Efficient Computation of Simplicial Homology through Acyclic Matching

2014 ◽  
Author(s):  
Ulderico Fugacci ◽  
Federico Iuricich ◽  
Leila De Floriani
Keyword(s):  
Efficient Computation ◽  
Simplicial Homology ◽  
Acyclic Matching

No fear of George Kingsley Zipf

10.1558/37291 ◽  
2018 ◽  
Vol 2 (2) ◽  
pp. 242-263
Author(s):  
Stefano Rastelli ◽  
Kook-Hee Gil
Keyword(s):  
Minimalist Program ◽  
Classroom Research ◽  
Language Design ◽  
Efficient Computation ◽  
Generative Linguistics ◽  
The Third ◽  
Factor Effect ◽  
Language Classroom ◽  
Recent Developments ◽  
Insight Into

This paper offers a new insight into GenSLA classroom research in light of recent developments in the Minimalist Program (MP). Recent research in GenSLA has shown how generative linguistics and acquisition studies can inform the language classroom, mostly focusing on what linguistic aspects of target properties should be integrated as a part of the classroom input. Based on insights from Chomsky’s ‘three factors for language design’ – which bring together the Faculty of Language, input and general principles of economy and efficient computation (the third factor effect) for language development – we put forward a theoretical rationale for how classroom research can offer a unique environment to test the learnability in L2 through the statistical enhancement of the input to which learners are exposed.

Efficient Computation of Representative Families with Applications in Parameterized and Exact Algorithms

2016 ◽  
Vol 63 (4) ◽  
pp. 1-60 ◽  
Author(s):  
Fedor V. Fomin ◽  
Daniel Lokshtanov ◽  
Fahad Panolan ◽  
Saket Saurabh
Keyword(s):  
Exact Algorithms ◽  
Efficient Computation

scholarly journals A Cortical-Inspired Sub-Riemannian Model for Poggendorff-Type Visual Illusions

2021 ◽  
Vol 7 (3) ◽  
pp. 41
Author(s):  
Emre Baspinar ◽  
Luca Calatroni ◽  
Valentina Franceschi ◽  
Dario Prandi
Keyword(s):  
Heat Kernel ◽  
Mathematical Description ◽  
Gradient Descent ◽  
Numerical Results ◽  
Visual Illusions ◽  
Efficient Computation ◽  
Functional Architecture ◽  
Descent Algorithms ◽  
Interaction Term

We consider Wilson-Cowan-type models for the mathematical description of orientation-dependent Poggendorff-like illusions. Our modelling improves two previously proposed cortical-inspired approaches, embedding the sub-Riemannian heat kernel into the neuronal interaction term, in agreement with the intrinsically anisotropic functional architecture of V1 based on both local and lateral connections. For the numerical realisation of both models, we consider standard gradient descent algorithms combined with Fourier-based approaches for the efficient computation of the sub-Laplacian evolution. Our numerical results show that the use of the sub-Riemannian kernel allows us to reproduce numerically visual misperceptions and inpainting-type biases in a stronger way in comparison with the previous approaches.

scholarly journals Fast computation and practical use of amplitudes at non-Fourier frequencies

2021 ◽  
Author(s):  
Erhard Reschenhofer ◽  
Manveer K. Mangat
Keyword(s):  
High Frequency ◽  
Superior Performance ◽  
High Frequency Data ◽  
Mean Square ◽  
Fast Computation ◽  
Efficient Computation ◽  
Frequency Data ◽  
Second Stage ◽  
Orthogonality Conditions ◽  
Memory Parameter

AbstractIn this paper, it is shown that the performance of various frequency-domain estimators of the memory parameter can be boosted by the inclusion of non-Fourier frequencies in addition to the regular Fourier frequencies. A fast two-stage algorithm for the efficient computation of the amplitudes at these additional frequencies is presented. In the first stage, the naïve sine and cosine transforms are computed with a modified version of the Fast Fourier Transform. In the second stage, these transforms are amended by taking the violation of the standard orthogonality conditions into account. A considerable number of auxiliary quantities, which are required in the second stage, do not depend on the data and therefore only need to be computed once. The superior performance (in terms of root-mean-square error) of the estimators based also on non-Fourier frequencies is demonstrated by extensive simulations. Finally, the empirical results obtained by applying these estimators to financial high-frequency data show that significant long-range dependence is present only in the absolute intraday returns but not in the signed intraday returns.

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