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value | date int32 2.02k 2.02k | text stringlengths 200 1.13M | token_count int32 36 500k | category stringclasses 1
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redpajama_arxiv | 2,019 | Introduction
Basic definitions
The game of Cops and Robbers is a well-known game on graphs that was introduced by Nowakowski and Winkler and Quilliot .
There are two players, one controls the cops and the other one controls the robber. The game starts with the cops selecting some vertices as their initial positions (... | 11,326 | academic |
redpajama_arxiv | 2,019 | Introduction
The cold and collisionless nature of dark matter (DM) is a central hypothesis of the standard CDM model of structure formation, which is largely consistent with the large scale structure of the Universe
, and is the cornerstone of current state-of-the-art simulations that model the complexity of galaxy f... | 6,870 | academic |
redpajama_arxiv | 2,019 | Abstract
We present a local interpolation method in four dimensions utilising cubic splines. An extension of the three-dimensional tricubic method, the interpolated function has C ^1 continuity and its partial derivatives are analytically accessible. The specific example of application of this work to a time-varying t... | 1,740 | academic |
redpajama_arxiv | 2,019 | Introduction
Quantum Field theory in curved spacetime is a well-established branch of modern physics, which has allowed the achievement of novel results since Hawking's discovery of black hole radiation . Within this framework, we consider the quantum dynamics of fields in a gravitational background, considered as a c... | 7,100 | academic |
redpajama_arxiv | 2,019 | Introduction
Throughout, we let the dimension d 2 .
We investigate a quite general class of divergence form operators with respect to a possibly non-symmetric diffusion matrix (a_ij+c_ij)_1 i,j d and perturbation H=(h_1,,h_d) , which can be written as
Lf & = & 12 _i,j=1^d _i((a_ij+c_ij)_j)f+_i=1^dh_i_i f, f C_0^( R^d... | 13,393 | academic |
redpajama_arxiv | 2,019 | Introduction
The prodigious development of the digital camera, computer hardware, Internet technology, and machine learning technologies makes millions or even billions of images accessible to people. Large scale image annotation has therefore become essential for many practical applications in image processing, compu... | 6,497 | academic |
redpajama_arxiv | 2,019 | "The Discrete Fourier Transform\n\nIn this section, we briefly present the decomposition of both the(...TRUNCATED) | 7,961 | academic |
redpajama_arxiv | 2,019 | "Introduction\n\nThe reduced Hartree-Fock (rHF) model is a non-linear model introduced in to describ(...TRUNCATED) | 12,403 | academic |
redpajama_arxiv | 2,019 | "Introduction\n\nTopological materials have attracted tremendous interest in\ncondensed matter physi(...TRUNCATED) | 4,335 | academic |
redpajama_arxiv | 2,019 | "Introduction\n\nLet (n) denote the sum of divisors function. While its average value is well-behave(...TRUNCATED) | 3,395 | academic |
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