Cosmology with minimal length uncertainty relations

We study the effects of the existence of a minimal observable length in the phase space of classical and quantum de Sitter (dS) and Anti de Sitter (AdS) cosmology. Since this length has been suggested in quantum gravity and string theory, its effects in the early universe might be expected. Adopting the existence of such a minimum length results in the Generalized Uncertainty Principle (GUP), which is a deformed Heisenberg algebra between minisuperspace variables and their momenta operators. We extend these deformed commutating relations to the corresponding deformed Poisson algebra in the classical limit. Using the resulting Poisson and Heisenberg relations, we then construct the classical and quantum cosmology of dS and Ads models in a canonical framework. We show that in classical dS cosmology this effect yields an inflationary universe in which the rate of expansion is larger than the usual dS universe. Also, for the AdS model it is shown that GUP might change the oscillatory nature of the corresponding cosmology. We also study the effects of GUP in quantized models through approximate analytical solutions of the Wheeler-DeWitt (WD) equation, in the limit of small scale factor for the universe, and compare the results with the ordinary quantum cosmology in each case.Comment: 11 pages, 4 figures, to appear in IJMP

Cyclic cosmology from Lagrange-multiplier modified gravity

We investigate cyclic and singularity-free evolutions in a universe governed by Lagrange-multiplier modified gravity, either in scalar-field cosmology, as well as in $f(R)$ one. In the scalar case, cyclicity can be induced by a suitably reconstructed simple potential, and the matter content of the universe can be successfully incorporated. In the case of $f(R)$-gravity, cyclicity can be induced by a suitable reconstructed second function $f_2(R)$ of a very simple form, however the matter evolution cannot be analytically handled. Furthermore, we study the evolution of cosmological perturbations for the two scenarios. For the scalar case the system possesses no wavelike modes due to a dust-like sound speed, while for the $f(R)$ case there exist an oscillation mode of perturbations which indicates a dynamical degree of freedom. Both scenarios allow for stable parameter spaces of cosmological perturbations through the bouncing point.Comment: 8 pages, 3 figures, references added, accepted for publicatio

Taming computational complexity: efficient and parallel SimRank optimizations on undirected graphs

SimRank has been considered as one of the promising link-based ranking algorithms to evaluate similarities of web documents in many modern search engines. In this paper, we investigate the optimization problem of SimRank similarity computation on undirected web graphs. We first present a novel algorithm to estimate the SimRank between vertices in O(n3+ Kn2) time, where n is the number of vertices, and K is the number of iterations. In comparison, the most efficient implementation of SimRank algorithm in [1] takes O(K n3 ) time in the worst case. To efficiently handle large-scale computations, we also propose a parallel implementation of the SimRank algorithm on multiple processors. The experimental evaluations on both synthetic and real-life data sets demonstrate the better computational time and parallel efficiency of our proposed techniques

Testing the Lorentz and CPT Symmetry with CMB polarizations and a non-relativistic Maxwell Theory

We present a model for a system involving a photon gauge field and a scalar field at quantum criticality in the frame of a Lifthitz-type non-relativistic Maxwell theory. We will show this model gives rise to Lorentz and CPT violation which leads to a frequency-dependent rotation of polarization plane of radiations, and so leaves potential signals on the cosmic microwave background temperature and polarization anisotropies.Comment: 7 pages, 2 figures, accepted on JCAP, a few references adde

FPTAS for Weighted Fibonacci Gates and Its Applications

Fibonacci gate problems have severed as computation primitives to solve other problems by holographic algorithm and play an important role in the dichotomy of exact counting for Holant and CSP frameworks. We generalize them to weighted cases and allow each vertex function to have different parameters, which is a much boarder family and #P-hard for exactly counting. We design a fully polynomial-time approximation scheme (FPTAS) for this generalization by correlation decay technique. This is the first deterministic FPTAS for approximate counting in the general Holant framework without a degree bound. We also formally introduce holographic reduction in the study of approximate counting and these weighted Fibonacci gate problems serve as computation primitives for approximate counting. Under holographic reduction, we obtain FPTAS for other Holant problems and spin problems. One important application is developing an FPTAS for a large range of ferromagnetic two-state spin systems. This is the first deterministic FPTAS in the ferromagnetic range for two-state spin systems without a degree bound. Besides these algorithms, we also develop several new tools and techniques to establish the correlation decay property, which are applicable in other problems