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 -