prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: How does the receptive field size affect the completion of shapes?

Read the following text and answer briefly.

Context 1: Paper Info

Title: CONTOUR COMPLETION USING DEEP STRUCTURAL PRIORS
Publish Date: 9 Feb 2023
Author List: Ali Shiraee, Morteza Rezanejad, Mohammad Khodadad, Dirk Walther, Hamidreza Mahyar

Figure

Figure 1: Just by looking at subfigure (a), we, as humans, can easily perceive a shape like the one in subfigure (b) This is an extraordinary capability of our human brain and in this paper, we tried to see whether convolutional neural networks can show such capabilities 
Figure 2: The trajectory from random noise X N to the incomplete image X I in image space The network will pass a completed version of the image, X C , throughout this trajectory 
Figure 4: This figure shows our iterative process to complete the fragmented contours of an image given as input to our pipeline 
Figure 5: This example shows how different scores change throughout a single run All three scores change in the range of [0, 100] Our goal is to maximize reconstruction_score and minimize the overfit_score, but we should consider that the minimization lower bound is data dependent and is not zero 
Figure 6: Evolutionary process of the deep structure prior The right column shows the incomplete shapes given to the model and the rest of the columns show how the model is overfitting gradually to produce the incomplete shapes In each column, we are showing an intermediate iteration of this process The loss-term setup enables our pipeline to let the completed image appears during this iterative process 
Average MSE and IoU values between the incomplete (Raw) images, the output of DIP and DSP methods, and ground truth for each image are provided in this table 
For this experiment, we ran the model over a subset of complex dataset with 500 incomplete images at various levels of alpha for 250 iterations After the image completion is done, we compared the evaluation metrics between the completed image and the ground truth to examine the performance of the model for different values of alpha 
In this table, we show the effect of the receptive filter size on our algorithm's capability to fill in bigger gap sizes The numbers in this table are showing the percentage of the time that DIP was successful to complete shapes with each gap size and corresponding receptive field size As predicted, the bigger the filter size, the more successful the algorithm is in filling in the gaps 

abstract

Humans can easily perceive illusory contours and complete missing forms in fragmented shapes  This work investigates whether such capability can arise in convolutional neural networks (CNNs) using deep structural priors computed directly from images  In this work, we present a framework that completes disconnected contours and connects fragmented lines and curves 
In our framework, we propose a model that does not even need to know which regions of the contour are eliminated  We introduce an iterative process that completes an incomplete image and we propose novel measures that guide this to find regions it needs to complete  Our model trains on a single image and fills in the contours with no additional training data 
Our work builds a robust framework to achieve contour completion using deep structural priors and extensively investigate how such a model could be implemented 

Introduction

The human visual system is used to seeing incomplete outlines  Our brains can effortlessly group visual elements and fragmented contours that seem to be connected to each other  This power enables us to make shapes, organize disconnected visual features, and even properties of 3D surfaces when projected on 2D planes 
demonstrated how early vision may quickly complete partially-occluded objects using monocular signals  This capability of perceptual grouping has been studied in vision science for decades   Although there has been some work on perceptual grouping in the past couple of years, it has been less studied in the past decade due to the enormous progress of deep neural networks and their success in dealing with the pixel-by-pixel inference of images 
Different types of lines and curves have been studied to maximize the connectivity of two broken ends in the planer contour completion problem   Different types of lines and curves have been studied to maximize the connectivity of two broken ends in the planer contour completion problem  Geometry-based constraints can be utilized to address some challenges of contour completion problems, such as smoothness and curvature consistency  
However, such approaches only work for simple, smooth contours and usually fail in more complex settings  On the other hand, we currently have deep models that could easily take an incomplete image and complete the missing regions using enough training data   The amazing capability of such models especially those that are trained on different modalities with millions or billions of training data raises the question of whether we need such a large amount of training to perceive all the visual cues that are present in an image, which underlies visual perception by humans 
In human vision, Gestalt psychology suggests that our brain is designed to perceive structures and patterns that are grouped by some known rules  In this work, we show that some perceptual structures can also be learned from the image itself directly using architectures that enable such learning  Earlier work has shown  This is an extraordinary capability of our human brain and in this paper, we tried to see whether convolutional neural networks can show such capabilities 
that some forms of perceptual grouping can be achieved using computational models, such as stochastic completion fields   This type of learning resonates with some of the Gestalt perceptual grouping principles including "proximity", "good continuation" and "similarity"  In scenarios where color and/or texture are present, the cue of "similarity" helps us group regions with consistent patterns  
When color and texture are present, they provide a collection of rich information for such cues  In the present article, we probe convolutional neural networks in a scenario where both are absent, and the neural network is dealing with just forms and shapes  Specifically, we explore whether the convolutional neural network architecture itself can give rise to some of these grouping cues when they are fed just contours and shapes alone 
For years, neural networks have been treated as black boxes that can generalize images very well to multiple classes when there are enough training exemplars  One of the reasons that neural networks are trained on many exemplars is to avoid the problem of overfitting  On the other hand, we know that CNNs that generalize well to large classes of exemplars can easily overfit when those class labels are randomly permuted  
Inspired by this observation, suggest that image priors can be learned to a large extent through a generator network architecture that is solely trained on a single image  This encouraged us to take a deeper look at what structural information can be learned from a single-shape image and whether we can reconstruct some of those perceptual grouping capabilities using a generator network 
Inspired by , in this work, we adopt a novel training regime to complete shapes and contours where we use a UNet architecture with random initial weights and try to complete the contours within a single image without any training data  In our model, we imagine that the input image (i e , the only image used to update the model's weights) is an image of fragmented contours 
In this work, instead of training the model on multiple images fetched from a big image dataset, we imagine a random fixed tensor noise image as input to this model  At each iteration, the random noise tensor is inferred through our generative network and the network produces an outcome image  We introduce a novel loss function that enables this network to complete contours 
This process repeats, and the weights of our network are updated gradually based on this loss function, which is an energy term defined based on the input image and the output of the network  The model will reconstruct the missing structures i e , group fragmented contours that perceptually seem to be connected, before it fully overfits to the incomplete input image 
Contributions of our work are summarized as follows: 1  In our pipeline, we propose a novel algorithm that enables us to complete contours that appear to be connected to each other in an illusory form  2  Our model is trained on just one single query image and does not need any training data  3  Our model does not need to know which regions of the image are masked or occluded, i e , we remove the dependency of the algorithm on the guiding mask (a guiding mask is a mask that informs the model on where the missing regions are located at) 
We also introduce two metrics to produce a stopping criterion to know when to stop training before the model fully overfits to the incomplete image, i e , we guide the model to stop when the completed image is produced 

Methods

Our eyes are trained to predict a missing region of an occluded object within a scene  We can easily perceive or make guesses about parts of objects or shapes that we do not necessarily see  Even when we are looking at an image, we might guess about the shape, property, or other attributes of an unknown object within a scene 
Such capability extends beyond just known objects or shapes  We can look at a disconnected set of contours and guess what the connected form may look like  This capability is rooted in our prior knowledge about the world  (see Figure )  In this work, we aim to achieve a similar capability using deep generative networks 
Most neural networks that we work with these days are trained with a massive amount of data and one might think that this is the only way that a neural network can obtain prior information  Authors of Deep Image Prior (DIP) suggest that the convolutional architecture can capture a fair amount of information about image distribution 
They show that the hourglass architectures like UNet can show some good performances in some inverse problems such as image denoising, super-resolution, and inpainting  In this work, we focus on completing fragmented contours end-to-end just by using a single image  To be able to address this problem, we first look at a similar problem in image editing, known as image inpainting 
Image inpainting is the task of completing an image where some regions of that image are covered or filtered by a mask  In image inpainting, the generative model receives a masked image with the mask that guides the algorithm to fill in those missing regions  Although in the problem of contour completion, we have a very similar goal, the additional challenge that we suffer from is that we do not necessarily have a mask that covers the regions of interest for us 
For example, when we look at Figure (left), we are not provided that which regions of the image are incomplete by a guiding mask  Our brain figures this out just by looking at the form and predicting those missing regions  Inspired by the image inpainting work of DIP , we propose a novel algorithm for the contour completion problem (see Figure ), where, unlike DIP, we do not have a guiding mask to know where to fill in the missing regions of our disconnected contours 
Let us assume that we are given a degraded image x I containing a fragmented contour  We propose an iterative process (see Figure ) that can connect those discontinuities and glue those fragmented pieces together as follows  We propose an hour-glass model structure (f ) that is initially set up with completely random parameters (θ 0 ) at first 
Through an iterative process, we start feeding our network with a fixed random tensor noise z signal and obtain the inferred output (f (z)) from that network  We then back-propagate the difference between the inferred output and the incomplete image to the network  We then repeat this process until the difference between the generated outcome of the network (f θ (z)) and the incomplete image (x I ) gets smaller and smaller and finally overfits the incomplete image (x I ) 
In this work, we propose a novel error metric to backpropagate in the model and update its weights  we set the metric in a way that enables us to complete the incomplete image before it overfits the incomplete image  This is where the magic of our algorithm happens  We also propose a stopping criterion, so that when the image is complete, we no longer overfit the outcome of the model and instead produce a plausible connected set of fragmented contour pieces 
As illustrated in Figure , this trajectory will pass through a complete version of the image in image space, which is close to the actual connected ground truth x gt , which we do not have access to directly 

Energy Function

We can model this iterative process mathematically by maximizing a posterior distribution  Let us assume that the optimal image x * that we want to achieve is on a path that connects a random tensor noise z to the incomplete image x I   With this assumption, we can eventually overfit any random tensor noise to the incomplete image x I , and we can formulate the posterior distribution of our wanted optimal image x * as follows:
No Prior To better recapitulate what we want to achieve using our generative model, we solve an energy minimization problem on the parameter space of the model, rather than explicitly working with probability distributions and optimizing on x (image space)  Thus, we solve an energy minimization problem that incorporates the incomplete image (x I ) and model parameters (f θ (z)):
As shown in Figure , the pipeline starts from a random initialized set of parameters θ and updates those weights until it reaches a local minimum θ *   The only information provided for the network is the incomplete image x I   When we reach the optimal θ * , the completed image is obtained as x * = f θ * (z) where z is random tensor noise 
In this work, we use a U-Net architecture with skip connections as the generator model  " As we mentioned previously, in this work we were inspired by an earlier work known as Deep Image Prior (DIP)   In this work, the authors suggested a mean-squared-error loss term that enables the network to compare the output of the generator to the incomplete input image:
where x I is the incomplete image with missing pixels in correspondence of a binary mask m ∈ {0, 1} H×W and operator is for point-wise multiplication of two image matrices  In the inpainting tasks, the existence of a mask is essential as the algorithm needs to know where to fill in the missing area, whereas, in our work, we wanted to know whether the network can perform completion on its own without the need for the mask 
In other words, is it possible for the network to predict where to fill in at the same time that it is trying to reconstruct the incomplete image through the iterative process? To answer this question, we tried to solve a much harder problem in which the mask is not provided to the model and the model is agnostic to it 
To better understand how a solution could be hypothesized for this problem, we first imagine that we want to consider all the available regions in our image that could be potential places to fill in, i e , we set the mask in the previous formula 1 to be equal to the incomplete image x I   This is problematic as the model quickly tries to fill in all white space and quickly reconstructs the incomplete image by doing so 
On the other hand, we can take the inverse problem of the current problem, where the model tries to just fill in the regions that fragmented contour lives in  Taking these two at the same time, we came up with a novel loss term for energy minimization term that helps us remove the need for the mask in the case of the contour completion problem:
In this term, we introduce a linear combination of the two loss terms, where one focuses on reconstructing the missing regions in the foreground, and one focuses on avoiding inpainting regions in the background  The logic behind this is that, if we assume the original image to be representative of the mask, then the model tries to reconstruct in all white regions (the foreground), and in the inverse problem we just want to reconstruct the regions that are already part of the ground truth 

Stopping Criteria

As shown in Figure , knowing when to stop iterating to the over-fitted model is a key to obtaining a completed shape  Therefore, we equipped our model with a criterion that uses two individual novel terms to know when to stop and output the result of the network  These two metrics expand the capability of the generator network beyond what it does currently and achieve a full end-to-end contour completion model that trains and infers on a single image of divided contour fragments 
These new terms are: reconstruction_score (ρ) and overfit_score (ω) 

Reconstruction Score

The first score that this paper suggests is the reconstruction score, i  e , we have to make sure that the model is trained enough that it can reconstruct at least the entire set of fragmented contours within the image  This is a trivial score and to compute the reconstruction_score (ρ), we apply a k-dimensional tree (KDTree) nearest-neighbor lookup to find the ratio of points in the original incomplete image (x 0 ) 
This score ranges from [0 − 100] 

Overfit Score

It is evident that the model overfits the fragmented contours  This is due to the fact that the error in our loss term is minimized as the x overfits to x I , i  e , replacing x with x I in the loss term would give us zero  As we hypothesize iterative process also produces the complete image before it overfits to the incomplete image, we can imagine that at some point the image is complete (x C ) and does not need to be fine-tuned any more to overfit to x I  
We suggest a new score called overfit_score  overfit_score determines how much of the reconstructed outcome is over the number of pixels that are already in the incomplete image (x I )  To compute the overfit_score (ω), we apply a k-dimensional tree (KDTree) nearest-neighbor lookup of points in the outcome of the input image and see what portions of those points are novel and not already in the incomplete image (x I ) 
Similar to reconstruction_score, the overfit_score also ranges from [0 − 100]  Our goal is to maximize reconstruction_score and minimize the overfit_score, but we should consider that the minimization lower bound is data dependent and is not zero 

Combined Score

To be able to find the best possible set of completed contours, we combine the two and have a loop that tries to achieve close to full reconstruction and avoids over-fitting at the same time  This is what we call an "ideal" stopping point in the contour completion problem  In each run throughout all iterations, we pick an output of the network that minimizes a dissimilarity term:
where δ represents our dissimilarity score  The reconstruction_score and overfit_score are obtainable given network output and the incomplete image  Ideally, we want to achieve an output image that has a reconstruction_score equal to 100 and an overfit_score of γ which is a hyperparameter that is dependent on the image and complexity of the shape 
Empirically, we observed that this value is highly correlated with the distance between gaps that are observed in fragmented contours, i  e , the larger the gap results in a larger γ value  We will discuss this in more detail in the next section (see Section 3)  For one sample image, we computed the two metrics reconstruction_score and overfit_score and the combined value of dissimilarity (δ) and showed how these values change (see Figure ) 
Our initial observations show that the reconstruction_score will increase to 100 quickly for the incomplete image indicating that the already existing fragments of the contours have been reconstructed in the output  However, as mentioned previously, we cannot solely rely on this score since we also want to minimize the overfitting 
Remember that our goal is to produce an output that: a) preserves the original contours in the incomplete image and b) fills in the gaps between the fragmented contours  It is evident that overfit_score decreases throughout an iterative run of our process until it reaches zero  The dissimilarity will also decrease along with the overfit to a point, then it will increase, as the model tries to reproduce the incomplete image 
This is where an ideal γ value can be picked, i e , where to stop when the reconstruction is good but we have not done a full overfit to the incomplete image  Thus, one should pick the value of γ empirically in the scenario that the ground truth is not available, whereas, assuming that the ground truth is available, we can easily compute the best γ value 
In our experiments, we tried two datasets of images with different gap sizes  We observed that the best the γ for one set of samples is ∼ 5 (the set with shorter gaps) while it is ∼ 23 for samples from the other set, i  e, the set with longer gaps (see Figure for some completed examples) 

Experiments and Results

Performing unsupervised contour completion is a difficult task to benchmark as one can never know what fragments exactly are connected to each other in a real-world scenario  This makes the problem of contour completion a hard problem to solve  In this paper, we tried to create artificial shapes that are occluded by some masks and then tried to see if our model can regenerate the missing pieces and glue those divided contours together 
To demonstrate our model's behavior, we will conduct experiments on datasets created for this task and will report on them in this section  To compare network results in different settings, we will use pixel-wise Mean Squared Error (MSE) and Intersection over Union (IoU) between the produced result of the network and unmasked ground truth data and the reconstructed image on black pixels (where contours live) 

Data

We prepared two datasets, one labeled "Simple" and one "Complex", in accordance with the number of gaps in each shape  Both datasets contain nine different categories of shapes  In order to generate the Complex dataset, we used FlatShapeNet which is a dataset for the educational game Ariga  The dataset includes the following categories: Circle, Kite, Parallelogram, Rectangle, Rhombus, Square, Trapezoid, Triangle and Overlap 
The "overlap" category contains images that are made as a mixture of two shapes that are overlapping from the previous categories  These are some standard shapes with a few gaps in simple dataset, while the complex dataset has some hand-drawn shapes with fragmented lines and more gaps that produce more variety in general 
For each instance, a ground truth image is available for comparison  Most of our experiments have been conducted using the complex dataset in order to evaluate the generalization of our approach  For the analysis of how γ values should be set for each shape, we used the simple dataset as a reference 

Evaluation

In this section, we compare our model to the original Deep Image Prior (DIP) inpainting model  DIP's inpainting module accepts a degraded image and a binary mask corresponding to that image  In order to make a fair comparison, instead of providing a binary mask, we used the incomplete images both as input and as a mask in order to see whether it can produce a result similar to ours 
For DIP, we run the iterative process for a maximum number of 2500 iterations with the U-net backbone  We used the exact same architecture and setting in our model for a fair comparison  Using our ground truth dataset images, we calculate the MSE loss between the network output and ground truth during each iteration instead of relying on our stopping mechanism described in the previous section 
We then store the output with minimal loss throughout all the iterations  Finally, we select the best output among all iterations, report the MSE and IoU with the ground truth, and save the iteration number which resulted in the lowest MSE  Table compares the results that are obtained using the DIP method, the DSP method (ours), and the difference between raw images and the ground truth 
We have presented the average MSE-loss, average IoU, and the average number of iterations for the best output for different methods  As can be seen from the table, our model improves both MSE and IoU between the incomplete image and ground truth in fewer iterations  The DIP method can neither generate a better result than the raw image nor provide stopping criteria to prevent overfitting 
We provide a more detailed analysis of this result in Figure   As results show, our algorithm not only provides a much faster convergence but also consistently provides a better-completed image (consistently less MSE loss and better IoU), whereas it is challenging for the DIP method to accomplish better results without a guiding mask 
We compare MSE loss between the degraded raw images that these algorithms started with (shown in blue) (a) Mean Squared Error Loss: we clearly see that for almost all images, DSP (green) achieves a lower MSE than the incomplete images (blue) whereas, the DIP completed images either do not improve the MSE or even worsen that for the incomplete images 
Note that, the MSE is computed to an available ground truth image hidden from our methods (the lower is better)  (b) Intersection Over Union: here, we are looking at the IoU metric that specifies the amount of intersection over the union between the obtained images and the ground truth data  Again, we see that DSP produces images that are much closer to the ground truth (in most cases) whereas the DIP can not achieve a similar result 
While we see few DIP completed images produce a better IoU than the degraded images (in terms of IoU), most of them are worse than the starting image (the higher is better)  (c) The number of iterations that are needed for each algorithm to obtain its best results  Here, we see that DSP can quickly produce the best outcome with the least MSE loss whereas the DIP algorithm's best results are when we run the iterative process for more iterations (the lower is better) 

Correlation of γ with the Gap Size

To better understand the γ parameter of our combined score, we conducted the following experiment  A total of 12000 samples were obtained by merging all of our images from the two datasets, simple and complex  As we have access to the ground truth for each degraded image in the combined dataset, we can easily calculate reconstruction_score and overfit_score for each degraded-ground truth pair 
As expected, we obtain a reconstruction_score of 100 for all samples, but the overfit_score varies among them  Intuitively, we hypothesized that an optimal value of overfit score should be intertwined with the total area of gaps  To test this hypothesis, we did the following experiment  We first define a function φ(x) which takes a binary, black and white image x and returns the number of black pixels in it 
Then we define a gap term as follows: where x I is the incomplete image and x gt is the ground truth  In this case, gap indicates the total area of the gap with respect to the whole shape  We found out that this term and the best result have a correlation of 97 43%  This indicates that the value of γ is highly correlated with the gap size, that is something expected in a way 

Effect of α

We conducted additional experiments concerning how α affects the quality of reconstruction  In the previous section, we defined Equation 2 as the loss term that guides our iterative process  The term α specifies the amount of emphasis the model should place on reconstructing missing regions, rather than filling in fragmented contours 
A lower α indicates a better grouping quality, as shown in Equation   However, we will not achieve completion if we remove the first term completely from the loss by setting α = 0  Therefore, the first term should be kept, but its weight should be very low in order to achieve a good completion  On the other hand, if we set α = 1 and omit the second term, we lose the contour completion regularization term and obtain the same output as a vanilla deep image prior, which does not complete shapes 

Effect of Receptive Field Size

To better understand the effect of receptive field size on our algorithm, we test the following hypothesis: can models with bigger receptive field size complete shapes with bigger gaps? In Table , we report showing the results of this experiment  As we can see, the bigger the receptive field size, the more complete shapes we can reconstruct using DSP 

Implementation Details

As shown in Figure , we use a model with 5 layers and 128 channels for downsampling and upsampling convolutions, and 64 channels for skip convolutions  The upsampling and downsampling modules use 3 × 3 filters, while the skip module uses 1 × 1 filters  In the upsample part of the network, the nearest neighbor algorithm is used 
We used 256 × 256 images with three channels in all of our experiments  In training, we use the MSE loss between the degraded image and the output of the network, and we optimize the loss using the ADAM optimizer and a learning rate equal to 0 01   In our experiments, we also used α = 0 15 as an optimal proportion coefficient for reconstruction loss 

Conclusion

In this work, we introduced a novel framework for contour completion using deep structure priors (DSP)  This work offers a novel notion of a maskless grouping of fragmented contours  In our proposed framework, we introduced a novel loss metric that does not require a strict definition of the mask  Instead, it lets the model learn the perceivable illusory contours and connects those fragmented pieces using a generator network that is solely trained on just the single incomplete input image 
Our model does not require any pre-training which demonstrates that the convolutional architecture of the hour-glass model is able to connect disconnected contours  We present an extended set of experiments that show the capability of our algorithm  We investigate the effect of each parameter introduced in our algorithm separately and show how one could possibly achieve the best result for their problem using this model 
In future work, we plan to extend this model and try to see how it performs with real images  In particular, we want to determine whether we can inpaint real-world photographs while retaining perceptually aware scene structures  The importance of shape in perception by deep neural networks has been highlighted in many adversarial examples to appearance-based networks  
The outcome of this work has strong potential to impact the designing and implementation of models that are robust to such perturbations 
Context 3: Margaret Way (b  Brisbane d  Cleveland, Queensland, Australia ) was an Australian writer of romance novels and women's fiction  A prolific author, Way wrote more than 120 novels since 1970, many through Mills & Boon, a romance imprint of British publisher Harlequin UK Ltd , owned by Harlequin Enterprises 

Biography
Before her marriage, she was a well-known pianist, teacher, vocal coach and accompanist  She began writing when her son, Laurence Way, was born, a friend took a pile of Mills & Boon books to her, she read all and decided that she also could write these types of novels  She began to write and promote her country with her stories set in Australia  She sold her first novels in 1970  Margaret Way lives with her family in her native Brisbane  Beginning in 2013, Margaret began to self-publish, releasing her first "e-book" mid-July 

Margaret died on the 10th of August 2022 in Cleveland, Queensland 

Bibliography

Single Novels
King Country (1970)
Blaze of Silk (1970)
The Time of the Jacaranda (1970)
Bauhinia Junction (1971)
Man from Bahl Bahla (1971)
Summer Magic (1971)
Return to Belle Amber (1971)
Ring of Jade (1972)
Copper Moon (1972)
Rainbow Bird (1972)
Man Like Daintree (1972)
Noonfire (1972)
Storm Over Mandargi (1973)
Wind River (1973)
Love Theme (1974)
McCabe's Kingdom (1974)
Sweet Sundown (1974)
Reeds of Honey (1975)
Storm Flower (1975)
Lesson in Loving (1975)
Flight into Yesterday (1976)
Red Cliffs of Malpara (1976)
Man on Half-moon (1976)
Swan's Reach (1976)
Mutiny in Paradise (1977)
One Way Ticket (1977)
Portrait of Jaime (1977)
Black Ingo (1977)
Awakening Flame (1978)
Wild Swan (1978)
Ring of Fire (1978)
Wake the Sleeping Tiger (1978)
Valley of the Moon (1979)
White Magnolia (1979)
Winds of Heaven (1979)
Blue Lotus (1979)
Butterfly and the Baron (1979)
Golden Puma (1980)
Temple of Fire (1980)
Lord of the High Valley (1980)
Flamingo Park (1980)
North of Capricorn (1981)
Season for Change (1981)
Shadow Dance (1981)
McIvor Affair (1981)
Home to Morning Star (1981)
Broken Rhapsody (1982)
The Silver Veil (1982)
Spellbound (1982)
Hunter's Moon (1982)
Girl at Cobalt Creek (1983)
No Alternative (1983)
House of Memories (1983)
Almost a Stranger (1984)
A place called Rambulara (1984)
Fallen Idol (1984)
Hunt the Sun (1985)
Eagle's Ridge (1985)
The Tiger's Cage (1986)
Innocent in Eden (1986)
Diamond Valley (1986)
Morning Glory (1988)
Devil Moon (1988)
Mowana Magic (1988)
Hungry Heart (1988)
Rise of an Eagle (1988)
One Fateful Summer (1993)
The Carradine Brand (1994)
Holding on to Alex (1997)
The Australian Heiress (1997)
Claiming His Child (1999)
The Cattleman's Bride (2000)
The Cattle Baron (2001)
The Husbands of the Outback (2001)
Secrets of the Outback (2002)
With This Ring (2003)
Innocent Mistress (2004)
Cattle Rancher, Convenient Wife (2007)
Outback Marriages (2007)
Promoted: Nanny to Wife (2007)
Cattle Rancher, Secret Son (2007)
Genni's Dilemma (2008)
Bride At Briar Ridge (2009)
Outback Heiress, Surprise Proposal (2009)
Cattle Baron, Nanny Needed (2009)

Legends of the Outback Series
Mail Order Marriage (1999)
The Bridesmaid's Wedding (2000)
The English Bride (2000)
A Wife at Kimbara (2000)

Koomera Crossing Series
Sarah's Baby (2003)
Runaway Wife (2003)
Outback Bridegroom (2003)
Outback Surrender (2003)
Home to Eden (2004)

McIvor Sisters Series
The Outback Engagement (2005)
Marriage at Murraree (2005)

Men Of The Outback Series
The Cattleman (2006)
The Cattle Baron's Bride (2006)
Her Outback Protector (2006)
The Horseman (2006)

Outback Marriages Series
Outback Man Seeks Wife (2007)
Cattle Rancher, Convenient Wife (2007)

Barons of the Outback Series Multi-Author
Wedding At Wangaree Valley (2008)
Bride At Briar's Ridge (2008)

Family Ties Multi-Author
Once Burned (1995)

Hitched! Multi-Author
A Faulkner Possession (1996)

Simply the Best Multi-Author
Georgia and the Tycoon (1997)

The Big Event Multi-Author
Beresford's Bride (1998)

Guardian Angels Multi-Author
Gabriel's Mission (1998)

Australians Series Multi-Author
7  Her Outback Man (1998)
17  Master of Maramba (2001)
19  Outback Fire (2001)
22  Mistaken Mistress (2002)
24  Outback Angel (2002)
33  The Australian Tycoon's Proposal (2004)
35  His Heiress Wife (2004)

Marrying the Boss Series Multi-Author
Boardroom Proposal (1999)

Contract Brides Series Multi-Author
Strategy for Marriage (2002)

Everlasting Love Series Multi-Author
Hidden Legacy (2008)

Diamond Brides Series Multi-Author
The Australian's Society Bride (2008)

Collections
Summer Magic / Ring of Jade / Noonfire (1981)
Wife at Kimbara / Bridesmaid's Wedding (2005)

Omnibus in Collaboration
Pretty Witch / Without Any Amazement / Storm Over Mandargi (1977) (with Lucy Gillen and Margaret Malcolm)
Dear Caliban / Heart of the Eagle / Swans' Reach (1978) (with Jane Donnelly and Elizabeth Graham)
The Bonds of Matrimony / Dragon Island / Reeds of Honey (1979) (with Elizabeth Hunter and Henrietta Reid)
The Man Outside / Castles in Spain / McCabe's Kingdom (1979) (with Jane Donnelly and Rebecca Stratton)
Winds From The Sea / Island of Darkness / Wind River (1979) (with Margaret Pargeter and Rebecca Stratton)
Moorland Magic / Tree of Idleness / Sweet Sundown (1980) (with Elizabeth Ashton and Elizabeth Hunter)
The Shifting Sands / Portrait of Jaime / Touched by Fire (1982) (with Jane Donnelly and Kay Thorpe)
Head of Chancery / Wild Heart / One-Way Ticket (1986) (with Betty Beaty and Doris Smith)
Heart of the Scorpion / The Winds of Heaven / Sweet Compulsion (1987) (with Janice Gray and Victoria Woolf)
One Brief Sweet Hour / Once More With Feeling / Blue Lotus (1990) (with Jane Arbor and Natalie Sparks)
Marry Me Cowboy (1995) (with Janet Dailey, Susan Fox and Anne McAllister)
Husbands on Horseback (1996) (with Diana Palmer)
Wedlocked (1999) (with Day Leclaire and Anne McAllister)
Mistletoe Magic (1999) (with Betty Neels and Rebecca Winters)
The Australians (2000) (with Helen Bianchin and Miranda Lee)
Weddings Down Under (2001) (with Helen Bianchin and Jessica Hart)
Outback Husbands (2002) (with Marion Lennox)
The Mother's Day Collection (2002) (with Helen Dickson and Kate Hoffmann)
Australian Nights (2003) (with Miranda Lee)
Outback Weddings (2003) (with Barbara Hannay)
Australian Playboys (2003) (with Helen Bianchin and Marion Lennox)
Australian Tycoons (2004) (with Emma Darcy and Marion Lennox)
A Mother's Day Gift (2004) (with Anne Ashley and Lucy Monroe)
White Wedding (2004) (with Judy Christenberry and Jessica Steele)
A Christmas Engagement (2004) (with Sara Craven and Jessica Matthews)
A Very Special Mother's Day (2005) (with Anne Herries)
All I Want for Christmas    (2005) (with Betty Neels and Jessica Steele)
The Mills and Boon Collection (2006) (with Caroline Anderson and Penny Jordan)
Outback Desire (2006) (with Emma Darcy and Carol Marinelli)
To Mum, with Love (2006) (with Rebecca Winters)
Australian Heroes (2007) (with Marion Lennox and Fiona McArthur)
Tall, Dark and Sexy (2008) (with Caroline Anderson and Helen Bianchin)
The Boss's Proposal (2008) (with Jessica Steele and Patricia Thayer)
Island Heat / Outback Man Seeks Wife / Prince's Forbidden Virgin / One Night Before Marriage / Their Lost-and-found Family / Single Dad's Marriage Wish (2008) (with Robyn Donald, Marion Lennox, Carol Marinelli, Sarah Mayberry and Anne Oliver)
Australian Billionaires (2009) (with Jennie Adams and Amy Andrews)
Cattle Baron : Nanny Needed / Bachelor Dad on Her Doorstep (2009) (with Michelle Douglas)

External links
Margaret Way at Harlequin Enterprises Ltd

Australian romantic fiction writers
Australian women novelists
Living people
Year of birth missing (living people)
Women romantic fiction writers



ground_truth: Bigger receptive field size leads to more successful shape completion.

prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: What is the significance of the interlayer Berry connection polarizability?

Read the following text and answer briefly.

Context 2: Paper Info

Title: Crossed Nonlinear Dynamical Hall Effect in Twisted Bilayers
Publish Date: 17 Mar 2023
Author List: 

Figure

FIG  1 (a) Schematics of experimental setup (b, c) Valence band structure and intrinsic Hall conductivity with respect to in-plane input for tMoTe2 at twist angles (b) θ = 1 2 • and (c) θ = 2 • in +K valley Color coding in (b) and (c) denotes the layer composition σ z n (k) 
FIG  2  (a) The interlayer BCP G, and (b) its vorticity [∂ k × G]z on the first valence band from +K valley of 1 2 • tMoTe2 Background color and arrows in (a) denote the magnitude and vector flow, respectively Grey curves in (b) show energy contours at 1/2 and 3/4 of the band width The black dashed arrow denotes direction of increasing hole doping level Black dashed hexagons in (a, b) denote the boundary of moiré Brillouin zone (mBZ) 
FIG  3  (a-c) Three high-symmetry stacking registries for tBG with a commensurate twist angle θ = 21 8 •  Lattice geometries with rotation center on an overlapping atomic site (a, b) and hexagonal center (c) (d) Schematic of the moiré pattern when the twist angle slightly deviates from 21 8 • , here θ = 21 •  Red squares marked by A, B and C are the local regions that resemble commensurate 21 8 • patterns in (a), (b) and (c), respectively (e, f) Low-energy band structures and intrinsic Hall conductivity of the two geometries [(a) and (b) are equivalent] The shaded areas highlight energy windows ∼ ω around band degeneracies where interband transitions, not considered here, may quantitatively affect the conductivity measured 
FIG  S4 Band structure and layer composition σ z n in +K valley of tBG (left panel) and the intrinsic Hall conductivity (right panel) at three different twist angle θ The shaded areas highlight energy windows ∼ ω around band degeneracies in which the conductivity results should not be considered Here σH should be multiplied by a factor of 2 accounting for spin degeneracy 

abstract

We propose an unconventional nonlinear dynamical Hall effect characteristic of twisted bilayers  The joint action of in-plane and out-of-plane ac electric fields generates Hall currents j ∼ Ė⊥ × E in both sum and difference frequencies, and when the two orthogonal fields have common frequency their phase difference controls the on/off, direction and magnitude of the rectified dc Hall current 
This novel intrinsic Hall response has a band geometric origin in the momentum space curl of interlayer Berry connection polarizability, arising from layer hybridization of electrons by the twisted interlayer coupling  The effect allows a unique rectification functionality and a transport probe of chiral symmetry in bilayer systems 
We show sizable effects in twisted homobilayer transition metal dichalcogenides and twisted bilayer graphene over broad range of twist angles  Nonlinear Hall-type response to an in-plane electric field in a two dimensional (2D) system with time reversal symmetry has attracted marked interests   Intensive studies have been devoted to uncovering new types of nonlinear Hall transport induced by quantum geometry and their applications such as terahertz rectification and magnetic information readout  
Restricted by symmetry , the known mechanisms of nonlinear Hall response in quasi-2D nonmagnetic materials are all of extrinsic nature, sensitive to fine details of disorders , which have limited their utilization for practical applications  Moreover, having a single driving field only, the effect has not unleashed the full potential of nonlinearity for enabling controlled gate in logic operation, where separable inputs (i e , in orthogonal directions) are desirable 
The latter, in the context of Hall effect, calls for control by both out-of-plane and in-plane electric fields  A strategy to introduce quantum geometric response to out-of-plane field in quasi-2D geometry is made possible in van der Waals (vdW) layered structures with twisted stacking   Taking homobilayer as an example, electrons have an active layer degree of freedom that is associated with an out-of-plane electric dipole , whereas interlayer quantum tunneling rotates this pseudospin about in-plane axes that are of topologically nontrivial textures in the twisted landscapes  
Such layer pseudospin structures can underlie novel quantum geometric properties when coupled with out-ofplane field  Recent studies have found layer circular photogalvanic effect and layer-contrasted time-reversaleven Hall effect , arising from band geometric quantities  In this work we unveil a new type of nonlinear Hall effect in time-reversal symmetric twisted bilayers, where an intrinsic Hall current emerges under the combined action of an in-plane electric field E and an out-of-plane ac field E ⊥ (t): j ∼ Ė⊥ × E [see Fig  ] 
Having the two driving fields (inputs) and the current response (output) all orthogonal to each other, the effect is dubbed as the crossed nonlinear dynamical Hall effect  This is also the first nonlinear Hall contribution of an intrinsic nature in nonmagnetic materials without external magnetic field, determined solely by the band structures, not relying on extrinsic factors such as disorders and relaxation times 
The effect arises from the interlayer hybridization of electronic states under the chiral crystal symmetry characteristic of twisted bilayers, and has a novel band geometric origin in the momentum space curl of interlayer Berry connection polarizability (BCP)  Having two driving fields of the same frequency, a dc Hall current develops, whose on/off, direction and magnitude can all be controlled by the phase difference of the two fields, which does not affect the magnitude of the double-frequency component 
Such a characteristic tunability renders this effect a unique approach to rectification and transport probe of chiral bilayers  As examples, we show sizable effects in small angle twisted transition metal dichalcogenides (tTMDs) and twisted bilayer graphene (tBG), as well as tBG of large angles where Umklapp interlayer tunneling dominates 
Geometric origin of the effect  A bilayer system couples to in-plane and out-of-plane driving electric fields in completely different ways  The in-plane field couples to the 2D crystal momentum, leading to Berry-phase effects in the 2D momentum space   In comparison, the outof-plane field is coupled to the interlayer dipole moment p in the form of −E ⊥ p, where p = ed 0 σz with σz as the Pauli matrix in the layer index subspace and d 0 the interlayer distance 
When the system has a more than twofold rotational axis in the z direction, as in tBG and tTMDs, any in-plane current driven by the out-of-plane field alone is forbidden  It also prohibits the off-diagonal components of the symmetric part of the conductivity tensor σ ab = ∂j a /∂E ||,b with respect to the in-plane input and output 
Since the antisymmetric part of σ ab is not allowed by the Onsager reciprocity in nonmagnetic systems, all the off-diagonal components of σ ab is forbidden, irrespective of the order of out-of-plane field  On the other hand, as we will show, an in-plane Hall conductivity σ xy = −σ yx can still be driven by the product of an in-plane field and the time variation rate of an outof-plane ac field, which is a characteristic effect of chiral bilayers 
To account for the effect, we make use of the semiclassical theory   The velocity of an electron in a bilayer system is given by where k is the 2D crystal momentum  Here and hereafter we suppress the band index for simplicity, unless otherwise noted  The three contributions in this equation come from the band velocity, the anomalous velocities induced by the k -space Berry curvature Ω k and by the hybrid Berry curvature Ω kE ⊥ in the (k, E ⊥ ) space 
For the velocity at the order of interest, the k-space Berry curvature is corrected to the first order of the variation rate of out-of-plane field Ė⊥ as Here A = u k |i∂ k |u k is the unperturbed k-space Berry connection, with |u k being the cell-periodic part of the Bloch wave, whereas is its gauge invariant correction , which can be identified physically as an in-plane positional shift of an electron induced by the time evolution of the out-of-plane field 
For a band with index n, we have whose numerator involves the interband matrix elements of the interlayer dipole and velocity operators, and ε n is the unperturbed band energy  Meanwhile, up to the first order of in-plane field, the hybrid Berry curvature reads Here A E || is the k-space Berry connection induced by E || field , which represents an intralayer positional shift and whose detailed expression is not needed for our purpose 
and is its first order correction induced by the in-plane field  In addition, ε = ε + δε, where δε = eE • G Ė⊥ is the field-induced electron energy   Given that A E || is the E ⊥ -space counterpart of intralayer shift A E || , and that E ⊥ is conjugate to the interlayer dipole moment, we can pictorially interpret A E || as the interlayer shift induced by in-plane field 
It indeed has the desired property of flipping sign under the horizontal mirror-plane reflection, hence is analogous to the so-called interlayer coordinate shift introduced in the study of layer circular photogalvanic effect , which is nothing but the E ⊥ -space counterpart of the shift vector well known in the nonlinear optical phenomenon of shift current 
Therefore, the E ⊥ -space BCP eG/ can be understood as the interlayer BCP  This picture is further augmented by the connotation that the interlayer BCP is featured exclusively by interlayer-hybridized electronic states: According to Eq  ( ), if the state |u n is fully polarized in a specific layer around some momentum k, then G (k) is suppressed 
With the velocity of individual electrons, the charge current density contributed by the electron system can be obtained from where [dk] is shorthand for n d 2 k/(2π) 2 , and the distribution function is taken to be the Fermi function f 0 as we focus on the intrinsic response  The band geometric contributions to ṙ lead to a Hall current
where is intrinsic to the band structure  This band geometric quantity measures the k-space curl of the interlayer BCP over the occupied states, and hence is also a characteristic of layer-hybridized electronic states  Via an integration by parts, it becomes clear that χ int is a Fermi surface property 
Since χ int is a time-reversal even pseudoscalar, it is invariant under rotation, but flips sign under space inversion, mirror reflection and rotoreflection symmetries  As such, χ int is allowed if and only if the system possesses a chiral crystal structure, which is the very case of twisted bilayers  
Moreover, since twisted structures with opposite twist angles are mirror images of each other, whereas the mirror reflection flips the sign of χ int , the direction of Hall current can be reversed by reversing twist direction  Hall rectification and frequency doubling  This effect can be utilized for the rectification and frequency doubling of an in-plane ac input E = E 0 cos ωt, provided that the out-of-plane field has the same frequency, namely E ⊥ = E 0 ⊥ cos (ωt + ϕ) 
The phase difference ϕ between the two fields plays an important role in determining the Hall current, which takes the form of j = j 0 sin ϕ + j 2ω sin(2ωt + ϕ)  ( Here ω is required to be below the threshold for direct interband transition in order to validate the semiclassical treatment, and σ H has the dimension of conductance and quantifies the Hall response with respect to the in-plane input 
In experiment, the Hall output by the crossed nonlinear dynamic Hall effect can be distinguished readily from the conventional nonlinear Hall effect driven by in-plane field alone, as they are odd and even, respectively, in the inplane field  One notes that while the double-frequency component appears for any ϕ, the rectified output is allowed only if the two crossed driving fields are not in-phase or antiphase 
Its on/off, chirality (right or left), and magnitude are all controlled by the phase difference of the two fields  Such a unique tunability provides not only a prominent experimental hallmark of this effect, but also a controllable route to Hall rectification  In addition, reversing the direction of the out-of-plane field switches that of the Hall current, which also serves as a control knob 
Application to tTMDs  We now study the effect quantitatively in tTMDs, using tMoTe 2 as an example (see details of the continuum model in )  For illustrative purposes, we take ω/2π = 0 1 THz and E 0 ⊥ d 0 = 10 mV in what follows  Figures ) and (c) present the electronic band structures along with the layer composition σ z n (k) at twist angles θ = 1 2 • and θ = 2 •  
In both cases, the energy spectra exhibit isolated narrow bands with strong layer hybridization  At θ = 1 2 • , the conductivity shows two peaks ∼ 0 1e 2 /h at low energies associated with the first two valence bands  The third band does not host any sizable conductivity signal  At higher hole-doping levels, a remarkable conductivity peak ∼ e 2 /h appears near the gap separating the fourth and fifth bands 
At θ = 2 • , the conductivity shows smaller values, but the overall trends are similar: A peak ∼ O(0 01)e 2 /h appears at low energies, while larger responses ∼ O(0 1)e 2 /h can be spotted as the Fermi level decreases  One can understand the behaviors of σ H from the interlayer BCP in Eq  ( )  It favors band near-degeneracy regions in k -space made up of strongly layer hybridized electronic states 
As such, the conductivity is most pro- nounced when the Fermi level is located around such regions, which directly accounts for the peaks of response in Fig  that [∂ k × G] z is negligible at lower energies, and it is dominated by positive values as the doping increases, thus the conductivity rises initially 
When the doping level is higher, regions with [∂ k × G] z < 0 start to contribute, thus the conductivity decreases after reaching a maximum  Application to tBG  The second example is tBG  We focus on commensurate twist angles in the large angle limit in the main text , which possess moiré-lattice assisted strong interlayer tunneling via Umklapp processes  
This case is appealing because the Umklapp interlayer tunneling is a manifestation of discrete translational symmetry of moiré superlattice, which is irrelevant at small twist angles and not captured by the continuum model but plays important roles in physical contexts such as higher order topological insulator and moiré excitons  
The Umklapp tunneling is strongest for the commensurate twist angles of θ = 21 8 • and θ = 38 2 • , whose corresponding periodic moiré superlattices have the smallest lattice constant ( √ 7 of the monolayer counterpart)  Such a small moiré scale implies that the exact crystalline symmetry, which depends sensitively on fine details of rotation center, has critical influence on lowenergy response properties 
To capture the Umklapp tunneling, we employ the tight-binding model   Figures ) and (c) show two distinct commensurate structures of tBG at θ = 21 8 • belonging to chiral point groups D 3 and D 6 , respectively  The atomic configurations in Figs  ) are equivalent, which are constructed by twisting AA-stacked bilayer graphene around an overlapping atom site, and that in Fig  ) is obtained by rotating around a hexagonal center 
Band structures of these two configurations are drastically different within a low-energy window of ∼ 10 meV around the κ point   Remarkably, despite large θ, we still get σ H ∼ O(0 001) e 2 /h (D 3 ) and ∼ O(0 1) e 2 /h (D 6 ), which are comparable to those at small angles (cf  Fig  in the Supplemental Material ) 
Such sizable responses can be attributed to the strong interlayer coupling enabled by Umklapp processes   Apart from different intensities, the Hall conductivities in the two stacking configurations have distinct energy dependence: In Fig  , σ H shows a single peak centered at zero energy; In Fig  (f), it exhibits two antisymmetric peaks around zero 
The peaks are centered around band degeneracies, and their profiles can be understood from the distribution of [∂ k × G] z   Figure (d) illustrates the atomic structure of tBG with a twist angle slightly deviating from θ = 21 8 • , forming a supermoiré pattern  In short range, the local stacking geometries resemble the commensurate configurations at θ = 21 8 • , while the stacking registries at different locales differ by a translation 
Similar to the moiré landscapes in the small-angle limit, there also exist high-symmetry locales: Regions A and B enclose the D 3 structure, and region C contains the D 6 configuration  Position-dependent Hall response is therefore expected in such a supermoiré  As the intrinsic Hall signal from the D 6 configuration dominates [see Figs 
3(e) vs (f)], the net response mimics that in Fig    Discussion  We have uncovered the crossed nonlinear dynamical intrinsic Hall effect characteristic of layer hybridized electronic states in twisted bilayers, and elucidated its geometric origin in the k -space curl of interlayer BCP  It offers a new tool for rectification and frequency doubling in chiral vdW bilayers, and is sizable in tTMD and tBG 
Here our focus is on the intrinsic effect, which can be evaluated quantitatively for each material and provides a benchmark for experiments  There may also be extrinsic contributions, similar to the side jump and skew scattering ones in anomalous Hall effect  They typically have distinct scaling behavior with the relaxation time τ from the intrinsic effect, hence can be distinguished from the latter in experiments  
Moreover, they are suppressed in the clean limit ωτ 1 [(ωτ ) 2 1, more precisely]   In high-quality tBG samples, τ ∼ ps at room temperature   Much longer τ can be obtained at lower temperatures  In fact, a recent theory explaining well the resistivity of tBG predicted τ ∼ 10 −8 s at 10 K   As such, high-quality tBG under low temperatures and sub-terahertz input (ω/2π = 0 1 THz) is located in the clean limit, rendering an ideal platform for isolating the intrinsic effect 
This work paves a new route to driving in-plane response by out-of-plane dynamical control of layered vdW structures   The study can be generalized to other observables such as spin current and spin polarization, and the in-plane driving can be statistical forces, like temperature gradient  Such orthogonal controls rely critically on the nonconservation of layer pseudospin degree of freedom endowed by interlayer coupling, and constitute an emerging research field at the crossing of 2D vdW materials, layertronics, twistronics and nonlinear electronics 
This work is supported by the Research Grant Council of Hong Kong (AoE/P-701/20, HKU SRFS2122-7S05), and the Croucher Foundation  W Y  also acknowledges support by Tencent Foundation  Cong Chen, 1, 2, * Dawei Zhai, 1, 2, * Cong Xiao, 1, 2, † and Wang Yao 1, 2, ‡ 1 Department of Physics, The University of Hong Kong, Hong Kong, China 2 HKU-UCAS Joint Institute of Theoretical and Computational Physics at Hong Kong, China Extra figures for tBG at small twist angles Figure (a) shows the band structure of tBG with θ = 1 47 • obtained from the continuum model  
The central bands are well separated from higher ones, and show Dirac points at κ/κ points protected by valley U (1) symmetry and a composite operation of twofold rotation and time reversal C 2z T   Degeneracies at higher energies can also be identified, for example, around ±75 meV at the γ point  As the two Dirac cones from the two layers intersect around the same area, such degeneracies are usually accompanied by strong layer hybridization [see the color in the left panel of Fig  ] 
Additionally, it is well-known that the two layers are strongly coupled when θ is around the magic angle (∼ 1 08 • ), rendering narrow bandwidths for the central bands  As discussed in the main text, coexistence of strong interlayer hybridization and small energy separations is expected to contribute sharp conductivity peaks near band degeneracies, as shown in Fig   
In this case, the conductivity peak near the Dirac point can reach ∼ 0 1e 2 /h, while the responses around ±0 08 eV are smaller at ∼ 0 01e 2 /h  The above features are maintained when θ is enlarged, as illustrated in Figs  ) and (c) using θ = 2 65 • and θ = 6 01 •   Since interlayer coupling becomes weaker and the bands are more separated at low energies when θ increases, intensity of the conductivity drops significantly 
We stress that G is not defined at degenerate points, and interband transitions may occur when energy separation satisfies |ε n − ε m | ∼ ω, the effects of which are not included in the current formulations  Consequently, the results around band degeneracies within energy ∼ ω [shaded areas in Fig  ] should be excluded 



ground_truth: The momentum space curl of the interlayer Berry connection polarizability generates the crossed nonlinear dynamical Hall effect.

prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: Where was Margaret Way born and where did she die?

Read the following text and answer briefly.

Context 4:  On May 7, 1998, former SEC Chairman Arthur Levitt joined Rubin and Greenspan in objecting to the issuance of the CFTC's concept release  Their response dismissed Born's analysis and focused on the hypothetical possibility that CFTC regulation of swaps and other OTC derivative instruments could create a "legal uncertainty" regarding such financial instruments,  hypothetically reducing the value of the instruments  They argued that the imposition of regulatory costs would "stifle financial innovation" and encourage financial capital to transfer its  transactions offshore  The disagreement between Born and the Executive Office's top economic policy advisors has been described not only as a classic Washington turf war, but also a war of ideologies,  insofar as it is possible to argue that Born's actions were consistent with Keynesian and neoclassical economics while Greenspan, Rubin, Levitt, and Summers consistently espoused neoliberal, and neoconservative policies 

In 1998, a trillion-dollar hedge fund called Long Term Capital Management (LTCM) was near collapse   Using mathematical models to calculate debt risk, LTCM used derivatives to leverage $5 billion into more than $1 trillion, doing business with fifteen of Wall Street's largest financial institutions   The derivative transactions were not regulated, nor were investors able to evaluate LTCM's exposures   Born stated, "I thought that LTCM was exactly what I had been worried about"   In the last weekend of September 1998, the President's working group was told that the entire American economy hung in the balance   After intervention by the Federal Reserve, the crisis was averted   In congressional hearings into the crisis, Greenspan acknowledged that language had been introduced into an agriculture bill that would prevent CFTC from regulating the derivatives which were at the center of the crisis that threatened the US economy   U S  Representative Maurice Hinchey (D-NY) asked "How many more failures do you think we'd have to have before some regulation in this area might be appropriate?"  In response, Greenspan brushed aside the substance of Born's warnings with the simple assertion that "the degree of supervision of regulation of the over-the-counter derivatives market is quite adequate to maintain a degree of stability in the system"  Born's warning was that there wasn't any regulation of them   Born's chief of staff, Michael Greenberger summed up Greenspan's position this way: "Greenspan didn't believe that fraud was something that needed to be enforced, and he assumed she probably did  And of course, she did "  Under heavy pressure from the financial lobby, legislation prohibiting regulation of derivatives by Born's agency was passed by the Congress   Born resigned on June 1, 1999 

The derivatives market continued to grow yearly throughout both terms of George W  Bush's administration  On September 15, 2008, the bankruptcy of Lehman Brothers forced a broad recognition of a financial crisis in both the US and world capital markets   As Lehman Brothers' failure temporarily reduced financial capital's confidence, a number of newspaper articles and television programs suggested that the failure's possible causes included the conflict between the CFTC and the other regulators Faiola, Anthony, Nakashima, Ellen and Drew, Jill  The Crash: Risk and Regulation - What Went Wrong, The Washington Post, October 15, 2008 

Born declined to publicly comment on the unfolding 2008 crisis until March 2009, when she said: "The market grew so enormously, with so little oversight and regulation, that it made the financial crisis much deeper and more pervasive than it otherwise would have been " She also lamented the influence of Wall Street lobbyists on the process and the refusal of regulators to discuss even modest reforms 

An October 2009 Frontline documentary titled "The Warning"  described Born's thwarted efforts to regulate and bring transparency to the derivatives market, and the continuing opposition thereto  The program concluded with an excerpted interview with Born sounding another warning: "I think we will have continuing danger from these markets and that we will have repeats of the financial crisis -- may differ in details but there will be significant financial downturns and disasters attributed to this regulatory gap, over and over, until we learn from experience "

In 2009 Born, along with Sheila Bair of the FDIC, was awarded the John F  Kennedy Profiles in Courage Award in recognition of the "political courage she demonstrated in sounding early warnings about conditions that contributed" to the 2007-08 financial crisis   According to Caroline Kennedy, "Brooksley Born recognized that the financial security of all Americans was being put at risk by the greed, negligence and opposition of  powerful and well connected interests     The catastrophic financial events of recent months have  proved them [Born and Sheila Bair] right "  One member of the President's working group had a change of heart about Brooksley Born   SEC Chairman Arthur Levitt stated "I've come to know her as one of the most capable, dedicated, intelligent and committed public servants that I have ever come to know", adding that "I could have done much better  I could have made a difference" in response to her warnings 

In 2010, a documentary film Inside Job further alleged that derivatives regulation was ineffective from the Clinton administration on  Along with fellow whistleblower, former IMF Chief Economist Raghuram Rajan, who was also scorned by the economic establishment, Brooksley Born was cited as one of the authorities arguing that financial derivatives increase economic risk 

 Personal life 
Born is married to Alexander E  Bennett (also retired from Arnold & Porter)   She has five adult children - two from a previous marriage to Jacob Landau and three stepchildren  Notably, Born was named a partner at Arnold & Porter while working part-time so she could raise her two young children   When both of her children were school-age, Born returned to practice full-time 

References

External links
Attorney profile at Arnold & Porter
Brooksley Born (2009 Winner) of the Profiles in Courage Award, with acceptance speech transcript and NECN video

Profile at MarketsWiki
Speeches and statements
"Testimony Of Brooksley Born Chairperson of the CFTC Concerning The Over-The-Counter Derivatives Market", before the House Committee On Banking And Financial Services, July 24, 1998 
"The Lessons of Long Term Capital Management L P ", Remarks of Brooksley Born, Chairperson of the CFTC, Chicago-Kent-IIT Commodities Law Institute, Chicago, Illinois, October 15, 1998 
 Interview: Brooksley Born for "PBS Frontline: The Warning", PBS, (streaming VIDEO 1 hour), October 20, 2009 
Articles
Manuel Roig-Franzia  "Credit Crisis Cassandra:Brooksley Born's Unheeded Warning Is a Rueful Echo 10 Years On", The Washington Post, May 26, 2009
 Taibbi, Matt  "The Great American Bubble Machine", Rolling Stone'', July 9–23, 2009

1940 births
American women lawyers
Arnold & Porter people
Clinton administration personnel
Columbus School of Law faculty
Commodity Futures Trading Commission personnel
Heads of United States federal agencies
Lawyers from San Francisco
Living people
Stanford Law School alumni
21st-century American women
Stanford University alumni 



ground_truth: Margaret Way was born in Brisbane and died in Cleveland, Queensland, Australia.