Resonant noise amplification in a predator-prey model with quasi-discrete generations.

Predator-prey models have been shown to exhibit resonance-like behaviour, in which random fluctuations in the number of organisms (demographic noise) are amplified when their frequency is close to the natural oscillatory frequency of the system. This behaviour has been traditionally studied in models with exponentially distributed replication and death times. Here we consider a biologically more realistic model, in which organisms replicate quasi-synchronously such that the distribution of replication times has a narrow maximum at some T > 0 corresponding to the mean doubling time. We show that when the frequency of replication f = 1 / T is tuned to the natural oscillatory frequency of the predator-prey model, the system exhibits oscillations that are much stronger than in the model with Poissonian (non-synchronous) replication and death. These oscillations lead to population instability and the extinction of one of the species much sooner than in the case of Poissonian replication. The effect can be explained by resonant amplification of coloured noise generated by quasi-synchronous replication events.

Current-density relation in the exclusion process with dynamic obstacles.

We investigate the totally asymmetric simple exclusion process (TASEP) in the presence of obstacles that dynamically bind and unbind from the lattice. The model is motivated by biological processes such as transcription in the presence of DNA-binding proteins. Similar models have been studied before using the mean-field approximation, but the exact relation between the particle current and density remains elusive. Here, we first show using extensive Monte Carlo simulations that the current-density relation in this model assumes a quasiparabolic form similar to that of the ordinary TASEP without obstacles. We then attempt to explain this relation using exact calculations in the limit of low and high density of particles. Our results suggest that the symmetric, quasiparabolic current-density relation arises through a nontrivial cancellation of higher-order terms, similarly as in the standard TASEP.

Compression therapy for leg oedema in patients with heart failure.

The presence of chronic heart failure (CHF) results in a significant risk of leg oedema. Medical compression (MC) treatment is one of the basic methods of leg oedema elimination in patients with chronic venous disease and lymphedema, but it is not routinely considered in subjects with CHF-related swelling. In the study, an overview of the current knowledge related to the benefits and risk of using MC in the supportive treatment of leg oedema in CHF patients is presented. The available studies dedicated the comprehensive management of leg swelling using MC in CHF patients published in the English language literature till December 2019 were evaluated in term of the treatment efficacy and safety. In studies performed on CHF populations, manual lymphatic drainage, MC stocking, multilayer bandaged, as well as intermittent pneumatic compression or electric calf stimulations were used. The current evidence is based on non-randomized studies, small study cohorts, as well as very heterogenous populations. The use of the intermittent pneumatic compression in CHF patients significantly increases the right auricular pressure and mean pulmonary artery pressures as well as decreases systemic vascular resistance in most patients without the clinical worsening. The transient and rapid increase in the human atrial natriuretic peptide, after an application of the MC stocking in New York Heart Association (NYHA) class II patients was observed without clinical exacerbation. An application of the multilayer bandages in NYHA classes III and IV patients lead a significant increase in the right arterial pressure and lead to transient deterioration of the right and the left ventricular functions. In the manual lymphatic drainage study, aside from expected leg circumference reduction, no clinical worsening was observed. In a pilot study performed in a small cohort of CHF patients, electrical calf stimulation use resulted in a reduction in the lean mass of the legs without cardiac function worsening. The use of local leg compression can be considered stable CHF patients without decompensated heart function for both CHF-related oedema treatment and for treatment of the concomitant diseases leading to leg swelling occurrence. The use of MC in more severe classes of CHF (NYHA III and IV) should be the subject of future clinical studies to select the safest and most efficient compression method as well as to select the patients who benefit most from this kind of treatment.

Evolution of Drug Resistance in Bacteria.

Resistance to antibiotics is an important and timely problem of contemporary medicine. Rapid evolution of resistant bacteria calls for new preventive measures to slow down this process, and a longer-term progress cannot be achieved without a good understanding of the mechanisms through which drug resistance is acquired and spreads in microbial populations. Here, we discuss recent experimental and theoretical advances in our knowledge how the dynamics of microbial populations affects the evolution of antibiotic resistance . We focus on the role of spatial and temporal drug gradients and show that in certain situations bacteria can evolve de novo resistance within hours. We identify factors that lead to such rapid onset of resistance and discuss their relevance for bacterial infections.

Mechanically driven growth of quasi-two-dimensional microbial colonies.

We study colonies of nonmotile, rod-shaped bacteria growing on solid substrates. In our model, bacteria interact purely mechanically, by pushing each other away as they grow, and consume a diffusing nutrient. We show that mechanical interactions control the velocity and shape of the advancing front, which leads to features that cannot be captured by established Fisher-Kolmogorov models. In particular, we find that the velocity depends on the elastic modulus of bacteria or their stickiness to the surface. Interestingly, we predict that the radius of an incompressible, strictly two-dimensional colony cannot grow linearly in time, unless it develops branches. Importantly, mechanical interactions can also account for the nonequilibrium transition between circular and branching colonies, often observed in the lab.

Spectrum of the product of independent random Gaussian matrices.

We show that the eigenvalue density of a product X=X1X2...XM of M independent NxN Gaussian random matrices in the limit N-->infinity is rotationally symmetric in the complex plane and is given by a simple expression rho(z,z)=1/Mpisigma(-2/M)|z|(-2+(2/M)) for |z|sigma. The parameter sigma corresponds to the radius of the circular support and is related to the amplitude of the Gaussian fluctuations. This form of the eigenvalue density is highly universal. It is identical for products of Gaussian Hermitian, non-Hermitian, and real or complex random matrices. It does not change even if the matrices in the product are taken from different Gaussian ensembles. We present a self-contained derivation of this result using a planar diagrammatic technique. Additionally, we conjecture that this distribution also holds for any matrices whose elements are independent centered random variables with a finite variance or even more generally for matrices which fulfill Pastur-Lindeberg's condition. We provide a numerical evidence supporting this conjecture.

Tuning the shape of the condensate in spontaneous symmetry breaking.

We investigate the conditions which determine the shape of a particle condensate in situations when it emerges as a result of spontaneous breaking of translational symmetry. We consider a model with particles hopping between sites of a one-dimensional grid and interacting if they are at the same site or at neighboring sites. We predict the envelope of the condensate and the scaling of its width with the system size for various interaction potentials and show how to tune the shape from a delta peak to a rectangular or paraboliclike form.

Localization of the maximal entropy random walk.

We define a new class of random walk processes which maximize entropy. This maximal entropy random walk is equivalent to generic random walk if it takes place on a regular lattice, but it is not if the underlying lattice is irregular. In particular, we consider a lattice with weak dilution. We show that the stationary probability of finding a particle performing maximal entropy random walk localizes in the largest nearly spherical region of the lattice which is free of defects. This localization phenomenon, which is purely classical in nature, is explained in terms of the Lifshitz states of a certain random operator.

Counting metastable states of Ising spin glasses on arbitrary graphs.

Using a field-theoretical representation of the Tanaka-Edwards integral, we develop a method to systematically compute the number Ns of one-spin stable states (local energy minima) of a glassy Ising system with nearest-neighbor interactions and random Gaussian couplings on an arbitrary graph. In particular, we use this method to determine Ns for K -regular random graphs and d -dimensional regular lattices for d=2,3 . The method works also for other graphs. Excellent accuracy of the results allows us to observe that the number of local energy minima depends mainly on local properties of the graph on which the spin glass is defined.

Approaching the thermodynamic limit in equilibrated scale-free networks.

We discuss how various models of scale-free complex networks approach their limiting properties when the size N of the network grows. We focus mainly on equilibrated networks and their finite-size degree distributions. Our results show that the position of the cutoff in the degree distribution, k_{cutoff} , scales with N in a different way than predicted for N-->infinity ; that is, subleading corrections to the scaling k_{cutoff} approximately N;{alpha} are strong even for networks of order N approximately 10;{9} nodes. We observe also a logarithmic correction to the scaling for degenerated graphs with the degree distribution pi(k) approximately k;{-3} . On the other hand, the distribution of the maximal degree k_{max} may have a different scaling than the cutoff and, moreover, it approaches the thermodynamic limit much faster. We argue that k_{max} approximately N;{alpha;{'}} with an exponent alpha;{'}=min[alpha,1(gamma-1)] , where gamma is the exponent in the power law pi(k) approximately k;{-gamma} . We also present some results on the cutoff function and the distribution of the maximal degree in equilibrated networks.

Condensation in zero-range processes on inhomogeneous networks.

We investigate the role of inhomogeneities in zero-range processes in condensation dynamics. We consider the dynamics of balls hopping between nodes of a network with one node of degree k_{1} much higher than a typical degree k , and find that the condensation is triggered by the inhomogeneity and that it depends on the ratio k_{1}k . Although, on the average, the condensate takes an extensive number of balls, its occupation can oscillate in a wide range. We show that in systems with strong inhomogeneity, the typical melting time of the condensate grows exponentially with the number of balls.

Finite-size effects in Barabási-Albert growing networks.

We investigate the influence of the network's size on the degree distribution pi k in Barabási-Albert model of growing network with initial attractiveness. Our approach based on moments of pi k allows us to treat analytically several variants of the model and to calculate the cutoff function, giving finite-size corrections to pi k. We study the effect of initial configuration as well as of addition of more than one link per time step. The results indicate that asymptotic properties of the cutoff depend only on the exponent gamma in the power-law describing the tail of the degree distribution. The method presented in this paper is very general and can be applied to other growing networks.

Balls-in-boxes condensation on networks.

We discuss two different regimes of condensate formation in zero-range processes on networks: on a q-regular network, where the condensate is formed as a result of a spontaneous symmetry breaking, and on an irregular network, where the symmetry of the partition function is explicitly broken. In the latter case we consider a minimal irregularity of the q-regular network introduced by a single Q node with degree Q>q. The statics and dynamics of the condensation depend on the parameter alpha=ln Q/q, which controls the exponential falloff of the distribution of particles on regular nodes and the typical time scale for melting of the condensate on the Q node, which increases exponentially with the system size N. This behavior is different than that on a q-regular network, where alpha=0 and where the condensation results from the spontaneous symmetry breaking of the partition function, which is invariant under a permutation of particle occupation numbers on the q nodes of the network. In this case the typical time scale for condensate melting is known to increase typically as a power of the system size.

Ankle-brachial pressure index estimated by laser Doppler in patients suffering from peripheral arterial obstructive disease.

Ankle-brachial index (ABI) measurements are widely used for evaluating the functional state of circulation in the lower limbs. However, there is some evidence that the value of ABI does not accurately reflect the degree of walking impairment in symptomatic patients with peripheral arterial obstructive disease (PAOD). We investigated the diagnostic value of ABI estimated by means of laser Doppler flowmetry (IT) for evaluating limb ischemia. We wanted to know whether laser Doppler could be more sensitive than the Doppler method in predicting walking capacity in patients with stable intermittent claudication. We analyzed a group of 30 patients with intermittent claudication (Fontain II, II/III) who were admitted for reconstructive treatment. There were 21 men and 9 women, aged 46-74 (mean 61) years. All patients underwent the treadmill test, and pain-free walking distances were measured. In each patient, we measured ABI using the two different methods: Doppler ultrasound device (ABI-Doppler) and laser Doppler (ABI-laser Doppler). The claudication distances were 25-200 m (mean 73 +/- 50.2 m). ABI-Doppler was 0.2-0.7 (0.582 +/- 0.195). ABI-laser Doppler measurements were 0.581 (+/-0.218). A correlation was found between ABI-Doppler and claudication distance (r = 0.46, P = 0.009). Also, ABI-laser Doppler values significantly correlated with claudication distances (r = 0.536, P = 0.002). The ABI evaluated by laser Doppler correlated well with claudication distances in patients with PAOD. Comparison of Doppler and laser Doppler measurements used for determining ABI showed that both methods have similar predictive power for walking capacity; however, higher correlation was observed between claudication distances and ABI measured by laser Doppler flowmetry. ABI-laser Doppler measurements are easier, are quicker, and seem to be better suited for noncompliant patients. Further investigation should be undertaken to determine whether laser Doppler is superior to the Doppler method in advanced occlusive arterial disease.

A possible association of recurrent streptococcal infections and acute onset of obsessive-compulsive disorder.

Rheumatic fever is an immunologically mediated disease that follows infection by group A beta-hemolytic Streptococcus (GABHS). In rheumatic fever, antibodies generated against GABHS cross-react with the heart, joints, skin, and other sites, inducing an inflammatory, multisystem disease. Brain tissue-specific antibodies have been demonstrated in a subset of children with Sydenham chorea (a component of the Jones criteria for the diagnosis of rheumatic fever), and most Sydenham chorea patients manifest obsessive-compulsive symptoms very similar to those in traditional obsessive-compulsive disorder. The parallels drawn from the paradigm of Sydenham's chorea to Pediatric Autoimmune Neuropsychiatric Disorders Associated with Streptococcal Infections (PANDAS) is an area of active controversy. Newly emerging information on the role of GABHS superantigens in the pathogenesis of rheumatic fever is of particular interest. In this article, we review the microbial characteristics of GABHS and the subsequent immune responses to GABHS as a possible etiology of PANDAS.

Radiotherapy of CD19 expressing Daudi tumors in nude mice with Yttrium-90-labeled anti-CD19 antibody.

Studies were performed to determine the suitability of using two different anti-CD19 monoclonal antibodies to deliver the high energy beta-particle emitting isotope 90Y to B-cell lymphoma grown as flank tumors in athymic nude mice. The antibodies BU12 and HD37, both of the IgG1 subclass, recognize CD19, an internalizing B-lineage-specific membrane glycoprotein and member of the Ig supergene family. The antibodies were readily labeled with 90Y using the highly stable chelate, 1B4M-MX-DTPA. The radioimmunoconjugates selectively bound to the CD19 expressing B cell line Daudi, but not to CD19 negative control cells. Significantly more 90Y anti-CD19 bound to Daudi tumors growing in nude mice than did a control non-binding antibody (p = 0.001). The biodistribution data correlated with an anti-tumor effect. Anti-tumor activity was dose dependent and the best results were observed in mice receiving a single dose of approximately 300 uCi. The anti-CD19 antibody had significantly better anti-tumor activity as compared to a control 90Y-labeled antibody and most mice survived over 119 days with no evidence of tumor (p < 0.003). Histology studies showed no significant injury to the kidney, liver, or small intestine. Because radiolabeled anti-CD19 antibody can be used to deliver radiation selectively to lymphohematopoietic tissue, these data support the use of 90Y anti-CD19 antibodies in treating B-cell malignancies.