TY - JOUR
AB - We develop an analytic model of vector correlations in rotationally inelastic atom-diatom collisions and test it against the much examined Ar-NO (X2Π) system. Based on the Fraunhofer scattering of matter waves, the model furnishes complex scattering amplitudes needed to evaluate the polarization moments characterizing the quantum stereodynamics. The analytic polarization moments are found to be in an excellent agreement with experimental results and with close-coupling calculations available at thermal energies. The model reveals that the stereodynamics is governed by diffraction from the repulsive core of the Ar-NO potential, which can be characterized by a single Legendre moment.
AU - Mikhail Lemeshko
AU - Friedrich, Břetislav
ID - 2194
IS - 5
JF - Physical Chemistry Chemical Physics
TI - An analytic model of the stereodynamics of rotationally inelastic molecular collisions
VL - 12
ER -
TY - JOUR
AB - Following upon our recent work on vector correlations in the Ar-NO collisions [Lemeshko and Friedrich, Phys. Chem. Chem. Phys. 12, 1038 (2010)], we compare model results with close-coupling calculations for a range of channels and collision energies for the He-NO system. The striking agreement between the model and exact polarization moments indicates that the stereodynamics of rotationally inelastic atom-molecule collisions at thermal energies is governed by diffraction of matter waves from a two-dimensional repulsive core of the atom-molecule potential. Furthermore, the model polarization moments characterizing the He-NO, He- O2, He-OH, and He-CaH stereodynamics are found to coalesce into a single, distinctive pattern, which can serve as a "fingerprint" to identify diffraction-driven stereodynamics in future work.
AU - Mikhail Lemeshko
AU - Jambrina, Pablo G
AU - De Miranda, Marcelo P
AU - Friedrich, Břetislav
ID - 2195
IS - 16
JF - Journal of Chemical Physics
TI - Communications: When diffraction rules the stereodynamics of rotationally inelastic collisions
VL - 132
ER -
TY - JOUR
AB - We evaluate the shifts imparted to vibrational and rotational levels of a linear molecule by a nonresonant laser field at intensities of up to 10 12 W/cm2. Both types of shift are found to be either positive or negative, depending on the initial rotational state acted upon by the field. An adiabatic field-molecule interaction imparts a rotational energy shift which is negative and exceeds the concomitant positive vibrational shift by a few orders of magnitude. The rovibrational states are thus pushed downward in such a field. A nonresonant pulsed laser field that interacts nonadiabatically with the molecule is found to impart rotational and vibrational shifts of the same order of magnitude. The nonadiabatic energy transfer occurs most readily at a pulse duration which amounts to about a tenth of the molecule's rotational period and vanishes when the sudden regime is attained for shorter pulses. We applied our treatment to the much-studied 87Rb2 molecule in the last bound vibrational levels of its lowest singlet and triplet electronic states. Our calculations indicate that 15 and 1.5 ns laser pulses of an intensity in excess of 5 × 109 W/cm2 are capable of dissociating the molecule due to the vibrational shift. Lesser shifts can be used to fine-tune the rovibrational levels and thereby affect collisional resonances by the nonresonant light. The energy shifts due to laser intensities of 109 W/cm2 may be discernible spectroscopically, with a 10 MHz resolution.
AU - Mikhail Lemeshko
AU - Friedrich, Břetislav
ID - 2196
IS - 36
JF - Journal of Physical Chemistry A
TI - Fine-tuning molecular energy levels by nonresonant laser pulses
VL - 114
ER -
TY - JOUR
AB - We present an analytic model of the refractive index for matter waves propagating through atomic or molecular gases. The model, which combines the Wentzel-Kramers-Brillouin (WKB) treatment of the long-range attraction with the Fraunhofer model treatment of the short-range repulsion, furnishes a refractive index in compelling agreement with recent experiments of Jacquey [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.98.240405 98, 240405 (2007)] on Li atom matter waves passing through dilute noble gases. We show that the diffractive contribution, which arises from scattering by a two-dimensional "hard core" of the potential, is essential for obtaining a correct imaginary part of the refractive index.
AU - Mikhail Lemeshko
AU - Friedrich, Břetislav
ID - 2197
IS - 2
JF - Physical Review A - Atomic, Molecular, and Optical Physics
TI - Multiple scattering of matter waves: An analytic model of the refractive index for atomic and molecular gases
VL - 82
ER -
TY - CONF
AB - Streaming string transducers [1] define (partial) functions from input strings to output strings. A streaming string transducer makes a single pass through the input string and uses a finite set of variables that range over strings from the output alphabet. At every step, the transducer processes an input symbol, and updates all the variables in parallel using assignments whose right-hand-sides are concatenations of output symbols and variables with the restriction that a variable can be used at most once in a right-hand-side expression. It has been shown that streaming string transducers operating on strings over infinite data domains are of interest in algorithmic verification of list-processing programs, as they lead to PSPACE decision procedures for checking pre/post conditions and for checking semantic equivalence, for a well-defined class of heap-manipulating programs. In order to understand the theoretical expressiveness of streaming transducers, we focus on streaming transducers processing strings over finite alphabets, given the existence of a robust and well-studied class of "regular" transductions for this case. Such regular transductions can be defined either by two-way deterministic finite-state transducers, or using a logical MSO-based characterization. Our main result is that the expressiveness of streaming string transducers coincides exactly with this class of regular transductions.
AU - Alur, Rajeev
AU - Cerny, Pavol
ID - 488
TI - Expressiveness of streaming string transducers
VL - 8
ER -
TY - CONF
AB - Graph games of infinite length are a natural model for open reactive processes: one player represents the controller, trying to ensure a given specification, and the other represents a hostile environment. The evolution of the system depends on the decisions of both players, supplemented by chance. In this work, we focus on the notion of randomised strategy. More specifically, we show that three natural definitions may lead to very different results: in the most general cases, an almost-surely winning situation may become almost-surely losing if the player is only allowed to use a weaker notion of strategy. In more reasonable settings, translations exist, but they require infinite memory, even in simple cases. Finally, some traditional problems becomes undecidable for the strongest type of strategies.
AU - Cristau, Julien
AU - David, Claire
AU - Horn, Florian
ID - 489
T2 - Proceedings of GandALF 2010
TI - How do we remember the past in randomised strategies?
VL - 25
ER -
TY - GEN
AB - We present an algorithmic method for the synthesis of concurrent programs that are optimal with respect to quantitative performance measures. The input consists of a sequential sketch, that is, a program that does not contain synchronization constructs, and of a parametric performance model that assigns costs to actions such as locking, context switching, and idling. The quantitative synthesis problem is to automatically introduce synchronization constructs into the sequential sketch so that both correctness is guaranteed and worst-case (or average-case) performance is optimized. Correctness is formalized as race freedom or linearizability.
We show that for worst-case performance, the problem can be modeled
as a 2-player graph game with quantitative (limit-average) objectives, and
for average-case performance, as a 2 1/2 -player graph game (with probabilistic transitions). In both cases, the optimal correct program is derived from an optimal strategy in the corresponding quantitative game. We prove that the respective game problems are computationally expensive (NP-complete), and present several techniques that overcome the theoretical difficulty in cases of concurrent programs of practical interest.
We have implemented a prototype tool and used it for the automatic syn- thesis of programs that access a concurrent list. For certain parameter val- ues, our method automatically synthesizes various classical synchronization schemes for implementing a concurrent list, such as fine-grained locking or a lazy algorithm. For other parameter values, a new, hybrid synchronization style is synthesized, which uses both the lazy approach and coarse-grained locks (instead of standard fine-grained locks). The trade-off occurs because while fine-grained locking tends to decrease the cost that is due to waiting for locks, it increases cache size requirements.
AU - Chatterjee, Krishnendu
AU - Cerny, Pavol
AU - Henzinger, Thomas A
AU - Radhakrishna, Arjun
AU - Singh, Rohit
ID - 5388
SN - 2664-1690
TI - Quantitative synthesis for concurrent programs
ER -
TY - GEN
AB - Boolean notions of correctness are formalized by preorders on systems. Quantitative measures of correctness can be formalized by real-valued distance functions between systems, where the distance between implementation and specification provides a measure of “fit” or “desirability.” We extend the simulation preorder to the quantitative setting, by making each player of a simulation game pay a certain price for her choices. We use the resulting games with quantitative objectives to define three different simulation distances. The correctness distance measures how much the specification must be changed in order to be satisfied by the implementation. The coverage distance measures how much the im- plementation restricts the degrees of freedom offered by the specification. The robustness distance measures how much a system can deviate from the implementation description without violating the specification. We consider these distances for safety as well as liveness specifications. The distances can be computed in polynomial time for safety specifications, and for liveness specifications given by weak fairness constraints. We show that the distance functions satisfy the triangle inequality, that the distance between two systems does not increase under parallel composition with a third system, and that the distance between two systems can be bounded from above and below by distances between abstractions of the two systems. These properties suggest that our simulation distances provide an appropriate basis for a quantitative theory of discrete systems. We also demonstrate how the robustness distance can be used to measure how many transmission errors are tolerated by error correcting codes.
AU - Cerny, Pavol
AU - Henzinger, Thomas A
AU - Radhakrishna, Arjun
ID - 5389
SN - 2664-1690
TI - Simulation distances
ER -
TY - GEN
AB - The class of ω regular languages provide a robust specification language in verification. Every ω-regular condition can be decomposed into a safety part and a liveness part. The liveness part ensures that something good happens “eventually.” Two main strengths of the classical, infinite-limit formulation of liveness are robustness (independence from the granularity of transitions) and simplicity (abstraction of complicated time bounds). However, the classical liveness formulation suffers from the drawback that the time until something good happens may be unbounded. A stronger formulation of liveness, so-called finitary liveness, overcomes this drawback, while still retaining robustness and simplicity. Finitary liveness requires that there exists an unknown, fixed bound b such that something good happens within b transitions. In this work we consider the finitary parity and Streett (fairness) conditions. We present the topological, automata-theoretic and logical characterization of finitary languages defined by finitary parity and Streett conditions. We (a) show that the finitary parity and Streett languages are Σ2-complete; (b) present a complete characterization of the expressive power of various classes of automata with finitary and infinitary conditions (in particular we show that non-deterministic finitary parity and Streett automata cannot be determinized to deterministic finitary parity or Streett automata); and (c) show that the languages defined by non-deterministic finitary parity automata exactly characterize the star-free fragment of ωB-regular languages.
AU - Chatterjee, Krishnendu
AU - Fijalkow, Nathanaël
ID - 5390
SN - 2664-1690
TI - Topological, automata-theoretic and logical characterization of finitary languages
ER -
TY - GEN
AB - Concurrent data structures with fine-grained synchronization are notoriously difficult to implement correctly. The difficulty of reasoning about these implementations does not stem from the number of variables or the program size, but rather from the large number of possible interleavings. These implementations are therefore prime candidates for model checking. We introduce an algorithm for verifying linearizability of singly-linked heap-based concurrent data structures. We consider a model consisting of an unbounded heap where each node consists an element from an unbounded data domain, with a restricted set of operations for testing and updating pointers and data elements. Our main result is that linearizability is decidable for programs that invoke a fixed number of methods, possibly in parallel. This decidable fragment covers many of the common implementation techniques — fine-grained locking, lazy synchronization, and lock-free synchronization. We also show how the technique can be used to verify optimistic implementations with the help of programmer annotations. We developed a verification tool CoLT and evaluated it on a representative sample of Java implementations of the concurrent set data structure. The tool verified linearizability of a number of implementations, found a known error in a lock-free imple- mentation and proved that the corrected version is linearizable.
AU - Cerny, Pavol
AU - Radhakrishna, Arjun
AU - Zufferey, Damien
AU - Chaudhuri, Swarat
AU - Alur, Rajeev
ID - 5391
SN - 2664-1690
TI - Model checking of linearizability of concurrent list implementations
ER -
TY - JOUR
AB - It is not well understood how the human Mediator complex, transcription factor IIH and RNA polymerase II (Pol II) work together with activators to initiate transcription. Activator binding alters Mediator structure, yet the functional consequences of such structural shifts remain unknown. The p53 C terminus and its activation domain interact with different Mediator subunits, and we find that each interaction differentially affects Mediator structure; strikingly, distinct p53-Mediator structures differentially affect Pol II activity. Only the p53 activation domain induces the formation of a large pocket domain at the Mediator-Pol II interaction site, and this correlates with activation of stalled Pol II to a productively elongating state. Moreover, we define a Mediator requirement for TFIIH-dependent Pol II C-terminal domain phosphorylation and identify substantial differences in Pol II C-terminal domain processing that correspond to distinct p53-Mediator structural states. Our results define a fundamental mechanism by which p53 activates transcription and suggest that Mediator structural shifts trigger activation of stalled Pol II complexes.
AU - Meyer, Krista
AU - Lin, Shih
AU - Bernecky, Carrie A
AU - Gao, Yuefeng
AU - Taatjes, Dylan
ID - 598
IS - 6
JF - Nature Structural and Molecular Biology
TI - P53 activates transcription by directing structural shifts in Mediator
VL - 17
ER -
TY - JOUR
AB - Defining the mutational landscape when individuals of a species grow separately and diverge over many generations can provide insights into trait evolution. A specific example of this involves studying changes associated with domestication where different lines of the same wild stock have been cultivated independently in different standard environments. Whole genome sequence comparison of such lines permits estimation of mutation rates, inference of genes' ancestral states and ancestry of existing strains, and correction of sequencing errors in genome databases. Here we study domestication of the C. elegans Bristol strain as a model, and report the genome sequence of LSJ1 (Bristol), a sibling of the standard C. elegans reference wild type N2 (Bristol). The LSJ1 and N2 lines were cultivated separately from shortly after the Bristol strain was isolated until methods to freeze C. elegans were developed. We find that during this time the two strains have accumulated 1208 genetic differences. We describe phenotypic variation between N2 and LSJ1 in the rate at which embryos develop, the rate of production of eggs, the maturity of eggs at laying, and feeding behavior, all the result of post-isolation changes. We infer the ancestral alleles in the original Bristol isolate and highlight 2038 likely sequencing errors in the original N2 reference genome sequence. Many of these changes modify genome annotation. Our study provides a starting point to further investigate genotype-phenotype association and offers insights into the process of selection as a result of laboratory domestication.
AU - Weber, Katherine P.
AU - De, Subhajyoti
AU - Kozarewa, Iwanka
AU - Turner, Daniel J.
AU - Babu, M. Madan
AU - de Bono, Mario
ID - 6142
IS - 11
JF - PLoS ONE
SN - 1932-6203
TI - Whole genome sequencing highlights genetic changes associated with laboratory domestication of C. elegans
VL - 5
ER -
TY - JOUR
AB - We study the average order of the divisor function, as it ranges over the values of binary quartic forms that are reducible over ℚ.
AU - Bretèche, Régis de la
AU - Browning, Timothy D
ID - 6320
IS - 646
JF - Crelles Journal
TI - Le problème des diviseurs pour des formes binaires de degré 4
VL - 2010
ER -
TY - JOUR
AB - We report resonant ultrasound spectroscopy (RUS), dilatometry/magnetostriction, magnetotransport, magnetization, specific-heat, and 119Sn Mössbauer spectroscopy measurements on SnTe and Sn0.995Cr0.005Te. Hall measurements at T=77 K indicate that our Bridgman-grown single crystals have a p-type carrier concentration of 3.4×1019 cm−3 and that our Cr-doped crystals have an n-type concentration of 5.8×1022 cm−3. Although our SnTe crystals are diamagnetic over the temperature range 2≤T≤1100 K, the Cr-doped crystals are room-temperature ferromagnets with a Curie temperature of 294 K. For each sample type, three-terminal capacitive dilatometry measurements detect a subtle 0.5 μm distortion at Tc≈85 K. Whereas our RUS measurements on SnTe show elastic hardening near the structural transition, pointing to co-elastic behavior, similar measurements on Sn0.995Cr0.005Te show a pronounced softening, pointing to ferroelastic behavior. Effective Debye temperature, θD, values of SnTe obtained from 119Sn Mössbauer studies show a hardening of phonons in the range 60–115 K (θD=162 K) as compared with the 100–300 K range (θD=150 K). In addition, a precursor softening extending over approximately 100 K anticipates this collapse at the critical temperature and quantitative analysis over three decades of its reduced modulus finds ΔC44/C44=A|(T−T0)/T0|−κ with κ=0.50±0.02, a value indicating a three-dimensional softening of phonon branches at a temperature T0∼75 K, considerably below Tc. We suggest that the differences in these two types of elastic behaviors lie in the absence of elastic domain-wall motion in the one case and their nucleation in the other.
AU - Salje, E. K. H.
AU - Safarik, D. J.
AU - Modic, Kimberly A
AU - Gubernatis, J. E.
AU - Cooley, J. C.
AU - Taylor, R. D.
AU - Mihaila, B.
AU - Saxena, A.
AU - Lookman, T.
AU - Smith, J. L.
AU - Fisher, R. A.
AU - Pasternak, M.
AU - Opeil, C. P.
AU - Siegrist, T.
AU - Littlewood, P. B.
AU - Lashley, J. C.
ID - 7078
IS - 18
JF - Physical Review B
SN - 1098-0121
TI - Tin telluride: A weakly co-elastic metal
VL - 82
ER -
TY - JOUR
AB - We prove a generating function formula for the Betti numbers of Nakajima quiver varieties. We prove that it is a q-deformation of the Weyl-Kac character formula. In particular this implies that the constant term of the polynomial counting the number of absolutely indecomposable representations of a quiver equals the multiplicity of a certain weight in the corresponding Kac-Moody algebra, which was conjectured by Kac in 1982.
AU - Tamas Hausel
ID - 1465
IS - 1
JF - Inventiones Mathematicae
TI - Kac's conjecture from Nakajima quiver varieties
VL - 181
ER -
TY - JOUR
AB - In Hausel et al. (2008) [10] we presented a conjecture generalizing the Cauchy formula for Macdonald polynomial. This conjecture encodes the mixed Hodge polynomials of the character varieties of representations of the fundamental group of a punctured Riemann surface of genus g. We proved several results which support this conjecture. Here we announce new results which are consequences of those in Hausel et al. (2008) [10].
AU - Tamas Hausel
AU - Letellier, Emmanuel
AU - Rodríguez Villegas, Fernando
ID - 1466
IS - 3-4
JF - Comptes Rendus Mathematique
TI - Topology of character varieties and representations of quivers
VL - 348
ER -
TY - CHAP
AB - This chapter surveys the motivations, related results, and progress made towards the following problem, raised by Hitchin in 1995: What is the space of L2 harmonic forms on the moduli space of Higgs bundles on a Riemann surface?
AU - Tamas Hausel
ID - 1468
T2 - The Many Facets of Geometry: A Tribute to Nigel Hitchin
TI - S-Duality in HyperkäHler Hodge Theory
ER -
TY - JOUR
AB - Control over all internal and external degrees of freedom of molecules at the level of single quantum states will enable a series of fundamental studies in physics and chemistry1,2. In particular, samples of ground-state molecules at ultralow temperatures and high number densities will facilitate new quantum-gas studies3 and future applications in quantum information science4. However, high phase-space densities for molecular samples are not readily attainable because efficient cooling techniques such as laser cooling are lacking. Here we produce an ultracold and dense sample of molecules in a single hyperfine level of the rovibronic ground state with each molecule individually trapped in the motional ground state of an optical lattice well. Starting from a zero-temperature atomic Mott-insulator state with optimized double-site occupancy6, weakly bound dimer molecules are efficiently associated on a Feshbach resonance7 and subsequently transferred to the rovibronic ground state by a stimulated four-photon process with >50% efficiency. The molecules are trapped in the lattice and have a lifetime of 8 s. Our results present a crucial step towards Bose-Einstein condensation of ground-state molecules and, when suitably generalized to polar heteronuclear molecules, the realization of dipolar quantum-gas phases in optical lattices8-10.
AU - Danzl, Johann G
AU - Mark, Manfred
AU - Haller, Elmar
AU - Gustavsson, Mattias
AU - Hart, Russell
AU - Aldegunde, Jesus
AU - Hutson, Jeremy
AU - Nägerl, Hanns
ID - 1044
IS - 4
JF - Nature Physics
TI - An ultracold high-density sample of rovibronic ground-state molecules in an optical lattice
VL - 6
ER -
TY - JOUR
AB - We report on the observation of confinement-induced resonances in strongly interacting quantum-gas systems with tunable interactions for one- and two-dimensional geometry. Atom-atom scattering is substantially modified when the s-wave scattering length approaches the length scale associated with the tight transversal confinement, leading to characteristic loss and heating signatures. Upon introducing an anisotropy for the transversal confinement we observe a splitting of the confinement-induced resonance. With increasing anisotropy additional resonances appear. In the limit of a two-dimensional system we find that one resonance persists.
AU - Haller, Elmar
AU - Mark, Manfred
AU - Hart, Russell
AU - Danzl, Johann G
AU - Reichsöllner, Lukas
AU - Melezhik, Vladimir
AU - Schmelcher, Peter
AU - Nägerl, Hanns
ID - 1045
IS - 15
JF - Physical Review Letters
TI - Confinement-induced resonances in low-dimensional quantum systems
VL - 104
ER -
TY - JOUR
AB - Particles in a perfect lattice potential perform Bloch oscillations when subject to a constant force, leading to localization and preventing conductivity. For a weakly interacting Bose-Einstein condensate of Cs atoms, we observe giant center-of-mass oscillations in position space with a displacement across hundreds of lattice sites when we add a periodic modulation to the force near the Bloch frequency. We study the dependence of these "super" Bloch oscillations on lattice depth, modulation amplitude, and modulation frequency and show that they provide a means to induce linear transport in a dissipation-free lattice.
AU - Haller, Elmar
AU - Hart, Russell
AU - Mark, Manfred
AU - Danzl, Johann G
AU - Reichsöllner, Lukas
AU - Nägerl, Hanns
ID - 1047
IS - 20
JF - Physical Review Letters
TI - Inducing transport in a dissipation-free lattice with super bloch oscillations
VL - 104
ER -