19,772 research outputs found
Lower bounds for several online variants of bin packing
We consider several previously studied online variants of bin packing and
prove new and improved lower bounds on the asymptotic competitive ratios for
them. For that, we use a method of fully adaptive constructions. In particular,
we improve the lower bound for the asymptotic competitive ratio of online
square packing significantly, raising it from roughly 1.68 to above 1.75.Comment: WAOA 201
Late-Time Convection in the Collapse of a 23 Solar Mass Star
The results of a 3-dimensional SNSPH simulation of the core collapse of a 23
solar mass star are presented. This simulation did not launch an explosion
until over 600ms after collapse, allowing an ideal opportunity to study the
evolution and structure of the convection below the accretion shock to late
times. This late-time convection allows us to study several of the recent
claims in the literature about the role of convection: is it dominated by an
l=1 mode driven by vortical-acoustic (or other) instability, does it produce
strong neutron star kicks, and, finally, is it the key to a new explosion
mechanism? The convective region buffets the neutron star, imparting a 150-200
km/s kick. Because the l=1 mode does not dominate the convection, the neutron
star does not achieve large (>450 km/s) velocities. Finally, the neutron star
in this simulation moves, but does not develop strong oscillations, the energy
source for a recently proposed supernova engine. We discuss the implications
these results have on supernovae, hypernovae (and gamma-ray bursts), and
stellar-massed black holes.Comment: 31 pages (including 13 figures), submitted to Ap
Studies on mouse Moloney virus induced tumours: I. The detection of p30 as a cytotoxic target on murine Moloney leukaemic spleen cells, and on an in vitro Moloney sarcoma line by antibody mediated cytotoxicity.
Antigenic determinants of p30, the most abundant internal virion protein of C type RNA viruses, were detected on the surface of spleen cells from mice bearing Moloney leukaemia and on an in vitro line of Moloney sarcoma, MSC. On both cell types, these determinants on the p30 molecules served as cytotoxic targets in a xenogenic complement dependent antibody mediated 51Cr release assay. Two antisera were used: a rat anti MLV -M induced lymphoma serum, and an antiserum raised in goats to either disrupted FeLV. The cytotoxic target antigens of these antisera were analysed by inhibition of cytotoxicity with viral and cellular proteins
The (weighted) metric dimension of graphs : hard and easy cases
Given an input undirected graph G=(V,E), we say that a vertex l separates u from v (where u,v ¿ V) if the distance between u and l differs from the distance from v to l. A set of vertices L¿V is a feasible solution if for every pair of vertices, u,v ¿ V (u¿v), there is a vertex l ¿ L that separates u from v. Such a feasible solution is called a landmark set, and the metric dimension of a graph is the minimum cardinality of a landmark set. Here, we extend this well-studied problem to the case where each vertex v has a non-negative cost, and the goal is to find a feasible solution with a minimum total cost. This weighted version is NP-hard since the unweighted variant is known to be NP-hard. We show polynomial time algorithms for the cases where G is a path, a tree, a cycle, a cograph, a k-edge-augmented tree (that is, a tree with additional k edges) for a constant value of k, and a (not necessarily complete) wheel. The results for paths, trees, cycles, and complete wheels extend known polynomial time algorithms for the unweighted version, whereas the other results are the first known polynomial time algorithms for these classes of graphs even for the unweighted version. Next, we extend the set of graph classes for which computing the unweighted metric dimension of a graph is known to be NP-hard. We show that for split graphs, bipartite graphs, co-bipartite graphs, and line graphs of bipartite graphs, the problem of computing the unweighted metric dimension of the graph is NP-hard
Online unit clustering in higher dimensions
We revisit the online Unit Clustering and Unit Covering problems in higher
dimensions: Given a set of points in a metric space, that arrive one by
one, Unit Clustering asks to partition the points into the minimum number of
clusters (subsets) of diameter at most one; while Unit Covering asks to cover
all points by the minimum number of balls of unit radius. In this paper, we
work in using the norm.
We show that the competitive ratio of any online algorithm (deterministic or
randomized) for Unit Clustering must depend on the dimension . We also give
a randomized online algorithm with competitive ratio for Unit
Clustering}of integer points (i.e., points in , , under norm). We show that the competitive ratio of
any deterministic online algorithm for Unit Covering is at least . This
ratio is the best possible, as it can be attained by a simple deterministic
algorithm that assigns points to a predefined set of unit cubes. We complement
these results with some additional lower bounds for related problems in higher
dimensions.Comment: 15 pages, 4 figures. A preliminary version appeared in the
Proceedings of the 15th Workshop on Approximation and Online Algorithms (WAOA
2017
Energy Density-Flux Correlations in an Unusual Quantum State and in the Vacuum
In this paper we consider the question of the degree to which negative and
positive energy are intertwined. We examine in more detail a previously studied
quantum state of the massless minimally coupled scalar field, which we call a
``Helfer state''. This is a state in which the energy density can be made
arbitrarily negative over an arbitrarily large region of space, but only at one
instant in time. In the Helfer state, the negative energy density is
accompanied by rapidly time-varying energy fluxes. It is the latter feature
which allows the quantum inequalities, bounds which restrict the magnitude and
duration of negative energy, to hold for this class of states. An observer who
initially passes through the negative energy region will quickly encounter
fluxes of positive energy which subsequently enter the region. We examine in
detail the correlation between the energy density and flux in the Helfer state
in terms of their expectation values. We then study the correlation function
between energy density and flux in the Minkowski vacuum state, for a massless
minimally coupled scalar field in both two and four dimensions. In this latter
analysis we examine correlation functions rather than expectation values.
Remarkably, we see qualitatively similar behavior to that in the Helfer state.
More specifically, an initial negative energy vacuum fluctuation in some region
of space is correlated with a subsequent flux fluctuation of positive energy
into the region. We speculate that the mechanism which ensures that the quantum
inequalities hold in the Helfer state, as well as in other quantum states
associated with negative energy, is, at least in some sense, already
``encoded'' in the fluctuations of the vacuum.Comment: 21 pages, 7 figures; published version with typos corrected and one
added referenc
Pedestrian Trajectory Prediction with Structured Memory Hierarchies
This paper presents a novel framework for human trajectory prediction based
on multimodal data (video and radar). Motivated by recent neuroscience
discoveries, we propose incorporating a structured memory component in the
human trajectory prediction pipeline to capture historical information to
improve performance. We introduce structured LSTM cells for modelling the
memory content hierarchically, preserving the spatiotemporal structure of the
information and enabling us to capture both short-term and long-term context.
We demonstrate how this architecture can be extended to integrate salient
information from multiple modalities to automatically store and retrieve
important information for decision making without any supervision. We evaluate
the effectiveness of the proposed models on a novel multimodal dataset that we
introduce, consisting of 40,000 pedestrian trajectories, acquired jointly from
a radar system and a CCTV camera system installed in a public place. The
performance is also evaluated on the publicly available New York Grand Central
pedestrian database. In both settings, the proposed models demonstrate their
capability to better anticipate future pedestrian motion compared to existing
state of the art.Comment: To appear in ECML-PKDD 201
The VCG Mechanism for Bayesian Scheduling
We study the problem of scheduling m tasks to n selfish, unrelated machines in order to minimize the makespan, in which the execution times are independent random variables, identical across machines. We show that the VCG mechanism, which myopically allocates each task to its best machine, achieves an approximation ratio of O(ln n&frac; ln ln n). This improves significantly on the previously best known bound of O(m/n) for prior-independent mechanisms, given by Chawla et al. [7] under the additional assumption of Monotone Hazard Rate (MHR) distributions. Although we demonstrate that this is tight in general, if we do maintain the MHR assumption, then we get improved, (small) constant bounds for m ≥ n ln n i.i.d. tasks. We also identify a sufficient condition on the distribution that yields a constant approximation ratio regardless of the number of tasks
A Superluminal Subway: The Krasnikov Tube
The ``warp drive'' metric recently presented by Alcubierre has the problem
that an observer at the center of the warp bubble is causally separated from
the outer edge of the bubble wall. Hence such an observer can neither create a
warp bubble on demand nor control one once it has been created. In addition,
such a bubble requires negative energy densities. One might hope that
elimination of the first problem might ameliorate the second as well. We
analyze and generalize a metric, originally proposed by Krasnikov for two
spacetime dimensions, which does not suffer from the first difficulty. As a
consequence, the Krasnikov metric has the interesting property that although
the time for a one-way trip to a distant star cannot be shortened, the time for
a round trip, as measured by clocks on Earth, can be made arbitrarily short. In
our four dimensional extension of this metric, a ``tube'' is constructed along
the path of an outbound spaceship, which connects the Earth and the star.
Inside the tube spacetime is flat, but the light cones are opened out so as to
allow superluminal travel in one direction. We show that, although a single
Krasnikov tube does not involve closed timelike curves, a time machine can be
constructed with a system of two non-overlapping tubes. Furthermore, it is
demonstrated that Krasnikov tubes, like warp bubbles and traversable wormholes,
also involve unphysically thin layers of negative energy density, as well as
large total negative energies, and therefore probably cannot be realized in
practice.Comment: 20 pages, LATEX, 5 eps figures, uses \eps
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