Related papers: On a New Method of Storing a Variable Size Array
We introduce a new technique for the efficient management of large sequences of multidimensional data, which takes advantage of regularities that arise in real-world datasets and supports different types of aggregation queries. More…
A new alternative method to approximate the Visibility Graph (VG) of a time series has been introduced here. It exploits the fact that most of the nodes in the resulting network are not connected to those that are far away from them. This…
This paper presents a general technique for optimally transforming any dynamic data structure that operates on atomic and indivisible keys by constant-time comparisons, into a data structure that handles unbounded-length keys whose…
We introduce a new feature map for barcodes that arise in persistent homology computation. The main idea is to first realize each barcode as a path in a convenient vector space, and to then compute its path signature which takes values in…
We propose a simple modification to the conventional attention mechanism applied by Transformers: Instead of quantifying pairwise query-key similarity with scaled dot-products, we quantify it with the logarithms of scaled dot-products of…
In this paper we present several new and very practical methods and techniques for range aggregation and selection problems in multidimensional data structures and other types of sets of values. We also present some new extensions and…
New superconvergent structures are introduced by the finite volume element method (FVEM), which allow us to choose the superconvergent points freely. The general orthogonal condition and the modified M-decomposition (MMD) technique are…
Many modern datasets don't fit neatly into $n \times p$ matrices, but most techniques for measuring statistical stability expect rectangular data. We study methods for stability assessment on non-rectangular data, using statistical learning…
Many neural nets appear to represent data as linear combinations of "feature vectors." Algorithms for discovering these vectors have seen impressive recent success. However, we argue that this success is incomplete without an understanding…
We define a new decidable logic for expressing and checking invariants of programs that manipulate dynamically-allocated objects via pointers and destructive pointer updates. The main feature of this logic is the ability to limit the…
We present a dynamic data structure that maintains a tree decomposition of width at most $9k+8$ of a dynamic graph with treewidth at most $k$, which is updated by edge insertions and deletions. The amortized update time of our data…
Symmetric tensor operations arise in a wide variety of computations. However, the benefits of exploiting symmetry in order to reduce storage and computation is in conflict with a desire to simplify memory access patterns. In this paper, we…
Vectors are universal mathematical objects that can represent text, images, speech, or a mix of these data modalities. That happens regardless of whether data is represented by hand-crafted features or learnt embeddings. Collect a large…
We propose a new way of thinking about one parameter persistence. We believe topological persistence is fundamentally not about decomposition theorems but a central role is played by a choice of metrics. Choosing a pseudometric between…
The article presents a systematic review of the results of the development of the theoretical basis and the pilot implementation of data storage technology with automatic replenishment of data from sources belonging to different thematic…
Eigenvalues are defined for any element of an algebra of observables and do not require a representation in terms of wave functions or density matrices. A systematic algebraic derivation based on moments is presented here for the harmonic…
Continual learning systems are increasingly deployed in environments where retraining or reset is infeasible, yet many approaches emphasize task performance rather than the evolution of internal representations over time. In this work, we…
In this paper we present new data structures for two extensively studied variants of the orthogonal range searching problem. First, we describe a data structure that supports two-dimensional orthogonal range minima queries in $O(n)$ space…
The paper proposes an adaptive observer of the state vector of a nonlinear time varying system based on measurements of the output variable. The problem is solved under the assumption that the control matrix (vector) and the nonlinear…
We define and construct a new data structure, the tables, this structure generalizes the (finite) $k$-sets sets of Eilenberg \cite{Ei}, it is versatile (one can vary the letters, the words and the coefficients). We derive from this…