Improved Algorithms for Decremental Single-Source Reachability on Directed Graphs

Recently we presented the first algorithm for maintaining the set of nodes reachable from a source node in a directed graph that is modified by edge deletions with $o(mn)$ total update time, where $m$ is the number of edges and $n$ is the number of nodes in the graph [Henzinger et al. STOC 2014]. The algorithm is a combination of several different algorithms, each for a different $m$ vs. $n$ trade-off. For the case of $m = \Theta(n^{1.5})$ the running time is $O(n^{2.47})$, just barely below $mn = \Theta(n^{2.5})$. In this paper we simplify the previous algorithm using new algorithmic ideas and achieve an improved running time of $\tilde O(\min(m^{7/6} n^{2/3}, m^{3/4} n^{5/4 + o(1)}, m^{2/3} n^{4/3+o(1)} + m^{3/7} n^{12/7+o(1)}))$. This gives, e.g., $O(n^{2.36})$ for the notorious case $m = \Theta(n^{1.5})$. We obtain the same upper bounds for the problem of maintaining the strongly connected components of a directed graph undergoing edge deletions. Our algorithms are correct with high probabililty against an oblivious adversary.Comment: This paper was presented at the International Colloquium on Automata, Languages and Programming (ICALP) 2015. A full version combining the findings of this paper and its predecessor [Henzinger et al. STOC 2014] is available at arXiv:1504.0795

Coupled Atomic Wires in a Synthetic Magnetic Field

We propose and study systems of coupled atomic wires in a perpendicular synthetic magnetic field as a platform to realize exotic phases of quantum matter. This includes (fractional) quantum Hall states in arrays of many wires inspired by the pioneering work [Kane et al. PRL {\bf{88}}, 036401 (2002)], as well as Meissner phases and Vortex phases in double-wires. With one continuous and one discrete spatial dimension, the proposed setup naturally complements recently realized discrete counterparts, i.e. the Harper-Hofstadter model and the two leg flux ladder, respectively. We present both an in-depth theoretical study and a detailed experimental proposal to make the unique properties of the semi-continuous Harper-Hofstadter model accessible with cold atom experiments. For the minimal setup of a double-wire, we explore how a sub-wavelength spacing of the wires can be implemented. This construction increases the relevant energy scales by at least an order of magnitude compared to ordinary optical lattices, thus rendering subtle many-body phenomena such as Lifshitz transitions in Fermi gases observable in an experimentally realistic parameter regime. For arrays of many wires, we discuss the emergence of Chern bands with readily tunable flatness of the dispersion and show how fractional quantum Hall states can be stabilized in such systems. Using for the creation of optical potentials Laguerre-Gauss beams that carry orbital angular momentum, we detail how the coupled atomic wire setups can be realized in non-planar geometries such as cylinders, discs, and tori

Numerical Computation of Dynamically Important Excited States of Many-Body Systems

We present an extension of the time-dependent Density Matrix Renormalization Group (t-DMRG), also known as Time Evolving Block Decimation algorithm (TEBD), allowing for the computation of dynamically important excited states of one-dimensional many-body systems. We show its practical use for analyzing the dynamical properties and excitations of the Bose-Hubbard model describing ultracold atoms loaded in an optical lattice from a Bose-Einstein condensate. This allows for a deeper understanding of nonadiabaticity in experimental realizations of insulating phases.Comment: Expanded version (12pp. 13 figures

Dynamics of cold bosons in optical lattices: Effects of higher Bloch bands

The extended effective multiorbital Bose-Hubbard-type Hamiltonian which takes into account higher Bloch bands, is discussed for boson systems in optical lattices, with emphasis on dynamical properties, in relation with current experiments. It is shown that the renormalization of Hamiltonian parameters depends on the dimension of the problem studied. Therefore, mean field phase diagrams do not scale with the coordination number of the lattice. The effect of Hamiltonian parameters renormalization on the dynamics in reduced one-dimensional optical lattice potential is analyzed. We study both the quasi-adiabatic quench through the superfluid-Mott insulator transition and the absorption spectroscopy, that is energy absorption rate when the lattice depth is periodically modulated.Comment: 23 corrected interesting pages, no Higgs boson insid

A new generation of inland modular vessels for polish east-west waterways with low depth

A new generation of inland environmentally friendly ships destined for waterways with critical limited depth is presented. General project concepts are supported by push system idea of standardized, optional equipped hulls for desirable exploitation necessities. A few traditional motor ships and barges are described as the background for comparison

Selected Issues Concerning the Use of Computational Techniques in the Design of Steel Pillars Subsequently Exposed to a Fire

Cel: Celem artykułu jest wskazanie możliwości wykorzystania dostępnych, zaawansowanych narzędzi numerycznych do wirtualnego testowania konstrukcji poddanych oddziaływaniom symulowanego pożaru. Przy poprawnie skalibrowanym modelu obliczeniowym, testy przeniesione na platformę wirtualną mogą stanowić wiarygodną alternatywę dla tradycyjnych, kosztownych metod badawczych, w szczególności badań doświadczalnych konstrukcji w skali naturalnej. Wprowadzenie: Modelowanie słupów stalowych w warunkach pożaru napotyka poważne trudności z uwagi na problemy z dopasowaniem i właściwą kalibracją modelu numerycznego w sposób zapewniający jak najlepsze odwzorowanie warunków pracy, zbliżonych do tych, w jakich znajduje się rzeczywista konstrukcja. W trakcie pożaru, w elementach nośnych (słupach, ryglach) rzeczywistej konstrukcji, przesztywnionej w sposób naturalny elementami doń dochodzącymi generują się dodatkowe siły wewnętrzne, trudne do przewidzenia i których wielkość zależy od sztywności elementów zbiegających się w węzłach, sposobu ich deformacji, rozkładu pól temperatury itp. Ograniczenie zarówno przemieszczeniowych, jak i obrotowych stopni swobody wywołuje dodatkowe obciążenie, które w połączeniu ze zmniejszoną (na skutek działania podwyższonej temperatury) sztywnością elementu może powodować jego wcześniejsze wyboczenie i tym samym – zmniejszenie jego odporności pożarowej, często poniżej poziomu wymaganego odpowiednimi przepisami techniczno-budowlanymi. Metodyka: W niniejszym opracowaniu zaprezentowano wyniki analiz i symulacji numerycznych przeprowadzonych z uwzględnieniem nieliniowego charakteru zjawisk. W pracy położono nacisk na doskonalenie przyjętego modelu obliczeniowego, jego weryfikację i wielokryterialną walidację. W analizach uwzględniono kilka wariantów warunków brzegowych – zarówno termicznych, jak i mechanicznych. Wyniki analiz porównano z wynikami autentycznych badań laboratoryjnych przeprowadzonych w Uniwersytecie Ulster we współpracy z Uniwersytetem w Sheffield (Wielka Brytania), które wykorzystano do walidacji modelu numerycznego. Wnioski: Ciągły rozwój technik obliczeniowych stwarza możliwości wykorzystania w analizie konstrukcji budowlanych nowoczesnych metod i narzędzi komputerowych, pozwalających na prowadzenie zaawansowanych analiz termo-mechanicznych. Dostępne narzędzia numeryczne umożliwiają dokładną ocenę przyrostu temperatury elementów konstrukcyjnych z równoczesną analizą wpływu warunków środowiska na mechaniczną odpowiedź konstrukcji. Na obecnym etapie stosowanie tego typu technik obliczeniowych wymaga, poza umiejętnościami obsługi skomplikowanych, komercyjnych narzędzi komputerowych, także zaawansowanej, gruntownej wiedzy teoretycznej. Przeprowadzone analizy wykazały, jak pozornie nieistotne i trudne do uchwycenia błędy modelowe mogą wpływać na jakość uzyskanych wyników.Aim: The purpose of this study is identification of accessible advanced computational tools to facilitate virtual testing of structures exposed to the thermal action of fire. With correctly calibrated numeric models, structure tests transferred to a virtual platform can provide a credible alternative to traditional costly research methods, particularly experimental research performed on actual scale constructions. Introduction: The modelling process for steel pillars exposed to action of a fire faces serious difficulties because of problems involving matching and proper calibration of the numeric model to ensure the best possible reproduction of working conditions, similar to those in the actual environment. During a fire incident, additional internal forces are generated, which are difficult to predict, culminating in deformation of pillars and adjoining structure elements. Axial and rotational restraints can produce significant loadings which, together with reduced rigidity caused by thermal action, may cause premature buckling of pillars, often below accepted parameters required by relevant building regulations, and reduce pillars’ resistance to the consequence of fire. Methodology: The paper reveals results from an analysis and performed numeric simulations, and takes account of the non-linear character of outcomes. The paper provides a focus on the development of a selected numeric model, its verification and validation. The analysis includes several variations of boundary conditions covering thermal as well as mechanical issues. For validation purposes, the numeric prediction of structural reaction during heating was compared with published experimental data for tests performed at the University of Ulster in collaboration with the University of Sheffield, UK. Conclusions: The continuous development of computational techniques provides opportunities in the application of modern techniques and computer technology for performing advanced structural-thermal analysis for building structures. Available numeric tools allow for an accurate assessment of temperature increases in structures. Simultaneously, they facilitate an examination of influences caused by environmental conditions on the mechanical reaction of structures. In order to use such a computational technique a prerequisite lies in the ability to manipulate complex commercial software. Additionally, it is necessary to have advanced and in depth theoretical knowledge of the topic. Examination by authors reveal how seemingly insignificant and difficult to identify modelling errors can affect the quality of final results

Stochastic graph exploration

Exploring large-scale networks is a time consuming and expensive task which is usually operated in a complex and uncertain environment. A crucial aspect of network exploration is the development of suitable strategies that decide which nodes and edges to probe at each stage of the process. To model this process, we introduce the stochastic graph exploration problem. The input is an undirected graph G = (V, E) with a source vertex s, stochastic edge costs drawn from a distribution πe, e ∈ E, and rewards on vertices of maximum value R. The goal is to find a set F of edges of total cost at most B such that the subgraph of G induced by F is connected, contains s, and maximizes the total reward. This problem generalizes the stochastic knapsack problem and other stochastic probing problems recently studied. Our focus is on the development of efficient nonadaptive strategies that are competitive against the optimal adaptive strategy. A major challenge is the fact that the problem has an Ω(n) adaptivity gap even on a tree of n vertices. This is in sharp contrast with O(1) adaptivity gap of the stochastic knapsack problem, which is a special case of our problem. We circumvent this negative result by showing that O(log nR) resource augmentation suffices to obtain O(1) approximation on trees and O(log nR) approximation on general graphs. To achieve this result, we reduce stochastic graph exploration to a memoryless process - the minesweeper problem - which assigns to every edge a probability that the process terminates when the edge is probed. For this problem, interesting in its own, we present an optimal polynomial time algorithm on trees and an O(log nR) approximation for general graphs. We study also the problem in which the maximum cost of an edge is a logarithmic fraction of the budget. We show that under this condition, there exist polynomial-time oblivious strategies that use 1 + budget, whose adaptivity gaps on trees and general graphs are 1 + and 8 + , respectively. Finally, we provide additional results on the structure and the complexity of nonadaptive and adaptive strategies