43 research outputs found
Iterative Approximate Consensus in the presence of Byzantine Link Failures
This paper explores the problem of reaching approximate consensus in
synchronous point-to-point networks, where each directed link of the underlying
communication graph represents a communication channel between a pair of nodes.
We adopt the transient Byzantine link failure model [15, 16], where an
omniscient adversary controls a subset of the directed communication links, but
the nodes are assumed to be fault-free.
Recent work has addressed the problem of reaching approximate consen- sus in
incomplete graphs with Byzantine nodes using a restricted class of iterative
algorithms that maintain only a small amount of memory across iterations [22,
21, 23, 12]. However, to the best of our knowledge, we are the first to
consider approximate consensus in the presence of Byzan- tine links. We extend
our past work that provided exact characterization of graphs in which the
iterative approximate consensus problem in the presence of Byzantine node
failures is solvable [22, 21]. In particular, we prove a tight necessary and
sufficient condition on the underlying com- munication graph for the existence
of iterative approximate consensus algorithms under transient Byzantine link
model. The condition answers (part of) the open problem stated in [16].Comment: arXiv admin note: text overlap with arXiv:1202.609
Asymptotic behaviour of random tridiagonal Markov chains in biological applications
Discrete-time discrete-state random Markov chains with a tridiagonal
generator are shown to have a random attractor consisting of singleton subsets,
essentially a random path, in the simplex of probability vectors. The proof
uses the Hilbert projection metric and the fact that the linear cocycle
generated by the Markov chain is a uniformly contractive mapping of the
positive cone into itself. The proof does not involve probabilistic properties
of the sample path and is thus equally valid in the nonautonomous deterministic
context of Markov chains with, say, periodically varying transitions
probabilities, in which case the attractor is a periodic path.Comment: 13 pages, 22 bibliography references, submitted to DCDS-B, added
references and minor correction
Towards Machine Wald
The past century has seen a steady increase in the need of estimating and
predicting complex systems and making (possibly critical) decisions with
limited information. Although computers have made possible the numerical
evaluation of sophisticated statistical models, these models are still designed
\emph{by humans} because there is currently no known recipe or algorithm for
dividing the design of a statistical model into a sequence of arithmetic
operations. Indeed enabling computers to \emph{think} as \emph{humans} have the
ability to do when faced with uncertainty is challenging in several major ways:
(1) Finding optimal statistical models remains to be formulated as a well posed
problem when information on the system of interest is incomplete and comes in
the form of a complex combination of sample data, partial knowledge of
constitutive relations and a limited description of the distribution of input
random variables. (2) The space of admissible scenarios along with the space of
relevant information, assumptions, and/or beliefs, tend to be infinite
dimensional, whereas calculus on a computer is necessarily discrete and finite.
With this purpose, this paper explores the foundations of a rigorous framework
for the scientific computation of optimal statistical estimators/models and
reviews their connections with Decision Theory, Machine Learning, Bayesian
Inference, Stochastic Optimization, Robust Optimization, Optimal Uncertainty
Quantification and Information Based Complexity.Comment: 37 page
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Leo Strauss and International Relations: The politics of modernity's abyss
This article argues that an engagement with the political philosophy of Leo Strauss is of considerable value in International Relations (IR), in relation to the study of both recent US foreign policy and contemporary IR theory. The question of Straussian activities within and close to the foreign policy-making establishment in the United States during the period leading up to the 2003 invasion of Iraq has been the focus of significant scholarly and popular attention in recent years. This article makes the case that several individuals influenced by Strauss exercised considerable influence in the fields of intelligence production, the media and think tanks, and traces the ways in which elements of Strauss’ thought are discernible in their interventions in these spheres. It further argues that Strauss’ political philosophy is of broader significance for IR insofar as it can be read as a securitising response to the dangers he associated with the foundationlessness of the modern condition. The article demonstrates that the politics of this response are of crucial importance for contemporary debates between traditional and critical IR theorists
Quantum channels and memory effects
Any physical process can be represented as a quantum channel mapping an
initial state to a final state. Hence it can be characterized from the point of
view of communication theory, i.e., in terms of its ability to transfer
information. Quantum information provides a theoretical framework and the
proper mathematical tools to accomplish this. In this context the notion of
codes and communication capacities have been introduced by generalizing them
from the classical Shannon theory of information transmission and error
correction. The underlying assumption of this approach is to consider the
channel not as acting on a single system, but on sequences of systems, which,
when properly initialized allow one to overcome the noisy effects induced by
the physical process under consideration. While most of the work produced so
far has been focused on the case in which a given channel transformation acts
identically and independently on the various elements of the sequence
(memoryless configuration in jargon), correlated error models appear to be a
more realistic way to approach the problem. A slightly different, yet
conceptually related, notion of correlated errors applies to a single quantum
system which evolves continuously in time under the influence of an external
disturbance which acts on it in a non-Markovian fashion. This leads to the
study of memory effects in quantum channels: a fertile ground where interesting
novel phenomena emerge at the intersection of quantum information theory and
other branches of physics. A survey is taken of the field of quantum channels
theory while also embracing these specific and complex settings.Comment: Review article, 61 pages, 26 figures; 400 references. Final version
of the manuscript, typos correcte
From Wald to Savage: homo economicus becomes a Bayesian statistician
Bayesian rationality is the paradigm of rational behavior in neoclassical economics. A rational agent in an economic model is one who maximizes her subjective expected utility and consistently revises her beliefs according to Bayes’s rule. The paper raises the question of how, when and why this characterization of rationality came to be endorsed by mainstream economists. Though no definitive answer is provided, it is argued that the question is far from trivial and of great historiographic importance. The story begins with Abraham Wald’s behaviorist approach to statistics and culminates with Leonard J. Savage’s elaboration of subjective expected utility theory in his 1954 classic The Foundations of Statistics. It is the latter’s acknowledged fiasco to achieve its planned goal, the reinterpretation of traditional inferential techniques along subjectivist and behaviorist lines, which raises the puzzle of how a failed project in statistics could turn into such a tremendous hit in economics. A couple of tentative answers are also offered, involving the role of the consistency requirement in neoclassical analysis and the impact of the postwar transformation of US business schools