Stochastic arbitrage return and its implication for option pricing

The purpose of this work is to explore the role that random arbitrage opportunities play in pricing financial derivatives. We use a non-equilibrium model to set up a stochastic portfolio, and for the random arbitrage return, we choose a stationary ergodic random process rapidly varying in time. We exploit the fact that option price and random arbitrage returns change on different time scales which allows us to develop an asymptotic pricing theory involving the central limit theorem for random processes. We restrict ourselves to finding pricing bands for options rather than exact prices. The resulting pricing bands are shown to be independent of the detailed statistical characteristics of the arbitrage return. We find that the volatility “smile” can also be explained in terms of random arbitrage opportunities.     

Hidden randomness between fitness landscapes limits reverse evolution

In biological evolution, adaptations to one environment can in some cases reverse adaptations to another environment. To study this "reverse evolution" on a genotypic level, we measured the fitness of E. coli strains with each possible combination of five mutations in an antibiotic-resistance gene in two distinct antibiotic environments. While adaptations to one environment generally lower fitness in the other, we find that reverse evolution is rarely possible and falls as the complexity of adaptations increases, suggesting a probabilistic, molecular form of Dollo's law.     

Dynamically orthogonal field equations for continuous stochastic dynamical systems

In this work we derive an exact, closed set of evolution equations for general continuous stochastic fields described by a Stochastic Partial Differential Equation (SPDE). By hypothesizing a decomposition of the solution field into a mean and stochastic dynamical component, we derive a system of field equations consisting of a Partial Differential Equation (PDE) for the mean field, a family of PDEs for the orthonormal basis that describe the stochastic subspace where the stochasticity ‘lives’ as well as a system of Stochastic Differential Equations that defines how the stochasticity evolves in the time varying stochastic subspace. These new evolution equations are derived directly from the original SPDE, using nothing more than a dynamically orthogonal condition on the representation of the solution. If additional restrictions are assumed on the form of the representation, we recover both the Proper Orthogonal Decomposition equations and the generalized Polynomial Chaos equations. We apply this novel methodology to two cases of two-dimensional viscous fluid flows described by the Navier–Stokes equations and we compare our results with Monte Carlo simulations.     

Complex energies and beginnings of time suggest a theory of scattering and decay

Many useful concepts for a quantum theory of scattering and decay (like Lippmann-Schwinger kets, purely outgoing boundary conditions, exponentially decaying Gamow vectors, causality) are not well defined in the mathematical frame set by the conventional (Hilbert space) axioms of quantum mechanics. Using the Lippmann-Schwinger equations as the takeoff point and aiming for a theory that unites resonances and decay, we conjecture a new axiom for quantum mechanics that distinguishes mathematically between prepared states and detected observables. Suggested by the two signs ±i? of the Lippmann-Schwinger equations, this axiom replaces the one Hilbert space of conventional quantum mechanics by two Hardy spaces. The new Hardy space theory automatically provides Gamow kets with exponential time evolution derived from the complex poles of the S-matrix. It solves the causality problem since it results in a semigroup evolution. But this semigroup brings into quantum physics a new concept of the semigroup time t = 0, a beginning of time. Its interpretation and observations are discussed in the last section.     

Progress in Lanthanides as Luminescent Probes

Lanthanides have recently found applications in different fields of biomolecular and medical research. Luminescent lanthanide chelates have created interest mainly due to their unique luminescent properties, such as their long Stokes’ shift and exceptional decay times allowing efficient temporal discrimination of background interferences in the assays, such as immunoassays. Recently, new organometallic complexes have been developed giving opportunities to novel applications, in heterogeneous and homogeneous immunoassays, DNA hybridization assays, high-throughput screening as well as in imaging. In addition, encapsulating the chelates into suitable matrix in beads enables the use of new members of lanthanides extending the emission wavelength to micrometer range and decays from a few microseconds to milliseconds. As the luminescence is derived from complicated intrachelate energy transfer, it also gives novel opportunities to exploit these levels in different types of energy transfer based applications. This review gives a short overview of recent development of lanthanide chelate-labels and discusses in more details of energy levels and their exploitation in new assay formats.     

Nonparametric dark energy reconstruction from supernova data

Understanding the origin of the accelerated expansion of the Universe poses one of the greatest challenges in physics today. Lacking a compelling fundamental theory to test, observational efforts are targeted at a better characterization of the underlying cause. If a new form of mass-energy, dark energy, is driving the acceleration, the redshift evolution of the equation of state parameter w(z) will hold essential clues as to its origin. To best exploit data from observations it is necessary to develop a robust and accurate reconstruction approach, with controlled errors, for w(z). We introduce a new, nonparametric method for solving the associated statistical inverse problem based on Gaussian process modeling and Markov chain Monte Carlo sampling. Applying this method to recent supernova measurements, we reconstruct the continuous history of w out to redshift z=1.5.     

Multishell intermetallic onions by symmetrical configuration of ordered domains

Ordered domains are utilized to construct new nanostructures, i.e., multishell intermetallic onions, which are formed by symmetrical configuration of ordered domains. Through density-functional theory calculations, we have shown that the energy penalties for introducing antiphase boundaries into the nanoparticles are small in some alloy systems compared to typical surface energies, making it feasible to prepare intermetallic onions by tuning surface energies. The unique surface atomic arrangements would provide opportunities for developing novel materials like efficient catalysts.     

Recent Developments in Ultrafast X-ray Techniques for Materials Science Applications

X-ray free electron lasers (XFELs) offer new ways to probe the structure and dynamics of matter with unprecedented details and in ways that were previously impossible. Continued development and upgrades to existing sources, together with the upcoming commissioning of several new sources, will rapidly expand the possibilities XFELs present for materials science. In this review, we discuss some recent experiments that exploit the unique features of XFELs—coherence, brightness, and time resolution—in order to highlight the opportunities in materials science presented by these facilities.     

Modeling Evolution of Weighted Clique Networks

We propose a weighted clique network evolution model, which expands continuously by the addition of a new clique (maximal complete sub-graph) at each time step. And the cliques in the network overlap with each other. The structural expansion of the weighted clique network is combined with the edges' weight and vertices' strengths dynamical evolution. The model is based on a weight-driven dynamics and a weights' enhancement mechanism combining with the network growth. We study the network properties, which include the distribution of vertices' strength and the distribution of edges' weight, and find that both the distributions follow the scale-free distribution. At the same time, we also find that the relationship between strength and degree of a vertex are linear correlation during the growth of the network. On the basis of mean-field theory, we study the weighted network model and prove that both vertices' strength and edges' weight of this model follow the scale-free distribution. And we exploit an algorithm to forecast the network dynamics, which can be used to reckon the distributions and the corresponding scaling exponents. Furthermore, we observe that mean-field based theoretic results are
consistent with the statistical data of the model, which denotes the theoretical result in this paper is effective.     

The cosmological constant is back

A diverse set of observations now compellingly suggest that the universe possesses a nonzero cosmological constant. In the context of quantum-field theory a cosmological constant corresponds to the energy density of the vacuum, and the favored value for the cosmological constant corresponds to a very tiny vacuum energy density. We discuss future observational tests for a cosmological constant as well as the fundamental theoretical challenges — and opportunities — that this poses for particle physics and for extending our understanding of the evolution of the universe back to the earliest moments.This essay received the fifth award from the Gravity Research Foundation, 1995-Ed.     

Open Topological Strings and Integrable Hierarchies: Remodeling the A-Model

We set up, purely in A-model terms, a novel formalism for the global solution of the open and closed topological A-model on toric Calabi-Yau threefolds. The starting point is to build on recent progress in the mathematical theory of open Gromov-Witten invariants of orbifolds; we interpret the localization formulae as relating D-brane amplitudes to closed string amplitudes perturbed with twisted masses through an analogue of the “loop insertion operator” of matrix models. We first generalize this form of open/closed string duality to general toric backgrounds in all chambers of the stringy Kähler moduli space; secondly, we display a neat connection of the (gauged) closed string side to tau functions of 1+1 Hamiltonian integrable hierarchies, and exploit it to provide an effective computation of open string amplitudes. In doing so, we also provide a systematic treatment of the change of flat open moduli induced by a phase transition in the closed moduli space. We test our proposal in detail by providing an extensive number of checks. We also use our formalism to give a localization-based derivation of the Hori-Vafa spectral curves as coming from a resummation of A-model disc instantons.     

Structure of reversible computation determines the self-duality of quantum theory

Predictions for measurement outcomes in physical theories are usually computed by combining two distinct notions: a state, describing the physical system, and an observable, describing the measurement which is performed. In quantum theory, however, both notions are in some sense identical: outcome probabilities are given by the overlap between two state vectors--quantum theory is self-dual. In this Letter, we show that this notion of self-duality can be understood from a dynamical point of view. We prove that self-duality follows from a computational primitive called bit symmetry: every logical bit can be mapped to any other logical bit by a reversible transformation. Specifically, we consider probabilistic theories more general than quantum theory, and prove that every bit-symmetric theory must necessarily be self-dual. We also show that bit symmetry yields stronger restrictions on the set of allowed bipartite states than the no-signalling principle alone, suggesting reversible time evolution as a possible reason for limitations of nonlocality.     

Nonlinear Study on FEM Amplifier with a Novel Elliptic-Groove Guide

FEM amplifier with a novel elliptic-groove guide is proposed and three-dimensional nonlinear theory for the elliptic-groove guide FEM amplifier is developed. A set of coupled nonlinear differential equations is derived and the characteristics of this FEM amplifier are numerically analyzed in detail including the evolution of power, efficiency and bandwidth. The effects on saturation efficiency due to electron momentum spread and wiggler taper are also studied.     

DNA折纸结构介导的多尺度纳米结构精准制造

原子及近原子尺度制造在近年来一直是物质科学领域被广泛探讨的前沿问题.当制造和加工的尺度从微米、纳米逐渐走向原子级别时,材料在常规尺度下所具备的性质已无法通过经典理论进行解释,相反地,会在这一尺度下展现出一系列新奇的特性.因而对材料极限制造尺度和颠覆性物性的不断追求始终是科学界共同关注的重点领域.作为一种在纳米尺度下对结构制造单元进行精细操控的先进手段,DNA纳米技术的开发和发展为纳米制造甚至原子制造提供了新的观点和思路,而DNA折纸术作为DNA纳米技术的重要组成部分,正在凭借其在结构制造过程当中的高度可编程性成为纳米尺度下进行各类物质精准制造的独特的解决方案,并可能为不同物质不同材料更小尺度和任意形状的精准构筑带来机遇.本文首先简单概述了DNA折纸术的基本原理和发展历程,然后根据制造策略的不同对DNA折纸结构的纳米制造的相关代表性工作做了总结,并在文末提出了对于DNA折纸结构在原子制造中的可行性的思考和未来发展方向的展望.     

Alternative adiabatic elimination schemes for fast variables in stochastic processes

We explore an alternative adiabatic elimination scheme for fast variables in stochastic processes, recently proposed by Haake. For the example of a Brownian particle in an external field we determine the reduced evolution operator, and the initial condition that should be used with it, by means of the Chapman-Enskog formalism. We exploit the close analogy between this formalism and the familiar perturbation theory for degenerate energy levels. We conclude that Haake's scheme is less suitable than other schemes already available in the literature for systems close to equilibrium; it may well be preferable far from equilibrium. We briefly discuss a still broader class of elimination procedures and a criterion for choosing between them.     

Nanotechnology in the Chemical Industry – Opportunities and Challenges

The traditional chemical industry has become a largely mature industry with many commodity products based on established technologies. Therefore, new product and market opportunities will more likely come from speciality chemicals, and from new functionalities obtained from new processing technologies as well as new microstructure control methodologies. It is a well-known fact that in addition to its molecular structure, the microstructure of a material is key to determining its properties. Controlling structures at the micro- and nano-levels is therefore essential to new discoveries. For this article, we define nanotechnology as the controlled manipulation of nanomaterials with at least one dimension less than 100nm. Nanotechnology is emerging as one of the principal areas of investigation that is integrating chemistry and materials science, and in some cases integrating these with biology to create new and yet undiscovered properties that can be exploited to gain new market opportunities. In this article market opportunities for nanotechnology will be presented from an industrial perspective covering electronic, biomedical, performance materials, and consumer products. Manufacturing technology challenges will be identified, including operations ranging from particle formation, coating, dispersion, to characterization, modeling, and simulation. Finally, a nanotechnology innovation roadmap is proposed wherein the interplay between the development of nanoscale building blocks, product design, process design, and value chain integration is identified. A suggestion is made for an R&D model combining market pull and technology push as a way to quickly exploit the advantages in nanotechnology and translate these into customer benefits.     

Nonlinear-closed equations for the first and the second moments of macroscopic variables

A quantum-mechanical theory of describing systems far from equilibrium is developed. A set of time evolution equations for every moment of macroscopic variables is derived with the aid of the new idempotent operator. From this set of equations nonlinear but closed equations for the first and the second moments are obtained directly. The theory is applied to the problem of a spin interacting with its surroundings. The Bloch equation with the Landau-Lifshitz friction term is derived quantum mechanically. The relation between this method and that of system size expansion is discussed.     

A continuum model of gas flows with localized density variations

We discuss the kinetic representation of gases and the derivation of macroscopic equations governing the thermomechanical behavior of a dilute gas viewed at the macroscopic level as a continuous medium. We introduce an approach to kinetic theory where spatial distributions of the molecules are incorporated through a mean-free-volume argument. The new kinetic equation derived contains an extra term involving the evolution of this volume, which we attribute to changes in the thermodynamic properties of the medium. Our kinetic equation leads to a macroscopic set of continuum equations in which the gradients of thermodynamic properties, in particular density gradients, impact on diffusive fluxes. New transport terms bearing both convective and diffusive natures arise and are interpreted as purely macroscopic expansion or compression. Our new model is useful for describing gas flows that display non-local-thermodynamic-equilibrium (rarefied gas flows), flows with relatively large variations of macroscopic properties, and/or highly compressible fluid flows.     

Extensive Adiabatic Invariants for Nonlinear Chains

We look for extensive adiabatic invariants in nonlinear chains in the thermodynamic limit. Considering the quadratic part of the Klein-Gordon Hamiltonian, by a linear change of variables we transform it into a sum of two parts in involution. At variance with the usual method of introducing normal modes, our constructive procedure allows us to exploit the complete resonance, while keeping the extensive nature of the system. Next we construct a nonlinear approximation of an extensive adiabatic invariant for a perturbation of the discrete nonlinear Schrödinger model. The fluctuations of this quantity are controlled via Gibbs measure estimates independent of the system size, for a large set of initial data at low specific energy. Finally, by numerical calculations we show that our adiabatic invariant is well conserved for times much longer than predicted by our first order theory, with fluctuation much smaller than expected according to standard statistical estimates.