11,596 research outputs found
An efficient Algorithm to partition a Sequence of Integers into Subsets with equal Sums
To partition a sequence of n integers into subsets with prescribed sums is an
NP-hard problem in general. In this paper we present an efficient solution for
the homogeneous version of this problem; i.e. where the elements in each subset
add up to the same sum.Comment: 12 page
A Markovian Model for Joint Observations, Bell's Inequality and Hidden States
While the standard approach to quantum systems studies length preserving
linear transformations of wave functions, the Markov picture focuses on trace
preserving operators on the space of Hermitian (self-adjoint) matrices. The
Markov approach extends the standard one and provides a refined analysis of
measurements and quantum Markov chains. In particular, Bell's inequality
becomes structurally clear. It turns out that hidden state models are natural
in the Markov context. In particular, a violation of Bell's inequality is seen
to be compatible with the existence of hidden states. The Markov model moreover
clarifies the role of the "negative probabilities" in Feynman's analysis of the
EPR paradox.Comment: 14 page
Homotopy theory with bornological coarse spaces
We propose an axiomatic characterization of coarse homology theories defined
on the category of bornological coarse spaces. We construct a category of
motivic coarse spectra. Our focus is the classification of coarse homology
theories and the construction of examples. We show that if a transformation
between coarse homology theories induces an equivalence on all discrete
bornological coarse spaces, then it is an equivalence on bornological coarse
spaces of finite asymptotic dimension. The example of coarse K-homology will be
discussed in detail.Comment: 220 pages (complete revision
On Hidden States in Quantum Random Walks
It was recently pointed out that identifiability of quantum random walks and
hidden Markov processes underlie the same principles. This analogy immediately
raises questions on the existence of hidden states also in quantum random walks
and their relationship with earlier debates on hidden states in quantum
mechanics. The overarching insight was that not only hidden Markov processes,
but also quantum random walks are finitary processes. Since finitary processes
enjoy nice asymptotic properties, this also encourages to further investigate
the asymptotic properties of quantum random walks. Here, answers to all these
questions are given. Quantum random walks, hidden Markov processes and finitary
processes are put into a unifying model context. In this context, quantum
random walks are seen to not only enjoy nice ergodic properties in general, but
also intuitive quantum-style asymptotic properties. It is also pointed out how
hidden states arising from our framework relate to hidden states in earlier,
prominent treatments on topics such as the EPR paradoxon or Bell's
inequalities.Comment: 26 page
Coarse cohomology theories
We propose the notion of a coarse cohomology theory and study the examples of
coarse ordinary cohomology, coarse stable cohomotopy and coarse cohomology
theories obtained by dualizing coarse homology theories. Our investigations of
coarse stable cohomotopy lead to a solution of J. R. Klein's conjecture that
the dualizing spectrum of a group is a coarse invariant. We further investigate
coarse cohomological -theory functors and explain why (an adaption of) the
functor of Emerson--Meyer does not seem to fit into our setting.Comment: 55 page
First-Class Functions for First-Order Database Engines
We describe Query Defunctionalization which enables off-the-shelf first-order
database engines to process queries over first-class functions. Support for
first-class functions is characterized by the ability to treat functions like
regular data items that can be constructed at query runtime, passed to or
returned from other (higher-order) functions, assigned to variables, and stored
in persistent data structures. Query defunctionalization is a non-invasive
approach that transforms such function-centric queries into the data-centric
operations implemented by common query processors. Experiments with XQuery and
PL/SQL database systems demonstrate that first-order database engines can
faithfully and efficiently support the expressive "functions as data" paradigm.Comment: Proceedings of the 14th International Symposium on Database
Programming Languages (DBPL 2013), August 30, 2013, Riva del Garda, Trento,
Ital
Security And Potential Level Preferences With
The security level models of Gilboa (1988) and of Jaffray (1988) as well as the security and potential level model of Cohen (1992) accomodate succesfully classical Allais paradoxa while they offer an interesting explanation for their occurrence. However, experimental data suggest a systematic violation of these models when lotteries with low probabilities of bad or good outcomes are involved. The present paper develops an axiomatic model that allows for thresholds in the perception of security and potential levels. The derived representation of preferences accommodates the observed violations of the original security and potential level models and provides a natural explanation for their occurence. Additionally, a more fundamental problem of the original models is resolved.
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