Forman's Ricci curvature - From networks to hypernetworks

Networks and their higher order generalizations, such as hypernetworks or multiplex networks are ever more popular models in the applied sciences. However, methods developed for the study of their structural properties go little beyond the common name and the heavy reliance of combinatorial tools. We show that, in fact, a geometric unifying approach is possible, by viewing them as polyhedral complexes endowed with a simple, yet, the powerful notion of curvature - the Forman Ricci curvature. We systematically explore some aspects related to the modeling of weighted and directed hypernetworks and present expressive and natural choices involved in their definitions. A benefit of this approach is a simple method of structure-preserving embedding of hypernetworks in Euclidean N-space. Furthermore, we introduce a simple and efficient manner of computing the well established Ollivier-Ricci curvature of a hypernetwork.Comment: to appear: Complex Networks '18 (oral presentation

A HyperNet Architecture

Network virtualization is becoming a fundamental building block of future Internet architectures. By adding networking resources into the “cloud”, it is possible for users to rent virtual routers from the underlying network infrastructure, connect them with virtual channels to form a virtual network, and tailor the virtual network (e.g., load application-specific networking protocols, libraries and software stacks on to the virtual routers) to carry out a specific task. In addition, network virtualization technology allows such special-purpose virtual networks to co-exist on the same set of network infrastructure without interfering with each other. Although the underlying network resources needed to support virtualized networks are rapidly becoming available, constructing a virtual network from the ground up and using the network is a challenging and labor-intensive task, one best left to experts. To tackle this problem, we introduce the concept of a HyperNet, a pre-built, pre-configured network package that a user can easily deploy or access a virtual network to carry out a specific task (e.g., multicast video conferencing). HyperNets package together the network topology configuration, software, and network services needed to create and deploy a custom virtual network. Users download HyperNets from HyperNet repositories and then “run” them on virtualized network infrastructure much like users download and run virtual appliances on a virtual machine. To support the HyperNet abstraction, we created a Network Hypervisor service that provides a set of APIs that can be called to create a virtual network with certain characteristics. To evaluate the HyperNet architecture, we implemented several example Hyper-Nets and ran them on our prototype implementation of the Network Hypervisor. Our experiments show that the Hypervisor API can be used to compose almost any special-purpose network – networks capable of carrying out functions that the current Internet does not provide. Moreover, the design of our HyperNet architecture is highly extensible, enabling developers to write high-level libraries (using the Network Hypervisor APIs) to achieve complicated tasks

Relation nets and hypernets

In many respects this report is a companion work of our book "Knowledge representation and relation nets. Kluwer Academic Publishers, Boston, 1999". In some senses it runs parallel to it, while in others it is a sequel to that book. Readers not familiar with the book will find themselves refering back to it several instances to follow some of the subtleties of this work, particularly in the case of concept-relationship knowledge stuctures, abbreviated CRKS in what follows. The main application of CRKS's - namely modelling study material - is not explicitly transscribed to this paper, but that whole notion is abstracted and made independent of any specific teaching/learning metalanguage through the implications of this abstraction. Two key factors emerge from this paper on hypernets. First, unlike the case for CRKS's in which little of the general theory of relation nets applies to CRKS's, the broad theory of hypernets, as far as it is covered in this report, is often applicable to the hypernet equivalent of a CRKS. Second, we will show a link between relation net isomorphism and hypernet isomorphism which makes it considerably easier to deal with CRKS isomorphism and, thus, with structural analogy as used in a modelling based approach to teaching/learning/analogical reasoning. Finally, we must mention that it appears that the domain of potential practical applications of hypernets must inevitably be wider than that for relation nets

Hypernet semantics of programming languages

Comparison is common practice in programming, even regarding a single programming language. One would ask if two programs behave the same, if one program runs faster than another, or if one run-time system produces the outcome of a program faster than another system. To answer these questions, it is essential to have a formal specification of program execution, with measures such as result and resource usage. This thesis proposes a semantical framework based on abstract machines that enables analysis of program execution cost and direct proof of program equivalence. These abstract machines are inspired by Girard’s Geometry of Interaction, and model program execution as dynamic rewriting of graph representation of a program, guided and controlled by a dedicated object (token) of the graph. The graph representation yields fine control over resource usage, and moreover, the concept of locality in analysing program execution. As a result, this framework enjoys novel flexibility, with which various evaluation strategies and language features, whether they are effects or not, can be modelled and analysed in a uniform way

HYPERTEXT-BASED RELATIONSHIP MANAGEMENT FOR DSS

There is a need for integrated access to a wide range of information related to the development and use of DSS in organizations. This information comes in many forms, both formal and informal, and is highly interrelated. To handle this complex information base, we argue that a separate relationship management component should be added to the three traditional components of a DSS (namely, the database, user interface and model management systems). The role of the relationship management component is to relieve DSS application programs of the need to maintain and provide access to the complex set of relationships that can exist between elements in the application domain. We discuss the kinds of information and relationships that arise during the development and use of a DSS, outline the requirements for an independent subsystem to manage this information base, and propose the use of an extended hypertext software system, H+, to simultaneously handle relationship management and provide an interesting and useful interface to users.Information Systems Working Papers Serie

Delving Deep into the Sketch and Photo Relation

"Sketches drawn by humans can play a similar role to photos in terms of conveying shape, posture as well as fine-grained information, and this fact has stimulated one line of cross-domain research that is related to sketch and photo, including sketch-based photo synthesis and retrieval. In this thesis, we aim to further investigate the relationship between sketch and photo. More specifically, we study certain under- explored traits in this relationship, and propose novel applications to reinforce the understanding of sketch and photo relation.Our exploration starts with the problem of sketch-based photo synthesis, where the unique trait of non-rigid alignment between sketch and photo is overlooked in existing research. We then carry on with our investigation from a new angle to study whether sketch can facilitate photo classifier generation. Building upon this, we continue to explore how sketch and photo are linked together on a more fine-grained level by tackling with the sketch-based photo segmenter prediction. Furthermore, we address the data scarcity issue identified in nearly all sketch-photo-related applications by examining their inherent correlation in the semantic aspect using sketch-based image retrieval (SBIR) as a test-bed. In general, we make four main contributions to the research on relationship between sketch and photo.Firstly, to mitigate the effect of deformation in sketch-based photo synthesis, we introduce the spatial transformer network to our image-image regression framework, which subtly deals with non-rigid alignment between the sketches and photos. The qualitative and quantitative experiments consistently reveal the superior quality of our synthesised photos over those generated by existing approaches.Secondly, sketch-based photo classifier generation is achieved with a novel model regression network, which maps the sketch to the parameters of photo classification model. It is shown that our model regression network is able to generalise across categories and photo classifiers for novel classes not involved in training are just a sketch away. Comprehensive experiments illustrate the promising performance of the generated binary and multi-class photo classifiers, and demonstrate that sketches can also be employed to enhance the granularity of existing photo classifiers.Thirdly, to achieve the goal of sketch-based photo segmentation, we propose a photo segmentation model generation algorithm that predicts the weights of a deep photo segmentation network according to the input sketch. The results confirm that one single sketch is the only prerequisite for unseen category photo segmentation, and the segmentation performance can be further improved by utilising sketch that is aligned with the object to be segmented in shape and position.Finally, we present an unsupervised representation learning framework for SBIR, the purpose of which is to eliminate the barrier imposed by data annotation scarcity. Prototype and memory bank reinforced joint distribution optimal transport is integrated into the unsupervised representation learning framework, so that the mapping between the sketches and photos could be automatically detected to learn a semantically meaningful yet domain-agnostic feature space. Extensive experiments and feature visualisation validate the efficacy of our proposed algorithm.

Recent advances in petri nets and concurrency

CEUR Workshop Proceeding