Exact Correspondence Research Articles

Observing shape in spacetime

The notion of "reference frame" is a central theoretical construct for interpreting the physical implications of spacetime diffeomorphism invariance in General Relativity. However, the alternative formulation of classical General Relativity known as Shape Dynamics suggest that a subset of spacetime diffeomorphisms - namely hypersurface deformations - are, in a certain sense, dual to spatial conformal (or Weyl) invariance. Moreover, holographic gauge/gravity dualities suggest that bulk spacetime diffeomorphism invariance can be replaced by the properties of boundary CFTs. How can these new frameworks be compatible with the traditional notion of reference frame so fundamental to our interpretation of General Relativity? In this paper, we address this question by investigating the classical case of maximally symmetric spacetimes with a positive cosmological constant. We find that it is possible to define a notion of "Shape Observer" that represents a conformal reference frame that is dual to the notion of inertial reference frame in spacetime. We then provide a precise dictionary relating the two notions. These Shape Observers are holographic in the sense that they are defined on the asymptotic conformal boundaries of spacetime but know about bulk physics. This leads to a first principles derivation of an exact classical holographic correspondence that can easily be generalized to more complicated situations and may lead to insights regarding the interpretation of the conformal invariance manifest in Shape Dynamics.

Edge-entanglement spectrum correspondence in a nonchiral topological phase and Kramers-Wannier duality

In a system with chiral topological order, there is a remarkable correspondence between the edge and entanglement spectra: the low-energy spectrum of the system in the presence of a physical edge coincides with the lowest part of the entanglement spectrum (ES) across a virtual cut of the system, up to rescaling and shifting. In this paper, we explore whether the edge-ES correspondence extends to nonchiral topological phases. Specifically, we consider the Wen-plaquette model which has Z_2 topological order. The unperturbed model displays an exact correspondence: both the edge and entanglement spectra within each topological sector a (a = 1,...,4) are flat and equally degenerate. Here, we show, through a detailed microscopic calculation, that in the presence of generic local perturbations: (i) the effective degrees of freedom for both the physical edge and the entanglement cut consist of a spin-1/2 chain, with effective Hamiltonians H_edge^a and H_ent.^a, respectively, both of which have a Z_2 symmetry enforced by the bulk topological order; (ii) there is in general no match between their low energy spectra, that is, there is no edge-ES correspondence. However, if supplement the Z_2 topological order with a global symmetry (translational invariance along the edge/cut), i.e. by considering the Wen-plaquette model as a symmetry enriched topological phase (SET), then there is a finite domain in Hamiltonian space in which both H_edge^a and H_ent.^a realize the critical Ising model, whose low-energy effective theory is the c = 1/2 Ising CFT. This is achieved because the presence of the global symmetry implies that both Hamiltonians, in addition to being Z_2 symmetric, are Kramers-Wannier self-dual. Thus, the bulk topological order and the global translational symmetry of the Wen-plaquette model as a SET imply an edge-ES correspondence at least in some finite domain in Hamiltonian space.

Automatic Feature-Based Geometric Fusion of Multiview TomoSAR Point Clouds in Urban Area

Interferometric synthetic aperture radar (InSAR) techniques, such as persistent scatterer interferometry (PSI) or SAR tomography (TomoSAR), deliver three-dimensional (3-D) point clouds of the scatterers' positions together with their motion information relative to a reference point. Due to the SAR side-looking geometry, minimum of two point clouds from cross-heading orbits, i.e., ascending and descending, are required to achieve a complete monitoring over an urban area. However, these two point clouds are usually not coregistered due to their different reference points with unknown 3-D positions. In general, no exact identical points from the same physical object can be found in such two point clouds. This article describes a robust algorithm for fusing such two point clouds of urban areas. The contribution of this paper is finding the theoretically exact point correspondence, which is the end positions of façades, where the two point clouds close. We explicitly define this algorithm as “L-shape detection and matching,” in this paper, because the façades commonly appear as L-shapes in InSAR point cloud. This algorithm introduces a few important features for a reliable result, including point density estimation using adaptive directional window for better façade points detection and L-shape extraction using weighed Hough transform. The algorithm is fully automatic. Its accuracy is evaluated using simulated data. Furthermore, the proposed method is applied on two TomoSAR point clouds over Berlin with ascending and descending geometry. The result is compared with the first PSI point cloud fusion method (S. Gernhardt and R. Bamler, “Deformation monitoring of single buildings using meter-resolution SAR data in PSI,” ISPRS J. Photogramm. Remote Sens., vol. 73, pp. 68-79, 2012.) for urban area. Submeter consistency is achieved.

Let bone and muscle talk together: a study of real and virtual dissection and its implications for femoral musculoskeletal structure of chimpanzees.

Proximal femoral morphology and associated musculature are of special relevance to the understanding of hominoid locomotor systems. Knowledge of bone-muscle correspondence in extant hominoids forms an important comparative basis for inferring structure-function relationships in fossil hominids. However, there is still a lack of consensus on the correspondence between muscle attachment sites and surface morphology of the proximal femoral diaphysis in chimpanzees. Two alternative observations have been proposed regarding the attachment site positions of gluteus maximus (GM) and vastus lateralis (VL) relative to two prominent surface features of the proximal femoral diaphysis, the lateral spiral pilaster and the inferolateral fossa. Here, we use a combination of virtual and physical dissection in an attempt to identify the exact correspondence between muscle attachment sites and osteological features in two specimens of Pan troglodytes verus. The results show that the insertion of the GM tendon is consistently inferolateral to the lateral spiral pilaster, and that a part of the inferolateral fossa consistently forms the attachment site of the VL muscular fibers. While overall musculoskeletal features are similar in the two specimens examined in this study, GM and VL exhibit different degrees of segregation at the level of the inferolateral fossa. One specimen exhibited tendinous GM fibers penetrating the posteromedial part of VL, with both GM and VL inserting at the inferolateral fossa. In the other specimen, GM and VL were separated by a lateral intermuscular septum, which inserted into the inferolateral fossa. Variation of proximal femoral muscle attachments in chimpanzees is thus greater than previously thought. Our results indicate that a conspicuous osteological feature such as the inferolateral fossa does not necessarily correspond to the attachment site of a single muscle, but could serve as a boundary region between two muscles. Caution is thus warranted when interpreting the surface topography of muscle attachment sites and inferring locomotor functions.

Exact Mapping from Singular-Value Spectrum of Fractal Images to Entanglement Spectrum of One-Dimensional Quantum Systems

We examine the snapshot entropy of general fractal images defined by their singular values. Remarkably, the singular values for a large class of fractals are in exact correspondence with the entanglement spectrum of free fermions in one dimension. These fermions allow for a holographic interpretation of the logarithmic scaling of the snapshot entropy, which is in agreement with the Calabrese-Cardy formula. However, the coarse-grained entropy exhibits a linear scaling due to the degeneracy of the spectrum, in contrast with the logarithmic scaling behavior in one-dimensional quantum near-critical systems.

Correspondences between quantum and classical orbits Berry phases and Hannay angles for harmonic oscillator system

On the basis of quantum-classical correspondence for two-dimensional anisotropic oscillator, we study quantum-classical correspondence for two-dimensional rotation and translation harmonic oscillator system from both quantum-classical orbits and geometric phases. Here, the two one-dimensional oscillators refer to a common harmonic oscillator and a rotation and translation harmonic oscillator. In terms of the generalized gauge transformation, we obtain the stationary Lissajous orbits and Hannay's angle. On the other hand, the eigenfunctions and Berry phases are derived analytically with the help of time-dependent gauge transformation. We may draw the conclusion that the nonadiabatic Berry phase in the original gauge is-n times the classical Hannay's angle, here n is the eigenfunction index. As a matter of fact, the quantum geometric phase and the classical Hannay's angle have the same nature according to Berry. Finally, by using the SU(2) coherent superposition of degenerate two-dimensional eigenfunctions for a fixed energy value, we construct the stationary wave functions and show that the spatial distribution of wave-function probability clouds is in excellent accordance with the classical orbits, indicating the exact quantum-classical correspondence. We also demonstrate the quantum-classical correspondences for the geometric phase-angle and the quantum-classical orbits in a unified form.

Reconstructing Sequential Patterns without Knowing Image Correspondences

In this paper, we propose a method for reconstructing 3D sequential patterns from multiple images without knowing exact image correspondences and without calibrating linear camera sensitivity parameters on intensity. The sequential pattern is defined as a series of colored 3D points. We assume that the series of the points are obtained in multiple images, but the correspondence of individual points is not known among multiple images. For reconstructing sequential patterns, we consider a camera projection model which combines geometric and photometric information of objects. Furthermore, we consider camera projections in the frequency space. By considering the multi-view relationship on the new projection model, we show that the 3D sequential patterns can be reconstructed without knowing exact correspondence of individual image points in the sequential patterns; moreover, the recovered 3D patterns do not suffer from changes in linear camera sensitivity parameters. The efficiency of the proposed method is tested using real images.

Impact vaporization as a possible source of Mercury’s calcium exosphere

Mercury’s calcium exosphere varies in a periodic way with that planet’s true anomaly. We show that this pattern can be explained by impact vaporization from interplanetary dust with variations being due to Mercury’s radial and vertical excursions through an interplanetary dust disk having an inclination within 5 degrees of the plane of Mercury’s orbit. Both a highly inclined dust disk and a two-disk model (where the two disks have a mutual inclination) fail to reproduce the observed variation in calcium exospheric abundance with Mercury true anomaly angle. However, an additional source of impacting dust beyond the nominal dust disk is required near Mercury’s true anomaly (ν) 25°±5°. This is close to but not coincident with Mercury’s true anomaly (ν=45°) when it crosses Comet 2P/Encke’s present day orbital plane. Interestingly, the Taurid meteor storms at Earth, which are also due to Comet Encke, are observed to occur when Earth’s true anomaly is ±20 or so degrees before and after the position where Earth and Encke orbital planes cross. The lack of exact correspondence with the present day orbit of Encke may indicate the width of the potential stream along Mercury’s orbit or a previous cometary orbit. The extreme energy of the escaping calcium, estimated to have a temperature >50,000K if the source is thermal, cannot be due to the impact process itself but must be imparted by an additional mechanism such as dissociation of a calcium-bearing molecule or ionization followed by recombination.

Fivebranes, dualities and non-geometry

In this contribution we would like to review and clarify the relation between a large class of extended objects in string theory and a set of generalized fluxes appearing in string compactifications. The main focus of this work is on the interplay between branes and dualities, which leads to novel states which are important for string physics. The main result that we would like to describe is the coupling of these new branes to the background fields of string theory and the exact correspondence between them and generalized stringy fluxes.

Tucidide, Pausania e l’iscrizione nel portico degli Ateniesi a Delfi

Summary Pausanias saw in the Athenian Stoa at Delphi an inscription, different from the one still visible on the Stoa’s stylobate, which he rightly connected with Phormio’s victories in the Corinthian Gulf in 429 BC (10, 11, 6). The not exact correspondence between its contents reported by Pausanias and some details of the narrative in Thucydides enables us to reconstruct with a greater precision the movements of Phormio after the two battles. On the other hand, the quite unnoticed exact correspondence between the Spartan allies listed in the inscription as reported by Pausanias and the catalogue of Spartan naval allies in Thuc. 2, 9, 3, as well as the absence from these lists of Anactorion, although her ships had joined the Peloponnesian fleet at least in the earliest phases of that campaign, give grounds for the suggestion that Thucydides’ catalogue mirrors the make-up of the Peloponnesian fleet that actually fought in 429 and that just the inscription seen by Pausanias may have been (one of) his source(s).

Classical irregular block, N $$ \mathcal{N} $$ = 2 pure gauge theory and Mathieu equation

Combining the semiclassical/Nekrasov-Shatashvili limit of the AGT conjecture and the Bethe/gauge correspondence results in a triple correspondence which identifies classical conformal blocks with twisted superpotentials and then with Yang-Yang functions. In this paper the triple correspondence is studied in the simplest, yet not completely understood case of pure SU(2) super-Yang-Mills gauge theory. A missing element of that correspondence is identified with the classical irregular block. Explicit tests provide a convincing evidence that such a function exists. In particular, it has been shown that the classical irregular block can be recovered from classical blocks on the torus and sphere in suitably defined decoupling limits of classical external conformal weights. These limits are "classical analogues" of known decoupling limits for corresponding quantum blocks. An exact correspondence between the classical irregular block and the SU(2) gauge theory twisted superpotential has been obtained as a result of another consistency check. The latter determines the spectrum of the 2-particle periodic Toda (sin-Gordon) Hamiltonian in accord with the Bethe/gauge correspondence. An analogue of this statement is found entirely within 2d CFT. Namely, considering the classical limit of the null vector decoupling equation for the degenerate irregular block a celebrated Mathieu's equation is obtained with an eigenvalue determined by the classical irregular block. As it has been checked this result reproduces a well known weak coupling expansion of Mathieu's eigenvalue. Finally, yet another new formulae for Mathieu's eigenvalue relating the latter to a solution of certain Bethe-like equation are found.

The Primary Substance in Plotinus’ Metaphysics: A Little-Known Concept

This article addresses primary and universal ousia, the first level of the intelligible, in Plotinus’ metaphysics. In Treatise 43 (6.2), Plotinus argues that the five ‘great kinds’ of the Sophist constitute its exclusive ‘completives’ (τὰ συµπληρωτικὰ τῆς οὐσίας); species only appear later within the intelligible realm, at the level of particular ousiai. The relationship between universal Intellect and particular intellects therefore finds an exact correspondence in the connection between primary ousia and particular ousiai within the intelligible realm. Plotinus’ innovative ontology thus integrates the heritage of the Sophist while breaking with the Aristotelian model connecting genus and species.

An Exact Correspondence of Linear Problems and Randomizing Linear Algorithms

A linear problem is completely solved by a randomizing linear algorithm if the set of data-solution pairs of the problem equals the set of input–output pairs of the algorithm over all randomizations. Linear problems are based on the predicate language over ordered fields. This class contains, for example, all linear programs, all bounded variable integer programs, all satisfiability problems in sentential logic, and models of conflict. Randomizing linear algorithms are based on a tree, arithmetic, comparisons, and random selections, over ordered fields, and with a restriction on certain operations. We show that the correspondence “completely solved by” is one-to-one and onto from equivalences of linear problems to equivalences of randomizing linear algorithms. †1947–2012.

Shh-proteoglycan interactions regulate maturation of olfactory glomerular circuitry.

The olfactory system relies on precise circuitry connecting olfactory sensory neurons (OSNs) and appropriate relay and processing neurons of the olfactory bulb (OB). In mammals, the exact correspondence between specific olfactory receptor types and individual glomeruli enables a spatially precise map of glomerular activation that corresponds to distinct odors. However, the mechanisms that govern the establishment and maintenance of the glomerular circuitry are largely unknown. Here we show that high levels of Sonic Hedgehog (Shh) signaling at multiple sites enable refinement and maintenance of olfactory glomerular circuitry. Mice expressing a mutant version of Shh (Shh(Ala/Ala)), with impaired binding to proteoglycan co-receptors, exhibit disproportionately small olfactory bulbs containing fewer glomeruli. Notably, in mutant animals the correspondence between individual glomeruli and specific olfactory receptors is lost, as olfactory sensory neurons expressing different olfactory receptors converge on the same glomeruli. These deficits arise at late stages in post-natal development and continue into adulthood, indicating impaired pruning of erroneous connections within the olfactory bulb. In addition, mature Shh(Ala/Ala) mice exhibit decreased proliferation in the subventricular zone (SVZ), with particular reduction in neurogenesis of calbindin-expressing periglomerular cells. Thus, Shh interactions with proteoglycan co-receptors function at multiple locations to regulate neurogenesis and precise olfactory connectivity, thereby promoting functional neuronal circuitry.

A device to achieve low Reynolds numbers in an open surface water channel

When investigating flow structures, and espe- cially flow transitions, research projects often seek to increase insight using complementary numerical and physical experiments. Obtaining exact Reynolds number correspondence can frequently be difficult in experiments, particularly when relatively low values are required. Often, available test facilities were designed and optimised for a specific velocity range, meaning they have restrictions on the minimum flow velocity. This study describes a device to reduce the flow velocity locally in an open surface water channel. The underlying idea is to divert a controlled fraction of the incoming flow from the working section by increasing the pressure there, resulting in reduced velocity. This idea is realised using a ‘sub-channel’ that can be inserted into the main test chamber, with a variable porosity perforated screen at its downstream end. This study assesses and optimises the flow quality inside this structure, such as usable test section length, uniformity of the velocity profiles and turbulence intensity. The results demonstrate that the device creates high quality low Reynolds number flows, which is exemplified with the canonical circular cylinder in cross-flow.

Genetic and molecular principles for the selection of Pseudomonas and Staphylococcus therapeutic bacteriophages

The content of empirically selected bacteriophage mixtures, produced by Microgen for the prevention and treatment of staphylococcal and pseudomonade infections, was investigated by negative stain electron microscopy. The main population of phages was shown to belong to the groups suitable for therapeutic purposes based on bioinformatics analysis of known genomes of Pseudomonas and Staphylococcus phages. However, the phage morphology studies did not always reveal the exact correspondence of the phage to the exact group. Therefore, we suggest group genotyping of the therapeutic bacteriophages on thebasis of genetic conservative locus.

Automatic registration of vestibular systems with exact landmark correspondence

Shape registration has a wide range of applications in geometric modeling, medical imaging, and computer vision. This paper focuses on the registration of the genus-3 vestibular systems and studies the geometric differences between the normal and Adolescent Idiopathic Scoliosis (AIS) groups. The non-trivial topology of the VS poses great technical challenges to the geometric analysis. To tackle these challenges, we present an effective and practical solution to register the vestibular systems. We first extract six geodesic landmarks for the VS, which are stable, intrinsic, and insensitive to the VS’s resolution and tessellation. Moreover, they are highly consistent regardless of the AIS and normal groups. The detected geodesic landmarks partition the VS into three patches, a topological annulus and two topological disks. For each pair of patches of the AIS subject and the control, we compute a bijective map using the holomorphic 1-form and harmonic map techniques. With a carefully designed boundary condition, the three individual maps can be glued in a seamless manner so that the resulting registration is a homeomorphism with exact landmark matching. Our method is robust, automatic and efficient. It takes only a few seconds on a low-end PC, which significantly outperforms the non-rigid ICP algorithm. We conducted a student’s t-test on the test data. Computational results show that using the mean curvature measure EH, our method can distinguish the AIS subjects and the normal subjects.

Spin torques and charge transport on the surface of topological insulator

We study various aspects of interplay between two-dimensional helical electrons, realized on the surface of a three-dimensional topological insulator, and the magnetization of a ferromagnet coupled to them. The magnetization is assumed to be perpendicular to the surface, with small transverse fluctuations $\mathbit{u}$. In the first part of this paper, we calculate spin torques that the helical electrons exert on the magnetization. Up to first orders with respect to $\mathbit{u}$, space/time derivative and electric current, we have determined all torques, which include Gilbert damping, spin renormalization, current-induced spin-orbit torques, and gradient corrections to them. Thanks to the identity between the velocity and spin in this model, these torques have exact interpretation in terms of transport phenomena, namely, diagonal conductivity, (anomalous) Hall conductivity, and corrections to them due to ordinary Hall effect on top of the anomalous one. These torque (and transport) coefficients are studied in detail with particular attention to the effects of vertex corrections and type of impurities (normal and magnetic). It is shown rigorously that the conventional current-induced torques, namely, spin-transfer torque and the so-called $\ensuremath{\beta}$ term, are absent. An electromotive force generated by spin dynamics, which is the inverse to the current-induced spin-orbit torque, is also studied. In the second part, we study the feedback effects arising as combinations of current-induced spin-orbit torques and spin-dynamics-induced electromotive force. It is demonstrated that the Gilbert damping process in this system is completely understood as a feedback effect. Another feedback effect, which may be called ``magnon-drag electrical conductivity,'' is shown to violate the exact correspondence between spin-torque and transport phenomena demonstrated in the first part.

Monte Carlo Simulation of Geminate Pair Recombination Dynamics in Organic Photovoltaic Devices: Multi-Exponential, Field-Dependent Kinetics and Its Interpretation

Monte Carlo simulations are used to examine charge-transfer (CT) state recombination dynamics considering the effects of energetic disorder and bulk heterojunction morphology. Strongly biexponential recombination kinetics were observed, in agreement with spectroscopy. Data over a range of electric fields 106 ≤ F ≤ 108 V m–1 suggest that the slow component of recombination is due to energetic and spatial trapping of charges, as increasing the field reduces the magnitude of the slow decay. This behavior could not be described using a simple Onsager–Braun type model; hence, an alternative kinetic framework including an intermediate “quasi-free” state between the CT state and free charges is proposed and subsequently shown to fit the MC data very well. The predictive capability of the modified model was then tested by repeating MC simulations with an altered recombination rate. It is shown that more than just the recombination rate had to be changed in the modified kinetic model to retrieve good agreement with MC simulations. This suggests that the derived rates from the modified kinetic model do not have exact correspondence with physical processes in organic photovoltaic blends. We attribute the difficulty in fitting kinetic models to CT recombination data to the dispersive nature of hopping transport.

Audio Search Based on Keyword Spotting in Arabic Language

Keyword spotting is an important application of speech recognition. This research introduces a keyword spotting approach to perform audio searching of uttered words in Arabic speech. The matching process depends on the utterance nucleus which is insensitive to its context. For spotting the targeted utterances, the matched nuclei are expanded to cover the whole utterances. Applying this approach to Quran and standard Arabic has promising results. To improve this spotting approach, it is combined with a text search in case of the existence of a transcript. This can be applied on Quran as there is exact correspondence between the audio and text files of each verse. The developed approach starts by text search to identify the verses that include the target utterance(s). For each allocated verse, the occurrence(s) of the target utterance is determined. The targeted utterance (the reference) is manually segmented from an allocated verse. Then Keyword spotting is performed for the extracted reference to the corresponding audio file. The accuracy of the spotted utterances achieved 97%. The experiments showed that the use of the combined text and audio search has reduced the search time by 90% when compared with audio search only tested on the same content. The developed approach has been applied to non transcribed audio files (preaches and News) for searching chosen utterances. The results are promising. The accuracy of spotting was around 84% in case of preaches and 88% in case of the news.