Yongzhe Zheng

Zhixin Li

Canlong Zhang
email: clzhang@gxnu.edu.cn

A hybrid architecture based on CNN for image semantic annotation

Keywords: semantic learning, image auto-annotation, convolutional neural network

Due to semantic gap, some image annotation models are not ideal in semantic learning. In order to bridge the gap between cross-modal data and improve the performance of image annotation, automatic image annotation has became an important research hotspots. In this paper, a hybrid approach is proposed to learn automatically semantic concepts of images, which is called Deep-CC. First we utilize the convolutional neural network for feature learning, instead of traditional methods of feature learning. Secondly, the ensembles of classifier chains (ECC) is trained based on obtained visual feature for semantic learning. The Deep-CC corresponds to generative model and discriminative model, respectively, which are trained individually. Deep-CC not only can learn better visual features, but also integrates correlations between labels, when it classifies images. The experimental results show that this approach performs for image semantic annotation more effectively and accurately.

Introduction

In the past decades, several state-of-the-art approaches have been proposed to solve the problems of automatic image annotation, which can be roughly categorized into two different models. The first one is based on generative model. The auto-annotation is first defined as a traditional supervised classification problem [START_REF] Liu | A survey of content-based image retrieval with high-level semantics[END_REF] and [START_REF] Li | Automatic Linguistic Indexing of Pictures by a statistical modeling approach[END_REF], which mainly depends on similarity between visual features and predefined tags to model the classifier, then a unknown image is annotated relevant tags by computing similarity of visual level. The other is based on discriminative model, which are treat image and text as equivalent data. These methods try to mine the correlation between visual features and labels on an unsupervised basis by estimating the joint distribution of multi-instance features and words of each image [START_REF] Liu | A survey of content-based image retrieval with high-level semantics[END_REF] and [START_REF] Smeulders | Content-based image retrieval at the end of the early[J][END_REF]. In brief, these methods extract various low-level visual features. These approaches greatly reduces the ability of feature presentation, therefore it makes the semantic gap become more serious between image and semantic.

Furthermore, the performances of image annotation are highly dependent on the representation of visual feature and semantic mapping. In view of the fact that deep convolutional neural networks (CNNs) has been demonstrated a outstanding performance in computer vision recently. Besides, Mahendran and Vedaldi [START_REF] He | Deep Residual Learning for Image Recognition[END_REF], [START_REF] Krizhevsky | ImageNet Classification with Deep Convolutional Neural Networks[END_REF], [START_REF] Mahendran | Understanding deep image representations by inverting them[END_REF] and [START_REF] Mnih | Human-level control through deep reinforcement learning[END_REF] have demonstrated that CNN has a better effect over existing methods of hand-crafted features in many applications, such as object classification, face recognition, and image annotation. Inspired these articles, this paper proposes a hybrid architecture based on CNN for image semantic annotation to improve the performances of image annotation.

In this paper, our main contributions are the following. Firstly, we use redesigned CNN model to learn high-level visual features. Secondly, we employ the ensembles of classifier chains (ECC) to train model on visual features and predefined tags. Finally, we propose a hybrid framework to learn semantic concepts of images based CNN (Deep-CC). Deep-CC not only can learn better visual features, but also integrates correlations between labels when it classifies images. The experimental results show that our approach performs more effectively and accurately.

CNN visual feature extraction

In the past few years, some recent articles [START_REF] Russakovsky | ImageNet Large Scale Visual Recognition Challenge[J[END_REF] and [START_REF] Wu | Deep multiple instance learning for image classification and auto-annotation[C]// Computer Vision and Pattern Recognition[END_REF] have demonstrated that the CNN models pre-trained on large datasets with data diversity, e.g., AlexNet [START_REF] Krizhevsky | ImageNet Classification with Deep Convolutional Neural Networks[END_REF] which can be directly transferred to extract CNN visual features for various visual recognition tasks such as image classification and object detection. CNN is a special form of neural network that consists of different types of layers, such as convolutional layers, spatial pooling layers, local response normalization layers and fully connected layers. Different network structures will show different ability of visual features representation. Krizhev et al. [START_REF] Krizhevsky | ImageNet Classification with Deep Convolutional Neural Networks[END_REF] have proved that the Rectified Linear Units (ReLUs) not only saves the computing time, but also implements the features of sparse representation, and ReLU also increases the sample characteristic diversity. So in order to improve the generalization ability of the feature representation, we extract fc7 visual vectors after ReLU. As shown in the top of the Fig. 1, our CNN model has the similar network structure to the AlexNet. As reflected in Fig. 1, which contains five convolutional layers (short as conv) and three fully-connected layers (short as fc). The CNN model is pre-trained in 1.2 million images of 1000 categories from ImageNet [START_REF] Russakovsky | ImageNet Large Scale Visual Recognition Challenge[J[END_REF].

Extracting Visual Features From pre-trained CNN Model

G Li et al. [START_REF] Li | Visual saliency based on multiscale deep features[C]// Computer Vision and Pattern Recognition[END_REF] and Razavian et al. [START_REF] Razavian | CNN Features Off-the-Shelf: An Astounding Baseline for Recognition[END_REF] have demonstrated the outstanding performance of the off-the-shelf CNN visual features in various recognition tasks, so we utilize the pre-trained CNN model to extract visual features. Particularly, each image is resized to 227 * 227 and fed into the CNN model. As shown in Fig. 1, it represents the feature flow extracted from the convolutional neural network. The fc7 features are extracted from the secondly convolution layer after ReLU. The fc7 denote the 4096 dimensional features of the last two fully-connected layers after the rectified linear units (ReLU) [START_REF] Krizhevsky | ImageNet Classification with Deep Convolutional Neural Networks[END_REF].

Exacting visual feature from fine-tuned CNN model

Taking into account the different categories (and the number of categories) between the target dataset and ImageNet, if we directly utilize the pre-trained model on the ImageNet to exact image visual features, it may not be the optimum strategy. To make the model fit the parameters better, we redesign the last hidden layer for visual feature learning task, later re-designed CNN model by fine-tuning parameters with each of images in the target dataset. Considering the rationality of the design of the convolutional neural networks, our CNN model has the similar network structure to the AlexNet. As show in the mid of Fig. 1, the overall architecture of our CNN model still contains five conv layers , followed by a pooling layer and three fully-connected layers. We redesign the last hidden layer for feature learning task. The number of neural units of the last fully-connected layer is modified from 1000 to m, where m is the number of the target dataset's categories. The output of the last fully-connected layer is then fed into a m-way softmax which produces a probability distribution over m categories.

Given one training sample x, the network extracts layer-wise representations from the first conv layer to the output of the last fully connected layer fc8 ∈ m , which can be viewed as high level features of the input image. Followed by a softmax layer, fc8 is transformed into a probability distribution p∈ m for objects of m categories, and cross entropy is used to measure the prediction loss of the network. Specifically, we define the following formula.

exp( ) and log( ) exp( )

i i i i i i v p L t p v     (1)
In formula (1), L is the loss of cross entropy. The gradients of the deep convolutional neural network is calculated via back propagation

    ii i L pt h (2) In formula (2), t = {t i |t i ∈{0, 1}, i = 1, . . . , m, ∑ m k=1 t i = 1}
denotes the true label of the sample x j , where the {x j | j =1,2,..., n}is a bag of instances. t = {t i |t i ∈{0, 1}, i = 1, . . . ,m} is the label of the bag; Convolutional neural network extracts representations of the bag, it can get a feature vector v = {v ij }∈ m×n , in which each column is the representation of an instance. The aggregated representation of the bag for visual vectors are defined as follows.

12 ( , ,..., )

i i i in v f v v v   (3)
In the training phase, similarly back propagation algorithm is used to optimize the loss function L. Suppose that we have a set of training images I = {M i }. The trained instances of traditional supervised learning in which training instances are given as pairs {(m i , l i )}, where m i ∈ m is a feature vector and l i ∈{0,1} is the corresponding label. In visual feature learning, trained sample is regarded as bags {I i }, and there are a number of instances x ij in each bag. Finally, the network extracts layer-wise representations from the first conv layer to the output of the last fully connected layer visual vectors v i , which can be viewed as high level features of the input image. By fine-tuning like this, the parameters can better adapt to the target dataset by rectifing the transferred parameters. For the task of visual feature learning, we first employ existing model to fine-tune the parameters in the target dataset, then we apply the fine-tuned CNN model to learn image visual features. Similarly, the FT-fc7 denotes the 4096 dimensional features of the last two fully-connected layers after the rectified linear units (ReLU).

Ensembles of classification classifiers for semantic learning

In the discriminative learning phase, the ensemble of classification classifiers (ECC) [START_REF] Read | Classifier chains for multi-label classification[END_REF] are used to accomplish the task of multi label classification, and each of the binary classifier is implemented by SVM. Taking into account the semantic correlations between tags, ECC can classify images into multiple semantic classes, with a high degree of confidence and acceptable computational complexity. Furthermore, by learning the semantic relevance between labels, classifier chain can effectively overcome the problems of label independence in image binary classification.

The classifier chain model consists of |L| binary classifiers, where L denotes the truth label set. Classifiers are linked along a chain where each classifier deals with the binary relevance problem associated with label l j ∈L. The feature space of each linked in the chain is extended with the {0,1} label associations of all previous links. The training procedure is outlined in Algorithm 1 in the left of Table 1. Lastly, we can note the notation for a training example (x, S), where S⊆L and x is an instance feature vector.

Hence a chain C 1 ,C 2 ,...,C i of binary classifier is formed. Each classifier C j in the chain is responsible for learning and predicting the binary association of label l j , which is given in the feature space and is augmented by all prior binary relevance predictions in the chain {l 1 , l 2 ,..., l j-1 }. The classification procedure begins at C 1 and propagates along the chain C 1 determines Pr(l 1 |x) and every following classifier C 2 ,...,C j predicts Pr(l j |x i ,l 1 ,l 2 ,...,l j-1 ). This classification procedure is described in Algorithm 2 in the right of Table 1 This training method passes label information between classifiers, with classifier chain taken into account label correlations, so it overcomes the label independence problem of binary relevance method. However, classifier chain still remains advantages of binary relevance method including low memory and runtime complexity. Although |L|/2 features are added to each instance on an average, this item is negligible in computational complexity because |L| is invariably limited in practice.

Different order of the chain clearly has a different effect on accuracy. This problem can be solved by using an ensemble framework with a different random train ordering for each iteration. Ensembles of classifier chains train m classifier chains C 1 , C 2 ,...,C m . Each C k model is trained with a random chain which can order the L outputs and get a random subset of D. Hence each C k model is likely to be unique and able to give different multi-label predictions. These predictions are summed by label so that each label receives a number of votes. A threshold is used to select the most popular labels which form the final predicted multi-label set. These predictions are summed by label so that each label receives a number of votes. A threshold is used to select the most popular labels which form the final predicted multi-label set.

Each kth individual model predicts vector y k = (l 1 ,l 2 ,...,l |L| )∈{0,1} |L| . The sums are stored in a vector W = (λ 1 ,λ 2 ,...,λ |L| )∈ |L| ,where λ j is defined as λ j = Σ m k = 1 l j ∈y k . Hence each λ j ∈W represents the sum of the votes for label l j ∈L. We then normalize W to W norm , which represents a distribution of scores for each label in [0,1]. A threshold is used to choose the final multi-label set Y such that l j ∈Y where λ j ≥t for threshold t. Hence the relevant labels in Y represent the final multi-label prediction.

Hybrid framework for image annotation

On the deep model and ensembles of classifier chains, we propose a hybrid learning framework to address cross-modal semantic annotation problem between images and text with Multi-label. As a comparison, we evaluate the deep feature's performance from the AlexNet CNN on those same benchmarks. Following by [START_REF] Monay | Modeling Semantic Aspects for Cross-Media Image Indexing[END_REF], we choose 5 words with highest confidence as annotations of the test image. After each image in the database is annotated, the retrieval algorithm ranks the images labeled with the query word by decreasing confidence.

In this section, we conduct experiments of our Deep-CC learning framework on both image classification and image auto-annotation. We choose a dataset Corel5K which is widely used in image classification and annotation. In order to make the experimental result more convinced, we simultaneously compare the experimental results with the existing traditional model and deep model.

Datasets and Evaluation measures

In order to test the effectiveness and accuracy of the proposed approach, we conduct our experiments on a baseline annotated image datasets Corel5K [START_REF] Duygulu | Object Recognition as Machine Translation: Learning a Lexicon for a Fixed Image Vocabulary[END_REF]. Corel5k is a basic comparative dataset for recent research works on image annotation. The dataset contains 5000 images from 50 Corel Stock Photo cds. We divided this dataset into 3 parts: a training set of 4000 images, a validation set of 500 images and a test set of 500 images. Like the Duygulu et al. [START_REF] Duygulu | Object Recognition as Machine Translation: Learning a Lexicon for a Fixed Image Vocabulary[END_REF], We divide separately the training set of 4500 images and the test set of 500 images.

Image annotation performance is evaluated by comparing the captions automatically generated for the test set with the human-produced ground truth. It is essential to include several evaluation measures in multi-label evaluation. Similar to Monay et al. [START_REF] Monay | Modeling Semantic Aspects for Cross-Media Image Indexing[END_REF], we use mAP as evaluation measures. Naturally, we define the automatic annotation as the top 5 semantic words of largest posterior probability, and compute the recall and precision of every word in the test set.

Results for image annotation on Corel5K

In this section, we demonstrate the performance of our model on the corel5k data set for image multi-label annotation, and compare the results with some existing image annotation methods, e.g. PLSA-WORDS [START_REF] Monay | Modeling Semantic Aspects for Cross-Media Image Indexing[END_REF], HGMD [START_REF] Li | Learning semantic concepts from image database with hybrid generative/discriminative approach[END_REF] and DNN [START_REF] Sermanet | OverFeat: Integrated Recognition, Localization and Detection using Convolutional Networks[END_REF]. We evaluate the returned keywords in a class-wise manner. The performance of image annotation is evaluated by comparing the captions automatically generated with the original manual annotations. Similar to Monay F et al. [START_REF] Monay | Modeling Semantic Aspects for Cross-Media Image Indexing[END_REF], we compute the recall and precision of every word in the test set and use the mean of these values to summarize the system performance. Table 2 reports results of several models on the set of all 260 words which occur in the training set. Data in precision and recall columns denotes mean precision and mean recall of each word. The off-the-shelf CNN features (i.e. fc7 and FT-fc7 ) obtain significant improvements ( 7.8% based on PLSA-WORDS, 3.4% based on HGDM ) compared with these traditional feature learning methods. After fine-tuning, a further improvement (8.2% based on PLSA-WORDS, 4.6% based on HGDM) can be achieved with the best performance of the CNN visual features FT-fc7.

Annotations of several images obtained by our Deep-CC annotation system are show in Fig. 2. We can see that annotations generated by Deep-CC are more accurate than HGDM in most cases. In order to be more intuitive to observe different precision-recall in various methods, the Fig. 3 presents the precision-recall curves of several annotation models on the Corel5k data set. As is shown in Fig. 3, Deep-CC performs consistently better than other models. Where the precision and recall values are the mean values calculated over all words.

Result analysis

In summary, the experimental results on Corel5k show that Deep-CC outperforms many state-of-the-art approaches, which proves that the redesigned CNN and the hybrid framework is effective in learning visual features and semantic concepts of images. We compare the CNN visual features with traditional visual features for learning semantic concepts of images over two traditional learning approaches and a deep model. Especially, the comparison in terms of rigid and articulated visual features among Corel5k is shown in Table 2, from which it can be seen that CNN feature outperforms almost all the original hand-crafted features. To verify this assumption, different visual features between traditional models (also from the authors of this paper) and CNN mode, and FT-fc7 is executed to make an enhanced prediction for Corel5k . Incredibly, the mAP score on Corel5k can surge to 35.2% as shown in Table 2, which demonstrates the great dominance in the deep networks. To sum up, based on the above reported experimental results, we can see that CNN visual features are very effective for semantic image annotation.

Conclusion

In this paper, we utilize CNN model to learn deep visual features, and we redesign the last hidden layer for feature learning task, and in order to obtain high performance of feature representation, we first train our deep model on ImageNet, then the pre-trained parameters are fine-tuned on target dataset. We showed under what conditions each visual feature can perform better, and propose a hybrid architecture. We demonstrated that re-designed CNN model and ensembles of classifier chains can effectively improve annotation accuracy.

In comparison to many state-of-the-art approaches, experimental results show that our method achieves superior results in the tasks of image classification and annotation on Corel5K. However, in the process of learning visual features, Deep-CC only employ single convolution neural network not fully understanding multiple instance in the image, and how to excavate the high-level semantic relevance between the tags, it can be deeply studied. In future research, we aim to take semi-supervised learning based on a large number of unlabeled data to improve its effectiveness.

Acknowledgement

This work is supported by the National Natural Science Foundation of China (Nos. 61663004, 61262005, 61363035), the Guangxi Natural Science Foundation (2013GXNSFAA019345, 2014GXNSFAA118368), the Guangxi "Bagui Scholar" Teams for Innovation and Research Project, Guangxi Collaborative Innovation Center of Multi-source Information Integration and Intelligent Processing.

Fig. 2 Fig. 1 .

 21 Fig. 1. The Pipeline of Image Annotation

Fig. 2 .

 2 Fig. 2. Comparison of annotations made by HGDM and Deep-CC on Corel5k

Fig. 3 .

 3 Fig. 3. Precision-recall curves of several models for image annotation on Corel5K

  .

		Tabel 1. Training and prediction procedures of ensembles of
		classifier chains for multi-label learning
		Algorithm 1.	Algorithm 2.
	Processing	Training steps of classifier chain	Classifying procedure ECC
	Input	Training set I = {(x1,S1),(x2,S2),...,(xn,Sn)} Test example x.
	Output	Classifier chains {C1,C2,...,C|L|}	Y ={l1,l2,...,l|L|}.
	procedures
	1	For i∈1,2,...|L|	Y←{}
	2	Semantic learning	For i∈1,2,...,|L|
	3	I′←{}	Do Y← Y ∪ (li←Ci:(xi,l1, l2,...lj-1))
	4	For (x,S)∈I	Return (x,Y)
	5	Do I′←I′∪((x,l1,l2,...,li-1),li)
	6	Train Ci to predict binary relevance of li
	7	Ci : I′→li ∈{0,1}

Table 2 .

 2 Performance (mAP in %) comparison in terms of different methods and visual features algorithms on Corel5k. (The "-" means to use their method)

	Method	Visual features	Result on all words Precision Recall	mAP
		-	22.1	12.1	19.1
	PLSA-WORDs	Fc7	27.5	21.7	26.9
		FT-fc7	29.3	22.6	27.3
		-	32.1	29.3	26.3
	HGDM	Fc7	36.4	30.5	29.7
		FT-fc7	37.6	32.9	30.9
	DNN	-	37.5	40.5	32.7
	Deep-CC(our)	-	39.7	37.6	35.2


Hengxun Li

Chun Liao
email: liaochun@iie.ac.cn

Ning Wang

Guangjun Hu

Opinion Targets Identification based on Kernel Sentences Extraction and Candidates Selection

Keywords: opinion targets identification, kernel sentence extraction, candidates selection, SVM

With the developing of the Internet, communication becomes more and more frequent, and the traditional opinion mining technology has been unable to meet the people's needs, especially in the field of opinion targets identification. Therefore, how to do appropriate pre-processing and postprocessing with opinion sentences to improve the quality of opinion sentence identification has become a hot issue in recent years. Researches on kernel information filtering and candidates screening of traditional opinion targets identification methods are insufficient. In this paper, we propose a novel opinion targets identification method which integrates kernel sentences extraction with candidates selection based on rules analysis and SVM screening. Experimental results on COAE2014 dataset show that this approach notably outperforms other baselines of opinion targets identification.

Introduction

With the widespread popularity of the Internet, Internet already becomes the main way for people to gain and share information. As an emerging platform for interaction and communication, microblog has become part of people's life gradually. According to the Thirty-seventh Statistical Report on The Development of China Internet Network published by the CNNIC, until December 2015, the total number of Internet users in China is Six hundred and eighty-eight million [START_REF]Thirty-seventh Statistical Report on The Development of China Internet Network[END_REF]. More and more people begin to pay attention to microblog, people share their moods and opinions and discuss the popular topics. Microblog has huge data and is time-limited. It can be dug out a lot of meaningful information. Therefore, it has attracted a large number of scholars to develop related research, one of the hottest direction of the research is the sentiment analysis about the microblog.

Sentiment analysis is also known as opinion mining. It refers to carry on the subjective analysis, the induction and the sentiment polarity judgment [START_REF] Zhao | Sentiment Analysis[J][END_REF]. According to the progressive level of the task of the sentiment analysis, the task of the sentiment analysis can be divided into three categories: the extraction of sentiment information, the classification of the sentiment information, and the retrieval and induction of the sentiment information. The extraction of sentiment information is the basic task of the sentiment analysis.

It means to excavate the structured information from unstructured text sentiment, including the opinion targets, opinion words, opinion tendency and opinion holders and so on. As the basic task of the sentiment analysis, it not only can serve the upper level of the sentiment analysis, such as the classification of the sentiment information, but also can be directly applied to the electronic commerce, information security and other fields. For example, in the statistics of commodity assessments, we can make other consumers understand the advantages and disadvantages of the goods clearly in all directions. It can also help to improve the marketing strategy and the performance of the goods.

Opinion targets is also known as sentiment targets or view targets. It mains the subject of discussion in a text. For example, " 对三星手机彻底没好感了", the opinion target is "三星手机". Extracting the correct opinion targets means that we can make more accurate analysis and inference to a certain object, which also means great commercial and social value.

In this paper, we propose a novel opinion targets identification method which integrates kernel sentences extraction with candidates selection based on rules analysis and SVM screening. We first extract the kernel sentences of the oral opinion sentences, then we adopt the CRF-based method to perform opinion targets identification to get candidate opinion targets. Finally, we screen all the candidate opinion targets based on SVM classifier and acquire the final opinion targets identification results. In experiments on the COAE 2014 dataset we find that our method can substantially extract opinion targets more effectively under different evaluation metrics.

Related Work

Hu [START_REF] Hu Minqing | Mining opinion features in customer reviews [C][END_REF] thought that the opinion targets was a noun or noun phrase. Gaining the candidate opinion targets by digging out the noun or frequent item sets of the noun phrase. Zhuang [START_REF] Zhuang | Movie review mining and summarization[END_REF] proposed a multi-knowledge-based approach which integrated WordNet, statistical analysis and movie knowledge. At the same time, it is considered that the nearest adjective to the opinion targets is the opinion words. Liu [START_REF] Hongyu | Comment Target Extraction and Sentiment Classification[J][END_REF] extracted the opinion targets by syntactic analysis, PMI and feature pruning. Li [START_REF] Li | A unified graph model for sentence-based opinion retrieval[END_REF] extracted tuples like <emotional words, opinion targets> based on emotional and topic-related lexicons. Li [START_REF] Fangtao | Structure-aware review mining and summarization[END_REF] and Ma [START_REF] Tengfei | Opinion target extraction in Chinese news comments[END_REF] transformed the opinion targets into the sequence labelling, and used conditional random fields model to extract the opinion targets. Xu [START_REF] Xu | Extraction of Opinion Targets Based on Shallow Parsing Features[J[END_REF] used the shallow parsing information and the heuristic location information and other features in the training of conditional random fields model, so that the extraction effect of opinion targets has been improved. Jakob [START_REF] Jakob | Extracting opinion targets in a singleand cross-domain setting with conditional random fields[END_REF] modelled the task as a sequence labelling question and employed CRF for opinion targets extraction. Wang [START_REF] Wang | Feature Engineering for CRFs Based Opinion Target Extraction[END_REF] used the new feature of the semantic role labelling in the training of conditional random fields model, there are four features used to training the conditional random fields model: morphology, dependence, relative position and semantic. Song [START_REF] Song | Comment Object Extraction Based on Pattern Matching and Semi-supervised Learning[END_REF] gained the seed set by sample survey, then expanded the seed set by semi-supervised learning to extract more accurate opinion tar-gets. Xu [START_REF] Xu | Mining Opinion Words and Opinion Targets in a Two-Stage Framework[C]// Meeting of the Association for Computational Linguistics[END_REF] used the syntactic analysis and random walk model to extract opinion targets.

It is not difficult to find whatever which way we use, statistics corpus will help a lot. Consequently, considering the specific features of Chinese microblog, we propose a new method for opinion tar-gets extraction towards microblog based on kernel sentence extraction and candidates selection.

Kernel Sentence Extraction

The key idea of kernel sentence extraction in this paper is mainly to delete redundancy, retain and evaluate the main components of the oral sentence. This paper aims to improve the accuracy of opinion targets identification by using the kernel sentence extraction. The principle of extracting the kernel sentences is to standardize the opinion sentences, and try not to lose the ingredients related to the original opinion sentences. Through statistics and observation of a large number of data, we sum up 10 kinds of rules, as shown in table 1.

Rules Examples Explanation

Delete the English and interrogative sentences;

I

Candidate opinion targets identification and selection

After kernel sentence extraction in section 3, we perform candidate opinion targets identification using CRF model. CRFs(Conditional Random Fields, CRFs) is proposed by Lafferty [START_REF] Lafferty | Conditional Random Fields: Probabilistic Models For Segmenting And Labelling Sequence Data[END_REF] in 2001. Its model structure is shown in Figure 1. Given a set of input random observed variables, this conditional probability distribution model can generate another set of implicit output random variables by training the model.

Fig.1. CRFs Model

In CRF-based method, the features we employed as input are of great importance. In this section, we refer to the features which are employed by Jakob [START_REF] Jakob | Extracting opinion targets in a singleand cross-domain setting with conditional random fields[END_REF] in English and meanwhile put forward some new features based on the specific grammar of Chinese. Generally, we think opinion targets extraction is primarily related with four kinds of features which are named as lexical features, dependency features, relative position features and semantic features. First, as words with the same Part-of-Speech usually appear around the opinion targets, we select the current word itself and the POS of current word as lexical features. Second, we select whether the dependency between current word and core word exists, the dependency type, parent word and the POS of parent word as the dependency features. Finally, considering here is a strong relationship between the sematic roles and POS of emotional words, we select the sematic role name of current word and POS of emotional word in this sentence for CRF. We perform candidate opinion targets selection after candidate opinion targets identification. Candidate opinion targets selection is to judge whether a candidate opinion target is the opinion target of this microblog. This paper considers that the process of screening candidate opinion targets is equivalent to a question of binaryclassification, and that is to judge whether the candidate opinion target is the opinion target of this microblog. So this paper adopts SVM classifier for candidate opinion We sum up three kinds of features for candidate opinion targets selection: semantic role, minimum distance and word frequency. For semantic role feature, we label the agent and patent of semantic role labelling result for candidate opinion targets selection. For example, a microblog of "相机很漂亮", through the semantic role analysis, "相机" is the agent, "漂亮" is patient. Thus, the agent or patient may be the opinion targets. In the experiments, we use the Language technology platform (LTP) [START_REF] Che | Ltp: A Chinese language technology platform[END_REF] of Harbin Institute of Technology for semantic role labelling. For the minimum distance feature, we select the number of words that are nearest to the opinion targets as minimum distance value. In this paper, it is considered that each opinion word has an emotional word to modify. For the word frequency feature, we select the occurrence frequency as the feature value. In a number of microblogs, if the occurrence frequency of a noun or noun phrase is very high, then the noun or noun phrase is the main description of the text, that is to say, it is likely to be the object target.

Finally, we construct the training model based on the methods in table 2 and finally complete the opinion targets identification.

Experiments and Analysis

In the experiment, we firstly obtained kernel sentences using methods in section 3, and then perform CRF-based method for candidate opinion targets identification. Finally, we adopt SVM classifier for candidate opinion targets selection to complete the opinion targets identification. Its structure model is illustrated in Figure 2.

For the experiment data, we adopt 7000 sentences which are provided by COAE2014, these sentences are acquired from microblog, forum and other social network platform. Considering the short, interactive, non-standard features of these sentences, we use rules in section 3 to acquire kernel sentences. Through filtration by these rules, we finally obtain 4,500 normalized sentences with opinion orientation. In this paper, we conduct experiments on such a dataset and assess it with traditional Precision, Recall and F-measure under strict and lenient evaluations which respectively represents the extraction result is exactly the same or overlapped with the labelled one.

Fig.2.Opinion Targets Identification based on Kernel Sentences Extraction and Candidates Selection

As the quality of kernel sentences extraction and candidates selection greatly influences the result of opinion targets extraction, we make a comparison of different approaches of opinion targets identification in this section. We conduct experiments of opinion targets identification with methods of CRF-based method(CRF), performing kernel sentence before the CRF-based method(KSE+CRF), performing kernel sentence before the CRF-based method and conducting candidate opinion targets selection after the CRF-based method(KSE+CRF+CS). The comparing results of these four approaches are represented in Table 3. It can be seen that the effect of opinion targets extraction is highly improved after adding kernel sentences extraction and candidate opinion targets selection, which is probably because they can standardize the corpus and reduce the noise of opinion targets identification. This method not only uses kernel sentences extraction method in section 3 to standardize the corpus, but also adopts machine learning method of SVM to screen the candidate opinion targets and so as to reach a higher precision, recall and F-measure. So this experiment strongly demonstrates the effectiveness and applicability of combination of kernel sentences extraction and candidates selection method. In this paper we propose a novel opinion targets identification method which takes kernel sentences extraction and candidates selection into consideration. We extract the kernel sentences of the oral opinion sentences through rules, and screen all the candidate opinion targets based on SVM classifier after CRF-based methods, finally acquire the opinion targets identification results. The experimental results show that it performs better than other baseline approaches.

Method

In the future work, we will excavate more kernel sentence extraction rules and features for opinion targets identification.

Table 1 .

 1 Rules of kernel sentences extractionWe perform kernel sentence extraction based on the rules in Table1and obtain a standardize corpus for opinion sentence identification.

		am a researcher.	This paper only focuses on
		……?	Chinese opinion targets identification.
	Turn over the sentences with	电池也很耐用//三星手机	This measure is to ensure
	"//"	不错	the forwarding relationship.
		http: ……	Remove the link address
		网址: ……	content and the expression
	Delete text sequence which		of the address, and the
	contains link address in it	地址: ……	extraction result of the opinion targets is not
			affected.
		@.......	"@"+user name, #......#
	Delete text sequence which	@.......转发微博	indicates the topic of
	contains microblog symbols in it	@.......回复 #.......#	microblog. The deletion of them will not affect opinion targets identification.
	Replace the consecutivepunctuations with the first one;	。。。 !!!! ??	This measure is to standardize the expression.
		【…】[…] (…) (…)	Words in brackets are
			generally supplementary
	Delete supplementary text sequence	文章来源	explanation of the main text, and the article source indicates the path, both will
			not influence opinion
			targets identification.
	Delete words of hypothetical tendencies in a sentence.	如果…… 希望…… 假如…… ……	These words would cause noise for opinion targets identification.
	Remove sentences which are for introduction of the following passage.	……的优点 ……的不足 ……的优势 ……

Table 2 .

 2 Feature description of candidates selection based on SVM

	Y1	Y2	Y3	...	Yn-1	Yn
				...
			X=X1, … Xn-1, Xn

Table 3 .

 3 Comparing results of opinion targets identification using different methods

		Strict Evaluation	Lenient evaluation
		Precision	Recall F-measure Precision	Recall F-measure
	CRF	0.6864	0.4513	0.5446	0.7398	0.4712	0.5757
	KSE+CRF	0.6925	0.4598	0.5527	0.7536	0.4873	0.5919
	KSE +CRF+CS	0.7035	0.4668	0.5612	0.7732	0.4963	0.6046


f ]or a few brief years, [the Mathematical Tables Project] was the largest computing organization in the world, and it prepared the way for the modern computing era." D. Grier, 1997 [29] "Blanch, more than any other individual, represents that transition from hand calculation to computing machines." D. Grier, 1997 [29] "[Gertrude Blanch] was virtually the backbone of the project, the hardest and most conscientious worker, and the one most responsible for the amount and high quality of the project's output."

H. E. Salzer, 1989 [66

I. Circular and hyperbolic functions, exponential and sine and cosine integrals, factorial and allied functions, hermitian probability functions (1931) II. Emden functions, being solutions of Emden's equation together with certain associated functions (1932) III. Minimum decompositions into fifth powers (1933) IV. Cycles of reduced ideals in quadratic fields (1934) V. Factor table giving the complete decomposition of all numbers less than 100,000 (1935) [START_REF] Peters | Factor table giving the complete decomposition of all numbers less than 100,000[END_REF] VI. Bessel functions. Part I. Functions of orders zero and unity. On the other hand, the Mathematical Tables Project computed a number of large tables mostly ab initio. Moreover, the purpose of the Project was not so much to complete the computations quickly, but to keep the (human) computers busy, and at the same time to conduct some useful work. At one point the Mathematical Tables Project employed 450 human computers, sometimes aided by mechanical calculating machines, a group which was reminiscent of the one set up for the famed French Tables du cadastre [START_REF] Roegel | The great logarithmic and trigonometric tables of the French Cadastre: a preliminary investigation[END_REF].

The main tables published between 1939 and 1949 by the Mathematical Tables Project are the following ones: • Tables of the moment of inertia and section modulus of ordinary angles, channels, and bulb angles with certain plate combinations, 1941

• Miscellaneous physical tables, 1941

3 Numbers such as MT1, MT2, etc. were given to each volume, but only at a later time. They served for a proper identification of each volume. However, the numbers given in the National Bureau of Standards's publication list [54] and by Grier [START_REF] David | The Math Tables Project of the Work Projects Administration: The reluctant start of the computing era[END_REF] do not completely coincide. It was possibly only after 1948 that a set of 28 "main tables" was presented, with numbers from MT1 to MT28. The list given here is that given by Grier.

• Tables of Bessel functions Y 0 (x), Y 1 (x), K 0 (x), K 1 (x), 0 ≤ x ≤ 1, 1949
Many other smaller or more specialized tables were also published by the Mathematical Tables Project. Lists of published tables are given in the appendices of each of the published volumes. The announcement published in 1941 [START_REF]Work Projects Administration, New York. Announcement of the project for the computation of mathematical tables[END_REF] also lists the tables published so far, those for which computation had been completed or was in progress, and those which were considered for calculation. Archibald's survey gives the status of computations by the end of 1942 [START_REF] Clare | The New York Mathematics Tables Project[END_REF].

The WPA was terminated in 1943, but the Mathematical Tables Project continued to operate in New York until 1948. That year, a number of members of the Mathematical Tables Project moved to Washington, DC to become the Computation Laboratory of the National Bureau of Standards, now the National Institute of Standards and Technology. But Blanch moved to Los Angeles to lead the computing office of the Institute for Numerical Analysis at UCLA, anf Lowan joined the faculty at Yeshiva University in New York. Other tables continued to be computed, of which a detailed list is given by Fletcher et al. [26, pp. 718-720].

The greatest legacy of the Project is the Handbook of Mathematical Functions [START_REF]Handbook of mathematical functions with formulas, graphs, and mathematical tables[END_REF], published in 1964, and edited by Milton Abramowitz and Irene A. Stegun (1919Stegun ( -2008)), two veterans of the Project. But more broadly, the Project developed "the numerical methods of scientific computation [and demonstrated] that computation could solve practical and important problems" [START_REF] David | Gertrude Blanch of the Mathematical Tables Project[END_REF].

An extensive table of natural logarithms was first computed by Isaac Wolfram, a Dutch lieutenant of artillery4 and published by Schulze in 1778 [START_REF] Karl | Neue und erweiterte Sammlung logarithmischer, trigonometrischer und anderer zum Gebrauch der Mathematik unentbehrlicher Tafeln[END_REF] (figure 1). Wolfram's table represents six years of work [17, p. 166]. The original table omits half-a-dozen logarithms which Wolfram could not compute because of an illness. These logarithms were supplied in the Berlin Ephemeris for 1783 [69, p. 191], [24, p. 602].

As highlighted by Archibald [12, p. 193], Wolfram made use of two or three different methods for the computation of the natural logarithms. A first way is to take an accurate value of the decimal logarithm and to multiply it by ln 10. Two other ways are to make use of the formulae

ln(1 + x) = ∞ m=1 (-1) m+1 x m m (1) ln 1 1 -x = ∞ m=1 x m m (2)
and to choose appropriate values for x. For instance, with x = 1/23400, we have

1 + x = 23401 23400 = 7 • 3343 2 3 • 3 2 • 5 • 13
and the computation of ln(1 + x), combined with the values of the logarithms of 2, 3, 5, 7, and 13, provides the logarithm of 3343. With x = 1 2651•10 3 , we have

1 -x = 2651 • 10 3 2651 • 10 3 -1 = 11 • 241 • 10 3 13 • 61 • 3343
and we have another way to compute ln 3343. This method was in fact anticipating the work of Edward Sang [START_REF] Sang | A new table of seven-place logarithms of all numbers from 20 000 to 200 000[END_REF] who proceeded much in the same way.

Apart from Wolfram's table which was reprinted in 1794 by Vega [START_REF] Vega | Thesaurus logarithmorum completus, etc[END_REF] (figure 2), in 1795 by Callet (first hundred primes, to 20 places) [START_REF] Callet | Tables portatives de logarithmes, contenant les logarithmes des nombres, depuis 1 jusqu'à 108000[END_REF], and in 1922 by Peters & Stein [START_REF] Theodor | Zehnstellige Logarithmentafel volume 1 : Zehnstellige Logarithmen von 1 bis 100000 nebst einem Anhang mathematischer Tafeln[END_REF], we mention the large tables of Thiele (1908, 48 decimals) [START_REF] Thiele | Tafel der Wolfram'schen hyperbolischen 48 stelligen Logarithmen[END_REF], Vietz (1825, 81 decimals) [START_REF] Vietz | Natürliche Logarithmen der Zahlen von 1-25 auf 81 Dezimalstellen[END_REF], Warmus (1954, 108 decimals) [START_REF] Warmus | Sur l'évaluation des tables de logarithmes et tables des logarithmes naturels à 36 décimales[END_REF], Uhler (1942, 137 decimals) [START_REF] Scudder | Original tables to 137 decimal places of natural logarithms for factors of the form 1 ± n • 10 -p , enhanced by auxiliary tables of logarithms of small integers[END_REF], and Uhler (1943, 155 decimals) [START_REF] Scudder | Natural logarithms of small prime numbers[END_REF]. Uhler (1940) [START_REF] Scudder | Recalculation and extension of the modulus and of the logarithms of 2, 3, 5, 7 and 17[END_REF] gave a few basic natural logarithms to about 330 places. The present table published in 1941 gave the logarithms to 16 places, and finally, Spenceley, [START_REF] Spenceley | Smithsonian logarithmic tables to base e and base 10[END_REF] [START_REF] Spenceley | Smithsonian logarithmic tables to base e and base 10[END_REF] gave them to 23 places.

Mention should also be made of Kulik who had prepared a table of natural logarithms to 48 places from 1 to 11000, based on Wolfram's table [START_REF] Philip | Canon logarithmorum naturalium in 48 notis decimalibus pro omnibus numeris inter 1 et 11000 denuo in computum vocatus[END_REF][START_REF] Philip | Auszug aus einem Briefe des Herrn Professors Kulik an den Herausgeber[END_REF][START_REF] Philip | Auszug aus einem Briefe des Herrn Professor Kulik an den Herausgeber[END_REF][START_REF] Clare | Kulik's table of natural logarithms[END_REF][START_REF] Clare | A volume of tables by Kulik[END_REF][START_REF] Clare | New information concerning Isaac Wolfram's life and calculations[END_REF]13], but although this table may have been printed, no copy has been located anywhere.

A number of extensive smaller tables of natural logarithms have also been published, in particular by [START_REF] Barlow | New mathematical tables, etc[END_REF] [START_REF] Barlow | New mathematical tables, etc[END_REF] (reprinted in Rees's Cyclopaedia (1819) [START_REF] Anonymous | Article "Hyperbolic logarithms[END_REF]) and Dase (1850) [START_REF] Martin | Tafel der natürlichen Logarithmen der Zahlen[END_REF].

For an extensive list of existing tables of natural logarithms by about 1960, see the survey published by Fletcher in 1962 [26, p. 249] 3 The Project's table of natural logarithms (1941)

Description

The Project's table of natural logarithms spans four volumes [START_REF] Noah | Table of natural logarithms[END_REF]. The first two volumes give the natural logarithms of the integers from 1 to 49999 and from 50000 to 99999 to sixteen decimal places. The last two volumes give the natural logarithms of the decimal numbers from 0 to 10, by steps of 0.0001, also to sixteen decimal places. The latter two volumes can be (and were) derived from the first two by subtracting ln(10000) = 4 ln 10, so that for instance ln 0.2805 = ln 2805 -4 ln 10.

The technical staff involved in the preparation of these volumes was made of Gertrude Blanch (1897-1996), Frederick G. King, Milton Abramowitz , Jack Laderman, William Kaufman, Matilda Persily, and Jacob Miller for volumes 1 and 2, in that order. In addition, volumes 3 and 4 list William Horenstein, Ida Rhodes and Herbert E. Salzer (1915Salzer ( -2006)), but this time the names are listed alphabetically.

Algorithms

The starting point of the Project's table was Wolfram's table of natural logarithms published by Schulze in 1778 [START_REF] Karl | Neue und erweiterte Sammlung logarithmischer, trigonometrischer und anderer zum Gebrauch der Mathematik unentbehrlicher Tafeln[END_REF]. This table gave the natural logarithms of the first 2200 integers and of primes and certain composite numbers up to 10009, all to 48 decimal places. The only omissions were the logarithms of 9769, 9781, 9787, 9771, 9783, and 9907. The Project used Vega's reprint published in 1794 [START_REF] Vega | Thesaurus logarithmorum completus, etc[END_REF], where the omissions had been filled.

The logarithms of composite numbers not found in Wolfram's table were obtained by the formula ln AB = ln A+ln B. Logarithms of primes greater than 10009 were computed as follows: using

argth(x) = x + x 3 3 + x 5 5 + x 7 7 + • • • (3)
and

argth(x) = 1 2 ln 1 + x 1 -x (4)
we have

argth 1 2n 2 -1 = 1 2 ln 1 + 1 2n 2 -1 1 -1 2n 2 -1 = 1 2 ln n 2 n 2 -1 (5) = ln n - ln(n 2 -1) 2 = ln n - ln(n -1) + ln(n + 1) 2 (6)
From that it follows that

ln n = ln(n -1) + ln(n + 1) 2 + argth 1 2n 2 -1 (7) = ln(n -1) + ln(n + 1) 2 + 1 2n 2 -1 + 1 3 • (2n 2 -1) 3 + 1 5 • (2n 2 -1) 5 + • • • (8)
Hence, ln n, where n is prime, was obtained from the logarithms of two even numbers, as well as a series. This series converges very rapidly, and when n > 10009, only the first term was used, all the others being very small.

These logarithms were computed to 20 places and differencing tests were applied to ensure that the 20th place was correct. 5 These 20-place values were then rounded to 16 places and further subjected to differencing tests. The 20-place worksheet values were also used to derive the last two volumes, by subtraction of 4 ln 10, and the values were then rounded to 16 places.

The first 20 decimal places of all of Wolfram's logarithms were compared with those found here, and several errors were found in Wolfram's table. Most, if not all, of these errors were actually typos, rather than genuine computation errors. 6In order to ensure the correctness of the table, the 20-place values were added by groups of ten, and comparisons were made between the two volumes, as the difference of two corresponding sums had to be 40 ln 10. Moreover, the values from 10000 to 20000 and from 30000 to 100000 were compared with Thompson's Logarithmetica Britannica [START_REF] John | Logarithmetica Britannica, being a standard table of logarithms to twenty decimal places of the numbers 10[END_REF], by adding the values in groups of ten and multiplying them by ln 10. Not a single error was found in either table. (The logarithms of integers from 20000 to 30000 had not yet been published by Thompson, whose work was only completed in 1952.)

In addition to the description of the construction of the table, Lowan also describes interpolation methods. For direct interpolations of logarithms, one might make use of Everett's formula, which is (with the original notations)

u p = pu 1 + qu 0 + 1 6 p(p 2 -1)d 2 u 1 + 1 6 q(q 2 -1)d 2 u 0
where p is the decimal part of the number, q = 1 -p, u 0 = ln x 0 , u 1 = ln(x 0 + 1), u p = ln(x 0 + p) and d 2 u 0 and d 2 u 1 are the second central differences corresponding to u 0 and u 1 respectively. In order to use this formula, it is therefore necessary to compute the second central differences from the values in the table, since the original table does not give them directly. We do not go into the details of Everett's formula here, and we direct the reader to our introduction to the reconstruction of Thompson's table of logarithms [START_REF] Roegel | A reconstruction of the tables of Thompson's Logarithmetica Britannica[END_REF].

On the other hand, it can often be dispensed with Everett's formula and in most cases, finding the logarithm of a decimal number can be done by using the development of ln(1 + x) and dividing the decimal number by its integral part. By linear inverse interpolation, it is possible to obtain ten significant digits in the argument. The introduction to the original volumes gives hints for more accurate methods of inverse interpolations, and sometimes it may be useful to make use of the table of exponentials [START_REF] Noah | Tables of the exponential function e x[END_REF]. But in any case, one should be aware that the number of meaningful figures in the argument is about the same as in the logarithms, so that for instance if a logarithm is given to 10 decimal places, this will often mean that there is an uncertainty of possibly 0.5 • 10 -10 and this uncertainly will be transferred to the argument. It is therefore usually useless to try to obtain more significant places in the arguments than there are significant places in the logarithms, except if the logarithm is considered to be exact, in which case different methods may be more appropriate anyway.

Notes on the layout

The layout of the tables is in general quite straightforward. There is just one idiosyncrasy. In volume 3 of the original tables, the logarithms up to 0.9999 are negative and the signs are given every five values. But when the integer part changes, the original table gives the absolute value of the logarithm, and not its real value. One has to assume that the sign should be taken from the previous full value given. This may be confusing. For instance, ln 0.0004 is given as 7.82404. . . , but it is really -7.82404 . . .. We have respected this peculiarity. There is only one such case where the original value is given with its sign, namely for ln 0.0498, but for reasons of consistency, we have also used the absolute value in our reconstruction.

Interestingly, the original volume 4 that we had in hands uses two different types of paper, one light, the other darker, and a note printed at the beginning of the volume reads "Because of a paper shortage caused by the war, it was necessary to use two types of paper for this volume."

  (1937) VII. The probability integral (1939) VIII. Number-divisor tables (1940) IX. Table of powers, giving integral powers of integers (1940) X. Bessel functions. Part II. Functions of positive integer order. (1952) Part-volume A. Legendre polynomials (1946) Part-volume B. The Airy integral, giving tables of solutions of the differential equation y = xy (1946)

  For instance, in order to compute ln 1.23456, one can write ln 1-ln 10000 = ln(1.0000486 . . .) + ln 12345 -ln 10000 and use the tabulated values of ln 10000 and ln 12345, and the series development for ln 1.0000486 . . .For inverse interpolation, the simplest method is by the linear interpolation formulax = x 0 + ln x -ln x 0 ln(x 0 + 1) -ln x 0 .

Figure 1 :

 1 Figure 1: An excerpt of Wolfram's table as published by Schulze [68], with the six missing values added later.

Figure 2 :

 2 Figure 2: An excerpt of Wolfram's table as published by Vega [79].

Figure 3 :

 3 Figure 3: An excerpt of the Project's table of natural logarithms (volume 1) [43].

Figure 6 :

 6 Figure 6: The list of mathematical tables available from the National Bureau of Standards in 1948 (2/3) [54].

Figure 7 :

 7 Figure 7: The list of mathematical tables available from the National Bureau of Standards in 1948 (3/3) [54].

Figure 8 :

 8 Figure 8: The list of mathematical tables from the British association for the advancement of science (excerpt from the 1968 edition of volume 4).

•

  Table of the first ten powers of the integers from 1 to 1000, 1939 • Tables of the exponential function e x , 1939 (reconstructed in [65]) • Tables of circular and hyperbolic sines and cosines for Radian arguments, 1939 • Tables of sines and cosines for Radian arguments, 1940 • Tables of sine, cosine and exponential integrals, 1940 (2 volumes) • Table of natural logarithms, 1941 (4 volumes)

•

  Table of sine and cosine integrals for arguments from 10 to 100, 1942 • Tables of probability functions, 1942 (2 volumes) • Table of arc tan x, 1942 • Table of reciprocals of the integers from 100,100 through 200,009, 1943 • Table of the Bessel functions J 0 (z) and J 1 (z) for complex arguments, 1943 • Table of circular and hyperbolic tangents and cotangents for radian arguments, 1943

	• Tables of Lagrangian interpolation coefficients, 1944
	• Table of arc sin x, 1945
	• Tables of associated Legendre functions, 1945
	• Tables of fractional powers, 1946
	• Tables of spherical Bessel functions, 1947 (2 volumes)
	• Tables of Bessel functions of fractional orders, 1948 & 1949 (2 volumes)

Arnold Noah Lowan (1898-1962) [START_REF] Clare | Mathematical table makers. Portraits, paintings, busts, monument[END_REF][START_REF] Anonymous | [END_REF] was born Leibovici in Iasi (Romania). He graduated from the Bucharest Polytechnical Institute of Chemical Engineering in 1924, and the same year moved to the United States. He obtained a Master of Science from New York University in 1929 and a PhD from Columbia University in 1934. He was a fellow at the Institute for Advanced Study, Princeton(1928)(1929)(1930)(1931), lecturer of mathematics at Brooklyn College, New York(1935)(1936)(1937)(1938)(1939)(1940).From 1938 to 1949, he was the director of the computation laboratory at the National Bureau of Standards, where he was directing the publication of a number of mathematical tables. From 1950 to 1952, he was a consultant at the US Naval Ordnance Laboratory and from 1955 to 1962, he was professor of mathematics at Yeshiva University, New York.

Gertrude Blanch (1897-1996) was born in Poland and moved to the United States around 1907. After having graduated from high school in 1914, she first worked as a clerk for 14 years, honing her skills and knowledge of accounting, inventory, planning, risk calculations, and so on. In 1928, she fulfilled her dream to become a mathematician and matriculated to New York University. She received a BSc in Mathematics from NYU in 1932 and a PhD in mathematics from Cornell University in 1935. Around the end of 1937, while attending a continuing education class on relativity taught by Arnold Lowan, Lowan offered her the job of technical director of the Mathematical Tables Project, which she joined in February 1938. Within that project, she designed algorithms that were executed by teams of human computers. Blanch also worked regularly with the Manhattan Project, both during and after the war. In the mid-1950s, she was hired by the Air Force and continued to work on numerical analysis, in particular on Mathieu functions.

Tables of natural logarithmsIn this section, we review the main tables of natural logarithms. Although sometimes called Napierian logarithms, the first table of natural logarithms was not published by Napier, but by Speidell a few years later[START_REF] Speidell | New logarithmes: the first inuention whereof, was, by the honourable Lo. Iohn Nepair, Baron of Marchiston, and printed at Edinburg in Scotland, anno 1614, in whose vse was and[END_REF][START_REF] Roegel | Napier's ideal construction of the logarithms[END_REF][START_REF] Maseres | Scriptores logarithmici[END_REF].

For more on Wolfram, see[START_REF] Whitbread | Report of the committee on mathematical tables[END_REF][START_REF] Clare | Wolfram's table[END_REF][START_REF] Clare | New information concerning Isaac Wolfram's life and calculations[END_REF] 13]. Wolfram had also been working on factor tables[START_REF] Heinrich | Zusätze zu den Logarithmischen und Trigonometrischen Tabellen zur Erleichterung und Abkürzung der bey Anwendung der Mathematik vorfallenden Berechnungen[END_REF] 40].

No details on these tests are given, but we can expect occasional errors of one unit in the 20th place.

A table of erroneous logarithms is given in the original introduction, but we do not reproduce it here. The faulty values are the logarithms of829, 1099, 1409, 1937, 1938, 2093, 3571, 4757, 6343,

7853, 8023, 8837, and 9623.

Note on the titles of the works: Original titles come with many idiosyncrasies and features (line splitting, size, fonts, etc.) which can often not be reproduced in a list of references. It has therefore seemed pointless to capitalize works according to conventions which not only have no relation with the original work, but also do not restore the title entirely. In the following list of references, most title words (except in German) will therefore be left uncapitalized. The names of the authors have also been homogenized and initials expanded, as much as possible.The reader should keep in mind that this list is not meant as a facsimile of the original works. The original style information could no doubt have been added as a note, but we have not done it here.

The present table was published by the agency established by President Roosevelt to alleviate unemployment through public works. The purpose of the Mathematical Tables Project WPA, much of the computation was done by hand. This project was in operation since January 1938 and its administrative director was Arnold Lowan. 1 The mathematical leader of the Project was Gertrude Blanch 2 [

Note

The four volumes of reconstructed tables are given in four separate documents.


domain: qfin shs

text:
James Mill

Jean-Baptiste Say

Victor Bianchini
email: victor.bianchini@univ-paris1.fr.

Nicolas Rieucau
email: nicolas.rieucau@univ-paris8.fr

L Darmstaedter

A. Heertje were purchased from a Parisian bookshop and, outside the private collections of autographs, to our knowledge, no correspondence between J. Mill and J.-B. Say had been hitherto reported. Thanks to the development of electronic catalogues, it is now possible to find other traces of the epistolary relationship between J. Mill and J.-B. Say. For example

Victor Bianchini & Nicolas Rieucau -An Unpublished Letter from James Mill to Jean-Baptiste Say letter reviewed here constitutes material proof of his intentions. Indeed, after J. Mill affirmed that J.-B. Say's response seemed "admirable; the matter most important, & the manner at once pointed & delicate", he said he had no doubt "about the propriety of publishing it" in one of his "more respectable journals"20 and that he "shall endeavor to make some of them notice it as soon as published". However, this letter was only ever published after the death of J.-B. Say in 1833 by his own son-in-law, Charles Comte [1782 -1837] in Mélanges et correspondances d'économie politique. It is difficult to know the reason or reasons for which J. Mill did not publish the letter through his channels. But one can imagine that J. Mill sang the praises of Say's letter, that he further proposed to publish it, out of simple courtesy towards someone that had hospitably welcomed his son in his home in Paris. Moreover, even if J. Mill and J.-B. Say shared certain ideas, notably on the hegemony of Napoléon21 or the colonization of India by Great Britain22 , the former did not have the best opinion of the economic ideas of the latter. Indeed, even though J. Mill had, in 1805, welcomed with praise the first edition of J.-B. Say's treatise [1803], pointing out in particular the law according to which supply cannot exceed demand23 and the triptych order of subject matter's exposition24 -laws of production, distribution, and the consumption of wealth; even though one can find this law in his Commerce Defended [1808, pp. 37-38] and this order of exposition -with several modifications -in his Elements of Political Economy [1821] 25 , it doesn't any less stand that he did not seem, from 1818, to be convinced by the ideas of J.-B. Say on the Victor Bianchini & Nicolas Rieucau -An Unpublished Letter from James Mill to Jean-Baptiste Say question of value and distribution. On this point, J. Mill was a convinced Ricardian26 . His work shows his proximity with D. Ricardo -and, hence, his distance with J.-B. Saywhen, for example, he underlined, in his Elements of Political Economy, the mechanism of differential rent 27 , the inverse relation between salary and profit 28 , or the manner in which value is determined 29 . But even more palpably, J. Mill's Ricardianism makes itself known in his correspondence, directly contrary to J.-B. Say's ideas 30 . If a "duty" of courtesy thus seems to motivate J. Mill when he claimed to appreciate J.-B. Say's letter to C. R. Prinsep and proposed to publish it, it appears that he was himself disposed to sending his own writing projects to J.-B. Say. The letter that we publish here reveals, in fact, that J. Mill sent him two texts, "Government" and "Jurisprudence" 31 , destined for the same publication [START_REF]Jurisprudence" and "Government" were finally published several years later[END_REF] and presented as an "outline of the business legislation". The first of these texts was judged favorably by J.-B. Say: "The praise you bestowed upon the article Government 33 , has emboldened me to beg your acceptance of another article (Jurisprudence) which I have prepared for the same publication". Further, J. Mill informed him that he will soon publish what he called a "school book of political Victor Bianchini & Nicolas Rieucau -An Unpublished Letter from James Mill to Jean-Baptiste Say backwardness to mix in conversation", which was, after all, nothing other than the timidity of a child that was precociously experiencing an intense and isolating intellectual education: "I doubt not a considerable remainder of the awkward manners which are the effect of the seclusion in which he had lived". J. Mill ended his letter attributing this timidity, literarily, to "vestiges of hardiness" (vestigia ruris) that should diminish with time, he hoped. This condescending point of view of a father for his son was maintained once J. S. Mill returned to Great Britain 46 . Yet, the manner in which J. S.

Mill related his time in France leads us to believe that the trip allowed him not only to develop his literary talent in the composition of a Traité De Logique 47 in a language he had begun to learn less than a year earlier, but also to open his spirit to the world 48 and become conscious of the intellectual limits of his family entourage 49 .

We do not know what was in J.-B. Say's response to J. Mill's letter. The only information we dispose is that it was addressed less than three months later, the 6 th of September 1821, by a certain "Clement" [START_REF] Mill | Repondu par Clement le 6 septembre 1821[END_REF] . If this delay suggests that the epistolary relationship between J.-B. Say and J. Mill was not necessarily intense, the few letters found to this day -five sum-total -characterizing a relationship that nonetheless lasted more than 10 years [START_REF]and last traces of this correspondence date respectively from 20[END_REF] , leaves one to imagine the presence of numerous gaps in this correspondence [START_REF] Moreover | the existence of certain unfound letters to this day is detectable from allusions made to them in other letters[END_REF] . No major publishing enterprise has yet been undertaken of the correspondence between J.-B. Say and J. Mill: let's hope that that consecrated to J.-B.

Victor Bianchini & Nicolas Rieucau -An Unpublished Letter from James Mill to Jean-Baptiste Say person to take a copy of it, but shall consult a friend or two who are admirers of yours 55 , before I act upon my own judgement. I shall take care of the translation, I shall procure 53 We have not managed to determine exactly whom they are speaking of here. 54 It cannot be the Scottish philosopher Thomas Brown, close to the French ideologues and a major influence on the thought of J. Mill: the author of the Inquiry into the relation of cause and effect [1814] had been dead for years. The consultation of the British Biographical Index [2008, vol. 2, p. 596] allows us to propose the name of the librarian and printer, Thomas Brown (1778 ?-1869), who co-published, in 1821, the first English translation of J.-B. Say's Traité. As was his father Christopher, T. Brown was a partner in the Longman Company, a famous London printing house. On the subject of T. Brown and the Longman Company, see respectively F. Boase [1965, p. 439] and J.-D. Mellot & E. Queval [2004, p. 369]. 55 Among these, J. Mill was perhaps thinking about Francis Place [1771-1854], who, some years later, was given the task of translating, from French to English, several of J.-B. Say's texts. See supra p. 2, n. 9.

Victor Bianchini & Nicolas Rieucau -An Unpublished Letter from James Mill to Jean-Baptiste Say the insertion in one of our most respectable journals. It is too long for our newspapers, otherwise I should have been disposed to have it printed in some of them, by which means it would have been more speedily known. I shall endeavour to make some of them notice it, as soon as published.

The praise you bestowed upon the article Government, has emboldened me to beg your acceptance of another article (Jurisprudence) which I have prepared for the same publication. [2 r] My wish has been, in the two taken together, to give a sort of outline of the business of legislation. I have also in hand another work, which if I could hope to execute it properly would, in this country, at least, be of considerable use -I mean a School book of Political Economy 56 . I aim at giving, if I am able, a clear statement of the leading doctrines in their natural order 57 & dependence. I hope to be able to do so in the compass of an 8 vo volume 58 , & even a small one. And if it answers my intention it will serve as an introduction to the study of the science, & will facilitate the perusal of the works which treat of it more profoundly & in detail.

I have now to return a thousand thanks for the two letters 59 which I have had the [2 v] pleasure to receive from you. -one extorted from you by my impatience to hear of my son from whom I had a letter 60 in the same day that yours arrived. For your kindness to him I know not how to thank you. I can hardly forgive myself for putting him in the way of encumbering your family for such a length of time. I can only assure you of our lasting gratitude, & our desire, if ever it is in our power, to make an adequate return. You have found in him, I perceive, the defect of which the Benthams have also complained, a backwardness to mix in conversation, & I doubt not a considerable remainder of the 56 Here J. Mill made reference to the Elements of Political Economy. 57 This terminology is similar to that which Mill [1805, p. 415-416] had used, in the Literary Journal, in his article on Say's Traité: « The object of Say himself is to present a view of the principles of political economy as completely adapted to the wants of the learner as possible; to exhibit them in the most natural and exact order; to explain them in the most simple manner, retrenching every thing but what is necessary to convey a clear idea of the point to be stated ». 58 An edition in-8° of the Elements of Political Economy was effectively published in 1821 in London, without an editor's name. An exemplary is conserved at the British Library, under the shelf mark 1027. E. 13. 59 These two letters have not yet been found. 60 We were not able to procure this letter for our research.

Victor Bianchini & Nicolas Rieucau -An Unpublished Letter from James Mill to Jean-Baptiste Say awkward manners which are the effect of the seclusion in which he had lived. These vestigia ruris will wear out I hope by degrees.

J.

  Mill to J.-B. Say, 6 th of June 1821, Staatsbibliothek zu Berlin. Shelf mark : 2 g 1804 (1) [1 r] [Above the date recorded by J. Mill, in Say's handwriting, one can read "James Mill", then, below the date, still in Say's handwriting, "Repondu par Clement le 6 septembre 1821"] [On the bottom left-hand corner of the folio (location frequently used at the time to designate the addressee of a letter), Mill wrote "M. Jean-Baptiste Say"] London 6 th June 1821 My Dear Sir I have this morning heard of an opportunity of writing to you, by a gentleman from Scotland 53 , who has a letter to deliver to you at any rate. & I gladly avail myself of it, to inform you that your letter to M r Prinsep was last night delivered to me by M r Brown 54 . I lost no time in perusing it, & have the satisfaction to say that it appears to me to be admirable ; the matter most important, & the manner at once pointed & delicate. I have no doubt [1 v] about the propriety of publishing it. Accordingly I have employed a

J. Mill was thinking perhaps of one of the reviews in which he had already written, among which figure notably The Edinburgh Review, The Westminster Review and The London Review. The integrality of these reviews was indexed by D.Winch [1966, p. 328-331].

J. Mill and J.-B. Say had, in fact, both vehemently criticized this hegemony. On J. Mill's engagement against the supremacy of Napoléon, see R.[START_REF] Yasukawa | James Mill on Peace and War[END_REF]. As for J.-B. Say, see J.[START_REF] Wolff | Jean-Baptiste Say et Napoléon[END_REF].

J.-B.Say [1824, p. 9] was inspired, on this issue, by Mill's History of British India [1817] that he even described as "excellent[e]"

J.Mill [1805, p. 419-421]. See also D.Winch [1966, p. 29].

J.Mill [1805, p. 415-416].

For as much as we know,E Halévy [1901-1904, vol. II, p. 147] is the first to have brought attention to this latter similarity. Nonetheless, the question of value and exchanges constitutes a chapter to itself in the Elements, while it appears, in the Traité, on the one hand, in book I on the production of wealth and, on the other hand, in book II on the distribution of wealth.

For a recent opinion on the divergences between Ricardo and J.-B. Say on the question of value and distribution, see C.[START_REF] Gehrke | Say and Ricardo on value and distribution[END_REF].

Victor Bianchini & Nicolas Rieucau -An Unpublished Letter from James Mill to Jean-Baptiste Say

Victor Bianchini & Nicolas Rieucau -An Unpublished Letter from James Mill to Jean-Baptiste Say Say, that will appear in several years within his complete works, will permit to fill in some of these gaps.