1,170 research outputs found
Logic and model checking for hidden Markov models
The branching-time temporal logic PCTL* has been introduced to specify quantitative properties over probability systems, such as discrete-time Markov chains. Until now, however, no logics have been defined to specify properties over hidden Markov models (HMMs). In HMMs the states are hidden, and the hidden processes produce a sequence of observations. In this paper we extend the logic PCTL* to POCTL*. With our logic one can state properties such as "there is at least a 90 percent probability that the model produces a given sequence of observations" over HMMs. Subsequently, we give model checking algorithms for POCTL* over HMMs
Ab initio transport results for strongly correlated fermions
Quantum transport of strongly correlated fermions is of central interest in
condensed matter physics. Here, we present first-principle nonequilibrium Green
functions results using -matrix selfenergies for finite Hubbard clusters of
dimension . We compute the expansion dynamics following a potential
quench and predict its dependence on the interaction strength and particle
number. We discover a universal scaling, allowing an extrapolation to
infinite-size systems, which shows excellent agreement with recent cold atom
diffusion experiments [Schneider et al., Nat. Phys. 8, 213 (2012)]
A probabilistic extension of UML statecharts: specification and verification
This paper is the extended technical report that corresponds to a published paper [14]. This paper introduces means to specify system randomness within UML statecharts, and to verify probabilistic temporal properties over such enhanced statecharts which we call probabilistic UML statecharts. To achieve this, we develop a general recipe to extend a statechart semantics with discrete probability distributions, resulting in Markov decision processes as semantic models. We apply this recipe to the requirements-level UML semantics of [8]. Properties of interest for probabilistic statecharts are expressed in PCTL, a probabilistic variant of CTL for processes that exhibit both non-determinism and probabilities. Verification is performed using the model checker Prism. A model checking example shows the feasibility of the suggested approach
Haldane Statistics in the Finite Size Entanglement Spectra of Laughlin States
We conjecture that the counting of the levels in the orbital entanglement
spectra (OES) of finite-sized Laughlin Fractional Quantum Hall (FQH) droplets
at filling is described by the Haldane statistics of particles in a
box of finite size. This principle explains the observed deviations of the OES
counting from the edge-mode conformal field theory counting and directly
provides us with a topological number of the FQH states inaccessible in the
thermodynamic limit- the boson compactification radius. It also suggests that
the entanglement gap in the Coulomb spectrum in the conformal limit protects a
universal quantity- the statistics of the state. We support our conjecture with
ample numerical checks.Comment: 4.1 pages, published versio
Bulk-Edge Correspondence in the Entanglement Spectra
Li and Haldane conjectured and numerically substantiated that the
entanglement spectrum of the reduced density matrix of ground-states of
time-reversal breaking topological phases (fractional quantum Hall states)
contains information about the counting of their edge modes when the
ground-state is cut in two spatially distinct regions and one of the regions is
traced out. We analytically substantiate this conjecture for a series of FQH
states defined as unique zero modes of pseudopotential Hamiltonians by finding
a one to one map between the thermodynamic limit counting of two different
entanglement spectra: the particle entanglement spectrum, whose counting of
eigenvalues for each good quantum number is identical (up to accidental
degeneracies) to the counting of bulk quasiholes, and the orbital entanglement
spectrum (the Li-Haldane spectrum). As the particle entanglement spectrum is
related to bulk quasihole physics and the orbital entanglement spectrum is
related to edge physics, our map can be thought of as a mathematically sound
microscopic description of bulk-edge correspondence in entanglement spectra. By
using a set of clustering operators which have their origin in conformal field
theory (CFT) operator expansions, we show that the counting of the orbital
entanglement spectrum eigenvalues in the thermodynamic limit must be identical
to the counting of quasiholes in the bulk. The latter equals the counting of
edge modes at a hard-wall boundary placed on the sample. Moreover, we show this
to be true even for CFT states which are likely bulk gapless, such as the
Gaffnian wavefunction.Comment: 20 pages, 6 figure
Rate-Based Transition Systems for Stochastic Process Calculi
A variant of Rate Transition Systems (RTS), proposed by Klin and Sassone, is introduced and used as the basic model for defining stochastic behaviour of processes. The transition relation used in our variant associates to each process, for each action, the set of possible futures paired with a measure indicating their rates. We show how RTS can be used for providing the operational semantics of stochastic extensions of classical formalisms, namely CSP and CCS. We also show that our semantics for stochastic CCS guarantees associativity of parallel composition. Similarly, in contrast with the original definition by Priami, we argue that a semantics for stochastic Ï-calculus can be provided that guarantees associativity of parallel composition
Compositional Performance Modelling with the TIPPtool
Stochastic process algebras have been proposed as compositional specification formalisms for performance models. In this paper, we describe a tool which aims at realising all beneficial aspects of compositional performance modelling, the TIPPtool. It incorporates methods for compositional specification as well as solution, based on state-of-the-art techniques, and wrapped in a user-friendly graphical front end. Apart from highlighting the general benefits of the tool, we also discuss some lessons learned during development and application of the TIPPtool. A non-trivial model of a real life communication system serves as a case study to illustrate benefits and limitations
Think Eternally: Improved Algorithms for the Temp Secretary Problem and Extensions
The Temp Secretary Problem was recently introduced by [Fiat et al., ESA 2015]. It is a generalization of the Secretary Problem, in which commitments are temporary for a fixed duration. We present a simple online algorithm with improved performance guarantees for cases already considered by [Fiat et al., ESA 2015] and give competitive ratios for new generalizations of the problem. In the classical setting, where candidates have identical contract durations gamma << 1 and we are allowed to hire up to B candidates simultaneously, our algorithm is (1/2) - O(sqrt{gamma})-competitive. For large B, the bound improves to 1 - O(1/sqrt{B}) - O(sqrt{gamma}).
Furthermore we generalize the problem from cardinality constraints towards general packing constraints. We achieve a competitive ratio of 1 - O(sqrt{(1+log(d) + log(B))/B}) - O(sqrt{gamma}), where d is the sparsity of the constraint matrix and B is generalized to the capacity ratio of linear constraints. Additionally we extend the problem towards arbitrary hiring durations.
Our algorithmic approach is a relaxation that aggregates all temporal constraints into a non-temporal constraint. Then we apply a linear scaling algorithm that, on every arrival, computes a tentative solution on the input that is known up to this point. This tentative solution uses the non-temporal, relaxed constraints scaled down linearly by the amount of time that has already passed
A Hierarchy of Scheduler Classes for Stochastic Automata
Stochastic automata are a formal compositional model for concurrent
stochastic timed systems, with general distributions and non-deterministic
choices. Measures of interest are defined over schedulers that resolve the
nondeterminism. In this paper we investigate the power of various theoretically
and practically motivated classes of schedulers, considering the classic
complete-information view and a restriction to non-prophetic schedulers. We
prove a hierarchy of scheduler classes w.r.t. unbounded probabilistic
reachability. We find that, unlike Markovian formalisms, stochastic automata
distinguish most classes even in this basic setting. Verification and strategy
synthesis methods thus face a tradeoff between powerful and efficient classes.
Using lightweight scheduler sampling, we explore this tradeoff and demonstrate
the concept of a useful approximative verification technique for stochastic
automata
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