Network Capacity Bound for Personalized PageRank in Multimodal Networks

In a former paper the concept of Bipartite PageRank was introduced and a theorem on the limit of authority flowing between nodes for personalized PageRank has been generalized. In this paper we want to extend those results to multimodal networks. In particular we introduce a hypergraph type that may be used for describing multimodal network where a hyperlink connects nodes from each of the modalities. We introduce a generalisation of PageRank for such graphs and define the respective random walk model that can be used for computations. we finally state and prove theorems on the limit of outflow of authority for cases where individual modalities have identical and distinct damping factors.Comment: 28 pages. arXiv admin note: text overlap with arXiv:1702.0373

Hypernetworks for reconstructing the dynamics of multilevel systems

Networks are fundamental for reconstructing the dynamics of many systems, but have the drawback that they are restricted to binary relations. Hypergraphs extend relational structure to multi-vertex edges, but are essentially set-theoretic and unable to represent essential structural properties. Hypernetworks are a natural multidimensional generalisation of networks, representing n-ary relations by simplices with n vertices. The assembly of vertices to make simplices is key for moving between levels in multilevel systems, and integrating dynamics between levels. It is argued that hypernetworks are necessary, if not sufficient, for reconstructing the dynamics of multilevel complex systems

Explicit construction of Ramanujan bigraphs

We construct explicitly an infinite family of Ramanujan graphs which are bipartite and biregular. Our construction starts with the Bruhat-Tits building of an inner form of $SU_3(\mathbb Q_p)$. To make the graphs finite, we take successive quotients by infinitely many discrete co-compact subgroups of decreasing size.Comment: 10 page

Conflict-Free Colourings of Graphs and Hypergraphs

A colouring of the vertices of a hypergraph H is called conflict-free if each hyperedge E of H contains a vertex of ‘unique' colour that does not get repeated in E. The smallest number of colours required for such a colouring is called the conflict-free chromatic number of H, and is denoted by χCF(H). This parameter was first introduced by Even, Lotker, Ron and Smorodinsky (FOCS 2002) in a geometric setting, in connection with frequency assignment problems for cellular networks. Here we analyse this notion for general hypergraphs. It is shown that $\chi_{\rm CF}(H)\leq 1/2+\sqrt{2m+1/4}$, for every hypergraph with m edges, and that this bound is tight. Better bounds of the order of m1/t log m are proved under the assumption that the size of every edge of H is at least 2t − 1, for some t ≥ 3. Using Lovász's Local Lemma, the same result holds for hypergraphs in which the size of every edge is at least 2t − 1 and every edge intersects at most m others. We give efficient polynomial-time algorithms to obtain such colourings. Our machinery can also be applied to the hypergraphs induced by the neighbourhoods of the vertices of a graph. It turns out that in this case we need far fewer colours. For example, it is shown that the vertices of any graph G with maximum degree Δ can be coloured with log2+ε Δ colours, so that the neighbourhood of every vertex contains a point of ‘unique' colour. We give an efficient deterministic algorithm to find such a colouring, based on a randomized algorithmic version of the Lovász Local Lemma, suggested by Beck, Molloy and Reed. To achieve this, we need to (1) correct a small error in the Molloy-Reed approach, (2) restate and re-prove their result in a deterministic for

OBJ2TEXT: Generating Visually Descriptive Language from Object Layouts

Generating captions for images is a task that has recently received considerable attention. In this work we focus on caption generation for abstract scenes, or object layouts where the only information provided is a set of objects and their locations. We propose OBJ2TEXT, a sequence-to-sequence model that encodes a set of objects and their locations as an input sequence using an LSTM network, and decodes this representation using an LSTM language model. We show that our model, despite encoding object layouts as a sequence, can represent spatial relationships between objects, and generate descriptions that are globally coherent and semantically relevant. We test our approach in a task of object-layout captioning by using only object annotations as inputs. We additionally show that our model, combined with a state-of-the-art object detector, improves an image captioning model from 0.863 to 0.950 (CIDEr score) in the test benchmark of the standard MS-COCO Captioning task.Comment: Accepted at EMNLP 201

An Introduction to Complex Networks in Climate Finance

In this perspective, we introduce recent research into the structure and function of complex investor networks supporting sustainability efforts. Using the case of solar, wind and hydro energy technologies, this perspective explores the complexity in low-carbon finance markets, defined as markets that direct capital flows towards low-carbon technologies, using network approaches to study their structure and dynamics. Investors are modeled as nodes which form a network or higher-order network connected by edges representing projects in which joint funding or security-related insurance was provided or other investment-related interaction occurred. We review the literature on investor networks generally, particularly in the case of complex networks, and address areas where these ideas were applied in this emerging field. The complex investor dynamics which emerge from the extant funding scenarios are not well understood. These dynamics have the potential to result in interesting non-linear behaviour, growth, and decline, which can be studied, explained and controlled using the tools of network science

A heuristic method for a congested capacitated transit assignment model with strategies

This paper addresses the problem of solving the congested transit assignment problem with strict capacities. The model under consideration is the extension made by Cominetti and Correa (2001), for which the only solution method capable of resolving large transit networks is the one proposed by Cepeda et al. (2006). This transit assignment model was recently formulated by the authors as both a variational inequality problem and a fixed point inclusion problem. As a consequence of these results, this paper proposes an algo- rithm for solving the congested transit assignment problem with strict line capacities. The proposed method consists of using an MSA-based heuristic for finding a solution for the fixed point inclusion formulation. Additionally, it offers the advantage of always obtain- ing capacity-feasible flows with equal computational performance in cases of moderate congestion and with greater computational performance in cases of highly congested net- works. A set of computational tests on realistic small- and large-scale transit networks un- der various congestion levels are reported, and the characteristics of the proposed method are analyzed.Peer ReviewedPostprint (author's final draft

Comparative analysis of PropertyFirst vs. EntityFirst modeling approaches in graph databases

While relational databases still hold the primary position in the database technology domain, and have been for the longest time of any Computer Science technology has since its inception, for the first time the relational databases now have valid and worthy opponent in the NoSQL database movement. NoSQL databases, even though not many people have heard of them, with a significant number of Computer Science people included, have spread rapidly in many shapes and forms and have done so in quite a chaotic fashion. Similarly to the way they appeared and spread, design and modeling for them have been undertaken in an unstructured manner. Currently they are subcategorized in 4 main groups as: Key-value stores, Column Family stores, Document stores and Graph databases. In this thesis, different modeling approaches for graph databases, applied to the same domain are analyzed and compared, especially from a design perspective. The database selected here as the implemented technology is Neo4J by Neo Technologies and is a directed property graph database, which means that relationships between its data entities must have a starting and ending (or source and destination) node. This research provides an overview of two competing modeling approaches and evaluates them in a context of a real world example. The work done here shows that both of these modeling approaches are valid and that it is possible to fully develop a data model based on the same domain data with both approaches and that both can be used later to support application access in a similar fashion. One of the models provides for faster access to data, but at a cost of higher maintenance and increased complexity