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Let $V(k)$ denote the waiting time, the number of trials needed to get a consecutive $k$ ones. We propose recurrence algorithms for the probability distribution function (pdf) and the probability generating function (pgf) of $V(k)$ in…
Now a days, data mining and knowledge discovery methods are applied to a variety of enterprise and engineering disciplines to uncover interesting patterns from databases. The study of Sequential patterns is an important data mining problem…
Recursive decoding techniques are considered for Reed-Muller (RM) codes of growing length $n$ and fixed order $r.$ An algorithm is designed that has complexity of order $n\log n$ and corrects most error patterns of weight up to…
Quantum key distribution allows for the generation of a secret key between distant parties connected by a quantum channel such as optical fibre or free space. Unfortunately, the rate of generation of a secret key by direct transmission is…
We introduce a class of stochastic integer sequences. In these sequences, every element is a sum of two previous elements, at least one of which is chosen randomly. The interplay between randomness and memory underlying these sequences…
Random Numbers determine the security level of cryptographic applications as they are used to generate padding schemes in the encryption/decryption process as well as used to generate cryptographic keys. This paper utilizes the QKD to…
Random numbers are a fundamental resource in science and engineering with important applications in simulation and cryptography. The inherent randomness at the core of quantum mechanics makes quantum systems a perfect source of entropy.…
In covariate-adaptive or response-adaptive randomization, the treatment assignment and outcome can be correlated. Under this situation, re-randomization tests are a straightforward and attractive method to provide valid statistical…
Computation of the probability that a random graph is connected is a challenging problem, so it is natural to turn to approximations such as Monte Carlo methods. We describe sequential importance resampling and splitting algorithms for the…
A new cryptographic approach -- Iterated Random Encryption (IRE) -- is presented here. Although it is very simple, and easy to implement, it provides a very high level of security. According to this approach, a sequence of operations…
A dual approach to defining the triangle sequence (a type of multidimensional continued fraction algorithm, initially developed in NT/9906016) for a pair of real numbers is presented, providing a new, clean geometric interpretation of the…
Random Reshuffling (RR) is an algorithm for minimizing finite-sum functions that utilizes iterative gradient descent steps in conjunction with data reshuffling. Often contrasted with its sibling Stochastic Gradient Descent (SGD), RR is…
Quantum communication enables the implementation of tasks that are unachievable with classical resources. However, losses on the communication channel preclude the direct long-distance transmission of quantum information in many relevant…
Conventional random number generators provide the speed but not necessarily the high quality output streams needed for large-scale stochastic simulations. Cryptographically-based generators, on the other hand, provide superior quality…
In this paper, we have used Recurrent Neural Networks to capture and model human motion data and generate motions by prediction of the next immediate data point at each time-step. Our RNN is armed with recently proposed Gated Recurrent…
Random features is one of the most popular techniques to speed up kernel methods in large-scale problems. Related works have been recognized by the NeurIPS Test-of-Time award in 2017 and the ICML Best Paper Finalist in 2019. The body of…
Random number generation is a fundamental security primitive for RFID devices. However, even this relatively simple requirement is beyond the capacity of today's average RFID tag. A recently proposed solution, Fingerprint Extraction and…
Recurrent Neural Networks (RNNs) are a class of machine learning algorithms used for applications with time-series and sequential data. Recently, there has been a strong interest in executing RNNs on embedded devices. However, difficulties…
Probability estimation is an elementary building block of every statistical data compression algorithm. In practice probability estimation is often based on relative letter frequencies which get scaled down, when their sum is too large.…
Binary sequences are widely used in various practical fields, such as telecommunications, radar technology, navigation, cryptography, measurement sciences, biology or industry. In this paper, a method to generate long binary sequences (LBS)…