Related papers: The On-Line Encyclopedia of Integer Sequences
A "tournament sequence" is an increasing sequence of positive integers (t_1,t_2,...) such that t_1=1 and t_{i+1} <= 2 t_i. A "Meeussen sequence" is an increasing sequence of positive integers (m_1,m_2,...) such that m_1=1, every nonnegative…
Order-independent (OI) queues, introduced by Berezner, Kriel, and Krzesinski in 1995, expanded the family of multi-class queues that are known to have a product-form stationary distribution by allowing for intricate class-dependent service…
In this paper, we investigate the quintessence models with an oscillating equation of state (EoS) and their potentials. From the constructed potentials, which have the EoS of $\omega_{\phi}=\omega_0+\omega_1\sin z$, we find they are all the…
A growing challenge in research and industrial engineering applications is the need for repeated, systematic analysis of large-scale computational models, for example, patient-specific digital twins of diseased human organs: The analysis…
Sequences have become first class citizens in supervised learning thanks to the resurgence of recurrent neural networks. Many complex tasks that require mapping from or to a sequence of observations can now be formulated with the…
We give a deterministic algorithm that very quickly proves the primality or compositeness of the integers N in a certain sequence, using an elliptic curve E/Q with complex multiplication by the ring of integers of Q(sqrt(-7)). The algorithm…
The diversity and Zipfian frequency distribution of natural language predicates in corpora leads to sparsity in Entailment Graphs (EGs) built by Open Relation Extraction (ORE). EGs are computationally efficient and explainable models of…
Recent advances in computational methods for intractable models have made network data increasingly amenable to statistical analysis. Exponential random graph models (ERGMs) emerged as one of the main families of models capable of capturing…
Retrial phenomenon naturally arises in various systems such as call centers, cellular networks and random access protocols in local area networks. This paper gives a comprehensive survey on theory and applications of retrial queues in these…
These lecture notes, prepared for the 2022 QUC summer school at KIAS, provide an introduction to Higgs Effective Field Theory and the use of field geometry in Quantum Field Theory. While not sounding the depths of any of these topics, we…
The binary heap of Williams (1964) is a simple priority queue characterized by only storing an array containing the elements and the number of elements $n$ - here denoted a strictly implicit priority queue. We introduce two new strictly…
We study the enumerative and analytic properties of some sequences constructed using tensor invariant theory. The octant sequences are constructed from the exceptional Lie group $G_2$ and the quadrant sequences from the special linear group…
Order patterns apply well to many fields, because of minimal stationarity assumptions. Here we fix the methodology of patterns of length 3 by introducing an orthogonal system of four pattern contrasts. These contrasts are statistically…
An improved upper bound is obtained for the density of sequences of positive integers that contain no k-term geometric progression.
Prediction based on Irregularly Sampled Time Series (ISTS) is of wide concern in the real-world applications. For more accurate prediction, the methods had better grasp more data characteristics. Different from ordinary time series, ISTS is…
Symbolic regression, i.e. predicting a function from the observation of its values, is well-known to be a challenging task. In this paper, we train Transformers to infer the function or recurrence relation underlying sequences of integers…
This paper analyzes the emergence and distribution of potential twin primes, pairs of integers that are both relatively prime to the first n primes or to a given set M of primes, and which are the breeding grounds of true twin primes. It…
This paper introduces recurrent equilibrium networks (RENs), a new class of nonlinear dynamical models} for applications in machine learning, system identification and control. The new model class admits ``built in'' behavioural guarantees…
Open Information Extraction (OpenIE) is a fundamental yet challenging task in Natural Language Processing, which involves extracting all triples (subject, predicate, object) from a given sentence. While labeling-based methods have their…
In this tribute to Neil Sloane, we revisit the first sequence in the On-Line Encyclopedia of Integer Sequences, sequence A435 (1, 8, 78, 944, 13800, 237432, 4708144, 105822432, ...), that he encountered when he was a graduate student, and…