arXiv subjects

M. Serva

Publications and source records attributed to M. Serva.

At least 19 recordsLinked to original sources

arXiv2025

Model Reduction of Multivariate Geometric Brownian Motions and Localization in a Two-State Quantum System

We develop a systematic framework for the model reduction of multivariate geometric Brownian motions (GBMs), a fundamental class of stochastic processes with broad applications in mathematical finance, population biology, and statistical physics. Our approach leverages the interplay between the method of invariant manifolds and adiabatic elimination to derive closed-form reduced equations for the deterministic drift. An extended formulation of the fluctuation-dissipation theorem is subsequently employed to characterize the stochastic component of the reduced description. As a concrete application, we apply our reduction scheme to a GBM arising from a two-state quantum system, showing that the reduced dynamics accurately capture the localization properties of the original model while significantly simplifying the analysis.

math-ph↗

arXiv2014

A percolation system with extremely long range connections and node dilution

We study the very long-range bond-percolation problem on a linear chain with both sites and bonds dilution. Very long range means that the probability $p_{ij}$ for a connection between two occupied sites $i,j$ at a distance $r_{ij}$ decays as a power law, i.e. $p_{ij} = \rho/[r_{ij}^\alpha N^{1-\alpha}]$ when $ 0 \le \alpha < 1$, and $p_{ij} = \rho/[r_{ij} \ln(N)]$ when $\alpha = 1$. Site dilution means that the occupancy probability of a site is $0 < p_s \le 1$. The behavior of this model results from the competition between long-range connectivity, which enhances the percolation, and site dilution, which weakens percolation. The case $\alpha=0$ with $p_s =1 $ is well-known, being the exactly solvable mean-field model. The percolation order parameter $P_\infty$ is investigated numerically for different values of $\alpha$, $p_s$ and $\rho$. We show that in the ranges $ 0 \le \alpha \le 1$ and $0 < p_s \le 1$ the percolation order parameter $P_\infty$ depends only on the average connectivity $\gamma$ of sites, which can be explicitly computed in terms of the three parameters $\alpha$, $p_s$ and $\rho$.

cond-mat.dis-nn↗

arXiv2013

Ising models on the Regularized Apollonian Network

We investigate the critical properties of Ising models on a Regularized Apollonian Network (RAN), here defined as a kind of Apollonian Network (AN) in which the connectivity asymmetry associated to its corners is removed. Different choices for the coupling constants between nearest neighbors are considered, and two different order parameters are used to detect the critical behaviour. While ordinary ferromagnetic and anti-ferromagnetic models on RAN do not undergo a phase transition, some anti-ferrimagnetic models show an interesting infinite order transition. All results are obtained by an exact analytical approach based on iterative partial tracing of the Boltzmann factor as intermediate steps for the calculation of the partition function and the order parameters.

cond-mat.stat-mech↗

arXiv2013

Solvable model for template coexistence in protocells

Compartmentalization of self-replicating molecules (templates) in protocells is a necessary step towards the evolution of modern cells. However, coexistence between distinct template types inside a protocell can be achieved only if there is a selective pressure favoring protocells with a mixed template composition. Here we study analytically a group selection model for the coexistence between two template types using the diffusion approximation of population genetics. The model combines competition at the template and protocell levels as well as genetic drift inside protocells. At the steady state, we find a continuous phase transition separating the coexistence and segregation regimes, with the order parameter vanishing linearly with the distance to the critical point. In addition, we derive explicit analytical expressions for the critical steady-state probability density of protocell compositions.

physics.bio-ph↗

arXiv2011

Malagasy Dialects and the Peopling of Madagascar

The origin of Malagasy DNA is half African and half Indonesian, nevertheless the Malagasy language, spoken by the entire population, belongs to the Austronesian family. The language most closely related to Malagasy is Maanyan (Greater Barito East group of the Austronesian family), but related languages are also in Sulawesi, Malaysia and Sumatra. For this reason, and because Maanyan is spoken by a population which lives along the Barito river in Kalimantan and which does not possess the necessary skill for long maritime navigation, the ethnic composition of the Indonesian colonizers is still unclear. There is a general consensus that Indonesian sailors reached Madagascar by a maritime trek, but the time, the path and the landing area of the first colonization are all disputed. In this research we try to answer these problems together with other ones, such as the historical configuration of Malagasy dialects, by types of analysis related to lexicostatistics and glottochronology which draw upon the automated method recently proposed by the authors \cite{Serva:2008, Holman:2008, Petroni:2008, Bakker:2009}. The data were collected by the first author at the beginning of 2010 with the invaluable help of Joselinà Soafara Néré and consist of Swadesh lists of 200 items for 23 dialects covering all areas of the Island.

cs.CL↗

arXiv2002

The origin of fat tailed distributions in financial time series

A classic problem in physics is the origin of fat tailed distributions generated by complex systems. We study the distributions of stock returns measured over different time lags $τ.$ We find that destroying all correlations without changing the $τ= 1$ d distribution, by shuffling the order of the daily returns, causes the fat tails almost to vanish for $τ>1$ d. We argue that the fat tails are caused by known long-range volatility correlations. Indeed, destroying only sign correlations, by shuffling the order of only the signs (but not the absolute values) of the daily returns, allows the fat tails to persist for $τ>1$ d.

cond-mat.dis-nn↗

arXiv2002

Kinematics of stock prices

We investigate the general problem of how to model the kinematics of stock prices without considering the dynamical causes of motion. We propose a stochastic process with long-range correlated absolute returns. We find that the model is able to reproduce the experimentally observed clustering, power law memory, fat tails and multifractality of real financial time series. We find that the distribution of stock returns is approximated by a Gaussian with log-normally distributed local variance and shows excellent agreement with the behavior of the NYSE index for a range of time scales.

cond-mat.dis-nn↗

arXiv2000

A macroscopically frustrated Ising model

A disordered spin glass model where both static and dynamical properties depend on macroscopic magnetizations is presented. These magnetizations interact via random couplings and, therefore, the typical quenched realization of the system exhibit a macroscopic frustration. The model is solved by using a revisited replica approach, and the broken symmetry solution turns out to coincide with the symmetric solution. Some dynamical aspects of the model are also discussed, showing how it could be a useful tool for describing some properties of real systems as, for example, natural ecosystems or human social systems.

cond-mat.dis-nn↗

arXiv2000

Moving averages and markets inefficiency

We introduce a stochastic price model where, together with a random component, a moving average of logarithmic prices contributes to the price formation. Our model is tested against financial datasets, showing an extremely good agreement with them. It suggests how to construct trading strategies which imply a capital growth rate larger than the growth rate of the underlying asset, with also the effect of reducing the fluctuations. These results are a clear evidence that some hidden information is not fully integrated in price dynamics, and therefore financial markets are partially inefficient. In simple terms, we give a recipe for speculators to make money as long as only few investors follow it.

cond-mat.dis-nn↗

arXiv1999

A general methodology to price and hedge derivatives in incomplete markets

We introduce and discuss a general criterion for the derivative pricing in the general situation of incomplete markets, we refer to it as the No Almost Sure Arbitrage Principle. This approach is based on the theory of optimal strategy in repeated multiplicative games originally introduced by Kelly. As particular cases we obtain the Cox-Ross-Rubinstein and Black-Scholes in the complete markets case and the Schweizer and Bouchaud-Sornette as a quadratic approximation of our prescription. Technical and numerical aspects for the practical option pricing, as large deviation theory approximation and Monte Carlo computation are discussed in detail.

cond-mat.dis-nn↗

arXiv1999

Efficiency in foreign exchange markets

A quantitative check of weak efficiency in US dollar/German mark exchange rates is developed using high frequency data. We show the existence of long term return anomalies. We introduce a technique to measure the available information and show it can be profitable following a particular trading rule.

cond-mat.dis-nn↗

arXiv1998

Optimal lag in dynamical investments

A portfolio of different stocks and a risk-less security whose composition is dynamically maintained stable by trading shares at any time step leads to a growth of the capital with a nonrandom rate. This is the key for the theory of optimal-growth investment formulated by Kelly. In presence of transaction costs, the optimal composition changes and, more important, it turns out that the frequency of transactions must be reduced. This simple observation leads to the definition of an optimal lag between two rearrangement of the portfolio. This idea is tested against an investment in a risky asset and a risk-less one. The price of the first is proportional to NYSE composite index while the price of the second grows according to the American Discount Rate. An application to a portfolio of many stochastically equivalent securities is also provided.

cond-mat.dis-nn↗

arXiv1998

Optimal Strategies for Prudent Investors

We consider a stochastic model of investment on an asset of a stock market for a prudent investor. She decides to buy permanent goods with a fraction $\a$ of the maximum amount of money owned in her life in order that her economic level never decreases. The optimal strategy is obtained by maximizing the exponential growth rate for a fixed $\a$. We derive analytical expressions for the typical exponential growth rate of the capital and its fluctuations by solving an one-dimensional random walk with drift.

cond-mat.dis-nn↗

arXiv1998

Localization induced by noise and non linearity

We introduce a model for a two configurations system, and we study the transition from quantum to classical behaviour. We first consider the effect of the interaction with the environment as an external noise and we show that it produces decoherence and suppression of tunnelling. These features are widely accepted as definition of classicality, while we believe that classicality implies that quantum delocalized states spontaneously evolve into localized ones. We than show that this evolution take place only when both noise and non linearity in the equations are present.

quant-ph↗

arXiv1997

A variational approach to Ising spin glasses in finite dimensions

We introduce a hierarchical class of approximations of the random Ising spin glass in $d$ dimensions. The attention is focused on finite clusters of spins where the action of the rest of the system is properly taken into account. At the lower level (cluster of a single spin) our approximation coincides with the SK model while at the highest level it coincides with the true $d$-dimensional system. The method is variational and it uses the replica approach to spin glasses and the Parisi ansatz for the order parameter. As a result we have rigorous bounds for the quenched free energy which become more and more precise when larger and larger clusters are considered.

cond-mat.dis-nn↗

arXiv1997

2d frustrated Ising model with four phases

In this paper we consider a 2d random Ising system on a square lattice with nearest neighbour interactions. The disorder is short range correlated and asymmetry between the vertical and the horizontal direction is admitted. More precisely, the vertical bonds are supposed to be non random while the horizontal bonds alternate: one row of all non random horizontal bonds is followed by one row where they are independent dichotomic random variables. We solve the model using an approximate approach that replace the quenched average with an annealed average under the constraint that the number of frustrated plaquettes is keep fixed and equals that of the true system. The surprising fact is that for some choices of the parameters of the model there are three second order phase transitions separating four different phases: antiferromagnetic, glassy-like, ferromagnetic and paramagnetic.

cond-mat.dis-nn↗

arXiv1996

The selection of altruistic behaviour

Altruistic behaviour is disadvantageous for the individual while is advantageous for its group. If the target of the selection is the individual, one would expect the selection process to lead to populations formed by wholly homogeneous groups, made up of either altruistic or egoistic individuals, where the winning choice depends on the balance beetwen group advantage and individual disadvantage. We show in a simple model that populations formed by inhomogeneous groups can be stabilized in some circumstances. We argue that this condition is realized when there is a relative advantage conferred by the presence of a few altruists to all the members of the group.

adap-org↗

arXiv1996

Beyond the Mean Field Approximation for Spin Glasses

We study the d-dimensional random Ising model using a Bethe-Peierls approximation in the framework of the replica method. We take into account the correct interaction only inside replicated clusters of spins. Our ansatz is that the interaction of the borders of the clusters with the external world can be described via an effective interaction among replicas. The Bethe-Peierls model is mapped into a single Ising model with a random gaussian field, whose strength (related to the effective coupling between two replicas) is determined via a self-consistency equation. This allows us to obtain analytic estimates of the internal energy and of the critical temperature in d dimensions.

cond-mat↗