On Near-Linear-Time Algorithms for Dense Subset Sum

In the Subset Sum problem we are given a set of $n$ positive integers $X$ and a target $t$ and are asked whether some subset of $X$ sums to $t$. Natural parameters for this problem that have been studied in the literature are $n$ and $t$ as well as the maximum input number $\rm{mx}_X$ and the sum of all input numbers $\Sigma_X$. In this paper we study the dense case of Subset Sum, where all these parameters are polynomial in $n$. In this regime, standard pseudo-polynomial algorithms solve Subset Sum in polynomial time $n^{O(1)}$. Our main question is: When can dense Subset Sum be solved in near-linear time $\tilde{O}(n)$? We provide an essentially complete dichotomy by designing improved algorithms and proving conditional lower bounds, thereby determining essentially all settings of the parameters $n,t,\rm{mx}_X,\Sigma_X$ for which dense Subset Sum is in time $\tilde{O}(n)$. For notational convenience we assume without loss of generality that $t \ge \rm{mx}_X$ (as larger numbers can be ignored) and $t \le \Sigma_X/2$ (using symmetry). Then our dichotomy reads as follows: - By reviving and improving an additive-combinatorics-based approach by Galil and Margalit [SICOMP'91], we show that Subset Sum is in near-linear time $\tilde{O}(n)$ if $t \gg \rm{mx}_X \Sigma_X/n^2$. - We prove a matching conditional lower bound: If Subset Sum is in near-linear time for any setting with $t \ll \rm{mx}_X \Sigma_X/n^2$, then the Strong Exponential Time Hypothesis and the Strong k-Sum Hypothesis fail. We also generalize our algorithm from sets to multi-sets, albeit with non-matching upper and lower bounds

Preliminary Results on HAT-P-4, TrES-3, XO-2, and GJ 436 from the NASA EPOXI Mission

EPOXI (EPOCh + DIXI) is a NASA Discovery Program Mission of Opportunity using the Deep Impact flyby spacecraft. The EPOCh (Extrasolar Planet Observation and Characterization) Science Investigation will gather photometric time series of known transiting exoplanet systems from January through August 2008. Here we describe the steps in the photometric extraction of the time series and present preliminary results of the first four EPOCh targets.Comment: 4 pages, 2 figures. To appear in the Proceedings of the 253rd IAU Symposium: "Transiting Planets", May 2008, Cambridge, M

Observing Dynamical Phases of a Bardeen-Cooper-Schrieffer Superconductor in a Cavity QED Simulator

In conventional Bardeen-Cooper-Schrieffer (BCS) superconductors, electrons with opposite momenta bind into Cooper pairs due to an attractive interaction mediated by phonons in the material. While superconductivity naturally emerges at thermal equilibrium, it can also emerge out of equilibrium when the system's parameters are abruptly changed. The resulting out-of-equilibrium phases are predicted to occur in real materials and ultracold fermionic atoms but have not yet been directly observed. This work realizes an alternate way to generate the proposed dynamical phases using cavity quantum electrodynamics (cavity QED). Our system encodes the presence or absence of a Cooper pair in a long-lived electronic transition in $^{88}$Sr atoms coupled to an optical cavity and represents interactions between electrons as photon-mediated interactions through the cavity. To fully explore the phase diagram, we manipulate the ratio between the single-particle dispersion and the interactions after a quench and perform real-time tracking of subsequent dynamics of the superconducting order parameter using non-destructive measurements. We observe regimes where the order parameter decays to zero ("phase I"), assumes a non-equilibrium steady-state value ("phase II"), or exhibits persistent oscillations ("phase III") in the form of a self-generated Floquet phase. The capability to emulate these dynamical phases in optical cavities without real Cooper pairs demonstrates that programmable simulators can overcome many challenges faced by traditional approaches. This opens up exciting prospects for quantum simulation, including the potential to engineer unconventional superconductors and to probe beyond mean-field effects like the spectral form factor, and for increasing coherence time for quantum sensing.Comment: Main Text with Supporting Material, 18 pages, 10 figure

Reducing congestion in obstructed highways with traffic data dissemination using adhoc vehicular networks

Vehicle-to-vehicle communications can be used effectively for intelligent transport systems (ITSs) and location-aware services. The ability to disseminate information in an ad hoc fashion allows pertinent information to propagate faster through a network. In the realm of ITS, the ability to spread warning information faster and further is of great advantage to receivers. In this paper we propose and present a message-dissemination procedure that uses vehicular wireless protocols to influence vehicular flow, reducing congestion in road networks. The computational experiments we present show how a car-following model and lane-change algorithm can be adapted to “react” to the reception of information. This model also illustrates the advantages of coupling together with vehicular flow modelling tools and network simulation tools

The Nucleus of Comet 9P-Tempel 1: Shape and Geology from Two Flybys

The nucleus of comet Tempel 1 has been investigated at close range during two spacecraft missions separated by one comet orbit of the Sun, 5 1/2 years. The combined imaging covers 70% of the surface of this object which has a mean radius of 2.83 +/- 0.1 km. The surface can be divided into two terrain types: rough, pitted terrain and smoother regions of varying local topography. The rough surface has round depressions from resolution limits (10 m/pixel) up to 1 km across, spanning forms from crisp steep-walled pits, to subtle albedo rings, to topographic rings, with all ranges of morphologic gradation. Three gravitationally low regions of the comet have smoother terrain, parts of which appear to be deposits from minimally modified flows, with other parts likely to be heavily eroded portions of multiple layer piles. Changes observed between the two missions are primarily due to backwasting of scarps bounding one of these probable flow deposits. This style of erosion is also suggested by remnant mesa forms in other areas of smoother terrain. The two distinct terrains suggest either an evolutionary change in processes, topographically- controlled processes, or a continuing interaction of erosion and deposition

A Search for Additional Planets in the NASA EPOXI Observations of the Exoplanet System GJ 436

We present time series photometry of the M dwarf transiting exoplanet system GJ 436 obtained with the the EPOCh (Extrasolar Planet Observation and Characterization) component of the NASA EPOXI mission. We conduct a search of the high-precision time series for additional planets around GJ 436, which could be revealed either directly through their photometric transits, or indirectly through the variations these second planets induce on the transits of the previously known planet. In the case of GJ 436, the presence of a second planet is perhaps indicated by the residual orbital eccentricity of the known hot Neptune companion. We find no candidate transits with significance higher than our detection limit. From Monte Carlo tests of the time series, we rule out transiting planets larger than 1.5 R_Earth interior to GJ 436b with 95% confidence, and larger than 1.25 R_Earth with 80% confidence. Assuming coplanarity of additional planets with the orbit of GJ 436b, we cannot expect that putative planets with orbital periods longer than about 3.4 days will transit. However, if such a planet were to transit, we rule out planets larger than 2.0 R_Earth with orbital periods less than 8.5 days with 95% confidence. We also place dynamical constraints on additional bodies in the GJ 436 system. Our analysis should serve as a useful guide for similar analyses for which radial velocity measurements are not available, such as those discovered by the Kepler mission. These dynamical constraints on additional planets with periods from 0.5 to 9 days rule out coplanar secular perturbers as small as 10 M_Earth and non-coplanar secular perturbers as small as 1 M_Earth in orbits close in to GJ 436b. We present refined estimates of the system parameters for GJ 436. We also report a sinusoidal modulation in the GJ 436 light curve that we attribute to star spots. [Abridged]Comment: 29 pages, 8 figures, 3 tables, accepted for publication in Ap

Hydrologic Variability Affects Invertebrate Grazing on Phototrophic Biofilms in Stream Microcosms

The temporal variability of streamflow is known to be a key feature structuring and controlling fluvial ecological communities and ecosystem processes. Although alterations of streamflow regime due to habitat fragmentation or other anthropogenic factors are ubiquitous, a quantitative understanding of their implications on ecosystem structure and function is far from complete. Here, by experimenting with two contrasting flow regimes in stream microcosms, we provide a novel mechanistic explanation for how fluctuating flow regimes may affect grazing of phototrophic biofilms (i.e., periphyton) by an invertebrate species (Ecdyonurus sp.). In both flow regimes light availability was manipulated as a control on autotroph biofilm productivity and grazer activity, thereby allowing the test of flow regime effects across various ratios of biofilm biomass to grazing activity. Average grazing rates were significantly enhanced under variable flow conditions and this effect was highest at intermediate light availability. Our results suggest that stochastic flow regimes, characterised by suitable fluctuations and temporal persistence, may offer increased windows of opportunity for grazing under favourable shear stress conditions. This bears important implications for the development of comprehensive schemes for water resources management and for the understanding of trophic carbon transfer in stream food webs

Streptococcus uberis strains isolated from the bovine mammary gland evade immune recognition by mammary epithelial cells, but not of macrophages

Streptococcus uberis is frequently isolated from the mammary gland of dairy cattle. Infection with some strains can induce mild subclinical inflammation whilst others induce severe inflammation and clinical mastitis. We compared here the inflammatory response of primary cultures of bovine mammary epithelial cells (pbMEC) towards S. uberis strains collected from clinical or subclinical cases (seven strains each) of mastitis with the strong response elicited by Escherichia coli. Neither heat inactivated nor live S. uberis induced the expression of 10 key immune genes (including TNF, IL1B, IL6). The widely used virulent strain 0140J and the avirulent strain, EF20 elicited similar responses; as did mutants defective in capsule (hasA) or biofilm formation (sub0538 and sub0539). Streptococcus uberis failed to activate NF-κB in pbMEC or TLR2 in HEK293 cells, indicating that S. uberis particles did not induce any TLR-signaling in MEC. However, preparations of lipoteichoic acid (LTA) from two strains strongly induced immune gene expression and activated NF-κB in pbMEC, without the involvement of TLR2. The immune-stimulatory LTA must be arranged in the intact S. uberis such that it is unrecognizable by the relevant pathogen receptors of the MEC. The absence of immune recognition is specific for MEC, since the same S. uberis preparations strongly induced immune gene expression and NF-κB activity in the murine macrophage model cell RAW264.7. Hence, the sluggish immune response of MEC and not of professional immune cells to this pathogen may aid establishment of the often encountered belated and subclinical phenotype of S. uberis mastitis

Discovery and Mass Measurements of a Cold, 10-Earth Mass Planet and Its Host Star

We present the discovery and mass measurement of the cold, low-mass planet MOA-2009-BLG-266Lb, made with the gravitational microlensing method. This planet has a mass of m_p = 10.4 +- 1.7 Earth masses and orbits a star of mass M_* = 0.56 +- 0.09 Solar masses at a semi-major axis of a = 3.2 (+1.9 -0.5) AU and an orbital period of P = 7.6 (+7.7 -1.5} yrs. The planet and host star mass measurements are enabled by the measurement of the microlensing parallax effect, which is seen primarily in the light curve distortion due to the orbital motion of the Earth. But, the analysis also demonstrates the capability to measure microlensing parallax with the Deep Impact (or EPOXI) spacecraft in a Heliocentric orbit. The planet mass and orbital distance are similar to predictions for the critical core mass needed to accrete a substantial gaseous envelope, and thus may indicate that this planet is a "failed" gas giant. This and future microlensing detections will test planet formation theory predictions regarding the prevalence and masses of such planets.Comment: 38 pages with 7 figure