Evolving nature of human contact networks with its impact on epidemic processes

Human contact networks are constituted by a multitude of individuals and pairwise contacts among them. However, the dynamic nature, which generates the evolution of human contact networks, of contact patterns is not known yet. Here, we analyse three empirical datasets and identify two crucial mechanisms of the evolution of temporal human contact networks, i.e. the activity state transition laws for an individual to be socially active, and the contact establishment mechanism that active individuals adopt. We consider both of the two mechanisms to propose a temporal network model, named the memory driven (MD) model, of human contact networks. Then we study the susceptible-infected (SI) spreading processes on empirical human contact networks and four corresponding temporal network models, and compare the full prevalence time of SI processes with various infection rates on the networks. The full prevalence time of SI processes in the MD model is the same as that in real-world human contact networks. Moreover, we find that the individual activity state transition promotes the spreading process, while, the contact establishment of active individuals suppress the prevalence. Apart from this, we observe that even a small percentage of individuals to explore new social ties is able to induce an explosive spreading on networks. The proposed temporal network framework could help the further study of dynamic processes in temporal human contact networks, and offer new insights to predict and control the diffusion processes on networks

The Impact of Information Dissemination on Vaccination in Multiplex Networks

The impact of information dissemination on epidemic control is essentially subject to individual behaviors. Unlike information-driven behaviors, vaccination is determined by many cost-related factors, whose correlation with the information dissemination should be better understood. To this end, we propose an evolutionary vaccination game model in multiplex networks by integrating an information-epidemic spreading process into the vaccination dynamics, and explore how information dissemination influences vaccination. The spreading process is described by a two-layer coupled susceptible-alert-infected-susceptible (SAIS) model, where the strength coefficient between two layers is defined to characterize the tendency and intensity of information dissemination. We find that information dissemination can increase the epidemic threshold, however, more information transmission cannot promote vaccination. Specifically, increasing information dissemination even leads to a decline of the vaccination equilibrium and raises the final infection density. Moreover, we study the impact of strength coefficient and individual sensitivity on social cost, and unveil the role of information dissemination in controlling the epidemic with numerical simulations

Reformulating the Quantum Uncertainty Relation

Uncertainty principle is one of the cornerstones of quantum theory. In the literature, there are two types of uncertainty relations, the operator form concerning the variances of physical observables and the entropy form related to entropic quantities. Both these forms are inequalities involving pairwise observables, and are found to be nontrivial to incorporate multiple observables. In this work we introduce a new form of uncertainty relation which may give out complete trade-off relations for variances of observables in pure and mixed quantum systems. Unlike the prevailing uncertainty relations, which are either quantum state dependent or not directly measurable, our bounds for variances of observables are quantum state independent and immune from the "triviality" problem of having zero expectation values. Furthermore, the new uncertainty relation may provide a geometric explanation for the reason why there are limitations on the simultaneous determination of different observables in $N$-dimensional Hilbert space.Comment: 15 pages, 2 figures; published in Scientific Report

On Wilson's Theorem and Polignac Conjecture

We introduce Wilson's theorem and Clement's result and present a necessary and sufficient condition for p and p+2k to be primes where k is a positive integer. By using Simiov's Theorem, we derive an improved version of Clement's result and characterizations of Polignac twin primes which parallel previous characterizations.Comment: 8 page

A Necessary and Sufficient Criterion for the Separability of Quantum State

Quantum entanglement has been regarded as one of the key physical resources in quantum information sciences. However, the determination of whether a mixed state is entangled or not is generally a hard issue, even for the bipartite system. In this work we propose an operational necessary and sufficient criterion for the separability of an arbitrary bipartite mixed state, by virtue of the multiplicative Horn's problem. The work follows the work initiated by Horodecki {\it et. al.} and uses the Bloch vector representation introduced to the separability problem by J. De Vicente. In our criterion, a complete and finite set of inequalities to determine the separability of compound system is obtained, which may be viewed as trade-off relations between the quantumness of subsystems. We apply the obtained result to explicit examples, e.g. the separable decomposition of arbitrary dimension Werner state and isotropic state.Comment: 33 pages; published in Scientific Report

Equivalence theorem of uncertainty relations

We present an equivalence theorem to unify the two classes of uncertainty relations, i.e., the variance-based ones and the entropic forms, which shows that the entropy of an operator in a quantum system can be built from the variances of a set of commutative operators. That means an uncertainty relation in the language of entropy may be mapped onto a variance-based one, and vice versa. Employing the equivalence theorem, alternative formulations of entropic uncertainty relations stronger than existing ones in the literature are obtained for qubit system, and variance based uncertainty relations for spin systems are reached from the corresponding entropic uncertainty relations.Comment: 18 pages, 1 figure; published in J. Phys. A: Math. Theo

Separable Decompositions of Bipartite Mixed States

We present a practical scheme for the decomposition of a bipartite mixed state into a sum of direct products of local density matrices, using the technique developed in Li and Qiao (Sci. Rep. 8: 1442, 2018). In the scheme, the correlation matrix which characterizes the bipartite entanglement is first decomposed into two matrices composed of the Bloch vectors of local states. Then we show that the symmetries of Bloch vectors are consistent with that of the correlation matrix, and the magnitudes of the local Bloch vectors are lower bounded by the correlation matrix. Concrete examples for the separable decompositions of bipartite mixed states are presented for illustration.Comment: 22 pages; published in Quantum Inf. Proces

State of the Art and Prospects of Structured Sensing Matrices in Compressed Sensing

Compressed sensing (CS) enables people to acquire the compressed measurements directly and recover sparse or compressible signals faithfully even when the sampling rate is much lower than the Nyquist rate. However, the pure random sensing matrices usually require huge memory for storage and high computational cost for signal reconstruction. Many structured sensing matrices have been proposed recently to simplify the sensing scheme and the hardware implementation in practice. Based on the restricted isometry property and coherence, couples of existing structured sensing matrices are reviewed in this paper, which have special structures, high recovery performance, and many advantages such as the simple construction, fast calculation and easy hardware implementation. The number of measurements and the universality of different structure matrices are compared

Nonaxisymmetric Rossby Vortex Instability with Toroidal Magnetic Fields in Radially Structured Disks

We investigate the global nonaxisymmetric Rossby vortex instability in a differentially rotating, compressible magnetized accretion disk with radial density structures. Equilibrium magnetic fields are assumed to have only the toroidal component. Using linear theory analysis, we show that the density structure can be unstable to nonaxisymmetric modes. We find that, for the magnetic field profiles we have studied, magnetic fields always provide a stabilizing effect to the unstable Rossby vortex instability modes. We discuss the physical mechanism of this stabilizing effect. The threshold and properties of the unstable modes are also discussed in detail. In addition, we present linear stability results for the global magnetorotational instability when the disk is compressible.Comment: ApJ accepte

Generation of Einstein-Podolsky-Rosen State via Earth's Gravitational Field

Although various physical systems have been explored to produce entangled states involving electromagnetic, strong, and weak interactions, the gravity has not yet been touched in practical entanglement generation. Here, we propose an experimentally feasible scheme for generating spin entangled neutron pairs via the Earth's gravitational field, whose productivity can be one pair in every few seconds with the current technology. The scheme is realized by passing two neutrons through a specific rectangular cavity, where the gravity adjusts the neutrons into entangled state. This provides a simple and practical way for the implementation of the test of quantum nonlocality and statistics in gravitational field.Comment: 12 pages, 9 figure