arXiv subjects

Dan Li

Publications and source records attributed to Dan Li.

At least 235 records · Page 13Linked to original sources

arXiv2017

Release Connection Fingerprints in Social Networks Using Personalized Differential Privacy

In social networks, different users may have different privacy preferences and there are many users with public identities. Most work on differentially private social network data publication neglects this fact. We aim to release the number of public users that a private user connects to within n hops, called n-range Connection fingerprints(CFPs), under user-level personalized privacy preferences. We proposed two schemes, Distance-based exponential budget absorption (DEBA) and Distance-based uniformly budget absorption using Ladder function (DUBA-LF), for privacy-preserving publication of the CFPs based on Personalized differential privacy(PDP), and we conducted a theoretical analysis of the privacy guarantees provided within the proposed schemes. The implementation showed that the proposed schemes are superior in publication errors on real datasets.

cs.CR↗

arXiv2017

Temporal Variations of Telluric Water Vapor Absorption at Apache Point Observatory

Time-variable absorption by water vapor in Earth's atmosphere presents an important source of systematic error for a wide range of ground-based astronomical measurements, particularly at near-infrared wavelengths. We present results from the first study on the temporal and spatial variability of water vapor absorption at Apache Point Observatory (APO). We analyze $\sim$400,000 high-resolution, near-infrared ($H$-band) spectra of hot stars collected as calibration data for the APO Galactic Evolution Explorer (APOGEE) survey. We fit for the optical depths of telluric water vapor absorption features in APOGEE spectra and convert these optical depths to Precipitable Water Vapor (PWV) using contemporaneous data from a GPS-based PWV monitoring station at APO. Based on simultaneous measurements obtained over a 3$^{\circ}$ field of view, we estimate that our PWV measurement precision is $\pm0.11$ mm. We explore the statistics of PWV variations over a range of timescales from less than an hour to days. We find that the amplitude of PWV variations within an hour is less than 1 mm for most (96.5%) APOGEE field visits. By considering APOGEE observations that are close in time but separated by large distances on the sky, we find that PWV is homogeneous across the sky at a given epoch, with 90% of measurements taken up to 70$^{\circ}$ apart within 1.5 hr having $Δ\,\rm{PWV}<1.0$ mm. Our results can be used to help simulate the impact of water vapor absorption on upcoming surveys at continental observing sites like APO, and also to help plan for simultaneous water vapor metrology that may be carried out in support of upcoming photometric and spectroscopic surveys.

astro-ph.IM↗

arXiv2017

Bott--Kitaev periodic table and index theory

We consider topological insulators and superconductors with discrete symmetries and clarify the relevant index theory behind the periodic table proposed by Kitaev. An effective Hamiltonian determines the analytical index, which can be computed by a topological index. We focus on the spatial dimensions one, two and three, and only consider the bulk theory. In two dimensions, the $\mathbb{Z}$-valued invariants are given by the first Chern number. Meanwhile, $\mathbb{Z}_2$-valued invariants can be computed by the odd topological index and its variations. The Bott-Kitaev periodic table is well-known in the physics literature, we organize the topological invariants in the framework of KR-theory.

math-ph↗

arXiv2017

Oscillating scalar fields in extended quintessence

We study a rapidly-oscillating scalar field with potential $V(ϕ) = k|ϕ|^n$ nonminally coupled to the Ricci scalar $R$ via a term of the form $(1- 8 πG_0 ξϕ^2) R$ in the action. In the weak coupling limit, we calculate the effect of the nonminimal coupling on the time-averaged equation of state parameter $γ= (p + ρ)/ρ$. The change in $\langle γ\rangle$ is always negative for $n \ge 2$ and always positive for $n < 0.71$ (which includes the case where the oscillating scalar field could serve as dark energy), while it can be either positive or negative for intermediate values of $n$. Constraints on the time-variation of $G$ force this change to be infinitesimally small at the present time whenever the scalar field dominates the expansion, but constraints in the early universe are not as stringent. The rapid oscillation induced in $G$ also produces an additional contribution to the Friedman equation that behaves like an effective energy density with a stiff equation of state, but we show that, under reasonable assumptions, this effective energy density is always smaller than the density of the scalar field itself.

gr-qc↗

arXiv2017

Quantum walks on regular uniform hypergraphs

Quantum walks on graphs have shown prioritized benefits and applications in wide areas. In some scenarios, however, it may be more natural and accurate to mandate high-order relationships for hypergraphs, due to the density of information stored inherently. Therefore, we can explore the potential of quantum walks on hypergraphs. In this paper, by presenting the one-to-one correspondence between regular uniform hypergraphs and bipartite graphs, we construct a model for quantum walks on bipartite graphs of regular uniform hypergraphs with Szegedy's quantum walks, which gives rise to a quadratic speed-up. Furthermore, we deliver spectral properties of the transition matrix, given that the cardinalities of the two disjoint sets are different in the bipartite graph. Our model provides the foundation for building quantum algorithms on the strength of quantum walks, suah as quantum walks search, quantized Google's PageRank and quantum machine learning, based on hypergraphs.

quant-ph↗

arXiv2017

Renormalization group flow, Entropy and Eigenvalues

The irreversibility of the renormalization group flow is conjectured to be closely related to the concept of entropy. In this paper, the variation of eigenvalues of the Laplacian in the Polyakov action under the renormalization group flow will be studied. Based on the one-loop approximation to the effective field theory, we will use the heat kernel method and zeta function regularization. In even dimensions, the variation of eigenvalues is given by the top heat kernel coefficient, and the conformal anomaly is relevant. In odd dimensions, we will conjecture a formula for the variation of eigenvalues through the holographic renormalization in the setting of geometric AdS/CFT correspondence.

math-ph↗

arXiv2017

Active Sampling for Large-scale Information Retrieval Evaluation

Evaluation is crucial in Information Retrieval. The development of models, tools and methods has significantly benefited from the availability of reusable test collections formed through a standardized and thoroughly tested methodology, known as the Cranfield paradigm. Constructing these collections requires obtaining relevance judgments for a pool of documents, retrieved by systems participating in an evaluation task; thus involves immense human labor. To alleviate this effort different methods for constructing collections have been proposed in the literature, falling under two broad categories: (a) sampling, and (b) active selection of documents. The former devises a smart sampling strategy by choosing only a subset of documents to be assessed and inferring evaluation measure on the basis of the obtained sample; the sampling distribution is being fixed at the beginning of the process. The latter recognizes that systems contributing documents to be judged vary in quality, and actively selects documents from good systems. The quality of systems is measured every time a new document is being judged. In this paper we seek to solve the problem of large-scale retrieval evaluation combining the two approaches. We devise an active sampling method that avoids the bias of the active selection methods towards good systems, and at the same time reduces the variance of the current sampling approaches by placing a distribution over systems, which varies as judgments become available. We validate the proposed method using TREC data and demonstrate the advantages of this new method compared to past approaches.

cs.IR↗

arXiv2017

Mid-Infrared Polarization of Herbig Ae/Be Discs

We measured mid-infrared polarization of protoplanetary discs to gain new insight into their magnetic fields. Using CanariCam at the 10.4 m Gran Telescopio Canarias, we detected linear polarization at 8.7, 10.3, and 12.5 $μ$m from discs around eight Herbig Ae/Be stars and one T-Tauri star. We analyzed polarimetric properties of each object to find out the most likely interpretation of the data. While the observed mid-infrared polarization from most objects is consistent with polarized emission and/or absorption arising from aligned dust particles, we cannot rule out polarization due to dust scattering for a few objects in our sample. For those objects for which polarization can be explained by polarized emission and/or absorption, we examined how the derived magnetic field structure correlates with the disc position angle and inclination. We found no preference for a certain type of magnetic field. Instead, various configurations (toroidal, poloidal, or complex) are inferred from the observations. The detection rate (64 per cent) of polarized mid-infrared emission and/or absorption supports the expectation that magnetic fields and suitable conditions for grain alignment are common in protoplanetary discs around Herbig Ae/Be stars.

astro-ph.EP↗

arXiv2017

Controlled Alternate Quantum Walks based Quantum Hash Function

Through introducing controlled alternative quantum walks, we present controlled alternate quantum walks (CAQW) based quantum hash function. CAQW based quantum hash function have excellent security, outstanding statistical performance and splendid expansibility. Furthermore, due to the structure of alternative quantum walks, implementing CAQW based quantum hash function significantly reduces the resources necessary for its feasible experimental realization than implementing other quantum hash functions. Besides, CAQW based quantum hash function has expansibility.

quant-ph↗

arXiv2017

Threshold dynamics and ergodicity of an SIRS epidemic model with Markovian switching

This paper studies the spread dynamics of a stochastic SIRS epidemic model with nonlinear incidence and varying population size, which is formulated as a piecewise deterministic Markov process. A threshold dynamic determined by the basic reproduction number $\mathcal{R}_{0}$ is established: the disease can be eradicated almost surely if $\mathcal{R}_{0}<1$, while the disease persists almost surely if $\mathcal{R}_{0}>1$. The existing method for analyzing ergodic behavior of population systems has been generalized. The modified method weakens the required conditions and has no limitations for both the number of environmental regimes and the dimension of the considered system. When $\mathcal{R}_{0}>1$, the existence of a stationary probability measure is obtained. Furthermore, with the modified method, the global attractivity of the $Ω$-limit set of the system and the convergence in total variation to the stationary measure are both demonstrated under a mild extra condition.

math.DS↗

arXiv2017

Detection of Polarized Infrared Emission by Polycyclic Aromatic Hydrocarbons in the MWC 1080 Nebula

Polycyclic aromatic hydrocarbons (PAHs) are ubiquitous in astrophysical environments, as revealed by their pronounced emission features at 3.3, 6.2, 7.7, 8.6, 11.3, and 12.7 $μ$m commonly ascribed to the C--H and C--C vibrational modes. Although these features have long been predicted to be polarized, previous searches for PAH polarization led to null or, at best, tentative detections. Here we report the definite detection of polarized PAH emission at 11.3 $μ$m in the nebula associated with the Herbig Be star MWC 1080. We measure a polarization degree of 1.9$\pm$0.2\%, which is unexpectedly high compared to models. This poses a challenge in the current understanding of the alignment of PAHs, which is required to polarize the PAH emission but thought to be substantially suppressed. PAH alignment with a magnetic field via a resonance paramagnetic relaxation process may account for such a high level of polarization.

astro-ph.GA↗

arXiv2017

Survivable and Bandwidth-Guaranteed Embedding of Virtual Clusters in Cloud Data Centers (Extended Version)

Cloud computing has emerged as a powerful and elastic platform for internet service hosting, yet it also draws concerns of the unpredictable performance of cloud-based services due to network congestion. To offer predictable performance, the virtual cluster abstraction of cloud services has been proposed, which enables allocation and performance isolation regarding both computing resources and network bandwidth in a simplified virtual network model. One issue arisen in virtual cluster allocation is the survivability of tenant services against physical failures. Existing works have studied virtual cluster backup provisioning with fixed primary embeddings, but have not considered the impact of primary embeddings on backup resource consumption. To address this issue, in this paper we study how to embed virtual clusters survivably in the cloud data center, by jointly optimizing primary and backup embeddings of the virtual clusters. We formally define the survivable virtual cluster embedding problem. We then propose a novel algorithm, which computes the most resource-efficient embedding given a tenant request. Since the optimal algorithm has high time complexity, we further propose a faster heuristic algorithm, which is several orders faster than the optimal solution, yet able to achieve similar performance. Besides theoretical analysis, we evaluate our algorithms via extensive simulations.

cs.NI↗

arXiv2016

Notes on topological insulators

This paper is a survey of the $\mathbb{Z}_2$-valued invariant of topological insulators used in condensed matter physics. The $\mathbb{Z}$-valued topological invariant, which was originally called the TKNN invariant in physics, has now been fully understood as the first Chern number. The $\mathbb{Z}_2$ invariant is more mysterious, we will explain its equivalent descriptions from different points of view and provide the relations between them. These invariants provide the classification of topological insulators with different symmetries in which K-theory plays an important role. Moreover, we establish that both invariants are realizations of index theorems which can also be understood in terms of condensed matter physics.

math-ph↗

arXiv2016

The Mid-Infrared Polarization of the Herbig Ae Star WL 16: An Interstellar Origin?

We present high-resolution (0".4) mid-infrared (mid-IR) polarimetric images and spectra of WL 16, a Herbig Ae star at a distance of 125 pc. WL 16 is surrounded by a protoplanetary disk of $\sim$ 900 AU in diameter, making it one of the most extended Herbig Ae/Be disks as seen in the mid-IR. The star is behind, or embedded in, the $ρ$ Ophiuchus molecular cloud, and obscured by 28 magnitudes of extinction at optical wavelengths by the foreground cloud. Mid-IR polarization of WL 16, mainly arises from aligned elongated dust grains present along the line of sight, suggesting a uniform morphology of polarization vectors with an orientation of 33\degr (East from North) and a polarization fraction of $\sim$ 2.0\%. This orientation is consistent with previous polarimetric surveys in the optical and near-IR bands to probe large-scale magnetic fields in the Ophiuchus star formation region, indicating that the observed mid-IR polarization toward WL 16 is produced by the dichroic absorption of magnetically aligned foreground dust grains by a uniform magnetic field. Using polarizations of WL 16 and Elias 29, a nearby polarization standard star, we constrain the polarization efficiency, \textit{$p_{10.3}/A_{10.3}$}, for the dust grains in the $ρ$ Ophiuchus molecular cloud to be $\sim$ 1.0\% mag$^{-1}$. WL 16 has polycyclic aromatic hydrocarbon (PAH) emission features detected at 8.6, 11.2, 12.0, and 12.7 $μ$m by our spectroscopic data, and we find an anti-correlation between the PAH surface brightness and the PAH ionization fraction between the NW and SW sides of the disk.

astro-ph.EP↗

arXiv2016

Noncommutative Chern-Simons theory on the quantum 3-sphere $S^3_θ$

We consider the $θ$-deformed quantum three sphere $S^3_θ$ and study its Chern--Simons theory from a spectral point of view. We first construct a spectral triple on $S^3_θ$ as a generalization of the Dirac geometry on $S^3 $. Since the choice of Dirac operator is not unique, we give two more natural spectral triples on $S^3_θ$ related to the standard round metric. We then compute the Chern--Simons action with respect to the three spectral triples, it turns out that it is not a topological invariant, that is, it depends on the choice of Dirac operators.

math-ph↗

arXiv2016

An Ordered Magnetic Field in the Protoplanetary Disk of AB Aur Revealed by Mid-Infrared Polarimetry

Magnetic fields (B-fields) play a key role in the formation and evolution of protoplanetary disks, but their properties are poorly understood due to the lack of observational constraints. Using CanariCam at the 10.4-m Gran Telescopio Canarias, we have mapped out the mid-infrared polarization of the protoplanetary disk around the Herbig Ae star AB Aur. We detect ~0.44% polarization at 10.3 micron from AB Aur's inner disk (r < 80 AU), rising to ~1.4% at larger radii. Our simulations imply that the mid-infrared polarization of the inner disk arises from dichroic emission of elongated particles aligned in a disk B-field. The field is well ordered on a spatial scale commensurate with our resolution (~50 AU), and we infer a poloidal shape tilted from the rotational axis of the disk. The disk of AB Aur is optically thick at 10.3 micron, so polarimetry at this wavelength is probing the B-field near the disk surface. Our observations therefore confirm that this layer, favored by some theoretical studies for developing magneto-rotational instability and its resultant viscosity, is indeed very likely to be magnetized. At radii beyond ~80 AU, the mid-infrared polarization results primarily from scattering by dust grains with sizes up to ~1 micron, a size indicating both grain growth and, probably, turbulent lofting of the particles from the disk mid-plane.

astro-ph.EP↗

arXiv2016

Noncommutative topological $\mathbb{Z}_2$ invariant

We generalize the $\mathbb{Z}_2$ invariant of topological insulators using noncommutative differential geometry in two different ways. First, we model Majorana zero modes by KQ-cycles in the framework of analytic K-homology, and we define the noncommutative $\mathbb{Z}_2$ invariant as a topological index in noncommutative topology. Second, we look at the geometric picture of the Pfaffian formalism of the $\mathbb{Z}_2$ invariant, i.e., the Kane--Mele invariant, and we define the noncommutative Kane--Mele invariant over the fixed point algebra of the time reversal symmetry in the noncommutative 2-torus. Finally, we are able to prove the equivalence between the noncommutative topological $\mathbb{Z}_2$ index and the noncommutative Kane--Mele invariant.

math-ph↗

arXiv2016

Classifying the behavior of noncanonical quintessence

We derive general conditions for the existence of stable scaling solutions for the evolution of noncanonical quintessence, with a Lagrangian of the form $\mathcal{L}(X,ϕ)=X^α-V(ϕ)$, for power-law and exponential potentials when the expansion is dominated by a background barotropic fluid. Our results suggest that in most cases, noncanonical quintessence with such potentials does not yield interesting models for the observed dark energy. When the scaling solution is not an attractor, there is a wide range of model parameters for which the evolution asymptotically resembles a zero-potential solution with equation of state parameter $w = 1/(2α-1)$, and oscillatory solutions are also possible for positive power-law potentials; we derive the conditions on the model parameters which produce both types of behavior. We investigate thawing noncanonical models with a nearly-flat potential and derive approximate expressions for the evolution of $w(a)$. These forms for $w(a)$ differ in a characteristic way from the corresponding expressions for canonical quintessence.

gr-qc↗