9,310 research outputs found
Fast Reliable Ray-tracing of Procedurally Defined Implicit Surfaces Using Revised Affine Arithmetic
Fast and reliable rendering of implicit surfaces is an important area in the field of implicit modelling. Direct rendering, namely ray-tracing, is shown to be a suitable technique for obtaining good-quality visualisations of implicit surfaces. We present a technique for reliable ray-tracing of arbitrary procedurally defined implicit surfaces by using a modification of Affine Arithmetic called Revised Affine Arithmetic. A wide range of procedurally defined implicit objects can be rendered using this technique including polynomial surfaces, constructive solids, pseudo-random objects, procedurally defined microstructures, and others. We compare our technique with other reliable techniques based on Interval and Affine Arithmetic to show that our technique provides the fastest, while still reliable, ray-surface intersections and ray-tracing. We also suggest possible modifications for the GPU implementation of this technique for real-time rendering of relatively simple implicit models and for near real-time for complex implicit models
The rotating wave system-reservoir coupling: limitations and meaning in the non-Markovian regime
This paper deals with the dissipative dynamics of a quantum harmonic
oscillator interacting with a bosonic reservoir. The Master Equations based on
the Rotating Wave and on the Feynman-Vernon system--reservoir couplings are
compared highlighting differences and analogies. We discuss quantitatively and
qualitatively the conditions under which the counter rotating terms can be
neglected. By comparing the analytic solution of the heating function relative
to the two different coupling models we conclude that, even in the weak
coupling limit, the counter rotating terms give rise to a significant
contribution in the non--Markovian short time regime. The main result of this
paper is that such a contribution is actually experimentally measurable and
thus relevant for a correct description of the system dynamics.Comment: 14 pages, 3 figure
Towards Interpretable Deep Learning Models for Knowledge Tracing
As an important technique for modeling the knowledge states of learners, the
traditional knowledge tracing (KT) models have been widely used to support
intelligent tutoring systems and MOOC platforms. Driven by the fast
advancements of deep learning techniques, deep neural network has been recently
adopted to design new KT models for achieving better prediction performance.
However, the lack of interpretability of these models has painfully impeded
their practical applications, as their outputs and working mechanisms suffer
from the intransparent decision process and complex inner structures. We thus
propose to adopt the post-hoc method to tackle the interpretability issue for
deep learning based knowledge tracing (DLKT) models. Specifically, we focus on
applying the layer-wise relevance propagation (LRP) method to interpret
RNN-based DLKT model by backpropagating the relevance from the model's output
layer to its input layer. The experiment results show the feasibility using the
LRP method for interpreting the DLKT model's predictions, and partially
validate the computed relevance scores from both question level and concept
level. We believe it can be a solid step towards fully interpreting the DLKT
models and promote their practical applications in the education domain
Dynamic Key-Value Memory Networks for Knowledge Tracing
Knowledge Tracing (KT) is a task of tracing evolving knowledge state of
students with respect to one or more concepts as they engage in a sequence of
learning activities. One important purpose of KT is to personalize the practice
sequence to help students learn knowledge concepts efficiently. However,
existing methods such as Bayesian Knowledge Tracing and Deep Knowledge Tracing
either model knowledge state for each predefined concept separately or fail to
pinpoint exactly which concepts a student is good at or unfamiliar with. To
solve these problems, this work introduces a new model called Dynamic Key-Value
Memory Networks (DKVMN) that can exploit the relationships between underlying
concepts and directly output a student's mastery level of each concept. Unlike
standard memory-augmented neural networks that facilitate a single memory
matrix or two static memory matrices, our model has one static matrix called
key, which stores the knowledge concepts and the other dynamic matrix called
value, which stores and updates the mastery levels of corresponding concepts.
Experiments show that our model consistently outperforms the state-of-the-art
model in a range of KT datasets. Moreover, the DKVMN model can automatically
discover underlying concepts of exercises typically performed by human
annotations and depict the changing knowledge state of a student.Comment: To appear in 26th International Conference on World Wide Web (WWW),
201
Automatic Integral Reduction for Higher Order Perturbative Calculations
We present a program for the reduction of large systems of integrals to
master integrals. The algorithm was first proposed by Laporta; in this paper,
we implement it in MAPLE. We also develop two new features which keep the size
of intermediate expressions relatively small throughout the calculation. The
program requires modest input information from the user and can be used for
generic calculations in perturbation theory.Comment: 23 page
Ray casting implicit fractal surfaces with reduced affine arithmetic
A method is presented for ray casting implicit surfaces defined by fractal combinations of procedural noise functions. The method is robust and uses affine arithmetic to bound the variation of the implicit function along a ray. The method is also efficient due to a modification in the affine arithmetic representation that introduces a condensation step at the end of every non-affine operation. We show that our method is able to retain the tight estimation capabilities of affine arithmetic for ray casting implicit surfaces made from procedural noise functions while being faster to compute and more efficient to store
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