Interactive Realizability and the elimination of Skolem functions in Peano Arithmetic

We present a new syntactical proof that first-order Peano Arithmetic with Skolem axioms is conservative over Peano Arithmetic alone for arithmetical formulas. This result - which shows that the Excluded Middle principle can be used to eliminate Skolem functions - has been previously proved by other techniques, among them the epsilon substitution method and forcing. In our proof, we employ Interactive Realizability, a computational semantics for Peano Arithmetic which extends Kreisel's modified realizability to the classical case.Comment: In Proceedings CL&C 2012, arXiv:1210.289

Quality-Aware Broadcasting Strategies for Position Estimation in VANETs

The dissemination of vehicle position data all over the network is a fundamental task in Vehicular Ad Hoc Network (VANET) operations, as applications often need to know the position of other vehicles over a large area. In such cases, inter-vehicular communications should be exploited to satisfy application requirements, although congestion control mechanisms are required to minimize the packet collision probability. In this work, we face the issue of achieving accurate vehicle position estimation and prediction in a VANET scenario. State of the art solutions to the problem try to broadcast the positioning information periodically, so that vehicles can ensure that the information their neighbors have about them is never older than the inter-transmission period. However, the rate of decay of the information is not deterministic in complex urban scenarios: the movements and maneuvers of vehicles can often be erratic and unpredictable, making old positioning information inaccurate or downright misleading. To address this problem, we propose to use the Quality of Information (QoI) as the decision factor for broadcasting. We implement a threshold-based strategy to distribute position information whenever the positioning error passes a reference value, thereby shifting the objective of the network to limiting the actual positioning error and guaranteeing quality across the VANET. The threshold-based strategy can reduce the network load by avoiding the transmission of redundant messages, as well as improving the overall positioning accuracy by more than 20% in realistic urban scenarios.Comment: 8 pages, 7 figures, 2 tables, accepted for presentation at European Wireless 201

A dynamic approach to rebalancing bike-sharing systems

Bike-sharing services are flourishing in Smart Cities worldwide. They provide a low-cost and environment-friendly transportation alternative and help reduce traffic congestion. However, these new services are still under development, and several challenges need to be solved. A major problem is the management of rebalancing trucks in order to ensure that bikes and stalls in the docking stations are always available when needed, despite the fluctuations in the service demand. In this work, we propose a dynamic rebalancing strategy that exploits historical data to predict the network conditions and promptly act in case of necessity. We use Birth-Death Processes to model the stations' occupancy and decide when to redistribute bikes, and graph theory to select the rebalancing path and the stations involved. We validate the proposed framework on the data provided by New York City's bike-sharing system. The numerical simulations show that a dynamic strategy able to adapt to the fluctuating nature of the network outperforms rebalancing schemes based on a static schedule

A "Game Semantical" Intuitionistic Realizability Validating Markov\u27s Principle

We propose a very simple modification of Kreisel\u27s modified realizability in order to computationally realize Markov\u27s Principle in the context of Heyting Arithmetic. Intuitively, realizers correspond to arbitrary strategies in Hintikka-Tarski games, while in Kreisel\u27s realizability they can only represent winning strategies. Our definition, however, does not employ directly game semantical concepts and remains in the style of functional interpretations. As term calculus, we employ a purely functional language, which is Goedel\u27s System T enriched with some syntactic sugar

On Natural Deduction in Classical First-Order Logic: Curry-Howard Correspondence, Strong Normalization and Herbrand's Theorem

International audienceWe present a new Curry-Howard correspondence for classical first-order natural deduction. We add to the lambda calculus an operator which represents, from the viewpoint of programming, a mechanism for raising and catching multiple exceptions, and from the viewpoint of logic, the excluded middle over arbitrary prenex formulas. The machinery will allow to extend the idea of learning -- originally developed in Arithmetic -- to pure logic. We prove that our typed calculus is strongly normalizing and show that proof terms for simply existential statements reduce to a list of individual terms forming a Herbrand disjunction. A by-product of our approach is a natural-deduction proof and a computational interpretation of Herbrand's Theorem

Pricing the Idiosyncratic Risk in the Cost of Capital: A Comprehensive Model

Despite the mixed evidence, recent empirical works highlight the importance of idiosyncratic risk in the stock market. On this basis, this note elaborates an approach to price directly the specific risk in the cost of capital, both for scientific empirical purposes and practitioner’s investment valuation. For ex- tremely high leverage values, the cost of risky debt tends to approximate the unlevered cost of capital. Exploiting a Merton model, we show a simple solu- tion to calculate in practice every cost of capital version, providing a compre- hensive framework. A worked example is provided to simplify the concrete application

Hybrid Spectrum Sharing in mmWave Cellular Networks

While spectrum at millimeter wave (mmWave) frequencies is less scarce than at traditional frequencies below 6 GHz, still it is not unlimited, in particular if we consider the requirements from other services using the same band and the need to license mmWave bands to multiple mobile operators. Therefore, an efficient spectrum access scheme is critical to harvest the maximum benefit from emerging mmWave technologies. In this paper, we introduce a new hybrid spectrum access scheme for mmWave networks, where data is aggregated through two mmWave carriers with different characteristics. In particular, we consider the case of a hybrid spectrum scheme between a mmWave band with exclusive access and a mmWave band where spectrum is pooled between multiple operators. To the best of our knowledge, this is the first study proposing hybrid spectrum access for mmWave networks and providing a quantitative assessment of its benefits. Our results show that this approach provides major advantages with respect to traditional fully licensed or fully unlicensed spectrum access schemes, though further work is needed to achieve a more complete understanding of both technical and non technical implications