Exact Correspondence Research Articles

Combinatorial properties of symmetric polynomials from integrable vertex models in finite lattice

We introduce and study several combinatorial properties of a class of symmetric polynomials from the point of view of integrable vertex models in a finite lattice. We introduce the L-operator related to the Uq(sl2) R-matrix and construct the wavefunctions and their duals. We prove the exact correspondence between the wavefunctions and symmetric polynomials which is a quantum group deformation of the Grothendieck polynomials. This is proved by combining the matrix product method and an analysis on the domain wall boundary partition functions. As applications of the correspondence between the wavefunctions and symmetric polynomials, we derive several properties of the symmetric polynomials such as the determinant pairing formulas and the branching formulas by analyzing the domain wall boundary partition functions and the matrix elements of the B-operators.

Classical spin spirals in frustrated magnets from free-fermion band topology

The formation of coplanar spin spirals is a common motif in the magnetic ordering of many frustrated magnets. For classical antiferromagnets, geometric frustration can lead to a massively degenerate ground state manifold of spirals whose propagation vectors can be described, depending on the lattice geometry, by points (triangular), lines (fcc), surfaces (frustrated diamond) or completely flat bands (pyrochlore). Here we demonstrate an exact mathematical correspondence of these spiral manifolds of classical antiferromagnets with the Fermi surfaces of free-fermion band structures. We provide an explicit lattice construction relating the frustrated spin model to a corresponding free-fermion tight-binding model. Examples of this correspondence relate the 120$^\circ$ order of the triangular lattice antiferromagnet to the Dirac nodal structure of the honeycomb tight-binding model or the spiral line manifold of the fcc antiferromagnet to the Dirac nodal line of the diamond tight-binding model. We discuss implications of topological band structures in the fermionic system to the corresponding classical spin system.

Building community-specific standards and vocabularies: prospects and challenges for linking to the broader community - The SINP Case

Biodiversity data may come from myriad sources. From data capture in the field through digitization processes, each source may choose distinctive ways to capture data. When it comes to sharing data more broadly at national or regional levels, it is imperative that data is presented in ways that encourage understanding both by humans and machines, allowing aggregation and serving the data back to the community. This implies two levels of agreement, one at a structural level, where data is organized under certain terms or fields, and another related to the actual values contained in such fields. Since its ratification in 2009, the Darwin Core standard Wieczorek et al. (2012) has been increasingly used across the community to respond to the first need, providing a relatively simple means to organize shared data. Nonetheless, despite its broad acceptance, efforts to develop different standards to answer the same problems are not uncommon among some stakeholders, and may introduce yet another issue: reconciling the data shared under different standards. The second level of agreement, at the value level, constitutes a much more complex issue, partly given the nature of biodiversity data and partly due to social constraints. Many potential, partial solutions involving the development of dictionaries and controlled vocabularies are found scattered across the community. As the lack of homogeneity renders data less discoverable (Zermoglio et al. 2016) and therefore less usable for research and decision making, there exists a growing need for unifying such efforts. As part of the Biodiversity Information System on Nature and Landscapes (SINP), the French National Museum of Natural History was appointed to develop biodiversity data exchange standards, with the goal of sharing French marine and terrestrial data at the national level, meeting national and European requirements (e.g., the European INSPIRE Directive European Commission 2017). The French data providers include a broad range of people with diverse backgrounds. While some stakeholders can provide data under very specific constraints and formats, others lack the capabilities or resources to do so. The variability in the data provided therefore extends through both the structure and the value levels. In order to integrate the data in a coherent national system, a dedicated working group was assembled, mobilizing a range of biodiversity stakeholders and experts. Existing standards were compared, existing vocabularies gathered and compiled for review by experts, and then presented to the working group. As a result, a set of terms and associated controlled vocabularies was established. Finally, the set was released to the public to test and amended as needed. The results of the French initiative proved useful to compile and share data at the national level, bringing together data providers that otherwise would have been excluded. However, at a global scale, it faces some challenges that still need to be fully addressed. For instance, the standards created do not have an exact correspondence with Darwin Core, and so a complex mapping is required in order to integrate the data with that of the rest of the community. A serious mapping effort is being carried out as the national standards progress and has already rendered good results (Jomier and Pamerlon 2016). Regardless of the problems that remain to be solved, some lessons can be learnt from this effort. Getting actively involved in the broader, global community can help identify available tools, resources and expertise, and avoid repeated efforts that can be costly and time-consuming. Furthermore, re-using elements that already have been proven to work, prevents the need for reconciliations and makes data integration easier. With the ultimate goal of making biodiversity data readily available, these lessons should be kept in mind for future initiatives.

Exact correspondence between walk in nucleotide and protein sequence spaces.

In the course of evolution, genes traverse the nucleotide sequence space, which translates to a trajectory of changes in the protein sequence in protein sequence space. The correspondence between regions of the nucleotide and protein sequence spaces is understood in general but not in detail. One of the unexplored questions is how many sequences a protein can reach with a certain number of nucleotide substitutions in its gene sequence. Here I propose an algorithm to calculate the volume of protein sequence space accessible to a given protein sequence as a function of the number of nucleotide substitutions made in the protein-coding sequence. The algorithm utilizes the power of the dynamic programming approach, and makes all calculations within a couple of seconds on a desktop computer. I apply the algorithm to green fluorescence protein, and get the number of sequences four times higher than estimated before. However, taking into account the astronomically huge size of the protein sequence space, the previous estimate can be considered as acceptable as an order of magnitude estimation. The proposed algorithm has practical applications in the study of evolutionary trajectories in sequence space.

Links between causal effects and causal association for surrogacy evaluation in a gaussian setting

Two paradigms for the evaluation of surrogate markers in randomized clinical trials have been proposed: the causal effects paradigm and the causal association paradigm. Each of these paradigms rely on assumptions that must be made to proceed with estimation and to validate a candidate surrogate marker (S) for the true outcome of interest (T). We consider the setting in which S and T are Gaussian and are generated from structural models that include an unobserved confounder. Under the assumed structural models, we relate the quantities used to evaluate surrogacy within both the causal effects and causal association frameworks. We review some of the common assumptions made to aid in estimating these quantities and show that assumptions made within one framework can imply strong assumptions within the alternative framework. We demonstrate that there is a similarity, but not exact correspondence between the quantities used to evaluate surrogacy within each framework, and show that the conditions for identifiability of the surrogacy parameters are different from the conditions, which lead to a correspondence of these quantities.

The Elucidatory Uses of Wittgenstein’s Scale of Nonsense in Lewis Carroll’s Wonderland Narratives

The world of Carroll’s Wonderland narratives, in which language tests its own limits, overlaps with Wittgenstein’s world of counterexample, and such convergence becomes most overt in Wittgenstein’s example of a nonsensical scale in his Philosophical Investigations (§142). Wittgenstein does not find much use for such a scale, but in this paper it is claimed that Alice’s (mis)adventures with nonsensical language in Wonderland both problematize and provide fresh insights into the use of language in our actual world. Several passages in the Alice books are analysed in order to show how the curious uses of nonsensical language function to negate any theory of the ordinary use of language that is based on the assumption that there is an exact correspondence between words and meanings. This article represents an effort to understand the ways in which nonsensical narratives can throw light on the way we use language in the world. The extraordinary uses of language in narratives like Alice’s Adventures in Wonderland provide a challenge to those theories of language that do not sufficiently take into account the ambiguous and imprecise nature of our ordinary use of language.

Bipartite entanglement in fermion systems

We discuss the relation between fermion entanglement and bipartite entanglement. We first show that an exact correspondence between them arises when the states are constrained to have a definite local number parity. Moreover, for arbitrary states in a four dimensional single-particle Hilbert space, the fermion entanglement is shown to measure the entanglement between two distinguishable qubits defined by a suitable partition of this space. Such entanglement can be used as a resource for tasks like quantum teleportation. On the other hand, this fermionic entanglement provides a lower bound to the entanglement of an arbitrary bipartition although in this case the local states involved will generally have different number parities. Finally the fermionic implementation of the teleportation and superdense coding protocols based on qubits with odd and even number parity is discussed, together with the role of the previous types of entanglement.

Spin-orbit coupling and transport in strongly correlated two-dimensional systems

Measuring the magnetoresistance (MR) of ultraclean GaAs two-dimensional holes for a large ${r}_{s}$ range of 20--50, two striking behaviors in relation to the spin-orbit coupling (SOC) emerge in response to strong electron-electron interaction. First, in exact correspondence to the zero-field metal-to-insulator transition (MIT), the sign of the MR switches from being positive in the metallic regime to being negative in the insulating regime when the carrier density crosses the critical density ${p}_{c}$ of MIT (${r}_{s}\ensuremath{\sim}39$). Second, as the SOC-driven correction $\mathrm{\ensuremath{\Delta}}\ensuremath{\rho}$ to the MR decreases with reducing carrier density (or the in-plane wave vector), it exhibits an upturn in the close proximity just above ${p}_{c}$ where ${r}_{s}$ is beyond 30, indicating a substantially enhanced SOC effect. This peculiar behavior echoes with a trend of delocalization long suspected for the SOC-interaction interplay. Meanwhile, for $pl{p}_{c}$ or ${r}_{s}g40$, in contrast to the common belief that a magnet field enhances Wigner crystallization, the negative MR is likely linked to enhanced interaction.

Resolvent expansions for the Schrödinger operator on the discrete half-line

Simplified models of transport in mesoscopic systems are often based on a small sample connected to a finite number of leads. The leads are often modelled using the Laplacian on the discrete half-line ℕ. Detailed studies of the transport near thresholds require detailed information on the resolvent of the Laplacian on the discrete half-line. This paper presents a complete study of threshold resonance states and resolvent expansions at a threshold for the Schrodinger operator on the discrete half-line ℕ with a general boundary condition. A precise description of the expansion coefficients reveals their exact correspondence to the generalized eigenspaces, or the threshold types. The presentation of the paper is adapted from that of Ito-Jensen [Rev. Math. Phys. 27, 1550002 (2015)], implementing the expansion scheme of Jensen-Nenciu [Rev. Math. Phys. 13(6), 717–754 (2001) and Rev. Math. Phys. 16(5), 675–677 (2004)] in its full generality.

Parallel Algorithms for Effective Correspondence Problem Solution in Computer Vision

We propose new parallel algorithms for correspondence problem solution in computer vision. We develop an industrial photogrammetric system that uses artificial retroreflective targets that are photometrically identical. Therefore, we cannot use traditional descriptor-based point matching methods, such as SIFT, SURF etc. Instead, we use epipolar geometry constraints for finding potential point correspondences between images. In this paper, we propose new effective graph-based algorithms for finding point correspondences across the whole set of images (in contrast to traditional methods that use 2-4 images for point matching). We give an exact problem solution via superclique and show that this approach cannot be used for real tasks due to computational complexity. We propose a new effective parallel algorithm that builds the graph from epipolar constraints, as well as a new fast parallel heuristic clique finding algorithm. We use an iterative scheme (with backprojection of the points, filtering of outliers and bundle adjustment of point coordinates and cameras’ positions) to obtain an exact correspondence problem solution. This scheme allows using heuristic clique finding algorithm at each iteration. The proposed architecture of the system offers a significant advantage in time. Newly proposed algorithms have been implemented in code; their performance has been estimated. We also investigate their impact on the effectiveness of the photogrammetric system that is currently under development and experimentally prove algorithms’ efficiency.

Correlation analysis of statistical facies fault models

This paper addresses seismic imaging of fault zones and analysis of the seismic data with the use of the fault facies model developed at Uni Research CIPR. Simulated and ideal seismic images were produced to generate a statistical ensemble of realizations of this model. The comparative analysis presented in this paper is focused on the statistical characteristics of the initial geological model and its seismic images. This paper analyzes cross-correlations between seismic images and ideal seismic images. The method proposed makes it possible to establish an exact correspondence between the initial fault facies models and the seismic images of these models.

Long-Range S-Wave Interactions in Bose-Einstein Condensates: An Exact Correspondence Between Truncated Free Energy and Dynamics

We consider the Gross-Pitaevskii(GP) model of a Bose-Einstein Condensate(BEC) with non-local s-wave interactions. The non-locality is represented by corrections to the local GP equation. Due to such corrections to the GP equation, there arise corrections to the free energy functional as well. We present here a proof of the exact correspondence between the free energy and the dynamics for typical terms appearing while considering corrections to the GP equation at any order. This non-trivial correspondence can be used to study BECs perturbatively while going beyond the Fermi pseudopotential.

Quantum Hall effect on odd spheres

We solve the Landau problem for charged particles on odd-dimensional spheres $S^{2k-1}$ in the background of constant SO(2k-1) gauge fields carrying the irreducible representation $\left ( \frac{I}{2}, \frac{I}{2}, \cdots, \frac{I}{2} \right)$. We determine the spectrum of the Hamiltonian, the degeneracy of the Landau levels and give the eigenstates in terms of the Wigner ${\cal D}$-functions, and for odd values of $I$ the explicit local form of the wave functions in the lowest Landau level (LLL). Spectrum of the Dirac operator on $S^{2k-1}$ in the same gauge field background together with its degeneracies is also determined and in particular the number of zero modes is found. We show how the essential differential geometric structure of the Landau problem on the equatorial $S^{2k-2}$ is captured by constructing the relevant projective modules. For the Landau problem on $S^5$, we demonstrate an exact correspondence between the union of Hilbert spaces of LLL's with $I$ ranging from $0$ to $I_{max} = 2K$ or $I_{max} = 2K+1$ to the Hilbert spaces of the fuzzy ${\mathbb C}P^3$ or that of winding number $\pm1$ line bundles over ${\mathbb C}P^3$ at level $K$, respectively.

Voltage Stabilization in Microgrids via Quadratic Droop Control

We consider the problem of voltage stability and reactive power balancing in islanded small-scale electrical networks outfitted with DC/AC inverters ("microgrids"). A droop-like voltage feedback controller is proposed which is quadratic in the local voltage magnitude, allowing for the application of circuit-theoretic analysis techniques to the closed-loop system. The operating points of the closed-loop microgrid are in exact correspondence with the solutions of a reduced power flow equation, and we provide explicit solutions and small-signal stability analyses under several static and dynamic load models. Controller optimality is characterized as follows: we show a one-to-one correspondence between the high-voltage equilibrium of the microgrid under quadratic droop control, and the solution of an optimization problem which minimizes a trade-off between reactive power dissipation and voltage deviations. Power sharing performance of the controller is characterized as a function of the controller gains, network topology, and parameters. Perhaps surprisingly, proportional sharing of the total load between inverters is achieved in the low-gain limit, independent of the circuit topology or reactances. All results hold for arbitrary grid topologies, with arbitrary numbers of inverters and loads. Numerical results confirm the robustness of the controller to unmodeled dynamics.

A Maximum a Posteriori Estimation Framework for Robust High Dynamic Range Video Synthesis.

High dynamic range (HDR) image synthesis from multiple low dynamic range exposures continues to be actively researched. The extension to HDR video synthesis is a topic of significant current interest due to potential cost benefits. For HDR video, a stiff practical challenge presents itself in the form of accurate correspondence estimation of objects between video frames. In particular, loss of data resulting from poor exposures and varying intensity makes conventional optical flow methods highly inaccurate. We avoid exact correspondence estimation by proposing a statistical approach via maximum a posterior estimation, and under appropriate statistical assumptions and choice of priors and models, we reduce it to an optimization problem of solving for the foreground and background of the target frame. We obtain the background through rank minimization and estimate the foreground via a novel multiscale adaptive kernel regression technique, which implicitly captures local structure and temporal motion by solving an unconstrained optimization problem. Extensive experimental results on both real and synthetic data sets demonstrate that our algorithm is more capable of delivering high-quality HDR videos than current state-of-the-art methods, under both subjective and objective assessments. Furthermore, a thorough complexity analysis reveals that our algorithm achieves better complexity-performance tradeoff than conventional methods.

The history of mercury pollution near the Spolana chlor-alkali plant (Neratovice, Czech Republic) as recorded by Scots pine tree rings and other bioindicators

We assessed >100years of mercury (Hg) pollution recorded in the tree rings of Scots Pine near a Czech chlor-alkali plant operating since 1941. Hg concentrations in tree rings increased with the launching of plant operations and decreased when Hg emissions decreased in 1975 due to an upgrade in production technology. Similar to traditional bioindicators of pollution such as pine needles, bark and forest floor humus, Hg concentrations in Scots Pine boles decreased with distance from the plant. Mean Hg in pine bole in the 1940s ranged from 32.5μg/kg Hg at a distance of 0.5km from the plant to 5.4μg/kg at a distance of >4.7km, where tree ring Hg was the same as at a reference site, and other bioindicators also suggest that the effect of the plant was no longer discernible. Tree ring Hg concentrations decreased by 8–29μg/kg since the 1940s at all study sites including the reference site. The lack of exact correspondence between changes at the plant and tree ring Hg indicated some smearing of the signal due to lateral translocation of Hg from sapwood to heartwood. Bole Hg concentrations reflected local and regional atmospheric Hg concentrations, and not Hg wet deposition.

Generalization of the ordinary state-based peridynamic model for isotropic linear viscoelasticity

This paper presents a generalization of the original ordinary state-based peridynamic model for isotropic linear viscoelasticity. The viscoelastic material response is represented using the thermodynamically acceptable Prony series approach. It can feature as many Prony terms as required and accounts for viscoelastic spherical and deviatoric components. The model was derived from an equivalence between peridynamic viscoelastic parameters and those appearing in classical continuum mechanics, by equating the free energy densities expressed in both frameworks. The model was simplified to a uni-dimensional expression and implemented to simulate a creep-recovery test. This implementation was finally validated by comparing peridynamic predictions to those predicted from classical continuum mechanics. An exact correspondence between peridynamics and the classical continuum approach was shown when the peridynamic horizon becomes small, meaning peridynamics tends toward classical continuum mechanics. This work provides a clear and direct means to researchers dealing with viscoelastic phenomena to tackle their problem within the peridynamic framework.

Dual wavefunction of the Felderhof model

We study the Felderhof free-fermion six-vertex model, whose wavefunction recently turned out to possess rich combinatorial structure of the Schur polynomials. We investigate the dual version of the wavefunction in this paper, which seems to be a harder object to analyze. We evaluate the dual wavefunction in two ways. First, we give the exact correspondence between the dual wavefunction and the Schur polynomials, for which two proofs are given. Next, we make a microscopic analysis and express the dual wavefunction in terms of strict Gelfand-Tsetlin pattern. As a consequence of these two ways of evaluation of the dual wavefunction, we obtain a dual version of the Tokuyama combinatorial formula for the Schur polynomials. We also give a generalization of the correspondence between the dual wavefunction of the Felderhof model and the factorial Schur polynomials.

Correspondent Functional Topography of the Human Left Inferior Parietal Lobule at Rest and Under Task Revealed Using Resting-State fMRI and Coactivation Based Parcellation.

The human left inferior parietal lobule (LIPL) plays a pivotal role in many cognitive functions and is an important node in the default mode network (DMN). Although many previous studies have proposed different parcellation schemes for the LIPL, the detailed functional organization of the LIPL and the exact correspondence between the DMN and LIPL subregions remain unclear. Mounting evidence indicates that spontaneous fluctuations in the brain are strongly associated with cognitive performance at the behavioral level. However, whether a consistent functional topographic organization of the LIPL during rest and under task can be revealed remains unknown. Here, they used resting-state functional connectivity (RSFC) and task-related coactivation patterns separately to parcellate the LIPL and identified seven subregions. Four subregions were located in the supramarginal gyrus (SMG) and three subregions were located in the angular gyrus (AG). The subregion-specific networks and functional characterization revealed that the four anterior subregions were found to be primarily involved in sensorimotor processing, movement imagination and inhibitory control, audition perception and speech processing, and social cognition, whereas the three posterior subregions were mainly involved in episodic memory, semantic processing, and spatial cognition. The results revealed a detailed functional organization of the LIPL and suggested that the LIPL is a functionally heterogeneous area. In addition, the present study demonstrated that the functional architecture of the LIPL during rest corresponds with that found in task processing. Hum Brain Mapp 38:1659-1675, 2017. © 2017 Wiley Periodicals, Inc.

휴머노이드 로봇의 안전한 차량 주행 전략 및 원격 제어 인터페이스 개발

In a fire disaster in a tunnel, people should be rescued immediately using the information obtained from cameras or sensors. However, in heavy smoke from a fire, people cannot be clearly identified by a mounted CCTV, which is only effective in a clear environment. A thermal camera can be an alternative to this in smoky situations and is capable of detecting people from their emitted thermal energy. On the other hand, the thermal image camera has a smaller field of view than an ordinary camera due to its lens characteristics and temperature error, etc. In order to cover a relatively wide area, panoramic image construction needs to be implemented. In this work, a template-based similarity matching algorithm for constructing the panorama image is proposed and its performance is verified through experiments. This scheme provides guidelines for coping with difficulty in image construction, which requires an exact correspondence search for two images in cases of heavy smoke.