Export dynamics as an optimal growth problem in the network of global economy

We analyze export data aggregated at world global level of 219 classes of products over a period of 39 years. Our main goal is to set up a dynamical model to identify and quantify plausible mechanisms by which the evolutions of the various exports affect each other. This is pursued through a stochastic differential description, partly inspired by approaches used in population dynamics or directed polymers in random media. We outline a complex network of transfer rates which describes how resources are shifted between different product classes, and determines how casual favorable conditions for one export can spread to the other ones. A calibration procedure allows to fit four free model-parameters such that the dynamical evolution becomes consistent with the average growth, the fluctuations, and the ranking of the export values observed in real data. Growth crucially depends on the balance between maintaining and shifting resources to different exports, like in an explore-exploit problem. Remarkably, the calibrated parameters warrant a close-to-maximum growth rate under the transient conditions realized in the period covered by data, implying an optimal self organization of the global export. According to the model, major structural changes in the global economy take tens of years

Mechanical unfolding and confinement of proteinsinvestigated through an Ising-like model

Un semplice modello alla Ising viene utilizzato per studiare le proprietà di equilibrio e la cinetica di biomolecole alle quali vengono applicate delle forze, tipicamente alle estremità, o tra particolari coppie di aminoacidi, o ancora confinandole tra una coppia di pareti rigide. Nel caso della fibronectina, più precisamente del suo decimo domino di tipo III, FnIII10, è stato studiato l'unfolding meccanico secondo i protocolli a forza costante e velocità costante. È stato possibile determinare i pathways di unfolding, confermando risultati precedenti nel caso di forze e velocità grandi, ed esplorando, grazie alla semplicità del modello, valori di forza e velocità più bassi, rilevanti per il comportamento in vivo della molecola. In questo caso è stato messo in evidenza un possibile fenomeno di fluttuazione tra 2 stati intermedi. Nel caso della proteina fluorescente verde (GFP), dopo aver confermato risultati precedenti per il caso in cui la molecola viene tirata dalle estremità, il lavoro si è concentrato sulla dipendenza dei parametri cinetici (forze e lunghezze di unfolding) dalla direzione, ovvero dalla coppia di aminoacidi ai quali la forza viene applicata. Questo lavoro ha dato risultati qualitativamente in accordo con gli esperimenti e, laddove disponibili, con simulazioni di modelli più dettagliati. Ha inoltre permesso di formulare una proposta per un sensore di forza basato su una poliproteina costituita da diversi moduli di GFP opportunamente connessi tra loro. Infine, il modello è stato esteso al caso del folding in uno spazio confinato, precisamente tra 2 pareti rigide inerti, mostrando che, nonostante la sua semplicità, il modello è in grado di descrivere i fenomeni di innalzamento della temperatura di denaturazione e del folding rate osservati sperimentalmente, e le rispettive leggi a potenza

Pathways of mechanical unfolding of FnIII10: Low force intermediates

We study the mechanical unfolding pathways of the $FnIII_{10}$ domain of fibronectin by means of an Ising--like model, using both constant force and constant velocity protocols. At high forces and high velocities our results are consistent with experiments and previous computational studies. Moreover, the simplicity of the model allows us to probe the biologically relevant low force regime, where we predict the existence of two intermediates with very close elongations. The unfolding pathway is characterized by stochastic transitions between these two intermediates

Analytic Solution of an Active Brownian Particle in a Harmonic Well

We provide an analytical solution for the time-dependent Fokker-Planck equation for a two-dimensional active Brownian particle trapped in an isotropic harmonic potential. Using the passive Brownian particle as basis states we show that the Fokker-Planck operator becomes lower diagonal, implying that the eigenvalues are unaffected by the activity. The propagator is then expressed as a combination of the equilibrium eigenstates with weights obeying exact iterative relations. We show that for the low-order correlation functions, such as the positional autocorrelation function, the recursion terminates at finite order in the P\'eclet number allowing us to generate exact compact expressions and derive the velocity autocorrelation function and the time-dependent diffusion coefficient. The nonmonotonic behavior of latter quantities serves as a fingerprint of the non-equilibrium dynamics.Comment: 11pages, 3 figure

Entanglement Entropy and Twist Fields

The entanglement entropy of a subsystem of a quantum system is expressed, in the replica approach, through analytic continuation with respect to n of the trace of the n-th power of the reduced density matrix. This trace can be thought of as the vacuum expectation value of a suitable observable in a system made with n independent copies of the original system. We use this property to numerically evaluate it in some two-dimensional critical systems, where it can be compared with the results of Calabrese and Cardy, who wrote the same quantity in terms of correlation functions of twist fields of a conformal field theory. Although the two calculations match perfectly even in finite systems when the analyzed subsystem consists of a single interval, they disagree whenever the subsystem is composed of more than one connected part. The reasons of this disagreement are explained.Comment: 25 pages, 10 figures v2: section 2.1 improved; matches published versio

Scaling symmetry, renormalization, and time series modeling

We present and discuss a stochastic model of financial assets dynamics based on the idea of an inverse renormalization group strategy. With this strategy we construct the multivariate distributions of elementary returns based on the scaling with time of the probability density of their aggregates. In its simplest version the model is the product of an endogenous auto-regressive component and a random rescaling factor designed to embody also exogenous influences. Mathematical properties like increments' stationarity and ergodicity can be proven. Thanks to the relatively low number of parameters, model calibration can be conveniently based on a method of moments, as exemplified in the case of historical data of the S&P500 index. The calibrated model accounts very well for many stylized facts, like volatility clustering, power law decay of the volatility autocorrelation function, and multiscaling with time of the aggregated return distribution. In agreement with empirical evidence in finance, the dynamics is not invariant under time reversal and, with suitable generalizations, skewness of the return distribution and leverage effects can be included. The analytical tractability of the model opens interesting perspectives for applications, for instance in terms of obtaining closed formulas for derivative pricing. Further important features are: The possibility of making contact, in certain limits, with auto-regressive models widely used in finance; The possibility of partially resolving the long-memory and short-memory components of the volatility, with consistent results when applied to historical series.Comment: Main text (17 pages, 13 figures) plus Supplementary Material (16 pages, 5 figures

Option pricing with non-Gaussian scaling and infinite-state switching volatility

Volatility clustering, long-range dependence, and non-Gaussian scaling are stylized facts of financial assets dynamics. They are ignored in the Black & Scholes framework, but have a relevant impact on the pricing of options written on financial assets. Using a recent model for market dynamics which adequately captures the above stylized facts, we derive closed form equations for option pricing, obtaining the Black & Scholes as a special case. By applying our pricing equations to a major equity index option dataset, we show that inclusion of stylized features in financial modeling moves derivative prices about 30% closer to the market values without the need of calibrating models parameters on available derivative prices.Comment: Revised version. 31 pages, 4 figure

Aftershock prediction for high-frequency financial markets' dynamics

The occurrence of aftershocks following a major financial crash manifests the critical dynamical response of financial markets. Aftershocks put additional stress on markets, with conceivable dramatic consequences. Such a phenomenon has been shown to be common to most financial assets, both at high and low frequency. Its present-day description relies on an empirical characterization proposed by Omori at the end of 1800 for seismic earthquakes. We point out the limited predictive power in this phenomenological approach and present a stochastic model, based on the scaling symmetry of financial assets, which is potentially capable to predict aftershocks occurrence, given the main shock magnitude. Comparisons with S&P high-frequency data confirm this predictive potential.Comment: Contribution to the proceedings of the Econophysics Kolkata VI International Workshop, 12 pages, 4 figures. Added references and minor correction