Exact Mapping Research Articles

Gauge invariances of higher derivative Maxwell-Chern-Simons field theory: A new Hamiltonian approach

A new method of abstracting the independent gauge invariances of higher derivative systems, recently introduced in [1], has been applied to higher derivative field theories. This has been discussed taking the extended Maxwell-Chern-Simons model as an example. A new Hamiltonian analysis of the model is provided. This Hamiltonian analysis has been used to construct the independent gauge generator. An exact mapping between the Hamiltonian gauge transformations and the U(1) symmetries of the action has been established.

Fast and accurate method for high order Zernike moments computation

Zernike moments (ZMs) which belong to a class of circularly orthogonal rotation invariant moments are very useful image descriptors for various image processing applications. They, however, suffer from various errors, such as discretization error, geometric error and numerical integration error. In this paper, we present an approach for their computation which reduces geometric error and numerical integration error. Geometric error is reduced by performing exact mapping of a square grid domain into a circular grid by using both the square and arc-grids. Numerical integration error is reduced by resorting to Gaussian numerical integration over the square and arc-grids. It is observed that the contribution of numerical integration error to the total error is much more than the geometric error. The effect of these two errors is more significant in small images as compared to large images. The use of numerical integration, however, enhances the time complexity. This problem is resolved by using recursive algorithms for the computation of radial polynomials, 8-way symmetry of radial polynomials and 8-way symmetry/anti-symmetry of angular part of the kernel function. Exhaustive experiments on synthetic and real images are performed to demonstrate the effectiveness of the proposed approach.

Effect of Partial Screening upon the Conductance Through Nanostructured Devices

Low-temperature transport properties of nanostructured semiconductor devices have been monitored in the laboratory for well over a decade now. Two basic arrangements have been most often studied: the single-electron transistor, in which a quantum dot bridges two independent electron gases, and the T-shaped device, in which the dot is side-coupled to a quantum wire. In both cases, the thermal dependence of the measured zero-bias conductances has been phenomenologically fitted by scaling and shifting the universal curve gu(T/TK) for the particle–hole symmetric Anderson Hamiltonian, where TK is the Kondo temperature. Here, an exact linear mapping between the conductance and the universal curve is derived. Under the assumption that the dot magnetic moment is partially screened at high temperatures, it fits the experimental data very well.

Inelastic transport: a pseudoparticle approach

We discuss a pseudoparticle NEGF approach as a tool to describe transport in molecular junctions in the language of many-body states of the molecule. A method developed by Oh et al. [Phys. Rev. B, 2011, 83, 205302] is applied to inelastic transport in the case of strong electron-vibron interaction. The approach can be seen as a generalization of the exact mapping developed by Bonca and Trugman [Phys. Rev. Lett., 1995, 75, 2566] which includes information on the Pauli exclusion principle and Fermi electron distribution in the leads. Within simple model calculations of inelastic transport in junctions, we compare the pseudoparticle approach to other approximate NEGF schemes.

Non-analytic quantum oscillator image of complete replica symmetry breaking

We describe the effect of replica symmetry breaking in the field distribution function P(h) of the T = 0 Sherrington–Kirkpatrick (SK) model as the difference between a split Gaussian and the first excited state ψ1 of a weakly anharmonic oscillator with non-analytic shift by means of the analogy P(h) ↔ |ψ1(x)|. New numerical calculations of the leading 100 orders of replica symmetry breaking (RSB) were performed in order to obtain P(h), employing the exact mapping between the density of states ρ(E) of the fermionic SK model and P(h) of the standard model, as derived by Perez-Castillo and Sherrington. Fast convergence towards a fixed point function ρ(E) for infinite steps of RSB is observed. A surprisingly small number of harmonic oscillator wavefunctions suffices to represent this fixed point function. This allows us to determine an anharmonic potential V(x) with non-analytic shift, whose first excited state represents ρ(E) and hence P(h). The harmonic potential with unconventional shift V 2(x) ∼ (|x| − x 0)2 = (x − x 0 sign(x))2 already yields a very good approximation, since anharmonic couplings of V(x) − V 2(x) ∼ |x| m , m > 2, decay rapidly with increasing m. We compare the pseudo-gap-forming effect of replica symmetry breaking, hosted by the fermionic SK model, with the analogous effect in the Coulomb glass as designed by Davies, Lee and Rice, and described by Müller and Pankov.

Finite-temperature properties of one-dimensional hard-core bosons in a quasiperiodic optical lattice

We investigate the properties of impenetrable bosons confined in a one-dimensional lattice at finite temperature in the presence of an additional incommensurate periodic potential. Relying on the exact Fermi-Bose mapping, we study the effects of temperature on the one-particle density matrix and related quantities such as the momentum distribution function and the natural orbitals. We found evidence of a finite-temperature crossover related to the zero-temperature superfluid-to-Bose-glass transition that induces a delocalization of the lowest natural orbitals.

OSCAM - optimized stereoscopic camera control for interactive 3D

This paper presents a controller for camera convergence and interaxial separation that specifically addresses challenges in interactive stereoscopic applications like games. In such applications, unpredictable viewer- or object-motion often compromises stereopsis due to excessive binocular disparities. We derive constraints on the camera separation and convergence that enable our controller to automatically adapt to any given viewing situation and 3D scene, providing an exact mapping of the virtual content into a comfortable depth range around the display. Moreover, we introduce an interpolation function that linearizes the transformation of stereoscopic depth over time, minimizing nonlinear visual distortions. We describe how to implement the complete control mechanism on the GPU to achieve running times below 0.2ms for full HD. This provides a practical solution even for demanding real-time applications. Results of a user study show a significant increase of stereoscopic comfort, without compromising perceived realism. Our controller enables 'fail-safe' stereopsis, provides intuitive control to accommodate to personal preferences, and allows to properly display stereoscopic content on differently sized output devices.

Dual fermion dynamical cluster approach for strongly correlated systems

We have designed a multiscale approach for strongly correlated systems by combining the dynamical cluster approximation (DCA) and the recently introduced dual fermion formalism. This approach employs an exact mapping from a real lattice to a DCA cluster of linear size ${L}_{c}$ embedded in a dual fermion lattice. Short-length-scale physics is addressed by the DCA cluster calculation, while longer-length-scale physics is addressed diagrammatically using dual fermions. The bare and dressed dual fermionic Green functions scale as $\mathcal{O}(1/{L}_{c})$, so perturbation theory on the dual lattice converges very quickly, e.g., the dual Fermion self-energy calculated with simple second-order perturbation theory is of order $\mathcal{O}(1/{L}_{c}^{3})$ with third-order and three-body corrections down by an additional factor of $\mathcal{O}(1/{L}_{c})$.

The convex hull for a random acceleration process in two dimensions

We compute exactly the mean perimeter 〈L(T)〉 and the mean area 〈A(T)〉 of the convex hull of a random acceleration process of duration T in two dimensions. We use an exact mapping that relates, via Cauchy's formulae, the computation of the perimeter and the area of the convex hull of an arbitrary two-dimensional stochastic process [x(t), y(t)] to the computation of the extreme value statistics of the associated one-dimensional component process x(t). The latter can be computed exactly for the one-dimensional random acceleration process even though the process is non-Markovian. Physically, our results are relevant in describing the average shape of a semi-flexible ideal polymer chain in two dimensions.

Bijection between spin [formula omitted] and a cluster of [formula omitted] spins [formula omitted

We propose a general method by which a spin-S is decomposed into spins less than S. We have obtained the exact mapping between spin S=pM−12 and a cluster of M spins σ=p−12, where p and M are positive integers. We have discussed the possible applications of such transformations. In particular we have shown how a general d+1 dimensional spin-p−12 model with general interactions can be reduced to a d-dimensional spin-S model with S=pM−12.

Worm-type Monte Carlo simulation of the Ashkin-Teller model on the triangular lattice

We investigate the symmetric Ashkin-Teller (AT) model on the triangular lattice in the antiferromagnetic two-spin coupling region (J<0). In the J→-∞ limit, we map the AT model onto a fully packed loop-dimer model on the honeycomb lattice. On the basis of this exact transformation and the low-temperature expansion, we formulate a variant of worm-type algorithms for the AT model, which significantly suppress the critical slowing down. We analyze the Monte Carlo data by finite-size scaling, and locate a line of critical points of the Ising universality class in the region J<0 and K>0, with K the four-spin interaction. Further, we find that, in the J→-∞ limit, the critical line terminates at the decoupled point K=0. From the numerical results and the exact mapping, we conjecture that this "tricritical" point (J→-∞,K=0) is Berezinsky-Kosterlitz-Thouless-like and the logarithmic correction is absent. The dynamic critical exponent of the worm algorithm is estimated as z=0.28(1) near (J→-∞,K=0).

Entanglement spectrum and boundary theories with projected entangled-pair states

In many physical scenarios, close relations between the bulk properties of quantum systems and theories associated with their boundaries have been observed. In this work, we provide an exact duality mapping between the bulk of a quantum spin system and its boundary using projected entangled-pair states. This duality associates to every region a Hamiltonian on its boundary, in such a way that the entanglement spectrum of the bulk corresponds to the excitation spectrum of the boundary Hamiltonian. We study various specific models: a deformed AKLT model [I. Affleck, T. Kennedy, E. H. Lieb, and H. Tasaki, Phys. Rev. Lett. 59, 799 (1987)], an Ising-type model [F. Verstraete, M. M. Wolf, D. Perez-Garcia, and J. I. Cirac, Phys. Rev. Lett. 96, 220601 (2006)], and Kitaev's toric code [A. Kitaev, Ann. Phys. 303, 2 (2003)], both in finite ladders and in infinite square lattices. In the second case, some of those models display quantum phase transitions. We find that a gapped bulk phase with local order corresponds to a boundary Hamiltonian with local interactions, whereas critical behavior in the bulk is reflected on a diverging interaction length of the boundary Hamiltonian. Furthermore, topologically ordered states yield nonlocal Hamiltonians. Because our duality also associates a boundary operator to any operator in the bulk, it in fact provides a full holographic framework for the study of quantum many-body systems via their boundary.

General solutions of plane problem for power function curved cracks

A new exact and universal conformal mapping is proposed. Using Muskhelishvili's complex potential method, the plane elasticity problem of power function curved cracks is investigated with an arbitrary power of a natural number, and the general solutions of the stress intensity factors (SIFs) for mode I and mode II at the crack tip are obtained under the remotely uniform tensile loads. The present results can be reduced to the well-known solutions when the power of the function takes different natural numbers. Numerical examples are conducted to reveal the effects of the coefficient, the power, and the projected length along the x-axis of the power function curved crack on the SIFs for mode I and mode II.

Quantum criticality in disordered bosonic optical lattices

Using the exact Bose-Fermi mapping, we study universal properties of ground-state density distributions and finite-temperature quantum critical behavior of one-dimensional hard-core bosons in trapped incommensurate optical lattices. Through the analysis of universal scaling relations in the quantum critical regime, we demonstrate that the superfluid to Bose glass transition and the general phase diagram of disordered hard-core bosons can be uniquely determined from finite-temperature density distributions of the trapped disordered system.

Numerical and experimental mapping of small root zones using optimized surface and borehole resistivity tomography

An exact mapping of root zones is essential to understand plant growth, root biomass, and soil functions important for environmental and climatic management and protection. Numerical and experimental techniques of the electrical resistivity tomography were applied in 2D and 3D to resolve small root zones in the centimeter range. Numerically, we studied two scenarios of conductive and resistive root zones as a function of (1) eight different quadripole electrode configurations (standard, nonstandard, and optimized), (2) four different survey designs with electrode arrays at the soil surface and in boreholes, and (3) eight different inversion constraints. The best resolved output tomogram was evaluated semiquantitatively using the criteria of visual similarity to the input model, least data set, rms error, and iteration number and quantitatively by the model difference relative to the input model. The results showed that the surface-borehole configurations have the best resolution for the whole root zone. The single-surface and borehole surveys resolve only the respective upper and middle-lower root parts. The results reflect the potential of the optimization approach to generate small data sets of far higher resolution than the standard sets. Based on these results, we used the surface-borehole survey around a young hibiscus planted in a sandy soil in a laboratory experiment. The surface-borehole surveys using small, optimized configurations result in an optimum spatiotemporal resolution for simultaneous applications for 3D mapping of targets (root zones and water and soil heterogeneities) and 4D monitoring of their processes.

Quantum rotor theory of spinor condensates in tight traps

In this work, we theoretically construct exact mappings of many-particle bosonic systems onto quantum rotor models. In particular, we analyze the rotor representation of spinor Bose-Einstein condensates. In a previous work [R. Barnett et al., Phys. Rev. A 82, 031602(R) (2010)] it was shown that there is an exact mapping of a spin-one condensate of fixed particle number with quadratic Zeeman interaction onto a quantum rotor model. Since the rotor model has an unbounded spectrum from above, it has many more eigenstates than the original bosonic model. Here we show that for each subset of states with fixed spin ${F}_{z}$, the physical rotor eigenstates are always those with the lowest energy. We classify three distinct physical limits of the rotor model: the Rabi, Josephson, and Fock regimes. The last regime corresponds to a fragmented condensate and is thus not captured by the Bogoliubov theory. We next consider the semiclassical limit of the rotor problem and make connections with the quantum wave functions through the use of the Husimi distribution function. Finally, we describe how to extend the analysis to higher-spin systems and derive a rotor model for the spin-two condensate. Theoretical details of the rotor mapping are also provided here.

TreeKO: a duplication-aware algorithm for the comparison of phylogenetic trees

Comparisons of tree topologies provide relevant information in evolutionary studies. Most existing methods share the drawback of requiring a complete and exact mapping of terminal nodes between the compared trees. This severely limits the scope of genome-wide analyses, since trees containing duplications are pruned arbitrarily or discarded. To overcome this, we have developed treeKO, an algorithm that enables the comparison of tree topologies, even in the presence of duplication and loss events. To do so treeKO recursively splits gene trees into pruned trees containing only orthologs to subsequently compute a distance based on the combined analyses of all pruned tree comparisons. In addition treeKO, implements the possibility of computing phylome support values, and reconciliation-based measures such as the number of inferred duplication and loss events.

Worm Monte Carlo study of the honeycomb-lattice loop model

We present a Markov-chain Monte Carlo algorithm of worm type that correctly simulates the O ( n ) loop model on any (finite and connected) bipartite cubic graph, for any real n > 0 , and any edge weight, including the fully-packed limit of infinite edge weight. Furthermore, we prove rigorously that the algorithm is ergodic and has the correct stationary distribution. We emphasize that by using known exact mappings when n = 2 , this algorithm can be used to simulate a number of zero-temperature Potts antiferromagnets for which the Wang–Swendsen–Kotecký cluster algorithm is non-ergodic, including the 3-state model on the kagome lattice and the 4-state model on the triangular lattice. We then use this worm algorithm to perform a systematic study of the honeycomb-lattice loop model as a function of n ⩽ 2 , on the critical line and in the densely-packed and fully-packed phases. By comparing our numerical results with Coulomb gas theory, we identify a set of exact expressions for scaling exponents governing some fundamental geometric and dynamic observables. In particular, we show that for all n ⩽ 2 , the scaling of a certain return time in the worm dynamics is governed by the magnetic dimension of the loop model, thus providing a concrete dynamical interpretation of this exponent. The case n > 2 is also considered, and we confirm the existence of a phase transition in the 3-state Potts universality class that was recently observed via numerical transfer matrix calculations.

Applying the archetype approach to the database of a biobank information management system

Purpose The purpose of this study is to investigate the feasibility of applying the openEHR archetype approach to modelling the data in the database of an existing proprietary biobank information management system. A biobank information management system stores the clinical/phenotypic data of the sample donor and sample related information. The clinical/phenotypic data is potentially sourced from the donor's electronic health record (EHR). The study evaluates the reuse of openEHR archetypes that have been developed for the creation of an interoperable EHR in the context of biobanking, and proposes a new set of archetypes specifically for biobanks. The ultimate goal of the research is the development of an interoperable electronic biomedical research record (eBMRR) to support biomedical knowledge discovery. Methods The database of the prostate cancer biobank of the Irish Prostate Cancer Research Consortium (PCRC), which supports the identification of novel biomarkers for prostate cancer, was taken as the basis for the modelling effort. First the database schema of the biobank was analyzed and reorganized into archetype-friendly concepts. Then, archetype repositories were searched for matching archetypes. Some existing archetypes were reused without change, some were modified or specialized, and new archetypes were developed where needed. The fields of the biobank database schema were then mapped to the elements in the archetypes. Finally, the archetypes were arranged into templates specifically to meet the requirements of the PCRC biobank. Results A set of 47 archetypes was found to cover all the concepts used in the biobank. Of these, 29 (62%) were reused without change, 6 were modified and/or extended, 1 was specialized, and 11 were newly defined. These archetypes were arranged into 8 templates specifically required for this biobank. A number of issues were encountered in this research. Some arose from the immaturity of the archetype approach, such as immature modelling support tools, difficulties in defining high-quality archetypes and the problem of overlapping archetypes. In addition, the identification of suitable existing archetypes was time-consuming and many semantic conflicts were encountered during the process of mapping the PCRC BIMS database to existing archetypes. These include differences in the granularity of documentation, in metadata-level versus data-level modelling, in terminologies and vocabularies used, and in the amount of structure imposed on the information to be recorded. Furthermore, the current way of modelling the sample entity was found to be cumbersome in the sample-centric activity of biobanking. Conclusions The archetype approach is a promising approach to create a shareable eBMRR based on the study participant/donor for biobanks. Many archetypes originally developed for the EHR domain can be reused to model the clinical/phenotypic and sample information in the biobank context, which validates the genericity of these archetypes and their potential for reuse in the context of biomedical research. However, finding suitable archetypes in the repositories and establishing an exact mapping between the fields in the PCRC BIMS database and the elements of existing archetypes that have been designed for clinical practice can be challenging and time-consuming and involves resolving many common system integration conflicts. These may be attributable to differences in the requirements for information documentation between clinical practice and biobanking. This research also recognized the need for better support tools, modelling guidelines and best practice rules and reconfirmed the need for better domain knowledge governance. Furthermore, the authors propose that the establishment of an independent sample record with the sample as record subject should be investigated. The research presented in this paper is limited by the fact that the new archetypes developed during this research are based on a single biobank instance. These new archetypes may not be complete, representing only those subsets of items required by this particular database. Nevertheless, this exercise exposes some of the gaps that exist in the archetype modelling landscape and highlights the concepts that need to be modelled with archetypes to enable the development of an eBMRR.

Haldane Phases and Ferrimagnetic Phases with Spontaneous Translational Symmetry Breakdown in Distorted Mixed Diamond Chains with Spins 1 and 1/2

The ground states of two types of distorted mixed diamond chains with spins 1 and 1/2 are investigated using exact diagonalization, DMRG, and mapping onto low-energy effective models. In the undistorted case, the ground state consists of an array of independent spin-1 clusters separated by singlet dimers. The lattice distortion induces an effective interaction between cluster spins. When this effective interaction is antiferromagnetic, several Haldane phases appear with or without spontaneous translational symmetry breakdown (STSB). The transition between the Haldane phase without STSB and that with ( n +1)-fold STSB ( n =1, 2, and 3) belongs to the same universality class as the ( n +1)-clock model. In contrast, when the effective interaction is ferromagnetic, the quantized and partial ferrimagnetic phases appear with or without STSB. An effective low-energy theory for the partial ferrimagnetic phase is presented.