Somwrita Sarkar

Spectral Characterization of Hierarchical Modularity in Product Architectures

Despite the importance of the architectural modularity of products and systems, existing modularity metrics or algorithms do not account for overlapping and hierarchically embedded modules. This paper presents a graph theoretic spectral approach to characterize the degree of modular hierarchical-overlapping organization in the architecture of products and complex engineered systems. It is shown that the eigenvalues of the adjacency matrix of a product architecture graph can reveal layers of hidden modular or hierarchical modular organization that are not immediately visible in the predefined architectural description. We use the approach to analyze and discuss several design, management, and system resilience implications for complex engineered systems.

Spectral Characterization of Hierarchical Network Modularity and Limits of Modularity Detection

Many real world networks are reported to have hierarchically modular organization. However, there exists no algorithm-independent metric to characterize hierarchical modularity in a complex system. The main results of the paper are a set of methods to address this problem. First, classical results from random matrix theory are used to derive the spectrum of a typical stochastic block model hierarchical modular network form. Second, it is shown that hierarchical modularity can be fingerprinted using the spectrum of its largest eigenvalues and gaps between clusters of closely spaced eigenvalues that are well separated from the bulk distribution of eigenvalues around the origin. Third, some well-known results on fingerprinting non-hierarchical modularity in networks automatically follow as special cases, threreby unifying these previously fragmented results. Finally, using these spectral results, it is found that the limits of detection of modularity can be empirically established by studying the mean values of the largest eigenvalues and the limits of the bulk distribution of eigenvalues for an ensemble of networks. It is shown that even when modularity and hierarchical modularity are present in a weak form in the network, they are impossible to detect, because some of the leading eigenvalues fall within the bulk distribution. This provides a threshold for the detection of modularity. Eigenvalue distributions of some technological, social, and biological networks are studied, and the implications of detecting hierarchical modularity in real world networks are discussed.

A LEARNING AND INFERENCE MECHANISM FOR DESIGN OPTIMIZATION PROBLEM (RE)- FORMULATION USING SINGULAR VALUE DECOMPOSITION

This paper presents a knowledge-lean learning and inference mechanism based on Singular Value Decomposition (SVD) for design optimization problem (re)-formulation at the problem modeling stage. The distinguishing feature of the mechanism is that it requires very few training cases to extract and generalize knowledge for large classes of problems sharing similar characteristics. The genesis of the mechanism is based on viewing problem (re)-formulation as a statistical pattern extraction problem. SVD is applied as a dimensionality reduction tool to extract semantic patterns from a syntactic formulation of the design problem. We explain and evaluate the mechanism on a model-based decomposition problem, a hydraulic cylinder design problem, and a medium-large scale Aircraft Concept Sizing problem. The results show that the method generalizes quickly and can be used to impute relations between variables, parameters, objective functions, and constraints when training data is provided in symbolic analytical form, and is likely to be extensible to forms when the representation is not in analytical functional form.Copyright

CHARACTERIZING MODULARITY, HIERARCHY AND MODULE INTERFACING IN COMPLEX DESIGN SYSTEMS

Modular engineering systems have multiple benefits over their more integral counterparts. Despite the importance of modularity, metrics and methods for a precise quantitative characterization of modularity, hierarchy and module interfacing remain relatively ambiguous. In this paper, using graph theory and linear algebra, we develop a spectral approach to establish: (1) a metric to characterize modularity, hierarchy and module interfacing in complex engineering systems; and, (2) a method for module identification and system decomposition that addresses hierarchical and overlapping organization of modularity in a complex system. The Singular Values (SV) signatures of random, regular, modular and hierarchically modular benchmark graph models are used to establish the metric. Then, the method is applied to a real design model and its modularity signature is assessed. The modularity signature of a real world system is shown to sit in the continuum established by the extremes of random, regular and modular and hierarchically modular graph models. The main contribution of the work is that it proposes that modularity is an aggregate concept that is measured in terms of multiple concepts expressed as graph properties. An ideal numeric modularity measurement index would have to incorporate these multiple criteria that affect modularity. The method can be used in the conceptual and detailed design stages for purposes of redesigning a product based on the degree of desired modularity.Copyright

Learning symbolic formulations in design: Syntax, semantics, and knowledge reification

Abstract An artificial intelligence (AI) algorithm to automate symbolic design reformulation is an enduring challenge in design automation. Existing research shows that design tools either require high levels of knowledge engineering or large databases of training cases. To address these limitations, we present a singular value decomposition (SVD) and unsupervised clustering-based method that performs design reformulation by acquiring semantic knowledge from the syntax of design representations. The development of the method was analogically inspired by applications of SVD in statistical natural language processing and digital image processing. We demonstrate our method on an analytically formulated hydraulic cylinder design problem and an aeroengine design problem formulated using a nonanalytic design structure matrix form. Our results show that the method automates various design reformulation tasks on problems of varying sizes from different design domains, stated in analytic and nonanalytic representational forms. The behavior of the method presents observations that cannot be explained by pure symbolic AI approaches, including uncovering patterns of implicit knowledge that are not readily encoded as logical rules, and automating tasks that require the associative transformation of sets of inputs to experiences. As an explanation, we relate the structure and performance of our algorithm with findings in cognitive neuroscience, and present a set of theoretical postulates addressing an alternate perspective on how symbols may interact with each other in experiences to reify semantic knowledge in design representations.

Inference of direct and multistep effective connectivities from functional connectivity of the brain and of relationships to cortical geometry

BACKGROUND The problem of inferring effective brain connectivity from functional connectivity is under active investigation, and connectivity via multistep paths is poorly understood. NEW METHOD A method is presented to calculate the direct effective connection matrix (deCM), which embodies direct connection strengths between brain regions, from functional CMs (fCMs) by minimizing the difference between an experimental fCM and one calculated via neural field theory from an ansatz deCM based on an experimental anatomical CM. RESULTS The best match between fCMs occurs close to a critical point, consistent with independent published stability estimates. Residual mismatch between fCMs is identified to be largely due to interhemispheric connections that are poorly estimated in an initial ansatz deCM due to experimental limitations; improved ansatzes substantially reduce the mismatch and enable interhemispheric connections to be estimated. Various levels of significant multistep connections are then imaged via the neural field theory (NFT) result that these correspond to powers of the deCM; these are shown to be predictable from geometric distances between regions. COMPARISON WITH EXISTING METHODS This method gives insight into direct and multistep effective connectivity from fCMs and relating to physiology and brain geometry. This contrasts with other methods, which progressively adjust connections without an overarching physiologically based framework to deal with multistep or poorly estimated connections. CONCLUSIONS deCMs can be usefully estimated using this method and the results enable multistep connections to be investigated systematically.

Back to the Future: Identifying Interface Trends from the Past, Present and Future in Immersive Applications

The new generation of Head Mounted Displays (HMDs) is beginning to make the much-anticipated arrival of augmented reality (AR) and virtual reality (VR) in consumer products reality. A large body of research from the last three decades has laid the foundation for the concepts now emerging in the market. Yet, there has been little focus on the analysis of consumer user interfaces being produced for these new platforms. As technology is progressing, there is an increasing need to study current trends in user and developer communities, and to contextualise them within the ongoing evolution of human-computer interfaces. In this paper, we specifically focus on mixed reality (MR) within immersed simulations enabled through combining VR headsets with vision sensors. We present an analysis of apps on the Leap Motion market and outline suggestions for developers and designers to assist with creating more natural user interface experiences.

Effective Urban Structure Inference from Traffic Flow Dynamics

Mobility in a city is represented as traffic flows in and out of defined urban travel or administrative zones. While the zones and the road networks connecting them are fixed in space, traffic flows between pairs of zones are dynamic through the day. Understanding these dynamics in real time is crucial for real time traffic planning in the city. In this paper, we use real time traffic flow data to generate dense functional correlation matrices between zones during different times of the day. Then, we derive optimal sparse representations of these dense functional matrices, that accurately recover not only the existing road network connectivity between zones, but also reveal new latent links between zones that do not yet exist but are suggested by traffic flow dynamics. We call this sparse representation the time-varying effective traffic connectivity of the city. A convex optimization problem is formulated and used to infer the sparse effective traffic network from time series data of traffic flow for arbitrary levels of temporal granularity. We demonstrate the results for the city of Doha, Qatar on data collected from several hundred bluetooth sensors deployed across the city to record vehicular activity through the citys traffic zones. While the static road network connectivity between zones is accurately inferred, other long range connections are also predicted that could be useful in planning future road linkages in the city. Further, the proposed model can be applied to socio-economic activity other than traffic, such as new housing, construction, or economic activity captured as functional correlations between zones, and can also be similarly used to predict new traffic linkages that are latently needed but as yet do not exist. Preliminary experiments suggest that our framework can be used by urban transportation experts and policy specialists to take a real time data-driven approach towards urban planning and real time traffic planning in the city, especially at the level of administrative zones of a city.

Spectral (Re)construction of Urban Street Networks: Generative Design Using Global Information from Structure

Modeling and analysis of urban form is typically performed using local generative design techniques, (e.g., shape grammars), with closed sets of local rules operating on elements. While this approach is powerful, the open variety of possible non-unique choices over the element and rule sets does not answer an important closure question: How much information, i.e., how many elements and rules, exhaustively capture all the information on structure? This paper investigates the inverted principle: using global system information to reconstruct a design. We show that orthogonal eigenmodes of a street network’s adjacency matrix capture global system information, and can be used to exactly reconstruct these networks. Further, by randomly perturbing the eigenmodes, new street networks of similar typology are generated. Thus, eigenmodes are global generators of structure. Outcomes provide new mechanisms for measuring and describing typology, morphology, and urban structure, and new future directions for generative design using global system information.

The scaling of income distribution in Australia: Possible relationships between urban allometry, city size, and economic inequality

Developing a scientific understanding of cities in a fast urbanizing world is essential for planning sustainable urban systems. Recently, it was shown that income and wealth creation follow increasing returns, scaling superlinearly with city size. We study scaling of per capita incomes for separate census defined income categories against population size for the whole of Australia. Across several urban area definitions, we find that lowest incomes grow just linearly or sublinearly (β = 0.94 to 1.00), whereas highest incomes grow superlinearly (β = 1.00 to 1.21), with total income just superlinear (β = 1.03 to 1.05). These findings show that as long as total or aggregate income scaling is considered, the earlier finding is supported: the bigger the city, the richer the city, although the scaling exponents for Australia are lower than those previously reported for other countries. But, we find an emergent scaling behavior with regard to variation in income distribution that sheds light on socio-economic inequality: the larger the population size and densities of a city, while lower incomes grow proportionately or less than proportionately, higher incomes grow more quickly, suggesting a disproportionate agglomeration of incomes in the highest income categories in big cities. Because there are many more people on lower incomes that scale sublinearly as compared to the highest that scale superlinearly, these findings suggest an empirical observation on inequality: the larger the population, the greater the income agglomeration in the highest income categories. The implications of these findings are qualitatively discussed for various income categories, with respect to living costs and access to opportunities and services that big cities provide.