period of the sequence of compositional iterates) is approximated asymptotically. It is much smaller than the expected value for the product of the cycle lengths.
We study termination time and recurrence time in programs with unbounded recursion, which are either randomized or operate on some statistically quantified inputs. As the underlying formal model for such programs we use probabilistic…
The increasing sophistication of wind turbine design and control generates a need for high-quality data. Therefore, the relatively limited set of measured wind data may be extended with computer-generated surrogate data, e.g. to make…
We present a nearly-linear time algorithm for counting and randomly generating simple graphs with a given degree sequence in a certain range. For degree sequence $(d_i)_{i=1}^n$ with maximum degree $d_{\max}=O(m^{1/4-\tau})$, our algorithm…
Algorithm and code to produce sequences whose members obey Gaussian distribution function is reported. Discreet and limited number of groups are defined in the distribution function, where each group is represented only with one value…
We introduce concepts of "recursive polynomial remainder sequence (PRS)" and "recursive subresultant," along with investigation of their properties. A recursive PRS is defined as, if there exists the GCD (greatest common divisor) of initial…
Time series forecasting is crucial for many fields, such as disaster warning, weather prediction, and energy consumption. The Transformer-based models are considered to have revolutionized the field of sequence modeling. However, the…
Natural numbers satisfying a certain unusual property are defined by the author in a previous note. Later, the author called such numbers $v$-palindromic numbers and proved a periodic phenomenon pertaining to such numbers and repeated…
Time series synthesis is an effective approach to ensuring the secure circulation of time series data. Existing time series synthesis methods typically perform temporal modeling based on random sequences to generate target sequences, which…