Top 5 Interesting Papers in Complexity
Good day Steemit community. Today I am going to share some interesting papers about computation.
Compact manifolds with computable boundaries
Zvonko Iljazovic
We investigate conditions under which a co-computably enumerable closed set in a computable metric space is computable and prove that in each locally computable computable metric space each co-computably enumerable compact manifold with computable boundary is computable. In fact, we examine the notion of a semi-computable compact set and we prove a more general result: in any computable metric space each semi-computable compact manifold with computable boundary is computable. In particular, each semi-computable compact (boundaryless) manifold is computable.
Aspects of Computability in Physics
Joseph Shipman
This paper reviews connections between physics and computation, and explores their implications. The main topics are computational "hardness" of physical systems, computational status of fundamental theories, quantum computation, and the Universe as a computer.
Unconventional Quantum Computing Devices
Seth Lloyd
This paper investigates a variety of unconventional quantum computation devices, including fermionic quantum computers and computers that exploit nonlinear quantum mechanics. It is shown that unconventional quantum computing devices can in principle compute some quantities more rapidly than `conventional' quantum computers.
A Survey of Current Trends in Distributed, Grid and Cloud Computing
Gaurav Mittal,Dr. Nishtha Kesswani,Kuldeep Goswami
Through the 1990s to 2012 the internet changed the world of computing drastically. It started its journey with parallel computing after it advanced to distributed computing and further to grid computing. And in present scenario it creates a new world which is pronounced as a Cloud Computing [1]. These all three terms have different meanings. Cloud computing is based on backward computing schemes like cluster computing, distributed computing, grid computing and utility computing. The basic concept of cloud computing is virtualization. It provides virtual hardware and software resources to various requesting programs. This paper gives a detailed description about cluster computing, grid computing and cloud computing and gives an insight of some implementations of the same. We try to list the inspirations for the advent of all these technologies. We also account for some present scenario faults of grid computing and also discuss new cloud computing projects which are being managed by the Government of India for learning. The paper also reviews the existing work and covers (analytically), to some extent, some innovative ideas that can be implemented.
Computable structures on topological manifolds
Marcelo A. Aguilar,Rodolfo Conde
We propose a definition of computable manifold by introducing computability as a structure that we impose to a given topological manifold, just in the same way as differentiability or piecewise linearity are defined for smooth and PL manifolds respectively. Using the framework of computable topology and Type-2 theory of effectivity, we develop computable versions of all the basic concepts needed to define manifolds, like computable atlases and (computably) compatible computable atlases. We prove that given a computable atlas $\Phi$ defined on a set $M$, we can construct a computable topological space $(M, \tau_\Phi, \beta_\Phi, \nu_\Phi)$, where $\tau_\Phi$ is the topology on $M$ induced by $\Phi$ and that the equivalence class of this computable space characterizes the computable structure determined by $\Phi$. The concept of computable submanifold is also investigated. We show that any compact computable manifold which satisfies a computable version of the $T_2$-separation axiom, can be embedded as a computable submanifold of some euclidean space $\mathbb{R}^{q}$, with a computable embedding, where $\mathbb{R}^{q}$ is equipped with its usual topology and some canonical computable encoding of all open rational balls.
Don't forget to Follow and Resteem. @arxivsanity
Keeping everyone inform.