1,822 research outputs found
Algorithmic Analysis of Qualitative and Quantitative Termination Problems for Affine Probabilistic Programs
In this paper, we consider termination of probabilistic programs with
real-valued variables. The questions concerned are:
1. qualitative ones that ask (i) whether the program terminates with
probability 1 (almost-sure termination) and (ii) whether the expected
termination time is finite (finite termination); 2. quantitative ones that ask
(i) to approximate the expected termination time (expectation problem) and (ii)
to compute a bound B such that the probability to terminate after B steps
decreases exponentially (concentration problem).
To solve these questions, we utilize the notion of ranking supermartingales
which is a powerful approach for proving termination of probabilistic programs.
In detail, we focus on algorithmic synthesis of linear ranking-supermartingales
over affine probabilistic programs (APP's) with both angelic and demonic
non-determinism. An important subclass of APP's is LRAPP which is defined as
the class of all APP's over which a linear ranking-supermartingale exists.
Our main contributions are as follows. Firstly, we show that the membership
problem of LRAPP (i) can be decided in polynomial time for APP's with at most
demonic non-determinism, and (ii) is NP-hard and in PSPACE for APP's with
angelic non-determinism; moreover, the NP-hardness result holds already for
APP's without probability and demonic non-determinism. Secondly, we show that
the concentration problem over LRAPP can be solved in the same complexity as
for the membership problem of LRAPP. Finally, we show that the expectation
problem over LRAPP can be solved in 2EXPTIME and is PSPACE-hard even for APP's
without probability and non-determinism (i.e., deterministic programs). Our
experimental results demonstrate the effectiveness of our approach to answer
the qualitative and quantitative questions over APP's with at most demonic
non-determinism.Comment: 24 pages, full version to the conference paper on POPL 201
Stochastic Invariants for Probabilistic Termination
Termination is one of the basic liveness properties, and we study the
termination problem for probabilistic programs with real-valued variables.
Previous works focused on the qualitative problem that asks whether an input
program terminates with probability~1 (almost-sure termination). A powerful
approach for this qualitative problem is the notion of ranking supermartingales
with respect to a given set of invariants. The quantitative problem
(probabilistic termination) asks for bounds on the termination probability. A
fundamental and conceptual drawback of the existing approaches to address
probabilistic termination is that even though the supermartingales consider the
probabilistic behavior of the programs, the invariants are obtained completely
ignoring the probabilistic aspect.
In this work we address the probabilistic termination problem for
linear-arithmetic probabilistic programs with nondeterminism. We define the
notion of {\em stochastic invariants}, which are constraints along with a
probability bound that the constraints hold. We introduce a concept of {\em
repulsing supermartingales}. First, we show that repulsing supermartingales can
be used to obtain bounds on the probability of the stochastic invariants.
Second, we show the effectiveness of repulsing supermartingales in the
following three ways: (1)~With a combination of ranking and repulsing
supermartingales we can compute lower bounds on the probability of termination;
(2)~repulsing supermartingales provide witnesses for refutation of almost-sure
termination; and (3)~with a combination of ranking and repulsing
supermartingales we can establish persistence properties of probabilistic
programs.
We also present results on related computational problems and an experimental
evaluation of our approach on academic examples.Comment: Full version of a paper published at POPL 2017. 20 page
Strong, Weak and Branching Bisimulation for Transition Systems and Markov Reward Chains: A Unifying Matrix Approach
We first study labeled transition systems with explicit successful
termination. We establish the notions of strong, weak, and branching
bisimulation in terms of boolean matrix theory, introducing thus a novel and
powerful algebraic apparatus. Next we consider Markov reward chains which are
standardly presented in real matrix theory. By interpreting the obtained matrix
conditions for bisimulations in this setting, we automatically obtain the
definitions of strong, weak, and branching bisimulation for Markov reward
chains. The obtained strong and weak bisimulations are shown to coincide with
some existing notions, while the obtained branching bisimulation is new, but
its usefulness is questionable
Bioactivity of the Murex Homeopathic Remedy and of Extracts from an Australian Muricid Mollusc against Human Cancer Cells
Marine molluscs from the family Muricidae are the source of a homeopathic remedy Murex, which is used to treat a range of conditions, including cancer. The aim of this study was to evaluate the in vitro bioactivity of egg mass extracts of the Australian muricid Dicathais orbita, in comparison to the Murex remedy, against human carcinoma and lymphoma cells. Liquid chromatography coupled with mass spectrometry (LC-MS) was used to characterize the chemical composition of the extracts and homeopathic remedy, focusing on biologically active brominated indoles. The MTS (tetrazolium salt) colorimetric assay was used to determine effects on cell viability, while necrosis and apoptosis induction were investigated using flow cytometry (propidium iodide and Annexin-V staining, resp.). Cells were treated with varying concentrations (1–0.01 mg/mL) of crude and semi-purified extracts or preparations (dilute 1 M and concentrated 4 mg/mL) from the Murex remedy (4 h). The Murex remedy showed little biological activity against the majority of cell lines tested. In contrast, the D. orbita egg extracts significantly decreased cell viability in the majority of carcinoma cell lines. Flow cytometry revealed these extracts induce necrosis in HT29 colorectal cancer cells, whereas apoptosis was induced in Jurkat cells. These findings highlight the biomedical potential of Muricidae extracts in the development of a natural therapy for the treatment of neoplastic tumors and lymphomas
Ranking and Repulsing Supermartingales for Reachability in Probabilistic Programs
Computing reachability probabilities is a fundamental problem in the analysis
of probabilistic programs. This paper aims at a comprehensive and comparative
account on various martingale-based methods for over- and under-approximating
reachability probabilities. Based on the existing works that stretch across
different communities (formal verification, control theory, etc.), we offer a
unifying account. In particular, we emphasize the role of order-theoretic fixed
points---a classic topic in computer science---in the analysis of probabilistic
programs. This leads us to two new martingale-based techniques, too. We give
rigorous proofs for their soundness and completeness. We also make an
experimental comparison using our implementation of template-based synthesis
algorithms for those martingales
Value Iteration for Long-run Average Reward in Markov Decision Processes
Markov decision processes (MDPs) are standard models for probabilistic
systems with non-deterministic behaviours. Long-run average rewards provide a
mathematically elegant formalism for expressing long term performance. Value
iteration (VI) is one of the simplest and most efficient algorithmic approaches
to MDPs with other properties, such as reachability objectives. Unfortunately,
a naive extension of VI does not work for MDPs with long-run average rewards,
as there is no known stopping criterion. In this work our contributions are
threefold. (1) We refute a conjecture related to stopping criteria for MDPs
with long-run average rewards. (2) We present two practical algorithms for MDPs
with long-run average rewards based on VI. First, we show that a combination of
applying VI locally for each maximal end-component (MEC) and VI for
reachability objectives can provide approximation guarantees. Second, extending
the above approach with a simulation-guided on-demand variant of VI, we present
an anytime algorithm that is able to deal with very large models. (3) Finally,
we present experimental results showing that our methods significantly
outperform the standard approaches on several benchmarks
Microscopic theory for the light-induced anomalous Hall effect in graphene
We employ a quantum Liouville equation with relaxation to model the recently
observed anomalous Hall effect in graphene irradiated by an ultrafast pulse of
circularly polarized light. In the weak-field regime, we demonstrate that the
Hall effect originates from an asymmetric population of photocarriers in the
Dirac bands. By contrast, in the strong-field regime, the system is driven into
a non-equilibrium steady state that is well-described by topologically
non-trivial Floquet-Bloch bands. Here, the anomalous Hall current originates
from the combination of a population imbalance in these dressed bands together
with a smaller anomalous velocity contribution arising from their Berry
curvature. This robust and general finding enables the simulation of electrical
transport from light-induced Floquet-Bloch bands in an experimentally relevant
parameter regime and creates a pathway to designing ultrafast quantum devices
with Floquet-engineered transport properties
Bloch Equations and Completely Positive Maps
The phenomenological dissipation of the Bloch equations is reexamined in the
context of completely positive maps. Such maps occur if the dissipation arises
from a reduction of a unitary evolution of a system coupled to a reservoir. In
such a case the reduced dynamics for the system alone will always yield
completely positive maps of the density operator. We show that, for Markovian
Bloch maps, the requirement of complete positivity imposes some Bloch
inequalities on the phenomenological damping constants. For non-Markovian Bloch
maps some kind of Bloch inequalities involving eigenvalues of the damping basis
can be established as well. As an illustration of these general properties we
use the depolarizing channel with white and colored stochastic noise.Comment: Talk given at the Conference "Quantum Challenges", Falenty, Poland,
September 4-7, 2003. 21 pages, 3 figure
On the relation between Differential Privacy and Quantitative Information Flow
Differential privacy is a notion that has emerged in the community of
statistical databases, as a response to the problem of protecting the privacy
of the database's participants when performing statistical queries. The idea is
that a randomized query satisfies differential privacy if the likelihood of
obtaining a certain answer for a database is not too different from the
likelihood of obtaining the same answer on adjacent databases, i.e. databases
which differ from for only one individual. Information flow is an area of
Security concerned with the problem of controlling the leakage of confidential
information in programs and protocols. Nowadays, one of the most established
approaches to quantify and to reason about leakage is based on the R\'enyi min
entropy version of information theory. In this paper, we analyze critically the
notion of differential privacy in light of the conceptual framework provided by
the R\'enyi min information theory. We show that there is a close relation
between differential privacy and leakage, due to the graph symmetries induced
by the adjacency relation. Furthermore, we consider the utility of the
randomized answer, which measures its expected degree of accuracy. We focus on
certain kinds of utility functions called "binary", which have a close
correspondence with the R\'enyi min mutual information. Again, it turns out
that there can be a tight correspondence between differential privacy and
utility, depending on the symmetries induced by the adjacency relation and by
the query. Depending on these symmetries we can also build an optimal-utility
randomization mechanism while preserving the required level of differential
privacy. Our main contribution is a study of the kind of structures that can be
induced by the adjacency relation and the query, and how to use them to derive
bounds on the leakage and achieve the optimal utility
Nonthermal pathways to ultrafast control in quantum materials
We review recent progress in utilizing ultrafast light-matter interaction to
control the macroscopic properties of quantum materials. Particular emphasis is
placed on photoinduced phenomena that do not result from ultrafast heating
effects but rather emerge from microscopic processes that are inherently
nonthermal in nature. Many of these processes can be described as transient
modifications to the free-energy landscape resulting from the redistribution of
quasiparticle populations, the dynamical modification of coupling strengths and
the resonant driving of the crystal lattice. Other pathways result from the
coherent dressing of a material's quantum states by the light field. We discuss
a selection of recently discovered effects leveraging these mechanisms, as well
as the technological advances that led to their discovery. A road map for how
the field can harness these nonthermal pathways to create new functionalities
is presented.Comment: 36 pages, 12 figures; all authors contributed equally to this wor
- …