Open Access. Powered by Scholars. Published by Universities.®
Discrete Mathematics and Combinatorics Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Institution
- Keyword
-
- Ad allocation (1)
- Balance (1)
- Bipartite graphs (1)
- Computational Neuroscience (1)
- Decision making (1)
-
- Frustration index (1)
- Frustration number (1)
- Graph convolution (1)
- Graph theory (1)
- Interference (1)
- Maximum frustration (1)
- Memory Capacity (1)
- Message passing (1)
- Neuroidal Model (1)
- Node embeddings (1)
- Online matching (1)
- Positional encodings (1)
- Probabilistic algorithms (1)
- Random Graphs (1)
- Sign-symmetric. (1)
- Signed graph (1)
- Switching (1)
- Switching isomorphism (1)
- Transformer (1)
Articles 1 - 4 of 4
Full-Text Articles in Discrete Mathematics and Combinatorics
A Bridge Between Graph Neural Networks And Transformers: Positional Encodings As Node Embeddings, Bright Kwaku Manu
A Bridge Between Graph Neural Networks And Transformers: Positional Encodings As Node Embeddings, Bright Kwaku Manu
Electronic Theses and Dissertations
Graph Neural Networks and Transformers are very powerful frameworks for learning machine learning tasks. While they were evolved separately in diverse fields, current research has revealed some similarities and links between them. This work focuses on bridging the gap between GNNs and Transformers by offering a uniform framework that highlights their similarities and distinctions. We perform positional encodings and identify key properties that make the positional encodings node embeddings. We found that the properties of expressiveness, efficiency and interpretability were achieved in the process. We saw that it is possible to use positional encodings as node embeddings, which can be …
Foundations Of Memory Capacity In Models Of Neural Cognition, Chandradeep Chowdhury
Foundations Of Memory Capacity In Models Of Neural Cognition, Chandradeep Chowdhury
Master's Theses
A central problem in neuroscience is to understand how memories are formed as a result of the activities of neurons. Valiant’s neuroidal model attempted to address this question by modeling the brain as a random graph and memories as subgraphs within that graph. However the question of memory capacity within that model has not been explored: how many memories can the brain hold? Valiant introduced the concept of interference between memories as the defining factor for capacity; excessive interference signals the model has reached capacity. Since then, exploration of capacity has been limited, but recent investigations have delved into the …
Signings Of Graphs And Sign-Symmetric Signed Graphs, Ahmad Asiri
Signings Of Graphs And Sign-Symmetric Signed Graphs, Ahmad Asiri
Theses and Dissertations
In this dissertation, we investigate various aspects of signed graphs, with a particular focus on signings and sign-symmetric signed graphs. We begin by examining the complete graph on six vertices with one edge deleted ($K_6$\textbackslash e) and explore the different ways of signing this graph up to switching isomorphism. We determine the frustration index (number) of these signings and investigate the existence of sign-symmetric signed graphs. We then extend our study to the $K_6$\textbackslash 2e graph and the McGee graph with exactly two negative edges. We investigate the distinct ways of signing these graphs up to switching isomorphism and demonstrate …
A Survey On Online Matching And Ad Allocation, Ryan Lee
A Survey On Online Matching And Ad Allocation, Ryan Lee
Theses
One of the classical problems in graph theory is matching. Given an undirected graph, find a matching which is a set of edges without common vertices. In 1990s, Richard Karp, Umesh Vazirani, and Vijay Vazirani would be the first computer scientists to use matchings for online algorithms [8]. In our domain, an online algorithm operates in the online setting where a bipartite graph is given. On one side of the graph there is a set of advertisers and on the other side we have a set of impressions. During the online phase, multiple impressions will arrive and the objective of …