Network Duality Research Articles

Duality in Financial Networks

Duality in Financial Networks

Virtual connections: a multidisciplinary study on behavior in social networks

This article investigates the impact of social networks on various aspects of contemporary society through a multidisciplinary approach. A theoretical review with a mixed approach was used which, after an evaluation of relevance, led to the identification of 21 articles that make up the research. Exploring the relationship between patterns of social network use and their effect on mental health, it is found that active interaction promotes psychological well-being, while passive consumption is linked to negative feelings such as loneliness and envy. In addition, we examine how these platforms influence identity formation and public opinion, highlighting their role in creating "echo chambers" that can intensify social polarization. It is also noted that while social networks enhance global connectivity, they can compromise the quality of interpersonal relationships. Nevertheless, they facilitate the formation of communities of support and solidarity, particularly in groups with common interests, contributing to community cohesion. This study underlines the duality of social networks as spaces of opportunity and challenge, highlighting the need for a conscious use to foster individual well-being and social cohesion.

Activity–weight duality in feed-forward neural networks reveals two co-determinants for generalization

Activity–weight duality in feed-forward neural networks reveals two co-determinants for generalization

The duality of networks and groups: Models to generate two-mode networks from one-mode networks

AbstractShared memberships, social statuses, beliefs, and places can facilitate the formation of social ties. Two-mode projections provide a method for transforming two-mode data on individuals’ memberships in such groups into a one-mode network of their possible social ties. In this paper, I explore the opposite process: how social ties can facilitate the formation of groups, and how a two-mode network can be generated from a one-mode network. Drawing on theories of team formation, club joining, and organization recruitment, I propose three models that describe how such groups might emerge from the relationships in a social network. I show that these models can be used to generate two-mode networks that have characteristics commonly observed in empirical two-mode social networks and that they encode features of the one-mode networks from which they were generated. I conclude by discussing these models’ limitations and future directions for theory and methods concerning group formation.

Relational sociology of Harrison White and his followers: Towards a theory of sociocultural duality

The paper presents an overview of the history of the cultural turn in social network analysis. The cultural turn has proclaimed the crucial role of not only social but also cultural structures. On the one hand, cultural structures construct a context for social interactions. On the other hand, social network mechanisms determine the features of the use of symbolic forms by actors. According to Harrison White and John Mohr, sociocultural duality can be defined as a process of mutual construction of social and cultural orders. It should be noted that the idea of White about the mutual construction of culture and structure (the concept of netdom) has become a starting point for theoretical and empirical debates on the duality of social and cultural networks. The concept of network domain (netdom) includes both social networks (net) and spaces of symbolic forms (dom). Hence, the task of this paper is to identify the theoretical and methodological arguments of researchers emphasising the importance of sociocultural duality. The paper discusses in detail the concepts of duality and relational sociology. But the main part of the article is focused on the analysis of the relational sociology of Harrison White and his followers (A.Mische, J.Fuhse, N.Crossley). Relational sociology rejects substantialist ideas and, therefore, it is directed to the research of processual social and cultural structures. The final arguments summarise cutting-edge topics for future research on sociocultural duality.

Spectral duality in graphs and microwave networks.

Quantum graphs and their experimental counterparts, microwave networks, are ideally suited to study the spectral statistics of chaotic systems. The graph spectrum is obtained from the zeros of a secular determinant derived from energy and charge conservation. Depending on the boundary conditions at the vertices, there are Neumann and Dirichlet graphs. The first ones are realized in experiments, since the standard junctions connecting the bonds obey Neumann boundary conditions due to current conservation. On average, the corresponding Neumann and Dirichlet eigenvalues alternate as a function of the wave number, with the consequence that the Neumann spectrum is described by random matrix theory only locally, but adopts features of the interlacing Dirichlet spectrum for long-range correlations. Another spectral interlacing is found for the Green's function, which in contrast to the secular determinant is experimentally accessible. This is illustrated by microwave studies and numerics.

Usefulness of Twitter for the Neurointensivist in the COVID-19 Outbreak: The Role of Social Media Platforms in Uncertain Times

Since the start of the coronavirus disease 2019 (COVID-19) pandemic, social networking has increased markedly.[1] The present list of virtual social networks is extensive, including Skype, YouTube, Zoom, WhatsApp, Signal, Twitter, LinkedIn, and so on. The use of social networks has been an important part of coping with this crisis.[1] The social networks that initially emerged as strategies for fun and socialization in recent years have become an important part of learning.[2] Virtual social networks facilitate the construction of knowledge based on personal and common interests. They have progressively occupied an important place in our society. An interesting duality of social networks is the possibility of uniting formal and informal environments in a common goal: continuous learning. The use of social networks facilitates creativity, creation, exchange, and collaboration.[3] In our world, the possibility of collaboration between remotely located cities and countries opens endless options.

Temporal-specific complexity of spiking patterns in spontaneous activity induced by a dual complex network structure

Temporal fluctuation of neural activity in the brain has an important function in optimal information processing. Spontaneous activity is a source of such fluctuation. The distribution of excitatory postsynaptic potentials (EPSPs) between cortical pyramidal neurons can follow a log-normal distribution. Recent studies have shown that networks connected by weak synapses exhibit characteristics of a random network, whereas networks connected by strong synapses have small-world characteristics of small path lengths and large cluster coefficients. To investigate the relationship between temporal complexity spontaneous activity and structural network duality in synaptic connections, we executed a simulation study using the leaky integrate-and-fire spiking neural network with log-normal synaptic weight distribution for the EPSPs and duality of synaptic connectivity, depending on synaptic weight. We conducted multiscale entropy analysis of the temporal spiking activity. Our simulation demonstrated that, when strong synaptic connections approach a small-world network, specific spiking patterns arise during irregular spatio-temporal spiking activity, and the complexity at the large temporal scale (i.e., slow frequency) is enhanced. Moreover, we confirmed through a surrogate data analysis that slow temporal dynamics reflect a deterministic process in the spiking neural networks. This modelling approach may improve the understanding of the spatio-temporal complex neural activity in the brain.

A Unified Random Coding Bound

In this paper, we prove a unified achievability bound that generalizes and improves random coding bounds for any combination of source coding, channel coding, joint source–channel coding, and coding for computing problems assuming blockwise node operation. As a general network setup, we consider an acyclic discrete memoryless network, where the network demands and constraints are specified by a joint-typicality constraint on the whole channel input and output sequences. For achievability, a basic building block for node operation consists of simultaneous nonunique decoding, simultaneous compression, and symbol-by-symbol mapping. Our bound can be useful for deriving random coding bounds without error analysis, especially for large and complex networks. In particular, our bound can be used for unifying and generalizing many known relaying strategies. For example, a generalized decode-compress-amplify-and-forward bound is obtained as a simple corollary of our main theorem, and it is shown to strictly outperform the previously known relaying schemes. Furthermore, by exploiting the symmetry in our bound, we formally define and characterize three types of network duality based on channel input–output reversal and network flow reversal combined with packing–covering duality.

Capacity Regions of Two-Receiver Broadcast Erasure Channels With Feedback and Memory

The two-receiver broadcast packet erasure channel with feedback and memory is studied. Memory is modeled using a finite-state Markov chain representing a channel state. Two scenarios are considered: 1) when the transmitter has causal knowledge of the channel state (i.e., the state is visible) and 2) when the channel state is unknown at the transmitter, but observations of it are available at the transmitter through feedback (i.e., the state is hidden). In both scenarios, matching outer and inner bounds on the rates of communication are derived and the capacity region is determined. It is shown that similar results carry over to channels with memory and delayed feedback and memoryless compound channels with feedback. When the state is visible, the capacity region has a single-letter characterization and is in terms of a linear program. Two optimal coding schemes are devised that use feedback to keep track of the sent/received packets via a network of queues: a probabilistic scheme and a deterministic backpressure-like algorithm. The former bases its decisions solely on the past channel state information and the latter follows a max-weight queue-based policy. The performance of the algorithms is analyzed using the frameworks of rate stability in networks of queues, max-flow min-cut duality in networks, and finite-horizon Lyapunov drift analysis. When the state is hidden, the capacity region does not have a single-letter characterization and is, in this sense, uncomputable. Approximations of the capacity region are provided and two optimal coding algorithms are outlined. The first algorithm is a probabilistic coding scheme that bases its decisions on the past $L$ acknowledgments and its achievable rate region approaches the capacity region exponentially fast in $L$ . The second algorithm is a backpressure-like algorithm that performs optimally in the long run.

Duality of graphical models and tensor networks

Abstract In this article we show the duality between tensor networks and undirected graphical models with discrete variables. We study tensor networks on hypergraphs, which we call tensor hypernetworks. We show that the tensor hypernetwork on a hypergraph exactly corresponds to the graphical model given by the dual hypergraph. We translate various notions under duality. For example, marginalization in a graphical model is dual to contraction in the tensor network. Algorithms also translate under duality. We show that belief propagation corresponds to a known algorithm for tensor network contraction. This article is a reminder that the research areas of graphical models and tensor networks can benefit from interaction.

Problems on multivariate reliability polynomial

The original results include: (i) homogenization of a reliability polynomial; (ii) compact hypersurfaces attached to homogeneous polynomials; (iii) an affine diffeomorphism that preserves a reliability polynomial; (iv) duality of networks via a diffeomorphism; (v) straight line segments in constant level sets associated to a reliability polynomial.

Transmit Beamforming and Power Control for Optimizing the Outage Probability Fairness in MISO Networks

This paper studies the joint beamforming and power control in a multiuser multi-input single-output network by utilizing the only statistical channel distribution information. Such information consists of slowly varying covariance matrices in the beamforming network that can be employed to reduce instantaneous feedback overhead in transmission. Utilizing solely the statistical channel information, we study how to minimize the maximum outage probability under a weighted sum power constraint that guarantees max–min fairness to all users. This problem is, however, generally hard to solve due to the nonconvexity and nonlinear coupling between beamformer and power variables. First, assuming a fixed beamformer set, we use the nonlinear Perron–Frobenius theory to design a decentralized algorithm with provable geometrically fast convergence rate to compute the optimal power. Then, for the general case, we examine a certainty-equivalent margin counterpart with outage-mapped thresholds that incorporate the statistical channel information. We show that a network duality for this certainty-equivalent problem can be useful to decouple the coupling between the beamformer and power variables. This nonlinear Perron–Frobenius theory motivated approach yields a feasible beamformer and power allocation that are near-optimal as compared to Monte Carlo averaging simulations.

Shortest Alternate Path Discovery through Recursive Bounding Box Pruning

Congestion is a dynamic phenomenon and hence efficiently computing alternate shortest route can only help expedite decongestion. This research is aimed to efficiently compute shortest path for road traffic network so that congestion can be eased resulting in reduced CO2 emission and improved economy. Congestion detection is achieved after evaluating road capacity and road occupancy. Congestion index, a ratio of road occupancy to road capacity is computed, congestion index higher than 0.6 necessitates computation of alternate shortest route. Various algorithms offer shortest alternate route. The paper discusses minimization of graph based by removing redundant nodes which don’t play a role in computation of shortest path. The proposal is based on continuous definition of a bounding box every time a next neighboring node is considered. This reduces maximum number of contentious nodes repeatedly and optimizes the network. The algorithm is deployed from both the ends sequentially to ensure zero error and validate the shortest path discovery. While discovering shortest path, the algorithm also offers an array of shortest path in ascending order of the path length. However, vehicular traffic exhibits network duality viz. static and dynamic network graphs. Shortest route for static distance graph is pre-computed and stored for look-up, alternate shortest path based on assignment of congestion levels to edge weights is triggered by congestion index. The research also supports directed graphs to address traffic rules for lanes having unidirectional and bidirectional traffic.

Minimax Duality for MIMO Interference Networks

A minimax duality for a Gaussian mutual information expression was introduced by Yu. An interesting observation is the relationship between cost constraints on the transmit covariances and noise covariances in the dual problem via Lagrangian multipliers. We introduce a minimax duality for general MIMO interference networks, where noise and transmit covariances are optimized subject to linear conic constraints. We observe a fully symmetric relationship between the solutions of both networks, where the roles of the optimization variables and Lagrangian multipliers are inverted. The least favorable noise covariance itself provides a Lagrangian multiplier for the linear conic constraint on the transmit covariance in the dual network, while the transmit covariance provides a Lagrangian multiplier for the constraint on the interference plus noise covariance in the dual network. The degrees of freedom available for optimization are constituted by linear subspaces, where the orthogonal subspaces induce the constraints in the dual network. For the proof of our duality we make use of the existing polite water-filling network duality and as a by-product we are able to show that maximization problems in MIMO interference networks have a zero-duality gap for a special formulation of the dual function. Our minimax duality unifies and extends several results, including the original minimax duality and other known network dualities. New results and applications are MIMO transmission strategies that manage and handle uncertainty due to unknown inter-cell interference and information theoretic proofs concerning cooperation in networks and optimality of proper signaling.

"They help, yet they hinder: Duality of social networks and opportunities for Ghanaian Self-Employed"

In this study, I seek to understand how subsistence entrepreneurs select specific replication opportunities to exploit, and the impact of this selection on growth. Replication opportunities are different from discovery, creation, and recognition opportunities, and are those opportunities that directly mimic readily observable businesses. While extant research points to the macro-level factors (such as a lack of education) that generally lead to countries’ dependence on replication opportunities, little is known at the micro-level; the level where interventions such as training programs work. I studied a group of self-employed across four research trips to Ghana, where I conducted 227 interviews and 233 hours of observation. My findings indicate that social networks both enable and constrain the selection of specific opportunities. They also indicate that opportunities are widely exploited based on the standard templates accessed through these networks. Similarly, social networks constrain and enable growt...

Equivalent multiplier and envelopment DEA models for measuring efficiency under general network structures

Data envelopment analysis (DEA) has been shown to be a very useful mathematical programming tool to measure the relative efficiency of decision making units (DMUs), especially when the so-called internal network structure of the production process is taken into account. Under a network structure, however, two standard directions of modeling the production process may generally lead to a pair of multiplier and envelopment DEA models so that the outcomes are not necessarily equivalent, i.e. a network duality problem occurs. Although, the duality problem has recently been addressed for specific cases of network structures, for more complex structures, DEA models have only been able to be developed by following either the envelopment form or multiplier form. Investigating this duality problem, this paper also proposes DEA models for general network structures with two additional properties. Due to the first property, all factors in a general network structure including main inputs/outputs and/or intermediate inputs/outputs can be shared among the divisions while the second property assumes that a factor in a structure may be considered as both intermediate input/output and main input/output simultaneously. We will show that the proposed network DEA models cannot only deal with the already existing general network structures in the literature, but are also represented by dual multiplier and envelopment linear programming-based problems by which consistent outcomes can be obtained. A comprehensive numerical example will be presented to explain the properties and features of the suggested models.

Iterative beamforming algorithm for improved throughput in multi‐cell multi‐antenna wireless systems

Mitigating the effects of inter-cell interference in a multi-cell wireless network is essential to improve the achieved performance. In this study, the authors develop an iterative distributed beamforming scheme that addresses the effect of inter-cell interference problem on the downlink of a multi-cell multi-antenna wireless system with linear beamformers. The proposed scheme attempts at improving the overall system performance by exploiting network duality principle to jointly compute the optimal transmit and receive beamforming weights such that the desired received power is maximised while minimising the caused interference to other users. Network duality allows the serving base stations and the intended users to jointly compute the beamforming weights of the transmit/receive antenna elements, which improve network performance. The proposed scheme considers variable levels of channel information feedback and different transmit–receive antenna configurations. Simulation results show that a significant performance improvement is achieved through the joint optimisation of the transmit/receive beamforming vectors. Results also indicate that compared with reference schemes, their scheme improves the achieved sum-rate by up to 50%.

Structural Modeling and Characteristics Analysis of Flow Interaction Networks in the Internet**Supported by the National Natural Science Foundation of China under Grant No 61100206, the Beijing Natural Science Foundation under Grant No 4142036, and the Research Fund for Doctoral Program of Higher Education of China under Grant No 20120005130001.

Applying network duality and elastic mechanics, we investigate the interactions among Internet flows by constructing a weighted undirected network, where the vertices and the edges represent the flows and the mutual dependence between flows, respectively. Based on the obtained flow interaction network, we find the existence of ‘super flow’ in the Internet, indicating that some flows have a great impact on a huge number of other flows; moreover, one flow can spread its influence to another through a limited quantity of flows (less than 5 in the experimental simulations), which shows strong small-world characteristics like the social network. To reflect the flow interactions in the physical network congestion evaluation, the ‘congestion coefficient’ is proposed as a new metric which shows a finer observation on congestion than the conventional one.

Power Minimization in Multi-Band Multi-Antenna Cognitive Radio Networks

This paper aims to design an optimal set of beam-vectors for multi-band multi-antenna cognitive radio networks that jointly allocate power over both space and frequency, so that the sum power of secondary users (SUs) is minimized, subject to rate demands at the SUs, as well as the interference constraints imposed by primary users. Unlike the rate maximization problems, which are always feasible, this power minimization (PM) problem may be infeasible due to the rate constraints. Therefore, we provide a complete analysis of the PM problem by splitting the solution into two separate phases. In phase I, a novel method is developed to check the feasibility of the PM problem by considering an alternative problem, where one additional variable is introduced. This alternative problem is always feasible and one algorithm based on network duality and geometric programs is developed to solve it. In phase II, a novel algorithm is developed to solve the PM problem. This algorithm can be implemented in an online fashion. Furthermore, this algorithm is proved to converge to a Karush-Kuhn-Tucker point of the PM problem. Simulation results show that the proposed algorithms converge in only a few iterations and significantly outperform the existing single-band method in terms of both the feasibility probabilities and power savings.