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

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

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

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

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

Scheduling over Scenarios on Two Machines

We consider scheduling problems over scenarios where the goal is to find a single assignment of the jobs to the machines which performs well over all possible scenarios. Each scenario is a subset of jobs that must be executed in that scenario and all scenarios are given explicitly. The two objectives that we consider are minimizing the maximum makespan over all scenarios and minimizing the sum of the makespans of all scenarios. For both versions, we give several approximation algorithms and lower bounds on their approximability. With this research into optimization problems over scenarios, we have opened a new and rich field of interesting problems.Comment: To appear in COCOON 2014. The final publication is available at link.springer.co