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A dynamic forest data structure maintains a forest (and associated data like edge weights) under edge insertions and deletions. Dynamic forests are widely used to solve online and offline graph problems. Well-known examples of dynamic…
In this article we discuss a data structure, which combines advantages of two different ways for representing graphs: adjacency matrix and collection of adjacency lists. This data structure can fast add and search edges (advantages of…
We introduce a ScatterNet that uses a parametric log transformation with Dual-Tree complex wavelets to extract translation invariant representations from a multi-resolution image. The parametric transformation aids the OLS pruning algorithm…
Tree-structured data naturally appear in various fields, particularly in biology where plants and blood vessels may be described by trees, but also in computer science because XML documents form a tree structure. This paper is devoted to…
The pattern analysis of tree structure holds significant scientific value for genetic breeding and forestry management. The current trunk and branch extraction technologies are mainly LiDAR-based or UAV-based. The former approaches obtain…
We present a new distributed representation in deep neural nets wherein the information is represented in native form as a matrix. This differs from current neural architectures that rely on vector representations. We consider matrices as…
Wavelet Transforms are a widely used technique for decomposing a signal into coefficient vectors that correspond to distinct frequency/scale bands while retaining time localization. This property enables an adaptive analysis of signals at…
In deep neural networks, better results can often be obtained by increasing the complexity of previously developed basic models. However, it is unclear whether there is a way to boost performance by decreasing the complexity of such models.…
Long document classification presents challenges in capturing both local and global dependencies due to their extensive content and complex structure. Existing methods often struggle with token limits and fail to adequately model…
This chapter is dedicated to recent developments in the field of wavelet analysis for scattered data. We introduce the concept of samplets, which are signed measures of wavelet type and may be defined on sets of arbitrarily distributed data…
Human language is known to exhibit a nested, hierarchical structure, allowing us to form complex sentences out of smaller pieces. However, many state-of-the-art neural networks models such as Transformers have no explicit hierarchical…
An important problem in geometric computing is defining and computing similarity between two geometric shapes, e.g. point sets, curves and surfaces, etc. Important geometric and topological information of many shapes can be captured by…
Survival analysis concerns the task of predicting the time until an event occurs. Often used in the medical field, survival analysis deals with incomplete (i.e., censored) data, for instance, from patients who did not experience the event…
We consider the wavelet transform of a finite, rooted, node-ranked, $p$-way tree, focusing on the case of binary ($p = 2$) trees. We study a Haar wavelet transform on this tree. Wavelet transforms allow for multiresolution analysis through…
Dynamic techniques are a scalable and effective way to analyze concurrent programs. Instead of analyzing all behaviors of a program, these techniques detect errors by focusing on a single program execution. Often a crucial step in these…
Compact and I/O-efficient data representations play an important role in efficient algorithm design, as memory bandwidth and latency can present a significant performance bottleneck, slowing the computation by orders of magnitude. While…
Information distributed through the Web keeps growing faster day by day, and for this reason, several techniques for extracting Web data have been suggested during last years. Often, extraction tasks are performed through so called…
Matrix is a new message-oriented data synchronization middleware, used as a federated platform for near real-time decentralized applications. It features a novel approach for inter-server communication based on synchronizing message history…
Trees are fundamental data structure for many areas of computer science and system engineering. In this report, we show how to ensure eventual consistency of optimistically replicated trees. In optimistic replication, the different replicas…
We introduce top trees as a design of a new simpler interface for data structures maintaining information in a fully-dynamic forest. We demonstrate how easy and versatile they are to use on a host of different applications. For example, we…