The increasing use of localization devices for location-based services has led to an explosion in user location data. This raises significant privacy concerns that often conflict with the need for identification and accountability in critical scenarios like criminal investigations or public health emergencies. Research is facing the challenge of balancing privacy with data utility, guaranteeing trust in verification. This paper proposes a novel blockchain-based solution to reconcile the conflicting requirements of user privacy and accountability in localization. Our scheme leverages the transparency and immutability of blockchain to record verifiable location proofs. To ensure user privacy against routine disclosure, the solution integrates elliptic curve cryptography and Zero-Knowledge Proofs, allowing a verifier to confirm a user's presence without revealing sensitive information. Our solution also prevents the verifier from disclosing proof of a user's past presence to third parties, further enhancing privacy. Moreover, the proposed system provides a mechanism for accountability, allowing a designated authority to override privacy safeguards and access location data when legally mandated for public interest reasons, thereby reconciling privacy and identification needs.

The aim of this paper is to introduce a novel equilibrium model based on trust and reputation systems to study cloud data centers, physical or virtual facilities that host and manage cloud computing resources to support the delivery of online services, applications, storage, and other IT resources. In our model, the physical hardware of the center, such as servers, evaluate each other with the objective of maximizing their utility (gain minus costs), expressed in terms of reputation. The reputation of each server is defined as a weighted sum of the trust values it receives, where weights are assigned based on the distance between servers. A variational approach is applied to determine an equilibrium configuration of the system from the user’s perspective. The equilibrium solution is analyzed with respect to its existence and uniqueness. Furthermore, numerical simulations are conducted to test and validate the model. Finally, a sensitivity analysis on the initial reputation of the servers and the distance parameter is performed.

One of the most common types of malicious behavior in social networks is represented by collusion, which consists of a secret cooperation between two or more agents providing mutual, highly positive feedback to each other. This collusion creates misleading advantages for the involved agents, deceiving others and distorting the actual reputation perception of the colluding members. Although the well-known EigenTrust algorithm can be fruitfully used to detect colluded agents, two important issues arise which limit its effectiveness: 1) it requires input information about which agents can be a-priori considered particularly trustworthy; and 2) it is not designed to handle situations in which we have several, different groups of colluded agents. These problems lead EigenTrust, to produce a significant number of false positives in some real situations. In this paper, we address the aforementioned issues. We introduce an automatic procedure to provide EigenTrust with the necessary inputs, and we propose an appropriate algorithm that combines EigenTrust with a clustering process. This procedure groups agents based on their reputation scores to tackle the presence of different groups of colluded agents. Through experiments, we demonstrate that our method, while maintaining the same effectiveness as EigenTrust in detecting malicious agents, is significantly more capable of avoiding the generation of false positives.

Trust and reputation systems play a pivotal role in modern decentralized environments, fostering cooperation and mitigating risks in various online interactions. This paper introduces a variational formulation approach to model and analyze trust and reputation systems. By formulating trust and reputation as variational problems, this approach offers a novel perspective on understanding the underlying mechanisms governing trust establishment. The variational formulation provides a mathematical framework to determine the equilibrium weighted trust values, taking into account that each trustee tries to maximize its gain, namely the benefit minus the costs. The paper illustrates the applicability of this variational formulation through a pletora of simulations, demonstrating its effectiveness in modeling trust and reputation systems. Insights gained from this approach offer valuable guidance for the design and implementation of more reliable and efficient trust and reputation mechanisms in decentralized environments

The purpose of the research is the study of a nonconstant gradient constrained problem for nonlinear monotone operators. In particular, we study a stationary variational inequality, defined by a strongly monotone operator, in a convex set of gradient-type constraints. We investigate the relationship between the nonconstant gradient constrained problem and a suitable double obstacle problem, where the obstacles are the viscosity solutions to a Hamilton–Jacobi equation, and we show the equivalence between the two variational problems. To obtain the equivalence, we prove that a suitable constraint qualification condition, Assumption S, is fulfilled at the solution of the double obstacle problem. It allows us to apply a strong duality theory, holding under Assumption S. Then, we also provide the proof of existence of Lagrange multipliers. The elements in question can be not only functions in L2, but also measures.

The introduction of trust-based approaches in social scenarios modeled as multi-agent systems (MAS) has been recognized as a valid solution to improve the effectiveness of these communities. In fact, they make interactions taking place in social scenarios much fruitful as possible, limiting or even avoiding malicious or fraudulent behaviors, including collusion. This is also the case of multi-layered neural networks (NN), which can face limited, incomplete, misleading, controversial or noisy datasets, produced by untrustworthy agents. Many strategies to deal with malicious agents in social networks have been proposed in the literature. One of the most effective is represented by Eigentrust, often adopted as a benchmark. It can be seen as a variation of PageRank, an algorithm for determining result rankings used by search engines like Google. Moreover, Eigentrust can also be viewed as a linear neural network whose architecture is represented by the graph of Web pages. A major drawback of Eigentrust is that it uses some additional information about agents that can be a priori considered particularly trustworthy, rewarding them in terms of reputation, while the non pre-trusted agents are penalized. In this paper, we propose a different strategy to detect malicious agents which does not modify the real reputation values of the honest ones. We introduce a measure of effectiveness when computing reputation in presence of malicious agents. Moreover, we define a metric of error useful to quantitatively determine how much an algorithm for the identification of malicious agents modifies the reputation scores of the honest ones. We have performed an experimental campaign of mathematical simulations on a dynamic multi-agent environment. The obtained results show that our method is more effective than Eigentrust in determining reputation values, presenting an error which is about a thousand times lower than the error produced by Eigentrust on medium-sized social networks.

In the Internet of Things, smart objects can build multidimensional and context-sensitive network infrastructures potentially rich of social interactions. Smart objects can be associated with software agents to boost social interactions and realizing complex and sophisticated forms of collaboration of objects with both other objects and people. In such a scenario, there exists the possibility to interact with unreliable partners exposing agents to the risks deriving by malicious behaviors. To mitigate these risks, Trust and Reputation Systems can be adopted to provide each agent with appropriate trustworthiness measures about the potential counterparts in order to select the best ones. In this context, our contribution consists of (i) a method to preliminarily identify the best candidates as malicious in order to consider them as pre-untrusted entities and (ii) a novel effective reputation model able to detect collusive malicious agents without introducing collateral effects with respect to the reputation scores of honest agents.

In this paper, we study a variational problem with nonconstant gradient constraints. Several aspects related to problems with gradient constraints have been studied in the literature and have seen new developments in recent years. In the case of constant gradient constraint, the problem is the well-known elastic–plastic torsion problem. A relevant issue in this type of problem is the existence of Lagrange multipliers. Here, we consider the equivalent Lagrange multiplier formulation of a nonconstant gradient-constrained problem, and we investigate the class of solutions having a radial symmetry. We rewrite the problem in the radial symmetry case, and we analyse the different situations that may arise. In particular, in the planar case, we derive a condition characterizing the free boundary and obtain the explicit radial solution to the problem and the Lp Lagrange multiplier. Some examples support the results.

In real and virtual communities, complex and sophisticated forms of social interactions and cooperation are increasingly taking place between heterogeneous actors such as people, intelligent objects and virtual entities. At the same time, in such communities the risks of interacting with unreliable partners engaged in malicious activities increase. Therefore, it is important to provide all players with adequate information in order to allow them to choose the most reliable partner to interact with. In this context, we have focused our attention on colluding activities. In particular we propose a reputation method that preliminarily identifies those actors who most likely can be considered colluding players. This method does not introduce side effects to trust scores of honest actors while detecting colluding ones with high accuracy. A simple example supports our results.

The paper deals with nonlinear monotone variational inequalities with gradient constraints. In particular, using a new strong duality principle, the equivalence between the problem under consideration and a suitable double obstacle problem is proved. Moreover, the existence of L 2 Lagrange multipliers is achieved. This article is part of the theme issue ‘Non-smooth variational problems and applications’.

The paper is devoted to the strong duality minimax theory, that works in infinite dimensional settings, and to its applications. In particular, we deal with the nonconstant gradient constrained problem and with the random traffic equilibrium problem. By means of this theory, we are able to show that, for both problems, the associated infinite dimensional variational inequalitiy on a convex feasible set is equivalent to a system of equations.

The aim of the paper is to study a gradient constrained problem associated with a linear operator. Two types of problems are investigated. The first one is the equivalence between a non-constant gradient constrained problem and a suitable obstacle problem, where the obstacle solves a Hamilton-Jacobi equation in the viscosity sense. The equivalence result is obtained under a condition on the gradient constraint. The second problem is the existence of Lagrange multipliers. We prove that the non-constant gradient constrained problem admits a Lagrange multiplier, which is a Radon measure if the free term of the equation f∈Lp, p>1. If f is a positive constant, we regularize the result, namely we prove that the Lagrange multipliers belong to L2.

In this chapter we improve some results in literature on the general financial equilibrium problem related to individual entities, called sectors, which invest in financial instruments as assets and as liabilities. Indeed the model, studied in the chapter, takes into account the insolvencies and we analyze how these insolvencies affect the financial problem. For this improved model we describe a variational inequality for which we provide an existence result. Moreover, we study the dual Lagrange problem, in which the Lagrange variables, which represent the deficit and the surplus per unit, appear and an economical indicator is provided. Finally, we perform the contagion by means of the deficit and surplus variables. As expected, the presence of the insolvencies makes it more difficult to reach the financial equilibrium and increases the risk of a negative contagion for all the systems.

September 19-20, 2019 Messina, Italia Organizers Patrizia Daniele, Maria B. Donato, Sofia Giuffrè, Monica Milasi, Laura Scrimali, Carmela Vitanza Supported by Accademia Peloritana dei Pericolanti INDAM – GNAMPA University of Catania University of Messina University Mediterranea of Reggio Calabria On the relations between principal eigenvalue and torsional rigidity

The paper is concerned with radial solutions to the elastic-plastic torsion problem, assuming the free term to belong to L-p (Omega). In particular, we obtain a necessary and sufficient condition in order that the plastic region exists and we characterize the free boundary. Moreover, we find the explicit radial solution u is an element of W-2,W-p (Omega) and the Lagrange multiplier (mu) over bar is an element of L-p (Omega).

In this chapter we first present some theoretic concepts related to the strong duality in the infinite-dimensional setting. Then, we apply such results to the general financial equilibrium economy, studying also the dual formulation of the problem, analyzing both the sector’s and the system’s viewpoints and deriving the contagion phenomenon. Further, we provide an evolutionary Markowitz-type measure of the risk with a memory term. Finally, we apply Assumption S to the elastic-plastic torsion problem for linear operators and investigate the existence of Lagrange multipliers to the elastic-plastic torsion problem for nonlinear monotone operators, providing an example of the so-called Von Mises functions and searching for radial solutions.

In this paper, we propose a new cybersecurity investment supply chain game theory model, assuming that the demands for the product are known and fixed and, hence, the conservation law of each demand market is fulfilled. The model is a generalized Nash equilibrium model with nonlinear budget constraints for which we define the variational equilibrium, which provides us with a variational inequality formulation. We construct an equivalent formulation, enabling the analysis of the influence of the conservation laws and the importance of the associated Lagrange multipliers. We find that the marginal expected transaction utility of each retailer depends on this Lagrange multiplier and its sign. Finally, numerical examples with reported equilibrium product flows, cybersecurity investment levels, and Lagrange multipliers, along with individual firm vulnerability and network vulnerability, illustrate the obtained results.