Space Of Contours Research Articles

Jewish Muslims in The Handsome Jew and Don’t Leave Me Here Alone: Conversion, Identity, and Liminality

The present article addresses the complex interplay of boundaries, belonging, and modes of identity and investigates the space between the distinct boundaries of religious identities. It focuses on the Jewish Muslim identity as it defies categorization and plays out in the liminal space of the Jewish Muslims, a space of fluid and blurred contours, haunted by ancestral religion and inherited culture, and obsessed by a crucial need to reconstruct a new sense of self. The article explores these concepts by referring to two narrative works: Ali Al-Muqri’s The Handsome Jew and Ihsan Abdel Quddous’s Don’t Leave Me Here Alone, which extensively elaborate on the relationship between conversion, identity, and liminality. It argues that Jewish Muslims stay within a liminal space due to their inability to forget their past and assimilate into the present, and that a non-binary Jewish Muslim subject lives in a place that borders the Jewish and Muslim spaces but never crosses into either position completely. The study aims to investigate discourses, as presented in the two texts under discussion, that construct boundaries between individuals of different religious affiliations and the motives for such constructions, and it tries to demonstrate the extent to which liminality can be used as an apt metaphor to define the life of Jewish converts to Islam.

Three Kinds of Rising-Falling Contours in German wh-Questions: Evidence From Form and Function

The intonational realization of utterances is generally characterized by regional as well as inter- and intra-speaker variability in f0. Category boundaries thus remain “fuzzy” and it is non-trivial how the (continuous) acoustic space maps onto (discrete) pitch accent categories. We focus on three types of rising-falling contours, which differ in the alignment of L(ow) and H(igh) tones with respect to the stressed syllable. Most of the intonational systems on German have described two rising accent categories, e.g., L+H*and L*+H in the German ToBI system. L+H*has a high-pitched stressed syllable and a low leading tone aligned in the pre-tonic syllable; L*+H a low-pitched stressed syllable and a high trailing tone in the post-tonic syllable. There are indications for the existence of a third category which lies between these two categories, with both L and H aligned within the stressed syllable, henceforth termed (LH)*. In the present paper, we empirically investigate the distinctiveness of three rising-falling contours [L+H*, (LH)*, and L*+H, all with a subsequent low boundary tone] in Germanwh-questions. We employ an approach that addresses both theformand thefunctionof the contours, also takingregional variationinto account. In Experiment 1 (form), we used a delayed imitation paradigm to test whether Northern and Southern German speakers can imitate the three rising-falling contours inwh-questions as distinct contours. In Experiment 2 (function), we used a free association task to investigate whether listeners interpret the pragmatic meaning of the three contours differently. Imitation results showed that German speakers—both from the North and the South—reproduced the three contours. There was a small but significant effect of regional variety such that contours produced by speakers from the North were slightly more distinct than those by speakers from the South. In the association task, listeners from both varieties attributed distinct meanings to the (LH)*accent as opposed to the two ToBI accents L+H*and L*+H. Combined evidence fromformandfunctionsuggests that three distinct contours can be found in the acoustic and perceptual space of German rising-falling contours.

Deep Learning-Augmented Head and Neck Organs at Risk Segmentation From CT Volumes

Purpose: A novel deep learning model, Siamese Ensemble Boundary Network (SEB-Net) was developed to improve the accuracy of automatic organs-at-risk (OARs) segmentation in CT images for head and neck (HaN) as well as small organs, which was verified for use in radiation oncology practice and is therefore proposed.Methods: SEB-Net was designed to transfer CT slices into probability maps for the HaN OARs segmentation purpose. Dual key contributions were made to the network design to improve the accuracy and reliability of automatic segmentation toward the specific organs (e.g., relatively tiny or irregularly shaped) without sacrificing the field of view. The first implements an ensemble of learning strategies with shared weights that aggregates the pixel-probability transfer at three orthogonal CT planes to ameliorate 3D information integrity; the second exploits the boundary loss that takes the form of a distance metric on the space of contours to mitigate the challenges of conventional region-based regularization, when applied to highly unbalanced segmentation scenarios. By combining the two techniques, enhanced segmentation could be expected by comprehensively maximizing inter- and intra-CT slice information. In total, 188 patients with HaN cancer were included in the study, of which 133 patients were randomly selected for training and 55 for validation. An additional 50 untreated cases were used for clinical evaluation.Results: With the proposed method, the average volumetric Dice similarity coefficient (DSC) of HaN OARs (and small organs) was 0.871 (0.900), which was significantly higher than the results from Ua-Net, Anatomy-Net, and SRM by 4.94% (26.05%), 7.80% (24.65%), and 12.97% (40.19%), respectively. By contrast, the average 95% Hausdorff distance (95% HD) of HaN OARs (and small organs) was 2.87 mm (0.81 mm), which improves the other three methods by 50.94% (75.45%), 88.41% (79.07%), and 5.59% (67.98%), respectively. After delineation by SEB-Net, 81.92% of all organs in 50 HaN cancer untreated cases did not require modification for clinical evaluation.Conclusions: In comparison to several cutting-edge methods, including Ua-Net, Anatomy-Net, and SRM, the proposed method is capable of substantially improving segmentation accuracy for HaN and small organs from CT imaging in terms of efficiency, feasibility, and applicability.

Boundary loss for highly unbalanced segmentation.

Widely used loss functions for CNN segmentation, e.g., Dice or cross-entropy, are based on integrals over the segmentation regions. Unfortunately, for highly unbalanced segmentations, such regional summations have values that differ by several orders of magnitude across classes, which affects training performance and stability. We propose a boundary loss, which takes the form of a distance metric on the space of contours, not regions. This can mitigate the difficulties of highly unbalanced problems because it uses integrals over the interface between regions instead of unbalanced integrals over the regions. Furthermore, a boundary loss complements regional information. Inspired by graph-based optimization techniques for computing active-contour flows, we express a non-symmetric L2 distance on the space of contours as a regional integral, which avoids completely local differential computations involving contour points. This yields a boundary loss expressed with the regional softmax probability outputs of the network, which can be easily combined with standard regional losses and implemented with any existing deep network architecture for N-D segmentation. We report comprehensive evaluations and comparisons on different unbalanced problems, showing that our boundary loss can yield significant increases in performances while improving training stability. Our code is publicly available1.

Accounting for the effect of heterogeneous plastic deformation on the formability of aluminium and steel sheets

Forming limit curves characterise “mean” failure strains of sheet metals. Safety levels from the curves define the deterministic upper limit of the processing and part design window, which can be small for high strength, low formability materials. Effects of heterogeneity of plastic deformation, widely accepted to occur on the microscale, are neglected. Marciniak tests were carried out on aluminium alloys (AA6111-T4, NG5754-O), dual-phase steel (DP600) and mild steel (MS3). Digital image correlation was used to measure the effect of heterogeneity on failure. Heterogeneity, based on strain variance, was modelled with the 2-component Gaussian mixture model, and a framework was proposed to (1) identify the onset of necking and to (2) re-define formability as a probability to failure. The results were “forming maps” in major-minor strain space of contours of constant probability (from probability, P = 0 to P = 1), which showed how failure risk increased with major strain. The contour bands indicated the unique degree of heterogeneity in each material. NG5754-O had the greatest width (0.07 strain) in plane strain and MS3 the lowest (0.03 strain). This novel characterisation will allow engineers to balance a desired forming window for a component design with the risk to failure of the material.

Probability prediction model for bridging defects induced by combined influences from lithography and etch variations

Background: As semiconductor technologies continue to shrink, the growth in the number of process variables and combined effects tighten the overall process window, which leads to a more serious yield loss. Yield cannot be totally guaranteed by design rule check and verifications of optical proximity correction, due to complex process variations. The joint effects from unreasonable designs and unstable control of critical dimensions and overlay mainly contribute to the formation of bridging defects in critical interconnect layers. Aim: Our paper puts forward a model to detect the potential bridging region and predicts the corresponding failure probability under a litho-etch-litho-etch process. Approach: The proposed model is based on input error sources from variations of lithography and etch processes. In this scheme, bridging is expected when the minimum space of simulated postetch contours within a specific range is smaller than a user-defined bridging threshold. Gaussian distribution characteristics of line edge roughness (LER) and overlay are considered in the proposed model. Moreover, the proposed model provides meaningful guidelines for bridging prediction with the use of process variation bands. Results: The experiment results indicate consistency and validity of theoretical derivation of the proposed model. The concrete impacts of LER and overlay on the model have been quantitatively analyzed as well. Conclusions: According to the predicted probabilities, the model can early discover potential bridging defects quantitatively by considering the statistical properties of process variations with very few calculations and can give a ranking of failure severity as a decision foundation for design rule optimization.

Stokes–Leibenson problem for Hele-Shaw flow: a critical set in the space of contours

The Stokes–Leibenson problem for Hele-Shaw flow is reformulated as a Cauchy problem of a nonlinear integro-differential equation with respect to functions a and b, linked by the Hilbert transform. The function a expresses the evolution of the coefficient longitudinal strain of the free boundary and b is the evolution of the tangent tilt of this contour. These functions directly reflect changes of geometric characteristics of the free boundary of higher order than the evolution of the contour point obtained by the classical Galin–Kochina equation. That is why we managed to uncover the reason of the absence of solutions in the sink-case if the initial contour is not analytic at at least one point, to prove existence and uniqueness theorems, and also to reveal a certain critical set in the space of contours. This set contains one attractive point in the source-case corresponding to a circular contour centered at the source-point. The main object of this work is the analysis of the discrete model of the problem. This model, called quasi-contour, is formulated in terms of functions corresponding to a and b of our integro-differential equation. This quasi-contour model provides numerical experiments which confirm the theoretical properties mentioned above, especially the existence of a critical subset of co-dimension 1 in space of quasi-contours. This subset contains one attractive point in the source-case corresponding to a regular quasi-contour centered at the source-point. The main contribution of our quasi-contour model concerns the sink-case: numerical experiments show that the above subset is attractive. Furthermore, this discrete model allows to extend previous results obtained by using complex analysis. We also provide numerical experiments linked to fingering effects.

Statistical analysis of trajectories on Riemannian manifolds: Bird migration, hurricane tracking and video surveillance

We consider the statistical analysis of trajectories on Riemannian manifolds that are observed under arbitrary temporal evolutions. Past methods rely on cross-sectional analysis, with the given temporal registration, and consequently may lose the mean structure and artificially inflate observed variances. We introduce a quantity that provides both a cost function for temporal registration and a proper distance for comparison of trajectories. This distance is used to define statistical summaries, such as sample means and covariances, of synchronized trajectories and "Gaussian-type" models to capture their variability at discrete times. It is invariant to identical time-warpings (or temporal reparameterizations) of trajectories. This is based on a novel mathematical representation of trajectories, termed transported square-root vector field (TSRVF), and the $\mathbb{L}^2$ norm on the space of TSRVFs. We illustrate this framework using three representative manifolds---$\mathbb{S}^2$, $\mathrm {SE}(2)$ and shape space of planar contours---involving both simulated and real data. In particular, we demonstrate: (1) improvements in mean structures and significant reductions in cross-sectional variances using real data sets, (2) statistical modeling for capturing variability in aligned trajectories, and (3) evaluating random trajectories under these models. Experimental results concern bird migration, hurricane tracking and video surveillance.

Problème de Cauchy pour lʼapproximation de Stokes–Leibenson dʼune cellule de Hele–Shaw en coin

The Helmholtz–Kirchhoff transformation gives us a new approach to solve the Hele–Shaw problem. Particularly, we derived a so-called quasi-contour method from which we built a numerical scheme. Following a previous article [1], we propose a way to improve significantly the numerical scheme, which leads to the resolution of a Cauchy problem. The tedious calculation of a surface integral (absent in the physical problem) was replaced with simple integrals along the contour of the fluid. We have then tested the new numerical scheme on the Stokes–Leibenson problem in a corner geometry, highlighting the gain in accuracy of the results. Besides, the existence of a critical manifold in the space of contours is confirmed (see [1]).

Attractors–Repellers in the Space of Contours in the Stokes–Leibenson Problem for Hele–Shaw Flows

It is shown that, in the space of quasicontours playing a role of free boundaries in the Stokes–Leibenson problem, there is a manifold of codimension 1 such that some points of this manifold are attractors in the case of sink and repellers in the case of source, whereas, on the contrary, other points are repellers in the case of sink and attractor in the case of source. Bibliography: 36 titles. Illustrations: 7 figures.

Shape space estimation by higher-rank of SOM

The aim of this study is to develop an estimation method for a shape space. In this work, “shape space” means a nonlinear subspace formed by a class of visual shapes, in which the continuous change in shapes is naturally represented. By using the shape space, various operations dealing with shapes, such as identification, classification, recognition, and interpolation can be carried out in the shape space. This paper introduces an algorithm based on a generative model of shapes. A higher-rank of the self-organizing map (SOM2) is used to implement the shape space estimation method. We use this method to estimate the shape space of artificial contours. In addition, we present results from a simulation of omnidirectional camera images taken from mobile robots. Our technique accurately predicts changes in image properties as the robot’s attitude changes. Finally, we consider the addition of local features to our method. We show that the inclusion of local features solves the correspondence problem. These results suggest the potential of our technique in the future.

Deform PF-MT: Particle Filter With Mode Tracker for Tracking Nonaffine Contour Deformations

We propose algorithms for tracking the boundary contour of a deforming object from an image sequence, when the nonaffine (local) deformation over consecutive frames is large and there is overlapping clutter, occlusions, low contrast, or outlier imagery. When the object is arbitrarily deforming, each, or at least most, contour points can move independently. Contour deformation then forms an infinite (in practice, very large), dimensional space. Direct application of particle filters (PF) for large dimensional problems is impractically expensive. However, in most real problems, at any given time, most of the contour deformation occurs in a small number of dimensions ("effective basis space") while the residual deformation in the rest of the state space ("residual space") is small. This property enables us to apply the particle filtering with mode tracking (PF-MT) idea that was proposed for such large dimensional problems in recent work. Since most contour deformation is low spatial frequency, we propose to use the space of deformation at a subsampled set of locations as the effective basis space. The resulting algorithm is called deform PF-MT. It requires significant modifications compared to the original PF-MT because the space of contours is a non-Euclidean infinite dimensional space.

Evidence for attractors in English intonation

Although the pitch of the human voice is continuously variable, some linguists contend that intonation in speech is restricted to a small, limited set of patterns. This claim is tested by asking subjects to mimic a block of 100 randomly generated intonation contours and then to imitate themselves in several successive sessions. The produced f0 contours gradually converge towards a limited set of distinct, previously recognized basic English intonation patterns. These patterns are "attractors" in the space of possible intonation English contours. The convergence does not occur immediately. Seven of the ten participants show continued convergence toward their attractors after the first iteration. Subjects retain and use information beyond phonological contrasts, suggesting that intonational phonology is not a complete description of their mental representation of intonation.

Supersymmetric null-surfaces

Single trace operators with the large R-charge in supersymmetric Yang-Mills theory correspond to the null-surfaces in AdS(5) x S-5. We argue that the moduli space of the null-surfaces is the space of contours in the super-grassmanian parametrizing the complex (2|2)-dimensional subspaces of the complex (4|4)-dimensional space. The odd coordinates on this super-grassmanian correspond to the fermionic degrees of freedom of the superstring.

Average performance of adaptive algorithms for programming co-ordinate measuring machines under budget constraint

In this paper we develop two adaptive algorithms for programming co-ordinate measuring machines assuming fixed sampling budget. Two different costs are considered: the travelling cost of the machine probe, and the sampling cost to read and store all measurements. Simulation is used to compare the average performance of the proposed algorithms under the assumption of Wiener measure on the space of all surface contours of the manufactured parts. Expected value of the probability of Type II error is the criterion that we use to characterize algorithms performance. Analysis shows that placing sample points according to the criterion of maximizing the expected gain demonstrates a substantial improvement in the average performance. Copyright © 1999 John Wiley & Sons, Ltd.

Classical Solutions of Multidimensional Hele--Shaw Models

Existence and uniqueness of classical solutions for the multidimensional expanding Hele{Shaw problem are proved.

Absence of mass gap for a class of stochastic contour models

We study a class of Markovian stochastic processes in which the state space is a space of lattice contours and the elementary motions are local deformations. We show, under suitable hypotheses on the jump rates, that the infinitesimal generator has zero mass gap. This result covers (among others) the BFACF dynamics for fixed-endpoint self-avoiding walks and the Sterling-Greensite dynamics for fixed-boundary self-avoiding surfaces. Our models also mimic the Glauber dynamics for the low-temperature Ising model. The proofs are based on two new general principles: the minimum hitting-time argument and the mean (or mean-exponential) hitting-time argument.

String representations and hidden symmetries for gauge fields

We show that gauge fields can be considered as chiral fields defined on the space of all possible contours. That leads to an infinite number of functionally conserved currents. A possible application of this result is discussed. Also a one-dimensional approximation is proposed.