@article{2129, abstract = {This paper continues the investigation of `Wasserstein-like' transportation distances for probability measures on discrete sets. We prove that the discrete transportation metrics on the d-dimensional discrete torus with mesh size 1/N converge, when Nā†’āˆž, to the standard 2-Wasserstein distance W_2 on the continuous torus in the sense of Gromov-Hausdorff. This is the first convergence result for the recently developed discrete transportation metrics. The result shows the compatibility between these metrics and the well-established 2-Wasserstein metric. }, author = {Gigli, Nicola and Jan Maas}, journal = {SIAM Journal on Mathematical Analysis}, number = {2}, pages = {879 -- 899}, publisher = {Society for Industrial and Applied Mathematics }, title = {{Gromov-Hausdorff convergence of discrete transportation metrics}}, doi = {10.1137/120886315 }, volume = {45}, year = {2013}, } @article{2139, abstract = {Recently it has been shown that pairs of atoms can form metastable bonds due to non-conservative forces induced by dissipation [Lemeshko&Weimer, Nature Comm. 4, 2230 (2013)]. Here we study the dynamics of interaction-induced coherent population trapping - the process responsible for the formation of dissipatively bound molecules. We derive the effective dissipative potentials induced between ultracold atoms by laser light, and study the time evolution of the scattering states. We demonstrate that binding occurs on short timescales of ~10 microseconds, even if the initial kinetic energy of the atoms significantly exceeds the depth of the dissipative potential. Dissipatively-bound molecules with preordained bond lengths and vibrational wavefunctions can be created and detected in current experiments with ultracold atoms.}, author = {Mikhail Lemeshko}, journal = {Frontiers Physics}, number = {17}, publisher = {Frontiers Media}, title = {{Manipulating scattering of ultracold atoms with light-induced dissipation}}, doi = {10.3389/fphy.2013.00017}, volume = {1}, year = {2013}, } @inproceedings{2181, abstract = {There is a trade-off between performance and correctness in implementing concurrent data structures. Better performance may be achieved at the expense of relaxing correctness, by redefining the semantics of data structures. We address such a redefinition of data structure semantics and present a systematic and formal framework for obtaining new data structures by quantitatively relaxing existing ones. We view a data structure as a sequential specification S containing all "legal" sequences over an alphabet of method calls. Relaxing the data structure corresponds to defining a distance from any sequence over the alphabet to the sequential specification: the k-relaxed sequential specification contains all sequences over the alphabet within distance k from the original specification. In contrast to other existing work, our relaxations are semantic (distance in terms of data structure states). As an instantiation of our framework, we present two simple yet generic relaxation schemes, called out-of-order and stuttering relaxation, along with several ways of computing distances. We show that the out-of-order relaxation, when further instantiated to stacks, queues, and priority queues, amounts to tolerating bounded out-of-order behavior, which cannot be captured by a purely syntactic relaxation (distance in terms of sequence manipulation, e.g. edit distance). We give concurrent implementations of relaxed data structures and demonstrate that bounded relaxations provide the means for trading correctness for performance in a controlled way. The relaxations are monotonic which further highlights the trade-off: increasing k increases the number of permitted sequences, which as we demonstrate can lead to better performance. Finally, since a relaxed stack or queue also implements a pool, we actually have new concurrent pool implementations that outperform the state-of-the-art ones.}, author = {Henzinger, Thomas A and Kirsch, Christoph and Payer, Hannes and Sezgin, Ali and Sokolova, Ana}, booktitle = {Proceedings of the 40th annual ACM SIGPLAN-SIGACT symposium on Principles of programming language}, isbn = {978-1-4503-1832-7}, location = {Rome, Italy}, pages = {317 -- 328}, publisher = {ACM}, title = {{Quantitative relaxation of concurrent data structures}}, doi = {10.1145/2429069.2429109}, year = {2013}, } @inproceedings{2182, abstract = {We propose a general framework for abstraction with respect to quantitative properties, such as worst-case execution time, or power consumption. Our framework provides a systematic way for counter-example guided abstraction refinement for quantitative properties. The salient aspect of the framework is that it allows anytime verification, that is, verification algorithms that can be stopped at any time (for example, due to exhaustion of memory), and report approximations that improve monotonically when the algorithms are given more time. We instantiate the framework with a number of quantitative abstractions and refinement schemes, which differ in terms of how much quantitative information they keep from the original system. We introduce both state-based and trace-based quantitative abstractions, and we describe conditions that define classes of quantitative properties for which the abstractions provide over-approximations. We give algorithms for evaluating the quantitative properties on the abstract systems. We present algorithms for counter-example based refinements for quantitative properties for both state-based and segment-based abstractions. We perform a case study on worst-case execution time of executables to evaluate the anytime verification aspect and the quantitative abstractions we proposed.}, author = {Cerny, Pavol and Henzinger, Thomas A and Radhakrishna, Arjun}, booktitle = {Proceedings of the 40th annual ACM SIGPLAN-SIGACT symposium on Principles of programming language}, location = {Rome, Italy}, pages = {115 -- 128}, publisher = {ACM}, title = {{Quantitative abstraction refinement}}, doi = {10.1145/2429069.2429085}, year = {2013}, } @inproceedings{2209, abstract = {A straight skeleton is a well-known geometric structure, and several algorithms exist to construct the straight skeleton for a given polygon or planar straight-line graph. In this paper, we ask the reverse question: Given the straight skeleton (in form of a planar straight-line graph, with some rays to infinity), can we reconstruct a planar straight-line graph for which this was the straight skeleton? We show how to reduce this problem to the problem of finding a line that intersects a set of convex polygons. We can find these convex polygons and all such lines in $O(nlog n)$ time in the Real RAM computer model, where $n$ denotes the number of edges of the input graph. We also explain how our approach can be used for recognizing Voronoi diagrams of points, thereby completing a partial solution provided by Ash and Bolker in 1985. }, author = {Biedl, Therese and Held, Martin and Huber, Stefan}, location = {St. Petersburg, Russia}, pages = {37 -- 46}, publisher = {IEEE}, title = {{Recognizing straight skeletons and Voronoi diagrams and reconstructing their input}}, doi = {10.1109/ISVD.2013.11}, year = {2013}, } @article{2204, abstract = {We introduce a new platform for quantum simulation of many-body systems based on nonspherical atoms or molecules with zero dipole moments but possessing a significant value of electric quadrupole moments. We consider a quadrupolar Fermi gas trapped in a 2D square optical lattice, and show that the peculiar symmetry and broad tunability of the quadrupole-quadrupole interaction results in a rich phase diagram encompassing unconventional BCS and charge density wave phases, and opens up a perspective to create a topological superfluid. Quadrupolar species, such as metastable alkaline-earth atoms and homonuclear molecules, are stable against chemical reactions and collapse and are readily available in experiment at high densities.}, author = {Bhongale, Satyan and Mathey, Ludwig and Zhao, Erhai and Yelin, Susanne and Lemeshko, Mikhail}, journal = {Physical Review Letters}, number = {15}, publisher = {American Physical Society}, title = {{Quantum phases of quadrupolar fermi gases in optical lattices}}, doi = {10.1103/PhysRevLett.110.155301}, volume = {110}, year = {2013}, } @article{2206, abstract = {Magnetic impurities embedded in inert solids can exhibit long coherence times and interact with one another via their intrinsic anisotropic dipolar interaction. We argue that, as a consequence of these properties, disordered ensembles of magnetic impurities provide an effective platform for realizing a controllable, tunable version of the dipolar quantum spin glass seen in LiHoxY1-xF4. Specifically, we propose and analyze a system composed of dysprosium atoms embedded in solid helium. We describe the phase diagram of the system and discuss the realizability and detectability of the quantum spin glass and antiglass phases.}, author = {Mikhail Lemeshko and Yao, Norman Y and Gorshkov, Alexey V and Weimer, Hendrik and Bennett, Steven D and Momose, Takamasa and Gopalakrishnan, Sarang}, journal = {Physical Review B - Condensed Matter and Materials Physics}, number = {1}, publisher = {American Physical Society}, title = {{Controllable quantum spin glasses with magnetic impurities embedded in quantum solids}}, doi = {10.1103/PhysRevB.88.014426}, volume = {88}, year = {2013}, } @misc{2205, abstract = {The goal of the present article is to review the major developments that have led to the current understanding of molecule-field interactions and experimental methods for manipulating molecules with electromagnetic fields. Molecule-field interactions are at the core of several, seemingly distinct areas of molecular physics. This is reflected in the organisation of this article, which includes sections on field control of molecular beams, external field traps for cold molecules, control of molecular orientation and molecular alignment, manipulation of molecules by non-conservative forces, ultracold molecules and ultracold chemistry, controlled many-body phenomena, entanglement of molecules and dipole arrays, and stability of molecular systems in high-frequency super-intense laser fields. The article contains 852 references.}, author = {Mikhail Lemeshko and Krems, Roman V and Doyle, John M and Kais, Sabre}, booktitle = {Molecular Physics}, number = {12-13}, pages = {1648 -- 1682}, publisher = {Taylor & Francis}, title = {{Manipulation of molecules with electromagnetic fields}}, doi = {10.1080/00268976.2013.813595}, volume = {111}, year = {2013}, } @article{2207, abstract = {The formation of molecules and supramolecular structures results from bonding by conservative forces acting among electrons and nuclei and giving rise to equilibrium configurations defined by minima of the interaction potential. Here we show that bonding can also occur by the non-conservative forces responsible for interaction-induced coherent population trapping. The bound state arises in a dissipative process and manifests itself as a stationary state at a preordained interatomic distance. Remarkably, such a dissipative bonding is present even when the interactions among the atoms are purely repulsive. The dissipative bound states can be created and studied spectroscopically in present-day experiments with ultracold atoms or molecules and can potentially serve for cooling strongly interacting quantum gases.}, author = {Mikhail Lemeshko and Weimer, Hendrik}, journal = {Nature Communications}, publisher = {Nature Publishing Group}, title = {{Dissipative binding of atoms by non-conservative forces}}, doi = {10.1038/ncomms3230}, volume = {4}, year = {2013}, } @inproceedings{2210, abstract = {A straight skeleton is a well-known geometric structure, and several algorithms exist to construct the straight skeleton for a given polygon. In this paper, we ask the reverse question: Given the straight skeleton (in form of a tree with a drawing in the plane, but with the exact position of the leaves unspecified), can we reconstruct the polygon? We show that in most cases there exists at most one polygon; in the remaining case there is an infinite number of polygons determined by one angle that can range in an interval. We can find this (set of) polygon(s) in linear time in the Real RAM computer model.}, author = {Biedl, Therese and Held, Martin and Huber, Stefan}, booktitle = {29th European Workshop on Computational Geometry}, location = {Braunschweig, Germany}, pages = {95 -- 98}, publisher = {TU Braunschweig}, title = {{Reconstructing polygons from embedded straight skeletons}}, year = {2013}, }