Related papers: String Periods in the Order-Preserving Model

In-place associative integer sorting technique was proposed for integer lists which requires only constant amount of additional memory replacing bucket sort, distribution counting sort and address calculation sort family of algorithms.…

In-place associative integer sorting technique was developed, improved and specialized for distinct integers. The technique is suitable for integer sorting. Hence, given a list S of n integers S[0...n-1], the technique sorts the integers in…

The ever increasing memory requirements of several applications has led to increased demands which might not be met by embedded devices. Constraining the usage of memory in such cases is of paramount importance. It is important that such…

Reduced order modeling methods are often used as a mean to reduce simulation costs in industrial applications. Despite their computational advantages, reduced order models (ROMs) often fail to accurately reproduce complex dynamics…

The ordinal patterns of a fixed number of consecutive values in a time series is the spatial ordering of these values. Counting how often a specific ordinal pattern occurs in a time series provides important insights into the properties of…

For a time-limited version of the H$_2$ norm defined over a fixed time interval, we obtain a closed form expression of the gradients. After that, we use the gradients to propose a time-limited model order reduction method. The method…

The neural ordinary differential equation (neural ODE) model has attracted increasing attention in time series analysis for its capability to process irregular time steps, i.e., data are not observed over equally-spaced time intervals. In…

Linear temporal logic (LTL) is a specification language for finite sequences (called traces) widely used in program verification, motion planning in robotics, process mining, and many other areas. We consider the problem of learning LTL…

We describe a data structure that supports access, rank and select queries, as well as symbol insertions and deletions, on a string $S[1,n]$ over alphabet $[1..\sigma]$ in time $O(\lg n/\lg\lg n)$, which is optimal even on binary sequences…

Considering the concept of time-dilation, there exist some major issues with recurrent neural Architectures. Any variation in time spans between input data points causes performance attenuation in recurrent neural network architectures.…

It is well known that n integers in the range [1,n^c] can be sorted in O(n) time in the RAM model using radix sorting. More generally, integers in any range [1,U] can be sorted in O(n sqrt{loglog n}) time. However, these algorithms use O(n)…

The concept of p-ordering for a prime p was introduced by Manjul Bhargava (in his PhD thesis) to develop a generalized factorial function over an arbitrary subset of integers. This notion of p-ordering provides a representation of…

We develop a rigorously controlled multi-time scale averaging technique; the averaging is done on a finite time interval, properly chosen, and then, via iterations and normal form transformations, the time intervals are scaled to arbitrary…

Partial differential equations (PDEs) describing thermodynamically isolated systems typically possess conserved quantities (like mass, momentum, and energy) and dissipated quantities (like entropy). Preserving these conservation and…

We investigate a generalised version of the recently proposed ordinal partition time series to network transformation algorithm. Firstly we introduce a fixed time lag for the elements of each partition that is selected using techniques from…

We propose new succinct representations of ordinal trees, which have been studied extensively. It is known that any $n$-node static tree can be represented in $2n + o(n)$ bits and a number of operations on the tree can be supported in…

We apply modern methods in computational topology to the task of discovering and characterizing phase transitions. As illustrations, we apply our method to four two-dimensional lattice spin models: the Ising, square ice, XY, and…

Hamiltonian Operator Inference has been introduced in [Sharma, H., Wang, Z., Kramer, B., Physica D: Nonlinear Phenomena, 431, p.133122, 2022] to learn structure-preserving reduced-order models (ROMs) for Hamiltonian systems. This approach…

Process mining starts from event data. The ordering of events is vital for the discovery of process models. However, the timestamps of events may be unreliable or imprecise. To further complicate matters, also causally unrelated events may…

This document contains notes based on lectures given by Hendrik Lenstra at the PCMI summer school 2022. There are many problems in algebraic number theory which one would like to solve algorithmically, for example computation of the maximal…