A quantum model of dark energy

We propose a quantum model of dark energy. The proposed candidate for dark energy is gluon field, as is well-known, gluons are the elementary particles. We assume that gluons may not be completely massless but have tiny masses, thus the gluon field can provide a non-zero energy-momentum tensor. This model corresponds to Einstein's cosmological constant which is one of the generally accepted models for dark energy. Besides the gluon field, we also discuss the properties of electroweak boson field and compare our results with previous known results.Comment: 4 page

Quantum gravity and mass of gauge field: a four-dimensional unified quantum theory

We present in detail a four-dimensional unified quantum theory. In this theory, we identify three class of parameters, coordinate-momentum, spin and gauge, as all and as the only fundamental parameters to describe quantum fields. The coordinate-momentum is formulated by the general relativity in four-dimensional space-time. This theory satisfies the general covariance condition and the general covariance derivative operator is given. In an unified and combined description, the matter fields, gravity field and gauge fields satisfy Dirac equation, Einstein equation and Yang-Mills equation in operator form. In the framework of our theory, we mainly realize the following aims: (1) The gravity field is described by a quantum theory, the graviton is massless, it is spin-2; (2) The mass problem of gauge theory is solved. Mass arises naturally from the gauge space and thus Higgs mechanism is not necessary; (3) Color confinement of quarks is explained; (4) Parity violation for weak interactions is obtained; (5) Gravity will cause CPT violation; (6) A dark energy solution of quantum theory is presented. It corresponds to Einstein's cosmological constant. We propose that the candidate for dark energy should be gluon which is one of the elementary particles.Comment: 86 pages, v2 typos correcte

Adaptive Policies for Scheduling with Reconfiguration Delay: An End-to-End Solution for All-Optical Data Centers

All-optical switching networks have been considered a promising candidate for the next generation data center networks thanks to its scalability in data bandwidth and power efficiency. However, the bufferless nature and the nonzero recon- figuration delay of optical switches remain great challenges in deploying all-optical networks. This paper considers the end-to- end scheduling for all-optical data center networks with no in- network buffer and nonzero reconfiguration delay. A framework is proposed to deal with the nonzero reconfiguration delay. The proposed approach constructs an adaptive variant of any given scheduling policy. It is shown that if a scheduling policy guarantees its schedules to have schedule weights close to the MaxWeight schedule (and thus is throughput optimal in the zero reconfiguration regime), then the throughput optimality is inherited by its adaptive variant (in any nonzero reconfiguration delay regime). As a corollary, a class of adaptive variants of the well known MaxWeight policy is shown to achieve throughput optimality without prior knowledge of the traffic load. Further- more, through numerical simulations, the simplest such policy, namely the Adaptive MaxWeight (AMW), is shown to exhibit better delay performance than all prior work

Direct Measure of Quantum Correlation

The quantumness of the correlation known as quantum correlation is usually measured by quantum discord. So far various quantum discords can be roughly understood as indirect measure by some special discrepancy of two quantities. We present a direct measure of quantum correlation by revealing the difference between the structures of classically and quantum correlated states. Our measure explicitly includes the contributions of the inseparability and local non-orthogonality of the eigenvectors of a density. Besides its relatively easy computability, our measure can provide a unified understanding of quantum correlation of all the present versions

The witness of sudden change of geometric quantum correlation

In this paper, we give a sufficient and necessary condition (witness) for the sudden change of geometric quantum discord by considering mathematical definition of the discontinuity of a function. Based on the witness, we can find out various sudden changes of quan- tum correlation by considering both the Markovian and the non-Markovian cases. In particular, we can accurately find out critical points of the sudden changes even though they are not quite obvious in the graphical representation. In addition, one can also find that sudden change of quantum correlation, like the frozen quantum correlation, strongly depends on the choice of the quantum correlation measure.Comment: 14 pages, 6 figures. To appear in Quantum Information and Computatio

Quantum Dissonance Is Rejected in an Overlap Measurement Scheme

The overlap measurement scheme accomplishes to evaluate the overlap of two input quantum states by only measuring an introduced auxiliary qubit, irrespective of the complexity of the two input states. We find a counterintuitive phenomenon that no quantum dissonance can be found, even though the auxiliary qubit might be entangled, classically correlated or even uncorrelated with the two input states based on different types of input states. In principle, this provides an opposite but supplementary example to the remarkable algorithm of the deterministic quantum computation with one qubit in which no entanglement is present. Finally, we consider a simple overlap measurement model to demonstrate the continuous change (including potential sudden death of quantum discord) with the input states from entangled to product states by only adjusting some simple initial parameters.Comment: 5pages and 3 figures,To appear in PR

Detecting a physical difference between the CDM halos in simulation and in nature

Numerical simulation is an important tool to help us understand the process of structure formation in the universe. However many simulation results of cold dark matter (CDM) halos on small scale are inconsistent with observations: the central density profile is too cuspy and there are too many substructures. Here we point out that these two problems may be connected with a hitherto unrecognized bias in the simulation halos. Although CDM halos in nature and in simulation are both virialized systems of collisionless CDM particles, gravitational encounter cannot be neglected in the simulation halos because they contain much less particles. We demonstrate this by two numerical experiments, showing that there is a difference on the microcosmic scale between the natural and simulation halos. The simulation halo is more akin to globular clusters where gravitational encounter is known to lead to such drastic phenomena as core collapse. And such artificial core collapse process appears to link the two problems together in the bottom-up scenario of structure formation in the $\Lambda$CDM universe. The discovery of this bias also has implications on the applicability of the Jeans Theorem in Galactic Dynamics.Comment: 5 pages, 4 figures, ApJ Letters submitted. Comments and suggestions welcom

K-sets+: a Linear-time Clustering Algorithm for Data Points with a Sparse Similarity Measure

In this paper, we first propose a new iterative algorithm, called the K-sets+ algorithm for clustering data points in a semi-metric space, where the distance measure does not necessarily satisfy the triangular inequality. We show that the K-sets+ algorithm converges in a finite number of iterations and it retains the same performance guarantee as the K-sets algorithm for clustering data points in a metric space. We then extend the applicability of the K-sets+ algorithm from data points in a semi-metric space to data points that only have a symmetric similarity measure. Such an extension leads to great reduction of computational complexity. In particular, for an n * n similarity matrix with m nonzero elements in the matrix, the computational complexity of the K-sets+ algorithm is O((Kn + m)I), where I is the number of iterations. The memory complexity to achieve that computational complexity is O(Kn + m). As such, both the computational complexity and the memory complexity are linear in n when the n * n similarity matrix is sparse, i.e., m = O(n). We also conduct various experiments to show the effectiveness of the K-sets+ algorithm by using a synthetic dataset from the stochastic block model and a real network from the WonderNetwork website

Power up! Robust Graph Convolutional Network against Evasion Attacks based on Graph Powering

Graph convolutional networks (GCNs) are powerful tools for graph-structured data. However, they have been recently shown to be prone to topological attacks. Despite substantial efforts to search for new architectures, it still remains a challenge to improve performance in both benign and adversarial situations simultaneously. In this paper, we re-examine the fundamental building block of GCN---the Laplacian operator---and highlight some basic flaws in the spatial and spectral domains. As an alternative, we propose an operator based on graph powering, and prove that it enjoys a desirable property of "spectral separation." Based on the operator, we propose a robust learning paradigm, where the network is trained on a family of "'smoothed" graphs that span a spatial and spectral range for generalizability. We also use the new operator in replacement of the classical Laplacian to construct an architecture with improved spectral robustness, expressivity and interpretability. The enhanced performance and robustness are demonstrated in extensive experiments

Quasireplicas and universal lengths of microbial genomes

Statistical analysis of distributions of occurrence frequencies of short words in 108 microbial complete genomes reveals the existence of a set of universal "root-sequence lengths" shared by all microbial genomes. These lengths and their universality give powerful clues to the way microbial genomes are grown. We show that the observed genomic properties are explained by a model for genome growth in which primitive genomes grew mainly by maximally stochastic duplications of short segments from an initial length of about 200 nucleotides (nt) to a length of about one million nt typical of microbial genomes. The relevance of the result of this study to the nature of simultaneous random growth and information acquisition by genomes, to the so-called RNA world in which life evolved before the rise of proteins and enzymes and to several other topics are discussed.Comment: 4 pages 3 figure