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Consider a one-dimensional environment with N randomly distributed sites. An agent explores this random medium moving deterministically with a spatial memory µ. A crossover from local to global exploration occurs in one dimension at a well-defined memory value µ_{1}=log_{2}N. In its stochastic version, the dynamics is ruled by the memory and by temperature T, which affects the hopping displacement. This dynamics also shows a crossover in one dimension, obtained computationally, between exploration schemes, characterized yet by the trajectory size (N_{p}) (aging effect). In this paper we provide an analytical approach considering the modified stochastic version where the parameter T plays the role of a maximum hopping distance. This modification allows us to obtain a general analytical expression for the crossover, as a function of the parameters µ, T, and N_{p}. Differently from what has been proposed by previous studies, we find that the crossover occurs in any dimension d. These results have been validated by numerical experiments and may be of great value for fixing optimal parameters in search algorithms.

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The extension of Boltzmann-Gibbs thermostatistics, proposed by Tsallis, introduces an additional parameter q to the inverse temperature ß. Here, we show that a previously introduced generalized Metropolis dynamics to evolve spin models is not local and does not obey the detailed energy balance. In this dynamics, locality is only retrieved for q=1, which corresponds to the standard Metropolis algorithm. Nonlocality implies very time-consuming computer calculations, since the energy of the whole system must be reevaluated when a single spin is flipped. To circumvent this costly calculation, we propose a generalized master equation, which gives rise to a local generalized Metropolis dynamics that obeys the detailed energy balance. To compare the different critical values obtained with other generalized dynamics, we perform Monte Carlo simulations in equilibrium for the Ising model. By using short-time nonequilibrium numerical simulations, we also calculate for this model the critical temperature and the static and dynamical critical exponents as functions of q. Even for q≠1, we show that suitable time-evolving power laws can be found for each initial condition. Our numerical experiments corroborate the literature results when we use nonlocal dynamics, showing that short-time parameter determination works also in this case. However, the dynamics governed by the new master equation leads to different results for critical temperatures and also the critical exponents affecting universality classes. We further propose a simple algorithm to optimize modeling the time evolution with a power law, considering in a log-log plot two successive refinements.

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We consider a nontrivial one-species population dynamics model with finite and infinite carrying capacities. Time-dependent intrinsic and extrinsic growth rates are considered in these models. Through the model per capita growth rate we obtain a heuristic general procedure to generate scaling functions to collapse data into a simple linear behavior even if an extrinsic growth rate is included. With this data collapse, all the models studied become independent from the parameters and initial condition. Analytical solutions are found when time-dependent coefficients are considered. These solutions allow us to perceive nontrivial transitions between species extinction and survival and to calculate the transition's critical exponents. Considering an extrinsic growth rate as a cancer treatment, we show that the relevant quantity depends not only on the intensity of the treatment, but also on when the cancerous cell growth is maximum.

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Consider N sites randomly and uniformly distributed in a d-dimensional hypercube. A walker explores this disordered medium going to the nearest site, which has not been visited in the last µ (memory) steps. The walker trajectory is composed of a transient part and a periodic part (cycle). For one-dimensional systems, travelers can or cannot explore all available space, giving rise to a crossover between localized and extended regimes at the critical memory µ1=log2 N. The deterministic rule can be softened to consider more realistic situations with the inclusion of a stochastic parameter T (temperature). In this case, the walker movement is driven by a probability density function parameterized by T and a cost function. The cost function increases as the distance between two sites and favors hops to closer sites. As the temperature increases, the walker can escape from cycles that are reminiscent of the deterministic nature and extend the exploration. Here, we report an analytical model and numerical studies of the influence of the temperature and the critical memory in the exploration of one-dimensional disordered systems.

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We analytically calculate the time-averaged electromagnetic energy stored inside a nondispersive magnetic isotropic cylinder that is obliquely irradiated by an electromagnetic plane wave. An expression for the optical-absorption efficiency in terms of the magnetic internal coefficients is also obtained. In the low absorption limit, we derive a relation between the normalized internal energy and the optical-absorption efficiency that is not affected by the magnetism and the incidence angle. This relation, indeed, seems to be independent of the shape of the scatterer. This universal aspect of the internal energy is connected to the transport velocity and consequently to the diffusion coefficient in the multiple scattering regime. Magnetism favors high internal energy for low size parameter cylinders, which leads to a low diffusion coefficient for electromagnetic propagation in 2D random media.

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Consider that an incident plane wave is scattered by a homogeneous and isotropic magnetic sphere of finite radius. We determine, by means of the rigorous Mie theory, an exact expression for the time-averaged electromagnetic energy within this particle. For magnetic scatterers, we find that the value of the average internal energy in the resonance picks is much larger than the one associated with a scatterer with the same nonmagnetic medium properties. This result is valid even, and especially, for low size parameter values. Expressions for the contributions of the radial and angular field components to the internal energy are determined. For the analytical study of the weak absorption regime, we derive an exact expression for the absorption cross section in terms of the magnetic Mie internal coefficients. We stress that, although the electromagnetic scattering by particles is a well-documented topic, almost no attention has been devoted to magnetic scatterers. Our aim is to provide some new analytical results, which can be used for magnetic particles, and emphasize the unusual properties of the magnetic scatters, which could be important in some applications.

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The Prisoner's Dilemma (PD) game is applied in several research fields due to the emergence of cooperation among selfish players. In this work the PD is studied in a one-dimensional lattice, where each cell represents a player, which in turn can interact with the neighbors playing the PD (cooperate or defect). The update of states adopts the Pavlovian Evolutionary Strategy (PES) or Darwinian Evolutionary Strategy (DES). Adopting PES, if a player receives a positive payoff greater than his/her aspiration level, he/she keeps the current state, and switches otherwise. Adopting DES, player compares his/her payoff with payoff of opponents. If it is not the highest, he/she copies the state of fittest player, switching the state if it is different of his/her current state. The critical temptation values obtained analytically are reported, and the cluster patterns that emerge from the interactions among the players are shown. Also we defined analytical functions that calculate the maximum/minimum size of defective/cooperative clusters. Also, the parameter space is explored with exhaustive computational simulations, which confirm the analytical results and reinforce that Pavlovian strategy foments cooperation among players. In steady state, system can reach the cooperative or quasi-regular phases, when adopting the PES, and cooperative, defective or chaotic phases, adopting the DES. The new quasi-regular phase occurs when several players switch their states in each round, but the proportion of cooperators does not show significant variation. Additionally, the present work shows that the lowest temptation level (T=1) may be considered a trivial case only for the particular case where the players interact with only one neighbor, otherwise system presents the same features that for higher temptation values.

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Consider a random medium consisting of N points randomly distributed so that there is no correlation among the distances separating them. 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, a walker moves to the nearest point, which has not been visited in the last mu steps (memory), producing a deterministic partially self-avoiding walk (the tourist walk). We have analytically obtained the distribution of the number n of points explored by the walker with memory mu=2 , as well as the transient and period joint distribution. This result enables us to explain the abrupt change in the exploratory behavior between the cases mu=1 (memoryless walker, driven by extreme value statistics) and mu=2 (walker with memory, driven by combinatorial statistics). In the mu=1 case, the mean newly visited points in the thermodynamic limit (N1) is just n=e=2.72... while in the mu=2 case, the mean number n of visited points grows proportionally to N;{12} . Also, this result allows us to establish an equivalence between the random link model with mu=2 and random map (uncorrelated back and forth distances) with mu=0 and the abrupt change between the probabilities for null transient time and subsequent ones.

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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 mu , leaves from the leftmost point and moves, at each discrete time step, to the nearest point that has not been visited in the preceding mu steps. Using open boundary conditions, we have calculated analytically the probability P{N}(mu)=(1-2{-mu}){N-mu-1} that all N points are visited, with N>>mu>>1 . This approximated expression for P{N}(mu) is reasonable even for small N and mu values, as validated by Monte Carlo simulations. We show the existence of a critical memory mu{1}=lnNln2 . For mumu{1}+e(2ln2) , the walker explores the whole system. Since the intermediate region increases as lnN and its width is constant, a sharp transition is obtained for one-dimensional large systems. This means that the walker need not have full memory of its trajectory to explore the whole system. Instead, it suffices to have memory of order log{2}N .

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The bioaccumulation of atrazine in bivalves is expected due to its wide use in agriculture and its moderate water solubility (33 mg/l). To assess the capacity of bioaccumulation, we performed a laboratory study in which two bivalves species (Anodontites trapesialis and Corbicula fluminea) were exposed to atrazine (concentrations of 0.06 to 0.34 microg/ml) during 48 h. The results showed that both bivalve species were able to bioaccumulate atrazine in their tissues. In another experiment, groups of bivalves from the specie A. trapesialis were exposed to atrazine at the concentration of 1 mug/ml and different organs of these animals were analyzed. The visceral mass, foot and mantle plus siphon showed the highest values of atrazine bioaccumulation.

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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 mu steps (deterministic tourist walk). Each trajectory generated by this dynamics has an initial nonperiodic part of t steps (transient) and a final periodic part of p steps (attractor). The neighborhood rank probabilities are parametrized by the normalized incomplete beta function Id= I1/4 [1/2, (d+1) /2] . The joint distribution S(N) (mu,d) (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 Sinfinity(1,d) (t,p) = [Gamma (1+ I(-1)(d)) (t+ I(-1)(d) ) /Gamma(t+p+ I(-1)(d)) ] delta(p,2), where t=0, 1,2, ... infinity, Gamma(z) is the gamma function and delta(i,j) is the Kronecker delta. The mean-field models are the random link models, which correspond to d-->infinity, and the random map model which, even for mu=0 , presents nontrivial cycle distribution [ S(N)(0,rm) (p) proportional to p(-1) ] : S(N)(0,rm) (t,p) =Gamma(N)/ {Gamma[N+1- (t+p) ] N( t+p)}. The fundamental quantities are the number of explored points n(e)=t+p and Id. Although the obtained distributions are simple, they do not follow straightforwardly and they have been validated by numerical experiments.

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Thioridazine (THD) is a phenothiazine neuroleptic drug used for the treatment of psychiatric disorders. After oral administration THD is extensively biotransformed to thioridazine 2-sulfone (THD 2-SO(2)), thioridazine 5-sulfoxide (THD 5-SO) and thioridazine 2-sulfoxide (THD 2-SO). THD 2-SO and THD 5-SO have two chiral centres and therefore exist as two diastereoisomeric pairs. The degradation and epimerization of THD 2-SO in human plasma, buffer and methanolic solutions were studied using an enantioselective HPLC method. The samples were prepared by liquid-liquid extraction with diethyl ether and the chiral resolution of the enantiomers was carried out on a Chiralpak AD column using a mobile phase consisting of hexane:ethanol:2-propanol (90:7:3, v/v/v) containing 0.2% diethylamine. The method was validated and used to study the degradation and epimerization under different conditions of incubation. Our results showed that both enantiomers were stable at varying temperatures, pH and ionic strengths; however, solubility problems were observed, mainly at pH 8.5. The influence of light on stability was studied using methanolic solutions and degradation and epimerization of the THD 2-SO enantiomers were observed under UV light of 366 and 254nm, respectively.

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We present two methods for the enantioselective analysis of thioridazine (THD) and thioridazine 2-sulfone (THD 2-SO(2)) in human plasma based on liquid-liquid extraction with diethyl ether and chiral resolution of the enantiomers on Chiralpak AD and Chiralcel OD-H columns, respectively. After validation, the methods were used to study the degradation and racemization of both drug and metabolite. Our results showed that both enantiomers of THD and THD 2-SO(2) were stable at varying temperatures, pH, and ionic strengths; however, solubility problems for THD and THD 2-SO(2) enantiomers were observed, mainly at pH 8.5. The influence of light on the stability of the THD and THD 2-SO(2) enantiomers was also studied. Degradation of the THD enantiomers was observed under UV light (254 and 366 nm) while THD 2-SO(2) enantiomers were stable at these wavelengths and also when exposed to visible light.

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In this study we evaluated a liquid-liquid extraction procedure and a solid-phase extraction procedure for sample preparation for the enantioselective analysis of atenolol in plasma and urine by high-performance liquid chromatography. A Chiralcel OD-H column was used for the resolution of atenolol enantiomers with hexane-ethanol (85:15, v/v) plus 0.1% diethylamine as the mobile phase. In the liquid-liquid extraction procedure, atenolol was extracted from alkalinized body fluids with 5 ml chloroform-2-propanol (4:1, v/v). In the solid-phase extraction procedure, atenolol was isolated from plasma using a C8 column and methanol. Both extraction procedures were efficient in recovering atenolol and removing endogenous interferents. The RSDs and deviation from nominal values were lower than 10% for both within-day and between-day assays. The results show that there were no statistically significant differences in between-day variation. The t-test showed that there were no significant differences between the real concentrations and the determined concentrations. The limit of quantitation was 10 ng/ml and the linear range was 10-5,000 ng/ml for both methods. These methods can be used in pharmacokinetic studies.

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