Multimodal Topic Learning for Video Recommendation

Facilitated by deep neural networks, video recommendation systems have made significant advances. Existing video recommendation systems directly exploit features from different modalities (e.g., user personal data, user behavior data, video titles, video tags, and visual contents) to input deep neural networks, while expecting the networks to online mine user-preferred topics implicitly from these features. However, the features lacking semantic topic information limits accurate recommendation generation. In addition, feature crosses using visual content features generate high dimensionality features that heavily downgrade the online computational efficiency of networks. In this paper, we explicitly separate topic generation from recommendation generation, propose a multimodal topic learning algorithm to exploit three modalities (i.e., tags, titles, and cover images) for generating video topics offline. The topics generated by the proposed algorithm serve as semantic topic features to facilitate preference scope determination and recommendation generation. Furthermore, we use the semantic topic features instead of visual content features to effectively reduce online computational cost. Our proposed algorithm has been deployed in the Kuaibao information streaming platform. Online and offline evaluation results show that our proposed algorithm performs favorably.

I. INTRODUCTION
With great commercial and academic value, video recommendation has received growing attention in recent years with various applications. One of the popular applications is the Kuaibao information streaming platform which utilizes a video recommendation system based on deep learning to attract tens of millions of users. Existing video recommendation systems [5] typically consist of the candidate generation module and the ranking module. When recommending videos to a user, the candidate generation module firstly retrieves hundreds of videos as candidates from a large-scale video pool. Then, the ranking module assigns scores to these candidates. A few videos with the highest scores are ranked by the scores and shown to the user. These two modules make decisions according to the features which are generated by feature crosses between features from users and features from videos. Existing deep video recommendation systems [8] have demonstrated great success by exploit features from different modalities (e.g., user personal data, user behavior data, video titles, video tags, and visual contents).
The deep networks in existing video recommendation systems are expected to online mine user-preferred topics implicitly from input features for preference scope determination. However, on the one hand, video topics are abstracted from * Equal Contribution

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Try retro hand account collage, you must admit that this is a very flavorful hand account. the contents of a large number of videos in the video pool, and there are no definite classes for video topics. On the other hand, existing approaches use the deep networks pre-trained on recognization datasets to generate features from video contents (i.e., video titles, video tags, and visual contents). Thus, existing video content features can not reflect on semantic topic information as these features lack global information related to the video pool. Although using features from video contents is critical for helping understand the content preferences of users, existing video content features without semantic topic information limit accurate recommendation generation. In addition, limited by computational resources, existing deep video recommendation systems mainly use convolutional neural networks (CNNs) to extract features from cover images of videos as the visual content representations. However, using CNN features for feature crosses still generates high dimensionality features which heavily downgrade the online computational efficiency of the deep networks in video recommendation systems. It is therefore of great importance to learn semantic topic features with low dimensionality from video contents to replace existing CNN features.
In this paper, we propose a multimodal topic learning (MTL) algorithm which uses three modalities (i.e., tags, titles, and cover images) to generate video topics offline. Figure  1 shows a video with these three modalities. The titles and cover images describe the video contents in general terms from the perspective of video publishers, and the tags describe the video contents more objectively and fine-grained. Our arXiv:2010.13373v1 [cs.IR] 26 Oct 2020 MTL algorithm explicitly learns semantic topics from these three modalities to facilitate preference scope determination and recommendation generation. In this algorithm, we firstly exploit a multi-task learning method to end-to-end learn deep features from cover images and titles. Meanwhile, a graph embedding approach is proposed to generate tag features. Then, we combine the deep features with the tag features as topic representations for each video. We collect a large-scale set of topic representations of videos from the video pool and use a topic clustering process to handle this set for semantics topics generation. After that, we assign semantic topics for each video according to their topic representations. The semantic topics of each video are used to improve existing video content features for accurate recommendation generation while using the low dimensionality topic features instead of CNN features effectively reduce online computational cost. Our proposed MTL algorithm has been adopted by the Kuaibao information streaming platform. Through extensive online and offline evaluations, we demonstrate that the proposed MTL algorithm performs favorably.
The main contributions of this work are: • We propose a multimodal topic learning algorithm to generate semantic topics. • We use the topics as semantic topic features to advance existing video recommendation systems. • We conduct extensive online and offline evaluations.
The results show that the proposed algorithm performs favorably.

II. RELATED WORK
Recommendation systems have been widely discussed in the literature [6]. In this section, we mainly discuss the representative recommendation algorithms, and multimodal learning most relevant to this work.
Recommendation algorithms. Historical behavior records of users build a binary relationship between users and items. Recommendation algorithms use this relationship to recommend items that the users may be interested in. Early recommendation algorithms [13] exploit shallow models to model this relationship. For example, the Collaborative Filtering (CF) method [21] exploits the similarities among users or items for recommendation. The FM algorithm [12,20] uses factorized parameters to perform second-order feature interactions. With the development of deep learning, existing recommendation algorithms have demonstrated great success by exploiting deep features [4,7,24] and decision-makers [3,9,26,28]. The Wide&Deep model [3] uses the memorization of the wide module and the generalization of the deep module to balance the accuracy and expansibility of recommendation systems. Since the Wide&Deep model, numerous methods have been developed to improve this framework for recommendation systems. The DeepFM approach [9] proposes to utilize the FM layer instead of the Wide module to improve the Wide&Deep model. The DCN method [26] uses the Cross network to replace the Wide module in the Wide&Deep model for high order feature interactions. The DIN algorithm [28] integrates an attention mechanism for feature selection into deep recommendation systems. Existing state-of-the-art deep video recommendation algorithms [6] focus on capturing video content features to understand user preferences. These video content features are mainly from the titles [7,19] and cover images [4,10,22,24,25] of videos. However, existing methods pay less attention to the global semantic topics as video content features. Our proposed algorithm assigns topics to each video to facilitate preference scope determination and recommendation generation.
Multimodal learning. Multimodal learning aims to achieve the ability to process and understand multi-source modality information include images, videos, audios, and semantics. The multimodal learning scheme has been widely exploited for many applications, include machine translation [1], image captioning [27], video captioning [17], speech synthesis [23], image semantic segmentation, mobile identity authentication, etc. In video recommendation, existing methods [11] directly use video content features from different modalities for recommendation decisions. The redundancy between modalities downgrades the recommendation performance. In this work, we propose a multimodal multitask learning approach to learn joint representations from the titles and cover images. Our approach aims to emphasize the complementarity and synchrony between modalities to represent and summarize the multimodal data.

III. PROPOSED METHOD
In this section, we first present how our multimodal topic learning algorithm generate topics, then we illustrate how the topics advance the candidate generation module and the ranking module in our video recommendation system.

A. Multimodal topic learning
As shown in Figure 2, the multimodal topic learning scheme consists of a multimodal multitask representation learning method to generate deep joint representations from the titles and cover images, a graph embedding approach for tag representation generation, and a clustering process to generate topics based on the concatenate representations of the deep joint representations and the tag representations. In the following, we introduce these three processes, respectively. 1) Multi-modal multi-task representation learning: Our network for the multimodal multitask representation learning method contains a feature extractor and a Multi-gate Mixture-of-Experts (MMoE) module [15]. The feature extractor consists of a pre-trained CNN module f C and a pre-trained transformer module f T to generate deep features from the cover image x I and the title consisting of words x W , respectively. x I and x W are from an input video. A straightforward method to generate the joint representations from the title and the cover image is concatenating the deep features f C (x I ) and f T (x W ). However, the redundancy between different modalities will downgrade the recommendation performance. We perform end-to-end Overview of the proposed multimodal topic learning algorithm. This algorithm consists of a multimodal multitask representation learning method, a graph embedding approach, and a clustering process. We use this algorithm to generate topics from multimodel data of input videos. For presentation clarity, multimodal representation learning to ensure the deep joint representations reflect the complementarity and synchrony between modalities to represent and summarize the multimodal data. To improve the generalization ability of the deep joint representations, we use a multitask learning strategy MMoE to perform multimodal representation learning. Compared to the early multitask learning methods that share bottom layers, the MMoE framework uses H expert networks coupled with N gating networks to generate representations for different N tasks. This strategy is effective to alleviate the task conflict problem. The MMoE strategy can be denoted as: where z is a input feature that is a concatenate representation of f C (x I ) and f T (x W ). f i is an expert network. g k is a gating network with the softmax function which ensures h k is a tower network that generates the output p k corresponding to the k-th task. In our method, p k is a prediction probability distribution that the input video belongs to the preset classes. N is 3 as we perform 3 classification tasks to learn the deep joint representation z. These three classification tasks include primary classification, secondary classification, and tag classification. We assign a primary-class label y 1 , a secondary-class label y 2 , and a tag label y 3 to each video in our system. The label y k (k ∈ {1, 2, 3}) is a binary vector in which if some elements are 1, the input video belongs to the classes corresponding to these elements. y 1 , y 2 , and y 3 describe the input video from coarse to fine, we use them to  define our loss function as: where M k is the length of the binary vector y k . Note that we construct our loss function based on one input video and our loss function is a cross-entropy loss corresponding to three classification tasks. We use Equation 2 to fine-tune the CNN module f C and the transformer module f T to ensure the deep joint representation z is effective to represent and summarize the multimodal data from the input video. The deep joint representation z is concatenated with the tag representation e to represent a video for clustering. How to generate the tag representation is illustrated in Section III-A2. Note that we do not use tags as one input modality for the multi-modal multi-task representation learning algorithm. We empirically find that adding the tag representation into the MMoE network leads to this network focus on the tag representation while ignoring the deep joint representation from the cover image and title. The reason is that the tag representation contains strong semantic information with human prior. Using such joint representations for clustering leads to that topics lack the semantic from the cover image and title.
2) Graph embedding: There are thousands of tags in our system while numerous tags contain similar semantic. Thus, it is not suitable to use one-hot coding to represent the tags of a video. We propose a graph embedding approach to generate one tag representation for each video in our system. In this approach, we set a tag as a node and convert all tags in our system into a completely connected graph. We set the value of the edge linking any two tag nodes as the number of the videos which contain these two tags. We remove the edges which value is 0 and generate the probability of each remaining edge as: where E is the number of edges, x ε is the value of ε-th edge and p ε is the probability of this edge.
After we obtain the probability graph, we perform the deep walk [18] and skip-gram algorithms to generate a tag embedding list that contains each tag and its corresponding embedding. Specifically, we simulate a random walk beginning from any tag node t 1 to generate a tag sequence with the length l. The tag node t n (n ∈ {1, · · · , l}) in this sequence is taken by sampling based on the probabilities of edges which linking the tag node t n−1 . We collect a set of tag sequences and use the skip-gram approach to handle these tag sequences to generate the tag embedding list which can be denoted as {t 1 : e 1 , · · · , t T : e T }, where T is the number of tags in our system, e j (j ∈ (1, · · · , T )) is the embedding of the tag t j . Note that T is the same as M 3 in Equation 2, we use T here for presentation clarity. Given tags {t 1 , · · · , t v } of a video, we lookup the tag embedding list to generate tag representations {e 1 , · · · , e v }.
The tag representation of this video is denoted as: 3) Clustering process: We concatenate the tag representation e and the deep joint representation z to be the final topic representation a of a video. The L2 normalization method is used for a to ensure that e and z contribute the same amount for the distance metric in the clustering process. We use the K-means algorithm [14] for clustering based on the topic representations from a large number of videos. The K clustering centers of these topic representations are treated as our topics. We assign topic IDs for each video according to the cosine similarity distances between the topic representation a of this video and the clustering centers considering the distance threshold τ 3 . Each video in our system contains an average of 4 topics.
To present the effectiveness of our topic representation a integrating multiple modalities, Figure 3 shows the distance ratios between average inter-class distances and average intra-class distances in 10 topic clustering results. We note that the distance ratios of our method using the cover image, title, and tags of each video are greater than that of the method using the cover image and title and that of the method only using the cover image. This visualization demonstrates that our topic representation with multimodal information is more discriminative for the topic generation.

B. Topic utilization
After we use the MTL algorithm to assign topics for each video, we use the topics in the candidate generation module and the ranking module of our recommendation system. In this following, we introduce how to use the topics in both modules. 1) Candidate generation module: The candidate generation module retrieves hundreds of videos as candidates for the subsequent ranking module. We use topics to facilitate the candidate generation module to determine preference scope. Specifically, we first set K topic queues, then assign all videos in our system to these queues according to the topics of these videos. In each topic queue, we delete the videos whose exposure times and click-through rate are less than the thresholds τ 1 and τ 2 , respectively. In addition, we randomly remain some fresh videos in this queue. These fresh videos account for 10% of all remaining videos in this queue. After that, we update the video rankings in each topic queue according to click-through rate in real-time. Figure 4 shows cover images of the videos in three topic queues. When recommending videos to a user, we count the number of times each topic in our system appears in the recent N 1 click videos of the user. We select the top N 2 topics of the user and generate N 3 video candidates from the corresponding topic queues according to the ranking of the videos in these queues. These video candidates are deliver to the subsequent ranking module.
2) Ranking module: The ranking module assigns scores to candidates from the candidate generation module. A few video candidates with the highest scores are ranked by the scores and shown to the user. We use topics to improve the ranking process for recommendation generation. Our ranking module is based on the Wide&Deep framework [3]. This framework transfer an ID feature to an embedding. The embedding from a video and the mean embedding from the historical click videos of a user are combined to input the deep module of this framework. The deep module of this framework uses multiple types of ID feature to generate the recommendation score of the video for the user. Our topics serving as a type of ID features are integrated into this framework.

IV. EXPERIMENTS
In this section, we first present the implementation details, dataset, and evaluation metrics of our method. Then we conduct ablation studies to analyze the effect of of each module in our model on performance improvement. Finally, we offline and online evaluate our method on a large scale dataset and on the Kuaibao information streaming platform.

A. Implementation details
In the multimodal multitask learning method, we construct our CNN and transformer module based on the Inception-ResNet-v2 network [24] and the BERT network [7]. The number H of the expert networks in the MMoE is set as 12. The tasks in the MMoE include primary classification, secondary classification, and tag classification. Equation 2 are 50, 367, and 12000 which are the number of primary-classes, the number of secondary-classes, and the number of tags in our system. We use the adaptive moment estimation optimizer to train the network using 200 iterations. The learning rate is 0.001 and the batch size is set as 300. The length l of a tag sequence in the graph embedding method is 100. We set the number of clustering centers K as 6000 and the cosine similarity distances threshold τ 3 is 0.6. In our recommendation system, the thresholds τ 1 and τ 2 are set as 10 and 0.07, respectively. We set N 1 , N 2 , and N 3 as 128, 4, and 600. The proposed MTL method is executed on a PC with Intel(R) Xeon(R) CPU E5-2680 v4 @ 2.40GHz CPU and 8 Tesla P40 GPU.

B. Datasets and evaluation metrics
Our experimental data is from the Kuaibao information streaming platform. Specifically, We construct a video content dataset and a click dataset for model learning and ablation studies. The video content dataset contains about 3 million samples. Each sample consists of the title, cover image, primary-class label, secondary-class label, and tags. There are 50 primary-classes, 367 secondary-classes, and 12000 video tags in this video content dataset. We use 90% of the samples in the video content dataset for the proposed topic learning and the remaining 10% of the samples are used to evaluate the representation ability of features generated by different models. The metrics for the representation ability evaluation are Adjusted Rand Index (ARI) and Normalized Mutual Information (NMI). The click dataset contains about 14 million samples which are produced in 5 days. Each sample is a click that corresponds to a user and a video. There are about 1.5 million users and 800 thousand videos in this click dataset. We use the samples from the first 4 days to train recommendation models, and then use the samples from the last day to offline evaluate the effect of topics generated by our algorithm on recommendation performance improvement. The metric for offline evaluation is Area Under ROC Curve (AUC) which is widely adopted in recommendation systems [2,16,28].

C. Ablation studies
In this section, we construct ablation studies from two perspectives: 1) We compare the representation ability of features generated by different models to demonstrate the effectiveness of our multi-task learning and graph embedding methods. 2) We add semantic topic features into existing recommendation algorithms to investigate whether the topics can improve performance generically. Table I shows the representation ability evaluation. We transfer the representation ability comparisons to clustering performance comparisons. Specifically, we use the K-means algorithm [14] to cluster the samples from the video content dataset. The value of K in this algorithm is set as the number of primary-classes (PC) or secondary-classes (SC) in this dataset. We use the ARI and NMI metrics to measure the clustering performance corresponding to the distributions of the primary-classes or the secondary-classes. As we use the same clustering algorithm to cluster sample features from different models, the clustering results reflect the representation ability of different features and evaluate the performance of different feature extractors. We firstly set the Inception-ResNet-v2 (IRv2) network [24] and the BERT network [7] as our baselines. These two networks extract features from cover images and from titles to represent samples, respectively. Then we use the MMOE framework with multi-task learning to end-to-end train these two baselines, the joint representations from these two networks are used to represent samples. Finally, we combine the joint representations with the tag features generated by our graph embedding method to represent samples. Table I shows that our multi-task learning method significantly improves the clustering performance. Combining the tag features achieves further improvements. We attribute the performance improvements to that our proposed algorithm is effective to fuse multimodal information to represent video content.
To present the generalization ability of the semantic topic features, Table II shows the comparisons between classical recommendation algorithms with and without the semantic topic features. These algorithms include the Logistic Regression (LR), Embedding&MLP (EMLP), and DCN [26]. The AUC metric is used to evaluate recommendation performance on the click dataset. methods without the topic features, which reflects the generalization and improvements brought by the proposed semantic topics.

D. Offline evaluation
In the offline evaluation, we use historical data from the Kuaibao to simulate the online process. Specifically, the process includes 3 steps: (1) We initialize the recommendation algorithms using the click dataset. (2) We use the recommendation algorithms to predict clicks in one day. (3) We collect the predicted clicks to update recommendation algorithms online. After that, we repeat the (2) and (3) steps. We collect the predicted clicks and real clicks in 5 consecutive days to perform the offline evaluation. The evaluation results are presented in terms of the AUC metric, the memory cost, and the time cost. In this evaluation, the baseline method is the same as the production model in the Kuaibao. We respectively add the CNN features from the cover image and the semantic topic features into the baseline method to perform comparisons. These two configurations are denoted as Baseline+CNN and Baseline+Topic. Figure 5 shows that the CNN features slightly improve the AUC results of the baseline, while our semantic topic features improve the baseline method by a large margin. The reason is that directly using CNN features in the recommendation systems can not integrate the global information related to the video pool of the recommendation systems. The visual content information is not enough to achieve significant improvements. Our semantic topic features are offline learned on a large scale dataset from the video pool. The high-level semantic information encoded in the topic features effectively help recommendation systems to understand the content preferences of users. In addition, Figure 6 shows the computational cost comparisons. We deliver one sample to the three configurations to compute the time and memory costs. The increments of the time and memory costs of the Baseline+CNN method are about 3 times greater than that of the Baseline+Topic approach. As CNN features have to remain high dimensionality (128 dimensionalities in the Baseline+CNN method) to integrate visual content information, it is inevitable to increase the computational cost. Our semantic topic features with low dimensionality (8 dimensionalities in the Baseline+Topic) effectively reduce the online computational cost brought by the CNN features.

E. Online evaluation
We perform an A/B test in the online evaluation. The process of the A/B test consists of 3 steps. Firstly, we divide 300, 000 users into 8 groups on average. Then, we measure the activity of each group for 7 days in terms of the UVD, UAVD, AVD, and ART metrics and we select two groups with similar activities as the experiment group and the control group. Finally, we execute our proposed approach and the baseline method in the experiment group and the control group respectively for 7 days. The UVD, UAVD, AVD, and ART metrics are used to evaluate test results.
In the online A/B test, we set the baseline method as the production model in the Kuaibao. We gradually add the topics generated by our proposed algorithm into the candidate generation (i.e., Recall) and ranking modules of the video recommendation model in the Kuaibao. We denote the two configurations as Recall+Topic and Baseline+Topic. Table III shows that when we use the topic in the candidate generation module (i.e., Recall+Topic), the recommendation performance is improved slightly. However, when we further add the topic features into the rank module (i.e., Baseline+Topic), we achieve significant performance improvements. Our proposed topics facilitate these two modules to advance existing recommendation systems.

V. CONCLUSION
In this paper, we propose a multimodal topic learning algorithm to generate video topics offline. We use the semantic topics as video content features to facilitate the candidate generation and ranking modules in our recommendation system. The semantic topics help our recommendation system to determine preference scope and generate recommendations. Online and offline experimental results demonstrate the effectiveness of our proposed algorithm.


extfieldsofstudy:
Computer Science
Mathematics

text:
Correlation Coefficient Analysis of the Age of Information in Multi-Source Systems

This paper studies the age of information (AoI) on an information updating system such that multiple sources share one server to process packets of updated information. In such systems, packets from different sources compete for the server, and thus they may suffer from being interrupted, being backlogged, and becoming stale. Therefore, in order to grasp structures of such systems, it is crucially important to study a metric indicating a correlation of different sources. In this paper, we aim to analyze the correlation of AoIs on a single-server queueing system with multiple sources. As our contribution, we provide the closed-form expression of the correlation coefficient of the AoIs. To this end, we first derive the Laplace-Stieltjes transform of the stationary distribution of each AoI for the multiple sources. Some nontrivial properties on the systems are revealed from our analysis results.

I. INTRODUCTION
In recent years, we can see the real-time information updating systems in many places because of the ever-increasing demand of controlling time-critical information throughout network systems. The typical examples are monitoring systems of weather reports, vehicular status update systems that assist self-driving of cars, remote controlling of construction machinery, etc. In such systems, various kinds of status are displayed on equipped monitors (e.g., temperature, humidity, and air pressure in weather reports; position, velocity, and acceleration in vehicular status). When updated status of one kind is captured by a sensor, a packet is generated by the associated source of an updated information. Thereafter, it is processed by one of servers, and then displayed on the corresponding monitor. In addition, while all the servers are busy with processing, a newly arriving packet is backlogged and becomes outdated. Note that these situations occur in practice if the arrival frequency of packets is beyond the processing power of servers. Owing to the above properties of the systems, the information displayed on the monitor is not always up-to-date. Therefore, the freshness of the displayed information should be quantified and managed for those information updating systems.
From such backgrounds, a performance metric called the age of information (AoI) was proposed [1]. To define the AoI, let η(t) denote the timestamp of the generation time of the information displayed on the monitor at time t. Then, the AoI at time t is defined by The AoI defined by ∆ t can indicate the freshness, because the above expression means the elapsed time from the generation of the information displayed on the monitor. We note that, in a system with multiple sources, the AoI is defined for each source.
The AoI in queueing systems have been studied in recent years. We here focus on previous studies which investigated the AoIs in queueing systems with multiple information sources. Yates and Kaul provided the pioneering study in [2]. They considered single-server queueing systems where two sources share one server to process updated information, and derived the userful expression of the average AoI of each information source. They also studied the first-come-firstserved (FCFS) M/M/1 system as a special case, and derived the closed-form expression of the average AoI of each source. Kaul and Yates [3] showed that two-source M/M/1/1 systems with preemption outperform two-source FCFS M/M/1 systems in terms of the average AoI, which triggered further studies for such without-queue systems. Najm and Telatar [4] derived the average AoI and the peak AoI of each source in two-source M/G/1 systems with preemption. The systems with general multiple information sources were investigated by Yates and Kaul [5]. They considered the average AoI on M/M/1/1 and M/M/1/2 systems, in both of which multiple sources share one server. In case of M/M/1/2, they utilized stochastic hybrid systems to discard waiting packets, and then they successfully reduced complexity of their analysis.
As described above, most of the works handling multiple information sources have been devoted to analyzing the average AoI of each source. To the best of our knowledge, no previous works try analytical studies about the correlation of the AoIs from different information sources. In order to grasp structures of the information updating systems with the multiple sources, it is crucially important to study a metric indicating a correlation of different sources in addition to the AoIs of the individual sources. Considering the correlation leads to a better management of an information updating system with multiple sources.
In this paper, we study the correlation of AoIs of a status updating system with multiple sources, which is modeled by an M/M/1/1 queueing system with preemption. Our model is assumed to consist of multiple information sources and the corresponding monitors and to share one server. Our model described above is defined in detail in Section II.
The contribution of this paper is as follows. We first derive the Laplace-Stieltjes transform (LST) of the stationary distribution of each AoI in our model. The LST enables to obtain the mean and the variance of the AoI. Next, assuming that the number of sources is two, we provide the closed-form expression of the correlation coefficient of the AoIs, which is the main contribution of this paper. Furthermore, using this result, we reveal some nontrivial properties on our model. The rest of this paper is organized as follows. In Section II, we describe the model of our investigating information updating systems. Sections III and IV present analysis results. In Section III, we derive the LST for each AoI. In Section IV, assuming that the number of sources is two, we obtain the correlation coefficient of the AoIs. Numerical experiments are conducted in Section V. Finally, this paper is concluded in Section VI.

II. SYSTEM MODEL
We consider an information updating system such that multiple sources generate information packets of updated status. Generated packets are immediately transmitted to an M/M/1/1 queueing system, which is illustrated in Fig. 1. Note that an M/M/1/1 queueing system has only one server and no buffer space. After being processed in the server, the packets are directly sent to monitors, and then the monitors display the updated information. Each source has the corresponding monitor, and updated information of a source is displayed on its corresponding monitor. The number of sources is denoted as K ∈ N, and K := {1, 2, . . . , K} denotes the set of type indexes of sources.
Packets are generated from source k (k ∈ K) according to the time-homogeneous Poisson process with rate λ k . Service times of packets are assumed to be independent and identically distributed (i.i.d.) with the exponential distribution having mean 1/µ; that is, packets from all sources have the same service time distribution. Besides, preemption is assumed in our system; that is, the packet which currently occupies the server will be pushed out if a new packet arrives before its service completion. We refer to a packet which completes its service without being pushed out as the valid packet. Henceforth, we refer to generation times of packets as arrival times. In addition, we define λ := k∈K λ k as the total arrival rate of the K sources.

III. AOI FOR EACH SOURCE
In this section, we derive the LST of stationary AoI of each source. For k ∈ K and n ∈ Z := {0, ±1, ±2, . . . }, let α k,n denote the nth arrival time of the packet of source k, and S k,n denote the service time of the packet of source k which arrives at α k,n . We define A k (t) as the AoI of source at time t ∈ R. Using these notations, we have the following expression, for k ∈ K and t ∈ R.
where β k,n := α k,n + S k,n . Samples paths of A k (t) are illustrated in Figs. 2 and 3. {(α k,n , S k,n )} n∈Z is the stationary and ergodic marked point process. Thus, we define A k , k ∈ K, as the random variable following the stationary distribution of In addition, we define some notations related to valid packets. For k ∈ K and n ∈ Z, we define α * k,n and S * k,n as the arrival time and service time of the nth valid packet of source k, respectively. We also define β * k,n as the nth departure times of the valid packet; that is, β * k,n = α * k,n + S * k,n . Without loss of generality, we assume that The service time distribution of valid packets is obtained as follows The service time of a valid packet of source k ∈ K follows the exponential distribution having mean 1/(λ + µ).

Proof.
Let X a denote a random variable following the exponential distribution with mean 1/a for a > 0. Note that packets arrive according to the Poisson process with rate λ if we ignore types of sources. In addition, a packet is valid if no other packets arrive until its service is completed. Thus, it follows that, for k ∈ K and n ∈ Z, ✷ Using this lemma, we obtain the LST of each source.

Theorem 1 The Laplace-Stieltjes transform of the stationary
AoI of source k ∈ K, denoted by A k (s), is given by

Proof.
We define A + k,n (resp. A − k,n ) as the AoI of the immediately after (resp. before) the nth update of source k.
where λ * k denotes the arrival rate of valid packets of source k. Note here that A + k,n is equivalent to the service time of the valid packet arriving at α * k,n . Thus, from Lemma 1, we obtain We define R k,n as the interval time of nth and (n+1)st updates of source k; that is, R k,n = β * k,n+1 − β * k,n . The following relation holds for k ∈ K and n ∈ Z.
We also have which is shown in Appendix A. Applying (2) and (4) to (3) yields Furthermore, a packet of source k ∈ K is valid with probability µ/(λ + µ), independently other packets. We then have Consequently, applying (2), (5), and (6) to (1), we obtain Theorem 1. ✷ Furthermore, using Theorem 1, we can easily obtain the expectation and variance of each AoI.

IV. CORRELATION COEFFICIENT
In this section, assuming that K = 2, we derive the correlation coefficient of stationary AoIs. For n ∈ Z, let α n denote the nth arrival time of packets of either sources 1 or 2, and let S n denote the service time of the packet arriving at α n .
In addition we define some notations related to valid packets. We define α * n and S * n as the arrival time and service time of the nth valid packet of either sources 1 or 2, respectively. We also define β * n as the nth departure times of the valid packet of either sources 1 or 2; that is, β * n = α * n + S * n . Without loss of generality, we assume that We define R n as the interval time of nth and (n+1)st updates; that is, R n = β * n+1 − β * n . We obtain the following lemma.
Lemma 2 R n follows the convolution of two independent random variables following exponential distributions having mean 1/λ and 1/µ.

The proof of Lemma 2 is shown in Appendix B.
We first consider the AoI of source k ∈ {1, 2} immediately after source 1 or 2 is updated. We define A † k,n := A k (β * n ) for k = 1, 2 and n ∈ Z. We obtain the following lemma.
Proof. For n ∈ Z, let C n denote the type of the valid packet arriving at α * n . For k = 1, 2 and n ∈ Z, we define D k,n := min {m ≤ n; C m = k} , which means that the D k,n th valid packet is the last packet which arrives from source k before the nth update. Note that D k,n = n if the valid packet arriving at α * n is generated by source k. Using this notation, we have A † k,n = S * D k,n + n−1 j=D k,n R j , which implies that {A † 1,n }, {A † 2,n } and {A † 1,n A † 2,n } are stationary and ergodicity.
Since all packets have the same service time distribution, {C n } are the i.i.d. random variables such that P(C n = 1) = λ 1 /λ and P(C n = 2) = λ 2 /λ. We then have Note that {D k,n } is independent of {S * n } and {R n }. It then follows from (7) and (8) that, for n ∈ Z and k = 1, 2, Applying Lemmas 1 and 2 to the above, we obtain In addition, we have, for m, ℓ ∈ Z, Note that S * n does not depend on S * n−m and R ℓ for ℓ = n − 1, but depends on R n−1 . Thus, from (7) and (9), we obtain By definitions of R n , we have Thus, it follows from Lemma 1 and (6) that (10) Applying Lemmas 1, 2 and (10) to the above, we obtain Using Lemma 3, we obtain the main theorem of this paper.

Theorem 2 The correlation coefficient of AoIs in 2-source M/M/1/1 push-out queue, denoted by ρ, is given by
Proof. Using the pointwise ergodic theorem (see, e.g., [6, Theorem 1.6.4]) yields Dividing the integral in (12) by update times {β n }, we have where N (t) denotes the total number of updates in [0, t) and Note that, for t ∈ [β * n , β * n+1 ), We estimate the right-hand side of (13). From (15), we have It follows from Lemmas 2 and 3 that R n and A k (β * n ) are finite w.p.1. Thus, it follows from (16) that Furthermore, {R n } is the i.i.d. random variables, because the system becomes empty at time β * n , n ∈ Z. Thus, it follows from the elementary renewal theorem and Lemma 2 that Furthermore, using the pointwise ergodic theorem, we have where the first equation holds because it follows from (18) that lim T →∞ N (T ) = ∞. Substituting (17)-(19) into (13) yields Next, we calculate E[F 0 ]. Applying (15) to (14), we have Using Lemmas 2 and 3, it follows from the above that Combining the above and (20), we obtain Consequently, from the above and Corollary 1, we obtain ✷ From Theorem 2, we can see some nontrivial properties on the systems as follows. The proof of Corollary 2 is omitted due to the page restriction.

V. NUMERICAL RESULTS
In this section, we provide numerical results of the correlation coefficient presented in Theorem 2, and confirm the statements presented in Corollary 2 through the numerical results. Fig. 4 shows the correlation coefficients which is numerically computed with several cases using Theorem 2, where the x-axis represents the value of λ 1 , the arrival rate of source 1. Note that the parameter µ is fixed for each curve in Fig. 4, and λ 2 is fixed as λ 2 = 2.
From Fig. 4, we observe that ρ is always negative, that is, the two AoIs in our model always have a negative correlation, which implies (i) in Corollary 2. We also find that the curves in the figures are all convergent to zero, so that (ii) in Corollary 2 is likely to hold with respect to λ 1 . Moreover, we see that the correlation coefficient has a minimum value with respect to λ 1 . This means that a certain arrival rate of packets from one source gives the strongest negative correlation with the other source. Furthermore, we see from the figure that the smallest minimum value of ρ is seen when µ = 4. Actually, the smallest value in the figure is −1/6, and is achieved when (λ 1 , λ 2 , µ) = (2, 2, 4), which corresponds to (iii) in Corollary 2.

VI. CONCLUSION
In this paper, we considered a correlation of the AoIs of two sources sharing one server to process information, and derived the closed form expression of the correlation coefficient, on the model of M/M/1/1 queueing systems. In addition, we also derived the expression of the LST of the stationary distribution of each AoI on the assumption that multiple K sources share the one server. From our analysis, we found that the correlation coefficient is always negative, and that the correlation coefficient has a certain minimum value. This indicates that there is always a negative correlation between the two AoIs, and the strongest negative correlation is achieved by adjusting the parameters introduced in our model.
For further study, it would be expected that the correlation coefficient is investigated with more generalized assumptions for modeling the systems because our model adopts an elemental M/M/1/1 queueing systems with the common service rate for all the sources. To consider the correlation among several sources is also an interesting research point.

APPENDIX A
This appendix is devoted to the proof of (4). For k ∈ K and n ∈ Z, let N k,n denote the number of arriving packets of source k in (0, β * n ]. We define M k,n as the number of arriving packets of source k in (β * n , β * n+1 ]; that is, M k,n = N k,n+1 − N k,n . In addition, we define U k,n := α k,n+1 − α k,n . Let also J k,n denote the length from the time that the nth valid packet departs to the time that a new packet arrives from source k; that is J k,n = U k,N k,n − S k,N k,n . We have the following relation (see Fig. 2). R k,n = J k,n + M k,n −1 ℓ=1 U k,N k,n +ℓ + S k,N k,n+1 . which leads to E e −sR k,n M k,n = E e −sJ k,n · E e −sS k,N k,n+1 × M k,n −1 ℓ=1 E e −sU k,N k,n +ℓ M k,n .(21) For ℓ = 1, . . . , M k,n − 1, the (N k,n + ℓ)-th arrival packet is not valid. We then have, for ℓ = 1, . . . , M k,n − 1, where X a denotes a random variable following the exponential distribution with mean 1/a for a > 0. Furthermore, it follows from the memoryless property that Note that S k,N k,n+1 is the service time of a valid packet. Thus, it follows from Lemma 1 that E[e −sS k,N k,n+1 ] = λ + µ s + λ + µ . (24) Applying (22)-(24) to (21), we obtain E e −sR k,n |M k,n = λ + µ s + λ + µ λ k s + λ k × λ + µ s + λ + µ λ k s + λ k s + λ λ M k,n −1 .

(25)
Finally, we show the distribution function of M k,n . A packet is valid if no packets (of all sources) arrive before its service completion. It then follows from the independence of {α k,n } and {S k,n } that a packet is valid with probability µ/(λ + µ), independently other packets. Therefore, for any n ∈ N and k ∈ K, M k,n follows the geometric distribution on N with parameter µ/(λ + µ). Thus, from (25), we obtain E[e −sR k,n ] = λ k µ (s + λ)(s + µ) − (λ − λ k )µ .
As similar to (21), for any n ∈ N, M n follows the geometric distribution on N with parameter µ/(λ + µ). Thus, from (31), we obtain E[e −sRn ] = λ s + λ µ s + µ , which means that R n follows the convolution of X λ and X µ .


Dynamic Certainty Equivalence Adaptive Control by Nonlinear Parameter Filtering

This paper presents a novel solution to the problem of designing an implementable (i.e., differentiator-free) model-reference output-feedback direct-adaptive controller for single-input-single-output linear time-invariant systems with relative degree possibly larger than one. The new paradigm is based on a version of the Dynamic Certainty Equivalence (DyCE) principle. The approach proposed in this work consists in realizing the DyCE control through surrogate parameter derivatives, made available by a Nonlinear Parameter Filter (NPF), instead of feeding the DyCE controller with the derivatives of the estimates produced High-Order Tuner (HOT). The proposed adaptive controller does not require error augmentation or normalization, allowing the use of large adaptation gains for fast convergence speed. Moreover, the proposed architecture can be easily equipped with well-known robust modifications of tuning laws. The performance of the proposed algorithm is demonstrated via comparative simulations with an error augmentation-based method and a simplified HOT algorithm.

I. INTRODUCTION AND PROBLEM FORMULATION
Model Reference Adaptive Control (MRAC) is undoubtedly one of the most intensively studied problems by the adaptive control community, dating back to the 1950s. Despite this long and rich history, there are still several open issues in MRAC design that involve, in particular, system with non-unitary relative degree.
The different MRAC approaches that have emerged from decades of research can be roughly grouped into two main categories: The first one, known as indirect-adaptive control, include identifiers of the plant and observers of the states. Its main restriction is the dependence of control and observation performance on the identification process, where lack of persistence of excitation (PE) of the regressor may degrade the control performance or even cause instability. The second category involves direct-adaptive control schemes, where the controller parameters are directly updated online without the need of estimating plant parameters. Typically, directadaptive schemes enjoy the favourable property of guaranteeing asymptotic convergence of the tracking error even in absence of PE. In this paper, we will only consider the directadaptive case.
The majority of direct MRAC schemes for uncertain linear time-invariant (LTI) systems reported in the literature relies on the certainty equivalence (CE) principle. This principle reposes on the fact that the ideal model-matching controller is time-invariant and affine in the state variables of the system. Based on this paradigm, the unavailable (unknown) parameters of the ideal model-matching controller are replaced by their estimates. CE type controllers can be readily applied to Strictly Positive Real (SPR) systems. Conversely, when applied to systems with relative degree larger than 2, direct MRAC schemes require error-augmentation and normalization of the parameter adaptation law [1]. Normalization makes the convergence speed trajectory-dependent (i.e., nonuniform in the initial conditions) and typically slower in presence of large initial parametric mismatch. These issues prompt an investigation of adaptive controllers that are not based on the CE paradigm and do not require normalization.
In this regard, an alternative approach to CE is DyCE adaptive control. This technique dates back to 1987, when Mudgett and Morse presented it in [2], although the name and the acronym for this method have been coined by Ortega in [3]. In order to apply DyCE control to systems with arbitrary relative degrees, high-order derivatives of the parameter vector are needed. Unfortunately, the tuners (adaptation laws for the parameters) available at the time of Widgett and Morse were only able to provide the first derivative [4], [5]. In the seminal work [6], Morse provided DyCE with a modified parameter adaptation scheme, named HOT, which did not require normalization. HOT update laws are able to produce -without direct differentiation -the estimated parameter vector plus its first ρ derivatives, where ρ is the relative degree of the plant. Compared to the augmented error CE methods, the DyCE+HOT architecture is characterized by an enhanced transient performance, due to the possibility of using large adaptation gains without normalization. The flip side of the coin is the increased complexity of the original HOT method of Morse, which -in absence of robust modifications -is known to suffer from a lack of robustness in case of poor excitation, which may cause parameter drift in the presence of unstructured perturbations. Nikiforov [7] incorporated a leakage modification to the HOT to make it robust in presence of bounded perturbations (in the sense of guaranteeing boundedness of all signals). Moreover, the dynamical order of the tuner was reduced by a factor of 2n via a simplification of its structure. However, it is known that leakage modifications alter the adaptation dynamics so that the parameters are not guaranteed to converge to the true values, even in case of Persistence of Excitation (PE). Other robust modifications used in conventional CE adaptive control, most noticeably parameter projections, are not affected by this problem and allow to achieve exact parameter convergence under PE conditions and in absence of unstructured perturbations. However, these modifications cannot be applied easily to the DyCE+HOT framework, due to the nonlinearity of the tuner.
Finally, it is worth mentioning that the Adaptive Backstepping method by Krstic, Kanellakopolous and Kokotovic [8], as is the case of DyCE+HOT and its variants, does not need normalization and achieves enhanced performances compared to CE adaptive control. Adaptive backstepping is inherently nonlinear as it involves the use of nonlinear tuning functions. However, backstepping design is less procedural than DyCE+HOT, in the sense that it calls for specific customization when applied to different plant models. This increased complexity with respect to DyCE+HOT comes with the advantage of bearing the possibility to cope with unmatched model uncertainties. As all other adaptive schemes, backstepping requires robust techniques such as projection, dead-zone and leakage modifications to enforce signal boundedness in case of poor excitation. Nonetheless, due to its complexity, it shares with the DyCE+HOT a certain lack of popularity among practitioners.
In this paper, we propose a new approach to DyCE adaptive control. Instead of relying on Morse's HOT, our method consists of filtering the estimated parameter vector through a NPF, combined with a conventional first-order tuner. The NPF devised in this work is able to produce surrogate signals to be used in the DyCE control law in place of the unavailable higher-order derivatives of the parameters. The proposed adaptive controller does not require error augmentation or normalization, allowing the designer to use large adaptation gains, thus achieving -in principle -a faster speed of convergence. As a noteworthy advantage versus conventional DyCE+HOT methods, the proposed architecture can be easily equipped with all robust modifications found in conventional adaptive control, like leakage and parameter projection.
Notation : The Laplace transform of a signal u(t) : R → R in the s-domain will be denoted by u(s) = u(t) . This notation slightly departs from the one (typical of the adaptivecontrol literature) making use of simple square brackets. Simple square brackets in this paper will be used for vectors and matrices, e.g. v = [1 0 0] ∈ R 3 . | · | denotes the absolute value, whereas (·) denotes the transpose of vectors and matrices.

II. CERTAINTY EQUIVALENCE CONTROLLER BY
NONLINEAR PARAMETER FILTERING Consider the single-input-single-output (SISO) LTI system described by: where u, y ∈ R denote the plant input and output, respectively. N (s) and D(s) are monic and coprime polynomials with unknown coefficients, b is the high-frequency gain of the system. The following standard assumptions of outputfeedback MRAC [5], [9] are made: (A.1) The degrees n and m of N (s) and D(s) are known and relative degree ρ := n − m ≥ 1; (A.2) b is non-zero, has known sign and is norm-bounded from above by a known constantb; (A.3) The polynomial N (s) is Hurwitz. The objective is to determine u(t) using a differentiator-free controller such that the trajectories of the closed-loop system are bounded, and the plant output y(t) tends asymptotically to the output y r (t) of the reference model where r(t) is referred to as the "reference command", and The reference model satisfies the following assumptions: (B.1) The command r(t) is a uniformly bounded piece-wise continuous function of time; (B.2) The polynomial D r (s) is a monic and Hurwitz polynomial of degree ρ = n − m.
Next, the DyCE will be used to design the MRAC. Using well-known results from adaptive control theory, the tracking errorỹ(t) := y(t) − y r (t) can be written in the form where (t) is an exponentially-decaying signal which incorporates the effect of the unknown initial conditions, θ ∈ R 2n is a vector of unknown constant parameters and η(t) ∈ R 2n is the regressor vector obtained by filtering the input, output and reference signals being L(s) an arbitrary Hurwitz polynomial of order n − 1.
The DyCE method consists in transforming (3), of relative degree ρ, into a new error equation of relative degree 0, for which the design of the parametric adaptation law becomes much simpler. Define a vector of filtered regressors, obtained by filtering η(t) as: Then the tracking error can be written as The DyCE paradigm applied to output-feedback MRAC consists in choosing a control law of the form whereθ(t) is the estimated parameter vector, whose update law will be determined later. Defining the estimation error θ(t) :=θ(t) − θ and substituting (6) in (5) yields the relative degree-0 (a.k.a. "algebraic" or "static") error model The main difficulty in this approach arises when one expresses (6) in time-domain, as u(t) will depend on the first ρ time-derivatives of both ξ(t) andθ(t), as seen in the following: where d i ∈ R, i = 0, . . . , ρ are the coefficients of the polynomial D r (s), with d ρ = 1.
It is noted that, in equation (7), the required ρ derivatives of ξ(t) are available without direct differentiation, due to the fact that ξ(t) is obtained from η(t) through the filter (4) having relative degree equal to ρ. Conversely, the need to compute the first ρ time-derivatives ofθ prompts the development of specific adaptation laws capable to produce all the required derivatives without direct differentiation. In this regard, the DyCE control scheme will be applied using a NPF to develop the tuner, alternative to HOT. The NPF method takes the current estimate of the parameter vector as input, and produces a filtered version together with all the needed derivatives. The parameter vector feeding the NPF can then by updated via a conventional first-order tuner (see (13) below), typically used in CE adaptive control. The proposed DyCE+NPF control law takes the following form: equivalent to the time-domain representation whereθ NPF (t),θ NPF (t) are the filtered parameter vector and its derivatives, all generated by the NPF to be determined.
Substituting the control law (8) into the error equation (5) and adding the term −b ξ(t) θ (t) to each side yields where the effect of the exponentially-decaying term (t) has been neglected. Defining the NPF error vector θ NPF (t) :=θ NPF (t) −θ(t), and the scalar signals (projected errors) equation (10) can be expressed in time-domain as Let the update law forθ(t) be given by the first-order tuneṙ where µ > 0 is an arbitrary scalar gain. Substituting (12) into (13) and considering (11), one obtainṡ This expression will be used later in the stability analysis.
The NPF that generates the filtered parameter vector θ NPF (t) takes on the following cascaded structure where Γ(t) ∈ R 2n×2n is a (possibly time-varying) gain matrix to be determined.
Remark 2.1: The use of a conventional first order adaptive law makes it easy to apply usual robust modifications, including σ and e 1 modifications. In particular, parameter projection can be used whenever a convex admissible parameter set is known a priori. The main advantage of using parameter projection is that in nominal noise-free conditions, the estimated parameters are guaranteed to converge to the true ones in case of sufficient excitation.

III. STABILITY ANALYSIS
In this section, we present the stability analysis of the proposed scheme using the following intermediate result: Lemma 3.1: (Invariance-like Lemma) If two scalar functions V (t), W (t) : R ≥0 → R ≥0 satisfy the following conditions: The proof of the above Lemma follows from the Lyapunovlike Lemma in [10] (that, in turn, is a derived from Barbȃlat's Lemma) and is omitted here due to the space limitations.
To aid the discussion, let us introduce the parametric differences between successive layers of the NPF:θ 1 (t) :=θ 1 (t) −θ(t) and Moreover, the layer-to-layer differences obey the dynamics: where we have taken advantage of the relatioṅ θ i (t) = −Γ(t)θ i (t). It is worth noticing that the NPF vector error,θ NPF (t), can be expressed as Moreover, defining the scalar signals then ε NPF (t) can be expressed as The main result concerning the stability of the proposed scheme is reported in the following theorem. Theorem 3.1: If Assumptions (A.1)-(B.2) hold, then for system (1) in closed-loop with the adaptive controller comprising the DyCE controller (9), the tuner (13) and the filter (15), there exists a proper choice of Γ(t) such that the trajectories of the closed-loop system originating from any initial condition are bounded and the tracking errorỹ(t) converges to zero asymptotically.
Proof: In view of (12), the following implication holds: Therefore, the proof consists in showing that the DyCE+NPF scheme makes ε θ (t) and ε NPF (t) converge to zero simultaneously. With this in mind, consider the following quadratic function as a building block of the overall candidate Lyapunov-like function: where α : 0 < α < 1 and σ Ξ > 0 are arbitrary positive scalars, and Ξ(t) := ξ(t)ξ(t) . Thanks to (11), (17) and (19), one can use V NPF as a brick of the candidate Lyapunovlike function to establish the convergence of ε NPF (t). Before proceeding further, Γ(t) is given the following structure: with Λ(t) to be determined. Taking into account (16) and (22), the derivative of V NPF along the trajectories of the closed-loop system reads aṡ To study the stability of the closed-loop adaptive system, consider the following candidate Lyapunov-like function The challenge is to design Λ(t) to make V a Lyapunov-like function for the closed-loop adaptive system. In what follows, the notation will be streamlined by omitting the explicit time-dependence of all signals, unless strictly required. By exploiting (14), the derivative of V along system's trajectory can be written aṡ Assigning the matrix Λ(t) = σ ΞΞ (t) + Λ(t), with Λ(t) a (possibly time-varying) symmetric positive-definite matrix to be determined, one obtainṡ Application of Young's inequality and the identity ε NPF = ρ i=1 ξ θ i to selected terms of the above expression yields where Ψ(t) is a time-varying non-negative-definite symmetric matrix defined as Ψ(t) := (I + σ Ξ Ξ(t))ξξ (I + σ Ξ Ξ(t)). Application of Young's inequality to the last two terms of the right-hand side of the inequality forV yields is a time-varying strict positive-definite symmetric matrix defined as Φ(t) := σ Ξ (I +Ξ(t) Ξ (t)). Accordingly, the derivative of the candidate Lyapunov-like function can be bounded as followṡ The previous inequality can be rewritten in compact form as: where γ 1 (Ψ, Φ, Ξ), γ ρ (Ψ, Φ, Ξ), γ i (Ψ, Φ, Ξ) are defined as for i = 2 · · · ρ − 1. Next, a selection of Λ must be made so that γ 1 , γ ρ and γ i become strictly positive for all t ≥ 0, to make the right-hand side of (24) negative semi-definite. To this end, Γ and Λ are selected as with λ > 0 is an arbitrary scalar constant, while the matrix Λ * will be assigned to be a time-varying positive-definite matrix dependent on available signals. Substituting (26) in (25) one obtains Next, Λ * = Λ * (Ψ, Φ, Ξ) will be designed such that γ j > 0, for all j = 1, 2, · · · ρ and t ≥ 0. Noticing that Λ ≥ Λ * +λΞ, by virtue of (26), one obtains where i = 2, .., ρ − 1 andρ := µb 1 + ρ 2 . Choosing for all i = 2, .., ρ − 1. As a result, both terms on the righthand side of (28) are positive, as for all i ∈ {2, .., ρ − 1}. Since 0 < α < 1, one can easily see that (1 + α)/(1 − α) > 1. Moreover, due to the choice of λ made in (29), we have so that the following bound holds for γ ρ : Finally, (29) also guarantees that for any α ∈ (0, 1). Therefore, one obtains Substituting the lower bounds in (31), (33) and (35) into (24), and due to the relations defined in (11), and (18) and recalling that Ξ(t) = ξ(t)ξ (t), one finally obtainṡ where It is straightforward to see that V (t), defined in (23), and W (t) are positive semi-definite, whileV (t) is negative semi-definite in view of (36). Therefore, from (21), (23) and (36) we can infer thatθ,θ i , i ∈ L ∞ and θ , i ∈ L 2 , for i = 1 · · · ρ. This result in turn implies that NPF ∈ L 2 , and thereforeỹ ∈ L 2 . By invoking to Assumptions A.3 and B.2 ( i.e., customary minimum-phase arguments) and owing to the fact that y is the sum of y r ∈ L ∞ andỹ ∈ L 2 , one can easily show that the both the filtered regressors'vector ξ and its first derivativeξ are bounded (the vector ξ can be written as the output of a bank of strict-proper stable linear filters taking the signal y as input). From the boundedness of ξ,ỹ we can conclude that alsoθ ∈ L ∞ , and consequently (being each layer of the filter (16) stable by design), alsoθ i ,θ i ∈ L ∞ , for i = 1 · · · ρ . Then, the boundedness ofθ,θ, ξ,ξ,θ i ,θ i yields thatẆ (t) is bounded. Hence, W (t) is a uniformly continuous function. Then, according to Lemma 3.1, W (t) converges to zero asymptotically, implying that ε θ (t) and ε i (t), with i = 1 · · · ρ, converge as well. Thanks to (19), the asymptotic convergence of ε NPF (t) follows. Finally, in the light of (20), the convergence of ε θ (t) and ε NPF (t) implies that ofỹ(t).
Remark 3.1 (Implementability-Causality): This remark is aimed at showing that the DyCE+NPF adaptive control is implementable. Compared to the HOT of Morse, which contains matrix-gain terms depending on Ξ(t) = ξ(t)ξ(t) , the gain matrix Γ(t) of the NPF reads as hence, Γ(t) depends on the regressor vector ξ(t) and its derivativeξ(t). The dependence of Γ(t) onξ(t) calls for further considerations about the implementability (that is, the realizability ofξ(t) via a causal system) of the ρ-th derivative of the filtered parameter vector. It is noted that the derivatives ofθ NPF (t) required in the implementation of the DyCE control satisfy the following functional dependencê θ (i) NPF (t) = f ρ θ ρ (t), . . . ,θ 1 (t),θ(t), ξ(t), . . . , ξ (ρ) (t) .
Since the derivatives of ξ(t) are available up to the ρ-th order, thenθ

IV. ILLUSTRATIVE EXAMPLE
In this section, a numerical example is provided to demonstrate the effectiveness of the proposed adaptive controller. The proposed algorithm is compared with the classical augmented-error based MRAC with normalization [9] and the simplified HOT [7] of Nikiforov. The Runge-Kutta integration method with fixed sampling interval T s = 10 −3 s has been employed for all simulations.
Consider the relative degree-two unstable LTI plant with unknown parameters a 2 = 2, a 1 = −1 and b = 2 and external disturbance d(t). The upper boundb = 4 is assumed on the high-frequency gain b, whose sign is is known a priori. The reference model is selected as y r (t) = 1 s 2 +2s+1 r(t) . We first consider a sinusoidal reference signal r(t) = 4 sin(0.8t) in a disturbance-free scenario, i.e., d(t) = 0. For all the three methods considered, the plant model is initialized with the same initial condition, y(0) =ẏ(0) = 0, whereas the gains are tuned so to achieve comparable convergence speed. More specifically, the AugE ( short for augmented error adaptive controller with normalization) is tuned with the following selection of the gains: Λ(s) = s + 2, γ = 0.5 and Γ = 0.5I 2×2 ; conversely, the parameters of HOT(short for Nikiforov's HOT controller) have been selected as λ = 1, µ = 1, γ = 1 and σ = 0. The parameters of the proposed controller, denoted by acronym NPF, have been chosen as: µ = 1, α = 0.5 and λ = 10, whereas Γ(t) is given by (27) and (29). The behavior of the tracking error for the three MRAC algorithms is shown in Figure 1.
From the analysis of Figure 1, it is noted that the three methods all succeed in tracking the reference signal with similar convergence time. However, the DyCE methods based on HOT and NPF display a better transient behavior.
Next, the performance of three algorithms in presence of the bounded disturbance d(t) = 2 sin(3t) + 0.1 sin(20t) is compared. The results of the simulations are reported in Figure 2, which suggests that the proposed method achieves a higher tolerance to high frequency disturbances than the other two methods. V. CONCLUDING REMARKS In this paper, we have proposed a new model-reference output-feedback controller for SISO LTI systems with relative-degree possibly larger than one. The new adaptive controller is based on the DyCE principle and consists of a nonlinear parameter filter equipped with a first-order tuner. The rationale behind the proposed architecture consists in designing a cascaded nonlinear low-pass filter that, once applied to the parameter vector obtained by standard adaptation laws, produces a filtered parameter vector that has computable derivatives, making the DyCE control law implementable.
One remarkable feature of the proposed adaptive controller is that it does not require normalization, that is instead mandatory in augmented-error adaptive controllers for systems with relative degree larger that two. Hence, the proposed DyCE adaptive controller with NPF is able to use large adaptation gains, thus achieving fast convergence, similarly to the HOT formulation of Morse. Moreover, the proposed architecture can be easily equipped with the robust modifications of update laws, including leakage modifications and parameter projection.


Increase in level of detection of secret embedding into compressed JPEG-images based on selection of informative features

The research of informational content of features in the spatial and the frequency domains at steganalysis of the compressed JPEG-images is presented. Modern steganalysis methods, based on which the feature set has been created, are considered. As a method of informative features selection has been applied the greedy algorithm with an exception which has allowed reducing number of features in the set from 43 to 26. The experiments have shown that steganalysis on the basis of informative features allows increasing the accuracy of correct classification of initial images to 94%, of images with attachments by the PM1 and the Jsteg methods by 25 and 18 percent respectively. The issue of steganalysis of images with artificially created distortions is mentioned. The experiments showed that steganalysis based on informative features allow classifying correctly such images with the accuracy 96%.

Introduction
It is difficult to present today any field of human activity where digital images are not used: photos, schemes, schedules, charts, drawings, etc. Every day users post into the Internet millions of images of various characters, save the pleasant pictures, without suspecting about their possible contents. Active flows of digital images in the Internet allow people imperceptibly exchanging the secret information by use of digital steganography. The authors in [1] explain steganography as the science about the ways of information transfer, storage, which provide concealment of existence of this information in some signal; it provides various methods of concealment of data in digital images.
The criteria of efficiency of steganographic embedding are capacity, obscurity (lack of visible distortions of digital objectsstego-containers) and stability before steganalysisthe science about ways of identification of the hidden messages' existence facts in digital objects. Steganalysis in most cases consists in search of characteristics (features) of a digital object, which change during steganographic embedding.
Identification of the unmasking features can be made by means of the analysis of images arrays (stego-images and images which aren't containing secret information). However there are tens of thousands of various features of digital images in the spatial and the frequency domains. Many of features are linearly dependent, and some do not bear information about distortions, which were made during steganographic embedding. As features in a set are considered in interaction, it is important to reveal a set of informative features.
where 0 () Efmean value of zero AC-coefficients frequencies at blocks; amounts at columns. The authors calculate each characteristic twice: for the researched image (J1) and for the image which is received by truncating of the researched image on top and at the left by 4 pixels (J2). The authors claim that when truncating the image at the left and on top, the division of the image into blocks moves, coefficients of the discrete cosine transform are exempted from influence of last quantization and contain only statistical data of the image, which are just important in steganalysis case.
Thus, the value of the functionality will be finite feature: For the solution of the steganalysis task it is possible to use not only the features created especially for its carrying out but also features representing some characteristics calculated for digital images. In particular, it can be the textural features applied in different tasks of image identification. 10 features given in [5] were included in the researched feature set as F16,…,F25.
The method provided in [6] is based on the Benford's law: the probability of appearance of digit on the first place in number is higher, than less is this digit. Based on outputs of the paper devoted to the Generally, digital objects steganalysis is considered as the task of two-class classification when for each analyzable object one of two outcomes is selected: it is an initial object or an object contains some hidden data.

Selection of Informative Features
Nowadays there is a wide choice of algorithms of informative features selection, the cornerstone of which is statistical dependences (between set elements, between elements of set and output values), comparative experiments and difficult calculations.
For research of the created earlier feature set the most suitable is the greedy algorithm with an exception as this method fast, effective according to [7][8], considers all elements of the set in total, but not as separate components.
Greedy algorithm of search is used often as it is fast and yields good result in many tasks. The group of algorithms has received such name because if one of features has been chosen in subset (or excluded), then further it remains in set (in case of the greedy inclusion) or will be forever removed (in case of the greedy exception) [9].
For formation of learning and test selections standard images for the steganography (Lena, Peppers, Baboon, Splash, Airplane, Tiffany, Girl, etc.) and images from the base UCID (Uncompressed Color Image Database) and from the base USC-SIPI ID (University of Southern California Signal and Image Processing Institute Image Database) 256х256 pixels were taken. Training (660) and test (440) selections contain images:  without attachment;  with attachment by classical steganographic methods: F5, PM1, Jsteg. As in research the greedy algorithm with an exception is applied, the full feature set with 43 elements described earlier is initially considered.
In the Tab. 2 results of experiments are provided. As the feature set is quite volume, the table contains five greatest probabilities of detection on each step.
Experiments have shown that the set of 43 features in the spatial and the frequency domains can be reduced by 17 elements. It allows increasing the general accuracy of classification by 19%.
It should be noted that 7 remote features on the basis of the Benford's law were removed quickly enough (remained only for values 3 and 4). Features based on combination of the Benford's law with the idea of the image shift were steadier and was removed only 1 feature (for value 1). It allows making conclusion on bigger informational content and a bigger contribution of the modified version of features.
In addition during the several first iterations the big accuracy of detection was shown by sets without structural features in the spatial domain (correlation, entropy, contrast, covariance). However after removal of these 4 features in the Tab. 2 presence of other elements from this group has not been noticed almost.  Remained features removed from the full setfive dual histograms. Paying attention for what values of coefficients there were these features:-4,-3, 3, 4, 5. It is known that after the DCT and quantization the greatest number of elements is accepted by values in the range [-1, 1], and the farther the value is from borders of this range, the less is the probability to meet it in the matrix of DCTcoefficients. Therefore, dual histograms for the above-stated values were removed from the general feature set.
The sets with an exception of the first 4 features: 3 on the basis of ratios of energies in the frequency domain and interblock correlation between blocks with proximity of DC-coefficients no more than 3,always showed result below an average. It means that these features have an important contribution to the general set and an informative component about contents of the digital image.

Computing Experiments
In case of steganalysis image's features in the spatial and the frequency domains are analyzed. However, distortions can be made in digital objects not only at steganographic embedding. Now there is a set of applications for editing images: imposing of ready filters and creation of various effects, including noise. When processing the image in an editor distortions are also made into the main features of the image. At steganalysis it is important not to classify artificially distorted image as the image with an attachment [10]. The experiments with the initial feature set and with the set of selected informative features were made separately for 5 types of images:  image without attachment (initial);  images with attachments by the steganographic methods: F5, PM1, Jsteg;  images without attachment but distorted in the popular photo editor Prisma.  The experimental results show that reduction of the feature set to 26 informative features allows increasing the volume of correct classification of images. For images with attachment by the PM1 and the Jsteg methods application of the reduced feature set show increase in accuracy of correct classification by 25 and 18,95 percent respectively. The accuracy of classification of images with artificial distortions (Prisma) increased by 9,26%, and clear images (initial)by 3,53%. Application of the reduced feature set has not exerted impact only on images with attachment by the F5 method. Generally the accuracy of classification has increased on average by 11,34%.

Conclusion
Modern steganalysis methods and features in the spatial and the frequency domains of digital images, which are widely applied in steganalysis, were investigated. On the research's basis the feature set was created.
The application of the greedy algorithm with an exception as the algorithm of informative features selection allowed reducing number of features in the set from 43 to 26.
Experiments have shown that steganalysis on the basis of informative features allows increasing the accuracy of the correct classification for images without attachment by 3,5%, with attachment by the PM1 and the Jsteg methods by 25 and 18,9% respectively.
The problem of steganalysis of images with the artificial distortions created by means of the photo editor Prisma was mentioned here. Experiments have shown that steganalysis based on informative features allows reaching the accuracy of correct classification 96%.
The conducted research shows that studying of informational content of features in the set allows achieving good results at identification of the fact of existence of confidential attachment in digital images.


extfieldsofstudy:
Computer Science
Engineering

text:
Beam Blockage in Optical Wireless Systems

In this paper, we use the percentage blockage as a metric when an opaque disc obstructs the Line-of-Sight link from the access point to the receiver in an optical wireless indoor communication system. The effect of the different parameters of the obstructing object are studied, these are the radius, the height, and the horizontal distance from the receiver in the positive y direction. The percentage of blocked room locations to the total number of room locations when varying the disc parameters is studied assuming a single serving link. It was found that depending on the dimensions of the obstructing object and the distance from the receiver in addition to which access point is serving the user, that blockage can vary between 0% up to 100%. Furthermore, the service received by a user, in terms of beam blockage depends on the access point they are connected to. The resulting fairness challenges will be addressed in resource allocation optimization in future work.

INTRODUCTION
Optical Wireless (OW) communication is a promising technology that can complement the radio frequency (RF) based communication systems and can help meet the exponentially increasing demand for data. Both OW and RF based systems have their advantages and disadvantages in relation to spectrum and channel characteristics. While the inability of light to penetrate opaque objects is considered a merit exploitable to provide physical layer security and increased capacity by the reuse of optical frequencies in other rooms in OW systems (as opposed to RF based systems), it is considered as a disadvantage if an object blocks the direct line-of-sight (LOS) beam within a room. Higher order reflections from different room surfaces can be utilized, however, the LOS beam has the highest contribution to the received optical power compared to n-order reflections that undergo diffusion and losses due to absorption by reflecting surface materials [1]. In addition, the multipath propagation due to optical rays arriving from reflecting surfaces results in pulse dispersion, creating inter-symbol-interference (ISI) and hence limiting the achievable data rate. Multi-gigabit per second OW systems were reported in literature [2]- [6]. These systems enhance the achievable data rate by improving the received power, reducing the effects of background noise, and the pulse delay spread employing different techniques. These techniques; such as multispot diffusing transmitters, diversity transmitters and receivers [7], and beam delay and power adaptation techniques [8], [9] with beam steering and Computer Generated Holograms (CGH) [10], [11]; aim at enhancing the received optical power by enhancing the LOS component of the received optical power and reducing the noise, which result in higher signal-to-noise ratio (SNR) and hence higher data rates. Ensuring the availability of a direct LOS link and the resilience against blockage is important for a reliable high data rate system that meets the service level agreement (SLA) requirements. In [12], shadowing and blockage were studied for the cellular and multispot diffusing MIMO systems. In [13], WiFi was proposed to provide an alternative service in case of optical link blockage. In this work a preliminary study of blockage is performed for a simplified object that can be later combined with other complex objects to represent real objects in the environment. Here the effects of the blockage of the LOS links by disc objects within an indoor environment is studied. The percentage of room locations at which the beam is blocked is calculated assuming a single serving access point (AP). The rest of this paper is organized as follows: Section 2 describes the procedure used to evaluate the percentage blockage under different obstructing object parameters. Section 3 shows the results obtained. Conclusions and future work are provided in Section 4.

LINE-OF-SIGHT BEAM BLOCKAGE BY A DISC
In this work, the effect of blockage of LOS links by objects within indoor room environment is studied. The room considered has dimensions of (4 m x 8 m x 3 m) for (width x length x height) respectively. Receivers are assumed to be distributed over the communication floor (CF) at 1 m above ground which is the height of a typical office desk. Eight sources of illumination (or access points) to provide sufficient illumination [4] are assumed at the (x,y,z) coordinates of (1,1,3), (1,3,3), (1,5,3), (1,7,3), (3,1,3), (3,3,3), (3,5,3) and (3,7,3) as shown in Fig. 1. The APs serve the receivers based on fixed allocation by the controller [14]. A horizontal disc with radius R, height h effectively calculated above the CF, and horizontal distance d between the receiver and the disc centre in the positive y direction, is assumed. The disc can be generalized and more complexity can be added so that it represents other realistic objects in the room (whether mobile or fixed), such as a human, a paper held by a human, or a piece of furniture.
Assuming a single receiver in the room assigned a single AP, two parameters of the disc are fixed, and the third parameter is varied as shown in Fig. 2. For specific R, h, and d,

RESULTS AND DISCUSSION
It can be seen that in Fig. 3 that one disc parameter is varied while the other two parameters are fixed at a minimum value, a maximum value, and a value in between.
The results obtained are shown in Fig. 3 when varying the values of R, h, and d. In Fig. 3 (a-c) where R is varied, it can be seen that increasing the radius of the disc leads to increased percentage of blockage. For a given value of h and d, if R is increased, blockage increases. This can be expected as shown in Fig. 2 (a) where the beam is blocked after a specific value of R for a given AP and receiver location and given h and d values.
In Fig. 3 (d-f) where h is varied, it can be seen that if the height is zero above the communication floor and the radius of the disc is greater than or equal to the horizontal distance between the disc centre and the receiver, the receiver is always blocked as it is covered by the disc, otherwise there is no blockage at h equal to zero. In addition to the relation between R and d and since the disc is assumed at a horizontal distance d in the positive yaxis direction and depending on whether the location of the assigned AP is to the left or right of the receiver, the probability of blocking varies over the whole CF. Given R is less than d and assuming the disc lies in between the receiver and AP (across a horizontal separation), and as illustrated by Fig. 2 (b) the percentage beam blockage starts from 0 when the LOS beam passes over the disk, and increases to some value and then decreases, when the beam passes under the disc. It can be seen that if R is greater than d, the beam blockage percentage starts from 1 and then decreases.
The results when varying d are shown in Fig. 3 (g-i). These results experience a similar pattern to the previous case when h was varied. This is also interpreted using Fig. 2(c); when d increases, the beam passes under the disc, gets blocked, and then passes over the disc. After the distance between the receiver and the obstructing object exceeds some value depending on the separation, the object no longer blocks the receiver and the percentage beam blockage goes to zero.

CONCLUSIONS AND FUTURE WORK
In this paper, the effect of direct line-of-sight beam blockage by an opaque object was studied. The blockage is studied for different values of the parameters of the obstructing object including the radius, height, and horizontal distance from the receiver; where blockage is measured using the percentage of beams blocked. In our planned future work, implementing resilience by assigning two or more links is expected to reduce blockage on average. The effect of the added traffic as a result of using redundant links, and its impact on the network can also be studied in the future.
In this paper only blockage of LOS links was considered, however, shadowing of higher order reflection components needs to be studies to evaluate the ability to work under a shadowing object for example. Also the problem of blockage can be examined to obtain the statistical distribution of the link blockage probability and this can be obtained both through simulations and measurements and can be used so that allocation of access points is blockage-aware in static environments while in dynamic environments, allocation can be handled using intelligent MAC protocols.