Incremental Medians via Online Bidding

In the k-median problem we are given sets of facilities and customers, and distances between them. For a given set F of facilities, the cost of serving a customer u is the minimum distance between u and a facility in F. The goal is to find a set F of k facilities that minimizes the sum, over all customers, of their service costs. Following Mettu and Plaxton, we study the incremental medians problem, where k is not known in advance, and the algorithm produces a nested sequence of facility sets where the kth set has size k. The algorithm is c-cost-competitive if the cost of each set is at most c times the cost of the optimum set of size k. We give improved incremental algorithms for the metric version: an 8-cost-competitive deterministic algorithm, a 2e ~ 5.44-cost-competitive randomized algorithm, a (24+epsilon)-cost-competitive, poly-time deterministic algorithm, and a (6e+epsilon ~ .31)-cost-competitive, poly-time randomized algorithm. The algorithm is s-size-competitive if the cost of the kth set is at most the minimum cost of any set of size k, and has size at most s k. The optimal size-competitive ratios for this problem are 4 (deterministic) and e (randomized). We present the first poly-time O(log m)-size-approximation algorithm for the offline problem and first poly-time O(log m)-size-competitive algorithm for the incremental problem. Our proofs reduce incremental medians to the following online bidding problem: faced with an unknown threshold T, an algorithm submits "bids" until it submits a bid that is at least the threshold. It pays the sum of all its bids. We prove that folklore algorithms for online bidding are optimally competitive.Comment: conference version appeared in LATIN 2006 as "Oblivious Medians via Online Bidding

The Power of Centralized PC Systems of Pushdown Automata

Parallel communicating systems of pushdown automata (PCPA) were introduced in (Csuhaj-Varj{\'u} et. al. 2000) and in their centralized variants shown to be able to simulate nondeterministic one-way multi-head pushdown automata. A claimed converse simulation for returning mode (Balan 2009) turned out to be incomplete (Otto 2012) and a language was suggested for separating these PCPA of degree two (number of pushdown automata) from nondeterministic one-way two-head pushdown automata. We show that the suggested language can be accepted by the latter computational model. We present a different example over a single letter alphabet indeed ruling out the possibility of a simulation between the models. The open question about the power of centralized PCPA working in returning mode is then settled by showing them to be universal. Since the construction is possible using systems of degree two, this also improves the previous bound three for generating all recursively enumerable languages. Finally PCPAs are restricted in such a way that a simulation by multi-head automata is possible

Comment on "Conjectures on exact solution of three-dimensional (3D) simple orthorhombic Ising lattices" [arXiv:0705.1045]

It is shown that a recent article by Z.-D. Zhang [arXiv:0705.1045] is in error and violates well-known theorems.Comment: LaTeX, 3 pages, no figures, submitted to Philosophical Magazine. Expanded versio

Incremental Grid-like Layout Using Soft and Hard Constraints

We explore various techniques to incorporate grid-like layout conventions into a force-directed, constraint-based graph layout framework. In doing so we are able to provide high-quality layout---with predominantly axis-aligned edges---that is more flexible than previous grid-like layout methods and which can capture layout conventions in notations such as SBGN (Systems Biology Graphical Notation). Furthermore, the layout is easily able to respect user-defined constraints and adapt to interaction in online systems and diagram editors such as Dunnart.Comment: Accepted to Graph Drawing 201

Magnetic properties of the rapidly solidified Gd3Zr10Fe55Co10Mo5W2B15 alloy

Studies of magnetic properties for the Gd3Zr10Fe55Co10Mo5W2B15 glassy alloy are presented. The morphous structure of melt-spun ribbon of investigated alloy was confirmed by X-ray diffractometry. The Curie temperature TC was determined analyzing M(H) dependences measured at various temperatures as well as from M(T) dependence measured at low constant magnetic field. Furthermore, the isothermal magnetic entropy changes j SMj were calculated from the magnetization curves to assess the possibility of potential application of studied samples as active elements in magnetic refrigerators

Temporal decorrelation of collective oscillations in neural networks with local inhibition and long-range excitation

We consider two neuronal networks coupled by long-range excitatory interactions. Oscillations in the gamma frequency band are generated within each network by local inhibition. When long-range excitation is weak, these oscillations phase-lock with a phase-shift dependent on the strength of local inhibition. Increasing the strength of long-range excitation induces a transition to chaos via period-doubling or quasi-periodic scenarios. In the chaotic regime oscillatory activity undergoes fast temporal decorrelation. The generality of these dynamical properties is assessed in firing-rate models as well as in large networks of conductance-based neurons.Comment: 4 pages, 5 figures. accepted for publication in Physical Review Letter

First, do no harm - Missing data treatment to support lake ecological condition assessment

Indicators of ecological condition status of water bodies associated with field measurements are often subject to data gaps. This obstacle can often lead to abandonment of assessment. Furthermore, it can lead to the use of methods, based merely on their availability. In response to these challenges, a systematic approach for expert-analyst interaction for missing data treatment is proposed. A combination of algorithms with hierarchical clustering of results is used. A particular emphasis is put on the preparation and interpretation of input data and the role of an expert in the workflow. The proposed approach enhances the decision-making process by improving communication and transparency throughout interactions between experts, analysts and decision makers. Future research should focus on assessing the scale of the ecological data drift phenomenon, which, based on the observed climate change, anthropological pressure and biodiversity loss, may impact the broad concept of indicator construction for lake water ecological assessmen

Comparison of various models of Monte Carlo geant 4 code in simulations of prompt gamma production

In this paper, results of simulations of the gamma-ray production in reactions with 70 MeV protons in a target of PMMA are presented. The data obtained by means of two versions of Geant 4 software, 9.3 and 10.01, have shown significant differences in the gamma-ray spectra. The comparison between the calculated spectra and the measured ones has been carried out. The tested versions do not give satisfactory agreement with the experimental result. The reason of the performed verification was the planned application of this simulation toolkit for the preparation of in vivo dosimetry based on the prompt gamma-ray measurements for the proton therapy

Online Multi-Coloring with Advice

We consider the problem of online graph multi-coloring with advice. Multi-coloring is often used to model frequency allocation in cellular networks. We give several nearly tight upper and lower bounds for the most standard topologies of cellular networks, paths and hexagonal graphs. For the path, negative results trivially carry over to bipartite graphs, and our positive results are also valid for bipartite graphs. The advice given represents information that is likely to be available, studying for instance the data from earlier similar periods of time.Comment: IMADA-preprint-c

Microstructural and magnetic characterization of Ni0.5Zn0.5Fe2O4 ferrite nanoparticles

International audienc