The Beylkin-Cramer Summation Rule and A New Fast Algorithm of Cosmic Statistics for Large Data Sets

Based on the Beylkin-Cramer summation rule, we introduce a new fast algorithm that enable us to explore the high order statistics efficiently in large data sets. Central to this technique is to make decomposition both of fields and operators within the framework of multi-resolution analysis (MRA), and realize theirs discrete representations. Accordingly, a homogenous point process could be equivalently described by a operation of a Toeplitz matrix on a vector, which is accomplished by making use of fast Fourier transformation. The algorithm could be applied widely in the cosmic statistics to tackle large data sets. Especially, we demonstrate this novel technique using the spherical, cubic and cylinder counts in cells respectively. The numerical test shows that the algorithm produces an excellent agreement with the expected results. Moreover, the algorithm introduces naturally a sharp-filter, which is capable of suppressing shot noise in weak signals. In the numerical procedures, the algorithm is somewhat similar to particle-mesh (PM) methods in N-body simulations. As scaled with $O(N\log N)$, it is significantly faster than the current particle-based methods, and its computational cost does not relies on shape or size of sampling cells. In addition, based on this technique, we propose further a simple fast scheme to compute the second statistics for cosmic density fields and justify it using simulation samples. Hopefully, the technique developed here allows us to make a comprehensive study of non-Guassianity of the cosmic fields in high precision cosmology. A specific implementation of the algorithm is publicly available upon request to the author.Comment: 27 pages, 9 figures included. revised version, changes include (a) adding a new fast algorithm for 2nd statistics (b) more numerical tests including counts in asymmetric cells, the two-point correlation functions and 2nd variances (c) more discussions on technic

Evolution of Cooperation in Public Goods Games with Stochastic Opting-Out

This paper investigates the evolution of strategic play where players drawn from a finite well-mixed population are offered the opportunity to play in a public goods game. All players accept the offer. However, due to the possibility of unforeseen circumstances, each player has a fixed probability of being unable to participate in the game, unlike similar models which assume voluntary participation. We first study how prescribed stochastic opting-out affects cooperation in finite populations. Moreover, in the model, cooperation is favored by natural selection over both neutral drift and defection if return on investment exceeds a threshold value defined solely by the population size, game size, and a player's probability of opting-out. Ultimately, increasing the probability that each player is unable to fulfill her promise of participating in the public goods game facilitates natural selection of cooperators. We also use adaptive dynamics to study the coevolution of cooperation and opting-out behavior. However, given rare mutations minutely different from the original population, an analysis based on adaptive dynamics suggests that the over time the population will tend towards complete defection and non-participation, and subsequently, from there, participating cooperators will stand a chance to emerge by neutral drift. Nevertheless, increasing the probability of non-participation decreases the rate at which the population tends towards defection when participating. Our work sheds light on understanding how stochastic opting-out emerges in the first place and its role in the evolution of cooperation.Comment: 30 pages, 4 figures. This is one of the student project papers arsing from the Mathematics REU program at Dartmouth 2017 Summer. See https://math.dartmouth.edu/~reu/ for more info. Comments are always welcom

Analysis of a Darcy-Cahn-Hilliard Diffuse Interface Model for the Hele-Shaw Flow and its Fully Discrete Finite Element Approximation

In this paper we present PDE and finite element analyses for a system of partial differential equations (PDEs) consisting of the Darcy equation and the Cahn-Hilliard equation, which arises as a diffuse interface model for the two phase Hele-Shaw flow. We propose a fully discrete implicit finite element method for approximating the PDE system, which consists of the implicit Euler method combined with a convex splitting energy strategy for the temporal discretization, the standard finite element discretization for the pressure and a split (or mixed) finite element discretization for the fourth order Cahn-Hilliard equation. It is shown that the proposed numerical method satisfies a mass conservation law in addition to a discrete energy law that mimics the basic energy law for the Darcy-Cahn-Hilliard phase field model and holds uniformly in the phase field parameter $\epsilon$. With help of the discrete energy law, we first prove that the fully discrete finite method is unconditionally energy stable and uniquely solvable at each time step. We then show that, using the compactness method, the finite element solution has an accumulation point that is a weak solution of the PDE system. As a result, the convergence result also provides a constructive proof of the existence of global-in-time weak solutions to the Darcy-Cahn-Hilliard phase field model in both two and three dimensions. Finally, we propose a nonlinear multigrid iterative algorithm to solve the finite element equations at each time step. Numerical experiments based on the overall solution method of combining the proposed finite element discretization and the nonlinear multigrid solver are presented to validate the theoretical results and to show the effectiveness of the proposed fully discrete finite element method for approximating the Darcy-Cahn-Hilliard phase field model.Comment: 30 pages, 4 tables, 2 figure

Baryon electric dipole moments from strong CP violation

The electric dipole form factors and moments of the ground state baryons are calculated in chiral perturbation theory at next-to-leading order. We show that the baryon electric dipole form factors at this order depend only on two combinations of low-energy constants. We also derive various relations that are free of unknown low-energy constants. We use recent lattice QCD data to calculate all baryon EDMs. In particular, we find d_n = -2.9\pm 0.9 and d_p = 1.1\pm 1.1 in units of 10^{-16} e \theta_0 cm. Finite volume corrections to the moments are also worked out. We show that for a precision extraction from lattice QCD data, the next-to-leading order terms have to be accounted for.Comment: 30 pages, 8 figures, to appear in JHE

Corrugated structure insertion for extending the SASE bandwidth up to 3% at the European XFEL

The usage of x-ray free electron laser (XFEL) in femtosecond nanocrystallography involves sequential illumination of many small crystals of arbitrary orientation. Hence a wide radiation bandwidth will be useful in order to obtain and to index a larger number of Bragg peaks used for determination of the crystal orientation. Considering the baseline configuration of the European XFEL in Hamburg, and based on beam dynamics simulations, we demonstrate here that the usage of corrugated structures allows for a considerable increase in radiation bandwidth. Data collection with a 3% bandwidth, a few microjoule radiation pulse energy, a few femtosecond pulse duration, and a photon energy of 5.4 keV is possible. For this study we have developed an analytical modal representation of the short-range wake function of the flat corrugated structures for arbitrary offsets of the source and the witness particles.Comment: 29 pages, 17 figure

Light quark mass dependence in heavy quarkonium physics

The issue of chiral extrapolations in heavy quarkonium systems is discussed. We show that the light quark mass dependence of the properties of heavy quarkonia is not always suppressed. For quarkonia close to an open flavor threshold, even a nonanalytic chiral extrapolation is needed. Both these nontrivial facts are demonstrated to appear in the decay widths of the hindered M1 transitions between the first radially excited and ground state P-wave charmonia. The results at a pion mass of about 500 MeV could deviate from the value at the physical pion mass by a factor of two. Our findings show the necessity of performing chiral extrapolations for lattice simulations of heavy quarkonium systems.Comment: 5 pages, 5 figures. Version to appear in Phys. Rev. Let

Effect of Local Magnetic Moments on the Metallic Behavior in Two Dimensions

The temperature dependence of conductivity $\sigma (T)$ in the metallic phase of a two-dimensional electron system in silicon has been studied for different concentrations of local magnetic moments. The local moments have been induced by disorder, and their number was varied using substrate bias. The data suggest that in the limit of $T\to 0$ the metallic behavior, as characterized by $d\sigma/dT < 0$, is suppressed by an arbitrarily small amount of scattering by local magnetic moments.Comment: 4 pages, revtex, plus four encapsulated postscript figure

Continuous Authentication for Voice Assistants

Voice has become an increasingly popular User Interaction (UI) channel, mainly contributing to the ongoing trend of wearables, smart vehicles, and home automation systems. Voice assistants such as Siri, Google Now and Cortana, have become our everyday fixtures, especially in scenarios where touch interfaces are inconvenient or even dangerous to use, such as driving or exercising. Nevertheless, the open nature of the voice channel makes voice assistants difficult to secure and exposed to various attacks as demonstrated by security researchers. In this paper, we present VAuth, the first system that provides continuous and usable authentication for voice assistants. We design VAuth to fit in various widely-adopted wearable devices, such as eyeglasses, earphones/buds and necklaces, where it collects the body-surface vibrations of the user and matches it with the speech signal received by the voice assistant's microphone. VAuth guarantees that the voice assistant executes only the commands that originate from the voice of the owner. We have evaluated VAuth with 18 users and 30 voice commands and find it to achieve an almost perfect matching accuracy with less than 0.1% false positive rate, regardless of VAuth's position on the body and the user's language, accent or mobility. VAuth successfully thwarts different practical attacks, such as replayed attacks, mangled voice attacks, or impersonation attacks. It also has low energy and latency overheads and is compatible with most existing voice assistants