Searcharxiv⌕ Search

arXiv subjects

Alexandre Souto Martinez

Publications and source records attributed to Alexandre Souto Martinez.

At least 37 records · Page 2Linked to original sources
arXiv2009

Prisoner's Dilemma: non-trivial results for the lowest temptation level in the Darwinian and Pavlovian evolutionary strategies

The lowest temptation level (T = 1) is considered a trivial case for the Prisoner's Dilemma. Here, we show that this statement is true only for a very particular case, where the players interact with only one player. Otherwise, if the players interact with more than one player, the system presents the same possible behaviors observed for $T > 1$. In the steady state, the system can reach the cooperative, chaotic or defective phases, when adopting the Darwinian Evolutionary Strategy and the cooperative or quasi-regular phases, adopting the Pavlovian Evolutionary Strategy.

physics.soc-ph↗
arXiv2009

Pavlovian Prisoner's Dilemma in one-dimensional cellular automata: analytical results, the quasi-regular phase, spatio-temporal patterns and parameter space exploration

The Prisoner's Dilemma (PD) game is used in several fields due to the emergence of cooperation among selfish players. Here, we have considered a one-dimensional lattice, where each cell represents a player, that can cooperate or defect. This one-dimensional geometry allows us to retrieve the results obtained for regular lattices and to keep track of the system spatio-temporal evolution. Players play PD with their neighbors and update their state using the Pavlovian Evolutionary Strategy. If the players receive a positive payoff greater than an aspiration level, they keep their states and switch them, otherwise. We obtain analitycally the critical temptation values, we present the cluster patterns that emerge from the players local interaction and we perform an exploration of paramater space. The numerical results are in accordance to the critical temptation analitycal results, it confirms that the Pavlovian strategy foment the cooperation among the players and avoid the defection. The system also presented a new phase in the steady state, the quasi-regular phase, where several players switch their states during round to round, but the proportion of cooperators does not alter significantly.

physics.soc-ph↗
arXiv2009

Generalized exponential function and discrete growth models

Here we show that a particular one-parameter generalization of the exponential function is suitable to unify most of the popular one-species discrete population dynamics models into a simple formula. A physical interpretation is given to this new introduced parameter in the context of the continuous Richards model, which remains valid for the discrete case. From the discretization of the continuous Richards' model (generalization of the Gompertz and Verhuslt models), one obtains a generalized logistic map and we briefly study its properties. Notice, however that the physical interpretation for the introduced parameter persists valid for the discrete case. Next, we generalize the (scramble competition) $θ$-Ricker discrete model and analytically calculate the fixed points as well as their stability. In contrast to previous generalizations, from the generalized $θ$-Ricker model one is able to retrieve either scramble or contest models.

physics.bio-ph↗
arXiv2008

Generalized Exponential Function and some of its Applications to Complex Systems

From the integration of non-symmetrical hyperboles, a one-parameter generalization of the logarithmic function is obtained. Inverting this function, one obtains the generalized exponential function. We show that functions characterizing complex systems can be conveniently written in terms of this generalization of the exponential function. The gamma function is then generalized and we generalize the factorial operation. Also a very reliable rank distribution can be conveniently described by the generalized exponential function. Finally, we turn the attention to the generalization of one- and two-tail stretched exponential functions. One obtains, as particular cases, the generalized error function, the Zipf-Mandelbrot probability density function (pdf), the generalized gaussian and Laplace pdf. One can also obtain analytically their cumulative functions and moments.

physics.data-an↗
arXiv2008

The influence of memory in deterministic walks in random media: analytical calculation within a mean field approximation

Consider a random medium consisting of points randomly distributed so that there is no correlation among the distances. This is the random link model, which is the high dimensionality limit (mean field approximation) for the euclidean random point structure. In the random link model, at discrete time steps, the walker moves to the nearest site, which has not been visited in the last $μ$ steps (memory), producing a deterministic partially self avoiding walk (the tourist walk). We have obtained analitically the distribution of the number $n$ of points explored by a walker with memory $μ= 2$, as well as the transient and period joint distribution. This result enables to explain the abrupt change in the exploratory behavior between the cases $μ= 1$ (memoryless, driven by extremal statistics) and $μ= 2$ (with memory, driven by combinatorial statistics). In the $μ= 1$ case, the mean newly visited points in the thermodynamic limit $(N \gg 1)$ is just $ = e = 2.72 ...$ while in the $μ= 2$ case, the mean number $ $ of visited points is proportional to $N^{1/2}$. Also, this result allows us to stabilish an equivalence between the random link model with $μ=2$ and random map (uncorrelated back and forth distances) with $μ=0$ and the drastic change between the cases where the transient time is null compared to non-null transient times.

cond-mat.stat-mech↗
arXiv2008

Continuous growth models in terms of generalized logarithm and exponential functions

Consider the one-parameter generalizations of the logarithmic and exponential functions which are obtained from the integration of non-symmetrical hyperboles. These generalizations coincide to the one obtained in the context of non-extensive thermostatistics. We show that these functions are suitable to describe and unify the great majority of continuous growth models, which we briefly review. Physical interpretation to the generalization function parameter is given for the Richards' model, which has an underlying microscopic model to justify it.

q-fin.GN↗
arXiv2008

An exhaustive exploration of the parameter space of the Prisoners' Dilemma in one-dimensional cellular automata

The Prisoner's Dilemma (PD) is one of the most popular games of the Game Theory due to the emergence of cooperation among competitive rational players. In this paper, we present the PD played in cells of one-dimension cellular automata, where the number of possible neighbors that each cell interacts, z, can vary. This makes possible to retrieve results obtained previously in regular lattices. Exhaustive exploration of the parameters space is presented. We show that the final state of the system is governed mainly by the number of neighbors z and there is a drastic difference if it is even or odd.

physics.soc-ph↗
arXiv2007

Prisoner's Dilemma in One-Dimensional Cellular Automata: Visualization of Evolutionary Patterns

The spatial Prisoner's Dilemma is a prototype model to show the emergence of cooperation in very competitive environments. It considers players, at site of lattices, that can either cooperate or defect when playing the Prisoner's Dilemma with other z players. This model presents a rich phase diagram. Here we consider players in cells of one-dimensional cellular automata. Each player interacts with other z players. This geometry allows us to vary, in a simple manner, the number of neighbors ranging from one up to the lattice size, including self-interaction. This approach has multiple advantages. It is simple to implement numerically and we are able to retrieve all the previous results found in the previously considered lattices, with a faster convergence to stationary values. More remarkable, it permits us to keep track of the spatio-temporal evolution of each player of the automaton. Giving rise to interesting patterns. These patterns allow the interpretation of cooperation/defection clusters as particles, which can be absorbed and collided among themselves. The presented approach represents a new paradigm to study the emergence and maintenance of cooperation in the spatial Prisoner's Dilemma.

physics.comp-ph↗
arXiv2007

Exact analytical calculation for the percolation crossover in deterministic partially self-avoiding walks in one-dimensional random media

Consider $N$ points randomly distributed along a line segment of unitary length. A walker explores this disordered medium moving according to a partially self-avoiding deterministic walk. The walker, with memory $μ$, leaves from the leftmost point and moves, at each discrete time step, to the nearest point which has not been visited in the preceding $μ$ steps. Using open boundary conditions, we have calculated analytically the probability $P_N(μ) = (1 - 2^{-μ})^{N - μ- 1}$ that all $N$ points are visited, with $N \gg μ\gg 1$. This approximated expression for $P_N(μ)$ is reasonable even for small $N$ and $μ$ values, as validated by Monte Carlo simulations. We show the existence of a critical memory $μ_1 = \ln N/\ln 2$. For $μ< μ_1 - e/(2\ln2)$, the walker gets trapped in cycles and does not fully explore the system. For $μ> μ_1 + e/(2\ln2)$ the walker explores the whole system. Since the intermediate region increases as $\ln N$ and its width is constant, a sharp transition is obtained for one-dimensional large systems. This means that the walker needs not to have full memory of its trajectory to explore the whole system. Instead, it suffices to have memory of order $\log_{2} N$.

cond-mat.dis-nn↗
arXiv2006

Optimum exploration memory and anomalous diffusion in deterministic partially self-avoiding walks in one-dimensional random media

Consider $N$ points randomly distributed along a line segment of unitary length. A walker explores this disordered medium moving according to a partially self-avoiding deterministic walk. The walker, with memory $μ$, leaves from the leftmost point and moves, at each discrete time step, to the nearest point, which has not been visited in the preceding $μ$ steps. We have obtained analytically the probability $P_N(μ) = (1 - 2^{-μ})^{N - μ- 1}$ that all $N$ points are visited in this open system, with $N \gg μ\gg 1$. The expression for $P_N(μ)$ evaluated in the mentioned limit is valid even for small $N$ and leads to a transition region centered at $μ_1 = \ln N/\ln 2$ and with width $ε= e/\ln2$. For $μ< μ_1 - ε/2$, the walker gets trapped in cycles and does not fully explore the system. For $μ> μ_1 + ε/2$ the walker explores the whole system. In both cases the walker presents diffusive behavior. Nevertheless, in the intermediate regime $μ\sim μ_1 \pm ε/2$, the walker presents anoumalous diffusion behavior. Since the intermediate region increases as $\ln N$ and its width is constant, a sharp transition is obtained for one-dimensional large systems. The walker does not need to have full memory of its trajectory to explore the whole system, it suffices to have memory of order $μ_1$.

cond-mat.dis-nn↗
arXiv2006

Analytical calculation of neighborhood order probabilities for high dimensional Poissonic processes and mean field models

Consider that the coordinates of $N$ points are randomly generated along the edges of a $d$-dimensional hypercube (random point problem). The probability that an arbitrary point is the $m$th nearest neighbor to its own $n$th nearest neighbor (Cox probabilities) plays an important role in spatial statistics. Also, it has been useful in the description of physical processes in disordered media. Here we propose a simpler derivation of Cox probabilities, where we stress the role played by the system dimensionality $d$. In the limit $d \to \infty$, the distances between pair of points become indenpendent (random link model) and closed analytical forms for the neighborhood probabilities are obtained both for the thermodynamic limit and finite-size system. Breaking the distance symmetry constraint drives us to the random map model, for which the Cox probabilities are obtained for two cases: whether a point is its own nearest neighbor or not.

cond-mat.dis-nn↗
arXiv2006

Topological features of proteins from amino acid residue networks

Topological properties of native folds are obtained from statistical analysis of 160 low homology proteins covering the four structural classes. This is done analysing one, two and three-vertex joint distribution of quantities related to the corresponding network of amino acid residues. Emphasis on the amino acid residue hydrophobicity leads to the definition of their center of mass as vertices in this contact network model with interactions represented by edges. The network analysis helps us to interpret experimental results such as hydrophobic scales and fraction of buried accessible surface area in terms of the network connectivity. To explore the vertex type dependent correlations, we build a network of hydrophobic and polar vertices. This procedure presents the wiring diagram of the topological structure of globular proteins leading to the following attachment probabilities between hydrophobic-hydrophobic 0.424(5), hydrophobic-polar 0.419(2) and polar-polar 0.157(3) residues.

physics.bio-ph↗
arXiv2005

An index to quantify an individual's scientific research valid across disciplines

The number h of papers with at least h citations has been proposed to evaluate individual's scientific research production. This index is robust in several ways but yet strongly dependent on the research field. We propose a complementary index hI = h^2/N_t, with N_t being the total number of authors in the considered h papers. A researcher with index hI has hI papers with at least hI citation if he/she had published alone. We have obtained the rank plots of h and hI for four Brazilian scientific communities. Contrasting to the h-index curve, the hI index present a perfect data collapse into a unique allowing comparison among different research areas.

physics.soc-ph↗
arXiv2005

Universal Behavior of a Research Productivity Index

Indexes that account for good representations of an individual's productivity are theme of major importance for the evaluation and comparison among researchers. Recently, a new index was proposed combining productivity with impact such that a researcher with index h has h papers with at least h citations. A drawback of this is the sensitivity to the research field. Here we propose a new index (hI) that accounts for the coauthorship effect. The statistics of h and hI are presented for Brazilian research. We have found a universal curve for different disciplines, allowing a comparison among scientists of different research areas.

physics.soc-ph↗
arXiv2005

An efficient algorithm to generate large random uncorrelated Euclidean distances: the random link model

A disordered medium is often constructed by $N$ points independently and identically distributed in a $d$-dimensional hyperspace. Characteristics related to the statistics of this system is known as the random point problem. As $d \to \infty$, the distances between two points become independent random variables, leading to its mean field description: the random link model. While the numerical treatment of large random point problems pose no major difficulty, the same is not true for large random link systems due to Euclidean restrictions. Exploring the deterministic nature of the congruential pseudo-random number generators, we present techniques which allow the consideration of models with memory consumption of order O(N), instead of $O(N^2)$ in a naive implementation but with the same time dependence $O(N^2)$.

cond-mat.dis-nn↗
arXiv2005

Analytical Results for the Statistical Distribution Related to Memoryless Deterministic Tourist Walk: Dimensionality Effect and Mean Field Models

Consider a medium characterized by N points whose coordinates are randomly generated by a uniform distribution along the edges of a unitary d-dimensional hypercube. A walker leaves from each point of this disordered medium and moves according to the deterministic rule to go to the nearest point which has not been visited in the preceding μsteps (deterministic tourist walk). Each trajectory generated by this dynamics has an initial non-periodic part of t steps (transient) and a final periodic part of p steps (attractor). The neighborhood rank probabilities are parameterized by the normalized incomplete beta function I_d = I_{1/4}[1/2,(d+1)/2]. The joint distribution S_{μ,d}^{(N)}(t,p) is relevant, and the marginal distributions previously studied are particular cases. We show that, for the memory-less deterministic tourist walk in the euclidean space, this distribution is: S_{1,d}^{(\infty)}(t,p) = [Γ(1+I_d^{-1}) (t+I_d^{-1})/Γ(t+p+I_d^{-1})] δ_{p,2}, where t=0,1,2,...,\infty, Γ(z) is the gamma function and δ_{i,j} is the Kronecker's delta. The mean field models are random link model, which corresponds to d \to \infty, and random map model which, even for μ= 0, presents non-trivial cycle distribution [S_{0,rm}^{(N)}(p) \propto p^{-1}]: S_{0,rm}^{(N)}(t,p) = Γ(N)/\{Γ[N+1-(t+p)]N^{t+p}\}. The fundamental quantities are the number of explored points n_e=t+p and I_d. Although the obtained distributions are simple, they do not follow straightforwardly and they have been validated by numerical experiments.

cond-mat.dis-nn↗
arXiv2005

The geometrical pattern of the evolution of cooperation in the Spatial Prisoner's Dilemma: an intra-group model

The Prisoner's Dilemma (PD) deals with the cooperation/defection conflict between two agents. The agents are represented by a cell of $L \times L$ square lattice. The agents are initially randomly distributed according to a certain proportion $ρ_c(0)$ of cooperators. Each agent does not have memory of previous behaviors and plays the PD with eight nearest neighbors and then copies the behavior of who had the greatest payoff for next generation. This system shows that, when the conflict is established, cooperation among agents may emerge even for reasonably high defection temptation values. Contrary to previous studies, which treat mean inter-group interaction, here a model where the agents are not allowed to self-interact, representing intra-group interaction, is proposed. This leads to short time and asymptotic behaviors similar to the one found when self-interaction is considered. Nevertheless, the intermediate behavior is different, with no possible data collapse since oscillations are present. Also, the fluctuations are much smaller in the intra-group model. The geometrical configurations of cooperative clusters are distinct and explain the $ρ_c(t)$ differences between inter and intra-group models. The boundary conditions do not affect the results.

cond-mat.stat-mech↗