New and simple algorithms for stable flow problems

Stable flows generalize the well-known concept of stable matchings to markets in which transactions may involve several agents, forwarding flow from one to another. An instance of the problem consists of a capacitated directed network, in which vertices express their preferences over their incident edges. A network flow is stable if there is no group of vertices that all could benefit from rerouting the flow along a walk. Fleiner established that a stable flow always exists by reducing it to the stable allocation problem. We present an augmenting-path algorithm for computing a stable flow, the first algorithm that achieves polynomial running time for this problem without using stable allocation as a black-box subroutine. We further consider the problem of finding a stable flow such that the flow value on every edge is within a given interval. For this problem, we present an elegant graph transformation and based on this, we devise a simple and fast algorithm, which also can be used to find a solution to the stable marriage problem with forced and forbidden edges. Finally, we study the stable multicommodity flow model introduced by Kir\'{a}ly and Pap. The original model is highly involved and allows for commodity-dependent preference lists at the vertices and commodity-specific edge capacities. We present several graph-based reductions that show equivalence to a significantly simpler model. We further show that it is NP-complete to decide whether an integral solution exists

Low-lying excitations of a trapped rotating Bose-Einstein condensate

We investigate the low-lying excitations of a weakly-interacting, harmonically-trapped Bose-Einstein condensed gas under rotation, in the limit where the angular mometum $L$ of the system is much less than the number of the atoms $N$ in the trap. We show that in the asymptotic limit $N \to \infty$ the excitation energy, measured from the energy of the lowest state, is given by $27 N_{3}(N_{3}-1) v_0 /68$, where $N_{3}$ is the number of octupole excitations and $v_{0}$ is the unit of the interaction energy.Comment: 3 pages, RevTex, 2 ps figures, submitted to PR

Emergence of fractal behavior in condensation-driven aggregation

We investigate a model in which an ensemble of chemically identical Brownian particles are continuously growing by condensation and at the same time undergo irreversible aggregation whenever two particles come into contact upon collision. We solved the model exactly by using scaling theory for the case whereby a particle, say of size $x$, grows by an amount $\alpha x$ over the time it takes to collide with another particle of any size. It is shown that the particle size spectra of such system exhibit transition to dynamic scaling $c(x,t)\sim t^{-\beta}\phi(x/t^z)$ accompanied by the emergence of fractal of dimension $d_f={{1}\over{1+2\alpha}}$. One of the remarkable feature of this model is that it is governed by a non-trivial conservation law, namely, the $d_f^{th}$ moment of $c(x,t)$ is time invariant regardless of the choice of the initial conditions. The reason why it remains conserved is explained by using a simple dimensional analysis. We show that the scaling exponents $\beta$ and $z$ are locked with the fractal dimension $d_f$ via a generalized scaling relation $\beta=(1+d_f)z$.Comment: 8 pages, 6 figures, to appear in Phys. Rev.

Extended microsatellite analysis in microsatellite stable, MSH2 and MLH1 mutation-negative HNPCC patients: Genetic reclassification and correlation with clinical features

Background: Hereditary nonpolyposis colorectal cancer (HNPCC) is an autosomal dominant disorder predisposing to predominantly colorectal cancer (CRC) and endometrial cancer frequently due to germline mutations in DNA mismatch repair (MMR) genes, mainly MLH1, MSH2 and also MSH6 in families seen to demonstrate an excess of endometrial cancer. As a consequence, tumors in HNPCC reveal alterations in the length of simple repetitive genomic sequences like poly-A, poly-T, CA or GT repeats (microsatellites) in at least 90% of the cases. Aim of the Study: The study cohort consisted of 25 HNPCC index patients ( 19 Amsterdam positive, 6 Bethesda positive) who revealed a microsatellite stable (MSS) - or low instable (MSI-L) - tumor phenotype with negative mutation analysis for the MMR genes MLH1 and MSH2. An extended marker panel (BAT40, D10S197, D13S153, D18S58, MYCL1) was analyzed for the tumors of these patients with regard to three aspects. First, to reconfirm the MSI-L phenotype found by the standard panel; second, to find minor MSIs which might point towards an MSH6 mutation, and third, to reconfirm the MSS status of hereditary tumors. The reconfirmation of the MSS status of tumors not caused by mutations in the MMR genes should allow one to define another entity of hereditary CRC. Their clinical features were compared with those of 150 patients with sporadic CRCs. Results: In this way, 17 MSS and 8 MSI-L tumors were reclassified as 5 MSS, 18 MSI-L and even 2 MSI-H ( high instability) tumors, the last being seen to demonstrate at least 4 instable markers out of 10. Among all family members, 87 malignancies were documented. The mean age of onset for CRCs was the lowest in the MSI-H-phenotyped patients with 40.5 +/- 4.9 years (vs. 47.0 +/- 14.6 and 49.8 +/- 11.9 years in MSI-L- and MSS-phenotyped patients, respectively). The percentage of CRC was the highest in families with MSS-phenotyped tumors (88%), followed by MSI-L-phenotyped ( 78%) and then by MSI-H-phenotyped (67%) tumors. MSS tumors were preferentially localized in the distal colon supposing a similar biologic behavior like sporadic CRC. MSH6 mutation analysis for the MSI-L and MSI-H patients revealed one truncating mutation for a patient initially with an MSS tumor, which was reclassified as MSI-L by analyzing the extended marker panel. Conclusion: Extended microsatellite analysis serves to evaluate the sensitivity of the reference panel for HNPCC detection and permits phenotype confirmation or upgrading. Additionally, it confirms the MSS status of hereditary CRCs not caused by the common mutations in the MMR genes and provides hints to another entity of hereditary CRC. Copyright (C) 2004 S. Karger AG, Basel

Optimal box-covering algorithm for fractal dimension of complex networks

The self-similarity of complex networks is typically investigated through computational algorithms the primary task of which is to cover the structure with a minimal number of boxes. Here we introduce a box-covering algorithm that not only outperforms previous ones, but also finds optimal solutions. For the two benchmark cases tested, namely, the E. Coli and the WWW networks, our results show that the improvement can be rather substantial, reaching up to 15% in the case of the WWW network.Comment: 5 pages, 6 figure

Multifractal Analysis of the Coupling Space of Feed-Forward Neural Networks

Random input patterns induce a partition of the coupling space of feed-forward neural networks into different cells according to the generated output sequence. For the perceptron this partition forms a random multifractal for which the spectrum $f(\alpha)$ can be calculated analytically using the replica trick. Phase transition in the multifractal spectrum correspond to the crossover from percolating to non-percolating cell sizes. Instabilities of negative moments are related to the VC-dimension.Comment: 10 pages, Latex, submitted to PR

How the geometry makes the criticality in two - component spreading phenomena?

We study numerically a two-component A-B spreading model (SMK model) for concave and convex radial growth of 2d-geometries. The seed is chosen to be an occupied circle line, and growth spreads inside the circle (concave geometry) or outside the circle (convex geometry). On the basis of generalised diffusion-annihilation equation for domain evolution, we derive the mean field relations describing quite well the results of numerical investigations. We conclude that the intrinsic universality of the SMK does not depend on the geometry and the dependence of criticality versus the curvature observed in numerical experiments is only an apparent effect. We discuss the dependence of the apparent critical exponent $\chi_{a}$ upon the spreading geometry and initial conditions.Comment: Uses iopart.cls, 11 pages with 8 postscript figures embedde

Operator-Algebraic Approach to the Yrast Spectrum of Weakly Interacting Trapped Bosons

We present an operator-algebraic approach to deriving the low-lying quasi-degenerate spectrum of weakly interacting trapped N bosons with total angular momentum \hbar L for the case of small L/N, demonstrating that the lowest-lying excitation spectrum is given by 27 g n_3(n_3-1)/34, where g is the strength of the repulsive contact interaction and n_3 the number of excited octupole quanta. Our method provides constraints for these quasi-degenerate many-body states and gives higher excitation energies that depend linearly on N.Comment: 7 pages, one figur

Is subdiffusional transport slower than normal?

We consider anomalous non-Markovian transport of Brownian particles in viscoelastic fluid-like media with very large but finite macroscopic viscosity under the influence of a constant force field F. The viscoelastic properties of the medium are characterized by a power-law viscoelastic memory kernel which ultra slow decays in time on the time scale \tau of strong viscoelastic correlations. The subdiffusive transport regime emerges transiently for t<\tau. However, the transport becomes asymptotically normal for t>>\tau. It is shown that even though transiently the mean displacement and the variance both scale sublinearly, i.e. anomalously slow, in time, ~ F t^\alpha, ~ t^\alpha, 0<\alpha<1, the mean displacement at each instant of time is nevertheless always larger than one obtained for normal transport in a purely viscous medium with the same macroscopic viscosity obtained in the Markovian approximation. This can have profound implications for the subdiffusive transport in biological cells as the notion of "ultra-slowness" can be misleading in the context of anomalous diffusion-limited transport and reaction processes occurring on nano- and mesoscales

Critical scaling in standard biased random walks

The spatial coverage produced by a single discrete-time random walk, with asymmetric jump probability $p\neq 1/2$ and non-uniform steps, moving on an infinite one-dimensional lattice is investigated. Analytical calculations are complemented with Monte Carlo simulations. We show that, for appropriate step sizes, the model displays a critical phenomenon, at $p=p_c$. Its scaling properties as well as the main features of the fragmented coverage occurring in the vicinity of the critical point are shown. In particular, in the limit $p\to p_c$, the distribution of fragment lengths is scale-free, with nontrivial exponents. Moreover, the spatial distribution of cracks (unvisited sites) defines a fractal set over the spanned interval. Thus, from the perspective of the covered territory, a very rich critical phenomenology is revealed in a simple one-dimensional standard model.Comment: 4 pages, 4 figure