TY - JOUR
AB - Games on graphs with omega-regular objectives provide a model for the control and synthesis of reactive systems. Every omega-regular objective 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. While for one-shot liveness (reachability) objectives, classical and finitary liveness coincide, for repeated liveness (Buchi) objectives, the finitary formulation is strictly stronger. In this work we study games with finitary parity and Streett objectives. We prove the determinacy of these games, present algorithms for solving these games, and characterize the memory requirements of winning strategies. We show that finitary parity games can be solved in polynomial time, which is not known for infinitary parity games. For finitary Streett games, we give an EXPTIME algorithm and show that the problem is NP-hard. Our algorithms can be used, for example, for synthesizing controllers that do not let the response time of a system increase without bound.
AU - Chatterjee, Krishnendu
AU - Henzinger, Thomas A
AU - Horn, Florian
ID - 3870
IS - 1
JF - ACM Transactions on Computational Logic (TOCL)
TI - Finitary winning in omega-regular games
VL - 11
ER -
TY - CONF
AB - Nondeterministic weighted automata are finite automata with numerical weights oil transitions. They define quantitative languages 1, that assign to each word v; a real number L(w). The value of ail infinite word w is computed as the maximal value of all runs over w, and the value of a run as the supremum, limsup liminf, limit average, or discounted sum of the transition weights. We introduce probabilistic weighted antomata, in which the transitions are chosen in a randomized (rather than nondeterministic) fashion. Under almost-sure semantics (resp. positive semantics), the value of a word v) is the largest real v such that the runs over w have value at least v with probability I (resp. positive probability). We study the classical questions of automata theory for probabilistic weighted automata: emptiness and universality, expressiveness, and closure under various operations oil languages. For quantitative languages, emptiness university axe defined as whether the value of some (resp. every) word exceeds a given threshold. We prove some, of these questions to he decidable, and others undecidable. Regarding expressive power, we show that probabilities allow its to define a wide variety of new classes of quantitative languages except for discounted-sum automata, where probabilistic choice is no more expressive than nondeterminism. Finally we live ail almost complete picture of the closure of various classes of probabilistic weighted automata for the following, provide, is operations oil quantitative languages: maximum, sum. and numerical complement.
AU - Chatterjee, Krishnendu
AU - Doyen, Laurent
AU - Henzinger, Thomas A
ID - 3871
TI - Probabilistic weighted automata
VL - 5710
ER -
TY - JOUR
AB - We compare anti-parasite defences at the level of multicellular organisms and insect societies, and find that selection by parasites at these two organisational levels is often very similar and has created a number of parallel evolutionary solutions in the host's immune response. The defence mechanisms of both individuals and insect colonies start with border defences to prevent parasite intake and are followed by soma defences that prevent the establishment and spread of the parasite between the body's cells or the social insect workers. Lastly, germ line defences are employed to inhibit infection of the reproductive tissue of organisms or the reproductive individuals in colonies. We further find sophisticated self/non-self-recognition systems operating at both levels, which appear to be vital in maintaining the integrity of the body or colony as a reproductive entity. We then expand on the regulation of immune responses and end with a contemplation of how evolution may shape the different immune components, both within and between levels. The aim of this review is to highlight common evolutionary principles acting in disease defence at the level of both individual organisms and societies, thereby linking the fields of physiological and ecological immunology.
AU - Cremer, Sylvia
AU - Sixt, Michael K
ID - 3946
IS - 1513
JF - Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences
TI - Analogies in the evolution of individual and social immunity
VL - 364
ER -
TY - CONF
AB - We describe an algorithm for segmenting three-dimensional medical imaging data modeled as a continuous function on a 3-manifold. It is related to watershed algorithms developed in image processing but is closer to its mathematical roots, which are Morse theory and homological algebra. It allows for the implicit treatment of an underlying mesh, thus combining the structural integrity of its mathematical foundations with the computational efficiency of image processing.
AU - Edelsbrunner, Herbert
AU - Harer, John
ID - 3968
TI - The persistent Morse complex segmentation of a 3-manifold
VL - 5903
ER -
TY - JOUR
AB - Populations living in a spatially and temporally changing environment can adapt to the changing optimum and/or migrate toward favorable habitats. Here we extend previous analyses with a static optimum to allow the environment to vary in time as well as in space. The model follows both population dynamics and the trait mean under stabilizing selection, and the outcomes can be understood by comparing the loads due to genetic variance, dispersal, and temporal change. With fixed genetic variance, we obtain two regimes: (1) adaptation that is uniform along the environmental gradient and that responds to the moving optimum as expected for panmictic populations and when the spatial gradient is sufficiently steep, and (2) a population with limited range that adapts more slowly than the environmental optimum changes in both time and space; the population therefore becomes locally extinct and migrates toward suitable habitat. We also use a population‐genetic model with many loci to allow genetic variance to evolve, and we show that the only solution now has uniform adaptation.
AU - Polechova, Jitka
AU - Barton, Nicholas H
AU - Marion, Glenn
ID - 4136
IS - 5
JF - American Naturalist
TI - Species' range: Adaptation in space and time
VL - 174
ER -
TY - JOUR
AB - Felsenstein distinguished two ways by which selection can directly strengthen isolation. First, a modifier that strengthens prezygotic isolation can be favored everywhere. This fits with the traditional view of reinforcement as an adaptation to reduce deleterious hybridization by strengthening assortative mating. Second, selection can favor association between different incompatibilities, despite recombination. We generalize this “two allele” model to follow associations among any number of incompatibilities, which may include both assortment and hybrid inviability. Our key argument is that this process, of coupling between incompatibilities, may be quite different from the usual view of reinforcement: strong isolation can evolve through the coupling of any kind of incompatibility, whether prezygotic or postzygotic. Single locus incompatibilities become coupled because associations between them increase the variance in compatibility, which in turn increases mean fitness if there is positive epistasis. Multiple incompatibilities, each maintained by epistasis, can become coupled in the same way. In contrast, a single-locus incompatibility can become coupled with loci that reduce the viability of haploid hybrids because this reduces harmful recombination. We obtain simple approximations for the limits of tight linkage, and strong assortment, and show how assortment alleles can invade through associations with other components of reproductive isolation.
AU - Barton, Nicholas H
AU - De Cara, Maria
ID - 4242
IS - 5
JF - Evolution; International Journal of Organic Evolution
TI - The evolution of strong reproductive isolation
VL - 63
ER -
TY - CONF
AB - Pseudo-code descriptions of STMs assume sequentially consistent program execution and atomicity of high-level STM operations like read, write, and commit. These assumptions are often violated in realistic settings, as STM implementations run on relaxed memory models, with the atomicity of operations as provided by the hardware. This paper presents the first approach to verify STMs under relaxed memory models with atomicity of 32 bit loads and stores, and read-modify-write operations. We present RML, a new high-level language for expressing concurrent algorithms with a hardware-level atomicity of instructions, and whose semantics is parametrized by various relaxed memory models. We then present our tool, FOIL, which takes as input the RML description of an STM algorithm and the description of a memory model, and automatically determines the locations of fences, which if inserted, ensure the correctness of the STM algorithm under the given memory model. We use FOIL to verify DSTM, TL2, and McRT STM under the memory models of sequential consistency, total store order, partial store order, and relaxed memory order.
AU - Guerraoui, Rachid
AU - Thomas Henzinger
AU - Vasu Singh
ID - 4383
TI - Software transactional memory on relaxed memory models
VL - 5643
ER -
TY - CONF
AB - For programs whose data variables range over boolean or finite domains, program verification is decidable, and this forms the basis of recent tools for software model checking. In this paper, we consider algorithmic verification of programs that use boolean variables, and in addition, access a single read-only array whose length is potentially unbounded, and whose elements range over a potentially unbounded data domain. We show that the reachability problem, while undecidable in general, is (1) Pspace-complete for programs in which the array-accessing for-loops are not nested, (2) decidable for a restricted class of programs with doubly-nested loops. The second result establishes connections to automata and logics defining languages over data words.
AU - Alur, Rajeev
AU - Cerny, Pavol
AU - Weinstein, Scott
ID - 4403
TI - Algorithmic analysis of array-accessing programs
VL - 5771
ER -
TY - CONF
AB - We present an on-the-fly abstraction technique for infinite-state continuous -time Markov chains. We consider Markov chains that are specified by a finite set of transition classes. Such models naturally represent biochemical reactions and therefore play an important role in the stochastic modeling of biological systems. We approximate the transient probability distributions at various time instances by solving a sequence of dynamically constructed abstract models, each depending on the previous one. Each abstract model is a finite Markov chain that represents the behavior of the original, infinite chain during a specific time interval. Our approach provides complete information about probability distributions, not just about individual parameters like the mean. The error of each abstraction can be computed, and the precision of the abstraction refined when desired. We implemented the algorithm and demonstrate its usefulness and efficiency on several case studies from systems biology.
AU - Thomas Henzinger
AU - Maria Mateescu
AU - Wolf, Verena
ID - 4453
TI - Sliding-window abstraction for infinite Markov chains
VL - 5643
ER -
TY - CONF
AB - Weighted automata are finite automata with numerical weights on transitions. Nondeterministic weighted automata define quantitative languages L that assign to each word w a real number L(w) computed as the maximal value of all runs over w, and the value of a run r is a function of the sequence of weights that appear along r. There are several natural functions to consider such as Sup, LimSup, LimInf, limit average, and discounted sum of transition weights.
We introduce alternating weighted automata in which the transitions of the runs are chosen by two players in a turn-based fashion. Each word is assigned the maximal value of a run that the first player can enforce regardless of the choices made by the second player. We survey the results about closure properties, expressiveness, and decision problems for nondeterministic weighted automata, and we extend these results to alternating weighted automata.
For quantitative languages L 1 and L 2, we consider the pointwise operations max(L 1,L 2), min(L 1,L 2), 1 − L 1, and the sum L 1 + L 2. We establish the closure properties of all classes of alternating weighted automata with respect to these four operations.
We next compare the expressive power of the various classes of alternating and nondeterministic weighted automata over infinite words. In particular, for limit average and discounted sum, we show that alternation brings more expressive power than nondeterminism.
Finally, we present decidability results and open questions for the quantitative extension of the classical decision problems in automata theory: emptiness, universality, language inclusion, and language equivalence.
AU - Chatterjee, Krishnendu
AU - Doyen, Laurent
AU - Henzinger, Thomas A
ID - 4542
TI - Alternating weighted automata
VL - 5699
ER -
TY - CONF
AB - We consider concurrent games played on graphs. At every round of a game, each player simultaneously and independently selects a move; the moves jointly determine the transition to a successor state. Two basic objectives are the safety objective to stay forever in a given set of states, and its dual, the reachability objective to reach a given set of states. We present in this paper a strategy improvement algorithm for computing the value of a concurrent safety game, that is, the maximal probability with which player 1 can enforce the safety objective. The algorithm yields a sequence of player-1 strategies which ensure probabilities of winning that converge monotonically to the value of the safety game. Our result is significant because the strategy improvement algorithm provides, for the first time, a way to approximate the value of a concurrent safety game from below. Since a value iteration algorithm, or a strategy improvement algorithm for reachability games, can be used to approximate the same value from above, the combination of both algorithms yields a method for computing a converging sequence of upper and lower bounds for the values of concurrent reachability and safety games. Previous methods could approximate the values of these games only from one direction, and as no rates of convergence are known, they did not provide a practical way to solve these games.
AU - Krishnendu Chatterjee
AU - de Alfaro, Luca
AU - Thomas Henzinger
ID - 4544
TI - Termination criteria for solving concurrent safety and reachability games
ER -
TY - CONF
AB - A stochastic game is a two-player game played oil a graph, where in each state the successor is chosen either by One of the players, or according to a probability distribution. We Survey Stochastic games with limsup and liminf objectives. A real-valued re-ward is assigned to each state, and the value of all infinite path is the limsup (resp. liminf) of all rewards along the path. The value of a stochastic game is the maximal expected value of an infinite path that call he achieved by resolving the decisions of the first player. We present the complexity of computing values of Stochastic games and their subclasses, and the complexity, of optimal strategies in such games.
AU - Chatterjee, Krishnendu
AU - Doyen, Laurent
AU - Henzinger, Thomas A
ID - 4545
TI - A survey of stochastic games with limsup and liminf objectives
VL - 5556
ER -
TY - CONF
AB - Most specification languages express only qualitative constraints. However, among two implementations that satisfy a given specification, one may be preferred to another. For example, if a specification asks that every request is followed by a response, one may prefer an implementation that generates responses quickly but does not generate unnecessary responses. We use quantitative properties to measure the “goodness” of an implementation. Using games with corresponding quantitative objectives, we can synthesize “optimal” implementations, which are preferred among the set of possible implementations that satisfy a given specification.
In particular, we show how automata with lexicographic mean-payoff conditions can be used to express many interesting quantitative properties for reactive systems. In this framework, the synthesis of optimal implementations requires the solution of lexicographic mean-payoff games (for safety requirements), and the solution of games with both lexicographic mean-payoff and parity objectives (for liveness requirements). We present algorithms for solving both kinds of novel graph games.
AU - Bloem, Roderick
AU - Chatterjee, Krishnendu
AU - Henzinger, Thomas A
AU - Jobstmann, Barbara
ID - 4569
TI - Better quality in synthesis through quantitative objectives
VL - 5643
ER -
TY - CONF
AB - Alpaga is a solver for two-player parity games with imperfect information. Given the description of a game, it determines whether the first player can ensure to win and, if so, it constructs a winning strategy. The tool provides a symbolic implementation of a recent algorithm based on antichains.
AU - Berwanger, Dietmar
AU - Krishnendu Chatterjee
AU - De Wulf, Martin
AU - Doyen, Laurent
AU - Thomas Henzinger
ID - 4580
TI - Alpaga: A tool for solving parity games with imperfect information
VL - 5505
ER -
TY - JOUR
AU - Weijers, Dolf
AU - Friml, Jirí
ID - 3051
IS - 6
JF - Cell
TI - SnapShot: Auxin signaling and transport
VL - 136
ER -
TY - JOUR
AB - The dynamic, differential distribution of the hormone auxin within plant tissues controls an impressive variety of developmental processes, which tailor plant growth and morphology to environmental conditions. Various environmental and endogenous signals can be integrated into changes in auxin distribution through their effects on local auxin biosynthesis and intercellular auxin transport. Individual cells interpret auxin largely by a nuclear signaling pathway that involves the F box protein TIR1 acting as an auxin receptor. Auxin-dependent TIR1 activity leads to ubiquitination-based degradation of transcriptional repressors and complex transcriptional reprogramming. Thus, auxin appears to be a versatile trigger of preprogrammed developmental changes in plant cells.
AU - Vanneste, Steffen
AU - Friml, Jirí
ID - 3052
IS - 6
JF - Cell
TI - Auxin: A trigger for change in plant development
VL - 136
ER -
TY - JOUR
AB - The differential distribution of the plant signaling molecule auxin is required for many aspects of plant development. Local auxin maxima and gradients arise as a result of local auxin metabolism and, predominantly, from directional cell-to-cell transport. In this primer, we discuss how the coordinated activity of several auxin influx and efflux systems, which transport auxin across the plasma membrane, mediates directional auxin flow. This activity crucially contributes to the correct setting of developmental cues in embryogenesis, organogenesis, vascular tissue formation and directional growth in response to environmental stimuli.
AU - Petrášek, Jan
AU - Friml, Jirí
ID - 3057
IS - 16
JF - Development
TI - Auxin transport routes in plant development
VL - 136
ER -
TY - JOUR
AB - The PIN-FORMED (PIN) proteins are secondary transporters acting in the efflux of the plant signal molecule auxin from cells. They are asymmetrically localized within cells and their polarity determines the directionality of intercellular auxin flow. PIN genes are found exclusively in the genomes of multicellular plants and play an important role in regulating asymmetric auxin distribution in multiple developmental processes, including embryogenesis, organogenesis, tissue differentiation and tropic responses. All PIN proteins have a similar structure with amino- and carboxy-terminal hydrophobic, membrane-spanning domains separated by a central hydrophilic domain. The structure of the hydrophobic domains is well conserved. The hydrophilic domain is more divergent and it determines eight groups within the protein family. The activity of PIN proteins is regulated at multiple levels, including transcription, protein stability, subcellular localization and transport activity. Different endogenous and environmental signals can modulate PIN activity and thus modulate auxin-distribution-dependent development. A large group of PIN proteins, including the most ancient members known from mosses, localize to the endoplasmic reticulum and they regulate the subcellular compartmentalization of auxin and thus auxin metabolism. Further work is needed to establish the physiological importance of this unexpected mode of auxin homeostasis regulation. Furthermore, the evolution of PIN-based transport, PIN protein structure and more detailed biochemical characterization of the transport function are important topics for further studies.
AU - Křeček, Pavel
AU - Skůpa, Petr
AU - Libus, Jiří
AU - Naramoto, Satoshi
AU - Tejos, Ricardo
AU - Friml, Jirí
AU - Zažímalová, Eva
ID - 3061
IS - 12
JF - Genome Biology
TI - The PIN-FORMED (PIN) protein family of auxin transporters
VL - 10
ER -
TY - JOUR
AB - The problem of obtaining the maximum a posteriori estimate of a general discrete Markov random field (i.e., a Markov random field defined using a discrete set of labels) is known to be NP-hard. However, due to its central importance in many applications, several approximation algorithms have been proposed in the literature. In this paper, we present an analysis of three such algorithms based on convex relaxations: (i) LP-S: the linear programming (LP) relaxation proposed by Schlesinger (1976) for a special case and independently in Chekuri et al. (2001), Koster et al. (1998), and Wainwright et al. (2005) for the general case; (ii) QP-RL: the quadratic programming (QP) relaxation of Ravikumar and Lafferty (2006); and (iii) SOCP-MS: the second order cone programming (SOCP) relaxation first proposed by Muramatsu and Suzuki (2003) for two label problems and later extended by Kumar et al. (2006) for a general label set.
We show that the SOCP-MS and the QP-RL relaxations are equivalent. Furthermore, we prove that despite the flexibility in the form of the constraints/objective function offered by QP and SOCP, the LP-S relaxation strictly dominates (i.e., provides a better approximation than) QP-RL and SOCP-MS. We generalize these results by defining a large class of SOCP (and equivalent QP) relaxations which is dominated by the LP-S relaxation. Based on these results we propose some novel SOCP relaxations which define constraints using random variables that form cycles or cliques in the graphical model representation of the random field. Using some examples we show that the new SOCP relaxations strictly dominate the previous approaches.
AU - Kumar, M Pawan
AU - Vladimir Kolmogorov
AU - Torr, Philip H
ID - 3197
JF - Journal of Machine Learning Research
TI - An analysis of convex relaxations for MAP estimation of discrete MRFs
VL - 10
ER -
TY - CONF
AB - We give polynomial-time algorithms for computing the values of Markov decision processes (MDPs) with limsup and liminf objectives. A real-valued reward is assigned to each state, and the value of an infinite path in the MDP is the limsup (resp. liminf) of all rewards along the path. The value of an MDP is the maximal expected value of an infinite path that can be achieved by resolving the decisions of the MDP. Using our result on MDPs, we show that turn-based stochastic games with limsup and liminf objectives can be solved in NP ∩ coNP.
AU - Krishnendu Chatterjee
AU - Thomas Henzinger
ID - 3503
TI - Probabilistic systems with limsup and liminf objectives
VL - 5489
ER -
TY - CONF
AB - We present a review of recent work on the mathematical aspects of the BCS gap equation, covering our results of Ref. 9 as well our recent joint work with Hamza and Solovej and with Frank and Naboko, respectively. In addition, we mention some related new results.
AU - Hainzl, Christian
AU - Robert Seiringer
ID - 2331
TI - Spectral properties of the BCS gap equation of superfluidity
ER -
TY - CONF
AB - We present a rigorous proof of the appearance of quantized vortices in dilute trapped Bose gases with repulsive two-body interactions subject to rotation, which was obtained recently in joint work with Elliott Lieb.14 Starting from the many-body Schrödinger equation, we show that the ground state of such gases is, in a suitable limit, well described by the nonlinear Gross-Pitaevskii equation. In the case of axially symmetric traps, our results show that the appearance of quantized vortices causes spontaneous symmetry breaking in the ground state.
AU - Robert Seiringer
ID - 2332
TI - Vortices and Spontaneous Symmetry Breaking in Rotating Bose Gases
ER -
TY - JOUR
AB - A lower bound is derived on the free energy (per unit volume) of a homogeneous Bose gas at density Q and temperature T. In the dilute regime, i.e., when a3 1, where a denotes the scattering length of the pair-interaction potential, our bound differs to leading order from the expression for non-interacting particles by the term 4πa(2 2}-[ - c]2+). Here, c(T) denotes the critical density for Bose-Einstein condensation (for the non-interacting gas), and [ · ]+ = max{ ·, 0} denotes the positive part. Our bound is uniform in the temperature up to temperatures of the order of the critical temperature, i.e., T ~ 2/3 or smaller. One of the key ingredients in the proof is the use of coherent states to extend the method introduced in [17] for estimating correlations to temperatures below the critical one.
AU - Robert Seiringer
ID - 2374
IS - 3
JF - Communications in Mathematical Physics
TI - Free energy of a dilute Bose gas: Lower bound
VL - 279
ER -
TY - JOUR
AB - We derive upper and lower bounds on the critical temperature Tc and the energy gap Ξ (at zero temperature) for the BCS gap equation, describing spin- 1 2 fermions interacting via a local two-body interaction potential λV(x). At weak coupling λ 1 and under appropriate assumptions on V(x), our bounds show that Tc ∼A exp(-B/λ) and Ξ∼C exp(-B/λ) for some explicit coefficients A, B, and C depending on the interaction V(x) and the chemical potential μ. The ratio A/C turns out to be a universal constant, independent of both V(x) and μ. Our analysis is valid for any μ; for small μ, or low density, our formulas reduce to well-known expressions involving the scattering length of V(x).
AU - Hainzl, Christian
AU - Robert Seiringer
ID - 2376
IS - 18
JF - Physical Review B - Condensed Matter and Materials Physics
TI - Critical temperature and energy gap for the BCS equation
VL - 77
ER -
TY - JOUR
AB - We prove that the critical temperature for the BCS gap equation is given by T c = μ ( 8\π e γ-2+ o(1)) e π/(2μa) in the low density limit μ→ 0, with γ denoting Euler's constant. The formula holds for a suitable class of interaction potentials with negative scattering length a in the absence of bound states.
AU - Hainzl, Christian
AU - Robert Seiringer
ID - 2377
IS - 2-3
JF - Letters in Mathematical Physics
TI - The BCS critical temperature for potentials with negative scattering length
VL - 84
ER -
TY - JOUR
AB - We derive a lower bound on the ground state energy of the Hubbard model for given value of the total spin. In combination with the upper bound derived previously by Giuliani (J. Math. Phys. 48:023302, [2007]), our result proves that in the low density limit the leading order correction compared to the ground state energy of a non-interacting lattice Fermi gas is given by 8πaσ uσ d , where σ u(d) denotes the density of the spin-up (down) particles, and a is the scattering length of the contact interaction potential. This result extends previous work on the corresponding continuum model to the lattice case.
AU - Robert Seiringer
AU - Yin, Jun
ID - 2378
IS - 6
JF - Journal of Statistical Physics
TI - Ground state energy of the low density hubbard model
VL - 131
ER -
TY - JOUR
AU - Frank, Rupert L
AU - Lieb, Élliott H
AU - Robert Seiringer
ID - 2379
IS - 4
JF - Journal of the American Mathematical Society
TI - Hardy-Lieb-Thirring inequalities for fractional Schrödinger operators
VL - 21
ER -
TY - JOUR
AB - The Bardeen-Cooper-Schrieffer (BCS) functional has recently received renewed attention as a description of fermionic gases interacting with local pairwise interactions. We present here a rigorous analysis of the BCS functional for general pair interaction potentials. For both zero and positive temperature, we show that the existence of a non-trivial solution of the nonlinear BCS gap equation is equivalent to the existence of a negative eigenvalue of a certain linear operator. From this we conclude the existence of a critical temperature below which the BCS pairing wave function does not vanish identically. For attractive potentials, we prove that the critical temperature is non-zero and exponentially small in the strength of the potential.
AU - Hainzl, Christian
AU - Hamza, Eman
AU - Robert Seiringer
AU - Solovej, Jan P
ID - 2380
IS - 2
JF - Communications in Mathematical Physics
TI - The BCS functional for general pair interactions
VL - 281
ER -
TY - JOUR
AB - We determine the sharp constant in the Hardy inequality for fractional Sobolev spaces. To do so, we develop a non-linear and non-local version of the ground state representation, which even yields a remainder term. From the sharp Hardy inequality we deduce the sharp constant in a Sobolev embedding which is optimal in the Lorentz scale. In the appendix, we characterize the cases of equality in the rearrangement inequality in fractional Sobolev spaces.
AU - Frank, Rupert L
AU - Robert Seiringer
ID - 2381
IS - 12
JF - Journal of Functional Analysis
TI - Non-linear ground state representations and sharp Hardy inequalities
VL - 255
ER -
TY - JOUR
AB - We show that the Lieb-Liniger model for one-dimensional bosons with repulsive δ-function interaction can be rigorously derived via a scaling limit from a dilute three-dimensional Bose gas with arbitrary repulsive interaction potential of finite scattering length. For this purpose, we prove bounds on both the eigenvalues and corresponding eigenfunctions of three-dimensional bosons in strongly elongated traps and relate them to the corresponding quantities in the Lieb-Liniger model. In particular, if both the scattering length a and the radius r of the cylindrical trap go to zero, the Lieb-Liniger model with coupling constant g ∼ a/r 2 is derived. Our bounds are uniform in g in the whole parameter range 0 ≤ g ≤ ∞, and apply to the Hamiltonian for three-dimensional bosons in a spectral window of size ∼ r -2 above the ground state energy.
AU - Robert Seiringer
AU - Yin, Jun
ID - 2382
IS - 2
JF - Communications in Mathematical Physics
TI - The Lieb-Liniger model as a limit of dilute bosons in three dimensions
VL - 284
ER -
TY - JOUR
AB - We study the relativistic electron-positron field at positive temperature in the Hartree-Fock approximation. We consider both the case with and without exchange terms, and investigate the existence and properties of minimizers. Our approach is non-perturbative in the sense that the relevant electron subspace is determined in a self-consistent way. The present work is an extension of previous work by Hainzl, Lewin, Séré and Solovej where the case of zero temperature was considered.
AU - Hainzl, Christian
AU - Lewin, Mathieu
AU - Robert Seiringer
ID - 2383
IS - 10
JF - Reviews in Mathematical Physics
TI - A nonlinear model for relativistic electrons at positive temperature
VL - 20
ER -
TY - CONF
AB - We review our proof that in a scaling limit, the time evolution of a quantum particle in a static random environment leads to a diffusion equation. In particular, we discuss the role of Feynman graph expansions and of renormalization.
AU - László Erdös
AU - Salmhofer, Manfred
AU - Yau, Horng-Tzer
ID - 2702
TI - Feynman graphs and renormalization in quantum diffusion
ER -
TY - JOUR
AB - The field of cavity quantum electrodynamics (QED), traditionally studied in atomic systems, has gained new momentum by recent reports of quantum optical experiments with solid-state semiconducting and superconducting systems. In cavity QED, the observation of the vacuum Rabi mode splitting is used to investigate the nature of matter-light interaction at a quantum-mechanical level. However, this effect can, at least in principle, be explained classically as the normal mode splitting of two coupled linear oscillators. It has been suggested that an observation of the scaling of the resonant atom-photon coupling strength in the Jaynes-Cummings energy ladder with the square root of photon number n is sufficient to prove that the system is quantum mechanical in nature. Here we report a direct spectroscopic observation of this characteristic quantum nonlinearity. Measuring the photonic degree of freedom of the coupled system, our measurements provide unambiguous spectroscopic evidence for the quantum nature of the resonant atom-field interaction in cavity QED. We explore atom-photon superposition states involving up to two photons, using a spectroscopic pump and probe technique. The experiments have been performed in a circuit QED set-up, in which very strong coupling is realized by the large dipole coupling strength and the long coherence time of a superconducting qubit embedded in a high-quality on-chip microwave cavity. Circuit QED systems also provide a natural quantum interface between flying qubits (photons) and stationary qubits for applications in quantum information processing and communication.
AU - Johannes Fink
AU - Göppl, M
AU - Baur, Matthias P
AU - Bianchetti, R
AU - Leek, Peter J
AU - Blais, Alexandre
AU - Wallraff, Andreas
ID - 1763
IS - 7202
JF - Nature
TI - Climbing the Jaynes-Cummings ladder and observing its √n nonlinearity in a cavity QED system
VL - 454
ER -
TY - JOUR
AB - High quality on-chip microwave resonators have recently found prominent new applications in quantum optics and quantum information processing experiments with superconducting electronic circuits, a field now known as circuit quantum electrodynamics (QED). They are also used as single photon detectors and parametric amplifiers. Here we analyze the physical properties of coplanar waveguide resonators and their relation to the materials properties for use in circuit QED. We have designed and fabricated resonators with fundamental frequencies from 2 to 9 GHz and quality factors ranging from a few hundreds to a several hundred thousands controlled by appropriately designed input and output coupling capacitors. The microwave transmission spectra measured at temperatures of 20 mK are shown to be in good agreement with theoretical lumped element and distributed element transmission matrix models. In particular, the experimentally determined resonance frequencies, quality factors, and insertion losses are fully and consistently explained by the two models for all measured devices. The high level of control and flexibility in design renders these resonators ideal for storing and manipulating quantum electromagnetic fields in integrated superconducting electronic circuits.
AU - Göppl, M
AU - Fragner, A
AU - Baur, Matthias P
AU - Bianchetti, R
AU - Filipp, Stefan
AU - Johannes Fink
AU - Leek, Peter J
AU - Puebla, G
AU - Steffen, L. Kraig
AU - Wallraff, Andreas
ID - 1765
IS - 11
JF - Journal of Applied Physics
TI - Coplanar waveguide resonators for circuit quantum electrodynamics
VL - 104
ER -
TY - JOUR
AB - We consider the linear stochastic Cauchy problem dX (t) =AX (t) dt +B dWH (t), t≥ 0, where A generates a C0-semigroup on a Banach space E, WH is a cylindrical Brownian motion over a Hilbert space H, and B: H → E is a bounded operator. Assuming the existence of a unique minimal invariant measure μ∞, let Lp denote the realization of the Ornstein-Uhlenbeck operator associated with this problem in Lp (E, μ∞). Under suitable assumptions concerning the invariance of the range of B under the semigroup generated by A, we prove the following domain inclusions, valid for 1 < p ≤ 2: Image omitted. Here WHk, p (E, μinfin; denotes the kth order Sobolev space of functions with Fréchet derivatives up to order k in the direction of H. No symmetry assumptions are made on L p.
AU - Jan Maas
AU - van Neerven, Jan M
ID - 2120
IS - 4
JF - Infinite Dimensional Analysis, Quantum Probability and Related Topics
TI - On the domain of non-symmetric Ornstein-Uhlenbeck operators in banach spaces
VL - 11
ER -
TY - JOUR
AB - Let H be a separable real Hubert space and let double struck F sign = (ℱt)t∈[0,T] be the augmented filtration generated by an H-cylindrical Brownian motion (WH(t))t∈[0,T] on a probability space (Ω, ℱ ℙ). We prove that if E is a UMD Banach space, 1 ≤ p < ∞, and F ∈ double struck D sign1,p(Ω E) is ℱT-measurable, then F = double struck E sign(F) + ∫0T Pdouble struck F sign(DF) dW H, where D is the Malliavin derivative of F and P double struck F sign is the projection onto the F-adapted elements in a suitable Banach space of Lp-stochastically integrable ℒ(H, E)-valued processes.
AU - van Neerven, Jan M
AU - Jan Maas
ID - 2121
JF - Electronic Communications in Probability
TI - A Clark-Ocone formula in UMD Banach spaces
VL - 13
ER -
TY - JOUR
AB - We present an analytic model of thermal state-to-state rotationally inelastic collisions of polar molecules in electric fields. The model is based on the Fraunhofer scattering of matter waves and requires Legendre moments characterizing the “shape” of the target in the body-fixed frame as its input. The electric field orients the target in the space-fixed frame and thereby effects a striking alteration of the dynamical observables: both the phase and amplitude of the oscillations in the partial differential cross sections undergo characteristic field-dependent changes that transgress into the partial integral cross sections. As the cross sections can be evaluated for a field applied parallel or perpendicular to the relative velocity, the model also offers predictions about steric asymmetry. We exemplify the field-dependent quantum collision dynamics with the behavior of the Ne–OCS(Σ1) and Ar–NO(Π2) systems. A comparison with the close-coupling calculations available for the latter system [Chem. Phys. Lett.313, 491 (1999)] demonstrates the model’s ability to qualitatively explain the field dependence of all the scattering features observed.
AU - Mikhail Lemeshko
AU - Friedrich, Břetislav
ID - 2146
IS - 2
JF - Journal of Chemical Physics
TI - An analytic model of rotationally inelastic collisions of polar molecules in electric fields
VL - 129
ER -
TY - JOUR
AB - Homeostasis of internal carbon dioxide (CO2) and oxygen (O2) levels is fundamental to all animals. Here we examine the CO2 response of the nematode Caenorhabditis elegans. This species inhabits rotting material, which typically has a broad CO2 concentration range. We show that well fed C. elegans avoid CO2 levels above 0.5%. Animals can respond to both absolute CO2 concentrations and changes in CO2 levels within seconds. Responses to CO2 do not reflect avoidance of acid pH but appear to define a new sensory response. Sensation of CO2 is promoted by the cGMP-gated ion channel subunits TAX-2 and TAX-4, but other pathways are also important. Robust CO2 avoidance in well fed animals requires inhibition of the DAF-16 forkhead transcription factor by the insulin-like receptor DAF-2. Starvation, which activates DAF-16, strongly suppresses CO2 avoidance. Exposure to hypoxia (<1% O2) also suppresses CO2 avoidance via activation of the hypoxia-inducible transcription factor HIF-1. The npr-1 215V allele of the naturally polymorphic neuropeptide receptor npr-1, besides inhibiting avoidance of high ambient O2 in feeding C. elegans, also promotes avoidance of high CO2. C. elegans integrates competing O2 and CO2 sensory inputs so that one response dominates. Food and allelic variation at NPR-1 regulate which response prevails. Our results suggest that multiple sensory inputs are coordinated by C. elegans to generate different coherent foraging strategies.
AU - Bretscher, A. J.
AU - Busch, K. E.
AU - de Bono, Mario
ID - 6146
IS - 23
JF - Proceedings of the National Academy of Sciences
SN - 0027-8424
TI - A carbon dioxide avoidance behavior is integrated with responses to ambient oxygen and food in Caenorhabditis elegans
VL - 105
ER -
TY - JOUR
AB - We calculate the E-polynomials of certain twisted GL(n,ℂ)-character varieties Mn of Riemann surfaces by counting points over finite fields using the character table of the finite group of Lie-type GL(n, q) and a theorem proved in the appendix by N. Katz. We deduce from this calculation several geometric results, for example, the value of the topological Euler characteristic of the associated PGL(n,ℂ)-character variety. The calculation also leads to several conjectures about the cohomology of Mn: an explicit conjecture for its mixed Hodge polynomial; a conjectured curious hard Lefschetz theorem and a conjecture relating the pure part to absolutely indecomposable representations of a certain quiver. We prove these conjectures for n=2.
AU - Tamas Hausel
AU - Rodríguez Villegas, Fernando
ID - 1460
IS - 3
JF - Inventiones Mathematicae
TI - Mixed Hodge polynomials of character varieties: With an appendix by Nicholas M. Katz
VL - 174
ER -
TY - JOUR
AB - We report on the control of interaction-induced dephasing of Bloch oscillations for an atomic Bose-Einstein condensate in an optical lattice. We quantify the dephasing in terms of the width of the quasimomentum distribution and measure its dependence on time for different interaction strengths which we control by means of a Feshbach resonance. For minimal interaction, the dephasing time is increased from a few to more than 20 thousand Bloch oscillation periods, allowing us to realize a BEC-based atom interferometer in the noninteracting limit.
AU - Gustavsson, Mattias
AU - Haller, Elmar
AU - Mark, Manfred
AU - Danzl, Johann G
AU - Rojas Kopeinig, Gabriel
AU - Nägerl, Hanns
ID - 1036
IS - 8
JF - Physical Review Letters
TI - Control of interaction-induced dephasing of bloch oscillations
VL - 100
ER -
TY - JOUR
AB - We experimentally demonstrate Cs2 Feshbach molecules well above the dissociation threshold, which are stable against spontaneous decay on the time scale of 1s. An optically trapped sample of ultracold dimers is prepared in a high rotational state and magnetically tuned into a region with a negative binding energy. The metastable character of these molecules arises from the large centrifugal barrier in combination with negligible coupling to states with low rotational angular momentum. A sharp onset of dissociation with increasing magnetic field is mediated by a crossing with a lower rotational dimer state and facilitates dissociation on demand with a well-defined energy.
AU - Knoop, Steven
AU - Mark, Michael
AU - Ferlaino, Francesca
AU - Danzl, Johann G
AU - Kraemer, Tobias
AU - Nägerl, Hanns
AU - Grimm, Rudolf
ID - 1037
IS - 8
JF - Physical Review Letters
TI - Metastable feshbach molecules in high rotational states
VL - 100
ER -
TY - JOUR
AB - Molecular cooling techniques face the hurdle of dissipating translational as well as internal energy in the presence of a rich electronic, vibrational, and rotational energy spectrum. In our experiment, we create a translationally ultracold, dense quantum gas of molecules bound by more than 1000 wave numbers in the electronic ground state. Specifically, we stimulate with 80% efficiency, a two-photon transfer of molecules associated on a Feshbach resonance from a Bose-Einstein condensate of cesium atoms. In the process, the initial loose, long-range electrostatic bond of the Feshbach molecule is coherently transformed into a tight chemical bond. We demonstrate coherence of the transfer in a Ramsey-type experiment and show that the molecular sample is not heated during the transfer. Our results show that the preparation of a quantum gas of molecules in specific rovibrational states is possible and that the creation of a Bose-Einstein condensate of molecules in their rovibronic ground state is within reach.
AU - Danzl, Johann G
AU - Haller, Elmar
AU - Gustavsson, Mattias
AU - Mark, Manfred
AU - Hart, Russell
AU - Bouloufa, Nadia
AU - Dulieu, Olivier
AU - Ritsch, Helmut
AU - Nägerl, Hanns
ID - 1039
IS - 5892
JF - Science
TI - Quantum gas of deeply bound ground state molecules
VL - 321
ER -
TY - JOUR
AB - We give many examples of applying Bogoliubov's forest formula to iterative solutions of various nonlinear equations. The same formula describes an extremely wide class of objects, from an ordinary quadratic equation to renormalization in quantum field theory.
AU - Morozov, Alexei Y
AU - Maksym Serbyn
ID - 965
IS - 2
JF - Theoretical and Mathematical Physics
TI - Nonlinear algebra and Bogoliubov's recursion
VL - 154
ER -
TY - JOUR
AB - Gene expression levels fluctuate even under constant external conditions. Much emphasis has usually been placed on the components of this noise that are due to randomness in transcription and translation. Here we focus on the role of noise associated with the inputs to transcriptional regulation; in particular, we analyze the effects of random arrival times and binding of transcription factors to their target sites along the genome. This contribution to the total noise sets a fundamental physical limit to the reliability of genetic control, and has clear signatures, but we show that these are easily obscured by experimental limitations and even by conventional methods for plotting the variance vs. mean expression level. We argue that simple, universal models of noise dominated by transcription and translation are inconsistent with the embedding of gene expression in a network of regulatory interactions. Analysis of recent experiments on transcriptional control in the early Drosophila embryo shows that these results are quantitatively consistent with the predicted signatures of input noise, and we discuss the experiments needed to test the importance of input noise more generally.
AU - Gasper Tkacik
AU - Gregor, Thomas
AU - Bialek, William S
ID - 3734
IS - 7
JF - PLoS One
TI - The role of input noise in transcriptional regulation
VL - 3
ER -
TY - JOUR
AB - In the simplest view of transcriptional regulation, the expression of a gene is turned on or off by changes in the concentration of a transcription factor (TF). We use recent data on noise levels in gene expression to show that it should be possible to transmit much more than just one regulatory bit. Realizing this optimal information capacity would require that the dynamic range of TF concentrations used by the cell, the input/output relation of the regulatory module, and the noise in gene expression satisfy certain matching relations, which we derive. These results provide parameter-free, quantitative predictions connecting independently measurable quantities. Although we have considered only the simplified problem of a single gene responding to a single TF, we find that these predictions are in surprisingly good agreement with recent experiments on the Bicoid/Hunchback system in the early Drosophila embryo and that this system achieves approximately 90% of its theoretical maximum information transmission.
AU - Gasper Tkacik
AU - Callan,Curtis G
AU - Bialek, William S
ID - 3740
IS - 34
JF - PNAS
TI - Information flow and optimization in transcriptional regulation
VL - 105
ER -
TY - JOUR
AB - It is widely acknowledged that detailed timing of action potentials is used to encode information, for example, in auditory pathways; however, the computational tools required to analyze encoding through timing are still in their infancy. We present a simple example of encoding, based on a recent model of time-frequency analysis, in which units fire action potentials when a certain condition is met, but the timing of the action potential depends also on other features of the stimulus. We show that, as a result, spike-triggered averages are smoothed so much that they do not represent the true features of the encoding. Inspired by this example, we present a simple method, differential reverse correlations, that can separate an analysis of what causes a neuron to spike, and what controls its timing. We analyze with this method the leaky integrate-and-fire neuron and show the method accurately reconstructs the model's kernel.
AU - Gasper Tkacik
AU - Magnasco, Marcelo O
ID - 3744
IS - 1-2
JF - Biosystems
TI - Decoding spike timing: The differential reverse-correlation method
VL - 93
ER -
TY - JOUR
AB - Revealing the spectrum of combinatorial regulation of transcription at individual promoters is essential for understanding the complex structure of biological networks. However, the computations represented by the integration of various molecular signals at complex promoters are difficult to decipher in the absence of simple cis regulatory codes. Here we synthetically shuffle the regulatory architecture-operator sequences binding activators and repressors-of a canonical bacterial promoter. The resulting library of complex promoters allows for rapid exploration of promoter encoded logic regulation. Among all possible logic functions, NOR and ANDN promoter encoded logics predominate. A simple transcriptional cis regulatory code determines both logics, establishing a straightforward map between promoter structure and logic phenotype. The regulatory code is determined solely by the type of transcriptional regulation combinations: two repressors generate a NOR: NOT (a OR b) whereas a repressor and an activator generate an ANDN: a AND NOT b. Three-input versions of both logics, having an additional repressor as an input, are also present in the library. The resulting complex promoters cover a wide dynamic range of transcriptional strengths. Synthetic promoter shuffling represents a fast and efficient method for exploring the spectrum of complex regulatory functions that can be encoded by complex promoters. From an engineering point of view, synthetic promoter shuffling enables the experimental testing of the functional properties of complex promoters that cannot necessarily be inferred ab initio from the known properties of the individual genetic components. Synthetic promoter shuffling may provide a useful experimental tool for studying naturally occurring promoter shuffling.
AU - Kinkhabwala, Ali
AU - Guet, Calin C
ID - 3751
IS - 4
JF - PLoS One
TI - Uncovering cis regulatory codes using synthetic promoter shuffling
VL - 3
ER -
TY - JOUR
AB - Dentate gyrus granule cells transmit action potentials (APs) along their unmyelinated mossy fibre axons to the CA3 region. Although the initiation and propagation of APs are fundamental steps during neural computation, little is known about the site of AP initiation and the speed of propagation in mossy fibre axons. To address these questions, we performed simultaneous somatic and axonal whole-cell recordings from granule cells in acute hippocampal slices of adult mice at approximately 23 degrees C. Injection of short current pulses or synaptic stimulation evoked axonal and somatic APs with similar amplitudes. By contrast, the time course was significantly different, as axonal APs had a higher maximal rate of rise (464 +/- 30 V s(-1) in the axon versus 297 +/- 12 V s(-1) in the soma, mean +/- s.e.m.). Furthermore, analysis of latencies between the axonal and somatic signals showed that APs were initiated in the proximal axon at approximately 20-30 mum distance from the soma, and propagated orthodromically with a velocity of 0.24 m s(-1). Qualitatively similar results were obtained at a recording temperature of approximately 34 degrees C. Modelling of AP propagation in detailed cable models of granule cells suggested that a approximately 4 times higher Na(+) channel density ( approximately 1000 pS mum(-2)) in the axon might account for both the higher rate of rise of axonal APs and the robust AP initiation in the proximal mossy fibre axon. This may be of critical importance to separate dendritic integration of thousands of synaptic inputs from the generation and transmission of a common AP output.
AU - Schmidt-Hieber, Christoph
AU - Peter Jonas
AU - Bischofberger, Josef
ID - 3822
IS - 7
JF - Journal of Physiology
TI - Action potential initiation and propagation in hippocampal mossy fibre axons
VL - 586
ER -
TY - JOUR
AB - Fast-spiking parvalbumin-expressing basket cells (BCs) represent a major type of inhibitory interneuron in the hippocampus. These cells inhibit principal cells in a temporally precise manner and are involved in the generation of network oscillations. Although BCs show a unique expression profile of Ca(2+)-permeable receptors, Ca(2+)-binding proteins and Ca(2+)-dependent signalling molecules, physiological Ca(2+) signalling in these interneurons has not been investigated. To study action potential (AP)-induced dendritic Ca(2+) influx and buffering, we combined whole-cell patch-clamp recordings with ratiometric Ca(2+) imaging from the proximal apical dendrites of rigorously identified BCs in acute slices, using the high-affinity Ca(2+) indicator fura-2 or the low-affinity dye fura-FF. Single APs evoked dendritic Ca(2+) transients with small amplitude. Bursts of APs evoked Ca(2+) transients with amplitudes that increased linearly with AP number. Analysis of Ca(2+) transients under steady-state conditions with different fura-2 concentrations and during loading with 200 microm fura-2 indicated that the endogenous Ca(2+)-binding ratio was approximately 200 (kappa(S) = 202 +/- 26 for the loading experiments). The peak amplitude of the Ca(2+) transients measured directly with 100 microm fura-FF was 39 nm AP(-1). At approximately 23 degrees C, the decay time constant of the Ca(2+) transients was 390 ms, corresponding to an extrusion rate of approximately 600 s(-1). At 34 degrees C, the decay time constant was 203 ms and the corresponding extrusion rate was approximately 1100 s(-1). At both temperatures, continuous theta-burst activity with three to five APs per theta cycle, as occurs in vivo during exploration, led to a moderate increase in the global Ca(2+) concentration that was proportional to AP number, whereas more intense stimulation was required to reach micromolar Ca(2+) concentrations and to shift Ca(2+) signalling into a non-linear regime. In conclusion, dentate gyrus BCs show a high endogenous Ca(2+)-binding ratio, a small AP-induced dendritic Ca(2+) influx, and a relatively slow Ca(2+) extrusion. These specific buffering properties of BCs will sharpen the time course of local Ca(2+) signals, while prolonging the decay of global Ca(2+) signals.
AU - Aponte, Yexica
AU - Bischofberger, Josef
AU - Peter Jonas
ID - 3825
IS - 8
JF - Journal of Physiology
TI - Efficient Ca(2+) buffering in fast-spiking basket cells of rat hippocampus
VL - 586
ER -
TY - CONF
AB - We study the problem of generating a test sequence that achieves maximal coverage for a reactive system under test. We formulate the problem as a repeated game between the tester and the system, where the system state space is partitioned according to some coverage criterion and the objective of the tester is to maximize the set of partitions (or coverage goals) visited during the game. We show the complexity of the maximal coverage problem for non-deterministic systems is PSPACE-complete, but is NP-complete for deterministic systems. For the special case of non-deterministic systems with a re-initializing “reset” action, which represent running a new test input on a re-initialized system, we show that the complexity is coNP-complete. Our proof technique for reset games uses randomized testing strategies that circumvent the exponentially large memory requirement of deterministic testing strategies.
AU - Krishnendu Chatterjee
AU - de Alfaro, Luca
AU - Majumdar, Ritankar S
ID - 3878
TI - The complexity of coverage
VL - 5356
ER -