7,681 research outputs found
Sublinear-Time Algorithms for Monomer-Dimer Systems on Bounded Degree Graphs
For a graph , let be the partition function of the
monomer-dimer system defined by , where is the
number of matchings of size in . We consider graphs of bounded degree
and develop a sublinear-time algorithm for estimating at an
arbitrary value within additive error with high
probability. The query complexity of our algorithm does not depend on the size
of and is polynomial in , and we also provide a lower bound
quadratic in for this problem. This is the first analysis of a
sublinear-time approximation algorithm for a # P-complete problem. Our
approach is based on the correlation decay of the Gibbs distribution associated
with . We show that our algorithm approximates the probability
for a vertex to be covered by a matching, sampled according to this Gibbs
distribution, in a near-optimal sublinear time. We extend our results to
approximate the average size and the entropy of such a matching within an
additive error with high probability, where again the query complexity is
polynomial in and the lower bound is quadratic in .
Our algorithms are simple to implement and of practical use when dealing with
massive datasets. Our results extend to other systems where the correlation
decay is known to hold as for the independent set problem up to the critical
activity
Quantitative Modeling and Verification of Evolving Software
Mit der steigenden Nachfrage nach Innovationen spielt Software in verschiedenenWirtschaftsbereichen
eine wichtige Rolle, wie z.B. in der Automobilindustrie, bei intelligenten Systemen als auch bei Kommunikationssystemen. Daher ist die
Qualität für die Softwareentwicklung von großer Bedeutung.
Allerdings ändern sich die probabilistische Modelle (die Qualitätsbewertungsmodelle)
angesichts der dynamischen Natur moderner Softwaresysteme. Dies führt dazu,
dass ihre Übergangswahrscheinlichkeiten im Laufe der Zeit schwanken, welches zu
erheblichen Problemen führt.
Dahingehend werden probabilistische
Modelle im Hinblick auf ihre Laufzeit kontinuierlich aktualisiert. Eine fortdauernde
Neubewertung komplexer Wahrscheinlichkeitsmodelle ist jedoch teuer. In
letzter Zeit haben sich inkrementelle Ansätze als vielversprechend für die Verifikation
von adaptiven Systemen erwiesen. Trotzdem wurden bei der Bewertung struktureller
Änderungen im Modell noch keine wesentlichen Verbesserungen erzielt. Wahrscheinlichkeitssysteme
werden als Automaten modelliert, wie
bei Markov-Modellen. Solche Modelle können in
Matrixform dargestellt werden, um die Gleichungen basierend auf Zuständen und
Übergangswahrscheinlichkeiten zu lösen.
Laufzeitmodelle wie Matrizen sind nicht signifikant,
um die Auswirkungen von Modellveränderungen erkennen zu können.
In dieser Arbeit wird ein Framework unter Verwendung stochastischer Bäume mit
regulären Ausdrücken entwickelt, welches modular aufgebaut ist und eine aktionshaltige
sowie probabilistische Logik im Kontext der Modellprüfung aufweist. Ein solches
modulares Framework ermöglicht dem Menschen die Entwicklung der Änderungsoperationen
für die inkrementelle Berechnung lokaler Änderungen, die im Modell auftreten
können. Darüber hinaus werden probabilistische Änderungsmuster beschrieben,
um eine effiziente inkrementelle Verifizierung, unter Verwendung von Bäumen mit regulären
Ausdrücken, anwenden zu können. Durch die Bewertung der Ergebnisse wird
der Vorgang abgeschlossen.Software plays an innovative role in many different domains, such as car industry, autonomous
and smart systems, and communication. Hence, the quality of the software
is of utmost importance and needs to be properly addressed during software evolution.
Several approaches have been developed to evaluate systems’ quality attributes, such
as reliability, safety, and performance of software. Due to the dynamic nature of modern software systems, probabilistic models representing the quality of the software and their transition probabilities change over time and fluctuate, leading to a significant problem that needs to be solved to obtain correct evaluation results of quantitative
properties. Probabilistic models need to be continually updated at run-time to
solve this issue. However, continuous re-evaluation of complex probabilistic models is
expensive. Recently, incremental approaches have been found to be promising for the
verification of evolving and self-adaptive systems. Nevertheless, substantial improvements
have not yet been achieved for evaluating structural changes in the model.
Probabilistic systems are usually
represented in a matrix form to solve the equations
based on states and transition probabilities. On the other side, evolutionary changes can create
various effects on theese models and force them to re-verify the whole system. Run-time
models, such as matrices or graph representations, lack the expressiveness to identify
the change effect on the model.
In this thesis, we develop a framework using stochastic regular expression trees,
which are modular, with action-based probabilistic logic in the model checking context.
Such a modular framework enables us to develop change operations for the incremental
computation of local changes that can occur in the model. Furthermore, we describe
probabilistic change patterns to apply efficient incremental quantitative verification using
stochastic regular expression trees and evaluate our results
Correlation function for the Grid-Poisson Euclidean matching on a line and on a circle
We compute the two-point correlation function for spin configurations which
are obtained by solving the Euclidean matching problem, for one family of
points on a grid, and the second family chosen uniformly at random, when the
cost depends on a power of the Euclidean distance. We provide the analytic
solution in the thermodynamic limit, in a number of cases ( open b.c.\ and
periodic b.c., both at criticality), and analyse numerically other parts
of the phase diagram.Comment: 34 pages, 10 figure
Black holes and the butterfly effect
We use holography to study sensitive dependence on initial conditions in
strongly coupled field theories. Specifically, we mildly perturb a thermofield
double state by adding a small number of quanta on one side. If these quanta
are released a scrambling time in the past, they destroy the local two-sided
correlations present in the unperturbed state. The corresponding bulk geometry
is a two-sided AdS black hole, and the key effect is the blueshift of the early
infalling quanta relative to the slice, creating a shock wave. We
comment on string- and Planck-scale corrections to this setup, and discuss
points that may be relevant to the firewall controversy.Comment: 29 pages, 4 figures. v2: references added/clarified, typos corrected.
v3: reference added, referencing clarifie
Sparse approaches for the exact distribution of patterns in long state sequences generated by a Markov source
We present two novel approaches for the computation of the exact distribution
of a pattern in a long sequence. Both approaches take into account the sparse
structure of the problem and are two-part algorithms. The first approach relies
on a partial recursion after a fast computation of the second largest
eigenvalue of the transition matrix of a Markov chain embedding. The second
approach uses fast Taylor expansions of an exact bivariate rational
reconstruction of the distribution. We illustrate the interest of both
approaches on a simple toy-example and two biological applications: the
transcription factors of the Human Chromosome 5 and the PROSITE signatures of
functional motifs in proteins. On these example our methods demonstrate their
complementarity and their hability to extend the domain of feasibility for
exact computations in pattern problems to a new level
Entropy of Some Models of Sparse Random Graphs With Vertex-Names
Consider the setting of sparse graphs on N vertices, where the vertices have
distinct "names", which are strings of length O(log N) from a fixed finite
alphabet. For many natural probability models, the entropy grows as cN log N
for some model-dependent rate constant c. The mathematical content of this
paper is the (often easy) calculation of c for a variety of models, in
particular for various standard random graph models adapted to this setting.
Our broader purpose is to publicize this particular setting as a natural
setting for future theoretical study of data compression for graphs, and (more
speculatively) for discussion of unorganized versus organized complexity.Comment: 31 page
Explain3D: Explaining Disagreements in Disjoint Datasets
Data plays an important role in applications, analytic processes, and many
aspects of human activity. As data grows in size and complexity, we are met
with an imperative need for tools that promote understanding and explanations
over data-related operations. Data management research on explanations has
focused on the assumption that data resides in a single dataset, under one
common schema. But the reality of today's data is that it is frequently
un-integrated, coming from different sources with different schemas. When
different datasets provide different answers to semantically similar questions,
understanding the reasons for the discrepancies is challenging and cannot be
handled by the existing single-dataset solutions.
In this paper, we propose Explain3D, a framework for explaining the
disagreements across disjoint datasets (3D). Explain3D focuses on identifying
the reasons for the differences in the results of two semantically similar
queries operating on two datasets with potentially different schemas. Our
framework leverages the queries to perform a semantic mapping across the
relevant parts of their provenance; discrepancies in this mapping point to
causes of the queries' differences. Exploiting the queries gives Explain3D an
edge over traditional schema matching and record linkage techniques, which are
query-agnostic. Our work makes the following contributions: (1) We formalize
the problem of deriving optimal explanations for the differences of the results
of semantically similar queries over disjoint datasets. (2) We design a 3-stage
framework for solving the optimal explanation problem. (3) We develop a
smart-partitioning optimizer that improves the efficiency of the framework by
orders of magnitude. (4)~We experiment with real-world and synthetic data to
demonstrate that Explain3D can derive precise explanations efficiently
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