MODEL : motif-based deep feature learning for link prediction

Link prediction plays an important role in network analysis and applications. Recently, approaches for link prediction have evolved from traditional similarity-based algorithms into embedding-based algorithms. However, most existing approaches fail to exploit the fact that real-world networks are different from random networks. In particular, real-world networks are known to contain motifs, natural network building blocks reflecting the underlying network-generating processes. In this article, we propose a novel embedding algorithm that incorporates network motifs to capture higher order structures in the network. To evaluate its effectiveness for link prediction, experiments were conducted on three types of networks: social networks, biological networks, and academic networks. The results demonstrate that our algorithm outperforms both the traditional similarity-based algorithms (by 20%) and the state-of-the-art embedding-based algorithms (by 19%). © 2014 IEEE

Generalisation of structural knowledge in the hippocampal-entorhinal system

A central problem to understanding intelligence is the concept of generalisation. This allows previously learnt structure to be exploited to solve tasks in novel situations differing in their particularities. We take inspiration from neuroscience, specifically the hippocampal-entorhinal system known to be important for generalisation. We propose that to generalise structural knowledge, the representations of the structure of the world, i.e. how entities in the world relate to each other, need to be separated from representations of the entities themselves. We show, under these principles, artificial neural networks embedded with hierarchy and fast Hebbian memory, can learn the statistics of memories and generalise structural knowledge. Spatial neuronal representations mirroring those found in the brain emerge, suggesting spatial cognition is an instance of more general organising principles. We further unify many entorhinal cell types as basis functions for constructing transition graphs, and show these representations effectively utilise memories. We experimentally support model assumptions, showing a preserved relationship between entorhinal grid and hippocampal place cells across environments

Entropy-scaling search of massive biological data

Many datasets exhibit a well-defined structure that can be exploited to design faster search tools, but it is not always clear when such acceleration is possible. Here, we introduce a framework for similarity search based on characterizing a dataset's entropy and fractal dimension. We prove that searching scales in time with metric entropy (number of covering hyperspheres), if the fractal dimension of the dataset is low, and scales in space with the sum of metric entropy and information-theoretic entropy (randomness of the data). Using these ideas, we present accelerated versions of standard tools, with no loss in specificity and little loss in sensitivity, for use in three domains---high-throughput drug screening (Ammolite, 150x speedup), metagenomics (MICA, 3.5x speedup of DIAMOND [3,700x BLASTX]), and protein structure search (esFragBag, 10x speedup of FragBag). Our framework can be used to achieve "compressive omics," and the general theory can be readily applied to data science problems outside of biology.Comment: Including supplement: 41 pages, 6 figures, 4 tables, 1 bo

A Multiple Case Study Exploring the Relationship Between Engagement in Model-Eliciting Activities and Pre-Service Secondary Mathematics Teachers\u27 Mathematical Knowledge for Teaching Algebra

The goal of this research study was to explore the nature of the relationship between engagement in model-eliciting activities (MEAs) and pre-service secondary mathematics teachers\u27 (PSMTs\u27) mathematical knowledge for teaching (MKT) algebra. The data collection took place in an undergraduate mathematics education content course for secondary mathematics education majors. In this multiple case study, PSMTs were given a Learning Mathematics for Teaching (LMT) pre-assessment designed to measure their MKT algebra, and based on those results, three participants were selected with varying levels of knowledge. This was done to ensure varied cases were represented in order to be able to examine and describe multiple perspectives. The three examined cases were Oriana, a PSMT with high MKT, Bianca, a PSMT with medium MKT, and Helaine, a PSMT with low MKT. Over the course of five weeks, the three PSMTs were recorded exploring three MEAs, participated in two interviews, and submitted written reflections. The extensive amount of data collected in this study allowed the researcher to deeply explore the PSMTs\u27 MKT algebra in relation to the given MEAs, with a focus on three specific constructs—bridging, trimming, and decompressing— based on the Knowledge of Algebra for Teaching (KAT) framework. The results of this study suggest that engaging in MEAs could elicit PSMTs\u27 MKT algebra, and in some cases such tasks were beneficial to their trimming, bridging, and decompressing abilities. Exploring MEAs immersed the PSMTs in generating descriptions, explanations, and constructions, that helped reveal how they interpreted mathematical situations that they encountered. The tasks served as useful tools for PSMTs to have deep discussions and productive discourse on various algebra topics, and make many different mathematical connections in the process

The Representation and Analysis of Dynamic Networks

Many real-world phenomena, such as article citations and social interactions, can be viewed in terms of a set of entities connected by relationships. Utilizing this abstraction, the system can be represented as a network. This universal nature of networks, combined with the rapid growth in scope of data collection, has caused significant focus to be placed on techniques for mining these networks of high-level information. However, despite the strong temporal dependencies present in many of these systems, such as social networks, substantially less is understood about the evolution of their structures. A dynamic network representation captures this additional dimension by containing a series of static network “snapshots.” The complexity and scale of such a representation poses several challenges regarding storage and analysis. This research explores a novel bit-vector representation of node interactions, which offers advantages in its ability to be compressed and manipulated through established methods from the fields of digital signal processing and information theory. The results have demonstrated high-level similarity between the considered datasets, giving insights into efficient representations. By way of the discrete Fourier transform, this research has also revealed underlying behavioral patterns, particularly in the social network realm. These approaches offer improved characterization and predictive capacity over that gained from analyzing the network as a static system, and the extent of this descriptive power obtainable through the bit-vector representation is a question which this research aims to address.National Science FoundationNo embarg

The Tolman-Eichenbaum Machine: Unifying Space and Relational Memory through Generalization in the Hippocampal Formation

The hippocampal-entorhinal system is important for spatial and relational memory tasks. We formally link these domains, provide a mechanistic understanding of the hippocampal role in generalization, and offer unifying principles underlying many entorhinal and hippocampal cell types. We propose medial entorhinal cells form a basis describing structural knowledge, and hippocampal cells link this basis with sensory representations. Adopting these principles, we introduce the Tolman-Eichenbaum machine (TEM). After learning, TEM entorhinal cells display diverse properties resembling apparently bespoke spatial responses, such as grid, band, border, and object-vector cells. TEM hippocampal cells include place and landmark cells that remap between environments. Crucially, TEM also aligns with empirically recorded representations in complex non-spatial tasks. TEM also generates predictions that hippocampal remapping is not random as previously believed; rather, structural knowledge is preserved across environments. We confirm this structural transfer over remapping in simultaneously recorded place and grid cells

Compact and indexed representation for LiDAR point clouds

[Abstract]: LiDAR devices are capable of acquiring clouds of 3D points reflecting any object around them, and adding additional attributes to each point such as color, position, time, etc. LiDAR datasets are usually large, and compressed data formats (e.g. LAZ) have been proposed over the years. These formats are capable of transparently decompressing portions of the data, but they are not focused on solving general queries over the data. In contrast to that traditional approach, a new recent research line focuses on designing data structures that combine compression and indexation, allowing directly querying the compressed data. Compression is used to fit the data structure in main memory all the time, thus getting rid of disk accesses, and indexation is used to query the compressed data as fast as querying the uncompressed data. In this paper, we present the first data structure capable of losslessly compressing point clouds that have attributes and jointly indexing all three dimensions of space and attribute values. Our method is able to run range queries and attribute queries up to 100 times faster than previous methods.Secretara Xeral de Universidades; [ED431G 2019/01]Ministerio de Ciencia e Innovacion; [PID2020-114635RB-I00]Ministerio de Ciencia e Innovacion; [PDC2021-120917C21]Ministerio de Ciencia e Innovación; [PDC2021-121239-C31]Ministerio de Ciencia e Innovación; [PID2019-105221RB-C41]Xunta de Galicia; [ED431C 2021/53]Xunta de Galicia; [IG240.2020.1.185

On the Memory Requirement of Hop-by-hop Routing: Tight Bounds and Optimal Address Spaces

Routing in large-scale computer networks today is built on hop-by-hop routing: packet headers specify the destination address and routers use internal forwarding tables to map addresses to next-hop ports. In this paper we take a new look at the scalability of this paradigm. We define a new model that reduces forwarding tables to sequential strings, which then lend themselves readily to an information-theoretical analysis. Contrary to previous work, our analysis is not of worst-case nature, but gives verifiable and realizable memory requirement characterizations even when subjected to concrete topologies and routing policies. We formulate the optimal address space design problem as the task to set node addresses in order to minimize certain network-wide entropy-related measures. We derive tight space bounds for many well-known graph families and we propose a simple heuristic to find optimal address spaces for general graphs. Our evaluations suggest that in structured graphs, including most practically important network topologies, significant memory savings can be attained by forwarding table compression over our optimized address spaces. According to our knowledge, our work is the first to bridge the gap between computer network scalability and information-theory