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Graphs are a natural representation for systems based on relations between connected entities. Combinatorial optimization problems, which arise when considering an objective function related to a process of interest on discrete structures,…

Graph topology identification (GTI) is a central challenge in networked systems, where the underlying structure is often hidden, yet nodal data are available. Conventional solutions to address these challenges rely on probabilistic models…

Fair graph clustering is crucial for ensuring equitable representation and treatment of diverse communities in network analysis. Traditional methods often ignore disparities among social, economic, and demographic groups, perpetuating…

Beta-sorted portfolios -- portfolios comprised of assets with similar covariation to selected risk factors -- are a popular tool in empirical finance to analyze models of (conditional) expected returns. Despite their widespread use, little…

Graphs are widely used in various fields of computer science. They have also found application in unrelated areas, leading to a diverse range of problems. These problems can be modeled as relationships between entities in various contexts,…

The mean-variance portfolio model, based on the risk-return trade-off for optimal asset allocation, remains foundational in portfolio optimization. However, its reliance on restrictive assumptions about asset return distributions limits its…

Valuing mineral assets is a challenging task that is highly dependent on the supply (geological) uncertainty surrounding resources and reserves, and the uncertainty of demand (commodity prices). In this work, a graph-based reasoning,…

Stochastic portfolio theory aims at finding relative arbitrages, i.e. trading strategies which outperform the market with probability one. Functionally generated portfolios, which are deterministic functions of the market weights, are an…

Graphs may be used to represent many different problem domains -- a concrete example is that of detecting communities in social networks, which are represented as graphs. With big data and more sophisticated applications becoming widespread…

The sparsest cut problem consists of identifying a small set of edges that breaks the graph into balanced sets of vertices. The normalized cut problem balances the total degree, instead of the size, of the resulting sets. Applications of…

Graph representations offer powerful and intuitive ways to describe data in a multitude of application domains. Here, we consider stochastic processes generating graphs and propose a methodology for detecting changes in stationarity of such…

In this paper we develop a concrete and fully implementable approach to the optimization of functionally generated portfolios in stochastic portfolio theory. The main idea is to optimize over a family of rank-based portfolios parameterized…

We present a scale-invariant, template-based segmentation paradigm that sets up a graph and performs a graph cut to separate an object from the background. Typically graph-based schemes distribute the nodes of the graph uniformly and…

We propose a universal end-to-end framework for portfolio optimization where asset distributions are directly obtained. The designed framework circumvents the traditional forecasting step and avoids the estimation of the covariance matrix,…

We present a framework for modeling asset and portfolio dynamics, incorporating this information into portfolio optimization. For this framework, we introduce the Commonality Principle, providing a solution for the optimal selection of…

We consider fair allocation of indivisible items under an additional constraint: there is an undirected graph describing the relationship between the items, and each agent's share must form a connected subgraph of this graph. This framework…

Graph partitioning is the problem of dividing the nodes of a graph into balanced partitions while minimizing the edge cut across the partitions. Due to its combinatorial nature, many approximate solutions have been developed, including…

This paper develops new mathematical techniques to identify temporal shifts among a collection of US equities partitioned into a new and more detailed set of market sectors. Although conceptually related, our three analyses reveal distinct…

Topology identification and inference of processes evolving over graphs arise in timely applications involving brain, transportation, financial, power, as well as social and information networks. This chapter provides an overview of graph…

Graph clustering is a fundamental computational problem with a number of applications in algorithm design, machine learning, data mining, and analysis of social networks. Over the past decades, researchers have proposed a number of…