Honesty by typing

We propose a type system for a calculus of contracting processes. Processes may stipulate contracts, and then either behave honestly, by keeping the promises made, or not. Type safety guarantees that a typeable process is honest - that is, the process abides by the contract it has stipulated in all possible contexts, even those containing dishonest adversaries

The Hausdorff moments in statistical mechanics

A new method for solving the Hausdorff moment problem is presented which makes use of Pollaczek polynomials. This problem is severely ill posed; a regularized solution is obtained without any use of prior knowledge. When the problem is treated in the L 2 space and the moments are finite in number and affected by noise or round‐off errors, the approximation converges asymptotically in the L 2 norm. The method is applied to various questions of statistical mechanics and in particular to the determination of the density of states. Concerning this latter problem the method is extended to include distribution valued densities. Computing the Laplace transform of the expansion a new series representation of the partition function Z(β) (β=1/k BT ) is obtained which coincides with a Watson resummation of the high‐temperature series for Z(β)

Universal Behavior of Extreme Price Movements in Stock Markets

Many studies assume stock prices follow a random process known as geometric Brownian motion. Although approximately correct, this model fails to explain the frequent occurrence of extreme price movements, such as stock market crashes. Using a large collection of data from three different stock markets, we present evidence that a modification to the random model -- adding a slow, but significant, fluctuation to the standard deviation of the process -- accurately explains the probability of different-sized price changes, including the relative high frequency of extreme movements. Furthermore, we show that this process is similar across stocks so that their price fluctuations can be characterized by a single curve. Because the behavior of price fluctuations is rooted in the characteristics of volatility, we expect our results to bring increased interest to stochastic volatility models, and especially to those that can produce the properties of volatility reported here.Comment: 4 pages, 3 figure

Verifying message-passing programs with dependent behavioural types

Concurrent and distributed programming is notoriously hard. Modern languages and toolkits ease this difficulty by offering message-passing abstractions, such as actors (e.g., Erlang, Akka, Orleans) or processes (e.g., Go): they allow for simpler reasoning w.r.t. shared-memory concurrency, but do not ensure that a program implements a given specification. To address this challenge, it would be desirable to specify and verify the intended behaviour of message-passing applications using types, and ensure that, if a program type-checks and compiles, then it will run and communicate as desired. We develop this idea in theory and practice. We formalise a concurrent functional language λπ ⩽, with a new blend of behavioural types (from π-calculus theory), and dependent function types (from the Dotty programming language, a.k.a. the future Scala 3). Our theory yields four main payoffs: (1) it verifies safety and liveness properties of programs via type– level model checking; (2) unlike previous work, it accurately verifies channel-passing (covering a typical pattern of actor programs) and higher-order interaction (i.e., sending/receiving mobile code); (3) it is directly embedded in Dotty, as a toolkit called Effpi, offering a simplified actor-based API; (4) it enables an efficient runtime system for Effpi, for highly concurrent programs with millions of processes/actors

A Fractional Hawkes Process

We modify ETAS models by replacing the Pareto-like kernel proposed by Ogata with a Mittag-Leffler type kernel. Provided that the kernel decays as a power law with exponent $\beta + 1 \in (1, 2 ]$, this replacement has the advantage that the Laplace transform of the Mittag-Leffler function is known explicitly, leading to simpler calculation of relevant quantities

Semi-Markov Graph Dynamics

In this paper, we outline a model of graph (or network) dynamics based on two ingredients. The first ingredient is a Markov chain on the space of possible graphs. The second ingredient is a semi-Markov counting process of renewal type. The model consists in subordinating the Markov chain to the semi-Markov counting process. In simple words, this means that the chain transitions occur at random time instants called epochs. The model is quite rich and its possible connections with algebraic geometry are briefly discussed. Moreover, for the sake of simplicity, we focus on the space of undirected graphs with a fixed number of nodes. However, in an example, we present an interbank market model where it is meaningful to use directed graphs or even weighted graphs.Comment: 25 pages, 4 figures, submitted to PLoS-ON

Modelling and verifying contract-oriented systems in Maude

We address the problem of modelling and verifying contractoriented systems, wherein distributed agents may advertise and stipulate contracts, but — differently from most other approaches to distributed agents — are not assumed to always behave “honestly”. We describe an executable specification in Maude of the semantics of CO2, a calculus for contract-oriented systems [6]. The honesty property [5] characterises those agents which always respect their contracts, in all possible execution contexts. Since there is an infinite number of such contexts, honesty cannot be directly verified by model-checking the state space of an agent (indeed, honesty is an undecidable property in general [5]). The main contribution of this paper is a sound verification technique for honesty. To do that, we safely over-approximate the honesty property by abstracting from the actual contexts a process may be engaged with. Then, we develop a model-checking technique for this abstraction, we describe an implementation in Maude, and we discuss some experiments with it

A Formal Model of Algorand Smart Contracts

We develop a formal model of Algorand stateless smart contracts (stateless ASC1). We exploit our model to prove fundamental properties of the Algorand blockchain, and to establish the security of some archetypal smart contracts. While doing this, we highlight various design patterns supported by Algorand. We perform experiments to validate the coherence of our formal model w.r.t. the actual implementation

Scaling in the Inter-Event Time of Random and Seasonal Systems

Interevent times have been studied across various disciplines in search for correlations. In this paper we show analytical and numerical evidence that at the population level a power-law can be obtained by assuming poissonian agents with different characteristic times, and at the individual level by assuming poissonian agents that change the rates at which they perform an event in a random or deterministic fashion. The range in which we expect to see this behavior and the possible deviations from it are studied by considering the shape of the rate distribution.Comment: 10 pages 2 figures. Physica A. (In Press