Concurrent Exception Handling and Resolution in Distributed Object Systems AbstractÐWe address the problem of how to handle exceptions in distributed object systems. In a distributed computing environment, exceptions may be raised simultaneously in different processing nodes and thus need to be treated in a coordinated manner. Mishandling concurrent exceptions can lead to catastrophic consequences. We take two kinds of concurrency into account: 1) Several objects are designed collectively and invoked concurrently to achieve a global goal and 2) multiple objects (or object groups) that are designed independently compete for the same system resources. We propose a new distributed algorithm for resolving concurrent exceptions and show that the algorithm works correctly even in complex nested situations, and is an improvement over previous proposals in that it requires only O(n max N 2 ) messages, thereby permitting quicker response to exceptions. The concept of CA actions offers a general and convenient framework for designing distributed and concurrent OO software. This paper has focused on important technical details of concurrent exception handling and resolution under the CA action framework (though the results are generally applicable to other atomic action schemes). Our solutions are intended for a wide set of OO languages and for practical systems that interact with their environments; such systems typically are incapable of simple backward recovery. The OO exception model developed in this paper extends and improves the models which may be found in sequential OO languages and the nonconcurrent models for some concurrent OO languages.. How to correctly cope with nested CA actions in exceptional situations is a significant and delicate problem, especially in a distributed computing environment. In [5] , the authors presented just a draft of their resolution algorithm, without discussing assumptions under which the algorithm may work. The semantics of the operation of raising abortion exceptions in nested actions and of the resuming/suspending mechanism in such nested actions were not addressed clearly. We have developed an abortion mechanism that coordinates recovery measures used in both participating objects of nested actions and external atomic objects. A new distributed algorithm for exception resolution has been designed to handle concurrent raising of multiple exceptions in interacting objects.. We have applied our approach to realistic industrial applications by developing robust software to control different types of production cells. A production cell model, based on a metal-processing plant in Karlsruhe, Germany, was first created by the FZI (Forschungszentrum Informatik) in 1993 [15] in order to evaluate different formal methods and to explore their practicability for industrial applications. Since then, this case study has attracted wide attention and has been investigated by over 35 different research groups. In 1996, the FZI presented the specification of two extended models, called the Fault-Tolerant Production Cell [17] and Real-Time Production Cell [18] . We have recently designed and implemented two control software systems for these case studies [27] , [31] . Analytical and experimental results have demonstrated the feasibility of our approach to concurrent exception handling and showed that the approach makes it possible to reason about complex exceptional behaviour of a system in a very disciplined and structured way.. Future research directions would be in two primary areas in terms of the further development of the CA action concept. The first is the introduction of an appropriate linguistic mechanism for specifying (nested) CA actions in a distributed environment. Second, it is important to investigate the implementation-related issues with CA action's run-time support mechanisms.

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Quantum computation, quantum theory and AI The main purpose of this paper is to examine some (potential) applications of quantum computation in AI and to review the interplay between quantum theory and AI. For the readers who are not familiar with quantum computation, a brief introduction to it is provided, and a famous but simple quantum algorithm is introduced so that they can appreciate the power of quantum computation. Also, a (quite personal) survey of quantum computation is presented in order to give the readers a (unbalanced) panorama of the field. The author hopes that this paper will be a useful map for AI researchers who are going to explore further and deeper connections between AI and quantum computation as well as quantum theory although some parts of the map are very rough and other parts are empty, and waiting for the readers to fill in. Quantum theory is without any doubt one of the greatest scientific achievements of the 20th century. It provides a uniform framework for the construction of various modern physical theories. After more than 50 years from its inception, quantum theory married with computer science, another great intellectual triumph of the 20th century and the new subject of quantum computation was born.. Quantum computers were first envisaged by Nobel Laureate physicist Feynman [47] in 1982. He conceived that no classical computer could simulate certain quantum phenomena without an exponential slowdown, and so realized that quantum mechanical effects should offer something genuinely new to computation. In 1985, Feynman's ideas were elaborated and formalized by Deutsch in a seminal paper [30] where a quantum Turing machine was described. In particular, Deutsch introduced the technique of quantum parallelism based on the superposition principle in quantum mechanics by which a quantum Turing machine can encode many inputs on the same tape and perform a calculation on all the inputs simultaneously. Furthermore, he proposed that quantum computers might be able to perform certain types of computation that classical computers can only perform very inefficiently.. One of the most striking advances was made by Shor [92] in 1994. By exploring the power of quantum parallelism, he discovered a polynomial-time algorithm on quantum computers for prime factorization of which the best known algorithm on classical computers is exponential. In 1996, Grover [52] offered another killer application of quantum computation, and he found a quantum algorithm for searching a single item in an unsorted database in square root of the time it would take on a classical computer. Since database search and prime factorization are central problems in computer science and cryptography, respectively, and the quantum algorithms for them are much faster than the classical ones, Shor and Grover's works stimulated an intensive investigation in quantum computation. Since then, quantum computation has been an extremely exciting and rapidly growing field of research.. Since it revolutionized the very notion of computation, quantum computation forces us to reexamine various branches of computer science, and AI is not an exception. Roughly speaking, AI has two overall goals: (1) engineering goal -develop intelligent machines; and (2) scientific goal -understand intelligent behaviors of humans, animals and machines [76] . AI researchers mainly employ computing techniques to achieve both the engineering and scientific goals. Indeed, recently, McCarthy [8] even pointed out that "computational intelligence" is a more suitable name of the subject of AI to highlight the key role played by computers in AI. Naturally, the rapid development of quantum computation leads us to ask the question: how can this new computing technique help us in achieving the goals of AI. It seems obvious that quantum computation will largely contribute to the engineering goal of AI by applying it in various AI systems to speedup the computational process, but it is indeed very difficult to design quantum algorithms for solving certain AI problems that are more efficient than the existing classical algorithms for the same purpose. At this moment, it is also not clear how quantum computation can be used in achieving the scientific goal of AI, and to the best of my knowledge there are no serious research pursuing this problem. Instead, it is surprising that quite a large amount of literature is devoted to applications of quantum theory in AI and vice versa, not through quantum computation. It can be observed from the existing works that due to its inherent probabilistic nature, quantum theory can be connected to numerical AI in a more spontaneous way than to logical AI.. The aim of this paper is two-fold: (1) to give AI researchers a brief introduction and a glimpse of the panorama of quantum computation; and (2) to examine connections between quantum computation, quantum theory and AI. The remainder of the paper is organized as follows: Section 2 is a tutorial of quantum computation for readers who are not familiar with quantum computation and quantum theory. Section 3 surveys some areas of quantum computation which the author is familiar with. Some potential applications of quantum computation in AI are considered in Section 4, and the interplay between quantum theory and AI is discussed in Section 5. A brief conclusion is drawn in Section 6. This paper identifies three classes of opportunities for AI researchers at the intersection of quantum computation, quantum theory and AI:. • Design quantum algorithms to solve problems in AI more efficiently;. • Develop more effective methods for formalizing problems in AI by borrowing ideas from quantum theory;. • Develop new AI techniques to deal with problems in the quantum world.. The first class of research is still in the initial stage of development, and not much progress has been made. Shor [93] listed some reasons to explain why quantum algorithms are so hard to discover. Unfortunately, these reasons are valid for the problems in AI too. Some fragmented and disconnected research belonging to the second class have a long history, and some basic ideas can even be traced back to Niels Bohr and related to philosophy and interpretation of quantum mechanics [59] . In recent years, research in this class has become very active, especially through the International Symposium on Quantum Interaction (2007-2009). But it seems that some of these works are quite superficial, and deeper theoretical analysis of the formal methods developed in these works are needed. In particular, more experimental research is required to test the effectiveness. It appears that research in the third class is making steady progress. My main concern is whether the AI techniques developed in this class of research will be useful in quantum physics and will be appreciated by physicists. Certainly, collaboration between AI researchers and physicists will highly benefit the development of this area. Perhaps, experience from bioinformatics can be used for reference where close collaboration between computer scientists and biologists frequently happens and leads to high impact research.

B I B I O O O O O O O O O O O O O O O B I O O O O O O O O B I O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O B I O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O B I O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O B I O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O B I B I O O O O O O O O O O O O O O O O O B I O O O O O O O B I O B I O O O O O O B I O O O O O O O O O O B I O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I B I O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


A geometric-process maintenance model for a deteriorating system under a random environment This paper studies a geometric-process maintenance-model for a deteriorating system under a random environment. Assume that the number of random shocks, up to time , produced by the random environment forms a counting process. Whenever a random shock arrives, the system operating time is reduced. The successive reductions in the system operating time are statistically independent and identically distributed random variables. Assume that the consecutive repair times of the system after failures, form an increasing geometric process; under the condition that the system suffers no random shock, the successive operating times of the system after repairs constitute a decreasing geometric process. A replacement policy , by which the system is replaced at the time of the failure , is adopted. An explicit expression for the average cost rate (long-run average cost per unit time) is derived. Then, an optimal replacement policy is determined analytically. As a particular case, a compound Poisson process model is also studied. A T THE initial stage of research in maintenance problems of a repairable system, a common assumption is "repair is perfect:" a repairable system after repair is "as good as new." Obviously, this assumption is not always true. In practice, most repairable systems are deteriorating because of the aging effect and accumulated wear. Thus, [4] introduced a minimal-repair model in which a system after repair has the same failure rate and the same effective age as at the time of failure. Reference [6] suggests an imperfect repair model, in which a repair is perfect with probability , and a minimal repair with probability . An alternate approach is to introduce a monotone process model. For a deteriorating system, it is reasonable to assume that the successive operating times of the system after repairs are stochastically decreasing and the consecutive repair times of the system after failures are stochastically increasing. According to this idea, [12] , [13] introduced GP model. This is a simple monotone process model but a good approximation to a more general monotone process model. Definition 1: Given 2 r.v. and , is stochastically greater than ( is stochastically less than ) if for all real or A stochastic process , is stochastically increasing (decreasing) if for all [29] . As a special monotone stochastic process, the GP was first introduced in [ On the other hand, if , then is stochastically decreasing:

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O B I O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Histology Image Retrieval in Optimized Multifeature Spaces Abstract-Content-based histology image retrieval systems have shown great potential in supporting decision making in clinical activities, teaching, and biological research. In content-based image retrieval, feature combination plays a key role. It aims at enhancing the descriptive power of visual features corresponding to semantically meaningful queries. It is particularly valuable in histology image analysis where intelligent mechanisms are needed for interpreting varying tissue composition and architecture into histological concepts. This paper presents an approach to automatically combine heterogeneous visual features for histology image retrieval. The aim is to obtain the most representative fusion model for a particular keyword that is associated with multiple query images. The core of this approach is a multiobjective learning method, which aims to understand an optimal visual-semantic matching function by jointly considering the different preferences of the group of query images. The task is posed as an optimization problem, and a multiobjective optimization strategy is employed in order to handle potential contradictions in the query images associated with the same keyword. Experiments were performed on two different collections of histology images. The results show that it is possible to improve a system for content-based histology image retrieval by using an appropriately defined multifeature fusion model, which takes careful consideration of the structure and distribution of visual features.Index Terms-Content-based image retrieval (CBIR), feature fusion, histology image retrieval, multiobjective optimization. I N BIOLOGY and medicine, histology is a fundamental tool that provides information on structure and composition of tissues at microscopic level. Nowadays, images of tissue slides are often digitized to document procedures and to support findings. These collections are often huge in size and thus hide a latent source of information that can be greatly exploited if suitable mechanisms are available for accessing the data [1] . Thus, a technology that can retrieve histological images according to given queries can potentially be a very useful tool for data archiving and analysis, teaching and training, assisting decision making in diagnosis, and so on. When more complex systems are being considered, for instance, a system which pro- vides suggestions on diagnosis based on existing histopathology databases, histological image retrieval can be employed as an essential component for initial search and indexing of content using carefully selected keywords, such as a basic tissue type. Conventional medical image retrieval systems often rely on tags associated with images in the databases. However, textbased approaches are often limited in practice since tags may be both expensive and ambiguous. This is because, generating manual annotation on images is extremely time consuming, highly subjective, and requires a good level of domain-related knowledge. Another kind of approaches exploit knowledge databases like unified medical language systems [2] , but they rely on the availability of knowledge databases and their relativity to the application domain.. Alternatively, content-based image retrieval (CBIR) systems apply computer vision techniques to the image retrieval problem by analyzing the actual contents of the image rather than semantic features such as keywords or tags. Recent research in CBIR indicates that such systems are capable of retrieving medical images according to its domain-specific image features [3] . Thus, such systems form an important alternative and complement to traditional text-based retrieval systems. In image retrieval systems, given a query image, or a keyword query that is associated with a group of representative images, the goal is to retrieve from a reference library, the similar images whose semantic meaning is as close to the query as possible, regardless of its visual appearance. Although extraction algorithms for low-level image features are well understood and able to capture subtle differences between colors, statistic and deterministic textures, global color layouts, dominant color distributions, etc., the link between such low-level primitives and high-level semantic concepts remains an open problem [4] , [5] . This problem is referred to as "the semantic gap.". To alleviate the semantic gap problem, there have emerged many systems aiming at applying content-based approaches in more sophisticate ways in medical image retrieval [6] - [12] . Many diagnostic imaging modalities, such as X-ray, computed tomography, magnetic resonance imaging are currently available and routinely used to support clinical decision making, diagnosing, state of an illness tracking, medical education and research, etc. Applications of content-based approaches in medical image retrieval have shown benefits in all these procedures. In addition to general image retrieval systems applied to medical images, there are also many specialized image retrieval systems developed to enable retrieval of various specific kinds of medical images, such as breast cancer biopsy slides [13] , positron emission tomographic functional images [14] , ultrasound images [15] , different types of pathology images [16] , radio-graphic images [8] , and histology images [11] , [17] . More interestingly, the ImageCLEF medical image retrieval task targets modality classification of medical images and has attracted wide attention from the area in recent years [18] .. Among these application domains, histology image retrieval has been an active research topic for modeling visual similarity measures and retrieving tissue slides in some semantic categories. In previously reported works on histology image classification and retrieval, accuracy is often limited due to the unreliable outputs from the feature metrics [3] , [19] . This is because, the systems often rely on single low-level features, which are not always capable of interpreting visual objects into varying and complicated semantic meanings. To tackle this problem, the combination of low-level features for semantic image retrieval has been widely considered in the literature. In [16] , a system was proposed for retrieving histology images from prostate, liver, and heart tissues, based on four different visual characteristics. The work in [20] described a system to index histology images of gastrointestinal tract, by categorizing image blocks into semantic classes based on local visual patterns. The approach proposed in [21] uses a boosting algorithm based on multiple distance measures computed on a fixed set of features to retrieve and classify breast histology slides. These works all intended achieving better performance in histology image understanding by employing heterogeneous visual features. However, the problems in feature combination are likely underestimated, when feature combination is done by simple concatenation of feature vectors.. Such approaches are called early fusion, and they share two main common problems. First, methods on concatenation of feature vectors can easily result in high-dimensional feature space and thus suffer from "the curse of dimensionality" [22] , [23] . Second but most importantly, different image features often have their own structures, distributions, and metric spaces. Direct concatenation of feature vectors could result in meaningless similarity measures. For instance, feature histograms are usually compared using a similarity measure for probability distributions while feature vectors should be matched using Euclidean metrics. In addition, even if two different features are being compared with the same metric, their scale, domain, and distribution may be completely different due to the intrinsic descriptor nature [24] .. In order to avoid these problems, in this paper, a late-fusion strategy is followed to combine low-level features for histology image retrieval. Similar approaches have been proposed in the literature, such as in [25] and [26] . However, such approaches have one common disadvantage that they assume equal importance of features in fusion. In this way, the performance of "good" and "bad" features is averaged and thus could not provide great improvements. Some other approaches assign weights to different features. For instance, genetic algorithm is used for finding the optimization weights for features in image retrieval in [27] . This approach considers feature fusion independent of query, while it is not possible to expect the obtained fusion model to be optimal to all possible queries. In [28] , multifeature fusion was achieved using an optimal combination of multiple kernel functions. Kernel functions were fused using a weighted linear combination, whose weights were found by an optimization process that maximizes the correlation between low-level features, represented by kernel functions, and high-level semantic concepts. Another important direction is to rely on human interactions to obtain query specific weights [29] . Such approaches might improve the effectiveness of weighting factors, but they still require heavy workload and specific expertise from the user.. In this paper, we propose a histology image retrieval method aiming at retrieving images with relevant semantic meanings based on visual content. In each query process, the user first has in mind a semantic term that can be associated with a specific keyword, and then uses multiple query images that represent the semantic term for retrieving more images that are relevant to the query on the semantic level. In the proposed method, we use multiple images, namely, a representative query group, in the CBIR process for representing each semantic term. This is because, for a particular keyword, it is usually tricky to find a query image as an ideal visual representation. In [6] , a multitiered CBIR system was proposed targeting microscopic images, enabling both multiimage query and slide-level image retrieval. In this paper, the focus was to adopt multiple image queries in one retrieval process using the weighting terms. In comparison, we also consider using multiple image queries to represent each keyword, but the main focus of the proposed approach is to derive a fusion model for heterogeneous visual features.. In addition, for each keyword, a different representative query group is used and a unique feature fusion model is derived. This is because, each semantic term is considered to have its own characteristic visual pattern and the feature fusion models should be keyword specific. The proposed approach is able to automatically learn the relative importance of each feature space corresponding to the keyword from its associating representative query group. The learning of a suitable feature fusion model is posed as an optimization problem. The optimization is carried out using a multiobjective learning (MOL) method, which involves a multiobjective optimization (MOO) strategy [30] . The main advantage in the MOL method is that it is able to find a multifeature model that can simultaneously encapsulate different aspects of the most representative visual patterns for each concept, without however assigning fixed relevance factors to each visual feature.. Without losing generality, several different texture features are considered in our experiments. Although the proposed method can be applied to more histological terms, the four fundamental tissue types in biology-connective, epithelial, muscular, and nervous tissues-are considered in our experiments as the keywords for retrieval. It is demonstrated that, using the proposed approach, it is possible to retrieve histological images according to their semantic relevance by using properly combined visual features. The proposed approach has been tested in two collections of histology images. The first set contains over 20 000 images, among which 2828 images have manual labels of the four fundamental tissue types. The second smaller set contains around 442 histology images, and 130 of them have manual labels on those four tissue types.. The remainder of this paper is organized as follows: Section II presents the visual analysis steps in histology databases, including feature extraction, distance calculation, and normalization.. Section III introduces the MOL method for feature fusion toward a multifeature-based retrieval in histology image databases. The evaluation procedure and experimental results are presented in Section IV and Section V discusses some concluding remarks. This paper proposes a strategy for multifeature-based retrieval in histology image databases. The multifeature fusion model is obtained using a MOL method, which automatically derives a suitable model for feature combination based on multiple query images that are associated with the keyword in concern. The advantage of the proposed feature fusion approach is that it considers a fusion model for each keyword individually. Two different histology image datasets and different sets of low-level features were considered in the experiments. Experimental performance of the proposed approach, as well as a comparison to retrievals relying on single features and other similar fusion models, were presented and analyzed. The evaluation of results showed that, in the used experimental setups, the proposed strategy was able to provide more precise retrieve results based on semantic keywords that were each represented by a set of query images.

B I I O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O B I B I I B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


An automorphic approach to verification pattern generation for SoC design verification using port-order fault model Currently, two main research directions can be identified in lowpower testing. The first research direction considers power dissipation during test as a minimization objective. The second direction considers power dissipation as a design constraint, while test application time becomes the minimization objective. This paper presented a link between the two separate research directions, using a new power profile manipulation approach based on the following components: test vector reordering, test sequence expansion, two local peak power approximation model, and test sequence rotation. Test vector reordering is used to lower and reshape the test power profiles. Test sequence expansion further lowers the power profiles of shorter tests which do not affect the total test application time. Then, the proposed two local peak power approximation model translates the power profile it into a simple, reliable, and accurate test power representation, which can be exploited by test sequence rotation in order to increase test concurrency under a power constraint. Since the proposed power profile manipulation is orthogonal to the test scheduling policy and the test set values, the distinctive feature of the proposed solution is that it can be equally included in, and consequently leverage the performance of, any existing power constrained test scheduling algorithm. Comput., vol. 47, pp. 256-262, Feb. 1998. [23] Y. Zorian, "A distributed BIST control scheme for complex VLSI devices," in Proc. 11th IEEE VLSI Test Symp., 1993, pp. 4-9. [24] Y. Zorian, E. J. Marinissen, and S. Dey, "Testing embedded core-based system chips, " Computer, vol. 32, no. 6, pp. 52-60, June 1999.REFERENCESChun-Yao Wang, Shing-Wu Tung, and Jing-Yang Jou Abstract-Embedded cores are being increasingly used in the design of large system-on-a-chip (SoC). Because of the high complexity of SoC, the design verification is a challenge for system integrators. To reduce the verification complexity, the port-order fault (POF) model was proposed. It has been used for verifying core-based designs and the corresponding verification pattern generation has been developed. Here, the authors present an automorphic technique to improve the efficiency of the automatic verification pattern generation ( Spurred by process technology leading to the availability of more than 1 million gates per chip, and more stringent requirements upon time-to-market and performance constraints, system level integration and platform-based design [1] are evolving as a new paradigm in system designs. A multitude of components that are needed to implement the required functionality make it hard for a company to design and manufacture an entire system in time and within reasonable cost. Hence, design reuse and reusable building blocks (cores) trading are becoming popular in the system-on-a-chip (SoC) era. However, present design methodologies are not enough to deal with cores which come from different design groups and are mixed and matched to create a new system design. In particular, verifying whether a design satisfies all requirements is one of the most difficult tasks.. Usage of cores divides the IC design community into two groups: core providers and system integrators. In traditional system-on-board (SoB) design, the components that go from provider to system integrator are ICs, which are designed, verified, manufactured, and tested. The system integrator verifies the design by using these components as fault-free building blocks. SoB verification is limited to detecting faults in the interconnection among the components. Similarly, in SoC design, the components are cores. The system integrator verifies the design by using the cores as design error-free building blocks. The focus of this core-based design verification should be on how the cores communicate with each other [2] . However, before the interface verification, the interconnection between the cores in an SoC have to be verified first. This is because the SoC integrator has to connect a large number of ports (hundreds or even thousands of ports) in an SoC. The likelihood of interconnection misplacements between the cores is high. Furthermore, the correct interconnection between the cores is the minimum requirement to verify the interface protocols. In other words, if the interconnections between the cores are misplaced, the process of the verification on the interface between the cores will be in vain. Thus, the interconnection verification can be conducted as the first step to the interface verification between the cores in a SoC.. Most previous work in testing interconnection focused on the development of deterministic tests for interconnection between chips at the board level [3] , [4] . The main purpose is to test if the interconnection are connected properly (neither short nor open). In the interconnection testing phase, the basic assumption for a system under test is that the system design is correct, and the faults are due to manufacturing defects on interconnection among components. For the core-based SoC design verification, however, the system is not fully verified yet and the most of system design errors are due to the incorrect interconnection among predesigned cores. The incorrect interconnections are normally introduced by the misinterpretation of port description of IP cores, and this misinterpretation is usually caused by some factors, such as ambiguous or cryptic port names, Big Endian or Little Endian byte order of address bus, etc. Therefore, the extension of these board level testing methods is inadequate for connectivity-based design verification. Fig. 1(a) and (b) shows the schemes to demonstrate the processes of interconnection testing and interconnection verification, respectively. In the interconnection testing, the test engineers focus on the success of implementation of interconnected wires between block1 and block2. The testing patterns and corresponding responses are applied and observed at the ends of the interconnects to check whether the interconnects are manufactured correctly. On the other hand, in the interconnection verification, the system integrators verify whether the interconnections between block1 and block2 are located in the correct ports. They apply the verification patterns to primary inputs (PIs) of the integrated design, then observe the corresponding responses in primary outputs (POs) of the integrated design, and match them against the specification instead.. By creating the testbenches at a high level, a connectivity-based design fault model, port-order fault (POF), proposed in [5] , is used for reducing the time on core-based design verification [6] , [7] . In [6] , we proposed an automatic verification pattern generation (AVPG) based on the POF model. The AVPG generates a pattern set to detect all possible misplacements among the ports of the cores. However, the approach of determining the undetected port sequences (UPSs) in the AVPG is deficient. It does not eliminate all detected port sequences from the fault set and generates redundant patterns for some detected port sequences sometimes.. In this paper, we present an automorphic technique, the superset of all automorphisms (SAA) technique, to calculate the remaining UPSs during the AVPG. This technique accelerates the AVPG and reduces the size of verification pattern set.. The remainder of this paper is organized as follows: the POF model and some terminology are introduced in Section II. Section III describes the mechanism of conducting POF verification and the verification environment which exploits the IEEE P1500 standard for embedded core test (SECT) [8] , [9] . The AVPG flow and the SAA technique are presented in Section IV. Section V presents the experimental results. Section VI concludes the paper. In the SoC era, the embedded cores are mixed and integrated to create a system chip. The verification of the core-based system design should be focused on how the cores communicate with each other. However, before the interface verification, the interconnections between the cores in an SoC have to be verified first. System integrators integrate those cores manually and have the possibility of incorrect integration due to the misplaced I/O ports. Therefore, we adopt the connectivity-based POF model to raise the abstraction level of the design verification and to reduce the time on functional verification in core-based design methodology.. In this paper, we have presented the graph automorphism technique to improve the UPSs_Calculation procedure proposed in [6] . However, due to the high complexity of the graph automorphism technique, we modify this technique to a linear time approach, the SAA approach.. The SAA approach gets more precise remaining UPSs and therefore accelerates the AVPG and generates a more efficient verification pattern set for verifying core-based designs.

O O O O B O O O B O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O B O O B O O O O O O O O O B O O B I I O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O B O O O O O O O B O O O O O O O O O B O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O B O O O O O O O O O O B O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O B O O O O O O O O O O B I I I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O B O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O B O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O


dsPIG: a tool to predict imprinted genes from the deep sequencing of whole transcriptomes Background: Dysregulation of imprinted genes, which are expressed in a parent-of-origin-specific manner, plays an important role in various human diseases, such as cancer and behavioral disorder. To date, however, fewer than 100 imprinted genes have been identified in the human genome. The recent availability of high-throughput technology makes it possible to have large-scale prediction of imprinted genes. Here we propose a Bayesian model (dsPIG) to predict imprinted genes on the basis of allelic expression observed in mRNA-Seq data of independent human tissues.Results: Our model (dsPIG) was capable of identifying imprinted genes with high sensitivity and specificity and a low false discovery rate when the number of sequenced tissue samples was fairly large, according to simulations. By applying dsPIG to the mRNA-Seq data, we predicted 94 imprinted genes in 20 cerebellum samples and 57 imprinted genes in 9 diverse tissue samples with expected low false discovery rates. We also assessed dsPIG using previously validated imprinted and non-imprinted genes. With simulations, we further analyzed how imbalanced allelic expression of non-imprinted genes or different minor allele frequencies affected the predictions of dsPIG. Interestingly, we found that, among biallelically expressed genes, at least 18 genes expressed significantly more transcripts from one allele than the other among different individuals and tissues.With the prevalence of the mRNA-Seq technology, dsPIG has become a useful tool for analysis of allelic expression and large-scale prediction of imprinted genes. For ease of use, we have set up a web service and also provided an R package for dsPIG at http://www.shoudanliang.com/dsPIG/. In this paper, we proposed a new method -dsPIG, applicable to all mammals with genomic imprinting, to predict imprinted genes based on mRNA-Seq data of various independent tissues. With enough sequenced samples, dsPIG is capable of predicting imprinted genes on a genome-wide scale with expected low FDRs. The power of dsPIG will be further enhanced after more data generated by mRNA-Seq technology become available in the near future. dsPIG operates under the assumption that if a gene is biallelically expressed, the transcript levels of two alleles are the same. However, because imbalance of allelic expression has been widely detected in human tissues [27, [44] [45] [46] , our assumption may not always be correct. Indeed, within our 29-tissue samples, allelic imbalance was observed even after excluding possible expression from imprinted genes (data not shown here). However, our simulation studies showed that our model can still distinguish imprinted genes from non-imprinted ones in most situations (Figure 4) , unless one specific allele is always expressed at <13% of the other allele's expression level across different samples (no supporting literature for this yet). Stochastic RT-PCR amplification [4] is not of particular concern in dsPIG because this has been taken into account as allelic imbalances. dsPIG is sensitive to biallelic expression and unlikely to falsely predict imprinted genes. A gene will get a very low posterior probability of imprinting when it obviously has biallelic expression in one tissue, even if only one allele of this gene is observed in the transcriptomes from all other tissues (Additional file 12: Figure S6 ). For example, a gene may have monoallelic expression because of allele-specific differences caused by either heterozygous SNPs or somatic mutations in the promoter region of the gene; as long as monoallelic expression caused by these conditions is not present population-wide and a large number (e.g., >25 in our study) of independent tissue samples is used in dsPIG, these genes will not be falsely predicted as imprinted genes. However, for the same reason, if transcriptomes are collected from various tissues, it becomes very hard for dsPIG to detect tissue-specific imprinted genes. This partially explains why dsPIG predicted much less imprinted genes in Group I samples than in Group II samples (another reason is that Group II has more samples than Group I).. One advantage of dsPIG is that it is able to predict imprinted genes without sequencing the genotype. Although a homozygous allele will also lead to identification of only one allele in the transcriptome, the result will not elevate the posterior belief of imprinting in our model. This is very important and practical for human because we no longer need to sequence the genome for genotypes. However, a disadvantage is that dsPIG cannot tell the parent of origin for predicted imprinted genes, which can be verified only by other studies. Posteriors were calculated based on Group I or II (see Table 5 ). The "Tissue" column indicates where genes were most likely biallelically expressed. Genes with contradictory evidence (i.e., genes had posteriors <10 -8 and posteriors ≥0.2) were discarded. IGF2, OSBPL5, SMPD1 and GPR172A had at least 2 SNPs with posteriors less than 10 -8 . Abbreviations are the same as in Table 2 .. One obvious limit of dsPIG is that it was modeled based on single SNPs. This means, if a gene has more than 1 SNP site in its exons, it may have different single-SNP-based allelic counts and thus different posterior probabilities from dsPIG. Therefore, one single strong posterior cannot determine the imprinting status of this gene. Instead, we have to look into all SNP sites of each gene and make sure no contradictory posterior exists for our predictions (as stated in results). In future, a possible improvement would be integration of all SNP information of a gene and calculate a single posterior to predict imprinting status. Diploid eukaryotic species inherit two copies (i.e., two alleles) of the same gene from both parents. If one allele fails to work properly, the other allele can still implement a gene's cellular function. For some genes, however, this protective mechanism is disabled because only one allele is expressed and its failure probably leads to cellular malfunction. These monoallelically expressed genes can be classified into one of three categories [1] : X-inactivated genes, which are regulated by a random process in which one of the two X chromosomes present in female mammals is silenced [2] ; autosomal genes subject to random monoallelic gene expression, such as the T cell receptors and natural killer cell receptors [3] [4] [5] [6] [7] [8] [9] ; and autosomal imprinted genes (e.g., CDKN1C and H19), which express from only one of the two alleles according to their parental origin [10] [11] [12] [13] . Imprinted genes play important functional roles in the control of embryonic growth and development, as well as in post-natal development [14] [15] [16] . As imprinted genes are expressed from only one of the two parental chromosomes, a de facto haploid state is caused by imprinting and leads to asymmetric functions of parental genomes and loss of diploid protection against recessive mutations [11] . Thus, imprinting dysregulation is linked to numerous human genetic diseases, such as developmental disorders (Prader-Willi syndrome, Angelman syndrome) and cancers (neuroblastoma, Wilms' tumor) [17] [18] [19] [20] . In addition, environmental factors can influence gene expression by targeting imprinted genes [21, 22] . Because imprinted genes are more susceptible to disease than non-imprinted genes [23, 24] , it is of great importance to identify novel imprinted genes for human.. Identifying imprinted genes experimentally has traditionally been a slow process, and the number of validated ones is much lower than the previous estimation (~1% of all human genes) [25] . However, recently developed high-throughput screening approaches (e.g., expression profiling and single-nucleotide polymorphism [SNP] microarrays) and recently identified DNA sequence characteristics (e.g., the number and type of repeated elements flanking a gene) have led to the proposal of several new methods to predict imprinted genes on a global scale [26] [27] [28] [29] [30] [31] . With advances in nextgeneration sequencing technology [32, 33] , mRNA-Seq is becoming a powerful tool for transcriptome profiling [34] . It can generate not only the number of reads mapped to exons, which reflects the expression levels of a gene, but also the actual sequence, which may identify the allele from which the mRNA is expressed. Therefore, inference can be made for predicting imprinted genes. For example, by sequencing whole transcriptomes from mice embryos, Babak et al. (2008) measured allelic expression bias and identified six novel imprinted genes [35] .. However, to our knowledge, prediction of imprinted genes by deeply sequencing transcriptomes (mRNA-Seq) from multiple independent tissues is still an open problem. In this study, we proposed a Bayesian model -dsPIG (deep sequencing-based Prediction of Imprinted Genes)to predict imprinted genes based on allelic expression inferred from observed SNPs in mRNA-Seq data of independent human tissues. With dsPIG, we were able to measure the imbalance of allelic expression among various tissues and calculate the posterior probability of imprinting status for each gene. Under a stringent probabilistic cut-off of the posteriors and other reasonable biological criteria, we identified 57 potentially imprinted genes from 9 diverse human tissues and 94 potentially imprinted genes from 20 cerebellar cortices, with an expected low false discovery rate (FDR). Furthermore, analysis of allelic expression of the same genes among different tissues revealed that, in some cases, even if a gene was biallelically expressed, one allele always had higher expression level than the other.

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I I O O O O B I O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O B I I I O O B I I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I I O O O O B O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Infinite Families of Optimal Splitting Authentication Codes Secure Against Spoofing Attacks of Higher Order Abstract. We consider the problem of constructing optimal authentication codes with splitting. New infinite families of such codes are obtained. In particular, we establish the first known infinite family of optimal authentication codes with splitting that are secure against spoofing attacks of order two.1. Introduction. In the standard model of authentication theory [13, 14, 15, 18] , a transmitter wants to send some information to a receiver across an insecure channel while an opponent with access to the channel wants to deceive the receiver. The opponent can either insert new messages into the channel, or intercept messages from the transmitter and modify them into his own. In each case, the opponent's goal is to deceive the receiver into believing that the new messages are authentic (coming from the transmitter). The first attack based on insertion of new messages is known as impersonation and the second attack based on modification of messages from the transmitter is known as substitution.More formally, let S denote the set of all source states, M be the set of all messages, and E be the set of all encoding rules. All these are finite sets. A source state is the information the transmitter wishes to communicate to the receiver. An encoding rule is an injection from S to 2 M . The transmitter and receiver agree beforehand on a secret encoding rule e ∈ E. To communicate a source state s ∈ S, the transmitter determines M = e(s) (note that M ⊆ M) and chooses a message m ∈ M to send to the receiver. The receiver accepts the received message as authentic if there exists an M in the image of e containing the received message.

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


A map of dependencies among three-valued logics Abstract. Three-valued logics arise in several fields of computer science, both inspired by concrete problems (such as in the management of the null value in databases) and theoretical considerations. Several three-valued logics have been defined. They differ by their choice of basic connectives, hence also from a syntactic and proof-theoretic point of view. Different interpretations of the third truth value have also been suggested. They often carry an epistemic flavor. In this work, relationships between logical connectives on three-valued functions are explored. Existing theorems of functional completeness have laid bare some of these links, based on specific connectives. However we try to draw a map of such relationships between conjunctions, negations and implications that extend Boolean ones. It turns out that all reasonable connectives can be defined from a few of them and so all known three-valued logics appear as a fragment of only one logic. These results can be instrumental when choosing, for each application context, the appropriate fragment where the basic connectives make full sense, based on the appropriate meaning of the third truth-value. Classical Boolean logic is unique in the sense that the definition of its basic connectives is not questionable and there is complete agreement on its model-based semantics. On the contrary, there exists a large body of scattered literature on 3-valued logics. Formal three-valued logic systems have been studied by various mathematicians, providing axiomatizations in the Hilbert or Gentzen style, and investigating their algebraic properties. There are well-known three-valued logics, like Lukasiewicz [Borowski(1970)] or Kleene [Kleene(1952) ], and less known ones like Sobociński's [Sobociński(1952) ] and Nelson's [Nelson(1949) ]. There seems to be no agreement about what these logics are good for and what should be the definition of their logical connectives. Nevertheless, they turned out to be useful in various areas, as heterogeneous as logic programming [Fitting(1985) ], electronic circuits [Smith(1981) ] and databases [Codd(1979) ], among other topics. Threevalued logics can also be viewed as special kinds of fuzzy logics [Hájek(1998) ], where the truth set is a chain of three elements. Fuzzy logics, that often assume the truth-set is infinite, have received considerable attention in the last 15 years. It is thus interesting to go back to the most elementary case not reducible to Boolean logic. As fuzzy logic underlies fuzzy sets, three-valued logics lead to three-valued sets, that can be modeled by pairs of nested sets or orthopairs of disjoint sets * AND D. DUBOIS O [Cattaneo and Ciucci(2003) , Yao(2012) ]. Several kinds of generalized sets can be associated with three-valued logics: rough sets [Ciucci and Dubois(2010) ], conditional events [Walker(1994) ], shadowed sets [Pedrycz(2009) ], interval sets [Yao(2009) ] . We note that even if similar mathematical frameworks underlie these approaches, they have different semantics and usage. Such three-valued sets lead to three-way decision processes [Yao(2012) ], that leave room for a non-committal attitude that differs from the mere acceptance and rejection of options.. One may argue that since Boolean logic is so basic for all kinds of scientific investigations, three-valued logic may be useful and as basic for a number of useful reasoning tasks. However there is no clear consensus about this claim, and even there is some confusion as to the potential uses of a third truth value, different from true and false. Indeed, there are various ways of interpreting it. We can comment on some of them:. • Possible: this interpretation was proposed by Lukasiewicz [Borowski(1970) ], the pioneer of multivalued logic. He motivated his departure from bivalence by the wish do deal with future contingents in a truth-functional way. A proposition is Possible if its truth-value will be only known in the future. Note that this question is better handled in temporal modal logics, nowadays, that is, Possible is more a modality than a truth-value.. • Unknown: this interpretation is proposed by Kleene [Kleene(1952) ] in 1952, and it is in some sense closely related to the previous one. A proposition is unknown if its (Boolean) truth-value cannot be computed for some reason (for instance, it is too time-consuming to do it). This interpretation has been very popular in various areas of computer science nowadays, and may lead to paradoxes, if truth-functionality is enforced [Urquhart(1986) , Dubois and Prade(2001) ]. This view of the third truthvalue also pervades the intuitions behind interval sets [Yao(2009) ] and rough sets [Ciucci and Dubois(2010) ]. It also suffers a limited expressive power: it can only account for epistemic states in terms of partial models, assigning an epistemic status to atoms only [Dubois(2008) ].. • Undefined : this is another proposal by Kleene, which applies to Boolean formulas viewed as recursive functions. The undefined state corresponds to the choice of the argument of the function outside its definition domain. This kind of truth value usually contaminates the result of the computation of the recursive function, that is the truth-value of a proposition involving undefined atoms is Undefined.. • Half-true: This is typical of fuzzy logic [Hájek(1998) ]. The intuition is that for some propositions, truth is a matter of degree. So the extension of the corresponding predicate involves elements that are peripheral, or borderline, as opposed to elements that are central. This is very natural for representing some words in natural language like bird, tall, etc. A robin is a prototypical bird (a central element) while a penguin is untypical as a bird (a peripheral element). The use of three-valued sets in linguistics goes back to Gentilhomme [Gentilhomme(1968) ]. In the case of words such as tall, the continuous representation of the height scale pleads in favor of a truth set larger than 3, namely the unit interval for instance, as commonly used in fuzzy logic. Shadowed sets [Pedrycz(2009) ] are based on the idea of turning fuzzy sets into three-valued sets using two cuts generalizing the core and support of a fuzzy set.. • Irrelevant: the idea is that in some possible worlds, atomic propositions are not applicable. For instance, the proposition "My car is blue" is neither true nor false if I have no car. However, there is no contamination effect in this case, namely if a component of a proposition is irrelevant, it is supposed not to take part in the evaluation of the truth of the whole. An example of such a three-valued entity is a rule "if A then B", viewed as a conditional event B|A [Dubois and Prade(1994) ], A and B being Boolean propositions. When the antecedent A is false, the rule B|A is irrelevant as it cannot be applied. So it has no role in the computation of a logical combination with other rules.. • Inconsistent: the third value stands for a proposition which is both true and false, so, in some sense, it is the dual of "unknown". Several works try to tame the notion of contradiction by means of a truth value (for instance, Priest [Priest(1979) ] and Belnap [Belnap(1977) ]). The stance of some paraconsistent logics is to treat contradictions locally without losing inference capabilities (for instance [Asenjo and Tamburino(1975)] ). The possible confusion between usual truth-values and the notion of contradiction has been criticized as also generating paradoxes [Fox(1990) , Dubois(2008) ].. The possible meanings of the third truth-value mentioned above are probably not exhaustive, but they are enough to lay bare an opposition between two kinds of understanding of the third truth value, we could call ontological and epistemic, respectively. The third truth-value is sometimes intrinsic to the definition of propositions: Undefined is needed for defining partial functions, Half-true for defining gradual or fuzzy predicates, Irrelevant is intrinsic to the commonsense notion of a rule that does not apply to some situations. Such truth-values are ontological, that is, satisfiability is defined in terms of interpretations w p having three values [Lawry and Tang(2012) ]. On the other hand, Unknown and Possible refer to situations where the Boolean nature of propositions is not questioned but their truth or falsity has not been yet established, but can eventually be so, by waiting for the proper moment, or by means of a stronger computer, or by bringing the proper information that is missing. Such truth-values are epistemic. They refer to the state of knowledge of an agent relative to propositions that are ontologically Boolean. In this case, the third truth-value refers not to the proposition it is supposed to qualify, but to the state of information concerning this proposition. These considerations drive us close to epistemic logics. The relationships between three-valued logics and epistemic logics are studied in [Ciucci and Dubois(2012b) ]. Here, we focus on the relationships among three-valued logics.. Clearly, Boolean connectives can be extended to three-valued logics in various ways, but there is only a finite number of logical 3-valued functions of a given arity. Contrary to the Boolean case, where the basic connectives, say conjunction and negation, are uniquely defined, there are degrees of freedom in 3-valued logics for the definition of such connectives. The choice of connectives can be driven by the algebraic properties one may wish to salvage, given that the Boolean structure is no longer possible. However this choice should also be driven by the preservation of Boolean tables for the two extreme truth-values and by the meaning of the third one. For instance, if it means half-true one may argue that the conjunction of * AND D. DUBOIS O a true proposition with an half-true one cannot be more than half-true in turn. In contrast if the third truth value means irrelevant, it looks plausible that the conjunction of a true proposition with an irrelevant one should remain true, as the second proposition is viewed as counting for nothing.. In the following, we extend and complete our study [Ciucci and Dubois(2012a) ] on three-valued connectives. First, we use a definition of conjunction, implication and negation obeying minimal intuitively meaningful properties and show that there are only 14 different such conjunctions and implications, and 3 negations, on threevalued sets. We also discuss the relationships between other definitions of conjunctions in many-valued logics, such as t-norms and uninorms [Klement et al.(2000) Klement, Mesiar, and Pap]. Further, generalising the connections between implication, entailment and conjunction in classical logic, we study the relationships among all these operations via standard transformations involving or not an involutive negation Prade(1984a), Fodor(1991) ] and classify them according to their mutual behaviour. It turns out that all the connectives can be mutually defined, so that starting from a simple structure we can obtain all of them. Finally, we show that any binary connective is definable using Lukasiewicz logic connectives, provided that the third truth value is part of the language. This paper is a preliminary attempt to clarify the connections between threevalued logics extending classical logic, from a truth-table point of view. As we have seen, basic connectives such three-valued systems are mathematically connected together and they can all be defined starting from very simple algebraic structures.. On this basis, these relationships should be exploited with respect also to their significance in knowledge representation in order to better understand which connectives make more sense in reference to the intended meaning of the third value, as reviewed in the introduction. In this way, we will be able to relate as many three-valued calculi as possible to a class of applications where the third truthvalue makes sense. This contrasts with many previous studies whose focus was essentially syntactic and proof-theoretic. The latter point of view is clearly instrumental for mechanizing three-valued reasoning tasks, but such machineries need sound appropriate canonical examples to be accepted and properly applied.. More recently, we have studied a case when an epistemic flavour is attached to the third value, interpreted as unknown, thus referring to the idea of lack of knowledge. In this case, a translation from the three-valued logic framework into an adequate epistemic logic setting encapsulating classical propositional logic has been provided, namely the subjective fragment of S5 modal logic with no nested modality [Banerjee and Dubois(2009) ]. First results [Ciucci and Dubois(2012b) ] indicate that Lukasiewicz logic is equivalent to a fragment of this modal logic, where modalities only apply to litterals. They suggest that any three-valued extension of classical propositional logic as studied in the present paper can be captured by this modal fragment, which lays bare the intuitive meaning of three-valued formulas when the third truth-value refers to the idea of unknown. It offers a bridge between epistemic logics and three-valued logics of incomplete information. Other translations of our three-valued setting can be envisaged, properly choosing the target language, for other understandings of the third truth-value.

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Stratified

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one

differential

equations

in

positive

characteristic

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Put,

M.,

Top,

J.

Stratified

order

one

differential

equations

in

positive

characteristic.

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page

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limited

to

maximum.

Stratification

for

nonlinear

differential

equations

in

positive

characteristic

is

introduced.

Testing

this

notion

for

first

order

equations

is

discussed,

and

related

to

the

Cartier

operator

on

curves.

A

variant

of

the

Grothendieck-Katz

conjecture

is

formulated,

and

proved

in

a

special

case.

Let

F

be

a

field

of

characteristic

p

A

higher

derivation

on

F

is

a

set

of

additive

maps

(n)

F

F

n

satisfying

the

formulas

(b)

(g)

and.

The

standard

higher

derivation

(n)

z

n

on

the

field

C

(z),

where

C

is

an

algebraically

closed

field

of

characteristic

p

is

given

and

determined

by

the

formulas

(n)

z

m

m

n

z

m−n

for

all

n,

m

These

formulas

imitate

the

maps.

n

The

standard

higher

derivation

on

C

(z)

extends

uniquely

to

a

higher

derivation

on

any

finite

separable

extension

K

of

C

(z)..

The

algebra

of

the

differential

operators

D

D

K

on

the

field

K

(see

Grothendieck,

particularly

Gieseker,

for

the

concept

and

terminology)

is

a

skew

K

-algebra

and

has

K

-basis

A

stratified

differential

module

M

over

K

is

a

left

D-module

which

has

finite

dimension

over

K

This

concept

coincides

with

that

of

iterative

differential

module

(ID-module)

over

K

(see

van

der

Put,

This

notion

is

seen

as

the

correct

analogue

in

positive

characteristic

of

complex

differential

modules..

The

naive

translation

of

a

differential

module

in

positive

characteristic

is

a

K

-vector

space

M

of

finite

dimension

over

K

equipped

with

an

additive

map

In

this

paper

we

introduce

the

notion

of

stratification

for

nonlinear

differential

equations.

We

restrict

ourselves

mainly

to

nonlinear

order

one

differential

equations

over

a

finite

separable

ex-.

The

derivation

D

on

A

extends

uniquely

to

its

field

of

fractions

F

We

note

that

F

is

the

function

field

of

a

curve

X

over

K

By

the

genus

of

f

we

will

mean

the

genus

of

X

Two

differential

equations

over

K

will

be

called

strictly

equivalent

if

the

corresponding

differential

fields

become

isomorphic

after

a

finite

separable

extension

of

K

(compare

Ngo

et

al.,

The

aim

of

this

paper,

which

is

a

sequel

to

Ngo

et

al.

is

to

produce

and

classify

stratified

order

one

differential

equations

in

positive

characteristic.

In

the

last

section,

a

conjecture

in

the

spirit

of

the

Grothendieck-Katz

conjecture

is

formulated.

A

proof

is

given

for

autonomous

equations.

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Implementing Panel-Corrected Standard Errors in R: The pcse Package This introduction to the R package pcse is a (slightly) modified version of Bailey and Katz (2011) , published in the Journal of Statistical Software.Time-series-cross-section (TSCS) data are characterized by having repeated observations over time on some set of units, such as states or nations. TSCS data typically display both contemporaneous correlation across units and unit level heteroskedasity making inference from standard errors produced by ordinary least squares incorrect. Panel-corrected standard errors (PCSE) account for these these deviations from spherical errors and allow for better inference from linear models estimated from TSCS data. In this paper, we discuss an implementation of them in the R system for statistical computing. The key computational issue is how to handle unbalanced data. Time-series-cross-section (TSCS) data are characterized by having repeated observations over time on some set of units, such as states or nations. TSCS data have become common in applied studies in the social sciences, particularly in comparative political science applications. These data often show non-spherical errors because of contemporaneous correlation across the units and unit level heteroskedasity. When fitting linear models to TSCS data, it is common to use this non-spherical error structure to improve inference and estimation efficiency by a feasible generalized least squares (FGLS) estimator suggested by Parks (1967) and made popular by Kmenta (1986) .. However, Beck and Katz (1995) showed that the Parks (1967) model had poor finite sample properties. In particular, in a simulation study they showed that the estimated standard errors for this model generated confidence intervals that were significantly too small, often underestimating variability by 50% or more, and with only minimal gains in efficiency over a simple linear model that ignored the non-spherical errors. Therefore, Beck and Katz (1995) suggested estimating linear models of TSCS data by ordinary least squares (OLS) 1 and they proposed a sandwich type estimator of the covariance matrix of the estimated parameters, which they called panel-corrected standard errors (PCSE) , that is robust to the possibility of non-spherical errors. 2 Although the PCSE covariance estimator bears some resemblance to heteroskedasity consistent (HC) estimators (see, for example, Huber 1967; White 1980; MacKinnon and White 1985) , these other estimators do not explicitly incorporate the known TSCS structure of the data. 3 This leads to important differences in implementation.. This paper describes an implementation of PCSEs in the R system for statistical computing (R Development Core Team 2011). All of the functions described here are available in the package pcse that is available from Comprehensive R Archive Network (CRAN) at http://CRAN. R-project.org/package=pcse. The key computational issue is how to handle unbalanced data. TSCS data is unbalanced when the number of observations for units vary.. R packages that estimate various models for panel data include plm (Croissant and Millo 2008) and systemfit (Henningsen and Hamann 2007) , that also implement different types of robust standard errors. Some of these are only robust to unit heteroskedasity and possible serial correlation. The pcse standard error estimate is robust not only to unit heteroskedacity, but it also robust against possible contemporaneous correlation across the units that is common in TSCS data. 4 Package plm also provides an implementation of Beck and Katz (1995) PCSE in the function vcovBK() 5 that can be applied to panel models estimated by plm().. The next section fixes notation by briefly reviewing the linear TSCE model and the derivation of PCSEs. Section 3 considers the computational issues with unbalanced panels. Section 4 illustrates the use of the package pcse. Finally, Section 5 concludes. This paper briefly reviews estimation of panel-corrected standard errors for time-series-crosssection (TSCS) data. It discusses an implementation of estimating them in the R system for statistical computing in the pcse package.

O O O O O B O B O O O O O B O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O B O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O B O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O B O O O O O O O O O O O O O O O B O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O B O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O B O