159 research outputs found
Algorithm 950: Ncpol2sdpa---Sparse Semidefinite Programming Relaxations for Polynomial Optimization Problems of Noncommuting Variables
A hierarchy of semidefinite programming (SDP) relaxations approximates the
global optimum of polynomial optimization problems of noncommuting variables.
Generating the relaxation, however, is a computationally demanding task, and
only problems of commuting variables have efficient generators. We develop an
implementation for problems of noncommuting problems that creates the
relaxation to be solved by SDPA -- a high-performance solver that runs in a
distributed environment. We further exploit the inherent sparsity of
optimization problems in quantum physics to reduce the complexity of the
resulting relaxations. Constrained problems with a relaxation of order two may
contain up to a hundred variables. The implementation is available in Python.
The tool helps solve problems such as finding the ground state energy or
testing quantum correlations.Comment: 17 pages, 3 figures, 1 table, 2 algorithms, the algorithm is
available at http://peterwittek.github.io/ncpol2sdpa
Evaluating probabilistic programming languages for simulating quantum correlations
This article explores how probabilistic programming can be used to simulate
quantum correlations in an EPR experimental setting. Probabilistic programs are
based on standard probability which cannot produce quantum correlations. In
order to address this limitation, a hypergraph formalism was programmed which
both expresses the measurement contexts of the EPR experimental design as well
as associated constraints. Four contemporary open source probabilistic
programming frameworks were used to simulate an EPR experiment in order to shed
light on their relative effectiveness from both qualitative and quantitative
dimensions. We found that all four probabilistic languages successfully
simulated quantum correlations. Detailed analysis revealed that no language was
clearly superior across all dimensions, however, the comparison does highlight
aspects that can be considered when using probabilistic programs to simulate
experiments in quantum physics.Comment: 24 pages, 8 figures, code is available at
https://github.com/askoj/bell-ppl
On the Origin of Risk Sensitivity: the Energy Budget Rule Revisited
The risk-sensitive foraging theory formulated in terms of the (daily) energy
budget rule has been influential in behavioural ecology as well as other
disciplines. Predicting risk-aversion on positive budgets and risk-proneness on
negative budgets, however, the budget rule has recently been challenged both
empirically and theoretically. In this paper, we critically review these
challenges as well as the original derivation of the budget rule and propose a
`gradual' budget rule, which is normatively derived from a gradual nature of
risk sensitivity and encompasses the conventional budget rule as a special
case. The gradual budget rule shows that the conventional budget rule holds
when the expected reserve is close enough to a threshold for overnight
survival, selection pressure being significant. The gradual view also reveals
that the conventional budget rule does not need to hold when the expected
reserve is not close enough to the threshold, selection pressure being
insignificant. The proposed gradual budget rule better fits the empirical
findings including those that used to challenge the conventional budget rule.Comment: 13 pages, 4 figure
Optimal randomness certification from one entangled bit
By performing local projective measurements on a two-qubit entangled state
one can certify in a device-independent way up to one bit of randomness. We
show here that general measurements, defined by positive-operator-valued
measures, can certify up to two bits of randomness, which is the optimal amount
of randomness that can be certified from an entangled bit. General measurements
thus provide an advantage over projective ones for device-independent
randomness certification.Comment: 7 pages, 1 figure, computational details at
http://nbviewer.ipython.org/github/peterwittek/ipython-notebooks/blob/master/Optimal%20randomness%20generation%20from%20entangled%20quantum%20states.ipyn
Somoclu: An Efficient Parallel Library for Self-Organizing Maps
Somoclu is a massively parallel tool for training self-organizing maps on
large data sets written in C++. It builds on OpenMP for multicore execution,
and on MPI for distributing the workload across the nodes in a cluster. It is
also able to boost training by using CUDA if graphics processing units are
available. A sparse kernel is included, which is useful for high-dimensional
but sparse data, such as the vector spaces common in text mining workflows.
Python, R and MATLAB interfaces facilitate interactive use. Apart from fast
execution, memory use is highly optimized, enabling training large emergent
maps even on a single computer.Comment: 26 pages, 9 figures. The code is available at
https://peterwittek.github.io/somoclu
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