text:
\section{Introduction}
\label{sec:intro}
Cancer is a condition of unrestricted cell growth in the human body and is among the deadliest diseases of the world. In 2018, cancer claimed 9.6 million lives globally, $70\%$ of which are from low and middle-income countries (LMIC) \citep{ref1}. Of the different types of cancer, acute lymphoblastic leukemia (ALL)  is pervasive childhood cancer that occurs due to the excessive generation of immature white blood cell (WBC) blasts in the bone marrow.   Although prompt diagnosis is a critical factor in cancer survival, LMIC suffer on this account due to the lack of costly infrastructure, trained human resources, and diagnostic tools at the required scale. Hence, these countries experience higher fatality rates. For example, $84\%$ of cases of ALL are reported from LMIC \citep{ref2}.

Preliminary diagnostic tests of ALL are based on the count and appearance of blood cells. For example, \textit{complete blood count} (CBC) makes a diagnosis based on cell count, while \textit{peripheral blood smear} test examines the appearance of cells in the blood. Bone marrow based tests such as \textit{bone marrow biopsy} and \textit{bone marrow aspiration} are crucial in ALL diagnosis and analyze bone marrow to evaluate the symptoms of leukemia. Higher accuracy tests for the identification of leukemia include \textit{cytochemistry}, \textit{immunohistochemistry}, and \textit{flow cytometry} that are based on the reaction of staining chemicals with the proteins of blood cells. Imaging tests such as X-rays, computed tomography (CT) scan, magnetic resonance imaging (MRI) scan, and ultrasound are not useful for ALL detection, but they help with the analysis of the overall impact of cancer on the body \citep{ref3}.

All these methods are time-intensive, require costly medical equipment, and trained medical professionals. Owing to these requirements, these tools cannot be deployed easily at a large scale, especially in rural areas. Computer-aided tools based on microscopic image analysis can overcome these limitations because these can be fully automated and do not require highly trained medical professionals to run the tests.

Several machine learning-based computer-aided ALL diagnosis methods have been presented over the last few years \citep{Mohapatra2011,Monica2012,Joshi2013,ref9,Mohapatra2014,Chatap2014,SiewChin2015,Carolina2015,Vincent2015,PATEL2015,ref10,ref11,MoradiAmin2016,Singhal2016,ref58,RAWAT2017,Mishra2017,Karthikeyan2017,MISHRA2019}.  All these methods utilize a predefined set of features based on the structure of the nucleus or cytoplasm of the cells to train classifiers such as na\"{i}ve Bayes, decision tree, support vector machine (SVM), random forest, and the ensemble of classifiers for the diagnosis of ALL. A significant drawback of these methods is the use of tiny datasets (consisting of 19 to 267 images only) for building the classifiers. A classifier trained on a small dataset is prone to overfitting and hence, may not perform satisfactorily on the prospective subjects' samples. Also, the performance reported on a small test set may be biased.
Another limitation of these methods stems from the utilization of predefined/hand-crafted features that may not always be the optimized set of features. All these factors can limit the performance of the classifier on deployment in a real-life setting. These limitations can be overcome by using a larger dataset for building a classifier and by utilizing an automated mechanism to extract the features.

Convolutional neural network (CNN) is a deep learning architecture consisting of two-dimensional convolutional filters that can check the limitation of predefined features by extracting task-specific features from the raw data through the minimization of a targeted loss function. In medical applications, CNNs are frequently used for classification \citep{ref22}, localization \citep{ref23}, detection \citep{ref24}, segmentation \citep{ref25}, and registration \citep{ref26}. In the recent past, numerous works have utilized CNNs for cancer classification. However, CNNs demand large training datasets that are generally not available in medical applications.

Transfer learning (TL) is a common approach to counter the data deficiency problem. In TL, an architecture, pre-trained on a larger dataset for one application, is used in another related but data-deficient task. \cite{ref32} have highlighted the limitation of a small dataset in medical applications and the benefits of transfer learning in computer-aided detection.  A similar analysis has been presented by \cite{ref38} for nuclei classification in colorectal adenocarcinoma histopathology images. It is also emphasized that the depth of a pre-trained architecture and source data distribution impact performance in transfer learning. Similarly, \cite{ref40} and \cite{ref41} used transfer learning approach for the classification of HEp-2 cells, \cite{ref33} for lesion detection in mammograms, \cite{ref29} for cervical cell image classification, \cite{ref36} for skin cancer classification, and \cite{ref37} for the classification of histopathology images of brain tumor.

On a similar note, \cite{ref59} and \cite{ref60} employed a pretrained AlexNet for the prediction of different subtypes of ALL. \cite{Vogado2017} used a pretrained VGG-F architecture for feature extraction followed by PCA for features selection, and an ensemble of classifiers for the diagnosis of ALL. A similar methodology is adapted by \cite{Vogado2018}, wherein a pretrained CNN is used as a feature extractor followed by a feature selection mechanism, and an SVM for the classification of leukocytes. Again, a major downside of these methods is the utilization of small datasets for fine-tuning or evaluation purposes. For example, the datasets consist of only 310 images \citep{ref59}, 330 images \citep{ref60}, 108 images \citep{Vogado2017}, and 891 images \citep{Vogado2018}. Performance with such small datasets cannot be considered as the true performance indicator which can limit their deployment in practical scenarios. Also, the use of pre-trained architectures in medical applications require resizing of input images to the predefined input shape of these networks that may alter the morphology of input images impacting the performance of classifiers. Also, these architecture are designed to perform on a 1000-class ImageNet dataset of non-medical images. Such methods may not be suitable in medical applications for two reasons: 1) these are not trained on medical images, and 2) medical applications have, in general, relatively fewer classes.

In our previous work \citep{ref45}, we used a large dataset with 13407 cell images for ALL diagnosis and proposed a trainable stain deconvolutional layer (SD-Layer) at the front end of the CNN. The input RGB images were first transformed to the optical density (OD) space followed by stain color deconvolution to obtain stain quantity images. It was envisaged that the texture of stain quantity images captures the sub-microscopic cellular features, and hence, a CNN trained on these images would perform better compared to the one trained on RGB images.
Indeed this architecture worked better with a CNN trained from scratch as compared to pre-trained architectures.

However, one of the most significant drawbacks was that the training data was not separated at the subject-level. The classifier was trained by pooling cell images of all the subjects into the respective
normal and cancer class. This pooling limited the performance of the classifier on prospective subjects' data because subject-specific characteristics
also aid in class discrimination.  Moreover, in real life, sample cell images of new subjects are never available apriori for training. Thus, a realistic classifier would require training on some subjects' data and testing on completely unseen subjects' data.

Hence, cell images were segmented again and the dataset was prepared in a curated manner by the expert oncologist at the subject-level with no intersection between the training subject-set and testing subject-set data. This strategy ensured that none of the cell images of a subject in the test data was used for training the classifier. This dataset is named C-NMC 2019 dataset \citep{ref49} and is publicly available at The Cancer Imaging Archive (TCIA). The dataset consists of a total of 15114 images collected from 118 subjects. As compared to the existing ALL datasets, C-NMC 2019 dataset contains a significantly large number of images that can prove helpful for developing a robust and deployable ALL diagnostic classifier.

In this paper, a novel deep learning architecture is proposed to differentiate malignant (cancer) immature  WBCs from normal (healthy) immature WBCs for computer-aided diagnosis of ALL. Instead of using transfer learning with a CNN architecture pre-trained on natural images, a CNN has been trained from scratch, as used by  \cite{ref27,ref34,ref30,ref35,ref45}. Because cell image features may differ widely from those of the natural images, a network trained from scratch on cell images may converge to a better solution . Although C-NMC 2019 dataset is quite large compared to the existing ALL datasets, still larger dataset would be required for training a very deep CNN architecture.  Hence, to curb this limitation, a compact CNN with fewer parameters is utilized. We have also exploited discrete cosine transform (DCT) to improve the classification performance. DCT finds use in numerous image processing applications including
JPEG compression \citep{ref47}, brain tumor classification \citep{ref46}, and face recognition \citep{ref48}. We have used DCT to capture inter-class separability in the frequency domain because images of different classes in this dataset are not visually differentiable in the spatial domain, as can be verified from Fig.~\ref{fig for samples images}.

\begin{figure}[!ht]
\centering
\begin{subfigure}[b]{0.15\textwidth}
\includegraphics[width=1.5cm,height=1.5cm]{all_1.png}
\end{subfigure}
\begin{subfigure}[b]{0.15\textwidth}
\includegraphics[width=1.5cm,height=1.5cm]{all_2.png}
\end{subfigure}
\begin{subfigure}[b]{0.15\textwidth}
\includegraphics[width=1.5cm,height=1.5cm]{all_3.png}
\end{subfigure}
\begin{subfigure}[b]{0.15\textwidth}
\includegraphics[width=1.5cm,height=1.5cm]{all_4.png}
\end{subfigure}

\begin{subfigure}[b]{0.15\textwidth}
\includegraphics[width=1.5cm,height=1.5cm]{hem_1.png}
\end{subfigure}
\begin{subfigure}[b]{0.15\textwidth}
\includegraphics[width=1.5cm,height=1.5cm]{hem_2.png}
\end{subfigure}
\begin{subfigure}[b]{0.15\textwidth}
\includegraphics[width=1.5cm,height=1.5cm]{hem_3.png}
\end{subfigure}
\begin{subfigure}[b]{0.15\textwidth}
\includegraphics[width=1.5cm,height=1.5cm]{hem_4.png}
\end{subfigure}
\captionsetup{justification=centering}
\caption{Sample images of different subjects from the cancer class (first row) and normal class (second row). This figure shows that the cell images are not distinguishable across classes or across subjects.}
\label{fig for samples images}
\end{figure}

Overall, the salient points of this work are as follows:
\begin{enumerate}
    \item A novel deep learning architecture is proposed for the classification of cell images of ALL. The proposed architecture, namely, SDCT-AuxNet$^{\theta}$, is a 2-module framework and is end-to-end trainable. It consists of a compact CNN as the main classifier in one module and a Kernel SVM as the auxiliary classifier in the other one.
    \item The input RGB images are first transformed to the OD space, and then stain color is deconvolved using a trainable stain deconvolutional layer (SD-Layer) appended at the front-end of the CNN to obtain stain quantity images. The texture of stain quantity images captures the sub-microscopic cellular features. Hence, a compact CNN trained on stain-deconvolved images in the OD space is envisaged to perform comparable or better than a deeper CNN trained on raw RGB images, overcoming the need of a big training dataset.
    \item A DCT layer is used immediately after the SD-layer in the proposed CNN. The inspiration for training on the DCT features is derived from the fact that, conventionally, the spectroscopy-based method, namely flow cytometry, is used for ALL diagnosis.
       \item While the CNN classifier utilizes features via bilinear pooling employed before the fully connected layer, averaging across feature maps (spectral averaging) is used to create features for the auxiliary classifier. Bilinear pooling \citep{lin2015bilinear} helps in capturing fine-grained local feature interactions, whereas averaging across feature maps on the same set of input helps in capturing spectral counterpart that is used in parallel by the auxiliary classifier in the proposed architecture. This strategy allows different features to be used by the two classifiers.

    \item A novel test strategy is proposed that exploits both the classifiers for decision making using the confidence scores of their predicted class labels.
\end{enumerate}

Training and testing are carried out on a recently released in-house dataset of ALL cancer of 118 subjects \citep{ref49}. Benchmark in performance is achieved by comparing the results with the highest performance recorded on the leaderboard of the recently conducted challenge on this dataset at IEEE ISBI conference 2019 \citep{ref50}.

\section{Materials}
\vspace{-0.5em}
Microscopic images are captured from the bone marrow aspirate smears of subjects in the raw BMP format with a size of $2560 \times 1920$ pixels. Before imaging, smears are stained using Jenner-Giemsa stain for better visibility of B-type immature white blood cells (WBCs) under the microscope. The images are first normalized for stain color variability across images using the in-house pipeline \citep{ref53,ref57}. Next, cells of interest are marked by expert oncologists. These labeled cells are segmented using the in-house segmentation pipeline \citep{ref54,ref55}. Normal cell images are collected from subjects who did not suffer from cancer, while cancer cell images are obtained from subjects who are initially diagnosed with cancer. A dataset of 118 subjects, 49 healthy and 69 cancer subjects, is prepared at Laboratory Oncology, AIIMS, New Delhi, India. A waiver for written informed consent is obtained from the Ethics Committee of AIIMS, New Delhi, on this dataset for research purposes. One of the co-authors (RG) had access to the subject identifying information which is removed entirely from the image dataset before sharing of data with the other co-authors.

This dataset is publicly available at The Cancer Imaging Archive (TCIA) \citep{ref49} and displayed according to TCIA standard protocols \citep{ref56}. This dataset was also used in the medical imaging challenge, \textit{Classification of Normal vs. Malignant Cells in B-ALL White Blood Cancer Microscopic Images (C-NMC) 2019} \citep{ref50}, organized at IEEE International Symposium on Biomedical Imaging (ISBI), 2019 conference.

Data is prepared at the subject-level and is split into the training set and testing set. Training set consists of 8491 cancer cell images collected from 60 cancer subjects and 4037 normal cell images collected from 41 healthy subjects, with a total of 12528 images \citep{ref50}. This training data of 12528 cells is split into seven-folds for cross-validation, where the splits are created such that each fold contains an approximately equal proportion of images of both the classes. Also, the folds are prepared at the subject-level, i.e., all cells belonging to a subject are placed in the same fold.

Test data contains a total of $2586$ cell images, collected from $9$ cancer subjects and $8$ healthy subjects \citep{ref50}. None of the cell images of these subjects are used for training the classifier and hence, results of the test data are unbiased. A detailed description of the training set and test set is provided in Table~\ref{data description}. Since original cell images are of different sizes, all images are zero-padded such that the centroid of every cell is at the center. After zero-padding, all cell images are made to the size of $350 \times 350$.

\begin{table}[!ht]
\vspace{-.5em}
\begin{small}
\centering
\captionsetup{justification=centering}
\caption{Description of training and test data. \\ Training data is split in seven folds. All cells belonging to a subject are placed in the same fold and no two folds have cell images belonging to the same subject.}
\vspace{-1em}
\label{data description}
\begin{tabular}{|c|c|c|c|c|}
\hline
\multicolumn{5}{|c|}{{\textbf{Training Data}}} \\ \hline
{Fold} & \multicolumn{2}{c|}{{Cancer Class}} & \multicolumn{2}{c|}{{Normal Class}} \\ \hline
{} & {No. of subjects} & {No. of images} & {No. of subjects} & {No. of images} \\ \hline
1 & 13 & 1234 & 9 & 529 \\ \hline
2 & 9 & 1166 & 7 & 546 \\ \hline
3 & 9 & 1269 & 6 & 516 \\ \hline
4 & 6 & 1275 & 4 & 624 \\ \hline
5 & 9 & 1135 & 6 & 618 \\ \hline
6 & 6 & 1197 & 4 & 603 \\ \hline
7 & 8 & 1215 & 5 & 601 \\ \hline
{Total} & {60} & {8491} & {41} & {4037} \\ \hline
\multicolumn{2}{|c|}{{Total no. of subjects}} & 101 & {Total no. of images} & 12528 \\ \hline
\multicolumn{5}{|c|}{{\textbf{Test Data}}} \\ \hline
\multicolumn{3}{|c|}{{Cancer Subjects}} & \multicolumn{2}{c|}{{Healthy Subjects}} \\ \hline
\multicolumn{3}{|c|}{9}  & \multicolumn{2}{|c|}{8}  \\ \hline
\multicolumn{3}{|c|}{{Total no. of subjects}} & \multicolumn{2}{|c|} {{17}} \\ \hline
\multicolumn{3}{|c|}{{Total no. of cell images in the test data}} & \multicolumn{2}{|c|} {2586} \\ \hline
\end{tabular}
\end{small}
\end{table}

\section{Methods}
In this section, the proposed SDCT-AuxNet$^\theta$ architecture and other variants are presented in detail.
\subsection{Base Network} The size of the input dataset is a crucial factor in designing a CNN because an architecture with large learnable parameters is prone to overfitting, while a CNN with too few learnable parameters tends to underfit. Hence, it is essential to design an architecture with an adequate number of tunable parameters. Moreover, transfer learning is not appropriate because all well-known architectures are trained on natural images, while this dataset specifically contains blood cell images. Recently, a compact CNN with fewer parameters was designed on this ALL dataset  \citep{SimmiLeukoNet} as shown in Fig. \ref{base_network}. This architecture has a convolutional layer with stride two at the front-end followed by five convolutional layers with batch-norm, maxpool, and ReLu. \cite{lin2015bilinear} introduced the idea of bilinear pooling, wherein the outer product of the feature vectors obtained through two different CNNs is connected to a common output layer. This idea is adopted in this base network, and the outer product of the feature vector with itself is connected to the classification layer.

The output of bilinear pooling is passed through a linear layer followed by the log-softmax layer. This network is referred to as the \textit{base network}. Here, \textit{base network} is used as the building block in SD-Net architecture as well as in the following proposed architectures. A comparison of the number of learnable parameters of the  \textit{base network} with some well-known architectures used in the transfer learning approach is shown in Table \ref{parameters comparison}. It is evident that the \textit{base Network} has fewer parameters compared to those in the existing architectures. Hence, base network is suitable for this dataset that is, although very large compared to existing public ALL datasets, is still relatively small compared to the ImageNet dataset on which often-used architectures are trained.

\begin{table*}[!t]
\begin{small}
\captionsetup{justification=centering}
\caption{Comparison on the number of learnable parameters. \\
The number of parameters in the \textit{base network} is significantly less as compared to existing architectures used commonly in transfer learning approach.}
\vspace{-1em}
\label{parameters comparison}
\centerline{
\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
{Architecture} & AlexNet & VGG16 & ResNet-18 & DenseNet-161 & Inception-v3 & Base Network \\ \hline
{Parameters} & 61100840 & 138357544 & 11689512 & 28681000 & 27161264 & \textbf{95362} \\ \hline
\end{tabular}%
}
Note: Least number of parameters are specified in bold.
\end{small}
\end{table*}

\begin{figure*}[!t]
\centering
\centerline{
\includegraphics[scale=0.3]
{base_network.pdf}}
\captionsetup{justification=centering}
\caption{Base network. This network is used as the building block in SD-Net as well as in the proposed architectures.}

\label{base_network}
\end{figure*}

\subsection{SD-Net Architecture}
In this architecture, SD-layer \citep{ref45} is stacked at the front-end of the \textit{base network}. It is, hereby, named as SD-Net (refer to Fig.~\ref{SD-Net_model}).  Images obtained from the SD-layer are the stain deconvolved images in the optical density (OD) space that are fed into the \textit{base network}.  The deconvolution of stain in the OD colorspace allows the computation of pixel stain quantities that enable the network to see tissue-specific stain absorption quantities. It has been shown by \cite{ref45} that the introduction of the SD-layer as the first layer leads to better performance of the classifier. Motivated by this, SD-Net utilizes SD-layer at the front-end and hence, works in the OD-space rather than the RGB space.
SD-Net is also used as the baseline classifier in experiments.

\begin{figure*}[!ht]
\centerline{
\includegraphics[scale=0.31]
{SD_Net.pdf}}
\captionsetup{justification=centering}
\caption{SD-Net architecture. SD-layer deconvolves stain color vector in the OD space and provides stain quantity images, i.e., images that contain the quantification of the absorbed stain, a characteristic of the tissue.}

\label{SD-Net_model}
\end{figure*}

\begin{figure}[!ht]
\centerline{
\includegraphics[scale=.7]
{orig_sd_dct.pdf}}
\captionsetup{justification=centering}
\caption{Impact of DCT-layer on the output images of SD-layer. Normal cell images are sparsified more  compared to cancer cell images with the DCT-layer.}

\label{dct output}
\end{figure}

\subsection{Proposed SDCT-Net Architecture}
We build upon the SD-Net to achieve better class discrimination capability. As seen in Fig. \ref{fig for samples images}, images of the two classes are visually indistinguishable. In such a scenario, it is more intuitive to work in another domain that is more helpful in capturing class-specific characteristics. The assumption is that each class would have some distinct properties that can be highlighted by applying a specific transform. For images, one such property is sparsity. A signal $\textbf{x}$ is $r-$ sparse if only $r$ elements are non-zero. In general,  compressibility, which is less strict condition than sparsity, is used frequently. The magnitude of sorted coefficients of a compressible signal decay quickly. Images are generally compressible in the discrete cosine transform (DCT) domain. The famous JPEG compression uses a compression technique based on DCT. This property of compressibility of DCT is used in many other applications, including denoising and compressive sensing based reconstruction \citep{ref52}.

 In general, images have different sparsification levels, depending upon their internal structure. This understanding can be extended to images of different classes as well, i.e., images of different classes will be sparsified differently. To analyze this effect,  we appended a DCT layer after the SD-layer. The output of the DCT-layer is given as:
\begin{equation}
\textbf{D}^j=\text{log}_{10}\big(\textbf{I}+ |\psi(\textbf{Z}^j)|\big),\ \ \ \ \ \ j=0,1,2,
\end{equation}
where $\psi(.)$ denotes the 2D-DCT operator, $\textbf{Z}^j$ denotes the  $j^\text{th}$ feature map input to the DCT layer, and \textbf{I} denotes a matrix with `1' at each position of the matrix. This `1' is added to the DCT output at every pixel before logarithm so that the resulting image \textbf{D} contains only positive quantities. Since the dynamic range of the DCT output image is broad, ``log" acts as the normalization function and allows the contribution from all pixels to be exploited by the following layers.

The feature maps/images obtained at the output of the SD-layer are passed to the above explained DCT-layer. The impact of DCT-layer on these feature maps is shown in Fig.~\ref{dct output}. Interestingly, it is observed that the normal cell images are sparsified more by DCT-layer compared to the cancer cell images. The dynamic range of DCT coefficients of the two classes is also different. This observation can be exploited by the following \textit{base network} to enhance its classification performance. This architecture with DCT layer between the SD-layer and the \textit{base network} is shown in Fig.~\ref{cnn_proposed_model} and is, hereby, named as SDCT-Net.  The size of the input image and feature maps at different layers of SDCT-Net are shown in Table~\ref{output size}. This architecture is a sub-part of the proposed architecture $\text{SDCT-AuxNet}^\theta$, described next.

\begin{figure*}[!ht]
\centering
\centerline{
\includegraphics[scale=0.31]
{SDCT-Net.pdf}}
\captionsetup{justification=centering}
\caption{Proposed SDCT-Net. DCT layer is appended after SD-layer which helps to learn class discriminative features by inducing different sparsity in cancer and normal cell images.}

\label{cnn_proposed_model}
\end{figure*}
\begin{table}[!ht]
\begin{small}
\centering
\caption{Size of input image, filters, and output feature maps at different layers of SDCT-Net}
\vspace{-1em}
\begin{tabular}{c c c c c}
\hline
Layer           & Layer Name & Filter Size & Input Size    & Size of Feature Map Output   \\ \hline
SD-layer & -      & - &$3 \times 350 \times 350$  & $3 \times 350 \times 350$   \\
DCT-layer & -      & - & $3 \times 350 \times 350$  & $3 \times 350 \times 350$   \\
First Conv layer  & C1& $5 \times 5$       & $3 \times 350 \times 350$  & $16 \times 174 \times 174$   \\
Second Conv layer         & C2 & $3 \times 3$       & $16 \times 174 \times 174$ & $16 \times 174 \times 174$    \\
First Pooling         & - & $2 \times 2$       & $16 \times 174 \times 174$ & $16 \times 87 \times 87$    \\
Third Conv layer & C3 & $3 \times 3$       & $16 \times 87 \times 87$ & $32 \times 87 \times 87$     \\
Second Pooling         & -& $2 \times 2$       & $32 \times 87 \times 87$ & $32 \times 43 \times 43$    \\
Fourth Conv layer & C4 & $3 \times 3$       & $32 \times 43 \times 43$   & $48 \times 43 \times 43$  \\
Third Pooling         & -& $2 \times 2$       & $48 \times 43 \times 43$ & $48 \times 21 \times 21$    \\
Fifth Conv layer  & C5& $3 \times 3$       &$ 48 \times 21 \times 21$   & $64 \times 21 \times 21$    \\
Fourth Pooling         &-&  $2 \times 2$       & $64\times 21 \times 21$ & $64 \times 10 \times 10$    \\
Sixth Conv layer &C6&  $3 \times 3$       & $64 \times 10 \times 10$   & $64 \times 10 \times 10$     \\
Bilinear Pooling & -       & $64 \times 10 \times 10$   & $4096\times 1$     \\
Linear          &    -         & $4096\times 1$    & $2\times 1$               \\ \hline
\end{tabular}
\label{output size}
\end{small}
\end{table}

\subsection{Proposed SDCT-AuxNet$^{\theta}$}
Next, we propose a novel framework that consists of SDCT-Net and an additional auxiliary classifier. An overview of this architecture is shown via a block diagram in Fig.~\ref{network subpart}. SDCT-AuxNet$^{\theta}$ has two sub-networks: i) features learning sub-network and ii) classification sub-network. In general, learned features are applied to a neural network after applying some transformations. But, SDCT-AuxNet$^{\theta}$ processes
the feature maps obtained from the feature learning sub-network through two different transformations: 1) bilinear pooling that feeds to the neural network for decision making and 2) spectral averaging that carries out averaging across all feature maps at every pixel position and feeds the output to the auxiliary classifier.

\subsubsection{Training Methodology for the proposed SDCT-AuxNet$^{\theta}$} The training procedure of SDCT-AuxNet$^{\theta}$ is depicted with more clarity in Fig.~\ref{training_strategy}. Although two different classifiers are used (main CNN classifier and auxiliary classifier), they are not trained simultaneously. Let $\{\textbf{X}_i^{train}\}_{i=1,2,...,K}$ with size $m \times n \times 3 $ represents a set of $K$ input images and $\{y_i^{train}\}_{i=1,2,...,K}$ represents true labels of the respective images. In Step-1, SDCT-Net (feature learning sub-network + neural network) is trained in an end-to-end fashion by minimizing the negative log likelihood loss function. Let $P(\hat{y}_{i,0}^{train})$ and $P(\hat{y}_{i,1}^{train})$ denote the probabilities that the $i^{th}$ training image belongs to normal class (label $0$) and
\begin{figure}[!ht]
\centering
\centerline{
\includegraphics[scale=.61]
{network_subpart}}
\captionsetup{justification=centering}
\caption{An overview of the proposed SDCT-AuxNet$^{\theta}$. The SDCT-AuxNet$^{\theta}$ can be interpreted as feature learning sub-network with two different classifiers, one classifier operating on the features obtained after bilinear pooling, and other classifier using the features obtained through spectral averaging.}
\label{network subpart}
\end{figure}
\begin{figure*}[!ht]
\centering
\centerline{
\includegraphics[scale=.28, trim=0 20 0 35]
{training_summary_2.pdf}}
\captionsetup{justification=centering}
\caption{Two-steps training of SDCT-AuxNet$^{\theta}$. In Step-1, SDCT-Net is trained in an end-to-end fashion on the entire training set containing $K$ training images with indices $i=1,2,...,K$. In Step-2, correctly classified training images by SDCT-Net are used to train an auxiliary classifier.
}
\label{training_strategy}
\end{figure*}

\noindent cancer class (label $1$), respectively. The predicted label is given as
\begin{align}x
  \hat{y}_i^{train}&=1\ \ \ \ \ \ \ \ \ \text{if}\ \ \ \ {P}(\hat{y}_{i,1}^{train})> (\hat{y}_{i,0}^{train}),\nonumber \\
  &= 0 \, \, \, \,  \,\, \text{\,\,\,\,\,Otherwise}
\label{eq.4}
\end{align}
Once SDCT-Net is trained, we predict labels of all the training images using this trained SDCT-Net. We define $s$ as a set of indices of training images for which SDCT-Net made the correct predictions, i.e.,
\begin{equation}
s:=\{i| \hat{y}_i^{train}={y}_i^{train}\}, \,\,\, \text{for   } \,\,\, i=1,2,...,K.
\end{equation}

In Step-2, images $\{\textbf{X}_j^{train}\}_{j \in s}$ are utilized to train the  auxiliary classifier. These images are first processed by the feature learning sub-network followed by the spectral averaging layer ($\phi(\cdot)$).
This is to note that only the images, whose labels are correctly predicted by the main CNN classifier (SDCT-Net), are used to train the auxiliary classifier. Also, the auxiliary classifier is not used to update the parameters of the feature learning sub-network. The strategy is to exploit two different classifiers and yet train the architecture in an end-to-end fashion. The intuition behind this approach is simple. Different transformations applied to learned features will capture different information and hence, two different but coupled classifiers trained on two distinct sets of features of the same images may perform better.

\subsubsection{Testing Methodology for proposed SDCT-AuxNet$^{\theta}$}
\label{section for testing strategy }
Once the SDCT-AuxNet$^{\theta}$ is trained, we use the following strategy to predict the label of an input test image
$\textbf{X}^{test}$.
\begin{figure*}[!ht]
\centering
\centerline{
\includegraphics[scale=0.28, trim=0 10 0 0]
{test_sumary_1.pdf}}
\captionsetup{justification=centering}
\caption{Testing strategy of the proposed SDCT-AuxNet$^{\theta}$. For each sample, probability of SDCT-Net decision label is compared against the confidence probability. If the probability of the predicted label by SDCT-Net is less than the confidence probability, it is predicted again using the auxiliary classifier.}
\label{testing_strategy}
\end{figure*}
First, a prediction is made using the main CNN classifier of the SDCT-AuxNet$^{\theta}$ via \eqref{eq.4}. Let $P(\hat{y}_{0}^{test})$ and $P(\hat{y}_{1}^{test})$ denote the prediction probabilities that the test image belongs to normal class (label $0$) and cancer class (label $1$), respectively. These prediction probabilities on the test image represent the confidence of the main CNN classifier in making the predictions for the respective labels. We introduce a confidence probability $\theta \in [0,1]$ as a user-defined variable. We assume the prediction from the CNN classifier to be correct if its predicted label's probability is higher than $\theta$. For more clarity, let us define
\begin{equation}
\tau = max \left(P(\hat{y}_0^{test}),P(\hat{y}_1^{test})\right).
\end{equation}
This parameter $\tau$ is compared with the user-defined confidence probability $\theta$ and the decision is made as below:
\begin{equation}
\hat{y}^{test}=c\ \ \ \text{if}\ \ \tau> \theta \text{\,\, and \,\,} P\left(\hat{y}_{c}^{test}\right)> P\left(\hat{y}_{1-c}^{test}\right), \ \ \text{\, where}\ \ c=0,1.
\end{equation}

However, if $\tau$ less than $\theta$, we use the auxiliary classifier to predict the label of that image and consider that to be the final prediction.

To predict a label using the auxiliary classifier, features of the input image obtained from \textit{feature learning sub-network} are given to the spectral averaging layer, and the output of this layer is fed to the auxiliary classifier. The prediction of the auxiliary classifier is given as:
\begin{equation}
\hat{y}^{test}=g(\phi(f(\textbf{D}^{test}))),
\end{equation}
where $\phi(f(\textbf{D}^{test}))$ is the output of spectral averaging layer and $f(\textbf{D}^{test})$ are the feature maps obtained from $f(\cdot)$. This process is demonstrated in Fig.~\ref{testing_strategy}. Using this approach, we take into consideration the impact of two different classifiers, a compact CNN classifier and an auxiliary classifier. Since we are making predictions with two different classifiers using different set of features, we hypothesize that the incorrect prediction of one classifier can be corrected by the other classifier.

\section{Results}
In this section, we analyze all the above discussed architectures and also compare their performances.
\subsection{System Configuration}
A forty core system with 126 GB RAM is used to train and test all the networks. We have also used an Nvidia GTX 1080 Ti GPU to boost up the training and testing process. Also, PyTorch deep learning library is used to implement all the architectures. We have used stochastic gradient descent (SGD) optimizer with an initial learning rate of 0.001 and a batch size of 64. A total of 130 epochs are used for training the networks, during which the learning rate is dropped regularly by a factor of 10.

\subsection{Performance Metrics}
We have used $F_1$ score, weighted $F_1$ score and balanced accuracy to evaluate the performance of classifiers. Weighted $F_1$ score and balanced accuracy are reported to take into account the class imbalance problem of the data. Further, we report $F_1$ score on each class to show class-wise performance. $F_1$ score is defined mathematically as
\begin{equation}
F_1=2\times \frac{precision\times recall}{precision + recall}.
\end{equation}
For binary data, weighted $F_1$ score is defined as
 \begin{equation}
 WF_1=\frac{\sum_{j=0}^1{n(c_j)F_1(c_j)}}{N},
 \end{equation}
where $F_1(c_j)$ is the $F_1$ score of $j^{th}$ class, $n(c_j)$ is the number of samples in $j^{th}$ class, and $N$ is total number of samples. Finally, balanced accuracy is defined as
\begin{equation}
BAC=\frac{recall+specificity}{2}.
\end{equation}
Precision is the ratio of correctly detected positive samples to  all predicted positive samples. Recall is defined as the ratio of correctly predicted positive samples to all positive samples in the ground truth. Specificity denotes the ratio of correctly classified negative samples to all negative samples in the ground truth.
Recall reflects the classifier's ability to correctly diagnose the disease, while specificity shows the classifier's effectiveness in discarding the healthy subjects. For an ideal classifier, the value of precision, recall, and specificity is 1.
\subsection{Classifiers' Training and Testing Information}
\label{majorityvoting}
For training and testing the networks, we used seven-fold cross-validation strategy. The training set is divided into seven-folds. At any time, six folds are used for training and the remaining one fold is used for validation. Therefore, for every architecture (SD-Net, SDCT-Net, or SDCT-AuxNet$^{\theta}$), we have a total of seven trained models: one for each different validation fold. To make the final prediction on the new test sample $\textbf{X}_{i}^{test}$, we note the individual prediction from each model as
\begin{equation}
\hat{y}_{i}^{test,m}=\gamma_m(\textbf{X}_{i}^{test})\ \ \ \ \ \ \ \ \ m=1,2,...,7, \text{\, and \,\,} i=1,2,...,N,
\end{equation}
where $\gamma_m(.)$ represents the output of the model trained using the $m^{th}$ fold as the validation set and $N$ denotes the total number of test samples.
The final prediction for each $i^{\text{th}}$ test sample is given by majority vote as:
\begin{equation}
\hat{y}_{i}^{test}=mode \{\hat{y}_{i}^{test,1},\hat{y}_{i}^{test,2},...,\hat{y}_{i}^{test,7}\}.
\end{equation}
To summarize, the label predicted by the majority of the models for an architecture (SD-Net, SDCT-Net, or SDCT-AuxNet$^{\theta}$) is chosen as its final prediction.

Another issue that needs to be addressed during the training is class imbalance because training using an imbalanced dataset may result in a biased classifier. From Table~\ref{data description}, it is noted that the training set is skewed towards the cancer class as the number of cancer cell images is approximately twice the total number of normal cell images. To resolve this, we have used the \textit{oversampling} strategy in which images of the minority class are duplicated, such that the total sample count of both the classes is the same.

Further, to enhance the performance, we have used augmentation techniques that simulate the conditions of real-life data preparation. In general, three types of augmentations are natural for these cell images. First, it is observed that 3-dimensional cells get sheared to some extent on the 2-dimensional slide when cells are pushed between two glass slides during the microscopic slide preparation. Secondly, cells would fall on the slide at varying orientations and hence, would be captured with different rotated angles. Thirdly, there can be variations in the sharpness of the images because the manual focusing of the microscope lens was carried out while capturing the images. Thus, to mimic these effects during the training process, shear augmentation is used within a range of [-20, 20]; augmentation of random rotation, horizontal flip, and vertical flip is used; and Gaussian blur augmentation is used within a range of [0.0, 0.75]. The same augmentations are used with all architectures: SD-Net, SDCT-Net, and SDCT-AuxNet$^{\theta}$.

Training curves of SDCT-Net are shown in Fig. \ref{training curves}. Graphs show the accuracy and loss of SDCT-Net trained with different folds as the validation sets. It is observed from the graphs that SDCT-Net converged in 130 epochs. Also, SDCT-Net is able to generalize well because the performance on training and validation sets is similar. Similar observation is noted for SDCT-AuxNet$^{\theta}$.
\begin{figure*}[!ht]
\centerline{
\begin{subfigure}[b]{0.4\textwidth}
\includegraphics[scale=0.318]{7_fold_1_accuracy}
\captionsetup{justification=centering}
\end{subfigure}
\begin{subfigure}[b]{0.4\textwidth}
\includegraphics[scale=0.318]{7_fold_2_accuracy}
\captionsetup{justification=centering}
\end{subfigure}
\begin{subfigure}[b]{0.4\textwidth}
\includegraphics[scale=0.318]{7_fold_5_accuracy}
\captionsetup{justification=centering}
\end{subfigure}}
\centerline{
\begin{subfigure}[b]{0.4\textwidth}
\includegraphics[scale=0.32]{7_fold_1_loss}
\captionsetup{justification=centering}
\end{subfigure}
\begin{subfigure}[b]{0.4\textwidth}
\includegraphics[scale=0.32]{7_fold_2_loss}
\captionsetup{justification=centering}
\end{subfigure}
\begin{subfigure}[b]{0.4\textwidth}
\includegraphics[scale=0.32]{7_fold_5_loss}
\captionsetup{justification=centering}
\end{subfigure}}
\captionsetup{justification=centering}
\caption{Training curves of SDCT-Net with three different folds as the validation sets.}
\label{training curves}
\end{figure*}

\subsection{Comparison of SD-Net and SDCT-Net}
Performance comparison of SD-Net and SDCT-Net in terms of $F_1$ score, $WF_1$ score, and $BAC$ is shown in Table \ref{comparison of SD-Net and SDCT-Net}. Results are tabulated using the individual models (Model1-Model7), i.e., models trained with a particular fold as the validation set and also using the majority voting as discussed in Section~\ref{majorityvoting}. From Table~\ref{comparison of SD-Net and SDCT-Net}, it is observed that SDCT-Net performs better than SD-Net on all three metrics for most of the models (Model1-Model7). Finally, with a majority voting on the decision of Model1 to Model7 SDCT-Net outperforms SD-Net with a good margin. The margin is maximum for $F_1$ score of normal class with SDCT-Net at  $0.862$ and SD-Net at $0.820$. SDCT-Net achieved $WF_1$ score of $0.908$ which is comparatively high compared to $WF_1$ score of $0.873$ with SD-Net. BAC with SDCT-Net and  SD-Net is $0.911$ and  $0.885$, respectively, showing superior performance of SDCT-Net.
\begin{table}[!ht]
\vspace{1em}
\begin{small}
\centering
\captionsetup{justification=centering}
\caption{Comparison of SD-Net  and SDCT-Net. SDCT-Net outperforms SD-Net on all performance metrics. Model1 represents the model trained with fold1 as the validation set and remaining folds as the training set. Similar notation applies to Model2 to Model7. Results are tabulated on the test set of 2586 images. Best results are depicted in boldcase.}
\vspace{-1em}
\label{comparison of SD-Net and SDCT-Net}
\centerline{
\begin{tabular}{c c c c c c c c c}
\hline
\multicolumn{9}{c}{{$F_1$ Score for Normal Class}} \\ \hline
{Architecture\textbackslash Model} & {Model1} & {Model2} & {Model3} & {Model4} & {Model5} & {Model6} & {Model7} & {Majority Voting} \\ \hline
{SD-Net} & 0.790 & 0.828 & 0.822 & 0.771 & 0.788 & {0.803} & {0.818} & 0.820 \\
{SDCT-Net} & {0.813} & {0.855} & {0.836} & {0.856} & {0.822} & 0.774 & {0.825} & \textbf{0.862} \\ \hline
\multicolumn{9}{c}{{ $F_1$ Score for Cancer Class}} \\ \hline
{Architecture\textbackslash Model} & {Model1} & {Model2} & {Model3} & {Model4} & {Model5} & {Model6} & {Model7} & {Majority Voting} \\ \hline
{SD-Net} & 0.877 & 0.908 & 0.904 & 0.872 & 0.875 & {0.885} & 0.891 & 0.8982 \\
{SDCT-Net} & {0.900} & {0.926} & {0.921} & {0.926} & {0.900} & 0.855 & {0.912} & \textbf{0.928} \\ \hline
\multicolumn{9}{c}{{Weighted $F_1$ ($WF_1$) Score}} \\ \hline
{Architecture\textbackslash Model} & {Model1} & {Model2} & {Model3} & {Model4} & {Model5} & {Model6} & {Model7} & {Majority Voting} \\ \hline
{SD-Net} & 0.849 & 0.883 & 0.879 & 0.840 & 0.848 & {0.859} & 0.868 & 0.873 \\
{SDCT-Net} & {0.873} & {0.904} & {0.894} & {0.904} & {0.875} & 0.829 & {0.885} & \textbf{0.908} \\ \hline
\multicolumn{9}{c}{{Balanced Accuracy (\textit{BAC})}} \\ \hline
{Architecture\textbackslash Model} & {Model1} & {Model2} & {Model3} & {Model4} & {Model5} & {Model6} & {Model7} & {Majority Voting} \\ \hline
{SD-Net} & 0.863 & 0.886 & {0.883} & 0.845 & 0.862 & {0.874} & {0.889} & 0.885 \\
{SDCT-Net} & {0.875} & {0.903} & {0.882} & {0.905} & {0.887} & 0.856 & {0.879} & \textbf{0.911} \\ \hline
\end{tabular}}
\end{small}
\end{table}

\begin{figure*}[!ht]
\centerline{
\begin{subfigure}[b]{0.43\textwidth}
\includegraphics[scale=0.37]{final_f1_normal.pdf}
\captionsetup{justification=centering}
\end{subfigure}
\begin{subfigure}[b]{0.43\textwidth}
\includegraphics[scale=0.38]{final_f1_cancer.pdf}
\captionsetup{justification=centering}
\end{subfigure}
\begin{subfigure}[b]{0.43\textwidth}
\includegraphics[scale=0.38]{final_BAC.pdf}
\captionsetup{justification=centering}
\end{subfigure}}
\captionsetup{justification=centering}
\caption{Performance of SDCT-AuxNet$^{\theta}$ for different values of confidence probability ($\theta$): (a) $F_1$ score of normal class, (b) $F_1$ score of cancer class and (c) Balanced Accuracy. Model1 represents model trained with fold1 as the validation set and remaining folds as training set. Similar notation applies to Model2 to Model7. M.V is the score with majority voting on Model2 to Model7. Performance improves consistently with the increasing value of $\theta$ until $\theta=0.9$, after which a decline in the performance is noted. Results are presented on the test set of 2586 images.}
\label{effect of theta on SDCT-AuxNet}
\end{figure*}

\begin{table*}[!ht]
\vspace{1.5em}
\centering
\captionsetup{justification=centering}
\caption{Weighted $F_1$ score of SDCT-AuxNet$^{\theta}$ for different values of confidence probability ($\theta$). Model1 represents the model trained with fold1 as the validation set and remaining folds as training set. Similar notation applies to Model2 to Model7. The weighted $F_1$ ($WF_1$) score improves with increasing $\theta$ until $\theta=0.9$, beyond which the performance starts declining. Results are presented on the test set of 2586 images. Best results are indicated in bold case.}
\vspace{-1em}
\label{effect of theta on wf1 in SDCT-AuxNet}
\begin{small}
\centerline{
\begin{tabular}{ccccccccc}
\hline
\multicolumn{9}{c}{Weighted $F_1$ ($WF_1$) Score} \\ \hline
\begin{tabular}[c]{@{}c@{}}Confidence\\ Probability ($\theta$) \textbackslash Models\end{tabular} & Model1 & Model2 & Model3 & Model4 & Model5 & Model6 & Model7 & Majority Voting \\ \hline
0.6 & 0.886 & 0.915 & 0.900 & 0.910 & 0.895 & 0.848 & 0.905 & 0.920 \\
0.65 & 0.894 & 0.917 & 0.904 & 0.911 & 0.899 & 0.856 & 0.912 & 0.924 \\
0.7 & 0.900 & 0.922 & 0.909 & 0.912 & 0.906 & 0.862 & 0.915 & 0.928 \\
0.75 & 0.906 & 0.925 & 0.912 & 0.916 & 0.907 & 0.872 & 0.920 & 0.933 \\
0.8 & 0.913 & 0.927 & 0.917 & 0.917 & 0.907 & 0.880 & 0.924 & 0.937 \\
0.85 & 0.919 & 0.932 & 0.923 & 0.919 & 0.907 & 0.888 & 0.926 & 0.943 \\
0.9 & {0.920} & {0.937} & {0.928} & 0.917 & 0.907 & {0.890} & 0.925 & \textbf{0.948} \\
0.95 & 0.921 & 0.926 & 0.920 & 0.848 & 0.907 & 0.873 & 0.909 & 0.943 \\ \hline
\end{tabular}}
\end{small}
\end{table*}

\vspace{2em}
\subsection{Experiments with SDCT-AuxNet$^{\theta}$}
In this section, we analyze the performance of SDCT-AuxNet$^{\theta}$ architecture according to the testing strategy as discussed in Section \ref{section for testing strategy }. Support Vector Machine (SVM) with radial basis function (RBF) kernel is used as the auxiliary classifier. We analyze  SDCT-AuxNet$^{\theta}$ using different experiments: 1) by studying the impact of confidence probability $\theta$ on the performance of SDCT-AuxNet$^{\theta}$, 2) by studying the performance comparison of SDCT-AuxNet$^{\theta}$, SDCT-Net$^{0}$, and SDCT-Net$^{1}$, 3) by studying the subject-level performance of SDCT-AuxNet$^{\theta}$.

\subsubsection{Impact of Confidence Probability } We experiment with different values of the confidence probability ($\theta$) to analyze its effect on the performance of the model. Results are summarized in Fig.~\ref{effect of theta on SDCT-AuxNet} and Table~\ref{effect of theta on wf1 in SDCT-AuxNet}. Fig.~\ref{effect of theta on SDCT-AuxNet} shows the effect of confidence probability on individual class $F_1$ score and balanced accuracy. It is observed that for the most of the models, performance improves with an increase of $\theta$ until $\theta=0.9$ after which a decline in performance is observed. The final prediction, i.e., prediction with majority voting also improves until $\theta=0.9$ and decreases thereafter. A similar pattern is observed for $BAC$, results for which are also summarized in Table~\ref{effect of theta on wf1 in SDCT-AuxNet}.

\subsubsection{Comparison of SDCT-AuxNet$^{\theta}$, SDCT-Net$^0$ and SDCT-Net$^1$}
We have compared the performance of SDCT-AuxNet$^{\theta}$ for $\theta=0.90$, $\theta=1$, and $\theta=0$ in Table~\ref{comparison of SDCT-Net and SDCT-AuxNet}. SDCT-AuxNet$^0$ and SDCT-AuxNet$^1$ correspond to the results with $\theta=0$ and $\theta=1$, respectively, in SDCT-AuxNet$^{\theta}$. This is to note that SDCT-AuxNet$^0$ is SDCT-AuxNet$^{\theta}$ without auxiliary classifier and hence, SDCT-AuxNet$^0$ is same as SDCT-Net. Similarly, SDCT-AuxNet$^1$ is SDCT-AuxNet$^{\theta}$ with only auxiliary classifier. Table~\ref{comparison of SDCT-Net and SDCT-AuxNet} shows the performance of SDCT-AuxNet$^{\theta}$ that exploits two different classifiers (SDCT-AuxNet$^0$ and SDCT-AuxNet$^1$ with different architectures) in a coupled fashion.
From the performance of individual models (Model1-Model7) of all these architectures, it can be inferred that SDCT-AuxNet$^{\theta}$ has achieved a significant gain over SDCT-AuxNet$^{0}$ and SDCT-AuxNet$^{1}$ in terms of all three performance metrics. Although majority voting is able to bridge the performance difference between SDCT-AuxNet$^{\theta}$ and SDCT-AuxNet$^{1}$, the former is leading the later for  most of the models (Model1-Model7), while the performance coincides in some cases. Compared to SDCT-AuxNet$^{0}$ (SDCT-Net), SDCT-AuxNet$^{\theta}$ provides a gain of $5.5\%$ for $F_1$ score of normal class, $3.5\%$ for $F_1$ score of cancer class, $4.0\%$ for weighted $F_1$ score, and $2.3\%$ for balanced accuracy. The highest gain is observed for $F_1$ score of normal class, which is $0.917$ with SDCT-AuxNet$^{\theta}$ as compared to $0.862$ with SDCT-AuxNet$^{0}$. To summarize, SDCT-AuxNet$^{\theta}$ ensembles the performance of SDCT-AuxNet$^{0}$ and SDCT-AuxNet$^{1}$ that results in significant performance improvement.

\begin{table*}[!t]
\begin{small}
\captionsetup{justification=centering}
\caption{Performance comparison of SDCT-AuxNet${^0}$, SDCT-AuxNet${^1}$, and SDCT-AuxNet${^\theta}$ for $\theta=0.9$. SDCT-Net is is a special case of SDCT-AuxNet${^\theta}$ with $\theta=0$ and is represented as SDCT-AuxNet$^{0}$. Similarly, SDCT-AuxNet${^1}$ is a spacial case of  SDCT-AuxNet${^\theta}$ with only the auxiliary classifier branch. Model1 represents the model trained with fold1 as the validation set and remaining folds as training set. Similar notation applies to Model2 to Model7. Best results are highlighted in black and equal performance is highlighted in blue color. SDCT-AuxNet${^\theta}$
performed better than SDCT-AuxNet${^0}$ or SDCT-AuxNet${^1}$. Results are presented on the test set of 2586 images.}
\vspace{-1em}
\label{comparison of SDCT-Net and SDCT-AuxNet}
\centerline{
\begin{tabular}{ccccccccc}
\hline
\multicolumn{9}{c}{$F_1$ Score for Normal Class} \\ \hline
Architecture\textbackslash Model & Model1 & Model2 & Model3 & Model4 & Model5 & Model6 & Model7 & Majority Voting \\ \hline
SDCT-AuxNet${^0}$ &  0.813 & 0.855 & 0.836 & 0.856 & 0.822 & 0.774 & 0.825 & 0.862 \\
SDCT-AuxNet${^1}$ & \textcolor{blue}{0.878} & 0.882& 0.865 & \textbf{0.868} & {0.860} & 0.794 & 0.849 & 0.915 \\
SDCT-AuxNet${^\theta}$ & \textcolor{blue}{0.878} & \textbf{0.902} & \textbf{0.882} & {0.864} & \textbf{0.861} & \textbf{0.830} & \textbf{0.879} & \textbf{0.917} \\ \hline
\multicolumn{9}{c}{$F_1$ Score for Cancer Class} \\ \hline
Architecture\textbackslash Model & Model1 & Model2 & Model3 & Model4 & Model5 & Model6 & Model7 & Majority Voting \\ \hline
SDCT-AuxNet${^0}$ & 0.900 & 0.926 & 0.921 & 0.926 & 0.900 & 0.855 & 0.912  & 0.928 \\
SDCT-AuxNet${^1}$ & \textcolor{blue}{0.940} & 0.946 & 0.945 & 0.936 & 0.928 & 0.908 & 0.936 & 0.961 \\
SDCT-AuxNet${^\theta}$ & \textcolor{blue}{0.940} & \textbf{0.954} & \textbf{0.950} & \textbf{0.941} & \textbf{0.929} & \textbf{0.918} & \textbf{0.947} & \textbf{0.963} \\ \hline
\multicolumn{9}{c}{Weighted $F_1$ ($WF_1$) Score} \\ \hline
Architecture\textbackslash Model & Model1 & Model2 & Model3 & Model4 & Model5 & Model6 & Model7 & Majority Voting \\ \hline
SDCT-AuxNet${^0}$ &  0.873 &  0.904 & 0.894 &  0.904 & 0.875 &  0.829 & 0.885 & 0.908 \\
SDCT-AuxNet${^1}$ & \textcolor{blue}{0.920} & 0.925 & 0.919 & 0.915& \textcolor{blue}{0.907} & 0.872 & 0.908 & 0.947 \\
SDCT-AuxNet${^\theta}$ & \textcolor{blue}{0.920} & \textbf{0.937} & \textbf{0.928} & \textbf{0.917} & \textcolor{blue}{0.907} & \textbf{0.89} & \textbf{0.925} & \textbf{0.948} \\ \hline
\multicolumn{9}{c}{Balanced Accuracy ($BAC$)} \\ \hline
Architecture\textbackslash Model & Model1 & Model2 & Model3 & Model4 & Model5 & Model6 & Model7 & Majority Voting \\ \hline
SDCT-AuxNet${^0}$ & {0.875} & { 0.903} & { 0.882} & {0.905} & { 0.887} & { 0.856} & {0.879} & {0.911} \\
SDCT-AuxNet${^1}$ & \textcolor{blue}{0.916} & {0.910} & {0.885} & \textbf{0.906} & \textcolor{blue}{0.908} & { 0.845} & {0.879} & {0.932} \\
SDCT-AuxNet${^\theta}$  & \textcolor{blue}{0.916} & \textbf{0.928} & \textbf{0.901} & {0.891} & \textcolor{blue}{0.908} & \textbf{0.879} & \textbf{0.904} & \textbf{0.934} \\ \hline
\end{tabular}}
\end{small}
\end{table*}
\subsubsection{Subject-Level Performance of SDCT-AuxNet$^{\theta}$}
We have also evaluated the performance of SDCT-AuxNet$^{\theta}$ for individual subjects in terms of accuracy. The subject-level accuracy and error rate for both the classes is depicted in Fig.~\ref{subject level analysis}. SDCT-AuxNet$^{\theta}$ performs consistently good for all the subjects. These results are encouraging since it shows that the model is robust to subject-level variability.

\begin{figure*}[!t]
\centerline{
\begin{subfigure}[b]{0.75\textwidth}
\includegraphics[scale=.8]{subject_level_cancer.pdf}
\captionsetup{justification=centering}
\end{subfigure}
\begin{subfigure}[b]{0.75\textwidth}
\includegraphics[scale=.79]{subject_level_normal.pdf}
\captionsetup{justification=centering}
\end{subfigure}}
\captionsetup{justification=centering}
\caption{Subject-level performance of SDCT-AuxNet$^{\theta}$ is observed to be consistent across all the subjects indicating that SDCT-AuxNet$^{\theta}$ is robust to subject-level variations.}
\label{subject level analysis}
\end{figure*}

\subsection{Comparison with the state-of-the-art Methods}
This C-NMC 2019 dataset has recently been used by \cite{JoansCNMC02} and \cite{LiuCNMC01}. \cite{JoansCNMC02} have used training set to fine-tune a pretrained SE-ResNeXt50 architecture. \cite{LiuCNMC01} have divided the larger class samples into two subsets, which are then combined with other class samples to train two different models initialized with pretrained Inception ResNets weights. These two models are then fine-tuned jointly on whole training dataset to obtain the final predictions. These methods are able to achieve a weighted $F_1$ score of $87.6\%$ \citep{LiuCNMC01}, and $88.9\%$ \citep{JoansCNMC02} as compared to $94.8\%$ of the proposed method.
Apart from these two approaches, other participants have used methodologies based on VGGNet, AlexNet, InceptionV3, DenseNet and MobileNet which have performed below the challenge winner's best performance of 91\%.

We also compared our results with the top entry at the final leaderboard of the challenge \citep{ref50}. The leaderboard shows the performance on final test set in terms of weighted $F_1$ score. It is observed from Table~\ref{comaprison with cnmc} that SDCT-AuxNet$^{\theta}$ is performing better than top entry method  with a significant margin of $3.8\%$.
\begin{table}[!h]
\centering
\captionsetup{justification=centering}
\caption{Comparison of SDCT-Net and SDCT-AuxNet$^{\theta}$ with the top entry of C-NMC 2019 Challenge. Best results are depicted in bold case.}
\begin{small}
\vspace{-1em}
\label{comaprison with cnmc}
\centerline{
\begin{tabular}{cccc }
\hline
Metric\textbackslash Architecture & C-NMC & SDCT-Net & SDCT-AuxNet$^{\theta}$ \\
\hline
Weighted $F_1$ ($WF_1$) & 0.910  & 0.908 & \textbf{0.948}\\ \hline
\end{tabular}}
\end{small}
\end{table}

\section{Discussion}
In this section, we have analyzed SDCT-AuxNet$^{\theta}$ from different perspectives. First, we analyze SDCT-AuxNet$^{\theta}$ as a generic architecture that can be modified to two different architectures through the setting of confidence probability ($\theta$). As discussed in above sections, confidence probability ($\theta$) that lies in the range $[0,1]$, plays a crucial role during the testing phase of SDCT-AuxNet$^{\theta}$.
By setting the value of $\theta$, we are deciding the contribution of two different classifiers in decision making. However, with two extreme values of $\theta$, i.e. $\theta=0$  or $\theta=1$, we can also choose only one classifier. This scenario is depicted in Fig.~\ref{sdctauxnet}. By setting $\theta=0$, SDCT-AuxNet$^{\theta}$ is reduced to SDCT-AuxNet$^{0}$ (SDCT-Net), which is the feature learning sub-network along with neural network as the classifier that utilizes bilinear pooling. For $\theta=1$, SDCT-AuxNet$^{\theta}$ becomes  SDCT-AuxNet$^{1}$, which utilizes feature learning sub-network along with spectral averaging and auxiliary classifier. Between these two extremes, SDCT-AuxNet$^{\theta}$ exploits bilinear pooling with neural network  and spectral averaging with auxiliary classifier. This methodology is an advantage of SDCT-AuxNet$^{\theta}$ because it provides flexibility to decide the contribution of the classifiers by simply setting the value of $\theta$. This flexibility is also the reason for the better performance of SDCT-AuxNet$^{\theta}$  over SDCT-AuxNet$^{0}$ (SDCT-Net) or SDCT-AuxNet$^{1}$. In fact, the coupling of SDCT-AuxNet$^{0}$ (SDCT-Net) and SDCT-AuxNet$^{1}$ in SDCT-AuxNet$^{\theta}$ can also be interpreted as an ensemble of two classifiers, with each classifier utilizing a different set of features. Results of Table~\ref{comparison of SDCT-Net and SDCT-AuxNet} validates our hypothesis that an appropriate coupling of two different classifiers (working on different sets of features) may lead to better performance as compared to an individual classifier utilizing a single set of features.
\begin{figure*}[!ht]
\centerline{
\includegraphics[scale=0.9]{sdctauxnet}}
\captionsetup{justification=centering}
\vspace{-1em}
\caption{SDCT-AuxNet$^{\theta}$ as a generic case utilizing two different classifiers in decision making. SDCT-Net is same as SDCT-AuxNet$^{\theta}$ for $\theta=0$ and utilizes only neural network. SDCT-AuxNet$^{1}$ is SDCT-AuxNet$^{\theta}$ with $\theta=1$ and use only the auxiliary classifier. SDCT-AuxNet$^{\theta}$ swings between SDCT-AuxNet$^{0}$ (SDCT-Net) and SDCT-AuxNet$^{1}$ depending upon the value of confidence probability $\theta$.}
\label{sdctauxnet}
\end{figure*}

\begin{table}[!t]
\vspace{1em}
\centering
\captionsetup{justification=centering}
\caption{The number of samples predicted by different classifiers at $\theta=0.9$. Contribution  of each classifier is approximately the same in majority of the cases, indicating significant role of both the classifiers in decision making.}
\vspace{-1em}
\label{contribution of classifiers}
\small
\begin{tabular}{ccccclll} \hline
\begin{tabular}[c]{@{}c@{}}Classifier/\\ Models\end{tabular} & Model1 & Model2 & Model3 & Model4 & Model5 & Model6 & Model7 \\ \hline
\begin{tabular}[c]{@{}c@{}}Neural \\ Network\end{tabular} & 1634 & 1396 & 428 & 1885 & 1199 & 1544 & 1056 \\ \hline
\begin{tabular}[c]{@{}c@{}}Auxiliary \\ Classifier\end{tabular} & 952 & 1190 & 2158 & 701 & 1387 & 1042 & 1530 \\ \hline
Total Samples & \multicolumn{7}{c}{2586} \\ \hline
\end{tabular}
\end{table}

We have also analyzed the contribution of each classifier in the final prediction (Table~\ref{contribution of classifiers}). It is observed that both the classifiers contribute approximately equally in most of the cases. These results prove the hypothesis that both the classifiers are involved in decision making, and the final outcome is not due to only one of the classifiers.

Next, we visualize the features of the second last convolutional layer and the final convolutional layer of SDCT-AuxNet$^{\theta}$  in order to understand if something different is learned by these layers. In Fig.~\ref{dct output}, we visualized the sparsity of the normal cell images and cancer cell images in the DCT domain. Normal cell images are observed to be sparsified more as compared to cancer cell images. We claimed that the difference in sparsity would help CNN to distinguish the two classes. This effect is propagated to the deeper layers as visualized in Fig.~\ref{last layer features}, where it is again observed that the features for the normal class are more sparse as compared to the cancer class. This observation implies that different sparsification induced by the DCT-layer may be one of the essential characteristics of class discrimination and hence, SDCT-AuxNet$^{\theta}$ could separate the two classes based on sparsity, even if the images of both classes are visually similar. This property is crucial for images in medical applications such as ALL classification because images are not visually differentiable. Hence, features like sparsity difference may help to enhance the performance of the classifier.

We have also visualized class discrimination at different layers in Fig.~\ref{layers output}. At the first convolutional layer, majority of the samples of the two classes are overlapping. However, as we go deeper into the network, the two classes start to diverge. Finally, at the last convolutional layer, the two classes can be linearly separated. This points to an intuitive understanding that difference in sparsity in SDCT-AuxNet$^{\theta}$ may be one of the significant causes of  separability of the two classes. Although some samples still lie on the opposite side of the boundary, majority of the samples can be classified correctly. These observations establish the validity of DCT-layer in ALL classification.

\begin{figure*}[!ht]
\centerline{
\begin{subfigure}[b]{0.31\textwidth}
\includegraphics[scale=0.5]{seventh_layer_cancer}
\captionsetup{justification=centering}
\caption{Features of Cancer Class }
\end{subfigure}
\begin{subfigure}[b]{0.31\textwidth}
\includegraphics[scale=0.5]{seventh_layer_normal}
\captionsetup{justification=centering}
\caption{Features of normal Class }
\end{subfigure}
\begin{subfigure}[b]{0.31\textwidth}
\includegraphics[scale=0.553]{last_layer_cancer}
\captionsetup{justification=centering}
\caption{Features of Cancer Class }
\end{subfigure}
\begin{subfigure}[b]{0.31\textwidth}
\includegraphics[scale=0.545]{last_layer_normal}
\captionsetup{justification=centering}
\caption{Features of normal Class }
\end{subfigure}}
\captionsetup{justification=centering}
\caption{Feature maps of second last (C5) and last convolutional  layer (C6) for cancer class (a,c) and normal class (b,d). The features for normal class are more sparse as compared to the features of cancer class. This difference in sparsity helps to improve the performance of the classifier.  }
\label{last layer features}
\end{figure*}

\begin{figure*}[!ht]
\vspace{1em}
\centerline{
\begin{subfigure}[b]{0.5\textwidth}
\centering
\includegraphics[scale=0.4]{first_layer.pdf}
\captionsetup{justification=centering}
\caption{First Convolutional Layer (C1)}
\end{subfigure}
\begin{subfigure}[b]{0.5\textwidth}
\centering
\includegraphics[scale=0.4]{last_layer.pdf}
\captionsetup{justification=centering}
\caption{Sixth Convolutional Layer (C6)}
\end{subfigure}}
\captionsetup{justification=centering}
\caption{Class discrimination at first (C1) and last convolutional layers (C6). The samples are separated as we progress deeper into the network. At the final layer, majority of the samples can be easily separated even with a linear boundary.}
\label{layers output}
\end{figure*}

Finally, samples in the medical domain are collected from different subjects, which may induce subject-level variations. Robustness to subject-level variability is a crucial factor for the practical implementation of the classifier. To mimic this effect, we trained and tested the architectures on folds separated at subject level. Results summarized in Fig.~\ref{subject level analysis} prove the robustness of SDCT-AuxNet$^{\theta}$ to subject-level variability. However, error rate for normal class is high as compared to cancer class. This results imply that classifier has relatively lower specificity as compared to recall. Hence, classifier yields excellent performance in predicting the disease in unhealthy subjects, but relatively poor performance in discarding the disease in healthy subjects.

\section{Conclusion and Future Work}

We proposed a novel framework, SDCT-AuxNet$^{\theta}$, for the challenging problem of ALL classification. The framework utilizes two different classifiers operating on two different set of features. SDCT-AuxNet$^{\theta}$  use sparsity in DCT domain to learn class discriminative features. In ALL classification, it is important to pool the data at subject-level due to inter-subject variability in cell images. We have used this approach to make SDCT-AuxNet$^{\theta}$ robust to subject-level variations. However, there is some performance margin between the performance for normal and cancer class. We will cover this issue in our future work. We also plan to design a multi task framework for cancer diagnosis.

\section{Acknowledgements}
\vspace{-0.5em}
Shiv Gehlot would like to thank University Grant Commission (UGC),
Govt. of India for the UGC-Junior Research Fellowship. We also acknowledge the Infosys Center for Artificial Intelligence, IIIT-Delhi for our research work.

\section*{References}

redpajama_set_name: RedPajamaArXiv


Three years after an accident left her in a wheelchair, artist Penny Diamond has made a new life for herself in a little cottage on the edge of Talyton St George.
Penny makes a living through her art, and with the aid of her assitance dog Sally and a carer who comes in during the day, she's managing to live an independent, if very quiet,life.
Until one day she gets a new carer. Declan is young - a lot younger than her - and he brings a breath of fresh air into her life. It doesn't hurt that he's also thoughtful, kind and good looking.
But what could a young man like Declan ever see in a woman like Penny?


We make comprehensive sound, HVAC and plumbing measurements at planning and construction sites. Our experts conduct all field measurements and tests related to housing comfort, system functionality, flue inspections and surveys, moisture measurements, leak location, infrared temperature measurement, and tightness tests for ducts, piping, and buildings.
Depending on the need, we can provide brief instructions for alteration, repair, renovation or modernisation measures, or draw up a complete and comprehensive overall plan.
One of the topics we investigate is acoustics, since impact sounds, the sound insulation of structures, and room acoustics are all key components of comfortable living. If you suspect problems related to sounds or acoustics on your site, we can take measurements with our laboratory equipment, and use this data to draw up a suggestion or solution plan.


text:
St. Caroline Series
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Summer Again: A St. Caroline Novel Summary
The town of St. Caroline had never felt like home to Sterling Matthew. Even though the Matthew family could date their residence back nearly 100 years, Sterling had grown up in boarding schools - and promptly decamped for the ski slopes of Europe after college.
When his father falls ill, his mother calls him home to run the family business, the renowned Chesapeake Inn. What Sterling finds, though, is a business on shaky financial footing and a staff resistant to the radical changes he has to make. No matter. He'll do what needs to be done...and then leave St. Caroline for good.
For years, Lucy Wyndham wondered whether she'd ever catch another glimpse of the boy she'd crushed on at the Chesapeake Inn's summer camp for disadvantaged kids. He'd been tall and quiet. Mysterious and aloof. And the owner's son. Now he's her boss and the attraction is just as strong - but they're no more compatible today than they were as teenagers. When he informs her that the camp must be eliminated to improve the resort's bottom line, she embarks on an ambitious campaign to save it. Even if the price is her job...and her heart.
Contains mature themes.
©2013 Julia Gabriel (P)2019 Tantor
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Summer Again: A St. Caroline Novel
St. Caroline Series, Book 1
By: Julia Gabriel
Narrated by: Samantha Desz
The town of St. Caroline had never felt like home to Sterling Matthew. Even though the Matthew family could date their residence back nearly 100 years, Sterling had grown up in boarding schools - and promptly decamped for the ski slopes of Europe after college. When his father falls ill, his mother calls him home to run the family business, the renowned Chesapeake Inn. What Sterling finds, though, is a business on shaky financial footing and a staff resistant to the radical changes he has to make. No matter. He'll do what needs to be done...and then leave St. Caroline for good.
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A St. Caroline Novel, Book 2
Becca Trevor never intended to come back to pretty little St. Caroline, Maryland, and her family's quilt shop. Growing up, she was the wild child...and the black sheep of the family...and the girl who couldn't get anything right. And she definitely never intended to see Jack Wolfe again. Those 15 minutes she'd spent with him at a graduation party seven years ago? Unforgettable - for a whole lot of reasons.
Two of Hearts
Cassidy Trevor is the backbone of her family's quilt shop, the one everyone relies on, the person who makes the trains run on time. She has a good life with loving parents and sisters, a job for life that she enjoys, and respect as a capable businesswoman within the community. Still, she can't help wondering...is there something more out there?
This Reminds Me of Us
St. Caroline
Narrated by: Cindy Kay
Deputy fire chief Oliver Wolfe had everything he ever wanted. A beautiful wife, two adorable (if rambunctious) sons, a job he loved, a comfortable home, and family and friends in his hometown of St. Caroline, Maryland…until the day he had to stand by helplessly and watch his wife's unconscious body get cut from the mangled wreckage of her car.

redpajama_set_name: RedPajamaCommonCrawl


We wish to express our sincerest thanks to Sangeeth A45WH and the Members of Royal Omani Amateur Radio Society A47RS (ROARS) led by His Majesty of Sultan Qaboos Bin Said (A41AA) for their invitation to operate from Muscat in the CQ WW RTTY 2017 in M/2.
It is the first time from A4 on RTTY as Multi station.
On the EME we used 2 x 13el Yagi V-pol + 35m of RLF-600, Preamp 0,6dB, PA and IC-9100.
We are sorry to all, thanks to WB noise we were able to be QRV only in the two small windows and were very limited.
QSL INFO: via OK2ZAW !!!


text:
The Broke Loose, Wagon Blasters, Closeness, Twinsmith, Clarence Tilton tonight; TFOA, Lupines, Bad Bad Men (John Wolf) Saturday…
Category: Blog — Tags: Bad Band Men, Clarence Tilton, Closeness, Lupines, The Broke Loose, Twimsmith, Wagon Blasters — @ 1:06 pm February 16, 2018
Twinsmith on the Maha Music Festival main stage back in 2014. The band plays tonight at Slowdown Jr.
It's a packed weekend for local shows, not much from a national-touring-indie perspective, but what else is new? It's February, after all. Who wants to tour through Omaha in February? Apparently no one.
The Brothers Lounge is really stepping up its game, hosting two shows this weekend. Tonight's headliner is The Broke Loose. The band released a single this past January called "Flatlands," and another in February called "Cold As Hell." Both were recorded with Rick Carson at Make Believe Studios. Frontman Glenn Antonucci said they're the first in a series of nine singles, all recorded at Make Believe, that they plan to release one by one over the course of 2018.
Why release a single at a time versus a full album?
"Well, a couple reasons," Antonucci said. "For one, we thought many of the individual tracks that came out of this session had a distinctive feel, and could stand on their own. And of course, it also gives us the ability to offer up something new each month (or thereabouts), rather than drop an album on people all at once and then retreat into silence for a year or more."
I like it. It's like the old days or rock 'n' roll when bands released 45s then compiled them into albums. Too bad Broke Loose songs aren't being released as 45s, but imagine how much that'd cost…
Opening for The Broke Loose tonight is legendary tractor-punk band Wagon Blasters (Gary Dean Davis and crew) and Ottumwa Iowa basement rockers X-Ray Mary. $5, 9 p.m.
Cold As Hell by The Broke Loose
Also tonight Closeness headlines at The Sydney in Benson. Seems like we haven't heard from the dynamic duo of Todd and Orenda Fink for quite a while. Will we be getting a glimpse of new Closeness music tonight? Opening is Lincoln's Universe Contest and garage-punkers FiFI NoNo. $5, 9 p.m.
That's not all. Tonight Saddle Creek Records band Twinsmith headlines at Slowdown Jr. The Sunks open at 9 p.m. $10.
And also tonight at fabulous O'Leaver's it's another shit-kicker of a bill headlined by Omaha's finest alt-country band Clarence Tilton, who just released a split LP with Monday Mourners. Opening for Tilton is fellow boot-scooters The Eletroliners and 24-Hour Cardlock. $5, 10 p.m.
Tomorrow night (Saturday) it's back to The Brothers for a special night of rock headlined by Those Far Out Arrows. The always awesome Lupines hold the second spot while a new band called Bad Bad Men, featuring John Wolf (Cellophane Ceiling, Bad Luck Charm), Chris Siebken (Lude Boys) and Jerry Hug (Ritual Device), has the opening slot. Lots o' curiosity about these bad hombres. $5, 9 p.m.
And that's all I got. If I missed your show put it in the comments section. Have a great weekend…


text:
HOMEOVERVIEWAVAILABILITIESLOCATIONOAKLANDCONSTRUCTIONCONTACTVIRTUAL TOURBROCHURE
When it comes to a thriving community, creativity, vibrant culture, social impact, and diversity, all roads lead to Oakland. The relocation into Oakland of tech companies such as Pandora Media and Ask.com initiated Oakland's credibility as a technology hub. With the emergence of Uptown, Oakland's most talked about neighborhood, and the relocation of more than 50 San Francisco tenants leasing over 800,000 square feet of space in Oakland, a new chapter is being written in its history. The positive changes happening in Oakland have transformed the city's atmosphere,
making it the MOST exciting city in the United States. With authentically Oakland projects positively impacting the economy and community (such as The Hive redevelopment, the restoration of the Fox Theater, and the creation of the event First Friday), Oakland has capitalized on its rich cultural roots, vibrant art scene, and diversity. It has seen an explosion in the number of businesses relocating and opening within the downtown area, and features a rich dining scene; today's Oakland has over 21 outdoor beer gardens for residents and visitors to enjoy!
Since the Fox opened, over 200 ground-floor storefronts opened within the core downtown area. With more than 9,400 residential units currently proposed or being developed in Downtown Oakland, the surge in demand has caused apartment rents and housing prices to spike, gaining national recognition as the hottest housing market in the country. A critical mass of new amenities and recreational activities along with the surge in residential development has helped Downtown Oakland become one of the country's most vibrant live–work–play environments.
The Oakland Metro is thriving; attracting a variety of travelers, business, and new residents, ranking among the top cities in food destinations, technology, and sustainability. The East Bay-Oakland area is ranked #1 in Top 10 Mid-Sized American Cities of the Future for Connectivity, and #2 city Overall.
on GoBanking list of "Best City to Score Your Dream Job" (2017)
on Travel Channel's list for "Top 10 U.S. Cities for International Foods" (2016)
"Best Place for Tech Careers" by Value Penguin (2016)
"West Coast Food City" by USA Today (2015)
on Forbes list of "America's Coolest Cities" (2014)
on Movoto's list of "America's Most Exciting Cities" (2013)
on the Thrillist list of "America's Most Hipster Cities" cited as luring young San Franciscans to the city (2013)
on The New York Times list of "Interesting Places to Visit" (2012)
Oakland restaurants are finalists for a prestigious James Beard Award (2018)
GO DUBS!
OAKLAND FIRST FRIDAYS
THE OFFICE LEASING TEAM
CHRISTOPHER T. ROEDER
chris.roeder@am.jll.com
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JON ELDER
jon.elder@am.jll.com
© 2019 Jones Lang LaSalle IP, Inc. All rights reserved. All information contained herein is from sources deemed reliable; however, no representation or warranty is made to the accuracy thereof.


We all feel tired and out of it from time to time. That's just being human, and it's something that everyone will need to deal with. But that's okay. As long as you can find ways around it, being tired isn't so bad after all. However, not everyone is entirely aware of what they need to do to feel like they're back up and running at full speed. To try and assist you with this, we're taking a look at five ways that you can boost your energy levels and also combat the feeling of being always tired.
Sleep is vital because it gives the body time to repair, recharge and shut down for a bit. However, if you don't get enough sleep, you'll find that your energy levels are down and that you're often exhausted. Making sure you sleep well is therefore really important. You accomplish this by avoiding heavy use of technology before bed and also cutting back on caffeine. If you do this, you should be able to boost your energy quickly.
Nothing helps to boost your energy like improving your fitness levels. Going to the gym or going out for a run will contribute to give you more energy because you're building your body up. Exercise is a great way for you to boost your energy and will ensure that you sleep better too, and so you'll feel less tired.
You get a lot of your energy from the foods you eat and the way that you structure your diet, so it is essential that you make sure that the foods you do eat are packed full of energy to ensure that your energy levels are up and at their max.
When it comes to improving your energy levels, the best way to do this is to do something for yourself, like go for a spa day or unwind with a good book. You'll feel better for taking time out of your day to do something which benefits you, and it will help your energy levels.
Now, we appreciate that this is only a temporary solution, but sometimes the temporary solution becomes the answer to the problem. Caffeine will help you to feel much more active and full of energy and will help you to feel less tired when it counts. Use coffee in moderation, however, and consider using one of the other ways to boost energy as a more permanent and healthier option.
Overall, these are five ways that you can boost your energy levels and feel less tired on a daily basis. We fully understand that it can be a very tiring life sometimes, and that's okay because you can take steps to pick yourself back up and get back to feeling happy and full of energy. Whether it is plenty of time at the gym, or just sleeping more, it's easy to bring your energy levels up.


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Q: Bean Validation 1.1 (JSR-349), implementation alternatives? Besides the reference implementation, Hibernate Validator 5.x, are there alternative implementations of JSR 349 (successor to JSR 303)?

A: Bean Validation 1.1 is not yet 100% finished (but it is close to be done), so other vendors are waiting for the final release.
You might watch

*

*https://code.google.com/p/gwt-validation/ and

*http://bval.apache.org/
These are implementations of Bean Validation 1.0, but soon or later they would like to catch up with the final 1.1

redpajama_set_name: RedPajamaStackExchange


text:
Between Two Ferns: The Movie – Netflix Film Review
Sep 20 Greg Wheeler
That Blooper Reel
Between Two Ferns: The Movie is not a very good film. It's not particularly well written and at times it feels tonally confused as it jumps between The Office-esque skits and interviews with a thinly veiled plot to hold it all together. Yet despite all this, I found myself laughing through Between Two Ferns more than any other film this year, raising a very interesting dilemma around just how to review this.
The film itself is really a tale of two halves. On the one hand, the majority of the laughs and comedy come from the interviews with Zach himself. For anyone who's ever seen the internet show, you'll know that Zach is ruthless and delivers a barrage of insults and cleverly written jokes that are as dry and sarcastic as they are hilarious. On the other side of the coin is the plot itself which begins with Zach almost killing Matthew McConaughey. Overseeing the show, Will Ferrell arrives and tells Zach he needs to travel across the country and collect 10 episodes of Between Two Ferns in 2 weeks. If he achieves that, he'll give Zach a talk show and let him live his dream.
It's silly, formulaic stuff and the film's plot plays out exactly as you'd expect. All the usual plot tropes show up here too, including the betrayal, the big dramatic return at the end and the montage segment in the middle as Zach begins firing off a barrage of interviews. These are easily the highlight of the film and alongside the highlight reel at the end during the credits, the interviews are likely going to get the most amount of laughs from people. Everything in between does well to keep things ticking by but largely fails to garner any sort of laughs beyond a few amusing observations and slapstick moments involving the ferns.
If there's one thing the film does have in abundance though, it's star power. From Brie Larson and John Legend through to David Letterman and Peter Dinklage, Between Two Ferns: The Movie crams its relatively mild run time of 1 hour 22 minutes with as many celebrities as possible. Unfortunately in doing so, some of the jokes feel a little rushed and the comedy during the interviews doesn't always have enough time to deliver as many laughs as it perhaps should. The interviews with Tiffany Haddish, Hailee Steinfeld and Adam Scott come to mind, with agonizingly short interviews that don't quite hit the right comedic mark as some of the others do.
Overall then, Between Two Ferns: The Movie feels like a film that had a lot of interview footage and needed a plot to tie it all together in a cohesive manner. If I'm honest, I'd have much preferred a Netflix Original series with 10 minute interviews as I feel this may have worked so much better than the feature film format we receive here. There are some nice ideas here they largely feel formulaic and designed to move from interview A to interview B without much thought to the comedy between. Still, despite that the film does have some good laughs and the end blooper reel is easily the highlight of the entire film.
In a way, Between Two Ferns: The Movie is likely to be the worst and best comedy of the year, making for quite the polarizing view. Personally I'm in the former and love the comedy but it's hard to ignore the glaring plot issues and mundane scripting around these segments. Whether the masses will take to the comedy and overlook the plot issues in quite the same way though, remains to be seen.
Click Here To Go Back To Our Film Reviews
Verdict - 6/10
Posted in 2019 films, ComedyTagged 2019, Adam Scott, Benedict Cumberbatch, brie larson, Chance the Rapper, Chrissy Teigen, comedy, david letterman, John Cho, John Legend, Jon Hamm, keanu reeves, Lauren Lapkus, Matthew McConaughey, Mike Cochrane, netflix, Peter Dinklage, Rashida Jones, Ryan Gaul, Tiffany Haddish, Will Ferrell, Zach Galifianakis


The Sustainable Business Leadership Council seeks to advance sustainable business practices through Networking and Education. Our Mission Statement.
Monthly Meeting- 2nd TUESDAY of every month!! Come learn how to incorporate "Green" into your business. Meet with other business owners, executives and regional leaders that are interested in "Goin Green"
Perhaps you're a lone leader in your company that's been wanting to make your business more sustainable, but you just don't know how you should begin or where to meet other companies with the same goals.
Perhaps you're searching for a credible certification process that applies to your particular business or industry.
Or perhaps you've developed a sustainable business since sustainability was called conservation. How do you keep your company in the midst of the synergy transforming the way business is done in America?
At whatever point you find yourself, Sustainable Business Leadership Council offers businesses a way to implement the most relevant sustainable practices for their businesses, while networking with like-minded firms.
Tuesday October 9, 2012 @ 6:30 pm.
The Solo Building in Costa Mesa.
Real sustainable change is getting rooted in Socal folks. And its at the heart of where we all know real change happens. Slow Money SoCal is about local investment opportunities that benefit southern California communities and southern California's local food systems. Its an amazing resource base for investors to find local opportunities to invest in, that specifically effect food system businesses. This ranges from farming to restaurant services and distribution to retail food sells and beyond. Investors coming together with entrepreneurs to cause real change.
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Tue, Jan 28 10:30 am to 11:00 am Mill Basin Library
Birth to Five Years early literacy toddler time
Join us for books, fingerplays, rhymes, playtime and songs! Specifically tailored for toddlers who are walking independently, up to age 3.
Build with DUPLO
Thu, Jan 30 11:00 am to 12:00 pm Midwood Library
Birth to Five Years build with duplo first five years
Babies and toddlers can socialize while playing with DUPLO and toys.
Discovery Table
Mon, Feb 3 10:00 am to 11:00 am McKinley Park Library
Birth to Five Years build with lego first five years
Discovery table fun with legos or train sets
Story Play
Mon, Feb 3 11:15 am to 12:00 pm Midwood Library
Birth to Five Years first five years story play
Story play is for ages 0-5 and includes stories, songs, and play.
*Space is limited. Tickets are given out at 11 am on a first come, first served basis (2nd floor information desk).
Tue, Feb 4 10:30 am to 11:00 am Mill Basin Library
Toddlers Explore
Wed, Feb 5 11:00 am to 12:00 pm Midwood Library
Birth to Five Years first five years toddler time
For ages 0-5. Toddlers can develop their fine and gross motor skills with play dough, giant stampers/crayons, and building materials such as magnatiles and foam blocks.
Thu, Feb 6 11:00 am to 12:00 pm Midwood Library
For ages 0-5. Open play with toys and DUPLO.
Mon, Feb 10 10:00 am to 11:00 am McKinley Park Library
Mon, Feb 10 11:15 am to 12:00 pm Midwood Library
Tue, Feb 11 10:30 am to 11:00 am Mill Basin Library
Thu, Feb 13 11:00 am to 12:00 pm Midwood Library
Wed, Feb 19 11:00 am to 12:00 pm Midwood Library
Urdu Storytime
Birth to Five Years first five years multilingual multilingual storytime
Join us for stories and songs in Urdu for children and their parents or caregivers.
آئیں ہمارے ساتھ اردو زبان میں کہانیاں سنیں اور گانے گائیں۔
Wed, Mar 4 11:00 am to 12:00 pm Midwood Library
Wed, Mar 11 11:00 am to 12:00 pm Midwood Library
Wed, Apr 1 11:00 am to 12:00 pm Midwood Library
Wed, Apr 15 11:00 am to 12:00 pm Midwood Library
Wed, May 6 11:00 am to 12:00 pm Midwood Library
Wed, May 13 11:00 am to 12:00 pm Midwood Library
Wed, Jun 3 11:00 am to 12:00 pm Midwood Library


Basic spoken English Classes is basically designed for those students who are not new to English Language. But they have poor knowledge of grammar and incorrect sentence formation. These students often suffer from some fundamental problems and make sentences with incorrect tenses, or have a weak vocabulary. This course is used to improve accuracy in Grammar, Expand Vocabulary, enhance reading skills, correct pronunciation, improve Conversation abilities, gives a platform to Communicate in English in day to day situations.
This English speaking training is structured in a way to improve your overall English competency across the four skills – reading, writing, listening & speaking. You will also improve your skill to use English grammar, pronunciation and vocabulary with self-confidence and accurateness.
Suitable For: Who often suffer from some fundamental problems and make sentences with incorrect tenses, or have a weak vocabulary.
This Basic Spoken English Classes in Delhi is not suitable for beginners. You can join us for two months and follows the steps as guided by our expert trainers. Definitely after successfully completion of this English language training you will be able to Read, Write, Listen & Speak English fluently.


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Home › Community/NRIs › Scholarships For Diaspora Children
"Scholarship Programme for Diaspora Children" (SPDC), for the academic year 2021-22
SPDC Flyer
Ministry of External Affairs (MEA), Government of India launched a scheme called " Scholarship Programme for Diaspora Children" (SPDC), for the academic year 2021-22 on May 31, 2021, for the Children of NRIs/ PIOs belonging to 69 countries (including Portugal) in pursuing under graduate courses in several disciplines in India. A copy of the revised guidelines are given in the link for ready reference. (https://www.eoilisbon.gov.in/docs/1623749866SPDC%20Guidelines%20for%20the%20AY%202021-22.pdf) Only fresh year students ( Ist year) shall be eligible to get the scholarship.
The following are the highlights of the SPDC for the academic year 2021-22:
(i) The scheme is open to four categories of applicants in the age group of 17 to 21 years as on July 31, 2021.
(a) Children of Persons of Indian Origin
(b) Children of Non-Resident of Indians
(c) Children of Indian workers of ECR countries – studying outside India.
(d) Children of Indian workers in ECR countries– studying in India.
(ii) The total seats of scholarships is 150, out of which 50 seats are reserved for the category (c) and (d). Of these 50 scholarships, 1/3rd shall be reserved for children who are pursuing studies in India, subject to the fulfilling eligibility conditions. If any of these seats are not filled up, they will be made available to applicants from other categories under SPDC and vice-versa.
(iii) Children of NRIs should have pursued at least three years of education, inclusive of 11th & 12th or equivalent ( not beyond), in a foreign country during the last six years, and should have passed the qualifying examination abroad.
(iv) Candidates would be selected on the basis of their performance in the qualifying examination ( equivalent to plus 2 stage in India) which decides the eligibility to apply for the scholarship scheme. The candidates would also have to fulfill all the criteria prescribed for the purpose.
(v) The institutions that are covered under this scheme are:
(a) NITs, IIITs, Schools of Planning and Architecture
(b) 'A' Grade institutions accredited by NAAC and recognized by UGC.
(c) Other institutions covered under DASA scheme.
(vi) The amount of scholarship admissible would be 75% of the total Institutional Economic Cost (IEC) subject to a maximum of US$ 4000/- per annum in respect of NITs and other Institutions covered under DASA Scheme. IEC includes Tuition fee, Hostel fee & other institutional charges ( Food charges are excluded).
(vii) The total monthly income of the parent(s) of the applicant should not exceed an amount of equivalent of US$ 5000/- . The parents of the applicants will provide a self attested salary certificate from the employer based in a foreign country.
(viii) After obtaining admission in selected courses in any of the specified Institutes as mentioned in Appendix "C", students who fulfill all other eligibility conditions can complete and submit the on-line application form on the SPDC portal ( www.spdc.india.gov.in).
(ix) The last date for submission of the duly filled in application forms in the prescribed format is November 30, 2021.
Government of India launched a scheme called Scholarship Programme for Diaspora Children (SPDC), in the academic year 2006-2007, for the wards of Persons of Indian Origin (PIOs) and Non-Resident Indians (NRIs) to assist them in pursuing Under Graduate courses in Indian Universities/Institutes. Under SPDC scheme, financial assistance for specific undergraduate courses in Professional and Non-Professional courses (except Medical and related courses) is provided towards tuition fee, admission fee and post admission services. The scheme is applicable to NRIs and PIOs from 66 countries (including Portugal).
For more details, please visit https://spdcindia.gov.in.
Ministry of External Affairs (MEA), Government of India launched a scheme called " Scholarship Programme for Diaspora Children" (SPDC), for the academic year 2021-22 on May 31, 2021, for the Children of NRIs/ PIOs belonging to 69 countries (including Portugal) in pursuing under graduate courses in several disciplines in India. A copy of the revised guidelines are given in the link for ready reference. Only fresh year students ( Ist year) shall be eligible to get the scholarship.
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Bac se numește o ambarcațiune cu fundul și capetele plate, cu care se fac scurte traversări de fluvii, râuri, canale sau de lacuri ori care este folosită pentru serviciile auxiliare ale unei nave. Când este folosită la transportul de persoane, animale și vehicule de la un mal la altul mai poartă și denumirea de pod umblător, pod mișcător sau pod plutitor, care poate fi cu sau fără propulsie proprie.

Corpul bacului este construit din lemn sau metal, are fundul plat, prova și pupa plate, pentru a putea acosta la maluri neamenajate.

În județul Alba, bacul este numit "brudină".

Clasificare

Criteriul "punte"
Bacurile pot fi puntate sau nepuntate.

Un bac puntat este o ambarcațiune, de regulă nepropulsată, cu fundul plat, destinată, transportului de mărfuri pe punte în limitele acvatoriului unui port.

În sectoarele cu trafic intens, legătura între maluri se realizează cu bacuri autopropulsate, cu 1 sau 2 punți dotate cu tot ce este necesar pentru transportul pasagerilor, gararea și fixarea autovehiculelor, depozitarea mărfurilor.

Criteriul "acces"
Bacurile pot fi cu acostare laterală sau cu dublu acces.

Bacul cu acostare laterală poate acosta lateral, lângă un ponton special prevăzut cu o estacadă.

Bacul cu dublu acces poate stabili o legătură cu malul cu oricare din capete, sunt de obicei de mici dimensiuni, iar deplasarea lor se face prin remorcare sau tragere  cu trolii și cabluri.

Istoric
Pe sectorul Dunării de Jos din cele mai vechi timpuri au făcut legătura numeroase bacuri pornind din porturile românești.

Note

Bibliografie
Ion A. Manoliu. Nave și Navigație, Editura Științifică și Enciclopedică, București, 1984

Vezi și
 Feribot

Legături externe
Bacul Călărași Chiciu Ostrov Fișier YouTube

Ambarcațiuni

redpajama_set_name: RedPajamaWikipedia