From random point processes to hierarchical cavity master equations for stochastic dynamics of disordered systems in random graphs: Ising models and epidemics.

We start from the theory of random point processes to derive n-point coupled master equations describing the continuous dynamics of discrete variables in random graphs. These equations constitute a hierarchical set of approximations that generalize and improve the cavity master equation (CME), a recently obtained closure for the usual master equation representing the dynamics. Our derivation clarifies some of the hypotheses and approximations that originally led to the CME, considered now as the first order of a more general technique. We tested the scheme in the dynamics of three models defined over diluted graphs: the Ising ferromagnet, the Viana-Bray spin-glass, and the susceptible-infectious-susceptible model for epidemics. In the first two, the equations perform similarly to the best-known approaches in literature. In the latter, they outperform the well-known pair quenched mean-field approximation.

Photodynamic therapy: Toward a systemic computational model.

We have designed a systemic model to understand the effect of Photodynamic Therapy (PDT) on long time scales. The model takes into account cell necrosis due to oxygen reactive species, cell apoptosis through the caspase pathway and the competition between healthy and tumor cells. We attempted to describe the system using state of the art computational techniques (necrosis and apoptosis) and simple models that allow a deeper understanding of the long time scale processes involved (healing and tumor growth). We analyzed the influence of the surface and tumor depth on the effectiveness of different treatment plans and we proposed, for the set of parameters used in this work, an optimum timing between sessions of PDT.

In silico modelling of apoptosis induced by photodynamic therapy.

Photodynamic therapy (PDT) is an emergent technique used for the treatment of several diseases. After PDT, cells die by necrosis, apoptosis or autophagy. Necrosis is produced immediately during photodynamic therapy by high concentration of reactive oxygen species, apoptosis and autophagy are triggered by mild or low doses of light and photosensitizer. In this work we model the cell response to low doses of PDT assuming a bi-dimensional matrix of interacting cells. For each cell of the matrix we simulate in detail, with the help of the Gillespie's algorithm, the two main chemical pathways leading to apoptosis. We unveil the role of both pathways in the cell death rate of the tumor, as well as the relevance of several molecules in the process. Our model suggests values of concentrations for several species of molecules to enhance the effectiveness of PDT.

Cavity master equation for the continuous time dynamics of discrete-spin models.

We present an alternate method to close the master equation representing the continuous time dynamics of interacting Ising spins. The method makes use of the theory of random point processes to derive a master equation for local conditional probabilities. We analytically test our solution studying two known cases, the dynamics of the mean-field ferromagnet and the dynamics of the one-dimensional Ising system. We present numerical results comparing our predictions with Monte Carlo simulations in three different models on random graphs with finite connectivity: the Ising ferromagnet, the random field Ising model, and the Viana-Bray spin-glass model.

Tumor reactive ringlet oxygen approach for Monte Carlo modeling of photodynamic therapy dosimetry.

Photodynamic therapy (PDT) is an emergent technique used for the treatment of several diseases. It requires the interaction of three components: a photosensitizer, a light source and tissue oxygen. Knowledge of the biophysical aspects of PDT is important for improving dosimetry protocols and treatment planning. In this paper we propose a model to simulate the spatial and temporal distribution of ground state oxygen ((3)O2), cumulative singlet excited state oxygen ((1)O2)rx and photosensitizer, in this case protoporphyrin IX (PpIX) in an ALA mediated PDT treatment. The results are analyzed in order to improve the treatment dosimetry. We compute the light fluence in the tissue using Monte Carlo simulations running in a GPU system. The concentration of (3)O2, ((1)O2)rx and the photosensitizer are calculated using this light fluence and a set of differential equations describing the photochemical reactions involved in PDT. In the model the initial photosensitizer concentration depends on tissue depth and type, moreover we consider blood vessel damage and its effect in the ground state oxygen concentration in the tissue. We introduce the tumor reactive single oxygen (TRSO) as a new dosimetry metric. It represents the amount of singlet oxygen per tumor volume that reacts, during the treatment, with the molecules in the tumor. This quantity integrates the effect of the light irradiance, the optical properties of the tumor and the normal tissue, the oxygen consumption and supply, and the photosensitizer biodistribution on the skin.

Simulated annealing algorithm for the multiple sequence alignment problem: the approach of polymers in a random medium.

We propose a probabilistic algorithm to solve the multiple sequence alignment problem. The algorithm is a simulated annealing that exploits the representation of the multiple alignment between D sequences as a directed polymer in D dimensions. Within this representation we can easily track the evolution of the alignment through local moves of low computational cost. In contrast with other probabilistic algorithms proposed to solve this problem, our approach allows the creation and deletion of gaps without extra computational cost. The algorithm was tested by aligning proteins from the kinase family. When D=3 the results are consistent with those obtained using a complete algorithm. For D>3 where the complete algorithm fails, we show that our algorithm still converges to reasonable alignments. We also study the space of solutions obtained and show that depending on the number of sequences aligned the solutions are organized in different ways, suggesting a possible source of errors for progressive algorithms. Finally, we test our algorithm in artificially generated sequences and prove that it may perform better than progressive algorithms. Moreover, in those cases in which a progressive algorithm works better, its solution may be taken as an initial condition of our algorithm and, again, we obtain alignments with lower scores and more relevant from the biological point of view.

Polynomial iterative algorithms for coloring and analyzing random graphs.

We study the graph coloring problem over random graphs of finite average connectivity c. Given a number q of available colors, we find that graphs with low connectivity admit almost always a proper coloring whereas graphs with high connectivity are uncolorable. Depending on q, we find with a one-step replica-symmetry breaking approximation the precise value of the critical average connectivity c(q). Moreover, we show that below c(q) there exists a clustering phase c in [c(d),c(q)] in which ground states spontaneously divide into an exponential number of clusters. Furthermore, we extended our considerations to the case of single instances showing consistent results. This leads us to propose a different algorithm that is able to color in polynomial time random graphs in the hard but colorable region, i.e., when c in [c(d),c(q)].

Quasiequilibrium during aging of the two-dimensional Edwards-Anderson model.

We test the quasiequilibrium picture of the aging dynamics--strictly valid in the asymptotic dynamical regime of aging systems--in the preasymptotic aging regime of the two-dimensional Edwards-Anderson spin glass model. We compare the fluctuation-dissipation characteristic for spin autocorrelation function and response with a corresponding one obtained for a suitably defined correlation function and its conjugated response. In agreement with the quasiequilibrium picture we find that after a short transient the two corresponding fluctuation-dissipation ratios (FDR's) coincide at equal times. Moreover we show that, as it happens for the usual FDR, the dynamic FDR at finite time coincides with the static one at finite size.

Coloring random graphs.

We study the graph coloring problem over random graphs of finite average connectivity c. Given a number q of available colors, we find that graphs with low connectivity admit almost always a proper coloring, whereas graphs with high connectivity are uncolorable. Depending on q, we find the precise value of the critical average connectivity c(q). Moreover, we show that below c(q) there exists a clustering phase c in [c(d),c(q)] in which ground states spontaneously divide into an exponential number of clusters and where the proliferation of metastable states is responsible for the onset of complexity in local search algorithms.

Kob-Andersen model: a nonstandard mechanism for the glassy transition.

We present results reflecting the analogies between the Kob-Andersen model and other glassy systems. Studying the stability of the blocked configurations above and below the transition we also give arguments that support their relevance for the glassy behavior of the model. However, we find, surprisingly, that the organization of the phase space of the system is different from the well known organization of other mean field spin glasses and structural glasses.

Learning to coordinate in a complex and nonstationary world.

We study analytically and by computer simulations a complex system of adaptive agents with finite memory. Borrowing the framework of the minority game and using the replica formalism we show the existence of an equilibrium phase transition as a function of the ratio between the memory lambda and the learning rates Gamma of the agents. We show that, starting from a random configuration, a dynamic phase transition also exists, which prevents agents from reaching optimal coordination. Furthermore, in a nonstationary environment, we show by numerical simulations that the phase transition becomes discontinuous.

[Survival, growth and development of very low birthweight infants until five years of age]. / Sobrevida, crecimiento y desarrollo de ninos de muy bajo peso al nacer hasta los 5 anos.

PIP: 761 infant weighing 1500 gms or less at birth were admitted to the Neonatal Intensive Care Unit at the Guatemalan Institute of Social Security between 1983-88. Cases with severe congenital or chromosomal anomalies were excluded. 386 infants survived this initial hospitalization. 150 completed 2 years and 65 completed 5 years of follow-up at a special multidisciplinary clinic. Follow-up visits were scheduled 1-3 months after discharge and subsequently at 4, 7, 10, 12, 15, 18, 21, and 24 months and every 6 months thereafter through age 5. The consultation focused on health protection, early diagnosis of growth or developmental delays, and prompt rehabilitation. 74 of 81 infants weighing 500-800 g died, as did 97 of 130 weighing 801-1000 g, 96 of 170 weighing 1001-1200 g, and 108 of 380 weighing 1201-1500 g. The proportion of very low birth weight infants increased from 7.6 to 11.7% of all births between 1983-88 and averaged 8.6% for the 6 years. Surviving infants were hospitalized an average of 33 days with a minimum of 15 and a maximum of 80. 90% of the infants has jaundice, 42% has respiratory disorders or hyaline membrane disease, and 26% has perinatal asphyxia. 76% of very low birth weight infants who were born with asphyxia died, compared to 32% not born asphyxiated. 4 infants has retinopathy related to prematurity. The children were on average in the 5th percentile of the National Center for Health Statistics weight curve and height curve at 5 years. The average head circumference was on the 10th percentile from 1 year of age. The mean differences from the normal standard at 5 years were 3180g for weight, 7 cm for height, and 1 cm for head circumference. 35% of infants has problems in large motor skills in the 1st year, but by the 2nd year only those with diagnoses of neurological problems still had problems with large motor skills. Over 50% showed delay in language development at 3 years, but by 5 years only 12% still had problems. Over 85% has delays in fine motor skills development from the 1st through the 5th year. Socioeconomics factors were the most important cause of failure to thrive and develop. Only 33% of the mothers had had prenatal care before the 7th month of pregnancy.^ieng