Estimating parameters in stochastic systems: A variational Bayesian approach

This work is concerned with approximate inference in dynamical systems, from a variational Bayesian perspective. When modelling real world dynamical systems, stochastic differential equations appear as a natural choice, mainly because of their ability to model the noise of the system by adding a variation of some stochastic process to the deterministic dynamics. Hence, inference in such processes has drawn much attention. Here a new extended framework is derived that is based on a local polynomial approximation of a recently proposed variational Bayesian algorithm. The paper begins by showing that the new extension of this variational algorithm can be used for state estimation (smoothing) and converges to the original algorithm. However, the main focus is on estimating the (hyper-) parameters of these systems (i.e. drift parameters and diffusion coefficients). The new approach is validated on a range of different systems which vary in dimensionality and non-linearity. These are the Ornstein-Uhlenbeck process, the exact likelihood of which can be computed analytically, the univariate and highly non-linear, stochastic double well and the multivariate chaotic stochastic Lorenz ’63 (3D model). As a special case the algorithm is also applied to the 40 dimensional stochastic Lorenz ’96 system. In our investigation we compare this new approach with a variety of other well known methods, such as the hybrid Monte Carlo, dual unscented Kalman filter, full weak-constraint 4D-Var algorithm and analyse empirically their asymptotic behaviour as a function of observation density or length of time window increases. In particular we show that we are able to estimate parameters in both the drift (deterministic) and the diffusion (stochastic) part of the model evolution equations using our new methods.     

Automated sample‐scanning methods for radiation damage mitigation and diffraction‐based centering of macromolecular crystals

Automated scanning capabilities have been added to the data acquisition software, JBluIce‐EPICS, at the National Institute of General Medical Sciences and the National Cancer Institute Collaborative Access Team (GM/CA CAT) at the Advanced Photon Source. A `raster' feature enables sample centering via diffraction scanning over two‐dimensional grids of simple rectangular or complex polygonal shape. The feature is used to locate crystals that are optically invisible owing to their small size or are visually obfuscated owing to properties of the sample mount. The raster feature is also used to identify the best‐diffracting regions of large inhomogeneous crystals. Low‐dose diffraction images taken at grid positions are automatically processed in real time to provide a quick quality ranking of potential data‐collection sites. A `vector collect' feature mitigates the effects of radiation damage by scanning the sample along a user‐defined three‐dimensional vector during data collection to maximize the use of the crystal volume and the quality of the collected data. These features are integrated into the JBluIce‐EPICS data acquisition software developed at GM/CA CAT where they are used in combination with a robust mini‐beam of rapidly changeable diameter from 5 µm to 20 µm. The powerful software–hardware combination is being applied to challenging problems in structural biology.     

M‐theory solutions invariant under D(2,1; γ) ⊕ D(2,1;γ)

We simplify and extend the construction of half‐BPS solutions to 11‐dimensional supergravity, with isometry superalgebra D(2,1;γ) ⊕ D(2,1;γ). Their space‐time has the form AdS₃× S³× S³ warped over a Riemann surface Σ. It describes near‐horizon geometries of M2 branes ending on, or intersecting with, M5 branes along a common string. The general solution to the BPS equations is specified by a reduced set of data (γ, h, G), where γ is the real parameter of the isometry superalgebra, and h and G are functions on Σ whose differential equations and regularity conditions depend only on the sign of γ. The magnitude of γ enters only through the map of h,G onto the supergravity fields, thereby promoting all solutions into families parametrized by |γ|. By analyzing the regularity conditions for the supergravity fields, we prove two general theorems: (i) that the only solution with a 2‐dimensional CFT dual is AdS₃× S³× S³× ℝ², modulo discrete identifications of the flat ℝ², and (ii) that solutions with γ < 0 cannot have more than one asymptotic higher‐dimensional AdS region. We classify the allowed singularities of h and G near the boundary of Σ, and identify four local solutions: asymptotic AdS₄/Z₂ or AdS₇^′ regions; highly‐curved M5‐branes; and a coordinate singularity called the “cap”. By putting these “Lego” pieces together we recover all known global regular solutions with the above symmetry, including the self‐dual strings on M5 for γ <0, and the Janus solution for γ > 0, but now promoted to families parametrized by |γ|. We also construct exactly new regular solutions which are asymptotic to AdS₄/Z₂ for γ < 0, and conjecture that they are a different superconformal limit of the self‐dual string. Finally, we construct exactly γ > 0 solutions with highly curved M5‐brane regions, which are the formal continuation of the self‐dual string solutions across the decompactification point at γ = 0.     

New Gaugings and Non‐Geometry

We discuss the possible realisation in string/M theory of the recently discovered family of four‐dimensional maximal gauged supergravities, and of an analogous family of seven‐dimensional half‐maximal gauged supergravities. We first prove a no‐go theorem that neither class of gaugings can be realised via a compactification that is locally described by ten‐ or eleven‐dimensional supergravity. In the language of Double Field Theory and its M theory analogue, this implies that the section condition must be violated. Introducing the minimal number of additional coordinates possible, we then show that the standard S ³ and S ⁷ compactifications of ten‐ and eleven‐dimensional supergravity admit a new class of section‐violating generalised frames with a generalised Lie derivative algebra that reproduces the embedding tensor of the and gaugings respectively. The physical meaning, if any, of these constructions is unclear. They highlight a number of the issues that arise when attempting to apply the formalism of Double Field Theory to non‐toroidal backgrounds. Using a naive brane charge quantisation to determine the periodicities of the additional coordinates restricts the gaugings to an infinite discrete set and excludes all the gaugings other than the standard one.     

Computational design of tetrazolone‐based high‐energy density energetic materials: Property prediction and decomposition mechanism

The density functional theory methods are used to design a series of new highly energetic tetrazolone‐based molecules by the combination of the linked tetrazolone framework and versatile substitutes. The molecular and electronic structures, physicochemical, and energetic properties were analyzed and predicted. The decomposition mechanisms were computationally simulated, and 3 potential decomposition channels were proposed. These newly designed tetrazolone‐based compounds show high densities (up to 2.08 g/cm³) and highly positive heats of formation (407.0‐1377.9 kJ/mol) due to all right content of nitrogen and oxygen. Most of them exhibit good detonation velocity (8.31‐9.62 km/s) and detonation pressure (32.40‐43.86 GPa), and some are comparative to excellent explosive CL‐20. Results show that compounds 6 , 10 , 11 , 12 , 15 , 16 , 17 , 22 , 23 , and 24 own superior detonation performance than widely used explosive HMX and may be promising candidates of green high‐performance energetic materials.     

Development of a Joule‐class Yb:YAG amplifier and its implementation in a CPA system generating 1 TW pulses

In this paper the development and implementation of a novel amplifier setup as an additional stage for the CPA pump laser of the Petawatt Field Synthesizer, currently developed at the Max‐Planck‐Institute of Quantum Optics, is presented. This amplifier design comprises 20 relay‐imaged passes through the active medium which are arranged in rotational symmetry. As the gain material, an in‐house‐developed Yb:YAG active‐mirror is used. With this setup, stretched 4 ns seed pulses are amplified to output energies exceeding 1 J with repetition rates of up to 2 Hz. Furthermore, a spectral bandwidth of 3.5 nm (FWHM) is maintained during amplification and the compression of the pulses down to their Fourier‐limit of 740 fs is achieved. To the best of our knowledge, this is the first demonstration of 1 TW pulses generated via CPA in diode‐pumped Yb:YAG.     

Improved blind‐source separation for spectra

A new method is proposed that improves the performance of independent component analysis (ICA) algorithms for separating overlapping spectra under certain circumstances. The method is designed for Raman spectra in particular, although it should be applicable to spectra with similar line shapes, such as nuclear magnetic resonance. In the zero‐noise case, conventional ICA fails to separate synthetic Raman spectra completely; by maximising smoothness, as opposed to other more traditional measures of statistical independence, better performance can be achieved. The new method is tested against artificial and real Raman spectra, and demonstrates improved performance for each. The algorithm is fully automated, requiring no user input or judgement in order to separate the spectra. Copyright © 2011 John Wiley & Sons, Ltd.     

Causal signal transmission by quantum fields. VI: The Lorentz condition and Maxwell’s equations for fluctuations of the electromagnetic field

The general structure of electromagnetic interactions in the so-called response representation of quantum electrodynamics (QED) is analysed. A formal solution to the general quantum problem of the electromagnetic field interacting with matter is found. Independently, a formal solution to the corresponding problem in classical stochastic electrodynamics (CSED) is constructed. CSED and QED differ only in the replacement of stochastic averages of c-number fields and currents by time-normal averages of the corresponding Heisenberg operators. All relations of QED connecting quantum field to quantum current lack Planck’s constant, and thus coincide with their counterparts in CSED. In Feynman’s terms, one encounters complete disentanglement of the potential and current operators in response picture.     

Dynamic view-dependent visualization of unstructured tetrahedral volumetric meshes

Abstract  

Visualization of large volumetric datasets has always been an important problem. Due to the high computational requirements of volume-rendering techniques, achieving interactive rates is a real challenge. We present a selective refinement scheme that dynamically refines the mesh according to the camera parameters. This scheme automatically determines the impact of different parts of the mesh on the output image and refines the mesh accordingly, without needing any user input. The view-dependent refinement scheme uses a progressive mesh representation that is based on an edge collapse-based tetrahedral mesh simplification algorithm. We tested our view-dependent refinement framework on an existing state-of-the-art volume renderer. Thanks to low overhead dynamic view-dependent refinement, we achieve interactive frame rates for rendering common datasets at decent image resolutions.     

Topological phase transitions in Calabi‐Yau compactifications of M‐theory

In this thesis we construct five‐dimensional gauged supergravity actions which describe flop and conifold transitions in M‐theory compactified on Calabi‐Yau threefolds. While the vector multiplet sector is determined exactly, we use the Wolf spaces to model the universal hypermultiplet together with N charged hypermultiplets corresponding to winding states of M2‐branes. After specifying the hypermultiplet sector the actions are uniquely determined by M‐theory. As an application we consider five‐dimensional Kasner cosmologies. Including the dynamics of the winding modes, we find smooth cosmological solutions which undergo flop and conifold transitions. Instead of the usual runaway behavior the scalar fields of these solutions generically stabilize in the transition region where they oscillate around the transition locus. The scalar potential thereby induces short episodes of accelerated expansion in the space‐time.     

Black hole attractors and the entropy function in four‐ and five‐dimensional N = 2 supergravity

In this overview of selected aspects of the black hole attractor mechanism, after introducing the necessary foundations, we examine the relationship between two ways to describe the attractor phenomenon in four‐dimensional N = 2 supergravity: the entropy function and the black hole potential. We also exemplify their practical application to finding solutions to the attractor equations for a conifold prepotential. Next we describe an extension of the original definition of the entropy function to a class of rotating black holes in five‐dimensional N = 2 supergravity based on cubic polynomials, exploiting a connection between four‐ and five‐dimensional black holes. This link allows further the derivation of five‐dimensional first‐order differential flow equations governing the profile of the fields from infinity to the event horizon and construction of non‐supersymmetric interpolating solutions in four dimensions by dimensional reduction. Finally, since four‐dimensional extremal black holes in N = 2 supergravity can be viewed as certain two‐dimensional string compactifications with fluxes, we discuss implications of the conifold example in the context of the entropic principle, which postulates as a probability measure on the space of these string compactifications the exponentiated entropy of the corresponding black holes.     

Effective aperture of X‐ray compound refractive lenses

A new definition of the effective aperture of the X‐ray compound refractive lens (CRL) is proposed. Both linear (one‐dimensional) and circular (two‐dimensional) CRLs are considered. It is shown that for a strongly absorbing CRL the real aperture does not influence the focusing properties and the effective aperture is determined by absorption. However, there are three ways to determine the effective aperture in terms of transparent CRLs. In the papers by Kohn [(2002). JETP Lett. 76 , 600–603; (2003). J. Exp. Theor. Phys. 97 , 204–215; (2009). J. Surface Investig. 3 , 358–364; (2012). J. Synchrotron Rad. 19 , 84–92; Kohn et al. (2003). Opt. Commun. 216 , 247–260; (2003). J. Phys. IV Fr, 104 , 217–220], the FWHM of the X‐ray beam intensity just behind the CRL was used. In the papers by Lengeler et al. [(1999). J. Synchrotron Rad. 6 , 1153–1167; (1998). J. Appl. Phys. 84 , 5855–5861], the maximum intensity value at the focus was used. Numerically, these two definitions differ by 50%. The new definition is based on the integral intensity of the beam behind the CRL over the real aperture. The integral intensity is the most physical value and is independent of distance. The new definition gives a value that is greater than that of the Kohn definition by 6% and less than that of the Lengeler definition by 41%. A new approximation for the aperture function of a two‐dimensional CRL is proposed which allows one to calculate the two‐dimensional CRL through the one‐dimensional CRL and to obtain an analytical solution for a complex system of many CRLs.     

Effect of non‐extensivity parameter q on the damping rate of dust ion acoustic waves in non‐extensive dusty plasma

Kinetic theory has been applied to study the damping characteristics of dust ion acoustic waves (DIAWs) in a dusty plasma comprising q‐non‐extensive distributed electrons and ions, while the dust particles are considered extensive following the Maxwellian velocity distribution function. It is found that the results of the three‐dimensional velocity distribution function are more accurate compared to the results of the one‐dimensional velocity distribution function. The numerical solution of the dispersion relation is carried out to study the effect of the non‐extensivity parameter q on the dispersion, the damping rate, and the range of the values of the normalized wavenumber ( k λ_D) for which the DIAWs are weakly damped. It is found that the change in the value of the electron non‐extensivity parameter q_e has a minor effect on the dispersion, the damping rate, and the range of the values of the normalized wavenumber ( k λ_D) for which the DIAWs are weakly damped, while on the other hand, ion non‐extensivity parameter q_i has a strong effect on these arguments. The effect of other parameters, such as the ratio of electron to ion number density and ratio of electron to ion temperature, on the damping characteristics of DIAWs is also highlighted.     

The study on interactions between 1‐ethyl‐3‐methylimidazolium chloride and benzene/pyridine /pyrrole/thiophene

The density functional theory was used to investigate the interactions between 1‐ethyl‐3‐methylimidazolium chloride ([EMIM]Cl) and benzene/pyridine/pyrrole/thiophene. The complexes formed between [EMIM]Cl and benzene/pyridine/pyrrole/thiophene were optimized at the ωB97XD/6‐31++G** level, and the optimized complexes were further analyzed by natural bond orbital, atoms in molecules, and noncovalent interaction. The calculated results show that the interaction energy between ionic liquid and benzene/pyridine/pyrrole/thiophene is in the order pyrrole > pyridine > thiophene > benzene. The major interactions between ionic liquid and benzene/pyridine/pyrrole/thiophene are hydrogen bonding and π‐π interaction, accompanied by C···H, N···H, H···H, and S···H weak interactions. Both cation and anion of ionic liquid are involved in interactions with aromatic compounds.     

Preference of online users and personalized recommendations

In a recent work [T. Zhou, Z. Kuscsik, J.-G. Liu, M. Medo, J.R. Wakeling, Y.-C. Zhang, Proc. Natl. Acad. Sci. 107 (2010) 4511], a personalized recommendation algorithm with high performance in both accuracy and diversity is proposed. This method is based on the hybridization of two single algorithms called probability spreading and heat conduction, which respectively are inclined to recommend popular and unpopular products. With a tunable parameter, an optimal balance between these two algorithms in system level is obtained. In this paper, we apply this hybrid method in individual level, namely each user has his/her own personalized hybrid parameter to adjust. Interestingly, we find that users are quite different in personalized hybrid parameters and the recommendation performance can be significantly improved if each user is assigned with his/her optimal personalized hybrid parameter. Furthermore, we find that users’ personalized parameters are negatively correlated with users’ degree but positively correlated with the average degree of the items collected by each user. With these understandings, we propose a strategy to assign users with suitable personalized parameters, which leads to a further improvement of the original hybrid method. Finally, our work highlights the importance of considering the heterogeneity of users in recommendation.     

Comment on ‘An optimal algorithm for counting networks motifs’ [Physica A 381 (2007) 482-490]

Network motifs in a given network are small connected subnetworks that occur at significantly higher frequencies than would be expected for a random network. In their 2007 article “An optimal algorithm for counting network motifs”, Itzhack, Mogilevski, and Louzoun present an algorithm for detecting network motifs. Based on an experimental comparison with a motif detection software called FANMOD, they claim that their algorithm is “more than a thousand times faster” than any previous motif detection algorithm. We show that this claim is not correct and based on a significant flaw in the experimental setup. Once the experimental data of Itzhack et al. is corrected for this flaw, the implementation of their algorithm actually turns out to be a little slower than FANMOD for random Erd?s-Rényi graphs. For random scale-free networks, the implementation of Itzhack et al. is faster only by a factor of ∼1.5, not the orders of magnitude claimed by Itzhack et al.     

守恒无伪解麦克斯韦方程间断元研究:(Ⅰ)一维和二维情况

考察了电、磁场分量分别基于不同近似函数空间展开的一维和二维Maxwell方程间断元求解方法。结合中心数值通量和电、磁场分量近似函数空间的不同组合,构造了各种间断元算子。通过用这些算子在规则和不规则网格上编码分析一维和二维金属腔的谐振模式,详细考察了算子的收敛和伪解支持性,并据此对基函数进行了优选。算子在时域和频域对谐振模式的计算结果彼此符合良好。优选的Maxwell方程间断元算子不仅同时具备能量守恒和免于伪解的特性,且无需引入辅助变量,为设计高品质Maxwell方程间断元算法和研发相关电磁场模拟软件提供了支撑。     

Geometric Quantization and Two Dimensional QCD

In this article, we will discuss geometric quantization of two dimensional Quantum Chromodynamics with fermionic or bosonic matter fields. We identify the respective large-N _c phase spaces as the infinite dimensional Grassmannian and the infinite dimensional Disc. The Hamiltonians are quadratic functions, and the resulting equations of motion for these classical systems are nonlinear. In [33], it was shown that the linearization of the equations of motion for the Grassmannian gave the 't Hooft equation. We will see that the linearization in the bosonic case leads to the scalar analog of the 't Hooft equation found in [36]. Received: 13 August 1996 / Accepted: 20 May 1997     

Field-theoretical three-body relativistic equations for the multichannel πN↔γN↔ππN↔γπN reactions

A new kind of the relativistic three-body equations for the coupled πN and γN scattering reactions with the ππN and γπN three particle final states are suggested. These equations are derived in the framework of the standard field-theoretical S-matrix approach in the time-ordered three-dimensional form. Therefore, corresponding relativistic covariant equations are three-dimensional from the beginning and the considered formulation is free of the ambiguities which appear due to a three dimensional reduction of the four dimensional Bethe-Salpeter equations. The solutions of the considered equations satisfy the unitarity condition and they are exactly gauge invariant even after the truncation of the multiparticle (n>3) intermediate states. Moreover, the form of these three-body equations does not depend on the choice of the model Lagrangian and it is the same for the formulations with and without quark degrees of freedom. The effective potential of the suggested equations is defined by the vertex functions with two on-mass shell particles. It is emphasized that these INPUT vertex functions can be constructed from experimental data. Special attention is given to the construction of the intermediate on shell and off shell Δ resonance states. These intermediate Δ states are obtained after separation of the Δ resonance pole contributions in the intermediate πN Green function. The resulting amplitudes for the Δ⇔Nπ; Δ⇔Nγ; Δ^′⇔Δγ transition have the same structure as the vertex functions for transitions between the on-mass shell particle states with spin 1/2 and 3/2. Therefore it is possible to introduce the real value for the magnetic momenta for the Δ^′⇔Δγ transition amplitudes in the same way as it is done for the N^′⇔Nγ vertex function.