Spurious Structures Research Articles

SPHERE/SHINE reveals concentric rings in the debris disk of HIP 73145

The debris disk of HIP73145 has been detected in scattered light in the near-IR, and at far-IR wavelengths before, but no substructure has been seen so far. Detection of such substructures in combination with detailed modeling can hint at the presence of perturbing planetary bodies, or reveal other mechanisms acting to replenish gas and dust reservoirs and forming structures such as spirals or rings. We obtained multiwavelength images with SPHERE in the near-IR in the H2 and H3 bands with the IRDIS camera and a 0.95-1.35 micron spectral cube with the IFS. Data were acquired in pupil-tracking mode, thus allowing for angular differential imaging. The SPHERE standard suite of angular differential imaging algorithms was applied. ALMA Band 6 observations complement the SPHERE data. We detect a bright ring of scattered light plus more structures inside, at least one of them forming a secondary, concentric ring with the first. This is the first detection of this disk in total-intensity scattered light. A second object is detected in the field at high contrast but concluded to be a background star. Forward modeling yields information on the primary parameters of the disk and confirms that the detected substructures are not due to the data analysis approach, which sometimes leads to spurious structures. We detect a series of concentric rings in the disk around HIP73145. This is one of the rare cases where multiple components are necessary to fit the SED and are also detected in scattered light. The presence of such ring structures somewhat questions the nature of the object as a pure debris disk, but the gas and dust content would presumably offer sufficient explanations for such structures to form.

Nuisance Regression of High-Frequency Functional Magnetic Resonance Imaging Data: Denoising Can Be Noisy.

Recently, emerging studies have demonstrated the existence of brain resting-state spontaneous activity at frequencies higher than the conventional 0.1 Hz. A few groups utilizing accelerated acquisitions have reported persisting signals beyond 1 Hz, which seems too high to be accommodated by the sluggish hemodynamic process underpinning blood oxygen level-dependent contrasts (the upper limit of the canonical model is ∼0.3 Hz). It is thus questionable whether the observed high-frequency (HF) functional connectivity originates from alternative mechanisms (e.g., inflow effects, proton density changes in or near activated neural tissue) or rather is artificially introduced by improper preprocessing operations. In this study, we examined the influence of a common preprocessing step-whole-band linear nuisance regression (WB-LNR)-on resting-state functional connectivity (RSFC) and demonstrated through both simulation and analysis of real dataset that WB-LNR can introduce spurious network structures into the HF bands of functional magnetic resonance imaging (fMRI) signals. Findings of present study call into question whether published observations on HF-RSFC are partly attributable to improper data preprocessing instead of actual neural activities.

Iterative averaging of spectra as a powerful way of suppressing spurious resonances in signal processing

The fast Padé transform (FPT) was applied to magnetic resonance spectroscopic (MRS) time signals encoded in vivo on a 1.5 T scanner from the parietal-temporal brain region of a pediatric patient who had suffered cerebral asphyxia. An iterative averaging procedure was implemented to the 9th iteration, whereby spurious structures on the total shape spectra were effectively suppressed. The parametric and non-parametric hbox {FPT}^{(pm )} were verified to reconstruct equivalent total shape spectra. Via the parametric FPT, the spectral region of interest was chosen to bypass the giant water resonance, automatically generating spectral envelopes without the need for windowing. The dense component spectra were reliably reconstructed by the hbox {FPT}^{(+)}, in the “usual” mode (mixture of absorption and dispersion components) and “ersatz” mode (reconstructed phases set to zero). Via the latter, interference effects were well-visualized for closely-overlapping and hidden resonances. The most stringent test was performed for the complex frequencies and associated complex amplitudes reconstructed by the hbox {FPT}^{(+)}. Exceedingly small variances were obtained for all four Padé-reconstructed parameters per genuine resonance, once convergence was achieved at the 7th to 9th iterated averages. This now fully-validated methodology can generate denoised spectra and accurate spectral parameters for in vivo MRS data encoded within neurodiagnostics. Such a multi-faceted Padé-based strategy for processing the dense spectra of the brain could vitally improve pediatric neurodiagnostics. A wider range of clinical applications becomes within reach, including areas of cancer diagnostics where the added value of in vivo MRS is urgently needed. The broad theoretical underpinnings of incorporating quantum mechanics into signal processing provide the basis for these innovative advances.

Detection of Fragmented Rectangular Enclosures in Very High Resolution Remote Sensing Images

We develop an approach for the detection of ruins of livestock enclosures (LEs) in alpine areas captured by high-resolution remotely sensed images. These structures are usually of approximately rectangular shape and appear in images as faint fragmented contours in complex background. We address this problem by introducing a rectangularity feature that quantifies the degree of alignment of an optimal subset of extracted linear segments with a contour of rectangular shape. The rectangularity feature has high values not only for perfectly regular enclosures but also for ruined ones with distorted angles, fragmented walls, or even a completely missing wall. Furthermore, it has a zero value for spurious structures with less than three sides of a perceivable rectangle. We show how the detection performance can be improved by learning a linear combination of the rectangularity and size features from just a few available representative examples and a large number of negatives. Our approach allowed detection of enclosures in the Silvretta Alps that were previously unknown. A comparative performance analysis is provided. Among other features, our comparison includes the state-of-the-art features that were generated by pretrained deep convolutional neural networks (CNNs). The deep CNN features, although learned from a very different type of images, provided the basic ability to capture the visual concept of the LEs. However, our handcrafted rectangularity-size features showed considerably higher performance.

Invariance of molecular charge transport upon changes of extended molecule size and several related issues.

As a sanity test for the theoretical method employed, studies on (steady-state) charge transport through molecular devices usually confine themselves to check whether the method in question satisfies the charge conservation. Another important test of the theory’s correctness is to check that the computed current does not depend on the choice of the central region (also referred to as the “extended molecule”). This work addresses this issue and demonstrates that the relevant transport and transport-related properties are indeed invariant upon changing the size of the extended molecule, when the embedded molecule can be described within a general single-particle picture (namely, a second-quantized Hamiltonian bilinear in the creation and annihilation operators). It is also demonstrates that the invariance of nonequilibrium properties is exhibited by the exact results but not by those computed approximately within ubiquitous wide- and flat-band limits (WBL and FBL, respectively). To exemplify the limitations of the latter, the phenomenon of negative differential resistance (NDR) is considered. It is shown that the exactly computed current may exhibit a substantial NDR, while the NDR effect is absent or drastically suppressed within the WBL and FBL approximations. The analysis done in conjunction with the WBLs and FBLs reveals why general studies on nonequilibrium properties require a more elaborate theoretical than studies on linear response properties (e.g., ohmic conductance and thermopower) at zero temperature. Furthermore, examples are presented that demonstrate that treating parts of electrodes adjacent to the embedded molecule and the remaining semi-infinite electrodes at different levels of theory (which is exactly what most NEGF-DFT approaches do) is a procedure that yields spurious structures in nonlinear ranges of current–voltage curves.

Methods for a quantitative evaluation of odd-even staggering effects

Odd-even effects, also known as "staggering" effects, are a common feature observed in the yield distributions of fragments produced in different types of nuclear reactions. We review old methods, and we propose new ones, for a quantitative estimation of these effects as a function of proton or neutron number of the reaction products. All methods are compared on the basis of Monte Carlo simulations. We find that some are not well suited for the task, the most reliable ones being those based either on a non-linear fit with a properly oscillating function or on a third (or fourth) finite difference approach. In any case, high statistic is of paramount importance to avoid that spurious structures appear just because of statistical fluctuations in the data and of strong correlations among the yields of neighboring fragments.

A quasi-finite basis for multi-loop Feynman integrals

We present a new method for the decomposition of multi-loop Euclidean Feynman integrals into quasi-finite Feynman integrals. These are defined in shifted dimensions with higher powers of the propagators, make explicit both infrared and ultraviolet divergences, and allow for an immediate and trivial expansion in the parameter of dimensional regularization. Our approach avoids the introduction of spurious structures and thereby leaves integrals particularly accessible to direct analytical integration techniques. Alternatively, the resulting convergent Feynman parameter integrals may be evaluated numerically. Our approach is guided by previous work by the second author but overcomes practical limitations of the original procedure by employing integration by parts reduction.

BLISS: Improved Symbolic Execution by\\ Bounded Lazy Initialization with SAT Support

Lazy Initialization (LI) allows symbolic execution to effectively deal with heap-allocated data structures, thanks to a significant reduction in spurious and redundant symbolic structures. Bounded lazy initialization (BLI) improves on LI by taking advantage of precomputed relational bounds on the interpretation of class fields in order to reduce the number of spurious structures even further. In this paper we present bounded lazy initialization with SAT support (BLISS), a novel technique that refines the search for valid structures during the symbolic execution process. BLISS builds upon BLI, extending it with field bound refinement and satisfiability checks. Field bounds are refined while a symbolic structure is concretized, avoiding cases that, due to the concrete part of the heap and the field bounds, can be deemed redundant. Satisfiability checks on refined symbolic heaps allow us to prune these heaps as soon as they are identified as infeasible, i.e., as soon as it can be confirmed that they cannot be extended to any valid concrete heap. Compared to LI and BLI, BLISS reduces the time required by LI by up to four orders of magnitude for the most complex data structures. Moreover, the number of partially symbolic structures obtained by exploring program paths is reduced by BLISS by over 50 percent, with reductions of over 90 percent in some cases (compared to LI). BLISS uses less memory than LI and BLI, which enables the exploration of states unreachable by previous techniques.

Fully automated liver segmentation from SPIR image series

Accurate liver segmentation is an important component of surgery planning for liver transplantation, which enables patients with liver disease a chance to survive. Spectral pre-saturation inversion recovery (SPIR) image sequences are useful for liver vessel segmentation because vascular structures in the liver are clearly visible in these sequences. Although level-set based segmentation techniques are frequently used in liver segmentation due to their flexibility to adapt to different problems by incorporating prior knowledge, the need to initialize the contours on each slice is a common drawback of such techniques. In this paper, we present a fully automated variational level set approach for liver segmentation from SPIR image sequences. Our approach is designed to be efficient while achieving high accuracy. The efficiency is achieved by (1) automatically defining an initial contour for each slice, and (2) automatically computing weight values of each term in the applied energy functional at each iteration during evolution. Automated detection and exclusion of spurious structures (e.g. cysts and other bright white regions on the skin) in the pre-processing stage increases the accuracy and robustness. We also present a novel approach to reduce computational cost by employing binary regularization of level set function. A signed pressure force function controls the evolution of the active contour. The method was applied to ten data sets. In each image, the performance of the algorithm was measured using the receiver operating characteristics method in terms of accuracy, sensitivity and specificity. The accuracy of the proposed method was 96%. Quantitative analyses of results indicate that the proposed method can accurately, efficiently and consistently segment liver images.

Spatial Optimal Interpolation of Aquarius Sea Surface Salinity: Algorithms and Implementation in the North Atlantic*

Abstract A method is presented for mapping sea surface salinity (SSS) from Aquarius level-2 along-track data in order to improve the utility of the SSS fields at short length [O(150 km)] and time [O(1 week)] scales. The method is based on optimal interpolation (OI) and derives an SSS estimate at a grid point as a weighted sum of nearby satellite observations. The weights are optimized to minimize the estimation error variance. As an initial demonstration, the method is applied to Aquarius data in the North Atlantic. The key element of the method is that it takes into account the so-called long-wavelength errors (by analogy with altimeter applications), referred to here as interbeam and ascending/descending biases, which appear to correlate over long distances along the satellite tracks. The developed technique also includes filtering of along-track SSS data prior to OI and the use of realistic correlation scales of mesoscale SSS anomalies. All these features are shown to result in more accurate SSS maps, free from spurious structures. A trial SSS analysis is produced in the North Atlantic on a uniform grid with 0.25° resolution and a temporal resolution of one week, encompassing the period from September 2011 through August 2013. A brief statistical description, based on the comparison between SSS maps and concurrent in situ data, is used to demonstrate the utility of the OI analysis and the potential of Aquarius SSS products to document salinity structure at ~150-km length and weekly time scales.

SU‐E‐J‐182: A Feasibility Study Evaluating Automatic Identification of Gross Tumor Volume for Breast Cancer Radiotherapy Using Dynamic Contrast‐Enhanced MR Imaging

Purpose:To develop a computerized pharmacokinetic model‐free Gross Tumor Volume (GTV) segmentation method based on dynamic contrastenhanced MRI (DCE‐MRI) data that can improve physician GTV contouring efficiency.Methods:12 patients with biopsy‐proven early stage breast cancer with post‐contrast enhanced DCE‐MRI images were analyzed in this study. A fuzzy c‐means (FCM) clustering‐based method was applied to segment 3D GTV from pre‐operative DCE‐MRI data. A region of interest (ROI) is selected by a clinician/physicist, and the normalized signal evolution curves were calculated by dividing the signal intensity enhancement value at each voxel by the pre‐contrast signal intensity value at the corresponding voxel. Three semi‐quantitative metrics were analyzed based on normalized signal evolution curves: initial Area Under signal evolution Curve (iAUC), Immediate Enhancement Ratio (IER), and Variance of Enhancement Slope (VES). The FCM algorithm wass applied to partition ROI voxels into GTV voxels and non‐GTV voxels by using three analyzed metrics. The partition map for the smaller cluster is then generated and binarized with an automatically calculated threshold. To reduce spurious structures resulting from background, a labeling operation was performed to keep the largest three‐dimensional connected component as the identified target. Basic morphological operations including hole‐filling and spur removal were useutilized to improve the target smoothness. Each segmented GTV was compared to that drawn by experienced radiation oncologists. An agreement index was proposed to quantify the overlap between the GTVs identified using two approaches and a thershold value of 0.4 is regarded as acceptable.Results:The GTVs identified by the proposed method were overlapped with the ones drawn by radiation oncologists in all cases, and in 10 out of 12 cases, the agreement indices were above the threshold of 0.4.Conclusion:The proposed automatic segmentation method was shown to be promising and might be used to improve physician contouring efficiency.J Horton receives grant from NIH and Varian Medical Systems; F‐F Yin receives grant from Varian Medical Systems

Autofocus Imaging: Image reconstruction based on inverse scattering theory

Conventional imaging algorithms assume single scattering and therefore cannot image multiply scattered waves correctly. The multiply scattered events in the data are imaged at incorrect locations resulting in spurious subsurface structures and erroneous interpretation. This drawback of current migration/imaging algorithms is especially problematic for regions where illumination is poor (e.g., subsalt), in which the spurious events can mask true structure. Here we discuss an imaging technique that not only images primaries but also internal multiples accurately. Using only surface-reflection data and direct-arrivals, we generate the up- and down-going wavefields at every image point in the subsurface. An imaging condition is applied to these up- and down-going wavefields directly to generate the image. Because the above algorithm is based on inverse-scattering theory, the reconstructed wavefields are accurate and contain multiply scattered energy in addition to the primary event. As corroborated by our synthetic examples, imaging of these multiply scattered energy helps eliminate spurious reflectors in the image. Other advantages of this imaging algorithm over existing imaging algorithms include more accurate amplitudes, target-oriented imaging, and a highly parallelizable algorithm.

The Milky Way in Johann Bayer's Uranometria, 1603

Johann Bayer's monumental star adas, Uranometria, is commonly regarded as the first modem celestial atlas, and it is one of the most famous. For a whole era, its design and aesthetical appeal set a standard for celestial cartography. But even more than their artistic value, the representations of the starry sky contained in the Uranometria were the first to be regarded as scientifically usable in astrometric and photometric terms, even if its accuracy was qualified by later research.'On its 50 plates, the Uranometria displays every of the 48 Ptolemaic constellations on separate star maps, while the twelve new southern constellations, which had been introduced only years before its publication, are shown on a single planispheric map of the southern celestial polar cap. These plates truly contain a wealth of information, and not least, no fewer than 31 of them show the course of the Milky Way among the stars. However, although this largest of all celestial structures is rather prominently engraved among the constellation figures, no major attempt to establish the data Bayer had used to accurately plot the Milky Way has previously been made, a fact that is surprising, considering the extensive research that has been undertaken to uncover the sources of the celestial data Bayer used to plot the stars in his maps. This paper intends to shed light on Bayer's sources for the Milky Way representations in the Uranometria.Doubtless a celestial structure as large as the Milky Way, and displayed in such large dimensions at is the case in the Uranometria, needed a substantial data basis. A source candidate for such a data basis must therefore contain enough positional details to explain as many of the peculiarities of Bayer's illustrations as possible. As we will show, there is no source, written or pictorial, that completely matches the Uranometria Milky Way, which leaves it not improbable that Bayer gathered the appropriate positional data on the Milky Way path through visual observations made by himself - a hypothesis recently advanced by Jurgen Hamel.2 But even a cursory comparison of Bayer's Milky Way and the real picture leaves Hamel's thesis unsustainable. The southern parts of the Milky Way (declinations south of about -40°) are invisible to observers from locations around 50° latitude, which would mean that Bayer would have had to have obtained the data during a journey to far southern latitudes - but no such journey is known, and is very improbable.3 Thus, at least for the southern Milky Way, Bayer must have used external data sources. On the other hand, systematical observations of the northern Milky Way can be excluded as well, because of the existence of quite a number of obvious differences - not to say errors - from the actual visual appearance. The most striking examples of such spurious structures can be found in the constellations Cassiopeia ('hole'; void in the Milky Way), Cygnus (missing bright parts east of a Cyg), Ophiuchus (missing gap in the western Milky Way branch); and the merging of the two Milky Way branches in 1southern Scorpius / Ara (see Figures 6-8 for representations of these peculiarities). For a complete analysis, however, these deviations need to be analysed and explained.True enough, the exclusion of systematic observations by Bayer does not imply that he made no use whatever of his own observational data. To the contrary, some small-scale Milky Way features may very well have been altered as a result of his own observations, and there are unambiguous indications of corrections of the pathway made only after a first draft of the star map plates had already been engraved. Examples for such corrections can be found in Cassiopeia, Cygnus, and especially Ophiuchus.The General PictureThe Milky Way can be traced as a great circle across the whole celestial sphere as depicted by Bayer, along 31 of the 50 plates of the Uranometria.4 This makes it a rather conspicuous structure, dominating much of the respective constellation illustrations. …

On the Visualization of Thermal Counterflow of He II Past a Circular Cylinder

Thermal counterflow of superfluid 4He is investigated experimentally in the proximity of a 3 mm diameter cylinder by analyzing the motions of micrometer-sized solid particles, focusing especially on the occurrence of macroscopic vortices. The influence of heating an opaque brass cylinder by the light source is studied, as thermal counterflow is generated from its surface, and compared with the case of a transparent plexiglass cylinder of the same size. Additionally, we report our preliminary investigation of vertical counterflow around the transparent cylinder. We find that care should be taken when applying conventional visualization techniques—particle image velocimetry and particle tracking velocimetry—as spurious vortical structures might be identified in quantum flows displaying two-fluid behavior.

Local-feature-based similarity measure for stochastic resonance in visual perception of spatially structured images

For images, stochastic resonance or useful-noise effects have previously been assessed with low-level pixel-based information measures. Such measures are not sensitive to coherent spatial structures usually existing in images. As a result, we show that such measures are not sufficient to properly account for stochastic resonance occurring in visual perception. We introduce higher-level similarity measures, inspired from visual perception, and based on local feature descriptors of scale invariant feature transform (SIFT) type. We demonstrate that such SIFT-based measures allow for an assessment of stochastic resonance that matches the visual perception of images with spatial structures. Constructive action of noise is registered in this way with both additive noise and multiplicative speckle noise. Speckle noise, with its grainy appearance, is particularly prone to introducing spurious spatial structures in images, and the stochastic resonance visually perceived and quantitatively assessed with SIFT-based measures is specially examined in this context.

A recurrence network approach for the analysis of skin blood flow dynamics in response to loading pressure

This paper presents a recurrence network approach for the analysis of skin blood flow dynamics in response to loading pressure. Recurrence is a fundamental property of many dynamical systems, which can be explored in phase spaces constructed from observational time series. A visualization tool of recurrence analysis called recurrence plot (RP) has been proved to be highly effective to detect transitions in the dynamics of the system. However, it was found that delay embedding can produce spurious structures in RPs. Network-based concepts have been applied for the analysis of nonlinear time series recently. We demonstrate that time series with different types of dynamics exhibit distinct global clustering coefficients and distributions of local clustering coefficients and that the global clustering coefficient is robust to the embedding parameters. We applied the approach to study skin blood flow oscillations (BFO) response to loading pressure. The results showed that global clustering coefficients of BFO significantly decreased in response to loading pressure (p<0.01). Moreover, surrogate tests indicated that such a decrease was associated with a loss of nonlinearity of BFO. Our results suggest that the recurrence network approach can practically quantify the nonlinear dynamics of BFO.

Spurious but systematic correlations in functional connectivity MRI networks arise from subject motion

Here, we demonstrate that subject motion produces substantial changes in the timecourses of resting state functional connectivity MRI (rs-fcMRI) data despite compensatory spatial registration and regression of motion estimates from the data. These changes cause systematic but spurious correlation structures throughout the brain. Specifically, many long-distance correlations are decreased by subject motion, whereas many short-distance correlations are increased. These changes in rs-fcMRI correlations do not arise from, nor are they adequately countered by, some common functional connectivity processing steps. Two indices of data quality are proposed, and a simple method to reduce motion-related effects in rs-fcMRI analyses is demonstrated that should be flexibly implementable across a variety of software platforms. We demonstrate how application of this technique impacts our own data, modifying previous conclusions about brain development. These results suggest the need for greater care in dealing with subject motion, and the need to critically revisit previous rs-fcMRI work that may not have adequately controlled for effects of transient subject movements.

Performance validation of phase diversity image reconstruction techniques

We present a performance study of a phase diversity (PD) image reconstruction algorithm based on artificial solar images obtained from MHD simulations and on seeing-free data obtained with the SuFI instrument on the Sunrise balloon borne observatory. The artificial data were altered by applying different levels of degradation with synthesised wavefront errors and noise. The PD algorithm was modified by changing the number of fitted polynomials, the shape of the pupil and the applied noise filter. The obtained reconstructions are evaluated by means of the resulting rms intensity contrast and by the conspicuousness of appearing artifacts. The results show that PD is a robust method which consistently recovers the initial unaffected image contents. The efficiency of the reconstruction is, however, strongly dependent on the number of used fitting polynomials and the noise level of the images. If the maximum number of fitted polynomials is higher than 21, artifacts have to be accepted and for noise levels higher than 10-3 the commonly used noise filtering techniques are not able to avoid amplification of spurious structures.

Pose-invariant face recognition by matching on multi-resolution MRFs linked by supercoupling transform

Recognition of faces in arbitrary pose is addressed in this paper. For this task, an MRF-based classification approach is proposed which employs the energy of the established match between a pair of images as a criterion of goodness-of-match. By incorporating an image matching method as part of the recognition process, the system is made robust to moderate global spatial transformations. The approach draws on a method [1] which has the potential to cope with pose changes but a direct application of which suffers from several shortcomings. In order to overcome these problems, a number of enhancements are proposed. First, by adopting a multi-scale relaxation scheme based on super coupling transform, the inference using sequential tree re-weighted message passing approach [2] is accelerated. Next, by taking advantage of a statistical shape prior for the matching, the results are regularized and constrained, making the system robust to spurious structures and outliers. For classification, both textural and structural similarities of the facial images are taken into account. The method is evaluated on two databases and promising results are obtained.

Formation of the Building Plan of the Human Heart

The intricate process of formation of the heart relies on the spatiotemporal regulation of differentiation and growth of its different parts. Errors in these processes can result in hypoplasia of the chambers and incorrect alignment of the atria and great arteries with the ventricles, with such abnormalities producing the worst forms of congenital heart disease.1 Although recent advances in molecular embryology have greatly improved our understanding of normal cardiac development, our insights into the pathogenesis of human cardiac malformations remain limited.2 With the current lack of data on gene expression in humans, inferences concerning morphogenesis rely on classic studies of human cardiac development or on extrapolation of experimental data from animal studies. Most textbooks on human embryology describe the embryonic heart tube as already possessing a linear array of the definitive components, despite this so-called segmental concept being disproved some time ago by fate-mapping experiments in chickens,3,4 which are now endorsed by recent molecular lineage analyses in mice.5 Proliferation studies in chickens revealed that the primary heart tube proliferates minimally and that its growth occurs through addition of differentiating cells from visceral mesoderm at the venous and arterial poles.6 These findings underscore previous lineage studies performed in mice, which have shown that transcription factors Islet1 and Tbx1 play a crucial role in the intricate balance between the cardiac precursor state and differentiation.7,8 Subsequent to its formation, the heart tube elongates and loops, producing its inner and outer curvatures and providing the general building plan for formation of the chambers and conduction system.9 The chambers themselves form by local proliferation and differentiation at the outer curvature.10,11 At the same time, the differentiating chamber myocardium remains flanked by primary myocardium, which is prevented from further differentiation by the …