Corporate payments networks and credit risk rating

Aggregate and systemic risk in complex systems are emergent phenomena depending on two properties: the idiosyncratic risks of the elements and the topology of the network of interactions among them. While a significant attention has been given to aggregate risk assessment and risk propagation once the above two properties are given, less is known about how the risk is distributed in the network and its relations with the topology. We study this problem by investigating a large proprietary dataset of payments among 2.4M Italian firms, whose credit risk rating is known. We document significant correlations between local topological properties of a node (firm) and its risk. Moreover we show the existence of an homophily of risk, i.e. the tendency of firms with similar risk profile to be statistically more connected among themselves. This effect is observed when considering both pairs of firms and communities or hierarchies identified in the network. We leverage this knowledge to show the predictability of the missing rating of a firm using only the network properties of the associated node

Scalarization and sensitivity analysis in Vector Optimization. The linear case.

In this paper we consider a vector optimization problem; we present some scalarization techniques for finding all the vector optimal points of this problem and we discuss the relationships between these methods. Moreover, in the linear case, the study of dual variables is carried on by means of sensitivity analysis and also by a parametric approach. We also give an interpretation of the dual variables as marginal rates of substitution of an objective function with respect to another one, and of an objective function with respect to a constraint.Vector Optimization, Image Space, Separation, Scalarization, Shadow Prices

Resolution of ranking hierarchies in directed networks

Identifying hierarchies and rankings of nodes in directed graphs is fundamental in many applications such as social network analysis, biology, economics, and finance. A recently proposed method identifies the hierarchy by finding the ordered partition of nodes which minimises a score function, termed agony. This function penalises the links violating the hierarchy in a way depending on the strength of the violation. To investigate the resolution of ranking hierarchies we introduce an ensemble of random graphs, the Ranked Stochastic Block Model. We find that agony may fail to identify hierarchies when the structure is not strong enough and the size of the classes is small with respect to the whole network. We analytically characterise the resolution threshold and we show that an iterated version of agony can partly overcome this resolution limit.Comment: 27 pages, 9 figure

Operational and abstract semantics of the query language G-Log

The amount and variety of data available electronically have dramatically increased in the led decade; however, data and documents are stored in different ways and do notusual# show their internal structure. In order to take ful advantage of thetopolk9dQ# structure ofdigital documents, andparticulIII web sites, theirhierarchical organizationshouliz explizatio introducing a notion of querysimil; to the one usedin database systems. A good approach, in that respect, is the one provided bygraphical querylrydM#99; original; designed to model object bases and lndd proposed for semistructured data, la, G-Log. The aim of this paper is to providesuitabl graph-basedsemantics to thislisd;BI# supporting both data structure variabil#I andtopol#Ik;M similpol#I between queries and document structures. A suite ofoperational semantics basedon the notion ofbisimulQM#I is introduced both at theconcr--h level (instances) andat theabstru( level (schemata), giving rise to a semantic framework that benefits from the cross-fertil9;dl of tool originalM designed in quite different research areas (databases, concurrency,loncur static analysis)

Semi-automatic support for evolving functional dependencies

During the life of a database, systematic and frequent violations of a given constraint may suggest that the represented reality is changing and thus the constraint should evolve with it. In this paper we propose a method and a tool to (i) find the functional dependencies that are violated by the current data, and (ii) support their evolution when it is necessary to update them. The method relies on the use of confidence, as a measure that is associated with each dependency and allows us to understand \u201dhow far\u201d the dependency is from correctly describing the current data; and of goodness, as a measure of balance between the data satisfying the antecedent of the dependency and those satisfying its consequent. Our method compares favorably with literature that approaches the same problem in a different way, and performs effectively and efficiently as shown by our tests on both real and synthetic databases

A graph-based meta-model for heterogeneous data management

The wave of interest in data-centric applications has spawned a high variety of data models, making it extremely difficult to evaluate, integrate or access them in a uniform way. Moreover, many recent models are too specific to allow immediate comparison with the others and do not easily support incremental model design. In this paper, we introduce GSMM, a meta-model based on the use of a generic graph that can be instantiated to a concrete data model by simply providing values for a restricted set of parameters and some high-level constraints, themselves represented as graphs. In GSMM, the concept of data schema is replaced by that of constraint, which allows the designer to impose structural restrictions on data in a very flexible way. GSMM includes GSL, a graph-based language for expressing queries and constraints that besides being applicable to data represented in GSMM, in principle, can be specialised and used for existing models where no language was defined. We show some sample applications of GSMM for deriving and comparing classical data models like the relational model, plain XML data, XML Schema, and time-varying semistructured data. We also show how GSMM can represent more recent modelling proposals: the triple stores, the BigTable model and Neo4j, a graph-based model for NoSQL data. A prototype showing the potential of the approach is also described