Constant-time distributed dominating set approximation

Abstract.: Finding a small dominating set is one of the most fundamental problems of classical graph theory. In this paper, we present a new fully distributed approximation algorithm based on LP relaxation techniques. For an arbitrary, possibly constant parameter k and maximum node degree $\Delta$ , our algorithm computes a dominating set of expected size ${\rm O}(k\Delta^{2/k}{\rm log}(\Delta)\vert DS_{\rm {OPT}}\vert)$ in ${\rm O}{(k^2)}$ rounds. Each node has to send ${\rm O}{(k^2\Delta)}$ messages of size ${\rm O}({\rm log}\Delta)$ . This is the first algorithm which achieves a non-trivial approximation ratio in a constant number of round

Effects of 3D Geometries on Cellular Gradient Sensing and Polarization

During cell migration, cells become polarized, change their shape, and move in response to various internal and external cues. Cell polarization is defined through the spatio-temporal organization of molecules such as PI3K or small GTPases, and is determined by intracellular signaling networks. It results in directional forces through actin polymerization and myosin contractions. Many existing mathematical models of cell polarization are formulated in terms of reaction-diffusion systems of interacting molecules, and are often defined in one or two spatial dimensions. In this paper, we introduce a 3D reaction-diffusion model of interacting molecules in a single cell, and find that cell geometry has an important role affecting the capability of a cell to polarize, or change polarization when an external signal changes direction. Our results suggest a geometrical argument why more roundish cells can repolarize more effectively than cells which are elongated along the direction of the original stimulus, and thus enable roundish cells to turn faster, as has been observed in experiments. On the other hand, elongated cells preferentially polarize along their main axis even when a gradient stimulus appears from another direction. Furthermore, our 3D model can accurately capture the effect of binding and unbinding of important regulators of cell polarization to and from the cell membrane. This spatial separation of membrane and cytosol, not possible to capture in 1D or 2D models, leads to marked differences of our model from comparable lower-dimensional models.Comment: 31 pages, 7 figure

X-ray astronomy in the new Millenium. A Summary

Recent X-ray observations have had a major impact on topics ranging from protostars to cosmology. They have also drawn attention to important and general physical processes that currently limit our understanding of thermal and nonthermal X-ray sources. These include unmeasured atomic astrophysics data (wavelengths, oscillator strengths etc.), basic hydromagnetic processes (e.g. shock structure, reconnection), plasma processes (such as electron-ion equipartition and heat conduction) and radiative transfer (in disks and accretion columns). Progress on these problems will probably come from integrative studies that draw upon observations, throughout the electromagnetic spectrum, of different classes of source. X-ray observations are also giving a new perspective on astronomical subjects, like the nature of galactic nuclei and the evolution of stellar populations. They are contributing to answering central cosmological questions including the measurement of the matter content of the universe, understanding its overall luminosity density, describing its chemical evolution and locating the first luminous objects. X-ray astronomy has a healthy future with several international space missions under construction and in development.Comment: 12 page

Malaria parasite detection increases during pregnancy in wild chimpanzees

Background: The diversity of malaria parasites (Plasmodium sp.) infecting chimpanzees (Pan troglodytes) and their close relatedness with those infecting humans is well documented. However, their biology is still largely unexplored and there is a need for baseline epidemiological data. Here, the effect of pregnancy, a well-known risk factor for malaria in humans, on the susceptibility of female chimpanzees to malaria infection was investigated. Methods: A series of 384 faecal samples collected during 40 pregnancies and 36 post-pregnancies from three habituated groups of wild chimpanzees in the Tai National Park, Cote d'Ivoire, were tested. Samples were tested for malaria parasites by polymerase chain reaction (PCR) and sequencing. Data were analysed using a generalized linear mixed model. Results: Probability of malaria parasite detection significantly increased towards the end of pregnancy and decreased with the age of the mother. Conclusions: This study provides evidence that susceptibility to malaria parasite infection increases during pregnancy, and, as shown before, in younger individuals, which points towards similar dynamics of malaria parasite infection in human and chimpanzee populations and raises questions about the effects of such infections on pregnancy outcome and offspring morbidity/mortality

Dynamic Analysis of the Arrow Distributed Protocol

Distributed queuing is a fundamental coordination problem that arises in a variety of applications, including distributed directories, totally ordered multicast, and distributed mutual exclusion. The arrow protocol is a solution to distributed queuing that is based on path reversal on a pre-selected spanning tree of the network. We present a novel and comprehensive competitive analysis of the arrow protocol. We consider the total cost of handling a finite number of queuing requests, which may or may not be issued concurrently, and show that the arrow protocol is $O(s\cdot \log D)$ -competitive to the optimal queuing protocol, where s and D are the stretch and the diameter, respectively, of the spanning tree. In addition, we show that our analysis is almost tight by proving that for every spanning tree chosen for execution, the arrow protocol is $\Omega(s \cdot \log(D/s)/{\log}\log(D/s))$ -competitive to the optimal queuing protocol. Our analysis reveals an intriguing connection between the arrow protocol and the nearest neighbor traveling salesperson tour on an appropriately defined grap

Single-Cell Migration in Complex Microenvironments: Mechanics and Signaling Dynamics

Cells are highly dynamic and mechanical automata powered by molecular motors that respond to external cues. Intracellular signaling pathways, either chemical or mechanical, can be activated and spatially coordinated to induce polarized cell states and directional migration. Physiologically, cells navigate through complex microenvironments, typically in three-dimensional (3D) fibrillar networks. In diseases, such as metastatic cancer, they invade across physiological barriers and remodel their local environments through force, matrix degradation, synthesis, and reorganization. Important external factors such as dimensionality, confinement, topographical cues, stiffness, and flow impact the behavior of migrating cells and can each regulate motility. Here, we review recent progress in our understanding of single-cell migration in complex microenvironments.National Cancer Institute (U.S.) (Grant No. 5U01CA177799)National Institutes of Health (U.S.) (Ruth L. Kirschstein National Research Service Award

On Implicit Bias in Overparameterized Bilevel Optimization

Many problems in machine learning involve bilevel optimization (BLO), including hyperparameter optimization, meta-learning, and dataset distillation. Bilevel problems consist of two nested sub-problems, called the outer and inner problems, respectively. In practice, often at least one of these sub-problems is overparameterized. In this case, there are many ways to choose among optima that achieve equivalent objective values. Inspired by recent studies of the implicit bias induced by optimization algorithms in single-level optimization, we investigate the implicit bias of gradient-based algorithms for bilevel optimization. We delineate two standard BLO methods -- cold-start and warm-start -- and show that the converged solution or long-run behavior depends to a large degree on these and other algorithmic choices, such as the hypergradient approximation. We also show that the inner solutions obtained by warm-start BLO can encode a surprising amount of information about the outer objective, even when the outer parameters are low-dimensional. We believe that implicit bias deserves as central a role in the study of bilevel optimization as it has attained in the study of single-level neural net optimization.Comment: ICML 202

Recent X-Ray Observations of SN1986J with ASCA and ROSAT

We present ASCA and ROSAT observations of SN 1986J covering the period 1991 August to 1996 January. From observations with the ROSAT HRI and PSPC, we find that the 0.5-2.5 keV flux decreased proportional to $t^{-2}$ during this period; the ASCA data are consistent with this result and extend it to the 2-10 keV band. ASCA spectra from 1994 January and 1996 January are consistent with thermal emission from a solar metallicity plasma at an equilibrium temperature kT = 5-7.5 keV, somewhat hotter than that observed from other X-ray supernovae. These spectra also show a clear Fe K emission line at 6.7 keV with FWHM < 20,000 km/s (90% confidence). This limit on the line width is consistent with the reverse shock model of Chevalier & Fransson (1994), but does not rule out the clumpy wind model of Chugai (1993).Comment: 20 pages, 9 postscript figures, latex, uses aastex4.0, submitted to The Astrophysical Journa