75,010 research outputs found
A Deeper Look at Student Learning of Quantum Mechanics: the Case of Tunneling
We report on a large-scale study of student learning of quantum tunneling in
4 traditional and 4 transformed modern physics courses. In the transformed
courses, which were designed to address student difficulties found in previous
research, students still struggle with many of the same issues found in other
courses. However, the reasons for these difficulties are more subtle, and many
new issues are brought to the surface. By explicitly addressing how to build
models of wave functions and energy and how to relate these models to real
physical systems, we have opened up a floodgate of deep and difficult questions
as students struggle to make sense of these models. We conclude that the
difficulties found in previous research are the tip of the iceberg, and the
real issue at the heart of student difficulties in learning quantum tunneling
is the struggle to build the complex models that are implicit in experts'
understanding but often not explicitly addressed in instruction.Comment: v2, v3 updated with more detailed analysis of data and discussion;
submitted to Phys. Rev. ST: PE
Using conceptual metaphor and functional grammar to explore how language used in physics affects student learning
This paper introduces a theory about the role of language in learning
physics. The theory is developed in the context of physics students' and
physicists' talking and writing about the subject of quantum mechanics. We
found that physicists' language encodes different varieties of analogical
models through the use of grammar and conceptual metaphor. We hypothesize that
students categorize concepts into ontological categories based on the
grammatical structure of physicists' language. We also hypothesize that
students over-extend and misapply conceptual metaphors in physicists' speech
and writing. Using our theory, we will show how, in some cases, we can explain
student difficulties in quantum mechanics as difficulties with language.Comment: Accepted for publication in Phys. Rev. ST:PE
The full Schwinger-Dyson tower for random tensor models
We treat random rank- tensor models as -dimensional quantum field
theories---tensor field theories (TFT)---and review some of their
non-perturbative methods. We classify the correlation functions of complex
tensor field theories by boundary graphs, sketch the derivation of the
Ward-Takahashi identity and stress its relevance in the derivation of the tower
of exact, analytic Schwinger-Dyson equations for all the correlation functions
(with connected boundary) of TFTs with quartic pillow-like interactions.Comment: Proceedings: Corfu 2017 Training School "Quantum Spacetime and
Physics Models
A Projected Gradient Descent Method for CRF Inference allowing End-To-End Training of Arbitrary Pairwise Potentials
Are we using the right potential functions in the Conditional Random Field
models that are popular in the Vision community? Semantic segmentation and
other pixel-level labelling tasks have made significant progress recently due
to the deep learning paradigm. However, most state-of-the-art structured
prediction methods also include a random field model with a hand-crafted
Gaussian potential to model spatial priors, label consistencies and
feature-based image conditioning.
In this paper, we challenge this view by developing a new inference and
learning framework which can learn pairwise CRF potentials restricted only by
their dependence on the image pixel values and the size of the support. Both
standard spatial and high-dimensional bilateral kernels are considered. Our
framework is based on the observation that CRF inference can be achieved via
projected gradient descent and consequently, can easily be integrated in deep
neural networks to allow for end-to-end training. It is empirically
demonstrated that such learned potentials can improve segmentation accuracy and
that certain label class interactions are indeed better modelled by a
non-Gaussian potential. In addition, we compare our inference method to the
commonly used mean-field algorithm. Our framework is evaluated on several
public benchmarks for semantic segmentation with improved performance compared
to previous state-of-the-art CNN+CRF models.Comment: Presented at EMMCVPR 2017 conferenc
Multiflow Transmission in Delay Constrained Cooperative Wireless Networks
This paper considers the problem of energy-efficient transmission in
multi-flow multihop cooperative wireless networks. Although the performance
gains of cooperative approaches are well known, the combinatorial nature of
these schemes makes it difficult to design efficient polynomial-time algorithms
for joint routing, scheduling and power control. This becomes more so when
there is more than one flow in the network. It has been conjectured by many
authors, in the literature, that the multiflow problem in cooperative networks
is an NP-hard problem. In this paper, we formulate the problem, as a
combinatorial optimization problem, for a general setting of -flows, and
formally prove that the problem is not only NP-hard but it is
inapproxmiable. To our knowledge*, these results provide
the first such inapproxmiablity proof in the context of multiflow cooperative
wireless networks. We further prove that for a special case of k = 1 the
solution is a simple path, and devise a polynomial time algorithm for jointly
optimizing routing, scheduling and power control. We then use this algorithm to
establish analytical upper and lower bounds for the optimal performance for the
general case of flows. Furthermore, we propose a polynomial time heuristic
for calculating the solution for the general case and evaluate the performance
of this heuristic under different channel conditions and against the analytical
upper and lower bounds.Comment: 9 pages, 5 figure
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