A 7/9 - Approximation Algorithm for the Maximum Traveling Salesman Problem

We give a 7/9 - Approximation Algorithm for the Maximum Traveling Salesman Problem.Comment: 6 figure

Truthful Mechanisms for Matching and Clustering in an Ordinal World

We study truthful mechanisms for matching and related problems in a partial information setting, where the agents' true utilities are hidden, and the algorithm only has access to ordinal preference information. Our model is motivated by the fact that in many settings, agents cannot express the numerical values of their utility for different outcomes, but are still able to rank the outcomes in their order of preference. Specifically, we study problems where the ground truth exists in the form of a weighted graph of agent utilities, but the algorithm can only elicit the agents' private information in the form of a preference ordering for each agent induced by the underlying weights. Against this backdrop, we design truthful algorithms to approximate the true optimum solution with respect to the hidden weights. Our techniques yield universally truthful algorithms for a number of graph problems: a 1.76-approximation algorithm for Max-Weight Matching, 2-approximation algorithm for Max k-matching, a 6-approximation algorithm for Densest k-subgraph, and a 2-approximation algorithm for Max Traveling Salesman as long as the hidden weights constitute a metric. We also provide improved approximation algorithms for such problems when the agents are not able to lie about their preferences. Our results are the first non-trivial truthful approximation algorithms for these problems, and indicate that in many situations, we can design robust algorithms even when the agents may lie and only provide ordinal information instead of precise utilities.Comment: To appear in the Proceedings of WINE 201

PIERNIK mhd code - a multi-fluid, non-ideal extension of the relaxing-TVD scheme (I)

We present a new multi-fluid, grid MHD code PIERNIK, which is based on the Relaxing TVD scheme. The original scheme has been extended by an addition of dynamically independent, but interacting fluids: dust and a diffusive cosmic ray gas, described within the fluid approximation, with an option to add other fluids in an easy way. The code has been equipped with shearing-box boundary conditions, and a selfgravity module, Ohmic resistivity module, as well as other facilities which are useful in astrophysical fluid-dynamical simulations. The code is parallelized by means of the MPI library. In this paper we shortly introduce basic elements of the Relaxing TVD MHD algorithm, following Trac & Pen (2003) and Pen et al. (2003), and then focus on the conservative implementation of the shearing box model, constructed with the aid of the Masset's (2000) method. We present results of a test example of a formation of a gravitationally bounded object (planet) in a self-gravitating and differentially rotating fluid.Comment: 6 pages, 3 figures, conference proceedings of the Torun Exoplanets 200

External Potential Modifies Friction of Molecular Solutes in Water

Stokes’s law for the friction of a sphere in water has been argued to work down to molecular scales, provided the effective hydrodynamic radius includes the hydration layer. In interpretations of experiments and in theoretical models, it is tacitly assumed that the solvent friction experienced by a solute does not depend on whether an external confinement potential acts on the solute. Using a novel method to extract the friction memory function from molecular dynamics simulations, we show that the solvent friction of a strongly harmonically confined methane molecule in water increases by 60% compared to its free-solution value, which is caused by an amplification of the slowest component of the memory function. The friction enhancement occurs for potential strengths typical of physical and chemical bonds and is accompanied by a significant slowing-down of the hydration water dynamics. Thus, the solvent friction acting on molecular solutes is not determined by solvent properties and solute-solvent interactions alone but results from the coupling between solute and solvent dynamics and thereby can be tuned by an external potential acting on the solute. This also explains why simulations of positionally constrained solutes do not reproduce free-solution diffusivities. Dynamic scaling arguments suggest similar effects also for macromolecular solutes provided the solution viscosity is sufficiently enhanced

MnAs dots grown on GaN(0001)-(1x1) surface

MnAs has been grown by means of MBE on the GaN(0001)-(1x1) surface. Two options of initiating the crystal growth were applied: (a) a regular MBE procedure (manganese and arsenic were delivered simultaneously) and (b) subsequent deposition of manganese and arsenic layers. It was shown that spontaneous formation of MnAs dots with the surface density of 1$\cdot 10^{11}$ cm$^{-2}$ and $2.5\cdot 10^{11}$ cm$^{-2}$, respectively (as observed by AFM), occurred for the layer thickness higher than 5 ML. Electronic structure of the MnAs/GaN systems was studied by resonant photoemission spectroscopy. That led to determination of the Mn 3d - related contribution to the total density of states (DOS) distribution of MnAs. It has been proven that the electronic structures of the MnAs dots grown by the two procedures differ markedly. One corresponds to metallic, ferromagnetic NiAs-type MnAs, the other is similar to that reported for half-metallic zinc-blende MnAs. Both system behave superparamagnetically (as revealed by magnetization measurements), but with both the blocking temperatures and the intra-dot Curie temperatures substantially different. The intra-dot Curie temperature is about 260 K for the former system while markedly higher than room temperature for the latter one. Relations between growth process, electronic structure and other properties of the studied systems are discussed. Possible mechanisms of half-metallic MnAs formation on GaN are considered.Comment: 20+ pages, 8 figure

Rapid onset of molecular friction in liquids bridging between the atomistic and hydrodynamic pictures

Friction in liquids arises from conservative forces between molecules and atoms. Although the hydrodynamics at the nanoscale is subject of intense research and despite the enormous interest in the non-Markovian dynamics of single molecules and solutes, the onset of friction from the atomistic scale so far could not be demonstrated. Here, we fill this gap based on frequency-resolved friction data from high-precision simulations of three prototypical liquids, including water. Combining with theory, we show that friction in liquids emerges abruptly at a characteristic frequency, beyond which viscous liquids appear as non-dissipative, elastic solids. Concomitantly, the molecules experience Brownian forces that display persistent correlations. A critical test of the generalised Stokes–Einstein relation, mapping the friction of single molecules to the visco-elastic response of the macroscopic sample, disproves the relation for Newtonian fluids, but substantiates it exemplarily for water and a moderately supercooled liquid. The employed approach is suitable to yield insights into vitrification mechanisms and the intriguing mechanical properties of soft materials

Separation of Ho3+ in Static Magnetic Field

Abstract The rare earths elements (REE) belong to the group of critical metals and they are achieving more and more interest due to their special properties. However, there occur some problems connected with their production. The most difficult phase is separation of REE. It includes a necessity to intensify currently applied processes and looking for new solutions. The present work introduces an idea to use differences in physical properties of the REE ions to get them separated. In the experimental part of the work some efforts were undertaken to analyse results presenting changes of holmium ions concentration under an influence of the magnetic field gradient. There was determined the gradient of magnetic field and concentration of Ho3+ ions depending on initial concentration of the solution and time. A simulation of changing the concentration of holmium ions in the solution under an influence of the magnetic field gradient was performed to compare the mathematical model with the obtained results