146,799 research outputs found
Detailed ultraviolet asymptotics for AdS scalar field perturbations
We present a range of methods suitable for accurate evaluation of the leading
asymptotics for integrals of products of Jacobi polynomials in limits when the
degrees of some or all polynomials inside the integral become large. The
structures in question have recently emerged in the context of effective
descriptions of small amplitude perturbations in anti-de Sitter (AdS)
spacetime. The limit of high degree polynomials corresponds in this situation
to effective interactions involving extreme short-wavelength modes, whose
dynamics is crucial for the turbulent instabilities that determine the ultimate
fate of small AdS perturbations. We explicitly apply the relevant asymptotic
techniques to the case of a self-interacting probe scalar field in AdS and
extract a detailed form of the leading large degree behavior, including closed
form analytic expressions for the numerical coefficients appearing in the
asymptotics.Comment: v2: 19 pages, expanded version accepted to JHE
A class of AM-QFT algorithms for power-of-two FFT
This paper proposes a class of power-of-two FFT (Fast Fourier Transform)
algorithms, called AM-QFT algorithms, that contains the improved QFT (Quick
Fourier Transform), an algorithm recently published, as a special case. The
main idea is to apply the Amplitude Modulation Double Sideband - Suppressed
Carrier (AM DSB-SC) to convert odd-indices signals into even-indices signals,
and to insert this elaboration into the improved QFT algorithm, substituting
the multiplication by secant function. The 8 variants of this class are
obtained by re-elaboration of the AM DSB-SC idea, and by means of duality. As a
result the 8 variants have both the same computational cost and the same memory
requirements than improved QFT. Differently, comparing this class of 8 variants
of AM-QFT algorithm with the split-radix 3add/3mul (one of the most performing
FFT approach appeared in the literature), we obtain the same number of
additions and multiplications, but employing half of the trigonometric
constants. This makes the proposed FFT algorithms interesting and useful for
fixed-point implementations. Some of these variants show advantages versus the
improved QFT. In fact one of this variant slightly enhances the numerical
accuracy of improved QFT, while other four variants use trigonometric constants
that are faster to compute in `on the fly' implementations
PyCARL: A PyNN Interface for Hardware-Software Co-Simulation of Spiking Neural Network
We present PyCARL, a PyNN-based common Python programming interface for
hardware-software co-simulation of spiking neural network (SNN). Through
PyCARL, we make the following two key contributions. First, we provide an
interface of PyNN to CARLsim, a computationally-efficient, GPU-accelerated and
biophysically-detailed SNN simulator. PyCARL facilitates joint development of
machine learning models and code sharing between CARLsim and PyNN users,
promoting an integrated and larger neuromorphic community. Second, we integrate
cycle-accurate models of state-of-the-art neuromorphic hardware such as
TrueNorth, Loihi, and DynapSE in PyCARL, to accurately model hardware latencies
that delay spikes between communicating neurons and degrade performance. PyCARL
allows users to analyze and optimize the performance difference between
software-only simulation and hardware-software co-simulation of their machine
learning models. We show that system designers can also use PyCARL to perform
design-space exploration early in the product development stage, facilitating
faster time-to-deployment of neuromorphic products. We evaluate the memory
usage and simulation time of PyCARL using functionality tests, synthetic SNNs,
and realistic applications. Our results demonstrate that for large SNNs, PyCARL
does not lead to any significant overhead compared to CARLsim. We also use
PyCARL to analyze these SNNs for a state-of-the-art neuromorphic hardware and
demonstrate a significant performance deviation from software-only simulations.
PyCARL allows to evaluate and minimize such differences early during model
development.Comment: 10 pages, 25 figures. Accepted for publication at International Joint
Conference on Neural Networks (IJCNN) 202
- …