The Traveling Salesman Problem: Low-Dimensionality Implies a Polynomial Time Approximation Scheme

The Traveling Salesman Problem (TSP) is among the most famous NP-hard optimization problems. We design for this problem a randomized polynomial-time algorithm that computes a (1+eps)-approximation to the optimal tour, for any fixed eps>0, in TSP instances that form an arbitrary metric space with bounded intrinsic dimension. The celebrated results of Arora (A-98) and Mitchell (M-99) prove that the above result holds in the special case of TSP in a fixed-dimensional Euclidean space. Thus, our algorithm demonstrates that the algorithmic tractability of metric TSP depends on the dimensionality of the space and not on its specific geometry. This result resolves a problem that has been open since the quasi-polynomial time algorithm of Talwar (T-04)

Description of non-specific DNA-protein interaction and facilitated diffusion with a dynamical model

We propose a dynamical model for non-specific DNA-protein interaction, which is based on the 'bead-spring' model previously developed by other groups, and investigate its properties using Brownian Dynamics simulations. We show that the model successfully reproduces some of the observed properties of real systems and predictions of kinetic models. For example, sampling of the DNA sequence by the protein proceeds via a succession of 3d motion in the solvent, 1d sliding along the sequence, short hops between neighboring sites, and intersegmental transfers. Moreover, facilitated diffusion takes place in a certain range of values of the protein effective charge, that is, the combination of 1d sliding and 3d motion leads to faster DNA sampling than pure 3d motion. At last, the number of base pairs visited during a sliding event is comparable to the values deduced from single-molecule experiments. We also point out and discuss some discrepancies between the predictions of this model and some recent experimental results as well as some hypotheses and predictions of kinetic models

Effects of Acute Febrile Diseases on the Periodontium of Rhesus Monkeys with Reference to Poliomyelitis

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/67269/2/10.1177_00220345510300050301.pd

Mathematical Analysis and Optimization of Infiltration Processes

A variety of infiltration techniques can be used to fabricate solid materials, particularly composites. In general these processes can be described with at least one time dependent partial differential equation describing the evolution of the solid phase, coupled to one or more partial differential equations describing mass transport through a porous structure. This paper presents a detailed mathematical analysis of a relatively simple set of equations which is used to describe chemical vapor infiltration. The results demonstrate that the process is controlled by only two parameters, alpha and beta. The optimization problem associated with minimizing the infiltration time is also considered. Allowing alpha and beta to vary with time leads to significant reductions in the infiltration time, compared with the conventional case where alpha and beta are treated as constants

Magnetic Fields in Quasar Cores II

Multi-frequency polarimetry with the Very Long Baseline Array (VLBA) telescope has revealed absolute Faraday Rotation Measures (RMs) in excess of 1000 rad/m/m in the central regions of 7 out of 8 strong quasars studied (e.g., 3C 273, 3C 279, 3C 395). Beyond a projected distance of ~20 pc, however, the jets are found to have |RM| < 100 rad/m/m. Such sharp RM gradients cannot be produced by cluster or galactic-scale magnetic fields, but rather must be the result of magnetic fields organized over the central 1-100 pc. The RMs of the sources studied to date and the polarization properties of BL Lacs, quasars and galaxies are shown to be consistent so far with the predictions of unified schemes. The direct detection of high RMs in these quasar cores can explain the low fractional core polarizations usually observed in quasars at centimeter wavelengths as the result of irregularities in the Faraday screen on scales smaller than the telescope beam. Variability in the RM of the core is reported for 3C 279 between observations taken 1.5 years apart, indicating that the Faraday screen changes on that timescale, or that the projected superluminal motion of the inner jet components samples a new location in the screen with time. Either way, these changes in the Faraday screen may explain the dramatic variability in core polarization properties displayed by quasars.Comment: Accepted to the ApJ. 27 pages, 9 figures including figure 6 in colo

Relations between heart failure, ejection fraction, arrhythmia suppression and mortality: Analysis of the Cardiac Arrhythmia Suppression Trial

Objectives.We studied the relations between heart failure, ejection fraction, arrhythmia suppression and mortality.Background.Both left ventricular ejection fraction and functional class of heart failure are strongly associated with mortality after acute myocardial infarction. Both are also related to the presence of ventricular arrhythmias and have been identified as factors related to the ability to suppress ventricular arrhythmias. Little has been reported about the relations between these two factors and arrhythmia suppression or mortality.Methods.Baseline data from the Cardiac Arrhythmia Suppression Trial were used to define several categories of heart failure and to relate both the resulting categories and ejection fraction to arrhythmia suppression and mortality using logistic and survival regression analytic methodologies.Results.Regardless of the prospective baseline definition of heart failure used, the data consistently showed that heart failure was a more powerful predictor of subsequent congestive heart failure events and arrhythmia suppression and was equally powerful in predicting death. However, each variable provided incremental information when included in the prediction model. Heart failure and ejection fraction appeared to be independent predictors of death. Interactions were observed: A low ejection fraction was more predictive of failure of arrhythmia suppression in patients with than without evidence of heart failure before or at baseline; a low ejection fraction was more predictive of subsequent congestive heart failure events in patients without than with evidence of heart failure before or at baseline.Conclusions.Although heart failure as a prognostic feature appears to be somewhat superior to ejection fraction, both are powerful predictors of arrhythmia suppression and cardiac events in patients with ventricular arrhythmia after myocardial infarction. Each provides incremental prediction

Discovery of SiCSi in IRC+10216: A missing link between gas and dust carriers of SiC bonds

We report the discovery in space of a disilicon species, SiCSi, from observations between 80 and 350 GHz with the IRAM 30m radio telescope. Owing to the close coordination between laboratory experiments and astrophysics, 112 lines have now been detected in the carbon-rich star CWLeo. The derived frequencies yield improved rotational and centrifugal distortion constants up to sixth order. From the line profiles and interferometric maps with the Submillimeter Array, the bulk of the SiCSi emis- sion arises from a region of 6 arcseconds in radius. The derived abundance is comparable to that of SiC2. As expected from chemical equilibrium calculations, SiCSi and SiC2 are the most abundant species harboring a SiC bond in the dust formation zone and certainly both play a key role in the formation of SiC dust grains.Comment: To be published in the Astrophysical Journal Letters; Accepted May 6 201

Numerical Evolution of axisymmetric vacuum spacetimes: a code based on the Galerkin method

We present the first numerical code based on the Galerkin and Collocation methods to integrate the field equations of the Bondi problem. The Galerkin method like all spectral methods provide high accuracy with moderate computational effort. Several numerical tests were performed to verify the issues of convergence, stability and accuracy with promising results. This code opens up several possibilities of applications in more general scenarios for studying the evolution of spacetimes with gravitational waves.Comment: 11 pages, 6 figures. To appear in Classical and Quantum Gravit