48,312 research outputs found
Predictability of extreme events in a branching diffusion model
We propose a framework for studying predictability of extreme events in
complex systems. Major conceptual elements -- hierarchical structure, spatial
dynamics, and external driving -- are combined in a classical branching
diffusion with immigration. New elements -- observation space and observed
events -- are introduced in order to formulate a prediction problem patterned
after the geophysical and environmental applications. The problem consists of
estimating the likelihood of occurrence of an extreme event given the
observations of smaller events while the complete internal dynamics of the
system is unknown. We look for premonitory patterns that emerge as an extreme
event approaches; those patterns are deviations from the long-term system's
averages. We have found a single control parameter that governs multiple
spatio-temporal premonitory patterns. For that purpose, we derive i) complete
analytic description of time- and space-dependent size distribution of
particles generated by a single immigrant; ii) the steady-state moments that
correspond to multiple immigrants; and iii) size- and space-based asymptotic
for the particle size distribution. Our results suggest a mechanism for
universal premonitory patterns and provide a natural framework for their
theoretical and empirical study
Everettian quantum mechanics without branching time
In this paper I assess the prospects for combining contemporary Everettian quantum mechanics (EQM) with branching-time semantics in the tradition of Kripke, Prior, Thomason and Belnap. I begin by outlining the salient features of âdecoherence-basedâ EQM, and of the âconsistent historiesâ formalism that is particularly apt for conceptual discussions in EQM. This formalism permits of both âbranching worldsâand âparallel worldsâ interpretations; the metaphysics of EQM is in this sense underdetermined by the physics. A prominent argument due to David Lewis [1986] supports the non-branching interpretation. Belnap et al. [2001] refer to Lewisâ argument as the âAssertion problemâ, and propose a pragmatic response to it. I argue that their response is unattractively ad hoc and complex, and that it prevents an Everettian who adopts branching-time semantics from making clear sense of objective probability. The upshot is that Everettians are better off without branching-time semantics. I conclude by discussing and rejecting an alternative possible motivation for branching time
The Problem of Confirmation in the Everett Interpretation
I argue that the Oxford school Everett interpretation is internally
incoherent, because we cannot claim that in an Everettian universe the kinds of
reasoning we have used to arrive at our beliefs about quantum mechanics would
lead us to form true beliefs. I show that in an Everettian context, the
experimental evidence that we have available could not provide empirical
confirmation for quantum mechanics, and moreover that we would not even be able
to establish reference to the theoretical entities of quantum mechanics. I then
consider a range of existing Everettian approaches to the probability problem
and show that they do not succeed in overcoming this incoherence
The Multidimensional Study of Viral Campaigns as Branching Processes
Viral campaigns on the Internet may follow variety of models, depending on
the content, incentives, personal attitudes of sender and recipient to the
content and other factors. Due to the fact that the knowledge of the campaign
specifics is essential for the campaign managers, researchers are constantly
evaluating models and real-world data. The goal of this article is to present
the new knowledge obtained from studying two viral campaigns that took place in
a virtual world which followed the branching process. The results show that it
is possible to reduce the time needed to estimate the model parameters of the
campaign and, moreover, some important aspects of time-generations relationship
are presented.Comment: In proceedings of the 4th International Conference on Social
Informatics, SocInfo 201
A mathematical theory of semantic development in deep neural networks
An extensive body of empirical research has revealed remarkable regularities
in the acquisition, organization, deployment, and neural representation of
human semantic knowledge, thereby raising a fundamental conceptual question:
what are the theoretical principles governing the ability of neural networks to
acquire, organize, and deploy abstract knowledge by integrating across many
individual experiences? We address this question by mathematically analyzing
the nonlinear dynamics of learning in deep linear networks. We find exact
solutions to this learning dynamics that yield a conceptual explanation for the
prevalence of many disparate phenomena in semantic cognition, including the
hierarchical differentiation of concepts through rapid developmental
transitions, the ubiquity of semantic illusions between such transitions, the
emergence of item typicality and category coherence as factors controlling the
speed of semantic processing, changing patterns of inductive projection over
development, and the conservation of semantic similarity in neural
representations across species. Thus, surprisingly, our simple neural model
qualitatively recapitulates many diverse regularities underlying semantic
development, while providing analytic insight into how the statistical
structure of an environment can interact with nonlinear deep learning dynamics
to give rise to these regularities
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