Universality of explosive percolation under product and sum rule

We study explosive percolation processes on random graphs for the so-called product rule (PR) and sum rule (SR), in which M candidate edges are randomly selected from all possible ones at each time step, and the edge with the smallest product or sum of the sizes of the two components that would be joined by the edge is added to the graph, while all other M-1 candidate edges are being discarded. These two rules are prototypical "explosive" percolation rules, which exhibit an extremely abrupt yet continuous phase transition in the thermodynamic limit. Recently, it has been demonstrated that PR and SR belong to the same universality class for two competing edges, i.e., M=2. Here we investigate whether the claimed PR-SR universality is valid for higher-order models with M larger than 2. Based on traditional finite-size scaling theory and largest-gap scaling, we obtain the percolation threshold and the critical exponents of the order parameter, susceptibility, and the derivative of entropy for PR and SR for M from 2 to 9. Our results strongly suggest PR-SR universality, for any fixed M.

Structure and function in artificial, zebrafish and human neural networks

Network science provides a set of tools for the characterization of the structure and functional behavior of complex systems. Yet a major problem is to quantify how the structural domain is related to the dynamical one. In other words, how the diversity of dynamical states of a system can be predicted from the static network structure? Or the reverse problem: starting from a set of signals derived from experimental recordings, how can one discover the network connections or the causal relations behind the observed dynamics? Despite the advances achieved over the last two decades, many challenges remain concerning the study of the structure-dynamics interplay of complex systems. In neuroscience, progress is typically constrained by the low spatio-temporal resolution of experiments and by the lack of a universal inferring framework for empirical systems. To address these issues, applications of network science and artificial intelligence to neural data have been rapidly growing. In this article, we review important recent applications of methods from those fields to the study of the interplay between structure and functional dynamics of human and zebrafish brain. We cover the selection of topological features for the characterization of brain networks, inference of functional connections, dynamical modeling, and close with applications to both the human and zebrafish brain. This review is intended to neuroscientists who want to become acquainted with techniques from network science, as well as to researchers from the latter field who are interested in exploring novel application scenarios in neuroscience.

Decisive conditions for strategic vaccination against SARS-CoV-2

While vaccines against severe acute respiratory syndrome coronavirus (SARS-CoV-2) are being administered, in many countries it may still take months until their supply can meet demand. The majority of available vaccines elicit strong immune responses when administered as prime-boost regimens. Since the immunological response to the first ("prime") dose may provide already a substantial reduction in infectiousness and protection against severe disease, it may be more effective-under certain immunological and epidemiological conditions-to vaccinate as many people as possible with only one dose instead of administering a person a second ("booster") dose. Such a vaccination campaign may help to more effectively slow down the spread of SARS-CoV-2 and reduce hospitalizations and fatalities. The conditions that make prime-first vaccination favorable over prime-boost campaigns, however, are not well understood. By combining epidemiological modeling, random-sampling techniques, and decision tree learning, we find that prime-first vaccination is robustly favored over prime-boost vaccination campaigns even for low single-dose efficacies. For epidemiological parameters that describe the spread of coronavirus disease 2019 (COVID-19), recent data on new variants included, we show that the difference between prime-boost and single-shot waning rates is the only discriminative threshold, falling in the narrow range of 0.01-0.02  day^-1 below which prime-first vaccination should be considered.

Decisive Conditions for Strategic Vaccination against SARS-CoV-2

While vaccines against SARS-CoV-2 are being administered, in most countries it may still take months until their supply can meet demand. The majority of available vaccines elicits strong immune responses when administered as prime-boost regimens. Since the immunological response to the first ("prime") injection may provide already a substantial reduction in infectiousness and protection against severe disease, it may be more effective-under certain immunological and epidemiological conditions-to vaccinate as many people as possible with only one shot, instead of administering a person a second ("boost") shot. Such a vaccination campaign may help to more effectively slow down the spread of SARS-CoV-2, reduce hospitalizations, and reduce fatalities, which is our objective. Yet, the conditions which make single-dose vaccination favorable over prime-boost administrations are not well understood. By combining epidemiological modeling, random sampling techniques, and decision tree learning, we find that single-dose vaccination is robustly favored over prime-boost vaccination campaigns, even for low single-dose efficacies. For realistic scenarios and assumptions for SARS-CoV-2, recent data on new variants included, we show that the difference between prime-boost and single-shot waning rates is the only discriminative threshold, falling in the narrow range of 0.01-0.02 day-1 below which single-dose vaccination should be considered.

Anomalous percolation features in molecular evolution

Self-replication underlies every species of living beings and simple physical intuition dictates that some sort of autocatalysis invariably constitutes a necessary ingredient for the emergence of molecular life. This led Worst et al. [E. G. Worst, P. Zimmer, E. Wollrab, K. Kruse, and A. Ott, New J. Phys. 18, 103003 (2016)NJOPFM1367-263010.1088/1367-2630/18/10/103003] to study a model of molecular evolution of self-replicating molecules where spontaneous ligation and simple autocatalysis are in competition for their building blocks. We revisit this model, where irreversible aggregation leads to a transition from a regime of small molecules to macromolecules, and find an array of anomalous percolation features, some of them predicted for very specific percolation processes [R. M. D'Souza and J. Nagler, Nat. Phys. 11, 531 (2015)1745-247310.1038/nphys3378].

Hysteretic Percolation from Locally Optimal Individual Decisions

The emergence of large-scale connectivity underlies the proper functioning of many networked systems, ranging from social networks and technological infrastructure to global trade networks. Percolation theory characterizes network formation following stochastic local rules, while optimization models of network formation assume a single controlling authority or one global objective function. In socioeconomic networks, however, network formation is often driven by individual, locally optimal decisions. How such decisions impact connectivity is only poorly understood to date. Here, we study how large-scale connectivity emerges from decisions made by rational agents that individually minimize costs for satisfying their demand. We establish that the solution of the resulting nonlinear optimization model is exactly given by the final state of a local percolation process. This allows us to systematically analyze how locally optimal decisions on the microlevel define the structure of networks on the macroscopic scale.

Unfair and Anomalous Evolutionary Dynamics from Fluctuating Payoffs

Evolution occurs in populations of reproducing individuals. Reproduction depends on the payoff a strategy receives. The payoff depends on the environment that may change over time, on intrinsic uncertainties, and on other sources of randomness. These temporal variations in the payoffs can affect which traits evolve. Understanding evolutionary game dynamics that are affected by varying payoffs remains difficult. Here we study the impact of arbitrary amplitudes and covariances of temporally varying payoffs on the dynamics. The evolutionary dynamics may be "unfair," meaning that, on average, two coexisting strategies may persistently receive different payoffs. This mechanism can induce an anomalous coexistence of cooperators and defectors in the prisoner's dilemma, and an unexpected selection reversal in the hawk-dove game.

Controlling percolation with limited resources

Connectivity, or the lack thereof, is crucial for the function of many man-made systems, from financial and economic networks over epidemic spreading in social networks to technical infrastructure. Often, connections are deliberately established or removed to induce, maintain, or destroy global connectivity. Thus, there has been a great interest in understanding how to control percolation, the transition to large-scale connectivity. Previous work, however, studied control strategies assuming unlimited resources. Here, we depart from this unrealistic assumption and consider the effect of limited resources on the effectiveness of control. We show that, even for scarce resources, percolation can be controlled with an efficient intervention strategy. We derive such an efficient strategy and study its implications, revealing a discontinuous transition as an unintended side effect of optimal control.

Critical Behaviors in Contagion Dynamics

We study the critical behavior of a general contagion model where nodes are either active (e.g., with opinion A, or functioning) or inactive (e.g., with opinion B, or damaged). The transitions between these two states are determined by (i) spontaneous transitions independent of the neighborhood, (ii) transitions induced by neighboring nodes, and (iii) spontaneous reverse transitions. The resulting dynamics is extremely rich including limit cycles and random phase switching. We derive a unifying mean-field theory. Specifically, we analytically show that the critical behavior of systems whose dynamics is governed by processes (i)-(iii) can only exhibit three distinct regimes: (a) uncorrelated spontaneous transition dynamics, (b) contact process dynamics, and (c) cusp catastrophes. This ends a long-standing debate on the universality classes of complex contagion dynamics in mean field and substantially deepens its mathematical understanding.

Failure and recovery in dynamical networks

Failure, damage spread and recovery crucially underlie many spatially embedded networked systems ranging from transportation structures to the human body. Here we study the interplay between spontaneous damage, induced failure and recovery in both embedded and non-embedded networks. In our model the network's components follow three realistic processes that capture these features: (i) spontaneous failure of a component independent of the neighborhood (internal failure), (ii) failure induced by failed neighboring nodes (external failure) and (iii) spontaneous recovery of a component. We identify a metastable domain in the global network phase diagram spanned by the model's control parameters where dramatic hysteresis effects and random switching between two coexisting states are observed. This dynamics depends on the characteristic link length of the embedded system. For the Euclidean lattice in particular, hysteresis and switching only occur in an extremely narrow region of the parameter space compared to random networks. We develop a unifying theory which links the dynamics of our model to contact processes. Our unifying framework may help to better understand controllability in spatially embedded and random networks where spontaneous recovery of components can mitigate spontaneous failure and damage spread in dynamical networks.

Interaction Control to Synchronize Non-synchronizable Networks

Synchronization constitutes one of the most fundamental collective dynamics across networked systems and often underlies their function. Whether a system may synchronize depends on the internal unit dynamics as well as the topology and strength of their interactions. For chaotic units with certain interaction topologies synchronization might be impossible across all interaction strengths, meaning that these networks are non-synchronizable. Here we propose the concept of interaction control, generalizing transient uncoupling, to induce desired collective dynamics in complex networks and apply it to synchronize even such non-synchronizable systems. After highlighting that non-synchronizability prevails for a wide range of networks of arbitrary size, we explain how a simple binary control may localize interactions in state space and thereby synchronize networks. Intriguingly, localizing interactions by a fixed control scheme enables stable synchronization across all connected networks regardless of topological constraints. Interaction control may thus ease the design of desired collective dynamics even without knowledge of the networks’ exact interaction topology and consequently have implications for biological and self-organizing technical systems.

Genuine non-self-averaging and ultraslow convergence in gelation

In irreversible aggregation processes droplets or polymers of microscopic size successively coalesce until a large cluster of macroscopic scale forms. This gelation transition is widely believed to be self-averaging, meaning that the order parameter (the relative size of the largest connected cluster) attains well-defined values upon ensemble averaging with no sample-to-sample fluctuations in the thermodynamic limit. Here, we report on anomalous gelation transition types. Depending on the growth rate of the largest clusters, the gelation transition can show very diverse patterns as a function of the control parameter, which includes multiple stochastic discontinuous transitions, genuine non-self-averaging and ultraslow convergence of the transition point. Our framework may be helpful in understanding and controlling gelation.

Gender Gap in the ERASMUS Mobility Program

Studying abroad has become very popular among students. The ERASMUS mobility program is one of the largest international student exchange programs in the world, which has supported already more than three million participants since 1987. We analyzed the mobility pattern within this program in 2011-12 and found a gender gap across countries and subject areas. Namely, for almost all participating countries, female students are over-represented in the ERASMUS program when compared to the entire population of tertiary students. The same tendency is observed across different subject areas. We also found a gender asymmetry in the geographical distribution of hosting institutions, with a bias of male students in Scandinavian countries. However, a detailed analysis reveals that this latter asymmetry is rather driven by subject and consistent with the distribution of gender ratios among subject areas.

Universality in boundary domain growth by sudden bridging

We report on universality in boundary domain growth in cluster aggregation in the limit of maximum concentration. Maximal concentration means that the diffusivity of the clusters is effectively zero and, instead, clusters merge successively in a percolation process, which leads to a sudden growth of the boundary domains. For two-dimensional square lattices of linear dimension L, independent of the models studied here, we find that the maximum of the boundary interface width, the susceptibility χ, exhibits the scaling χ ~ L^γ with the universal exponent γ = 1. The rapid growth of the boundary domain at the percolation threshold, which is guaranteed to occur for almost any cluster percolation process, underlies the the universal scaling of χ.

Paradoxical effects of coupling infectious livestock populations and imposing transport restrictions

Spatial heterogeneity of a host population of mobile agents has been shown to be a crucial determinant of many aspects of disease dynamics, ranging from the proliferation of diseases to their persistence and to vaccination strategies. In addition, the importance of regional and structural differences grows in our modern world. Little is known, though, about the consequences when traits of a disease vary regionally. In this paper, we study the effect of a spatially varying per capita infection rate on the behaviour of livestock diseases. We show that the prevalence of an infectious livestock disease in a community of animals can paradoxically decrease owing to transport connections to other communities in which the risk of infection is higher. We study the consequences for the design of livestock transportation restriction measures and establish exact criteria to discriminate those connections that increase the level of infection in the community from those that decrease it.

Emergence of core-peripheries in networks

A number of important transport networks, such as the airline and trade networks of the world, exhibit a characteristic core-periphery structure, wherein a few nodes are highly interconnected and the rest of the network frays into a tree. Mechanisms underlying the emergence of core-peripheries, however, remain elusive. Here, we demonstrate that a simple pruning process based on removal of underutilized links and redistribution of loads can lead to the emergence of core-peripheries. Links are assumed beneficial if they either carry a sufficiently large load or are essential for global connectivity. This incentivized redistribution process is controlled by a single parameter, which balances connectivity and profit. The obtained networks exhibit a highly resilient and connected core with a frayed periphery. The balanced network shows a higher resilience than the world airline network or the world trade network, revealing a pathway towards robust structural features through pruning.

How do online social networks grow?

Online social networks such as Facebook, Twitter and Gowalla allow people to communicate and interact across borders. In past years online social networks have become increasingly important for studying the behavior of individuals, group formation, and the emergence of online societies. Here we focus on the characterization of the average growth of online social networks and try to understand which are possible processes behind seemingly long-range temporal correlated collective behavior. In agreement with recent findings, but in contrast to Gibrat's law of proportionate growth, we find scaling in the average growth rate and its standard deviation. In contrast, Renren and Twitter deviate, however, in certain important aspects significantly from those found in many social and economic systems. Whereas independent methods suggest no significance for temporally long-range correlated behavior for Renren and Twitter, a scaling analysis of the standard deviation does suggest long-range temporal correlated growth in Gowalla. However, we demonstrate that seemingly long-range temporal correlations in the growth of online social networks, such as in Gowalla, can be explained by a decomposition into temporally and spatially independent growth processes with a large variety of entry rates. Our analysis thus suggests that temporally or spatially correlated behavior does not play a major role in the growth of online social networks.

Possible origin of stagnation and variability of earth's biodiversity

The magnitude and variability of Earth's biodiversity have puzzled scientists ever since paleontologic fossil databases became available. We identify and study a model of interdependent species where both endogenous and exogenous impacts determine the nonstationary extinction dynamics. The framework provides an explanation for the qualitative difference of marine and continental biodiversity growth. In particular, the stagnation of marine biodiversity may result from a global transition from an imbalanced to a balanced state of the species dependency network. The predictions of our framework are in agreement with paleontologic databases.

Microtransition cascades to percolation

We report the discovery of a discrete hierarchy of microtransitions occurring in models of continuous and discontinuous percolation. The precursory microtransitions allow us to target almost deterministically the location of the transition point to global connectivity. This extends to the class of intrinsically stochastic processes the possibility to use warning signals anticipating phase transitions in complex systems.

Unstable supercritical discontinuous percolation transitions

The location and nature of the percolation transition in random networks is a subject of intense interest. Recently, a series of graph evolution processes have been introduced that lead to discontinuous percolation transitions where the addition of a single edge causes the size of the largest component to exhibit a significant macroscopic jump in the thermodynamic limit. These processes can have additional exotic behaviors, such as displaying a "Devil's staircase" of discrete jumps in the supercritical regime. Here we investigate whether the location of the largest jump coincides with the percolation threshold for a range of processes, such as Erdős-Rényipercolation, percolation via edge competition and via growth by overtaking. We find that the largest jump asymptotically occurs at the percolation transition for Erdős-Rényiand other processes exhibiting global continuity, including models exhibiting an "explosive" transition. However, for percolation processes exhibiting genuine discontinuities, the behavior is substantially richer. In percolation models where the order parameter exhibits a staircase, the largest discontinuity generically does not coincide with the percolation transition. For the generalized Bohman-Frieze-Wormald model, it depends on the model parameter. Distinct parameter regimes well in the supercritical regime feature unstable discontinuous transitions-a novel and unexpected phenomenon in percolation. We thus demonstrate that seemingly and genuinely discontinuous percolation transitions can involve a rich behavior in supercriticality, a regime that has been largely ignored in percolation.

Phase transitions in supercritical explosive percolation

Percolation describes the sudden emergence of large-scale connectivity as edges are added to a lattice or random network. In the Bohman-Frieze-Wormald model (BFW) of percolation, edges sampled from a random graph are considered individually and either added to the graph or rejected provided that the fraction of accepted edges is never smaller than a decreasing function with asymptotic value of α, a constant. The BFW process has been studied as a model system for investigating the underlying mechanisms leading to discontinuous phase transitions in percolation. Here we focus on the regime αε[0.6,0.95] where it is known that only one giant component, denoted C(1) , initially appears at the discontinuous phase transition. We show that at some point in the supercritical regime C(1) stops growing and eventually a second giant component, denoted C(2), emerges in a continuous percolation transition. The delay between the emergence of C(1) and C(2) and their asymptotic sizes both depend on the value of α and we establish by several techniques that there exists a bifurcation point α(c)=0.763±0.002. For αε[0.6,α(c)), C(1) stops growing the instant it emerges and the delay between the emergence of C(1) and C(2) decreases with increasing α. For αε(α(c),0.95], in contrast, C(1) continues growing into the supercritical regime and the delay between the emergence of C(1) and C(2) increases with increasing α. As we show, α(c) marks the minimal delay possible between the emergence of C(1) and C(2) (i.e., the smallest edge density for which C(2) can exist). We also establish many features of the continuous percolation of C(2) including scaling exponents and relations.

Discriminating the effects of spatial extent and population size in cyclic competition among species

We introduce a population model for species under cyclic competition. This model allows individuals to coexist and interact on single cells while migration takes place between adjacent cells. In contrast to the model introduced by Reichenbach, Mobilia, and Frey [Reichenbach, Mobilia, and Frey, Nature (London) 448, 1046 (2007)], we find that the emergence of spirals results in an ambiguous behavior regarding the stability of coexistence. The typical time until extinction exhibits, however, a qualitatively opposite dependence on the newly introduced nonunit carrying capacity in the spiraling and the nonspiraling regimes. This allows us to determine a critical mobility that marks the onset of this spiraling state sharply. In contrast, we demonstrate that the conventional finite size stability analysis with respect to spatial size is of limited use for identifying the onset of the spiraling regime.

The nature and perception of fluctuations in human musical rhythms

Although human musical performances represent one of the most valuable achievements of mankind, the best musicians perform imperfectly. Musical rhythms are not entirely accurate and thus inevitably deviate from the ideal beat pattern. Nevertheless, computer generated perfect beat patterns are frequently devalued by listeners due to a perceived lack of human touch. Professional audio editing software therefore offers a humanizing feature which artificially generates rhythmic fluctuations. However, the built-in humanizing units are essentially random number generators producing only simple uncorrelated fluctuations. Here, for the first time, we establish long-range fluctuations as an inevitable natural companion of both simple and complex human rhythmic performances. Moreover, we demonstrate that listeners strongly prefer long-range correlated fluctuations in musical rhythms. Thus, the favorable fluctuation type for humanizing interbeat intervals coincides with the one generically inherent in human musical performances.

Impact of microscopic motility on the swimming behavior of parasites: straighter trypanosomes are more directional

Microorganisms, particularly parasites, have developed sophisticated swimming mechanisms to cope with a varied range of environments. African Trypanosomes, causative agents of fatal illness in humans and animals, use an insect vector (the Tsetse fly) to infect mammals, involving many developmental changes in which cell motility is of prime importance. Our studies reveal that differences in cell body shape are correlated with a diverse range of cell behaviors contributing to the directional motion of the cell. Straighter cells swim more directionally while cells that exhibit little net displacement appear to be more bent. Initiation of cell division, beginning with the emergence of a second flagellum at the base, correlates to directional persistence. Cell trajectory and rapid body fluctuation correlation analysis uncovers two characteristic relaxation times: a short relaxation time due to strong body distortions in the range of 20 to 80 ms and a longer time associated with the persistence in average swimming direction in the order of 15 seconds. Different motility modes, possibly resulting from varying body stiffness, could be of consequence for host invasion during distinct infective stages.

Burden of antimicrobial resistance in European hospitals: excess mortality and length of hospital stay associated with bloodstream infections due to Escherichia coli resistant to third-generation cephalosporins

OBJECTIVES

This study determined excess mortality and length of hospital stay (LOS) attributable to bloodstream infection (BSI) caused by third-generation-cephalosporin-resistant Escherichia coli in Europe.

METHODS

A prospective parallel matched cohort design was used. Cohort I consisted of patients with third-generation-cephalosporin-resistant E. coli BSI (REC) and cohort II consisted of patients with third-generation-cephalosporin-susceptible E. coli BSI (SEC). Patients in both cohorts were matched for LOS before infection with patients free of the respective BSI. Thirteen European tertiary care centres participated between July 2007 and June 2008.

RESULTS

Cohort I consisted of 111 REC patients and 204 controls and cohort II consisted of 1110 SEC patients and 2084 controls. REC patients had a higher mortality at 30 days (adjusted odds ratio = 4.6) and a higher hospital mortality (adjusted hazard ratio = 5.7) than their controls. LOS was increased by 8 days. For SEC patients, these figures were adjusted odds ratio = 1.9, adjusted hazard ratio = 2.0 and excess LOS = 3 days. A 2.5 times [95% confidence interval (95% CI) 0.9-6.8] increase in all-cause mortality at 30 days and a 2.9 times (95% CI 1.2-6.9) increase in mortality during entire hospital stay as well as an excess LOS of 5 days (95% CI 0.4-10.2) could be attributed to resistance to third-generation cephalosporins in E. coli BSI.

CONCLUSIONS

Morbidity and mortality attributable to third-generation-cephalosporin-resistant E. coli BSI is significant. If prevailing resistance trends continue, high societal and economic costs can be expected. Better management of infections caused by resistant E. coli is becoming essential.

[Placement of stimulus electrodes and heart rate during electroconvulsive therapy]

OBJECTIVE

Bifrontal stimulation in electroconvulsive therapy (ECT) has been increasingly administered and evaluated over the past years. However, no attention has been paid to cardiac side effects of this novel form of treatment during the application of the electrical stimuli.

METHOD

Cardiac responses to different electrode positions were compared intraindividually, using synchronised electrocardiograms and waveforms of pulse oximetry.

RESULTS

Unilateral ECT gave rise to a marked cardiac response during stimulation. Intervals between two consecutive heartbeats increased from 0.6 ± 0.0 sec to 4.1 ± 3.4 sec (mean ± standard deviation). In contrast, stable heart actions were documented in the same patients during bifrontal stimulation.

CONCLUSION

The placement of the stimulus electrodes for ECT determines the incidence of asystole events during stimulation. Bifrontal electrode positioning results in less activation of the vagus nerve than unilateral treatment. The longer distance from the electrode site to the nerve in bifrontal treatment could account for these findings.

How random is dice tossing?

Tossing the dice is commonly considered a paradigm for chance. But where in the process of throwing a cube does the randomness reside? After all, for all practical purposes the motion is described by the laws of deterministic classical mechanics. Therefore the undisputed status of dice as random number generators calls for a careful analysis. This paper is an attempt in that direction. As a simplified model of a dice a barbell with two marked masses at its tips and only two final positions is considered. It is shown how, depending on initial conditions and the degree of dissipation during bounces, the outcome is only more or less unpredictable: the system is not truly random but pseudorandom--even under conditions where it appears to be random.

Leaking billiards

Billiards are idealizations for systems where particles or waves are confined to cavities, or to other homogeneous regions. In billiard systems a point particle moves freely except for specular reflections from rigid walls. However, billiard walls are not always completely reflective and measurements inside can also open the billiard. Since boundary openings have been studied extensively in the literature, we rather model leakages inside the billiard. In particular, we investigate the classical dynamics of a leakage for a continuous family of billiard systems, that is, the stadium-lemon-billiard family. With a single parameter the geometry of the billiard can be tuned from stadium (being fully hyperbolic) over circle (integrable) to the lemon-shaped billiard (mixed chaotic). For the stadium billiard we found an algebraically decaying mean escape time with the linear size of the leakage n(esc) approximately epsilon-1 together with an exponential decay of the survival probability distribution. The finding is nearly independent of the position and size of the leakage, as long as the leakage is much smaller than the system size, and it is in good agreement with a stochastic map approximation of the dynamics. Due to the mixed phase space for lemon billiards, the mean escape time depends both on the position and geometry of the leakage. For systems where quasiregular motion dominates, we found a linear dependence of the mean escape time, n(esc) approximately 1-epsilon, which we refer to as flooding law. Our findings are helpful in understanding dynamics of leaking Hamiltonian systems.

Directed and undirected multiurn models in a one-dimensional ring

The flea model by Ehrenfest describes the jumps of a fixed number of fleas between two dogs. In each time step a randomly selected flea jumps on the other dog. We study directed and undirected multiurn models in a one-dimensional ring. The introduced models represent generalizations of three recently proposed multiurn models which themselves are generalizations of Ehrenfest's model. The models are solved analytically. For the directed case we find oscillations of the average number of balls or fleas in a certain urn before the system reaches its equilibrium state. The discussed models may serve as basic models of dynamics of granular media in connected periodic compartment systems.

1/f(alpha) spectra in elementary cellular automata and fractal signals

We systematically compute the power spectra of the one-dimensional elementary cellular automata introduced by Wolfram. On the one hand our analysis reveals that one automaton displays 1/f spectra though considered as trivial, and on the other hand that various automata classified as chaotic or complex display no 1/f spectra. We model the results generalizing the recently investigated Sierpinski signal to a class of fractal signals that are tailored to produce 1/f(alpha) spectra. From the widespread occurrence of (elementary) cellular automata patterns in chemistry, physics, and computer sciences, there are various candidates to show spectra similar to our results.

Crash test for the restricted three-body problem

The restricted three-body problem serves to investigate the chaotic behavior of a small body under the gravitational influence of two heavy primary bodies. We analyze numerically the phase space mixing of bounded motion, escape, and crash in this simple model of (chaotic) celestial mechanics. The presented extensive numerical analysis reveals a high degree of complexity. We extend the recently presented findings for the Copenhagen case of equal main masses to the general case of different primary body masses. Collisions of the small body onto the primaries are comparatively frequent, and their probability displays a scale-free dependence on the size of the primaries as shown for the Copenhagen case. Interpreting the crash as leaking in phase space the results are related to both chaotic scattering and the theory of leaking Hamiltonian systems.

Sierpinski signal generates 1/f alpha spectra

We investigate the row sum of the binary pattern generated by the Sierpinski automaton: Interpreted as a time series we calculate the power spectrum of this Sierpinski signal analytically and obtain a unique rugged fine structure with underlying power law decay with an exponent of approximately 1.15. Despite the simplicity of the model, it can serve as a model for 1/f(alpha) spectra in a certain class of experimental and natural systems such as catalytic reactions and mollusc patterns.

Crash test for the Copenhagen problem

The Copenhagen problem is a simple model in celestial mechanics. It serves to investigate the behavior of a small body under the gravitational influence of two equally heavy primary bodies. We present a partition of orbits into classes of various kinds of regular motion, chaotic motion, escape and crash. Collisions of the small body onto one of the primaries turn out to be unexpectedly frequent, and their probability displays a scale-free dependence on the size of the primaries. The analysis reveals a high degree of complexity so that long term prediction may become a formidable task. Moreover, we link the results to chaotic scattering theory and the theory of leaking Hamiltonian systems.

Meckel's diverticulitis in an elderly man diagnosed by computed tomography

Meckel's diverticulum is the most common congenital abnormality of the gastrointestinal tract. Complications most frequently arise in children younger than 2 years who present with gastrointestinal bleeding. The diagnosis is usually made via radionuclide scintigraphy or intraoperatively. The authors report a 71-year-old man who developed a sudden onset of right lower quadrant abdominal pain, without bleeding, and was diagnosed as having Meckel's diverticulitis via computed tomography. The presence of Meckel' s diverticulitis was confirmed at surgery. Complications of a Meckel's diverticulum must be considered at any age. Computed tomography is another modality that may be helpful in the preoperative diagnosis.

Self-organized criticality in a nutshell

In order to gain insight into the nature of self-organized criticality (SOC), we present a minimal model exhibiting this phenomenon. In this analytically solvable model, the state of the system is fully described by a single-integer variable. The system organizes in its critical state without external tuning. We derive analytically the probability distribution of durations of disturbances propagating through the system. As required by SOC, this distribution is scale invariant and follows a power law over several orders of magnitude. Our solution also reproduces the exponential tail of the distribution due to finite size effects. Moreover, we show that large avalanches are suppressed when stabilizing the system in its critical state. Interestingly, avalanches are affected in a similar way when driving the system away from the critical state. With this model, we have reduced SOC dynamics to a leveling process as described by Ehrenfest's famous flea model.

Erythropoietin response is blunted in critically ill patients

OBJECTIVES

Critically ill patients often develop anaemia which can be related to a number of factors. However, the exact causes of anaemia in many patients remain unexplained. We hypothesized that the relationship between erythropoietin (EPO) and haematocrit may be altered in critically ill patients.

DESIGN

Serum concentrations of EPO were serially determined by the ELISA method in 36 critically ill, non-hypoxaemic patients who stayed more than 7 days in the Intensive Care Unit, including 22 patients with sepsis and 14 without. Eighteen ambulatory patients with iron-deficiency anaemia served as a control group.

SETTING

Two University Hospital Intensive Care Departments.

RESULTS

A significant inverse correlation between serum EPO and haematocrit levels was found in the control patients (r = -0.81, p < 0.001), but not in the critically ill patients (r = -0.09, NS), except in a subgroup of non-septic patients without renal failure (r = -0.61, p < 0.01).

CONCLUSIONS

EPO levels can be inappropriately low in critically ill patients, so that EPO deficiency may contribute to the development of anaemia in these patients. This phenomenon is observed not only in the presence of acute renal failure, but also in the presence of sepsis.

Benign ulcer in a hiatus hernia complicated with a pericardial fistula

Penetration of the pericardium by upper gastrointestinal lesions is uncommon. It usually results from trauma, perforation of foreign objects, perforation from gastric or thoracic neoplasm or spontaneous perforation. Unfrequently it is a complication of a benign peptic ulcer of the esophagus or the stomach. Survival from peptic ulcers penetrating to the heart is very rare. From a review of the English literature only 11 survivors have been described. We report the successful outcome of a 76 year old lady with a benign ulcus in a hiatus hernia perforating into the pericardium. Diagnosis of the fistula was established after methylene blue swallow. Treatment consisted of early pericardiotomy and drainage followed by surgical correction of the ulcer and fundoplication of the hiatus hernia.

Escherichia coli endocarditis of a native mitral valve with paravalvular pseudoaneurysm formation and fatal hemopericardium

Until recently only few cases have been described of acute infective endocarditis with E. Coli limited to a normal native mitral valve. Furthermore, mechanisms of so called abcess formation and rupture are still uncompletely understood. We report the case of an E. Coli endocarditis developing a rapidly progressive pseudoaneurysm of the mitral annulus. At necropsy diffuse infectious tissue weakening with pseudoaneurysm formation of the mitral ring and dissection into an hemorraghic pericard were seen. The authors further discuss the changing pattern of infectious agents causing acute infective endocarditis of the native mitral valve, transesophageal echocardiographic characteristics of paravalvular cavities and insights in mechanisms of pseudoaneurysm formation and dissection from clinicopathological findings.

Guanidino compound levels in brain regions of non-dialyzed uremic patients

Guanidino compounds have been suggested to contribute to the complex neurological complications associated with uremia. Several of them have previously been reported to accumulate in physiological fluids of renal insufficient subjects. We report on guanidino compound levels in 28 brain regions in control and uremic brains. In all brain regions studied, in controls as well as in uremic patients, concentrations of alpha-keto-delta-guanidinovaleric acid, alpha-N-acetylarginine and beta-guanidinopropionic acid remained below detection limits. Creatine, guanidinoacetic acid, argininic acid, gamma-guanidinobutyric acid, arginine and homoarginine were not increased in uremic patients. Argininic acid and homoarginine were detectable in some brain regions only. Creatine concentrations varied from 2500 +/- 2100 nmol/g tissue in hypophysis to 10500 +/- 1200 nmol/g tissue in cerebellar cortex. Even more pronounced regional differences were found for gamma-guanidinobutyric acid with the lowest concentration in the caudate nucleus (0.6 +/- 0.3 nmol/g tissue) and highest in substantia nigra, pallidum and cerebellar dentate nucleus (8.3 +/- 2.8 nmol/g tissue). The guanidinosuccinic acid levels were below detection limit in controls in the majority of brain regions. Taking into account the detection limit of guanidinosuccinic acid for a certain amount of tissue applied to the analytical system, important increases (approx. up to > 100 fold) were observed in all brain regions of uremic patients. Accumulation of guanidinosuccinic acid increased with increasing degree of renal failure with levels up to 65 nmol/g tissue in the hypophysis. Creatinine concentrations were also found to be increased in uremic brain regions but increases seemed to be less strictly related to serum urea levels. Guanidine and methylguanidine were found only occasionally in brain regions of controls while respectively 100- and 30-fold increases were found in brain regions of uremic subjects. Levels of guanidinosuccinic acid and creatinine in uremic brain were comparable to those previously observed in brain of experimental animals displaying convulsions following intraperitoneal injection of the respective compounds. Our findings further establish guanidino compounds as probable uremic toxins contributing to the neurological complications in uremia.

The pedagogic characteristics of a clinical conference for senior residents and faculty

OBJECTIVE

To determine the pedagogic characteristics of a clinical conference for senior pediatric residents and selected faculty.

PARTICIPANTS AND SETTING

Nineteen senior pediatric residents and 14 selected faculty members participated in a daily clinical conference at Children's Hospital, Boston, Mass.

DESIGN

Qualitative research design using videotapes of nine consecutive hour-long sessions to generate pedagogic topics to be investigated using a questionnaire administered to participating residents and faculty. Narrative responses were analyzed to find pedagogic themes.

RESULTS

Analysis of videotapes generated the following three topics: What facilitated learning? What was learned? What makes the process of teaching and learning effective? In the questionnaire residents indicated that learning was facilitated by resident-faculty interactions (19/19), faculty participation (19/19), and information resources (12/19). Content learned included information (16/19), approach to diagnosis (11/19), management strategies (14/19), and different perspective (14/19). An effective process of teaching and learning was attributed to case-based resident initiated discussion (19/19), facilitation by the chief resident (16/19), and non-competitive discussions in which expert faculty played a nondominant role (19/19). Faculty identified identical factors relating to all three themes. The mean rating of the conference was 4.5/5 (SD, +/- 0.50) and 4.7/5 (SD, +/- 0.45) by residents and faculty, respectively (Likert scale, 1 to 5).

CONCLUSIONS

The pedagogic effectiveness of this conference was attributed to a resident-centered, case-based learning format and a discussion process characterized by noncompetitive interactions among faculty and residents, strong group facilitation by the chief resident, and participation of faculty experts in a nondominant role.

Asymptomatic metachronous metastatic renal cell adenocarcinoma to the gallbladder. Report of a case and guidelines for evaluation of intraluminal polypoid gallbladder masses

A case of asymptomatic metachronous metastatic unilateral renal cell adenocarcinoma to the gallbladder detected five years after resection of the primary renal neoplasm is reported here. The lesion was diagnosed by contrast enhancement of a gallbladder mass on abdominal computerized tomography scan and by color Doppler sonographic study of the gallbladder, both of which demonstrated the vascular supply to the intraluminal gallbladder mass. The biological behavior of renal cell adenocarcinoma is reviewed. Guidelines for the evaluation of intraluminal gallbladder masses are suggested.

Blastocystis hominis in inflammatory bowel disease

We retrospectively examined the hospital course of 12 patients with exacerbated inflammatory bowel disease (IBD), who also had stool specimens positive for Blastocystis hominis to determine the effect of B. hominis on their disease. Bloody bowel movements were common with ulcerative colitis patients and watery diarrhea with Crohn's disease; other findings included abdominal pain, fever, nausea, and vomiting. All patients responded favorably to medical therapy. Three responded to treatment with corticosteroids alone, and one patient improved with bowel rest without medications. Five patients failed to improve on metronidazole; four of them responded to a subsequent course of corticosteroids, whereas the fifth patient became asymptomatic after erythromycin treatment for concomitant Campylobacter jejuni. Finally, three patients responded to treatment with metronidazole alone, which is known to eradicate B. hominis but may also have a beneficial effect on IBD. In no case did corticosteroid treatment worsen the condition. Our findings indicate that B. hominis is not a significant pathogen in IBD and treatment must be directed toward the underlying illness.