Time-domain damping models in structural acoustics using digital filtering This paper describes a new approach in order to formulate well-posed timedomain damping models able to represent various frequency domain profiles of damping properties. The novelty of this approach is to represent the behavior law of a given material directly in a discrete-time framework as a digital filter, which is synthesized for each material from a discrete set of frequency-domain data such as complex modulus through an optimization process. A key point is the addition of specific constraints to this process in order to guarantee stability, causality and verification of thermodynamics second law when transposing the resulting discrete-time behavior law into the time domain. Thus, this method offers a framework which is particularly suitable for time-domain simulations in structural dynamics and acoustics for a wide range of materials (polymers, wood, foam...), allowing to control and even reduce the distortion effects induced by time-discretization schemes on the frequency response of continuous-time behavior laws. Damping plays a major role in vibration of structures because of its huge influence on various characteristics of dynamical response and radiated acoustic field [1, 2] . A good understanding of this phenomenon is of importance to achieve multiple goals ranging from the attenuation of noise and vibrations [3] 5 to the improvement of efficiency regarding radiated sound fields, e.g. in audio transducers or musical instruments. In this context, the study and prediction of transient vibroacoustic response generated by structures under impulse-type excitation is a major field of interest which requires a fine description of damping.. One may find various applications in transportation acoustics, e.g. in railways 10 industry when studying impact noise generated by wheel-rail contact [4] or in building and room acoustics through the concept of auralization [5] . Another major area of application is related to the concept of sound synthesis by means of physical modeling [6] and its applications in the acoustics of musical instruments [7] [8] [9] , where psychoacoustical studies have highlighted the major role played by 15 damping on the perception of sounds [10] .. For a given material, damping is often characterized in the frequency domain from experimental measurement of the complex modulus E * or loss factor η, that may be obtained using various techniques including viscoanalysers. Such results generally exhibit frequency behaviors which differ a lot depending on the type of 20 observed material and on external conditions like temperature and hygrometry (see e.g. some experimental results for a wide range of damping materials in [11] ). This leads to a wide range of frequency-domain damping models (see e.g. [12] ), which may not be directly transferable to the time domain.. On the other hand, time-domain formalism appears to be more natural 25 when dealing with structures excited by impulses as it naturally takes transient aspects of simulated response into account, or in presence of nonlinear vibrations. In this framework, the literature is plentiful of models initially developed in the framework of linear viscoelasticity [13] . The most simple ones are well-known Maxwell, Kelvin-Voigt and Zener (also called Standard Linear

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


Application of a Failure Driven Test Profile in Random Testing Random testing techniques have been extensively used in reliability assessment, as well as in debug testing. When used to assess software reliability, random testing selects test cases based on an operational profile; while in the context of debug testing, random testing often uses a uniform distribution. However, generally neither an operational profile nor a uniform distribution is chosen from the perspective of maximizing the effectiveness of failure detection. Adaptive random testing has been proposed to enhance the failure detection capability of random testing by evenly spreading test cases over the whole input domain.In this paper, we propose a new test profile, which is different from both the uniform distribution, and operational profiles. The aim of the new test profile is to maximize the effectiveness of failure detection.We integrate this new test profile with some existing adaptive random testing algorithms, and develop a family of new random testing algorithms. These new algorithms not only distribute test cases more evenly, but also have better failure detection capabilities than the corresponding original adaptive random testing algorithms. As a consequence, they perform better than the pure random testing. RT, a fundamental software testing method, usually selects test cases according to a uniform distribution (for debug testing), or an operational profile (for reliability assessment). Failure detection capability is an important attribute of any testing method. Generally speaking, the better failure detection capability a testing method has, the more effectively program bugs can be removed, and In this paper, motivated by the argument that the uniform-distributed test profile is not designed to ensure a good failure detection capability of RT, we proposed to use a different test profile at the candidate generation process. As an example of illustration, we selected a dynamic nonuniform distribution as the failure driven test profile to guide the random selection of candidates.. We integrated this new test profile with the test case identification criteria of some existing ART algorithms, and developed a family of new ART algorithms, namely adaptive random testing with . Obviously, when 0 ≤ y − (1 − α)x 2 α < 1, i.e.,. otherwise, f X 1 y − (1 − α)x 2 α = 0. Therefore, f Y (y) can be calculated by the following steps.. • When y < 0, f Y (y) = 0.. • When y ≥ 1, f Y (y) = 0.. • (1 − α) . In this paper, for convenience of illustration, we assume that the program under test only has numeric inputs. Applications of RT, and ART on non-numeric programs have been studied in [22] , [26] , and [9] , [10] , [16] , [19] , respectively.

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


Two generalized complex orthogonal space-time block codes of rates 7/11 and 3/5 for 5 and 6 transmit antennas Abstract-Space-time block codes from orthogonal designs have two advantages, namely, fast maximum-likelihood (ML) decoding and full diversity. Rate 1 real (pulse amplitude modulation-PAM) space-time codes (real orthogonal designs) for multiple transmit antennas have been constructed from the real Hurwitz-Radon families, which also provides the rate 1 2 complex (quadrature amplitude modulation-QAM) space-time codes (complex orthogonal designs) for any number of transmit antennas. Space-time coding for multiple transmit antenna systems in broad-band wireless communications has attracted considerable attention lately, see for example [1] , [2] - [11] . To design "good" space-time block codes is a challenging problem. Since a space-time block code is a collection of some matrices, even for a small block size and a reasonable rate, the set of a space-time block code can be significantly large and therefore, its maximum-likelihood (ML) decoding may have a high complexity. On the other hand, the performance of a space-time block code depends on the diversity of the code. Therefore, a "good" space-time block code should possess two properties: i) the decoding at the receiver is reasonably fast; and ii) the diversity of the code is not small. Based on these two properties, space-time block codes based on orthogonal designs have been first proposed in Alamouti [3] for two transmit antennas and then generalized in Tarokh, Jafarkhani, and Calderbank [4] for n 2 transmit antennas by connecting the space-time codes to orthogonal designs and the Hurwitz-Radon theory, see, for example, [12] , [13] . A similar scheme was suggested in Ganesan and Stoica [6] from a maximum signal-to-noise ratio (SNR) approach.. Consider a space-time block code from complex orthogonal design G for n transmit antennas and block length p, i.e., G is a p2n generator.. Consider a signal constellation S, for example the binary phase shift keying (BPSK) f1; 01g or the quaternary phase shift keying (QPSK) f1; 01; j; 0jg. Let x 1 ; x 2 ; . . . ; x k be information symbols in S.. The entries of the complex orthogonal design of G are formed from complex linear combinations of x 1 ; x 3 1 ; x 2 ; x 3 2 ; . . . ; x k ; x 3 k such that the columns of G are orthogonal to each other, where x 3 is the complex conjugate of x. More detailed definition is reviewed later. See [4] for more about its encoding scheme and fast decoding algorithm. The rate of the code is R = k=p, which means that each codeword with block length p carries k information symbols. For a fixed n and rate R, it is desired to have the block length p as small as possible for decreasing the time delay in decoding. It was shown in [2] , [4] that R 1, i.e., p k. Clearly, for a given k, the smallest possible block length p is k. When the signal constellation S has all real symbols, such as pulse amplitude modulation (PAM), rate R = 1, i.e., p = k, real orthogonal designs for any fixed transmit antenna number n have been given in, for example, [4] from the real Hurwitz-Radon families [12] . These real orthogonal designs also provide a method to construct complex orthogonal designs of rate R = k=(2k) = 1=2 for any fixed transmit antenna number n [4] where the block length p = 2k and k depends on n (see details later). Examples of rate 3=4 complex orthogonal designs for n = 3 and n = 4 transmit antennas have appeared in [4] , [6] - [8] . It was proved in [4] that 424 complex orthogonal designs of rate 1 do not exist and a simpler proof was given in [6] by using the amicable design theory [12] , [13] . This implies that the only square complex orthogonal design of rate 1 is the 2 22 complex orthogonal design proposed in [3] .. To the best of our knowledge, there are no known high-rate (R > 1=2) complex orthogonal designs for transmit antenna number n 5.. The main contribution of this correspondence is to present rate 7=11 and rate 3=5 generalized complex orthogonal designs for n = 5 and n = 6 transmit antennas, respectively. We also present some constructions of rate 1=2 complex orthogonal designs with smaller block length p than those presented in [4] .

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Robust Learning with Infinite Additional Information The present work investigates Gold style algorithmic learning from inputoutput examples whereby the learner has access to oracles as additional information. Furthermore this access has to be robust, that means that a single learning algorithm has to succeed with every oracle which meets a given speci cation. The rst main result considers oracles of the same Turing degree: Robust learning with any oracle from a given degree does not achieve more than learning without any additional information. Gold style inductive inference 7, 13 ] is an abstract model for learning: the learner receives the course of values f(0); f(1); : : : of a recursive function to be learned and synthesizes from this information a program for f. This synthesis has to meet certain convergence requirements. The special model considered in the present paper is that the learner has in addition access to nonrecursive information on the class S from which the function f is taken. This information is provided as a function oracle. But the access to this oracle has to be robust, i.e., ignorant of the actual coding of this information. So the learner has to cope with every oracle which meets a given speci cation. Four types of such speci cations are used in this paper: (1) the oracle is a list of all functions in S; (2) the oracle is a predictor which predicts every f 2 S under the model \next value"; (3) the oracle is a one-sided classi er which converges on a function f to 1 i f 2 S; (4) the oracle is a martingale which succeeds on every function in S. Learning with additional information has several roots in the literature which are presented now.. Adleman and Blum 1] as well as Gasarch and Pleszkoch 12] transferred the concept of using nonrecursive oracles to inductive inference. Such oracles can be very helpful, for example every high oracle allows to learn all recursive functions in the limit 1]. Also every nonrecursive oracle allows to learn some class nitely which can not be nitely learned without any oracle. But in these models, the machines always depend on the actual form of the oracle. Indeed Theorem 2.1 shows the following: if a class S can be learned via a xed machine succeeding with any oracle inside a given Turing degree then S can be learned without any help of an oracle. So it is in this context more suitable to specify the oracles by some structural properties which allow to derive some information in a uniform way than by their Turing degree.. A second root is the notion of learning with additional information in the way as introduced by Freivalds and Wiehagen 11] . They presented a model where the additional information is just a number (and not an in nite object as an oracle) which depends on the function f (and not only on the class S). One important result is the following: they presented in addition to the values of the function an upper bound of the size of some program of f. This nite information is already su cient to learn the whole class of all recursive functions, REC, in the limit. Jain and Sharma 15] extended this work. Baliga and Case 4] modi ed this setting such that the learner receives as additional information an index of a higher-order program instead of this upper bound of the program size. This concept is not so powerful as that of Freivalds and Wiehagen 11] , as it does not allow the inference of REC. But it still permits inference of larger classes than without any additional information. Jain and Sharma 14] gave as additional information programs which are de ned on a \su ciently large" domain and coincide with the function f to be learned on their domain.. Case, Kaufmann, Kinber and Kummer 9] considered as additional information an index of a certain tree such that among other requirements the function to be learned is an in nite branch of it. These trees had to ful ll certain requirements as having bounded width; they showed that { depending on the parameters of the tree { the class REC of all recursive functions is learnable via a team of machines using this additional information. Furthermore, Merkle and Stephan 19] showed, that there is a class S which can be learned in the limit only if as additional information an index of such a tree is provided, on which the function to be learned is an isolated in nite branch.. Finally Osherson, Stob and Weinstein 23] already went in the direction of the present paper by synthesizing learner for a whole class from additional information on the class S to be learned.. The third root is the work of Angluin 3] whose notion of \minimal adequate teacher" is some kind of in nite additional information. The in nity is given by the fact that the teacher has to answer each query from a given in nite query-language correctly. The answers to the queries are not always unique; e.g., there may be several ways to select counterexamples to a learner's hypothesis. So the learner has in her model to be robust in the sense that learning has to succeed with every teacher which meets the speci cation. Similarly robust learning in the present paper is modelled by the in nite concept of a \minimal adequate oracle".. Main recursion theoretic notions follow the books of Odifreddi 21] and Soare 26] . l N is the set of natural numbers. A; B; C denote subsets of l N and are identi ed with their characteristic function: A(x) = 1 for x 2 A and A(x) = 0 for x = 2 A. f and g denote total recursive functions from l N to l N. REC denotes this class of all total recursive functions and REC 0;1 = ff 2 REC : (8x) f(x) 1]g. Strings ; ; 2 l N are nite sequences of natural numbers and binary strings ; ; range over f0; 1g .. Strings are also identi ed with a partial function: If = abcc then (x) equals a for x = 0, b for x = 1, c for x = 2; 3 and is unde ned for x > 3. A string is pre x of some other string (or function f or set A) i (x) = (x)# (f(x) or A(x), respectively) for all x in the domain of (which is denoted by dom( )). denotes the pre x-relation ( ). ' e is the e-th partial recursive function w.r.t. some xed acceptable numbering. This numbering is also always used as hypotheses space unless explicitly stated otherwise. Now an overview on the most important de nitions from learning theory 7, Inside Given Degrees: The oracles in this notion are (other than the previous ones) independent of S. A class S is robust learnable inside a given degree a of oracles i there is a machine M which Ex-learns every f 2 S with any oracle A 2 a. It is shown that for all common notions of degrees (Turing, tt, wtt, btt, m) except the notion of 1-degrees this kind of additional information allows only to learn classes which can already be learned without access to any oracle. Now the concepts are presented in detail each in one section starting with the notion of learning inside given degrees.

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


An Ontology to Model e-portfolio and Social Relationship in Web 2.0 Informal Learning Environments Abstract: Web 2.0 applications and the increasingly use of social networks have been creating new informal learning opportunities. Students interact and collaborate using new learning environments which are structurally different from traditional e-learning environments. In these informal unstructured learning contexts the boundaries between the learning contexts and social spheres disappear, and the definition of the students competences appears more and more important. In this paper we propose a semantic web approach in order to create the basis for a software platform to model learner profiles. In particular we propose to extend the FOAF ontology, used to describe people and their personal relationships, with an ontology related to the IMS Learning Portfolio used to model students' competencies. This ontology could be a fundamental layer for a new Web 2.0 learning environment in which students' informal learning activities carried out in social networks can be managed and evaluated. Collaborative group activities are frequently used by teachers in the educational curriculum. In these activities it is necessary to create well balanced groups with the aim of maximizing the attainment of the learning objectives.. To ensure the success of a learning activity, teachers must consider the constraints that can affect the entire group or an individual performance, such as previous experiences by students in similar educational contexts, cultural background or interests. The greater the number of constraints to consider, the more complex becomes the management of the learning experience.. Semantic web technologies offer the substrate needed to overcome the problems of social network with large groups of students. The versatility of these technologies means that they can be successfully applied for describing social networks and competences in learning experiences.. An interesting approach for creating an ontological system based on semantic web technologies that makes it possible to define a social network considering the competences of participants, the quality of the group and its robustness, is based on the use of an ontology as a result of an extension of the FOAF vocabulary, to create a semantic data base including specific references to educational paths.. In particular, the approach proposed in this work is based on the creation of a specifically designed ontology that extends FOAF ontology, in order to describe the domain of competences as defined by the IMS e-portoflio standard.

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Spatiotemporal realization of an artificial retina model and performance evaluation through ISI- and spike count-based image reconstruction methods Abstract: Development of an artificial retina model that can mimic the biologic retina is a highly challenging task and this task is an important step in the development of a visual prosthesis. The receptive field structure of the retina layer is usually modeled as a 2D difference of Gaussian (DOG) filter profile. In the present study, as a different approach, a retina model including a 3D 2-stage DOG filter (3D-ADOG) that has an adaptively changing bandwidth with respect to the local image statistic is developed. Using this modeling, the adaptive image processing of the retina can be realized. The contribution of the developed model in terms of the image quality is evaluated via simulation studies using test images. The first simulation results, including only the spike count-based reconstruction for a test video sequence, were previously published. In this study, in addition to the spike count-based reconstruction, the interspike interval measure is also used in the simulation study. The reconstruction results are compared using the statistical parameters of the mean squared error (MSE), universal quality index (UQI), and histogram similarity ratio (HSR), which characterize the image likelihood. To evaluate the performance of the model versus time, time-dependent changes in the MSE, HSR, and UQI parameters are obtained and compared to the standard model. From these results, it is concluded that the 3D-ADOG filter-based retina model preserves the spatial details of the image and produces a larger number of different gray tone levels, which are important for the visual perception of an image, in comparison with the well-known classical DOG filter-based retina model. The retina implant systems based on this model can provide better visual perception for implant recipients. The visual system presents most of the environmental data to the brain. The absence of visual data greatly decreases quality of life. Although preventive treatments exist, there is no treatment method for complete vision loss caused by retinal diseases such as age-related macular degeneration, retinal detachment, and retinitis pigmentosa, which lead to photoreceptor loss [1] [2] [3] . In recent years, by overcoming this handicap, to create useful vision, many studies have been started to develop artificial vision systems (or visual prostheses) that electrically stimulate the remaining retinal ganglion cells [1, [4] [5] [6] [7] [8] [9] [10] [11] .. In the visual system, the first step of visual processing starts in the eye. In the perception process of the image, the transformation of light into action potentials, called the 'phototransduction process', takes the first place in the process chain. The phototransduction process takes place through 5 different cell layers of the retina. These layers are the photoreceptor, horizontal, bipolar, amacrine, and ganglion cell layers, from outside to inside, respectively. The photoreceptor cells introduce excitatory signals, whereas the horizontal cells introduce inhibitory signals. The horizontal cells make the lateral synapses with receptors along the whole retina. The synapses of the receptors and horizontal cells converge on the bipolar cells. Amacrine cells are somewhat similar to horizontal cells in terms of their functions and their synapses. The synapses of the bipolar and amacrine cells converge on the ganglion cells and the bipolar cells introduce excitatory signals, whereas amacrine cells introduce inhibitory signals. The last cell group, the ganglion cells, form the optic nerve with their axons. These cells convert the potentials from the bipolar and amacrine cells into action potentials and produce spike signals by a special coding mechanism. As the ganglion cells remain functional during vision loss due to photoreceptor loss, sight can be restored with the appropriate electrical stimulation signals.. In sight restoration studies, the main task is to convert the image data into encoded spike pulses that are meaningful for the visual cortex. After this step, these encoded pulses are sent to the targeted place of the visual pathway on which the microelectrode matrix placed. Based on electrode placement strategies, visual prostheses can be grouped into 3 main categories, as the visual cortex, optic nerve, and retinal implants [1, 2] . Due to the ease of electrode placement and less surgical risks, many studies are focused on the retina implant system. In the retina implant system, the epiretinal approach uses an electrode array placed on the retina surface and aims to mimic the processing of the healthy retina layer. In the literature, aside from wavelet and Gabor filter-based approaches, the receptive field of the retina layer is implemented based on the spatiotemporal difference of Gaussian (DOG) filter and the spike generation of the retina is implemented based on a 'noisy leaky-integrate and fire' (nLIF) neuron model [5, 9] .. The nonlinear transduction and adaptation mechanism of the retina cannot be modeled based only on the DOG filter structure. However, it describes many of the biologic properties of the filtering behavior of the retina [12] [13] [14] . Furthermore, the image data are processed by the retina in both the spatial and temporal domains [5, 15] , and this concept is the basis of retina modeling studies [4, 5, 9] .. Although standard DOG filter-based retina models are widely accepted in the literature, there are still some issues that should be improved. First, they do not include the local adaptation mechanism of the retina layer. However, there are some studies on modeling the adaptation mechanism that do not involve the DOG filter profile and deal with the adaptation problem as a distinct approach [4, 9] . Second, some important parameters of the DOG filter-based retina model are determined by time-consuming trial and error techniques [6] . Finally, the spatial receptive field profile of the DOG filter cannot correctly model the contiguous structure of the receptive field of the retina [16] . By considering these issues, standard DOG filter-based retina models show user-dependent and relatively parametric characteristics.. In the present study, to overcome these disadvantages of the standard DOG filter-based retina models, a multistage DOG filter-based artificial retina model that changes the bandwidths of the DOG filters depending on the statistical characteristics of the local image data is proposed. The proposed model has a 2-stage spatiotemporal filtering structure that is based on the inner cell layers of the biologic retina, and the interactions of both the receptor-horizontal and bipolar-amacrine cells are modeled using an adaptive DOG filter [17, 18] . The nLIF cell model, which is a good approximation for modeling the firing mechanism of ganglion cells, is used for the realization of the spike generation process in artificial retina models. The nLIF model is adopted to generate the outputs for the ON-center, OFF-center, and ON/OFF-center ganglion cells. Since there are both 2-stage spatial and temporal image filtering, the developed artificial retina model is referred to as a 3D 2-stage adaptive DOG filter-based retina model (3D-ADOG).. To evaluate the efficiency of the proposed retina model in terms of an image reconstruction perspective, the obtained spike outputs are reconstructed as an image. This reconstruction process is performed with more conventional rate-based codes, which are based on the total number of spikes produced by each ganglion cell and measures of their interspike intervals (ISI) [14] . The ISI code is regarded as more robust to neural noise than other spike count-and spike latency-based coding alternatives [14] . For a comparative analysis, reconstructed images for both the proposed adaptive artificial retina model and the standard DOG model are compared using some statistical parameters. In a previous study [17] , aside from the histogram similarity ratio (HSR) and universal quality index (UQI) parameters, the mean gray level values were used as a measure for comparison.. In the comparisons of this study, aside from the HSR and UQI parameters, the mean squared error (MSE) measure, which is a well-known error comparison parameter, is used. Furthermore, different from the previous study, time-dependent changes in the MSE and UQI parameters are also evaluated for test images.. The rest of the paper is organized as follows. In Section 2, a detailed description of the proposed adaptive artificial retina model is given. Section 3 gives the simulation results and quantitative analysis with spike countand ISI-based reconstructed images for the proposed and standard models. The discussion and conclusion of the study are presented in Section 4. In this study, by considering a biologic model of the retina layer, a bioinspired 3D-ADOG was developed. This model is based on the 2-layered (inner and outer plexiform layers) structure and adaptive processing behavior of the biological retina. Both stages in the model include adaptive spatiotemporal filtering stages, which are not included in the classical DOG filter-based retina model. In order to generate the proper spike activities of the retinal ganglion cells, the nLIF-based spiking cell model was used.. In this study, the aim was to achieve a higher visual perception performance for retina implant users via the developed model. The qualitative and quantitative performance of the model was evaluated by performing simulation studies. In the simulation studies, spike count-and ISI measure-based image reconstruction methods were used for the image reconstruction process. In the quantitative analyses, aside from the well-known classical MSE measure, the reconstructed images were compared using HSR and UQI parameters. Since the HSR parameter is important for analyzing the contrast range of the image, this parameter was used to measure the similarity of the gray tone levels in the reconstructed images. The UQI is a compact parameter for measuring contrast distortion, luminance distortion, and correlation loss of images. Using these 3 evaluation parameters, appearance-based, content-based, and compact statistical comparison-based performance analyses were performed.. When the spike count-and ISI-based reconstructed images were compared, it was seen that the ISI-based reconstructed images for all of the retina models include a larger number of different gray tone levels than the spike count-based reconstructed images. Thus, the HSR values were slightly lower for the ISI measure-based reconstruction than for the spike count-based reconstruction. Although it is possible to employ other encoding strategies (for example, rank order coding [14] ) in the image reconstruction stage of this study, the well-known spike count-and ISI-based methods are regarded as reliable for verifying the relative comparisons of the models.. Simulation results based on the spike count showed that the proposed model yields better scores for the MSE, HSR, and UQI parameters for the ON and ON/OFF channels than the standard DOG filter-based retina model ( Table 2 ). The ISI measure-based simulation results showed that our model yields higher values for the HSR and UQI (Table 3) . Although the 3D-ADOG model preserves the spatial details in the images better, for the ISI-based reconstruction results for both the ON and ON/OFF channels, this model yielded relatively higher MSE values than the standard model. As the MSE measure depends on the difference of the pixel values in a [0 ∼ 255] interval, unimportant changes (e.g., small changes in the light conditions) for visual perception may cause important error values for this measure. Therefore, it can be considered that the HSR and UQI measures may coincide with visual perception because these measures have a relatively small variation in range.. It should be noted that the proposed model provides higher HSR and UQI values and a lower MSE value than the standard DOG-based model according to the time-dependent analysis of the MSE, HSR, and UQI values. This means that, using this model, it can be possible to create a meaningful visual image in a patient's mind with a short duration of electrical stimulation.. The proposed model shows a significant improvement compared to the standard model in the simulation results, but we should keep in mind that the real performance of the model can be evaluated only by clinical trials with real implant users. Qualitative and quantitative results in the study show that the adaptive behavior of the retina can be realized by implementing the 2-stage adaptive bandwidth-DOG filters and the quality of the obtained images from the retina implant devices can be improved using this adaptive retina model, which preserves the spatial image details well.

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


Entropy/Length Profiles, Bounds on the Minimal Covering of Bipartite Graphs, and Trellis Complexity of Nonlinear Codes Abstract-In this paper, the trellis representation of nonlinear codes is studied from a new perspective. We introduce the new concept of entropy/length profile (ELP). This profile can be considered as an extension of the dimension/length profile (DLP) to nonlinear codes. This elaboration of the DLP, the entropy/length profiles, appears to be suitable to the analysis of nonlinear codes. Additionally and independently, we use wellknown information-theoretic measures to derive novel bounds on the minimal covering of a bipartite graph by complete subgraphs. We use these bounds in conjunction with the ELP notion to derive both lower and upper bounds on the state complexity and branch complexity profiles of (nonlinear) block codes represented by any trellis diagram. We lay down no restrictions on the trellis structure, and we do not confine the scope of our results to proper or one-to-one trellises only. The basic lower bound on the state complexity profile implies that the state complexity at any given level cannot be smaller than the mutual information between the past and the future portions of the code at this level under a uniform distribution of the codewords. We also devise a different probabilistic model to prove that the minimum achievable state complexity over all possible trellises is not larger than the maximum value of the above mutual information over all possible probability distributions of the codewords. This approach is pursued further to derive similar bounds on the branch complexity profile. To the best of our knowledge, the proposed upper bounds are the only upper bounds that address nonlinear codes. The novel lower bounds are tighter than the existing bounds. The new quantities and bounds reduce to well-known results when applied to linear codes. A TRELLIS diagram can be viewed as an efficient representation of a code for a maximum-likelihood softdecision decoding. Trellis description of block codes was originally introduced in 1974 by Bahl et al. [1] for maximum a posteriori decoding. In 1978, Wolf [28] used a trellis construction based on the parity-check matrix to apply the Viterbi algorithm for soft-decision decoding of block codes. In the same year, Massey [19] introduced an alternative trellis Manuscript received November 12, 1996 ; revised June 4, 1997. The material in this paper was presented in part at the IEEE International Symposium on Information Theory, Ulm, Germany, June 1997.. The authors are with the Department of Electrical Engineering-Systems, Tel-Aviv University, Ramat Aviv 69978, Tel-Aviv, Israel.. Publisher Item Identifier S 0018-9448(98) 00656-7. construction. The formal definition of the trellis construction for linear block codes was made by Forney [4] . All the above references confine their scope to linear codes. Muder [21] provided a rigorous graph-theoretic definition of trellises and showed that Forney's trellis is the minimal trellis representation of any linear block code. In his paper Muder also addressed nonlinear codes and pointed out that the minimal proper trellis for a nonlinear code need not be the minimal trellis. The fact that the original trellis introduced by Bahl et al. is isomorphic to the minimal trellis presented later by Forney and Muder was announced by Kot and Leung [13] , and later by Zyablov and Sidorenko [29] . Another significant contribution to the trellis analysis of block codes is due to Kschischang and Sorokine [15] . In their paper, the authors examined the trellis structure of general block codes and concluded that minimal trellises for nonlinear codes are computationally intractable. The solutions of this minimization may result in improper or unobservable trellises. Most of the study in [15] is dedicated, however, to the construction of the minimal trellis for linear codes by forming a product of elementary trellises. These trellises correspond to the one-dimensional subcodes generated by the so-called "atomic codewords." The trellis-oriented generator matrix that was introduced by Forney [4] is composed of these codewords. In a recent survey on trellis theory for linear block codes McEliece [20] showed that among all trellises that represent a linear code, the BCJR trellis [1] has the fewest edges and the minimum vertex count at each level, simultaneously. Recently, Vardy and Kschischang [26] showed that this minimal trellis also minimizes the expansion index of the trellis (the total number of "bifurcations"). Moreover, they extended these results to the general class of rectangular [14] (separable [22] , [23] ) codes. All these complexity measures are minimized in the unique biproper trellis of these codes ( [14] , [26] ). These results were independently obtained by Sidorenko [22] . Every block code has a unique minimal proper trellis. If is a linear code then this trellis is also the minimal trellis. This minimal trellis is characterized by the fact that any other trellis for has at least as many states and as many edges as the minimal trellis in every level of the diagram. The problem of finding a trellis representation for a nonlinear block code that minimizes measures of trellis complexity (state complexity and branch complexity), even under a given coordinate permutation, appears to be computationally infeasible. The analysis of the complexity measures of a trellis representation 0018-9448/98$10.00 © 1998 IEEE of a nonlinear code raises several difficulties that are not encountered in the analysis of trellis diagrams for linear codes.. 1) The unique minimal proper trellis which exists for all block codes (under a given coordinate permutation) need not be a minimal trellis of a nonlinear code. Furthermore, the solution of this minimization problem may not be unique.. 2) The minimal trellis for nonlinear codes may include several edges emanating from the same vertex with the same label (improper trellis). Improper trellises for nonlinear codes may have fewer vertices than that of proper diagrams ( [15] , [21] ). Moreover, a minimal trellis of a nonlinear code may not be observable ("one-toone"), i.e., the inclusion of distinct paths that represent the same codeword may reduce complexity measures (e.g., [15] ).. 3) The minimization of the number of vertices (states) at one level, under a given coordinate ordering, may impose an increase of the vertex count at an other level [15] . Given a coordinate ordering, the state and the branch complexity profiles of a linear block code are simple functions of the ordered dimension/length profile (DLP) [5] , and the appropriate diagrams are easily computed. The DLP lower bound on the state complexity profile of a code under any permutation of its coordinates is determined by the (unordered) DLP. The minimal trellis of a nonlinear code may not be unique, and there is no equivalent formula to determine the state and the branch complexity profiles of its trellis diagram. Thus the problem of deriving lower and upper bounds on the trellis complexity of nonlinear codes has a considerable practical importance. Lafourcade and Vardy [16] developed new lower bounds on the state and branch complexity profiles. These bounds are obtained by dividing the index axis of the code into several sections. The authors generalize the bounds to nonlinear codes by the introduction of the cardinality/length profile. This quantity does not utilize the asymmetry of nonlinear codes and thus their appropriate bounds for nonlinear codes do not appear to be tight. The authors thus use combinatorial properties of the specific codes under discussion to tighten the lower bounds. The latter technique is stated to biproper trellises only.. In this paper we study the trellis complexity (state complexity and branch complexity profiles) of nonlinear codes. We employ information-theoretic measures to extend the notion of DLP to nonlinear codes by the introduction of the entropy/length profile (ELP). The entropy/length profiles appear to be advantageous descriptive characteristics of nonlinear codes and the suitable tools to derive tight bounds on the trellis complexity of any trellis representation of these codes. The novel bounds, which also apply to improper and non-one-toone trellis representations, result in a significant improvement upon the existing bounds. The ordered ELP bounds the trellis complexity of nonlinear codes under a given permutation, and the trellis complexity of the code under any coordinate ordering is bounded by the unordered ELP. The prescribed bounds reduce to well-known results when applied to linear codes.. These results can be reinterpreted from our new viewpoint. The new tools can also be used to derive new bounds on trellis complexity of linear codes (e.g., Corollary 4 and Theorem 10 herein) though we believe that their main contribution is to the investigation of nonlinear codes.. The bounds on the state and the branch complexity profiles are preceded by some general new results regarding the problem of minimal covering of a bipartite graph by complete subgraphs. In [15] , Kschischang and Sorokine have observed that the problem of minimizing the vertex count of a trellis representation of a code at a given index is equivalent to the aforementioned graphical problem. This interpretation of the problem involves the representation of the past/future relation of a code via a Cartesian array. In this paper we elaborate on this observation and show that minimizing the branch count between any two indices can also be treated as the same problem of covering by product-form subsets. This analysis poses a Cartesian product representation of a different relation induced by the code. This observation enables the use of unified basic proofs to establish bounds on both state and branch complexity profiles.. In addition to the practical use of the new measures, our study has also a conceptual merit. It shows the close relation between trellis representation and mutual information. The trellis complexity of a linear code is completely defined in terms of the dimensions of projections of the code and its subcodes. Recently, McEliece [20] presented an informationtheoretic interpretation of the vertex count of the BCJR trellis. In this paper we elaborate this relation and we bound the trellis complexity of nonlinear codes by some informationtheoretic measures. The derived relations by contrast to the corresponding relation for linear codes require relatively complex proofs based on definitions of appropriate probabilistic models. The complexity of a trellis representation for nonlinear codes cannot be expressed in closed-form terms. These trellises are subject to some anomalies peculiar to nonlinear codes. In this paper we prove, however, that the complexity of any possible trellis representation cannot be smaller than some well-defined information-theoretic measures, regardless of the trellis structure.. The paper is organized as follows. Preliminaries and basic notations are presented in Section II. The next two sections develop two distinct frameworks which are combined in the subsequent sections to derive bounds on the state and branch complexity profiles of nonlinear block codes. Section III introduces the different entropy/length profiles and develops their relationships and their basic properties. It is shown that the prescribed profiles are natural extension of the DLP to nonlinear codes. The ELP reduces to the DLP when applied to linear codes. Section IV is devoted to the problem of covering a bipartite graph by complete subgraphs. We present a lower and an upper bound on the minimum number of these constituent complete subgraphs. These bounds are phrased as the mutual information between the two disjoint subsets of vertices of the bipartite graph. In Section V, we use the general results of Section IV in conjunction with the ELP notion that was developed in Section III to present both upper and lower bounds on the state complexity profile of (nonlinear) codes described by any trellis diagram. The state complexity of a code under a given permutation is lower-bounded by the ordered ELP, and the lower bound for any coordinate ordering is a simple function of the unordered profiles. The basic theorem for a given coordinate permutation determines that the state complexity of any trellis representation of the code at any given level cannot be smaller than the mutual information between the past and the future portions of the code at this same level, under a uniform distribution of the codewords. These new bounds exhibit an appreciable improvement on the CLP bounds for nonlinear codes [16] . We also present an additional bound on the state complexity, i.e., on the maximum value of the state complexity profile. This bound is obtained by partitioning of the index axis for the code. Afterwards we develop an upper bound on the state complexity profile. We present a graph-theoretic bound that actually furnishes a constructive procedure to derive a (one-to-one) trellis diagram that meets the bound at any given index. This complexity profile may not be achieved at all the levels of the diagram simultaneously. Thereafter, we prove that this bound can be expressed as a maximum value of the mutual information between the past and the future portions of the code with respect to the probability distribution of the codewords.. Notably, as an example, we apply the bounds to the Nordstrom-Robinson code. Our upper bound disproves the conjecture of Lafourcade and Vardy [16] that the known state profile of the construction by Forney [4] and due to Vardy [24] is optimal componentwise. We devise a new construction of the code. The trellis complexity of the new construction is smaller than that of the known construction of the code at some indices. The new construction also infers that the new lower bounds are rather tight.. Section VI extends the results of Section V to the branch complexity profile, when this profile refers to the logarithm of the total number of paths through the trellis between two levels and , where need not necessarily be equal to The lower and upper bounds on the branch complexity profile are also expressed in terms of ELP and mutual information. The lower bounds on the trellis complexity can also be considered as an additional proof to the optimality of the minimal biproper trellis for group codes ( [5] , [6] , [14] ). Moreover, these bounds indicate that this trellis also minimizes the total number of trellis branches between any two indices. Finally, concluding remarks are given in Section VII. A considerable advance in the study of trellis representation for linear block codes has been achieved in recent studies. Yet, less is known about the trellis structure of nonlinear codes. The problem of minimizing the vertex count of nonlinear codes may have several solutions, unlike the corresponding problem for linear codes. Furthermore, minimal trellis representations for nonlinear codes may not be proper or one-to-one. In this paper, we have defined entropy/length profiles. These profiles seem useful to the study of nonlinear codes. Additionally, we have established bounds on the minimal covering of a bipartite graph by complete subgraphs. The minimization of the vertex set of a trellis representation for the code is known to be equivalent to the minimal covering problem. Furthermore, we have derived a model under which the minimization of the branch count between any two levels in the trellis can also be considered as a minimal covering problem. Equipped with these models (analogies) and the entropy/length profiles, we have derived both lower and upper bounds on the trellis state and branch complexity profiles of (nonlinear) block codes. The new approach, which is also applicable to improper and non-one-to-one trellis structures, leads to appreciably tight bounds on the complexity measures of nonlinear codes. It is argued that the state complexity at any given level cannot be smaller than the mutual information between the past and the future portions of the code at this level under a uniform distribution of the codewords. The prescribed lower bounds are tighter than other known bounds. Apparently, they also establish the validity of the CLP-based bound to nonone-to-one trellises. We have also devised a particular trellis construction and an appropriate probabilistic model to prove that the minimum achievable state complexity over all possible trellises is not larger than the maximum value of the above mutual information over all possible probability distributions of the codewords. Moreover, we have shown how to construct a diagram that meets the bound. This construction yields a oneto-one trellis diagram endowed with special properties. Similar lower and upper bounds on the branch complexity profile and on the branch complexity are also derived.. A legitimate question that may arise at this stage is what is the computational complexity of our information-theoretic bounds? For brevity we give some final conclusions regarding this issue in gross. The total number of operations required to compute the lower bound on the entire state (or branch) complexity profile of an code over GF under a given permutation is upper-bounded by This is actually the complexity of the computation of the ordered ELP. The computational complexity of the CLP bound is the same. The derivation of the actual trellis representation of the code (also under a given permutation) can be carried out in an time algorithm [22] , [26] . This algorithm applies to rectangular codes only. The computation of our upper bound is equivalent to the construction of a maximum matching in a bipartite graph. This search is known as the Hungarian Method due to Kuhn (e.g., [27] ). One can think of the following efficient algorithm to implement this search: put the codewords into a two-dimensional array, scan a part of the array, and exchange rows and columns (when necessary). The computational complexity of each of the constituent steps of this algorithm is bounded above by per a given index. Hence the derivation of a bound for all the trellis levels requires operations. We see that the construction of the trellis (for rectangular codes) entails larger computational complexity than the proposed lower bound but it necessitates less operations than the proposed upper bound.. We end this section with a brief summary of the bounds on the state and branch complexity and the state and branch complexity profiles with the relations between the different bounds.. •

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


A review on the public benchmark databases for static keystroke dynamics Keystroke dynamics allows to authenticate individuals through their way of typing their password or a free text on a keyboard. In general, in biometrics, a novel algorithm is validated through a comparison to the state of the art one's using some datasets in an offline way. Several benchmark datasets for keystroke dynamics have been proposed in the literature. They differ in many ways and their intrinsic properties influence the performance of the algorithms under evaluation. In this work, we (a) provide a literature review on existing benchmark datasets of keystroke dynamics; (b) present several criteria and tests in order to characterize them; (c) and apply these criteria on these available public benchmark datasets. The review analysis shows a great disparity in the acquisition protocol, the population involved, the complexity of the passwords, or the expected performance (there is a relative difference of 76% between the EER on the worst and best performing datasets with the same authentication method). Keystroke dynamics [1] is a behavioural biometric modality, which allows the authentication of individuals through their way of typing their password on a keyboard. It is a behavioural biometrics which presents the advantage of not requiring additional sensor than the keyboard at hand and which allows authentication through time (on-line authentication). It is probably the cheapest biometric modality available of a personal computer.. Biometric systems are validated thanks to datasets that are collected for this purpose and can be qualified in function of the problem that one wants to solve. For instance, if one wants to benchmark algorithms for face recognition, the algorithms may give very different performance on a dataset which contains no variability (visage is frontal with no expression and no illumination variation) and on other dataset which contains some of these variabilities. The choice of the dataset is therefore guided by the precise problem the algorithm aims at solving. A good evaluation framework corresponds to the association of a reference system, a dataset and an associated evaluation protocol which fixes the way the dataset is used. This way, it is possible to compare different systems between them without providing any bias and to report comparative results using some error measures which very often in biometrics corresponds to EER and ROC curves [2, 3] . Such protocols have been proposed for most of the biometric modalities as described in [4] . Keystroke dynamics is a recent modality for which no such framework has been yet proposed. One of the aims of the present work is to give some report of the existing situation in terms of publicly available datasets and to suggest some criteria that could guide the construction of new datasets helpful for the research community.. Although the authentication is done in real time (i.e., online) in a real world system, scientists working on keystroke dynamics do not analyze the performance of their system online (i.e, by asking users to authenticate themselves in real time and to impersonate other users). Indeed, they work in an offline way by using samples previously collected, probably by other researchers, and stored in a benchmark dataset. Thus, data collection and algorithms evaluation are often two separated tasks. The evaluation of algorithms is eased thanks to this offline procedure. If scientists share the same common benchmark, they can fairly compare their algorithms by considering error results and time consumption. Experiments become easily reproducible, which is an important criterion in scientific studies (although datasets could contain errors). Data collection is a tedious and time consuming task, which can explain why there are only few benchmark datasets of high quality. It is important to characterize the datasets in order to be able to easily compare them, and to choose the adequate one depending on the study.. A keystroke dynamic (KD) system (KDS) is composed of two main modules: the enrollment and the verification modules. Each user must enroll himself in the KDS which computes a biometric reference given multiple samples (i.e., several inputs of the password) acquired during the enrollment step. For each input, a sequence of timing information is captured (i.e., time when each key is pressed or released) from which some features are extracted (i.e., latencies and durations) and used to learn the model which characterizes each user. During a verification request, the claimant types his/her password. The system extracts the features and compares them to the biometric reference of the claimant. If the obtained distance is below a threshold, the user is accepted, otherwise he/she is rejected. An optional module can be used to automatically update the model of the user [5] . This can be important, as the KD data is not permanent and evolves with time [5, 6] . First works on KD have been done in the eighties [7] , although the idea of using a keyboard to automatically identify individuals has first been presented in 1975 [8] . In the preliminary report of Gaines et al. [7] , seven secretaries typed several paragraphs of text and researchers showed that it is possible to differentiate users with their typing patterns. Since then, several studies have been done, allowing to decrease the quantity of information needed to build the biometric reference, while improving the performances [9, 10, 11, 12, 13] . However, most studies are not comparable because they use different datasets or protocols [13, 14] .. In this paper, we present a review of existing publicly accessible benchmark datasets for keystroke dynamics. We also propose a methodology to characterize these KD benchmark datasets (KDB). Although, it would be fruitful to rank them according to some criteria, it is actually difficult to give them a score because such score cannot be generic, as it would depend on the kind of study we want to do, and would be based on too many subjective points. Consequently, in this work, we aim at considering all the interesting points to analyze in order to qualify a KDB; using this information, the scientist will be able to choose the best dataset adapted to his particular experiment. Alternatively, it can also help him to create a new dataset of higher quality than the existing ones and maybe more suitable to the problem he wants to tackle with. In this work, we focus only on static password KD authentication systems (i.e., each user is authenticated thanks to the typing of an expected password, and not free text). The originality of this work is (a) the proposition of a complete set of criteria for characterizing different datasets, which is lacking in this field, and (b) the analysis of all the existing public KDB with respects to these criteria. We think this work is important, because it is known that KD studies are not fair as (i) acquisition protocols are different between studies [13] ; (ii) there is not always a comparative study [14] when authors propose new algorithms; and (iii) there are not always a valuable statistical evaluation [14] . Our work helps to solve the two first problems, while methods presented in [15] can solve the third one.. The paper is organized as follows. Section 2 presents a review of existing benchmark datasets for keystroke dynamics. Section 3 presents the various important elements to consider when characterizing KDB. Section 4 realizes a comparative study of public KDB by using all the criteria defined in the previous sections. Section 5 concludes this paper. We have presented in this paper a review of all the public benchmark datasets in the literature for keystroke dynamics with static password. We defined a set of criteria aiming at characterizing existing and expected keystroke dynamics datasets allowing easily choosing the adequate dataset for a particular study, or helping to build high quality keystroke dynamics datasets. We have used these criteria for characterizing all the public datasets for keystroke dynamics available in the literature. We have shown that the requirements to obtain a strong password are not compatible with the requirements to obtain a good password for keystroke dynamics. As it was expected, we have this way shown that there are differences in the meta-data of these datasets, but we have also shown there are differences of performance on a baseline authentication method for keystroke dynamics. There is a relative difference of 76% in EER between the two extreme datasets where the baseline performs the best and the worst. This result points out a huge problem as, in each keystroke dynamics paper, the keystroke authentication method is evaluated on a single dataset which is not always public. The obtained performance on this dataset can be really different from a result which would be obtained on another dataset which is more close to the targeted population. Ranking datasets of keystroke dynamics remains quite difficult because of the huge amount of differences between them (number of users, samples, presence of sessions or not, delay between sessions, . . . ). We have seen that each dataset has few strong points (according to the ideal dataset) and a lot of weaknesses. Scientists are far to have at their disposal the best datasets as possible, and we suggest that they use our criteria in order to collect the dataset which fits the need of their studies. The software provided by the GREYC lab 13 could help for that.. We therefore hope that the characterization criteria that we have provided in this paper will help to build future interesting datasets. This way, we can expect a better evaluation of the on-coming works on keystroke dynamics as well as an increase of their quality. Table 1 : Symbols used for representing benchmark datasets. Table 2 : There is a great disparity in the acquisition protocol of each dataset, and information concerning the acquisition procedure remains partial ("??" symbolizes a fact not presented in the original paper, "Y" stands for "yes" and "N" stands for "no"). ??. ??. ??. ?? difficulty. Mean and standard deviation are presented for BB (as there is one password per user), "Y" stands for "yes" and "N" stands for "no". Typing difficulty 8.71 13.3 9.4 (1.8) 11.1 8.1 7.5 7.6 8.2 8.2 9.8 9.3 6.7 6.6 9.6 6.6 6.8 1 "greyc laboratory", 2 "laboratoire greyc" + "sésame", 3 Each user has chosen a different one, 4 ".tie5Roanl", 5 "drizzle", 6 "jeffrey allen" , 7 "pr7q1z", 8 "chocolate, zebra, banana, taxi", 9 "computador calcula", 10 "try4-mbs" 11 "leonardo dicaprio" Table 6 : Comparison and ranking of the datasets for selecting the adequate dataset. The results show that most of the dataset do not match enough requirements to be used efficiently. For each score or rank line, the best(s) dataset is (are) presented in bold. These short descriptions already show the great variability of the KD datasets. Our objective in this paper is to deeply analyze these benchmark datasets in order to give the most complete information to researchers working in the field of keystroke dynamics and who would like to test their algorithms using them. In the next section, we define the important elements to consider for the characterization of keystroke dynamics datasets.. This analysis shows that these KDB are all different and do not share lots of common properties. This lack of common properties does not ease the task of comparison and dataset selection for assessing performance of a KD recognizer. Table 2 showed that for almost all datasets we do not have at disposal the required information about the acquisition process. No assumption can therefore be made between the performance of authentication by KD and the way the data is acquired. Table 3 showed, once again, that a lot of information is missing about the users properties. No assumption can therefore be made between KD users and KD authentication performance. By the way, most datasets have few individuals and samples. Moreover, results showed that the performance of the baseline classifier differs a lot among the various datasets. Table 6 presents a comparison between the tested KDB. It aims at quickly showing some properties of the datasets in order to select which ones are interesting to use in a new KD study. As there is no generic and objective ways of constructing such kind of table, we have built it by considering our own concerns about KDB:. • The dataset must contain as many users as possible in order to have the most accurate error rate. 50 users seems to be an acceptable minimum, even if it is still a low number.. • The number of samples per user must be greater than 20. Indeed, we need enough samples for computing the biometric reference of the user and the recognition scores without using a Leave One Out (or similar sampling method) which would not allow keeping the sample chronology.. • The number of acquisition sessions must be greater or equal to 3 [37] : one session can therefore be used for computing the model parameters and two sessions to compute the different evaluation measures. It is a nonsense to only work with samples captured on a short time span as it is known that template ageing is quite important for KD.. With our criteria, the datasets are ranked as follows: DSL2009, GREYC, WEBGREYC, KEYSTROKE100, GREYC-NISLAB, PRESSURE, BIOCHAVES. Note that other researchers with other criteria could obtain a different ranking.. Of course, these best ranked datasets are not sufficient for all the possible studies. That is why it will be necessary, for researchers who work on specific parts not presented in Table 6 , to acquire new datasets. These new datasets should match all the requirements of Table 6 as well as the additional requirements specifics to their own study. For example, a study on the impact of the shape of a keyboard on the recognition rate, should add criteria on the number of different keyboards used during the acquisition.

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


By all these lovely tokens... Merging Conflicting Tokenizations Given the contemporary trend to modular NLP architectures and multiple annotation frameworks, the existence of concurrent tokenizations of the same text represents a pervasive problem in everyday's NLP practice and poses a non-trivial theoretical problem to the integration of linguistic annotations and their interpretability in general. This paper describes a solution for integrating different tokenizations using a standoff XML format, and discusses the consequences for the handling of queries on annotated corpora. Alg. 3.1 produces a PAULA project with one single tokenization. So, it is possible to define queries spanning across annotations with originally different tokenization:. Extension and precedence queries are tokenization-independent: Markables refer to the term layer, not the tok layer, structs also (indirectly) dominate term nodes. Dominance queries for struct nodes and tokens yield results whenever the struct node dominates only nodes with tok-compatible source tokenization: Structs dominate tok nodes wherever the original tokenization was consistent with the privileged tokenization tok (case A and C in Fig. 1 ). Distance queries are defined with respect to the tok layer, and are applicable to all elements that are are defined with reference to the tok layer (in figure 1: tok a , tok a , tok b , tok b in case A; tok ab in case B; tok a , tok b , tok ab in case C; tok ab , tok c in case D). They are not applicable to elements that do not refer to the tok layer (B: tok a , tok b ; D: tok a , tok bc ).. 3 Notation: prim -primary data / tok, term -annotation layers / t ∈ L -t is a node on a layer L / a..b -continuous span from tok/term a to tok/term b / a, b -list of tok/term/markable nodes a, b / t = [a] -t is a node (struct, markable, tok) that points to a node, span or list a. The algorithm is unsupervised, and the token concept of the output tokenization is well-defined and consistent (if one of the input tokenizations is adopted as target tokenization). Also, as shown below, it is integrative (enabling queries across different tokenizations) and information-preserving (reversible).

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Location Models for Airline Hubs Behaving as M/D/c Queues Models are presented for the optimal location of hubs in airline networks, that take into consideration the congestion effects. Hubs, which are the most congested airports, are modeled as M/D/c queuing systems, that is, Poisson arrivals, deterministic service time, and c servers. A formula is derived for the probability of a number of customers in the system, which is later used to propose a probabilistic constraint. This constraint limits the probability of b airplanes in queue, to be lesser than a value α. Due to the computational complexity of the formulation, The model is solved using a meta-heuristic based on tabu search. Computational experience is presented. Networks involving hubs are important in transportation and telecommunications.. In both cases, when there is traffic between several origins and several destinations, there are economical benefits if this traffic is concentrated on some arcs of the network. A hub is a point where traffic from several origins is concentrated and sent either to another hub, taking advantage of the economies of scale, or to its final destination. Since the eighties, models and heuristic algorithms have been presented for the location of a fixed number of hubs, or a number of hubs to be determined by the solution to the model. The goal in all cases has been to find the least expensive hub network (considering transportation and fixed costs), given the traffic volumes between each origin-destination node pair.. Most of the hub models and algorithms discussed in the literature have been oriented to the location of hubs in airline networks for transportation of both cargo and passengers (selection of certain airports as hubs). Although there is a profuse literature on the design of telecommunications networks, the models are generally not oriented to location of hubs alone, because in these networks there are some other difficulties, as for example, those related to arc capacities.. Telecommunications models include typically the effects of transmission delay (on arcs) and congestion at nodes. The goal of these models is to keep average transmission delay and average waiting times at nodes, as low as possible. On the other hand, airline hub location models have never considered congestion; there is a parallel body of literature concerning congestion at airports.. As it is (particularly in the last few years) evident for all airline users, hub airports are more congested because they receive higher traffics than other airports in the network. We formulate hub location models that consider congestion at hub airports. The models we propose are oriented to the design of hub networks, or to the analysis of existing hub networks with planning purposes, as for example, to determine in which existing hub it is worth adding an additional runway.. Congestion in airports is hard to deal with, because of several complicating issues.. In the first place, arrival rate of the planes is highly variable throughout the day.. Although flights follow a schedule, they are subject to delays at their origin airports and during the flight itself, which make their arrival non-deterministic. Secondly, although it can be considered constant during short periods of time, the service rate is also variable, mainly depending on weather conditions and the type of planes that are serviced. In general, service times are not independent, identically distributed, because there are passengers that transfer between flights. Thus, service time for a flight may depend on the arrival time of other flights. In the third place, at their arrival to the airport, airplanes have to go through three stages of service: landing at a landing runway, service at a gate and departure through a takeoff runway. Service at the gate includes waiting for passengers transferring from other flights. The probabilistic distributions of these service times are difficult to determine, although they can be approximated. Due to these issues, detailed models for congestion at airports are very complicated and it is extremely difficult to use them for planning purposes. Thus, some of the detail must be avoided through approximations, if models for planning purposes are to be developed.. We focus on the queue formed by airplanes waiting for landing. Under certain assumptions, the analysis is applicable to takeoff runways or combined landingdeparture runways. We use a peak hour analysis, assuming that during the peak hour the average arrival rate and the service rate are both constant. This allows us to model an airport as a M/D/c queuing system, i.e. Poisson arrivals, deterministic service time and several (c) servers. This election of probabilistic modeling is justified in the body of the paper. We state an analytic formula for the steady state probabilities of different numbers of customers in an M/D/c system, found using an approach similar to the one used by Gross and Harris (1974) for single server queues and Prabhu (1965) for waiting time distribution. Later, we use this formula for the development of a deterministic equivalent of a probabilistic constraint in an integer optimization formulation for the location of congested hubs.. In the next section, we review briefly the related literature. Next, we develop the probabilistic analysis and the probabilistic constraint. We present the full model and show some computational experience obtained through the use of exact and heuristic algorithms. Further research on congested hub systems could include more exact models of the congestion, although any improvement on these could lead to intractable formulations. (12), which can be then put in the following form (Syski, 1986

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