ANNSyS: an Analog Neural Network Synthesis System A synthesis system based on a circuit simulator and a silicon assembler for analog neural networks to be implemented in MOS technology is presented. The system approximates on-chip training of the neural network under consideration and provides the best starting point for 'chip-in-the-loop training'. Behaviour of the analog neural network circuitry is modeled according to its SPICE simulations and those models are used in the initial training of the analog neural networks prior to the fine tuning stage. In this stage, the simulator has been combined with Madaline Rule III for approximating on chip training by software, thus minimizing the effects of circuit nonidealities on neural networks. The circuit simulator partitions the circuit into decoupled blocks which can be simulated separately, with the output of one block being the input for the next one. Finally, the silicon assembler generates the layout for the neural network by reading analog standard cells from a library. The system's performance has been demonstrated by several examples. ᭧ Neural networks have gained popularity in the last few years due to their success in diverse applications. However, many applications require real time or very fast operation. This is possible only with dedicated neural network hardware. Due to the inherently parallel nature of neural networks, they are suitable for VLSI implementation. These implementations may be digital or analog. Many digital implementations have been reported in the literature owing to the fact that they offer several advantages such as predictable accuracy, high noise immunity, ease of multiplexing communication and computation, availability of well-established tools for digital design, and ease of interfacing with other digital systems (Beiu, 1997) . Analog implementations, on the other hand, have many advantages such as small size, high speed, and straightforward interfacing with the outside world which is analog by nature (Annema, 1995) .. Synapses, which are the most common elements in a neural network, can be represented at the circuit level by multipliers. Parallel digital multipliers require a very large area compared to analog multipliers of comparable precision which use less than 20 transistors. For instance, parallel digital multipliers of 8 × 8 input word lengths have transistor counts of the order of at least several thousand (Binici et al., 1995) . Serial digital multipliers are smaller than their parallel counterparts; however, they are much slower. On the other hand, the speed of an analog multiplier is limited mostly by its settling time. When one looks at neurons, a similar picture can be seen. Again, an adder and nonlinearity can be realized by less than 20 transistors in the analog Neural Networks 12 (1999) [325] [326] [327] [328] [329] [330] [331] [332] [333] [334] [335] [336] [337] [338] domain, whereas the same operations require transistor counts which are at least an order of magnitude larger in the digital domain assuming that multiple input parallel adders and efficient look-up tables for the nonlinearity are utilized. (Treleaven et al., 1989; Intel, 1991; Rossetto et al., 1989; Dündar and Rose, 1992) .. However, analog neural network implementations have been rather ad hoc in that very few, if any, have explored the constraints that circuit non-idealities bring about. Examples are nonlinear synapses Ş imşek et al., 1996) , neurons that deviate from ideal functions, or errors and limitations in storing weights (Dündar and Rose, 1995; Dolenko and Card, 1995; Piché, 1995) . It has previously been shown (Hollis and Paulos, 1990; Lont and Guggenbühl, 1992; Edwards and Murray, 1996; Dündar et al., 1996; Ş imşek et al., 1996) that for many applications, multiplier nonlinearity can be a very severe problem even for nonlinearity factors of less than 10%. Limited precision in storing weights has also proven to be a crucial problem in analog neural network design. The work in this area has been mostly limited to predicting these effects either through simulation or through theoretical analysis, and developing some methods to partially overcome these problems. Ş imşek et al. (1996) studied the effects of some non-idealities through circuit simulation with SPICE and the importance of circuit level simulation in analog neural network design has been demonstrated. Although SPICE is the standard tool for circuit simulation, it is not specially tailored for simulating neural networks. Neural networks consist of the interconnection of many identical blocks so that by partitioning the network during simulation, it is expected that the simulation speed will be increased tremendously.. Different approaches are used to obtain the weights of an analog neural network which also dictate the implementation style and the architecture of the network. These approaches can be summarized as follows (Annema, 1995) :. • Non-learning network. In this method, the weights are hardwired through the implementation of the fixed gain multiplier. In this case, the weights to be hardwired must be calculated before the operation of the neural network. The calculations are done on a computer which uses the model of the analog neural network. The performance of this method depends heavily on the matching between the model and the real circuit, which is a task that is very difficult to achieve.. • Neural networks in analog hardware implementation with externally adjustable weight construction. For this realization, the weights are again computed on a host computer and downloaded to the chip. Then the weights are fine tuned. The chip is used for forward pass, host computer is used for feedback (weight adaptation). In this way, the matching of the model and analog hardware is considerably increased.. • Neural network with on-chip learning. In this scheme, both the feedforward structure and all circuitry required to adapt the weights are realized on the chip. A major disadvantage of this approach and the previous one is that they both require additional hardware which is used only at the training stage.. An implementation of a general purpose analog VLSI neural network with on-chip learning has been presented in Montalvo et al. (1997a Montalvo et al. ( , 1997b . One commercial implementation of analog neural networks is the ETANN 80170NX chip (Intel, 1991) . This chip has been plagued by limited resolution in storing the synapse weights in that the long time resolution of the weights is not more than five bits. Implementing Madaline Rule III (Widrow and Lehr, 1990) has been suggested for the ETANN chip; however, this requires a host computer and external hardware besides there being many timing problems which limit the performance of training. Problems like these have prevented the success of this chip on the market so that commercial applications using this chip and similar ones have been limited. Several applications reported in the literature have demonstrated successful operation, whereas other reported applications have suffered from the aforementioned problems. Another major deficiency of this chip is the issue of cyclability in the weight storing EAROMs. Therefore the number of iterations required for chip-in-the-loop training has to be minimized or eliminated if possible. This can be achieved by having a suitable initial weight set.. The best approximation to a circuit is its SPICE model. The difference between the actual chip and its SPICE model is mainly due to variations in process parameters over which the user has no control and most often no a priori information. For this purpose, the approximation of on-chip training by software using circuit models of the actual nonideal synapse and neuron circuitry is proposed and a special circuit simulator has been developed. The proposed system approximates on-chip training of the neural network under consideration and provides the best starting point for 'chipin-the-loop training'. Moreover, starting chip-in-the-loop or on-chip training from scratch will introduce convergence problems, since the error surface will have many spurious local minima and plateaus. In the approach presented in this paper, the nonidealities are incorporated using soft constraints; that is, we start gradient descent assuming ideal components and thereby converge rapidly to the relevant part of the weight space. Afterwards, we switch to the analytical models of the nonideal components and also introduce weight decay to keep the weight values small by adding a soft penalty term to the error function. The final part of the training is performed on the circuit simulator using Madaline Rule III and it follows that the best starting point is achieved with minimal convergence problems.. The outline of this paper is as follows. Section 2 introduces the Analog Neural Network Simulation System (ANNSiS) which is based on circuit partitioning techniques. This system is used to simulate neural networks composed of the building blocks discussed in Section 3 at circuit level.. Modeling those nonideal components for best performance is discussed in Section 4. Training on ANNSyS is proposed in Section 5. SAFANN: Silicon Assembler For Analog Neural Networks, which generates the layout of the analog neural network for VLSI realization, is introduced in Section 6, with sample layouts generated by SAFANN. The design examples are discussed in Section 7. Finally, Section 8 concludes the paper. In this study, an Analog Neural Network Synthesis System (ANNSyS) was developed. This package consists of an Analog Neural Network Simulation System (ANNSiS), a Silicon Assembler For Analog Neural Networks (SAFANN), a function approximator for synapses and neurons, a modified backpropagation algorithm, and a circuit level neural network trainer using modified Madaline Rule III as well as a control shell. ANNSiS is based on circuit partitioning techniques and has superior performance compared to other circuit simulators for simulating analog neural networks.. In this work, a new approach to designing and training analog neural networks was presented. Analog synapse and neuron circuitry were designed and these were modeled analytically by various methods. Although the models looked adequate by themselves, the performance of neural networks trained using these methods were well below expectations. The errors obtained by ANNSiS before Madaline Rule were larger than the errors estimated by the backpropagation algorithm. This shows that, even in simple examples, small model mismatches (less than 5%) can create considerable problems. This performance loss was especially severe in function approximation applications rather than pattern classification applications. From these results, it was clear that using models for neural network components was not enough for training the neural networks and that the network itself should be used in training. However, using the neural network chip in the training loop is something that should be avoided as much as possible. Hence, a circuit level representation of the chip was used in training instead. This had previously been prohibitive due to the huge simulation times. As an example, for the speech recognition task described above, the 21 × 8 × 6 network employs more than 4300 MOS transistors so that the computational load is very high. A software package that allows one to realize this training in a reasonable computation time with the help of ANNSiS was developed, where the neural network is partitioned for simulation. For the same example, the largest partition to be simulated at one time contains 386 transistors only. Furthermore, the efficient implementation of the Madaline Rule III allows each Madaline iteration to run in approximately just twice the time required for a single forward pass calculation. For applications where high performance is desirable, the weight set obtained via ANNSyS can be utilized as the best starting point for chip-in-the-loop training given reasonably accurate device models. Furthermore, the results of training with ANNSyS can be made more robust with respect to device mismatches in the actual circuit by perturbing device sizes and threshold voltages during training.

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


Using Convex Nonlinear Relaxations in the Global Optimization of Nonconvex Generalized Disjunctive Programs In this paper we present a framework to generate tight convex relaxations for nonconvex generalized disjunctive programs. The proposed methodology builds on our recent work on bilinear and concave generalized disjunctive programs for which strong linear relaxations can be generated and extends its application by allowing nonlinear relaxations. This is particular important for those cases in which the convex envelopes of the nonconvex functions arising in the formulations are nonlinear (e.g. fractional terms). This extension is now possible by using the latest developments in convex disjunctive programming. We test the performance of the method in three typical process systems engineering problems, namely, the optimization of process networks, reactor networks and heat exchanger networks. Many problems in engineering can be reduced to finding a set of conditions that will lead to the best design or operation of a system. Often these problems are represented by a set of algebraic expressions using continuous and discrete variables, leading to a Mixed-integer Nonlinear Program (MINLP). In order to represent accurately the behavior of physical, chemical, biological, financial or social systems, nonlinear expressions are often used. In general, this leads to an MINLP where the solution space is nonconvex and hence difficult to solve since this may give rise to local solutions. In the last decade, many global optimization algorithms for nonconvex problems have been proposed [14] [10] . However, most of them can be regarded as some particular implementation of the spatial branch and bound framework [2] . The efficiency of these methods heavily relies on having tight relaxations and that is why many of the contributions in this area have been related to this subject. However, in general, finding the global optimum of large-scale nonconvex MINLP models in reasonable computational time, remains a largely unsolved problem.. In 1994, Raman and Grossmann [6] presented an alternative way to represent discrete/continuous optimization problems by using not only algebraic expressions but also disjunctions and logic propositions giving birth to Generalized Disjunctive Programming (GDP), which can be regarded as an extension of Disjunctive Programming [1] . This higher abstraction level representation not only facilitates the modeling, but also keeps the underlying logical structure of the problem, which can be exploited to find stronger relaxations and hence, develop more efficient solution methods. With this in mind, we presented a method to solve nonconvex Generalized Disjunctive Programs that involve bilinear and concave functions [7] . The main idea behind this methodology to find strong relaxations relies on a two step procedure. In the first step the nonconvex functions are replaced with polyhedral relaxations leading to a Linear GDP. In the second step the results of Sawaya and Grossmann [9] are used. These authors showed that a stronger relaxation of Linear GDPs can be obtained by the application of basic steps, a process that consists of intersecting disjunctions to obtain equivalent disjunctive sets whose hull relaxation is tighter. Even though the method we presented showed significant improvements when compared to traditional approaches, the efficiency of the method depends on the strength of the polyhedral relaxations of the nonconvex functions. In this paper we aim at generalizing this approach by allowing the use of nonlinear convex relaxations, which in some cases have shown to be order of magnitude tighter than linear relaxations (see Appendix B). This leads to a nonlinear convex GDP which relaxation can be strengthen by using recently results from the work of Ruiz and Grossmann [8] . Typical examples of nonlinear convex relaxations can be found in Appendix C. This paper is organized as follows. In section 2 we define the general nonconvex GDP problem that we aim at solving and the traditional method to find relaxations. In section 3 we show how we can strengthen the relaxation of the traditional approach by presenting a systematic procedure to generate a hierarchy of relaxations based on the recent developments in convex disjunctive programming. In section 4 we outline a set of rules that will lead to a more efficient implementation of the method. Finally in section 5,6 and 7 we test the performance of the method in process network, reactor network and heat exchanger network problems. We have proposed a framework to generate tight relaxation for the global optimization of nonconvex generalized disjunctive programs. We extended the method proposed in a recent work on bilinear and concave disjunctive programming by allowing the use of nonlinear relaxations. This is now possible from the latest developments in convex disjunctive programming. We tested the method in several instances and show significant improvements in the lower bounds predicted, which is a direct indication of tightening.

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


An Objective Perceptual Quality-Based ADTE for Adapting Mobile SVC Video Content In this paper, we propose an Adaptation Decision-Taking Engine (ADTE) that targets the delivery of scalable video content in mobile usage environments. Our ADTE design relies on an objective perceptual quality metric in order to achieve video adaptation according to human visual perception, thus allowing to maximize the Quality of Service (QoS). To describe the characteristics of a particular usage environment, as well as the properties of the scalable video content, MPEG-21 Digital Item Adaptation (DIA) is used. Our experimental results show that the proposed ADTE design provides video content with a higher subjective quality than an ADTE using the conventional maximum-bit-allocation method. The fast adoption of feature-rich portable devices has resulted in an increasing demand for the consumption of multimedia content in a mobile setting. However, the diverse properties of present-day networks (e.g., bandwidth, delay, and jitter) and devices (e.g., display resolution and energy consumption) impose restrictions on the way multimedia resources can be accessed and consumed. This observation explains the need for multimedia services that are in line with the vision of Universal Multimedia Access (UMA) [1] .. H.264/AVC Scalable Video Coding (SVC) [2] is a video coding format that allows for a wide range of adaptation strategies in order to meet the constraints and capabilities of a particular usage environment [3] . Consequently, SVC can be seen as a technology that makes it possible to achieve an optimal QoS in heterogeneous usage environments [4] . To do so, a decision needs to be taken on how to optimally adapt the scalable video content. Such logic can for instance be provided by an ADTE [5] - [7] .. Quality of video can be expressed using objective video parameters such as bit rate, Mean Squared Error (MSE), and Peak Signal-to-Noise Ratio (PSNR). For example, given a particular bandwidth, maximizing the number of bits in an extracted bitstream is a common operation for an ADTE handling SVC bitstreams [5] , [6] . However, it is well-known that objective video parameters correlate poorly with subjective quality, especially at lower bit rates [8] . Such bit rates are common in mobile usage environments. On the other hand, objective perceptual quality metrics can be used to model the visual perception of an end-user. Moreover, in order to optimally adapt SVC bitstreams along the different scalability axes, an objective perceptual quality metric can also be used to steer the adaptation decision-taking process.. In this paper, we discuss the design and operation of an ADTE that targets the delivery of scalable video content in mobile usage environments, relying on an objective perceptual quality metric. To demonstrate the efficiency of the proposed ADTE design, a test bed was implemented. Further, description tools part of MPEG-21 DIA [9] are used to describe the characteristics of a particular mobile usage environment, as well as to communicate the properties of the scalable video content. The proposed ADTE selects bitstreams whose subjective quality is the highest among candidate sub-bitstreams by measuring their objective perceptual quality score. Experimental results show that the proposed adaptation method offers consumers video quality closer to subjective quality than the conventional maximumbit-allocation method.. The remainder of this paper is organized as follows: Section 2 offers an overview of the enabling technologies. In Sect. 3, our ADTE design using an objective perceptual quality metric is presented. Section 4 outlines experimental results to demonstrate the efficiency of the proposed ADTE design. Finally, the paper is concluded in Sect. 5. As the consumption of multimedia content increases in mobile environments, adaptation techniques are becoming more important in order to provide end-users with video content having a high quality. In this paper, we propose an ADTE that uses an objective perceptual quality metric for guiding the adaptation of scalable video content. Our experimental results show that maximizing the bit rate, an objective video parameter, does not always guarantee a high subjective quality. Further, the video content adapted by the proposed objective perceptual quality-based ADTE has a better quality than when making use of an objective quality-based ADTE. As such, by making use of the proposed ADTE, a higher QoS can be provided when consuming video content in diverse mobile usage environments.

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


An efficient algorithm to compute differences between structured documents Abstract-SGML/XML are having a profound impact on data modeling and processing. This paper presents an efficient algorithm to compute differences between old and new versions of an SGML/XML document. The difference between the two versions can be considered to be an edit script that transforms one document tree into another. The proposed algorithm is based on a hybridization of bottom-up and top-down methods: The matching relationships between nodes in the two versions are produced in a bottom-up manner and then the top-down breadth-first search computes an edit script. Faster matching is achieved because the algorithm does not need to investigate the possible existence of matchings for all nodes. Furthermore, it can detect structurally meaningful changes such as the movement and copy of a subtree as well as simple changes to the node itself like insertion, deletion, and update. S INCE SGML (Standard Generalized Markup Language) [1] and XML (eXtensible Markup Language) [2] are good tools for embedding logical structure information into documents, they are widely accepted as a standard format for representing documents in various fields such as CALS (Commerce At Light Speed), EC (Electronic Commerce), Digital Library, and the Web. Thus, a lot of attempts have been made to process structured documents based on SGML/XML. 1 Computing differences between structured documents is important for various fields such as version management [3] , [4] , [5] , [6] , [7] , data warehousing [8] , and active database [9] . Recently, the availability of large repositories of XML documents is increasing on the Web. Accordingly, automated change detection of XML documents that are visited often by users will be able to provide a more convenient Web environment. For example, it can automatically inform the user, who invests in a stock or bids on an auction item, whether the price of the stock has been changed or a new bid has been posted for the item.. SGML/XML documents include logical structures with hierarchy. For example, SGML/XML representations of technical journal articles have hierarchical structures with logical components such as a title, authors, an abstract, keywords, sections, paragraphs, etc. Therefore, logical structures as well as textual data should be considered for efficient change detection in SGML/XML documents.. Most previous works for computing differences have dealt with flat-file [10] , [11] , [12] , [13] , relational data [14] , or hierarchical data [15] , [16] , [17] , [18] , [19] , [20] , [21] . However, because the works based on flat-file or relational data do not take hierarchical information into consideration, they do not handle structured documents effectively. Most previous works targeting hierarchical data extract only simple changes such as the insertion, deletion, and update of nodes. They represent the movement or copy of a subtree as a set of deletions and insertions or a set of insertions, respectively. However, these are not structurally meaningful especially in SGML/XML documents. Therefore, structurally meaningful changes such as the movement and copy of a subtree should be supported. Previous works that detect meaningful changes have a shortcoming of being too slow.. In this paper, we present an efficient algorithm for detecting meaningful changes in structured documents more quickly than previous works. To this end, the method is designed according to the domain characteristics of SGML/XML documents. Specifically, the proposed algorithm takes the hybrid of top-down and bottom-up methods to compute differences between old and new versions of a structured document. Matchings 2 between nodes in two versions are created by applying a path-matching algorithm in a bottom-up manner. Top-down, breadth-first search computes an edit script, 3 which is a sequence of edit operations needed to transform an old version of a document to its new version. Furthermore, for more efficient representation of structured documents, we propose a document model, which reflects their domain 1 . This paper uses the three terms "structured document," "SGML/XML document," and "structured document based on SGML/XML" with the same meaning.. 2. The notion of a correspondence between nodes that are identical or similar is formalized as a matching between nodes as was in the work of Chawathe et al. [20] , whereas the Zhang and Shasha method [15] defines it as a mapping.. 3. An edit script means a sequence of operations that transforms an old version of a document into its new version. As with the Zhang and Shasha method and the work of Chawathe et al., we define these operations as edit operations.. characteristics, based on a rooted ordered tree that has a root node and order among nodes.. Compared with the previous works, [15] , [16] , [17] , which detect simple changes such as the insertion, deletion, and update of a node, the proposed method makes it possible to detect the movement and copy of a subtree because it supports not only one-to-one but also one-tomany matchings. In addition, since the algorithm does not investigate possible existence of matchings for all nodes, it produces matchings faster than the work of Chawathe et al. and the Chawathe and Molina method [21] , which detect structurally meaningful changes such as the movement or copy of a subtree. The algorithm proposed to produce matchings runs in time Oðl 1 l 2 þ ðm 1 =l 1 þ m 2 =l 2 Þl 2 Þ, where m 1 (and m 2 ) and l 1 (and l 2 ) denote the numbers of interior and leaf nodes of an old version (and a new version), respectively. With the increasing number of XML documents and the growing interest in their sophisticated processing, the application potential of the proposed method is very high.. The organization of this paper is as follows: In Section 2, a document model that represents structured documents is proposed. Edit operations are defined and a cost model for computing an edit script is introduced. In Section 3, a brief discussion about related work and the properties and constraint of our work are given. In Section 4, the proposed algorithm is presented in two steps: producing matchings and computing an edit script. In Section 5, the performance of the algorithm is analyzed, and the conclusions are summarized in Section 6. In this paper, we have presented an efficient algorithm for computing differences between old and new versions of an SGML/XML document faster than previous works. To this end, the proposed method is based on the domain characteristics of structured documents.. The proposed algorithm is based on a hybridization of bottom-up and top-down methods: The matching relationships between nodes in the two versions are produced in a bottom-up manner and then the top-down breadth-first search computes an edit script. Because the proposed path-matching algorithm does not need to investigate possible existence of matchings for all nodes, faster matching is achieved. We have also proposed the document model that facilitates the efficient representation of structured documents.. Additionally, we have introduced the concept of the similarity ofa matching and supported not only one-to-one but also one-to-many matchings in order to extract structurally meaningful changes. Therefore, the proposed algorithm can detect meaningful changes such as the movement and copy of a subtree as well as simple changes to the node itself like insertion, deletion, and update.. The larger the resultant edit script is, the more expensive it is to apply this script later. The "undo" that recovers an old version from the newest version of a document requires computing inverse operations of the resultant edit operations. The more concise the edit script is, the less time it takes to compute the inverse operations. In this perspective, the proposed edit operations are efficient because the move and copy operations can represent a set of deletions and insertions and a set of insertions, respectively.. As mentioned before, this paper does not prove that the edit script found is minimal. As a future work, we will investigate whether the proposed method can detect changes with minimum cost. On the other hand, for a more thorough evaluation of the proposed method, our future works include experiments with a larger set of documents includingboth data-centric and document-centric documents as well as comparisons with recently published algorithms [28] , [29] . As mentioned before, previous works can be categorized into three classes by their targets that are flat-file, relational data, and hierarchical data. In this section, a brief discussion about conventional methods that deal with hierarchical data, especially ordered trees, is presented along with their constraints. Additionally, the properties and constraints of our approach are introduced.. The Zhang and Shasha method and the Shasha and Zhang method target a labeled ordered tree and represent differences between two trees as simple operations such as the insertion, deletion, and update of a node. They have several constraints. First, they allow only one-to-one matchings 8 between nodes. As a result, the copy of a subtree is not supported. However, as illustrated in the DTD of Fig. 1 , because repeated subtrees are common in XML documents, subtree operations such as copy and movement should be supported. 5. This paper does not prove that the edit script found is minimal. This means that it may be nonminimal.. 6. This means the subtree that has a node x as its root node. 7. jlcsðv 1 ; v 2 Þj, jv 1 j, and jv 2 j denote the length of an LCS of v 1 and v 2 , the length of v 1 , and the length of v 2 , respectively.. 8. For any matchings ½i 1 ; j 1 and ½i 2 ; j 2 ,. Second, because they have the constraint that the sibling order 9 between nodes that give rise to matchings should be preserved, they cannot detect the movement of a subtree. For example, in Fig. 4 where subtree 4 has been moved to the first child of node 1, they do not allow matchings 1 , 2 , and 3 that violate the sibling order but are meaningful and intuitive. Therefore, they cannot detect the movement of the subtree 4. Third, the ancestor order 10 among nodes that form matching relationships must be preserved. For example, assume that T 1 has been transformed into T 2 by applying two move operations sequentially as shown in Fig. 5 .. Likewise, matchings 1 and 2 in Fig. 6 are not allowed because they violate the ancestor order. The matchings that are accepted by the Zhang and Shasha method are as shown in Fig. 7 . The resultant edit script is a sequence of three deletions (deletion of nodes 4, 6, and 7) and three insertions (insertion of nodes 12, 14, and 16).. However, if the method allowed the matchings, 1 and 2 , of Fig. 6 , it could detect more cost-effective and structurally meaningful changes, movements of subtree 4 and subtree 2 as in Fig. 5 .. Zhang [17] proposes an algorithm with a time complexity OðjT 1 jjT 2 jÞ with additional constraints to the Zhang and Shasha method that runs in time OðjT 1 jjT 2 j minðdepth ðT 1 Þ; leaves ðT 1 ÞÞ minðdepth ðT 2 Þ; leaves ðT 2 ÞÞÞ: Chang et al. [18] and Wang et al. [19] have implemented a system that computes differences in SGML documents based on the Zhang and Shasha method.. Chawathe et al. propose an algorithm for change detection in structured data. The algorithm consists of two stages: finding matchings and computing an edit script. It can detect the movement of a subtree as well as the insertion, deletion, and update of nodes. However, it assumes an acyclic labels condition for labels. For this reason, it cannot process a document that contains cyclic elements (e.g., elements ITEM and LIST contain LIST and ITEM, respectively, as shown in Fig. 6 ). Actually, the article and book DTDs of ISO 12083 [26] allow the parent and child ITEM and LIST elements to be inverted. Another constraint is that any two-leaf nodes do not have the same or similar values. Because the work of Chawathe et al. targets structured data with limited conditions, it has faster processing speed compared to the Zhang and Shasha method. However, an SGML/XML document has not only quite a few cyclic elements but also textual data that are the same or almost identical. Therefore, the method proposed by Chawathe et al. cannot extract an optimal edit script and its possible area of application is limited.. On the other hand, Chawathe and Molina have recently presented a heuristic algorithm for meaningful change detection that supports the movement and copy of a subtree and has no constraints of the work of Chawathe et al. The method deals with the problem for an unordered tree, of which the NP-hardness has been proven by the work of Zhang et al. [27] . Although this is a current state of the art method, it is slow and its data model is missing ordering information about elements defined in an SGML/XML DTD.. Our work aims at developing an algorithm that computes meaningful changes in SGML/XML documents faster than previous works. To this end, the proposed method is based on the domain characteristics of SGML/XML documents. First, we require that the labels of parent nodes of text nodes, which match each other, be the same. This is because the minimum independent logical unit in an SGML/XML document is an element. Second, it is inefficient to investigate possible existence of matchings for all interior nodes that have the same label. The nodes whose leaf-node descendents matcheach other are compared.. Definition 1: Path. For a node x, P ath ðxÞ is a sequence of nodes from the parent node of x to the root node if x is not the root.. Definition 2: The Corresponding Paths (CP). Two paths, P ath ðxÞ and P ath ðyÞ, are called corresponding when there is a matching relationship ½x; y. The correspondence of P ath ðxÞ and P ath ðyÞ is denoted by CP ðx; yÞ. For example, P ath ð5Þ and P ath ð7Þ correspond to P ath ð17Þ and P ath ð16Þ, respectively, in Fig. 6 .. Particularly, we constrain the ancestor order not in the whole trees but in the corresponding paths to be preserved. This is because the movements of subtrees are not allowed within the corresponding path under the definition of the move operation. For example, we allow the matchings 1 and 2 in Fig. 6 , which violate the ancestor order in the whole trees but preserve the ancestor order in the corresponding paths. Specifically, because the text nodes 5 and 17 match each other, matchings [3, 15] , 1 , and [1, 11] are created from the corresponding paths, {3, 2, 1} and {15, 13, 12, 11}. Additionally, matchings [6, 14] and 2 are produced from CP (7, 16).. In Fig. 8 , where a new version has been created by actually deleting node 4 and inserting node 12, we don't allow matching 5 because it violates the ancestor order in CP (7, 17) . In the case of matching 5 , where the two nodes have the same label and share common descendents, if a method for producing matchings does not consider the proposed ancestor-order preservation of the corresponding paths, it may not compute an optimal edit script or should use an additional search module that explores matchings to find a better solution with an exploration that may be extremely time-consuming. Previous works that support the movement of a subtree does not consider this constraint. Section 4.1 describes the proposed method for producing matchings based on these properties and constraints in detail. In this section, a document model is proposed for efficient representation of structured documents. We define edit operations that describe meaningful changes between structured documents. Differences from the operations of conventional methods are also highlighted. Finally, a cost model is introduced to determine an edit script.

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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 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 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 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 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 B O O O O O O 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The matricial relaxation of a linear matrix inequality Abstract. Given linear matrix inequalities (LMIs) L1 and L2 it is natural to ask: (Q1) when does one dominate the other, that is, does L1(X) 0 imply L2(X) 0? (Q2) when are they mutually dominant, that is, when do they have the same solution set?The matrix cube problem of Ben-Tal and Nemirovski is an example of LMI domination. Hence such problems can be NP-hard. This paper describes a natural relaxation of an LMI, based on substituting matrices for the variables xj. With this relaxation, the domination questions (Q1) and (Q2) have elegant answers, indeed reduce to constructible semidefinite programs. As an example, to test the strength of this relaxation we specialize it to the matrix cube problem and obtain essentially the relaxation given in . Thus our relaxation could be viewed as generalizing it.Assume there is an X such that L1(X) and L2(X) are both positive definite, and suppose the positivity domain of L1 is bounded. For our "matrix variable" relaxation a positive answer to (Q1) is equivalent to the existence of matrices Vj such thatAs for (Q2) we show that L1 and L2 are mutually dominant if and only if, up to certain redundancies described in the paper, L1 and L2 are unitarily equivalent. Algebraic certificates for positivity, such as (A1) for linear polynomials, are typically called Positivstellensätze. The paper goes on to derive a Putinar-type Positivstellensatz for polynomials with a cleaner and more powerful conclusion under the stronger hypothesis of positivity on an underlying bounded domain of the form {X | L(X) 0}.An observation at the core of the paper is that the relaxed LMI domination problem is equivalent to a classical problem. Namely, the problem of determining if a linear map τ from a subspace of matrices to a matrix algebra is "completely positive". Complete positivity is one of the main techniques of modern operator theory and the theory of operator algebras. On one hand it provides tools for studying LMIs and on the other hand, since completely positive maps are not so far from representations and generally are more tractable than their merely positive counterparts, the theory of completely positive maps provides perspective on the difficulties in solving LMI domination problems.

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Exemplar longest common subsequence In this paper, we investigate the computational and approximation complexity of the Exemplar Longest Common Subsequence of a set of sequences (ELCS problem), a generalization of the Longest Common Subsequence problem, where the input sequences are over the union of two disjoint sets of symbols, a set of mandatory symbols and a set of optional symbols. We show that different versions of the problem are APX-hard even for instances with two sequences. Moreover, we show that the related problem of determining the existence of a feasible solution of the Exemplar Longest Common Subsequence of two sequences is NP-hard. On the positive side, we first present an efficient algorithm for the ELCS problem over instances of two sequences where each mandatory symbol can appear in total at most three times in the sequences. Furthermore, we present two fixed parameter algorithms for the ELCS problem over instances of two sequences where the parameter is the number of mandatory symbols.Longest common subsequence, comparative genomics, algorithm design and analysis, combinatorial algorithms, analysis of algorithms and problem complexity. Algorithmic studies in comparative genomics have produced powerful tools for the analysis of genomic data which has been successfully applied in several contexts, from gene functional annotation to phylogenomics and whole genome comparison. A main goal in this research field is to explain differences in gene order in two (or more) genomes in terms of a limited number of rearrangement operations.. When there are no duplicates in the considered genomes, the computation of the similarity measure is usually polynomial-time solvable, e.g., number of breakpoints, reversal distance for signed genomes, number of conserved intervals, number of common intervals, maximum adjacency disruption, summed adjacency disruption [8] - [10] . However, aside a few exceptions, several copies of the same gene or several highly homologous genes are usually scattered across the genome, and hence it is major problem to handle those duplicates when computing the similarity between two genomes. One approach to overcome this difficulty is based on the concept of exemplar [11] : for each genome, an exemplar sequence is constructed by deleting all but one occurrence of each gene family. Another approach is based on matching [12] : in this two-step procedure, the two genomes are first made balanced (the number of occurrences of genes from the same family must be the same in both genomes) by removing a minimum number of genes and next a one-to-one correspondence (among genes of each family) between genes of the genomes is computed.. Unfortunately, in the presence of duplicates, most similarity measures turn out to be NP-hard to be computed [12] - [15] for both the exemplar and the matching models, so that we generally have to rely on approximation algorithms or heuristic approaches. We discuss here one such general heuristic approach, the EXEMPLAR LCS problem, which is basically a constrained string alignment problem. The basic idea of the general framework we propose here is based on the observation that, for most similarity measures and for both the exemplar and the matching models, specific common subsequences may correspond to highly conserved sets of genes. This suggests the following greedy heuristic algorithm: find a common subsequence of significant lengthbut compact enough -between the two genomes, replace in the two genomes the substring that contains the common subsequence (the substring that starts at the first character of the common subsequence and ends at the last character of the common subsequence) by a new letter and continue in a similar way. Observe that after we have identified a common subsequence of the genomes, we can establish a one-to-one correspondence between genes of the two genomes.. At each iteration of this simple heuristic algorithm, one however has to be cautious in how to choose the common subsequence, as bad choices may have a disastrous impact for the rest of the algorithm. Let us take the exemplar model as a very simple explanatory example, and suppose that we are searching for a common subsequence between two precise substrings of the two genomes. For one, if one gene family has occurrences elsewhere in the two genomes, then taking or not one occurrence of this particular gene family in the common subsequence is thus not based on necessity but on the length of the obtained solution. For another, if there do not exist any other occurrences of one gene family except one in the two considered substrings, definitively one has to take this occurrence in the common subsequence (observe that in this case the obtained common subsequence may not be the longest one). This simple example suggests to consider an LCS-like problem that deals with two types of letters (mandatory and optional symbols) to allow greater flexibility in the searching process.. In this paper we will formally define such framework with a simple combinatorial problem that generalizes the well-known LCS problem and we will study its computational and approximation . Let S be a set of sequences, then a longest common subsequence of S is a longest possible sequence s that is a subsequence of each sequence in S.. A simple way to informally define a subsequence is by using the notion of threading scheme.. First write the two sequences on two parallel lines, then a threading scheme is a set of lines, each one connecting two identical symbols of different sequences, so that no two lines are crossing.. In this case a common subsequence consists of symbols connected by the non-crossing lines.. Given a set of sequences S, the LCS problem asks for a longest common subsequence of S.. The complexity of the LCS problem has been deeply studied in the past. In [7] it is shown that the problem is NP-hard even for sequences over binary alphabet. However, when the instance of the problem consists of a fixed number of sequences, the LCS can be solved in polynomial time via dynamic programming algorithms [4] , [5] , [16] .. The EXEMPLAR LCS problem (ELCS) is related to the LCS problem. The input of the ELCS problem consists of a set S of sequences over alphabet Output: a longest common subsequence of all sequences in S that contains an occurrence of each mandatory symbol in A m .. Given an instance S of ELCS, by exemplar common subsequence we mean a feasible solution of ELCS over S. It is possible to define different versions of the problem, according to the number of occurrences of each symbol in the solution, as represented in Table I . In this paper we will deal with such different versions of ELCS. First notice that ELCS(1) and ELCS(≥ 1). are generalizations of the LCS problem. Indeed LCS problem can be seen as the restriction of ELCS(1) and ELCS(≥ 1) with an empty set of mandatory symbols. Therefore all the hardness results for LCS apply to ELCS(1) and ELCS(≥ 1). Moreover, we will show that the above problems are hard also on instances of only two sequences (while the LCS problem can be solved in polynomial time for any fixed number of sequences). When dealing with the restriction of ELCS containing only a fixed number of sequences, we will denote such restriction prefixing the problem name with the number of sequences, e.g. 2-ELCS(1, ≤ 1) is the restriction of ELCS(1, ≤ 1) to instances of two sequences.

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


Robust

and

automated

three-dimensional

segmentation

of

densely

packed

cell

nuclei

in

different

biological

specimens

with

Lines-of-Sight

decomposition

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compare

the

decomposition

performance

of

the

seeded

ImageJ

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with

our

LoS

approach,

we

applied

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with

different

pre-processing

steps.In

general,

three

parameters

can

be

adjusted

for

the

ImageJ

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Figure

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parameter

"Seeds

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only

considers

seeds

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a

value

larger

than

"Seeds

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is

used

to

cluster

voxels

with

values

larger

than

"Image

Threshold".

If

automatic

seed

detection

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chosen,

the

parameter

"Radius

for

automatic

seeds"

can

be

set

accordingly.

These

parameters

only

affect

the

pre-processing

steps

prior

to

the

watershed

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chose

three

Watershed

I.

The

raw

image

was

supplied

as

input.

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image

threshold

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set

according

to

the

respective

image

for

the

mouse

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for

the

breast

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spheroid

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for

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pancreatic

cancer

spheroid).

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automated

seed

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for

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in

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Possible

parameter

value

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for

the

Watershed

plugin.

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B 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 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


Correlations in spiking neuronal networks with distance dependent connections Abstract Can the topology of a recurrent spiking network be inferred from observed activity dynamics? Which statistical parameters of network connectivity can be extracted from firing rates, correlations and related measurable quantities? To approach these questions, we analyze distance dependent correlations of the activity in small-world networks of neurons with current-based synapses derived from a simple ring topology. We find that in particular the distribution of correlation coefficients of subthreshold activity can tell apart random networks from networks with distance dependent connectivity. Such distributions can The collective dynamics of balanced random networks was extensively studied, assuming different neuron models as constituting dynamical units Sompolinsky 1996, 1998; Brunel and Hakim 1999; Brunel 2000; Mattia and Del Guidice 2002; Timme et al. 2002; Mattia and Del Guidice 2004; Kumar et al. 2008b; Jahnke et al. 2008; Kriener et al. 2008) .. Some of these models have in common that they assume random network topologies with a sparse connectivity ≈ 0.1 for a local, but large neuronal network, embedded into an "external" population that supplies unspecific white noise drive to the local network. These systems are considered as minimal models for cortical networks of about 1 mm 3 volume, because they can display activity states similar to those observed in vivo, such as asynchronous irregular spiking. Yet, as recently reported (Song et al. 2005; , local cortical networks are characterized by a circuitry, which is specific and hence, non-random even on a small spatial scale. Since it is still impossible to experimentally uncover the whole coupling structure of a neuronal network, it is necessary to infer some of its features from its activity dynamics. Timme (2007) e.g. studied networks of N coupled phase oscillators in a stationary phase locked state. In these networks it is possible to reconstruct details of the network coupling matrix (i.e. topology and weights) by slightly perturbing the stationary state with different driving conditions and analyzing the network response. Here, we focus on both network structure and activity dynamics in spiking neuronal networks on a statistical level. We consider several abstract model networks that range from strict distance dependent connectivity to random topologies, and examine their activity dynamics by means of numerical simulation and quantitative analysis. We focus on integrate-andfire neurons arranged on regular rings, random networks, and so-called small-world networks (Watts and Strogatz 1998) . Small-world structures seem to be optimal brain architectures for fast and efficient interareal information transmission with potentially low metabolic consumption and wiring costs due to a low characteristic path length (Chklovskii et al. 2002) , while at the same time they may provide redundancy and error tolerance by highly recurrent computation (high clustering coefficient C, for the general definitions of and C, cf. e.g. Watts and Strogatz (1998) , Albert and Barabasi (2002) ). Also on an intra-areal level cortical networks may have pronounced small-world features as was shown in simulations by Sporns and Zwi (2004) , who assumed a local Gaussian connection probability and a uniform long-range connection probability for local cortical networks, assumptions that are in line with experimental observations (Hellwig 2000; Stepanyants et al. 2007 ). Network topology is just one aspect of neuronal network coupling, though. Here, we also demonstrate the crucial role of the weight distribution, especially with regard to the notion that all inhibitory neurons project only hyperpolarizing synapses onto their postsynaptic targets, and excitatory neurons only project depolarizing synapses. This assumption is sometimes referred to as Dale's principle (Li and Dayan 1999; Dayan and Abbott 2001; Hoppensteadt and Izhikevich 1997) . Strikingly, this has strong implications for the dynamical states of random networks already (Kriener et al. 2008 ). Yet, the main focus of the present study is put on the distance dependence and overall distribution of correlation coefficients. Especially the joint statistics of subthreshold activity, i.e. correlations and coherences between the incoming currents that neurons integrate, has been shown to contain elusive information about network parameters, e.g. the mean connectivity in random networks (Tetzlaff et al. 2007 ).. The paper is structured as follows: In Section 2 we give a short description of the details of the neuron model and the simulation parameters used throughout the paper. In Section 3 we introduce the notion of small-world networks and in Section 4 we discuss features of the activity dynamics in dependence of the topology. In ring and small-world networks groups of neighboring neurons tend to spike highly synchronously, while the population dynamics in random networks is asynchronous-irregular. To understand the source of this differences in the population dynamics, we analyze the correlations of the inputs of neurons in dependence of the network topology. Section 5 is devoted to the theoretical framework we apply to calculate the input correlations in dependence of the pairwise distance in sparse ring (Section 5.1) and smallworld networks (Section 5.2). In Section 6 we finally derive the full distribution of correlation coefficients for ring and random networks. Random networks have rather narrow distributions centered around the mean correlation coefficient, while sparse ring and smallworld networks have distributions with heavy tails. This is due to the high probability to share a common input partner if the neurons are topological neighbors, and very low probability if they are far apart, yielding distributions with a few high correlation coefficients and many small ones. This offers a way to potentially distinguish random topologies from topologies with smallworld features by their subthreshold activity dynamics on a statistical level. We analyzed the activity dynamics in sparse neuronal networks with ring, small-world and random topologies. In networks with a high clustering coefficient C such as ring and small-world networks, neighboring neurons tend to fire highly synchronously. With increasing randomness, governed by the rewiring probability p r , activity becomes more asynchronous, but even in random networks we observe a high Fano factor FF of the population spike counts, indicating its residual synchrony. 4 As shown by Kriener et al. (2008) these fluctuations become strongly attenuated for hybrid neurons which have both excitatory and inhibitory synaptic projections.. Here, we demonstrated that the introduction of hybrid neurons leads to highly asynchronous (FF ≈ 1) population activity even in networks with ring topology. Recent experimental data suggest, that there are abundant fast and reliable couplings between pyramidal cells, which are effectively inhibitory (Ren et al. 2007 ) and which might be intepreted as hybrid-like couplings. However, the hybrid concept contradicts the general paradigm that pyramidal cells depolarize all their postsynaptic targets while inhibitory interneurons hyperpolarize them, a paradigm known as Dale's principle (Li and Dayan 1999; Dayan and Abbott 2001; Hoppensteadt and Izhikevich 1997) . As we showed here, a severe violation of Dale's principle turns the specifics of network topology meaningless, and might even impede functionally potentially important processes, as for example pattern formation or line attractors in ring networks (see e.g. Ben-Yishai et al. 1995; Ermentrout and Cowan 1979) , or propagation of synchronous activity in recurrent cortical networks (Kumar et al. 2008a) .. We demonstrated that the difference of the amplitude of population activity fluctuations in Daleconform and hybrid networks can be understood from the differences in the input correlation structure in both network types. We extended the ansatz presented in Kriener et al. (2008) to networks with ring and small-world topology and derived the input correlations in dependence of the pairwise distance of neurons and the rewiring probability. Because of the strong overlap of the input pools of neighboring neurons in ring and small-world networks, the assumption that the spike trains of different neurons are uncorrelated, an assumption justified in sparse balanced random networks, is no longer valid. We fitted the distance dependent instantaneous spike train correlations and took them adequately into account. This lead to a highly accurate prediction of input correlations.. A fully self-consistent treatment of correlations is however beyond the scope of the analysis presented here. As we saw in Section 5.1, in Dale-conform ring graphs neurons cover basically the whole spectrum of positive input correlation strengths between almost one (depending on the level of variance of the uncorrelated external input) and zero as a function of pairwise distance D. If we look at the ratio between input and output correlation strength, we see that it is not constant, but that stronger correlations have a higher gain. The exact mechanisms of this non-linear correlation transmission needs further analysis. Recent analysis of correlation transfer in integrate-and-fire neurons by De la Rocha et al. (2007) and Shea-Brown et al. (2008) showed that the spike train correlations can be written as a linear function of the input correlations, given they are small C in ∈ [0, 0.3]. For larger C in (De la Rocha et al. 2007; Shea-Brown et al. 2008) , however, report supralinear correlation transmission. Such correlation transmission properties were also observed and analytically derived for arbitrary input correlation strength in an alternative approach that makes use of correlated Gauss processes (Tchumatchenko et al. 2008) . These results are all in line with the non-linear dependence of spike train correlations on the strength of input correlations that we observed and fitted by an exponential decay with interneuronal distance.. We saw that correlations are weakened as they are transferred to the output side of the neurons, but, as is to be expected, they are much higher for neighboring neurons in ring networks as it is the case in the homogeneously correlated random networks that receive more or less uncorrelated external inputs. The assumption that the spike train covariance functions are deltashaped is certainly an over-simplification, especially in the Dale-conform ring networks (cf. the examples of spike train cross-correlation functions ψ ij (τ, D, 0), Fig. 4(d) ). The temporal width of the covariance functions leads to an increase in the estimation of spike train correlations if the spike count bin-size h is increased. In Dale-conform ring graphs we found c ij (1, 0) ≤ 0.041 for time bins h = 0.1 ms (cf. Fig. 4(c), (d) ). For h = 10 ms, a time window of the order of the membrane time constant τ m , we observed c ij (1, 0) ≤ 0.25 (not shown). This covers the spectrum of correlations reported in experimental studies, which range from 0.01 to approximately 0.3 (Zohary et al. 1994; Vaadia et al. 1995; Shadlen and Newsome 1998; Bair et al. 2001) . For hybrid networks, however, the pairwise correlations have a narrow distribution around zero, irrespective of the topology. This explains the highly asynchronous dynamics in hybrid neuronal networks.. Finally, we suggest that the distribution of pairwise correlation coefficients of randomly chosen intracellularly recorded neurons may provide a means to distinguish different neuronal network topologies. Real neurons, however, have conductance-based synapses, and their filtering is strongly dependent on the membrane depolarization (Destexhe et al. 2003; Kuhn et al. 2004) . Moreover, spikes are temporally extended events, usually with different synaptic time scales, and transmission delays are distributed and likely dependent on the distance between neurons. These effects, amongst others, might distort the results presented here. Still, though intracellular recordings are technically more involved than extracellular recordings, they are basically analog signals, and hence much shorter periods of recording time are necessary to get a sufficiently good statistics, as compared to estimation of pairwise spike train correlations from low rate spiking neurons (Lee et al. 2006) . So, bell-shaped distributions of membrane potential correlations may hint towards an underlying random network structure, while heavytail distributions should be observed for networks with locally confined neighborhoods. Naturally, the distribution will depend on the relation between the sampled region and the footprint of the neuron-type one is interested in. This is true for both the model as well as for real neuronal tissue. Some idea about the potential input footprint, e.g. from reconstructions of the axonal and dendritic arbors (Hellwig 2000; Stepanyants et al. 2007) , can help to estimate the spatial distance that must be covered. It also is a matter of the spatial scale that one is interested in: if one is mostly interested in very small, local networks < 200 μm, where the connection probability might be considered approximately homogeneous (Hellwig 2000; Stepanyants et al. 2007) , the correlation coefficient distribution will be akin to that of a random topology. If one, however, samples several millimeter, the distribution may tend more to a heavytail shape, due to the increase of the relative number of weakly correlated neuron pairs. At this scale radial inhomogeneities, as for example due to axonal patches (Lund et al. 2003 ), in two dimensions or different connection probabilities within and between cortical layers (Binzegger et al. 2004 ) in three dimensions must be taken into account as well, as they will distort the oversimplified assumption of the connectivity made here.. In conclusion, we think that a further extension of the line of research presented here might provide a way to access structural features of neuronal networks by the analysis of their input statistics. This could eventually prove helpful in separating correlations that arise due to the specifics of the network structure from those that arise due to correlated input from other areas, e.g. sensory inputs, and provide insight into the relation between structure and function.

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


Analysis of the Maximum Straight Line Length for Prairie Highway using Driver's Heart Rate Variability The attention of driver traveling along a long straight line of prairie highway is easy to be distracted. In this paper, the correlation of straight line length and driver's attention is studied through laboratory simulation experiment and regression analysis. It can be theoretically concluded that the maximum straight line length for prairie highway within which the driver could travel with proper attention is 5km. This study is significant both for prairie highway construction and Intelligent Transportation System. Prairie is widely distributed in Inner Mongolia in China, natural prairie area is 86667 thousands hectares, which account for 73.26% of the total land area of Inner Mongolia. The terrain is flat, and the landscape is monotonous in prairies. The main particularity of prairie highway is long straight line. The straight line of prairie highway is over-long and monotonous, the attention of driver traveling along it is easy to be distracted. Under this condition, a traffic accident may take place in case of urgent situations, because the driver almost has no time to react, so the straight line length is suggested to be limited. The long straight line has negative effect on safe driving and the maximum straight line length should be limited, which have become consensus in road engineering academia. [1] [2] [3] At present, recommendation value of the maximum straight line length is stipulated according to experience and survey, relevant theoretical research is few and far between. The maximum straight line length (in meter) in Japan, Germany and China is suggested to be 20 times of the design speed (in kilometre per hour) at most; the recommendation value of it respectively is 8km and 4.83km in the former Soviet Union and United States; France deems that the long straight line should be replaced by using large radius curve of 5km to 15km. 4, 5 Refs.1,2 brought forward the restricted models of the maximum straight line length for different horizontal alignment combinations, which based on that the maximum traveling time was 70s along the straight line. 7 At present, there are many literatures applying the new theory to study alignment of freeway and mountainous highway, most literatures focus on studying curve's radius and gradient, [8] [9] [10] [11] [12] [13] and physiological index heart rate is frequently studied. [8] [9] [10] [11] 14, 15 Vehicle monitoring system, as portion of the Intelligent Transportation Systems which applies state-of-the-art information technologies to provide more efficient and effective solutions to current traffic congest and traffic safety problems, [16] [17] [18] detects road environment, vehicle condition and driver condition, and alert the driver under potential safety hazard. The maximum straight line length could be an input to vehicle monitoring system, i.e. if vehicle monitoring system detects that the straight line length reaches the maximum, it will alert the driver to make the driver's attention centralized. This paper intends to study the maximum straight line length for prairie highway. The maximum straight line length can guarantee that the driver could travel with proper attention within it. In this paper, new theory of road alignment design is applied to study the maximum straight line length, and driver's physiological index heart rate variability is selected for the purpose because heart rate variability can indicate the driver's attention level. Laboratory simulation experiment is carried out to study the correlation between the straight line length and driver's attention. Aiming at the phenomenon that the attention of the driver traveling along a long straight line of prairie highway is easy to be distracted due to the over-long and monotonous straight line, and a traffic accident may occur when meeting an emergency, the correlation of straight line length and driver's attention is studied through laboratory simulation experiment and regression analysis, and regression models between straight line length and SDNN , SDSD , 50 PNN are established in this paper. By analyzing the established models, we can infer that with the increase of the straight line length, the driver's attention is gradually distracted, and after it comes to a tipping point, it is gradually focused. And it can be theoretically concluded that the maximum straight line length for prairie highway within which the driver could travel with proper attention level is 5km. In term of prairie highway construction, the straight line whose length reaches 5km should be connected with a curve, and the number of curve should be increased to make the driver's attention centralized to guarantee safe driving. In term of Intelligent Transportation, the 5km could be an input to vehicle monitoring system as one of the in-vehicle support systems, 28 i.e. when the straight line length reaches 5km, this monitoring system will warn the driver with sound or light to make the driver's attention centralized.

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