Expansion Scheme Research Articles

Doubling bialgebras of graphs and Feynman rules

In this article, we define a doubling procedure for the bialgebra of specified Feynman graphs introduced in a previous paper \cite {DMB}. This is the vector space generated by the pairs $(\bar \Gamma, \bar \gamma)$ where $\bar \Gamma$ is a locally $1PI$ specified graph of a perturbation theory $\Cal T$ with $\bar \gamma \subset \bar \Gamma$ locally $1PI$ and where $\bar \Gamma / \bar \gamma $ is a specified graph of $\Cal T$. We also define a convolution product on the characters of this new bialgebra with values in an endomorphism algebra, equipped with a commutative product compatible with the composition. We then express in this framework the renormalization as formulated by A. Smirnov \cite [§8.5, 8.6] {Sm}, adapting the approach of A. Connes and D. Kreimer for two renormalization schemes: the minimal renormalization scheme and the Taylor expansion scheme. Finally, we determine the finite parts of Feynman integrals using the BPHZ algorithm after dimensional regularization procedure, by following the approach by P. Etingof \cite{PE} (see also \cite{RM}).

An optimization model design for energy systems planning and management under considering air pollution control in Tangshan City, China

In this study, an interval-parameter fuzzy programming mixed integer programming method (IFMIP) is designed for supporting the planning of energy systems management (ESM) and air pollution mitigation control under multiple uncertainties. The IFMIP-ESM model is based on an integration of interval-parameter programming (IPP), fuzzy programming (FP), and mixed-integer programming (MIP), which can reflect multiple uncertainties presented as both interval values and fuzzy distributions numbers. Moreover, it can successfully identify dynamics of capacity expansion schemes, reflect dual dynamics in terms of interval membership function, and analyze various emission-mitigation scenarios through incorporating energy and environmental policies. The designed model is applied to a case of energy systems management in Tangshan City, China, and the results indicate that reasonable solutions obtained from the model would be helpful for decision makers to effectively (a) adjust the allocation patterns of energy resources and transform the patterns of energy consumption and economic development, (b) facilitate the implement of air pollution control action plan, and (c) analysis dynamic interactions among system cost, energy-supply security, and environmental requirement.

Landau gauge Yang-Mills correlation functions

We investigate Landau gauge $SU(3)$ Yang-Mills theory in a systematic vertex expansion scheme for the effective action with the functional renormalisation group. Particular focus is put on the dynamical creation of the gluon mass gap at non-perturbative momenta and the consistent treatment of quadratic divergences. The non-perturbative ghost and transverse gluon propagators as well as the momentum-dependent ghost-gluon, three-gluon and four-gluon vertices are calculated self-consistently with the classical action as only input. The apparent convergence of the expansion scheme is discussed and within the errors, our numerical results are in quantitative agreement with available lattice results.

The neutral emergence of error minimized genetic codes superior to the standard genetic code

The standard genetic code (SGC) assigns amino acids to codons in such a way that the impact of point mutations is reduced, this is termed ‘error minimization’ (EM). The occurrence of EM has been attributed to the direct action of selection, however it is difficult to explain how the searching of alternative codes for an error minimized code can occur via codon reassignments, given that these are likely to be disruptive to the proteome. An alternative scenario is that EM has arisen via the process of genetic code expansion, facilitated by the duplication of genes encoding charging enzymes and adaptor molecules. This is likely to have led to similar amino acids being assigned to similar codons. Strikingly, we show that if during code expansion the most similar amino acid to the parent amino acid, out of the set of unassigned amino acids, is assigned to codons related to those of the parent amino acid, then genetic codes with EM superior to the SGC easily arise. This scheme mimics code expansion via the gene duplication of charging enzymes and adaptors. The result is obtained for a variety of different schemes of genetic code expansion and provides a mechanistically realistic manner in which EM has arisen in the SGC. These observations might be taken as evidence for self-organization in the earliest stages of life.

Optimization of transport network in the Basin of Yangtze River with minimization of environmental emission and transport/investment costs

The capacity of the ship-lock at the Three Gorges Dam has become bottleneck of waterway transport and caused serious congestion. In this article, a continual network design model is established to solve the problem with minimizing the transport cost and environmental emission as well as infrastructure construction cost. In this bi-level model, the upper model gives the schemes of ship-lock expansion or construction of pass-dam highway. The lower model assigns the containers in the multi-mode network and calculates the transport cost, environmental emission, and construction investment. The solution algorithm to the model is proposed. In the numerical study, scenario analyses are done to evaluate the schemes and determine the optimal one in the context of different traffic demands. The result shows that expanding the ship-lock is better than constructing pass-dam highway.

Only a pawn in their games? environmental (?) migration in Kiribati – past, present and future

The Pacific Island Countries and Territories (PICT) are exposed to the impacts of climate change. In extreme cases entire states may disappear. Kiribati is one of these countries. Within its own territory there are no ­places to where people could be safely resettled when their home islands become unsuitable for human habitation. Large-scale resettlement is nothing new to the people of Kiribati. In colonial times people from various islands were resettled. The Phoenix Island Settlement Scheme (PISS) is one of these efforts to allegedly bring people to safety. Making use of primary sources that have become available only recently the paper raises the question if there is anything to learn from PISS for present times, or if PISS has historical value only, as the ­United Kingdom’s last colonial expansion scheme. The paper asks about conflicting intentions of colonial authorities and assesses if and possibly why strategic political considerations resulted in a situation where humanitarian motivations retreated into the background leading to a sub-optimal preparation of the scheme, which then finally led to its failure. The paper comes to the conclusion that behind reportedly noble purposes there is a layer of colonial interests which lets settlers appear as objects in a larger colonial game.

A bi-level integrated generation-transmission planning model incorporating the impacts of demand response by operation simulation

If all the resources in power supply side, transmission part, and power demand side are considered together, the optimal expansion scheme from the perspective of the whole system can be achieved. In this paper, generation expansion planning and transmission expansion planning are combined into one model. Moreover, the effects of demand response in reducing peak load are taken into account in the planning model, which can cut back the generation expansion capacity and transmission expansion capacity. Existing approaches to considering demand response for planning tend to overestimate the impacts of demand response on peak load reduction. These approaches usually focus on power reduction at the moment of peak load without considering the situations in which load demand at another moment may unexpectedly become the new peak load due to demand response. These situations are analyzed in this paper. Accordingly, a novel approach to incorporating demand response in a planning model is proposed. A modified unit commitment model with demand response is utilized. The planning model is thereby a bi-level model with interactions between generation-transmission expansion planning and operation simulation to reflect the actual effects of demand response and find the reasonably optimal planning result.

Quantum Monte Carlo with very large multideterminant wavefunctions.

An algorithm to compute efficiently the first two derivatives of (very) large multideterminant wavefunctions for quantum Monte Carlo calculations is presented. The calculation of determinants and their derivatives is performed using the Sherman-Morrison formula for updating the inverse Slater matrix. An improved implementation based on the reduction of the number of column substitutions and on a very efficient implementation of the calculation of the scalar products involved is presented. It is emphasized that multideterminant expansions contain in general a large number of identical spin-specific determinants: for typical configuration interaction-type wavefunctions the number of unique spin-specific determinants Ndetσ ( σ=↑,↓) with a non-negligible weight in the expansion is of order O(Ndet). We show that a careful implementation of the calculation of the Ndet -dependent contributions can make this step negligible enough so that in practice the algorithm scales as the total number of unique spin-specific determinants, Ndet↑+Ndet↓, over a wide range of total number of determinants (here, Ndet up to about one million), thus greatly reducing the total computational cost. Finally, a new truncation scheme for the multideterminant expansion is proposed so that larger expansions can be considered without increasing the computational time. The algorithm is illustrated with all-electron fixed-node diffusion Monte Carlo calculations of the total energy of the chlorine atom. Calculations using a trial wavefunction including about 750,000 determinants with a computational increase of ∼400 compared to a single-determinant calculation are shown to be feasible. © 2016 Wiley Periodicals, Inc.

Deterministic generation of large scale atomic W states.

We present a deterministic scheme for generating large-scale atomic W states in a cavity QED system via a simple expansion mechanism, which is realized only by a detuned interaction between two identical atoms and a vacuum cavity mode. With the presented scheme, a W-type Bell pair can be created and an n-atom W state can be expanded to a 2n-atom W state with a unit probability of success in principle. No multi-atom gates, quantum memories or quantum non-demolition measurements are required, greatly simplifying the experimental realization of the scheme. The feasibility analysis shows that our expansion scheme can be implemented with state-of-the-art technologies. Our scheme enables advances not only in quantum information and communication but also in quantum thermodynamics, where atomic W states plays a crucial role.

A framework of query expansion for image retrieval based on knowledge base and concept similarity

We study several semantic concept-based query expansion and re-ranking scheme and compare different ontology-based expansion methods in image search and retrieval. To improve the query expansion efficiency and accuracy, we employ the CYC knowledge base to generate the expansion candidate concepts, while filter and rank the expansion results by calculating concept similarities using the Semantic Relatedness Metrics. Using our knowledge-based query expansion in image retrieval, the efficiency and accuracy has been improved.

Efficient and exact numerical approach for many multi-level systems in open system CQED

In this paper we generalize the numerically exact expansion scheme for many two-level systems coupled to a bosonic (cavity) mode under open system conditions to the case of multi-level systems. For the two-level systems the method is derived from physical and intuitive arguments and the efficient numerical modeling up to hundreds of two-level systems is described. We thereby perform an analysis that allows a natural generalization to multi-level systems. The focus of the paper lies on a comprehensible view on the underlying physics. This facilitates direct application of the method and the use of additional generalizations and approximations.

Lagrangian bias of generic large-scale structure tracers

The dark matter halos that host galaxies and clusters form out of initial high-density patches, providing a biased tracer of the linear matter density field. In the simplest local bias approximation, the halo field is treated as a perturbative series in the average overdensity of the Lagrangian patch. In more realistic models, however, additional quantities will affect the clustering of halo-patches, and this expansion becomes a function of several stochastic variables. In this paper, we present a general multivariate expansion scheme that can parametrize the clustering of any biased Lagrangian tracer, given only the variables involved and their symmetry (in our case rotational invariance). This approach is based on an expansion in the orthonormal polynomials associated with the relevant variables, so that no renormalization of the coefficients ever occurs. We provide explicit expression for the series coefficients, or Lagrangian bias parameters, in the case of peaks of the linear density field. As an application of our formalism, we present a simple derivation of the original BBKS formula, and compute the non-Gaussian bias in the presence of a primordial trispectrum of the local shape.

A multiyear DG-incorporated framework for expansion planning of distribution networks using binary chaotic shark smell optimization algorithm

In this paper, a new model for MEPDN (multiyear expansion planning of distribution networks) is proposed. By solving this model, the optimal expansion scheme of primary (i.e. medium voltage) distribution network including the reinforcement pattern of primary feeders as well as location and size of DG (distributed generators) during an ascertained planning period is determined. Furthermore, the time-based feature of proposed model allows it to specify the investments/reinforcements time (i.e. year). Moreover, a minimum load shedding-based analytical approach for optimizing the network's reliability is introduced. The associated objective function of proposed model is minimizing the total investment and operation costs. To solve the formulated MEPDN model as a complex multi-dimensional optimization problem, a new evolutionary algorithm-based solution method called BCSSO (Binary Chaotic Shark Smell Optimization) is presented. The effectiveness of the proposed MEPDN model and solution approach is illustrated by applying them on two widely-used test cases including 12-bus and 33-bus distribution network and comparing the acquired results with the results of other solution methods.

High‐dynamic range image generation from single low‐dynamic range image

Due to the growing popularity of high-dynamic range (HDR) image and the high complexity to capture HDR image, researchers focus on converting low-dynamic range (LDR) content to HDR, which gives rise to a number of dynamic range expansion methods. Most of the existing methods try their best to tackle highlight areas during the expanding, however, in some cases, they cannot achieve approving results. In this study, a novel LDR image expansion technique is presented. The technique first detects the highlight areas in image; then preprocesses them and reconstructs the information of these regions; finally, expands the LDR image to HDR. Unlike the existing schemes, the proposed approach escapes the complicated treatment to highlight areas in the process of expansion, which makes the expansion straightforward; at the same time, it facilitates the expansion scheme and minimises the formation of the artefacts. The experimental results show that the proposed method performs well; the tone mapped versions of the produced HDR images are popular. The results of the image quality metric also illustrate that the novel approach can recover more image details with minimised contrast loss and reversal, compared with the existing schemes considered in the comparison.

Logarithmic divergences in the k-inflationary power spectra computed through the uniform approximation

We investigate a calculation method for solving the Mukhanov-Sasaki equation in slow-roll k-inflation based on the uniform approximation (UA) in conjunction with an expansion scheme for slow-roll parameters with respect to the number of e-folds about the so-called turning point. Earlier works on this method have so far gained some promising results derived from the approximating expressions for the power spectra among others, up to second order with respect to the Hubble and sound flow parameters, when compared to other semi-analytical approaches (e.g., Green's function and WKB methods). However, a closer inspection is suggestive that there is a problem when higher-order parts of the power spectra are considered; residual logarithmic divergences may come out that can render the prediction physically inconsistent. Looking at this possibility, we map out up to what order with respect to the mentioned parameters several physical quantities can be calculated before hitting a logarithmically divergent result. It turns out that the power spectra are limited up to second order, the tensor-to-scalar ratio up to third order, and the spectral indices and running converge to all orders. This indicates that the expansion scheme is incompatible with the working equations derived from UA for the power spectra but compatible with that of the spectral indices. For those quantities that involve logarithmically divergent terms in the higher-order parts, existing results in the literature for the convergent lower-order parts calculated in the equivalent fashion should be viewed with some caution; they do not rest on solid mathematical ground.

A Low-Latency List Successive-Cancellation Decoding Implementation for Polar Codes

Due to their provably capacity-achieving performance, polar codes have attracted a lot of research interest recently. For a good error-correcting performance, list successive-cancellation decoding (LSCD) with large list size is used to decode polar codes. However, as the complexity and delay of the list management operation rapidly increase with the list size, the overall latency of LSCD becomes large and limits the applicability of polar codes in high-throughput and latency-sensitive applications. Therefore, in this work, the low-latency implementation for LSCD with large list size is studied. Specifically, at the system level, a selective expansion method is proposed such that some of the reliable bits are not expanded to reduce the computation and latency. At the algorithmic level, a double thresholding scheme is proposed as a fast approximate-sorting method for the list management operation to reduce the LSCD latency for large list size. A VLSI architecture of the LSCD implementing the selective expansion and double thresholding scheme is then developed, and implemented using a UMC 90 nm CMOS technology. Experimental results show that, even for a large list size of 16, the proposed LSCD achieves a decoding throughput of 460 Mbps at a clock frequency of 658 MHz.

Superfluid phase transition with activated velocity fluctuations: Renormalization group approach.

A quantum field model that incorporates Bose-condensed systems near their phase transition into a superfluid phase and velocity fluctuations is proposed. The stochastic Navier-Stokes equation is used for a generation of the velocity fluctuations. As such this model generalizes model F of critical dynamics. The field-theoretic action is derived using the Martin-Siggia-Rose formalism and path integral approach. The regime of equilibrium fluctuations is analyzed within the perturbative renormalization group method. The double (ε,δ)-expansion scheme is employed, where ε is a deviation from space dimension 4 and δ describes scaling of velocity fluctuations. The renormalization procedure is performed to the leading order. The main corollary gained from the analysis of the thermal equilibrium regime suggests that one-loop calculations of the presented models are not sufficient to make a definite conclusion about the stability of fixed points. We also show that critical exponents are drastically changed as a result of the turbulent background and critical fluctuations are in fact destroyed by the developed turbulence fluctuations. The scaling exponent of effective viscosity is calculated and agrees with expected value 4/3.

High-order Numerical Method for Generalized Black-Scholes Model

This work presents a high order numerical method for the solution of generalized Black-Scholes model for European call option. The numerical method is derived using a two-step backward differentiation formula in the temporal discretization and a High-Order Difference approximation with Identity Expansion (HODIE) scheme in the spatial discretization. The present scheme gives second order accuracy in time and third order accuracy in space. Numerical experiments are conducted in support of the theoretical results.

An Inexact Credibility Chance-Constrained Integer Programming for Greenhouse Gas Mitigation Management in Regional Electric Power System under Uncertainty

Electric power system (EPS) management considering greenhouse gas (GHG) mitigation is a challenging task, since many system parameters such as electric demand, resource availability, system cost as well as their interrelationships may appear uncertain. To reflect these uncertainties, in this study, an interval-parameter credibility constrained programming (ICCP) method was developed for electric power system planning in light of GHG mitigation. The method was advantageous in tackling uncertainties expressed as not only fuzzy possibilistic distributions associated with the right-hand-side components of model constraints but also discrete intervals in the objective function. In addition, ICCP allowed satisfaction of system constraints at specified confidence level, leading to model solutions with low system cost under acceptable risk magnitudes. The obtained results indicated that stable intervals for the objective function and decision variables could be generated, which were useful for helping decision makers identify the desired electric power generation patterns, capacity expansion schemes and GHG-emission reduction under complex uncertainties, and gain in-depth insights into the trade-offs between system economy and reliability.

O(N)model within theΦ-derivable expansion to orderλ2: On the existence and UV/IR sensitivity of the solutions to self-consistent equations

We discuss various aspects of the O(N)-model in the vacuum and at finite temperature within the Phi-derivable expansion scheme to order lambda^2. In continuation to an earlier work, we look for a physical parametrization in the N=4 case that allows to accommodate the lightest mesons. Using zero-momentum curvature masses to approximate the physical masses, we find that, in the parameter range where a relatively large sigma mass is obtained, the scale of the Landau pole is lower compared to that obtained in the two-loop truncation. This jeopardizes the insensitivity of the observables to the ultraviolet regulator and could hinder the predictivity of the model. Both in the N=1 and N=4 cases, we also find that, when approaching the chiral limit, the (iterative) solution to the Phi-derivable equations is lost in an interval around the would-be transition temperature. In particular, it is not possible to conclude at this order of truncation on the order of the transition in the chiral limit. Because the same issue could be present in other approaches, we investigate it thoroughly by considering a localized version of the Phi-derivable equations, whose solution displays the same qualitative features, but allows for a more analytical understanding of the problem. In particular, our analysis reveals the existence of unphysical branches of solutions which can coalesce with the physical one at some temperatures, with the effect of opening up a gap in the admissible values for the condensate. Depending on its rate of growth with the temperature, this gap can eventually engulf the physical solution.