Filtering with raster signatures Efficient evaluation of spatial queries is an important issue in spatial database. Among spatial operations, spatial join is very useful, intersection being the most common predicate. However, the exact intersection test of two spatial objects is the most timeconsuming and I/O-consuming step in processing spatial joins. On the other hand, the use of approximations can reduce the need for examining the exact geometry of spatial objects in order to find the intersecting ones. This work proposes a new raster approximation (Three-Color Raster Signature -3CRS) for representing different data types (polygons, polylines and points), and to be used as filter in the second step of the Multi-Step Query Processor. We have also executed experimental tests over real datasets, the results having demonstrated the effectiveness of our approach. The increase in storage capacity and the decrease of hardware prices have enabled applications to deal with large amounts of data, involving Gigabytes, Terabytes and even Petabytes of information. This characteristic is common to Spatial Databases where data usually have high complexity and are available in huge amounts.. Spatial data consists of spatial objects made up of points, lines, regions, rectangles, surfaces, volumes, and even data of higher dimension which includes time [13] . Examples of spatial data include cities, rivers, roads, counties, states, crop coverage, mountain ranges etc. It is often desirable to attach spatial with non-spatial attribute information. Examples of non-spatial data are road names, addresses, telephone numbers, city names, etc. Since spatial and non-spatial data are so intimately connected, it is not surprising that many of the issues that need to be addressed are in fact database issues.. There are numerous applications in the area of spatial database systems, such as: traffic supervision, flight control, weather forecasting, urban planning, route optimization, cartography, agriculture, natural resources administration, coastal monitoring, fire and epidemics control, precision agriculture and intelligent highways ( [1] , [8] and [14] ). Each type of application deals with different features, scales and spatiotemporal properties.. Efficient evaluation of spatial queries is an important issue in spatial database. Among spatial operations, spatial join is one of the most useful. Intersection is the most common join predicate. Many works point the exact geometry test as the most time consuming operation regarding both I/O and CPU time. [6] show experimental results confirming that the exact geometry test, usually plane-sweep ( [3] and [7] ) is responsible for most of the CPU cost. The I/O cost associated with the exact geometry test is due to the access to the real representation of spatial objects, which can be very large. Spatial joins have been well studied in the literature, and there are many approaches to processing spatial join operations. Considering points, polylines and polygons as the three data types most commonly found in spatial databases, there are nine classes of different spatial joins. For its usefulness and complexity, the polygon join has been the most investigated, while the point join has been the less investigated because of its similarity with the relational join ( [13] ), while there are some proposals for processing polylines × polylines joins and polygon × polyline joins. In order to improve the efficiency, organization and study of indices and filters for spatial data, [6] proposed a three-step architecture for spatial join processing, named Multi-. Step Query Processor. The main target of this architecture is to accelerate the most costly step by reducing the number of spatial objects left to be compared. Such a reduction is done by applying filters in previous steps. This work proposes a new raster approximation suitable to performing spatial joins as a filter in the second step of the MultiStep Query Processor, involving these three common data types (polygon, polyline and point) and the classes of different spatial joins involving them. We propose a raster signature named Three Color Raster Signature (3CRS), based on the Four-Color Raster Signature (4CRS) proposed by [15] . The 3CRS signature has the main advantage of faster generation time and that it can be used to represent polygons, polylines and points (without any specific characteristic). Besides, the same algorithm can be used to evaluate the join predicate involving these three data types. Also, the fast generation time allows on-the-fly signature generation. For instance, instead of storing the signature, it can be generated only when it is needed, saving storage space. In order to evaluate the effectiveness of our proposal, we executed spatial joins using 3CRS against the processing without using signatures and the processing using 4CRS. The experimental tests were executed over real data and the results demonstrated the effectiveness of the approach. This paper is divided in sections, as follows: Section 1 is this introduction; Section 2 surveys the related literature; in Section 3, we present our raster approximation and its implementation as the second step of the MSQP architecture; Section 4 shows the experimental results; finally, in Section 5 we present our conclusions. Spatial operations are very costly. The literature presents different approaches for processing spatial operations. This work proposed a new raster signature, the 3CRS, based on the 4CRS ( [15] ), that can be used as a second filter step in the Multi-Step Query Processor of [6] . 3CRS has the good performance of the 4CRS when compared against the 2-step processing. Moreover, 3CRS has faster generation time over 4CRS and it is also more flexible, since it can be used to represent different spatial data types, such as polygons, polylines and points. Due to its faster generation time, 3CRS can also be calculated on-the-fly, for example, when the optimizer decides to use it in case of intermediate results of multi-joins. For example, the average time spent to perform the experiments using 500 cells (30.48 seconds - Table 7 ) plus the time required to generate the signatures (13.97 seconds - Table 5) is less than the time spent to perform the query using only 2-steps (66.10 seconds - Table 7 ). This makes the 3CRS approach a better choice to be implemented in core spatial databases than 4CRS. Another advantage is that the intersection of two 3CRS (as a result of a previous operation, for example in a multi-join) can be computed using only the 3CRS signatures themselves: it is not necessary to retrieve the object from disk. We only have to compute empty, inconclusive and full cells to find the resulting 3CRS.. The experiments we executed to evaluate the new signature demonstrated the effectiveness of 3CRS. It only needed, on average, 2.85% of the storage requirement to store 3CRS related to the real datasets. It showed a significant reduction in generation time (30% reduction, on average) in relation to 4CRS. The time and number of disk accesses to process the queries where much smaller than the time to execute the queries without the signature. The filter step identifies more than 75% of the candidate pairs, which are not sent to the exact geometry test. In relation to 4CRS, the processing using 3CRS produces a small growth of inconclusive answers. In other words, the increase of the total processing time/number of disk accesses is very small, and encourages the use of 3CRS in processing spatial joins.. As future works, we intend to develop a different storage mechanism to reduce storage requirements. We also plan to evaluate the use of 3CRS to representing polylines and points. Another future work is to implement this signature in SECONDO ( [9] ).

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


Detection and localization of specular surfaces using image motion cues Abstract Successful identification of specularities in an image can be crucial for an artificial vision system when extracting the semantic content of an image or while interacting with the environment. We developed an algorithm that relies on scale and rotation invariant feature extraction techniques and uses motion cues to detect and localize specular surfaces. Appearance change in feature vectors is used to quantify the appearance distortion on specular surfaces, which has previously been shown to be a powerful indicator for specularity (Doerschner et al. in Curr Biol, 2011). The algorithm combines epipolar deviations (Swaminathan et al. in Lect Notes Comput Sci 2350:508-523, 2002) and appearance distortion, and succeeds in localizing specular objects in computer-rendered and real scenes, across a wide range of camera motions and speeds, object sizes and shapes, and performs well under image noise and blur conditions. Surface reflectance estimation is a fundamental problem in computer vision. Not only is known surface reflectance a prerequisite for the successful recovery of 3D shape [3] [4] [5] [6] [7] [8] , but it also provides crucial information about the semantic identity of objects (Fig. 1) . For an artificial agent, visual extraction of reflectance properties may be a crucial prerequisite for properly planning interactions with the environment, for example in the biomedical context [9] , or in real-time, real-world 3D reconstruction scenarios [10, 11] .. Visual estimation of surface reflectance properties is mathematically under-constrained since the object's reflectance properties, its 3D shape and the illumination have to be estimated simultaneously from the 2D patterns of light arriving at the sensor. Thus, the majority of previous work on reflectance classification has relied on specific assumptions about the spectral BRDF [13] [14] [15] , knowledge of camera motion [16, 17] or has been made under specific conditions, such as specialized sensing or lighting [18] . 1 Previously, we showed that reflectance can be rapidly classified based on the statistical differences between the image motion generated by moving diffuse and specular surfaces without any restrictive assumptions [20] . Our approach was inspired by the human visual system which is able to extract surface material properties from single [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] and multiple images [1, [37] [38] [39] with ease, despite the simultaneous shape-material-illumination estimation challenge. More recent evidence suggests that one particular powerful image motion cue that the human visual system seems to be sensitive to when estimating surface reflectance is the distortion of appearance that moving specular surfaces give rise to [1] (Figs. 2, 5 ). 1 Surface reflectance, appearance and identity. The shape in these three photographs is the same but the identity of the object changes as a function of its surface reflectance characteristics. Semantic labeling would be impossible on the basis of shape alone. From left to right ping-pong ball, chrome ball bearing, black plastic sphere. To optimally interact with these objects, e.g., to pick them up without breaking or dropping them, visual estimation of surface reflectance is crucial. This figure has been re-printed with permission from [12] , copyright John Wiley and Sons, 2013. Fig. 2 Appearance distortion on specular objects. a As the object rotates on the platform, the pattern reflected from its surface varies markedly across frames. Appearance distortions tend to be more pronounced at low curvature region [5, 40] where the pattern of distortion varies with the sign of the curvature. Examples of appearance distortions on this object are highlighted in red squares in a and extracted and magnified in b. Appearance distortion is a powerful cue that the human visual system uses to distinguish specular from diffusely reflecting surfaces [1] . In this paper, we utilize this motion feature to develop an algorithm that detects and localizes specular surfaces in real-world scenes. Photographs by Maarten Wijntjes Appearance distortion is an attractive motion feature to be extracted by a specularity detecting algorithm because it does not require any assumptions about the object, the illumination or the camera trajectory, it can be computed from just two images of a motion sequence, and it is a robust feature: it consistently occurs on specular surfaces, regardless of object shape, motion, or the reflected environment. These are significant advantages over previous approaches which classified objects as matte or specular solely on the basis of the bi-modality of the image velocity histogram [20] . We show below (Fig. 3 ) that bi-modality does not predict surface reflectance for complex objects rotating around arbitrary axes, thus its applicability is limited.. We developed an algorithm that relies on scale and rotation invariant feature extraction techniques and uses motion cues to detect and localize specular surfaces in both computerrendered and real image sequences. Appearance change in feature vectors is used to quantify the appearance distortion on specular surfaces. Our algorithm combines a novel appearance distortion cue and epipolar deviations [2] and succeeds in localizing specular objects across a wide range of camera motions and speeds, object sizes and shapes, and performs well under image noise and blur conditions. The paper is organized as follows: in Sect. 2 we review related work and introduce the concept of appearance distortion. In Sect. 3 we introduce the algorithm for detection and localization of specularities in image sequences. Section 4 describes the test sets and in Sect. 5 we present the experimental results for various camera motions, camera speeds, object sizes, object shapes, surface reflectance properties in computer-generated scenes, as well as for real indoor and outdoor videos. We end with a brief discussion in Sect. 6. The specular region detection algorithm that we propose takes a pair of images and outputs bounding boxes of detected specularities. SIFT features [56, 64] not only provide scale and rotation invariance in image analysis, but also feature vectors that quantify local appearance. This makes them a perfect tool to directly capture the appearance distortions 7 that occur on specular surfaces, without relying on optical flow.. A flowchart of the algorithm is shown in Fig. 6 and it involves two stages: in stage 1 epipolar deviations and appearance distortion are computed using SIFT features. These two data are combined in the second stage to yield the specularity field. This field is thresholded and specular image regions are extracted using connected component labeling. We evaluate the algorithm's performance by computing precision-recall curves as defined below. This field quantifies the density of epipolar deviations in the image. See Fig. 7a .

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An automated methodology for performing time synchronous averaging of a gearbox signal without speed sensor In this paper we extend a sensorless algorithm proposed by Bonnardot & al. for angular resampling of the acceleration signal of a gearbox submitted to limited speed fluctuation. The previous algorithm estimates the shaft angular position by narrowband demodulation of one harmonic of the mesh frequency. The harmonic was chosen by trial and error. This paper proposes a solution to select automatically the mesh harmonic used for the shaft angular position estimation. To do so it evaluates the local signal to noise ratio associated to the mesh harmonic and deduces the associated low-pass filtering effect on the time synchronous average (TSA) of the signal. Results are compared with the TSA obtained when using a tachometer on an industrial gearbox used for wastewater treatment. The proposed methodology requires only the knowledge of an approximate value of the running speed and the number of teeth of the gears. It forms an automated scheme which can prove useful for real time diagnostic applications based on TSA where speed measurement is not possible or not advisable due to difficult environmental conditions. Time domain averaging or time synchronous averaging (TSA) is a well adopted signal processing technique which enables periodic waveforms to be extracted from noisy signals [1, 2] . It is particularly suited for the vibration analysis of mechanical systems such as gearboxes, as it enables the vibration of a single gear to be separated from the vibration of the complete system. This technique requires the measurement of the "trigger" signal, i.e. a signal phase-locked with the angular position of one rotating shaft in the system. This speed measurement is typically delivered by a tachometer which delivers one pulse per revolution. An optical encoder (with multiple pulses per revolution) can also be used for a better angular resolution.. In some particular environments however, a speed sensor could be rather inconvenient -if not impossible -to use for condition monitoring purposes. Optical encoders need to be attached to the end of a shaft, which is possible for limited applications only. Optical "pick-up" sensors (tachometers) could be easier to manipulate, but in some environments they can cause problems, for example in high ambient light conditions or where they are subjected to contaminants like dust, oil or steam. In these conditions, a condition monitoring methodology that would operate without the need of any speed measurement would be of great interest in practice.. Recently, an original method has been proposed by Bonnardot & al. [3] for angular resampling of the vibration signal of a gearbox without the need of a speed sensor, when the gearbox is submitted to limited speed fluctuation (i.e. under relatively steady load condition). The idea was to estimate the angular position of the shaft by narrow-band demodulation of one harmonic of the mesh frequency. The harmonic was chosen by trial and error. However, in order for this method to be applicable in a real time and industrial environment, different parameters in the method need to be adjusted in an automated and reliable fashion, i.e. without the need of any visual inspection of the frequency spectrum of the signal or of the estimated speed.. The objective of this paper, which can be viewed as a extension of this previous work [3] , is to propose an automated methodology in order to obtain the time synchronous averaged signal for any particular shaft in a gearbox without speed sensor. In that purpose, different points in the methodology must be discussed: which stage in the gearbox and which mesh harmonic to select, how to quantify the accuracy of the estimated speed and of the TSA, and which interpolation method to use for resampling the signal.. In section 2 we first briefly recall the method proposed in [3] for estimation of the instantaneous shaft angular position and we show that the phase error of the estimation can be quantified by the local signal to noise ratio of the demodulated mesh harmonic. In section 3 we discuss the interpolation method to use for performing angular resampling and TSA, and we quantify the lowpass filtering effect on the TSA due to the phase error by what we call the "cut-off order" of the TSA. These results are then illustrated in section 4 on an industrial gearbox used in wastewater treatment. Finally, a complete methodology is proposed in section 5 for the selection of the mesh harmonic to demodulate and the estimation of the TSA of a particular shaft in the gearbox.. 2 Shaft speed estimation from a mesh harmonic The purpose of this paper was to extend the original idea proposed in [3] for angular resampling by using the mesh vibration of a gearbox and to propose a general methodology that could be used as an automated scheme for condition monitoring of gear systems without the need of a speed sensor. First the angular precision of the shaft has been quantified by the phase error standard deviation, which is related to the local signal/noise ratio (SNR) of the demodulated mesh harmonic. By assuming a normal distribution of the phase error, the corresponding low-pass filtering effect on the TSA can be quantified by its 3dB cut-off order, which depends on both the rank and the local SNR of the selected mesh harmonic.. Comparison on a real case shows good agreement between the predicted and measured (from a tachometer) phase errors of the estimated shaft angular position, and the filtering effect on the TSA signal has also been observed for some mesh harmonics. Furthermore an alternative method for angular resampling of the signal from the estimated speed has been proposed: the Tacho Pulse instants Recovery. This method showed no significant difference compared to the spline interpolation method. Its advantage is to be much less demanding in computation time and in memory space, especially for relatively long signal duration, and is thus better adapted to real time applications. Finally a methodology has been proposed for estimation of the TSA without speed sensor, which requires only an a priori estimation of the shaft speed and the number of teeth of the meshing gears. The choice of the stage to use has been discussed and will generally depend on the application considered. The proposed methodology forms an automated scheme which could be easily implemented and can be useful for condition monitoring applications where speed measurement is not advisable due to difficult environmental conditions. One drawback of the method is obviously that no more angular reference is available for the TSA for the localisation of a fault on the gear. A Relation between phase error and local SNR in the demodulation band. The signal from model (1) after band-pass filtering of mesh harmonic k and frequency shift to zero is written. where ϕ k (t) = φ k (t) + Φ k is the phase modulation to be recovered and b(t) is the noise present in the filter bandwidth, assumed zero mean and with variance σ The analytic signalx is represented as a vector in the complex plane on figure A.1. At one given instant t, the effect of the additive noise of amplitude B will be to create a phase error δ on the estimated phase ϕ. The resulting position of the analytic signal is located on a circle of radius B, all points on this circle being equiprobable since angle β is assumed randomly distributed. From this figure we can write the trigonometric relation: tan δ = B sin β X k + B cos β (A.5). By assuming a relatively good SNR, the noise amplitude B remains small compared to X k , so that (A.5) can be simplified by tan δ δ B sin β X k (A.6). The mean phase error of δ is zero. The variance is Due to the phase error of the shaft angular position estimation, the tacho pulse instant at rotation i is estimated with an jitter error i . After angular resampling, the shaft ith rotation period x i (t) can be written. where s(t) is the deterministic part of the signal which is periodic with the rotation period of interest and b(t) represents the random and non-synchronous sources. The "ideal" time synchronous averaged (TSA) signal, i.e. after sufficient number of averaging, is. 2). The TSA being exactly periodic, its spectrum (orders) is simply computed by a Fourier transform. Assuming commutativity with expectancy (linear opera-tors) we get:. where S(f ) = F T {s(t)} is deterministic. By denoting p( i ) the probability density function of random variable i , we obtain: where Φ(f ) represents the Fourier transform of p( i ), which acts as a low-pass filter on the TSA spectrum. The narrower is p( i ) (the lower is the phase error), the higher is the cut-off frequency (or cut-off order) of filter Φ(f ) and the more orders of signal s(t) can be recovered in the TSA. A particular problem mentioned in [3] can arise when a "parasite" component is included in the demodulation bandwidth of a particular mesh harmonic. The effect of the parasite component will be first to decrease the local SNR and so to lower the cut-off order for this harmonic, and second to create an additional strong fluctuation in the estimated speed, so that it is likely that the mesh harmonic will not pass the speed fluctuation test in that case. Table 3 Selection of input stage mesh harmonic for estimating the inner shaft TSA. The third harmonic is here selected (highest cut-off order). The SNR of first harmonic is low here due to a parasite component close to this mesh. cut-off order 84 938 1478 448 1376 Table 3 presents an interesting case when estimating the inner shaft TSA for a different type of load coupled to the same gearbox. In this case the input stage is used and the mesh frequency is estimated at 452.5Hz after peak detection. The filter half bandwidth is set to B max = 2.7Hz (inner shaft speed is 5.4Hz).. The local SNRs and the cut-off orders are estimated for the first five mesh harmonics (see table 3 ). The third harmonic is here selected due to its highest cut-off order. Note that the first harmonic SNR is abnormally low here: an inspection of the spectrum reveals an electrical component at 450Hz which is inside the demodulation bandwidth of this harmonic. This parasite component is the reason for this low SNR. The estimated speed fluctuation for the third harmonic is 0.11% (0.19% max.). By using first harmonic it would have been 0.33% due to the parasite, which is however still in the allowed range (0.58%). Thus in this particular case the parasite is discarded by the SNR estimation rather than by the test on the speed fluctuation.. The proposed methodology has also been tested with success on other types of industrial gearboxes, especially with spur gears. However the helical gearbox presented here was a more difficult case since the mesh harmonics were found to be lower than that of the spur gears. The tested gearboxes being used under relatively steady loading conditions, we have not found so far cases where the speed fluctuation limitation prevented the method to perform. It should be mentioned however that one drawback of the method is that, contrary to a tachometer, we have obviously no more angular reference available here for the localisation of a fault on the gear, as shown on figure 11.

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


Model for biological communication in a nanofabricated cell-mimic driven by stochastic resonance Cells offer natural examples of highly efficient networks of nanomachines. Accordingly, both intracellular and intercellular communication mechanisms in nature are looked to as a source of inspiration and instruction for engineered nanocommunication. Harnessing biological functionality in this manner requires an interdisciplinary approach that integrates systems biology, synthetic biology, and nanofabrication. Here, we present a model system that exemplifies the synergism between these realms of research. We propose a synthetic gene network for operation in a nanofabricated cell mimic array that propagates a biomolecular signal over long distances using the phenomenon of stochastic resonance. Our system consists of a bacterial quorum sensing signal molecule, a bistable genetic switch triggered by this signal, and an array of nanofabricated cell mimic wells that contain the genetic system. An optimal level of noise in the system helps to propagate a time-varying AHL signal over long distances through the array of mimics. This noise level is determined both by the system volume and by the parameters of the genetic network. Our proposed genetically driven stochastic resonance system serves as a testbed for exploring the potential harnessing of gene expression noise to aid in the transmission of a timevarying molecular signal.Published by Elsevier B.V. Given the remarkable properties of the cell [21, 66] coupled with its ability to communicate and interact with other cells, it is not surprising that the idea of harnessing biological functions for engineering applications at the nanoscale has drawn much attention [52, 31, 23, 1] . Recent years have seen the amassing of a tremendous wealth of data from the sequencing of new organisms and from high throughput expression experiments. At the same time, great progress has been made towards developing a fundamental understanding of individual cell function. The availability of well characterized biological components coupled with a deeper understanding of cell function has led to efforts both to engineer living cells and to create biolike functionality in non-living substrates.. Living cells ranging from mammalian cells to bacteria communicate with one another using a variety of molecules such as calcium ions [60] , peptides [43] , and alcohols [15] . Here, we focus on quorum sensing systems found in Gram negative bacteria. These systems enable cells to coordinate certain functions in a population density dependent fashion [74] . In Gram negative bacteria, most quorum sensing systems are comprised of an I-protein, an R-protein, and a small signal molecule, typically an N-acyl homoserine lactone (AHL). This AHL signal can diffuse through the cell membrane into the surrounding environment. At low cell densities, only basal levels of AHL are produced. However, as local cell density increases, AHL can accumulate within the cell such that AHL binds the R-protein, changing its conformation and enabling it to bind and activate target DNA promoters. Often, one of the activated promoters controls I-protein synthesis itself, and since I-protein catalyzes AHL synthesis, a positive feedback loop is formed. Therefore, quorum sensing can allow bacteria to coordinate behavior in a density dependent manner. In nature, these quorum sensing systems have been shown to coordinate a wide range of processes such as virulence factor production [81, 14] , biofilm formation [19] , and antimicrobial resistance [29] .. Although bacterial cells can coordinate behavior at the population level, studies at the single cell level have revealed the importance of noise in gene expression. Noise is often significant due to the low number of many molecular species in the cell and due to the random and discrete nature of reactions driving cell function. Cells have evolved to either minimize or utilize this stochastic noise. In engineered systems, a great amount of work has focused on minimizing noise, especially in the field of communications. While there are some examples of using noise to improve function, such as dithering, great potential lies in the area of harnessing noise, especially in systems that operate at and below the scale of the cell.. We propose a signal propagation system that utilizes genetic components of bacterial quorum sensing systems and also harnesses noise. The signal in our system is a time-varying AHL molecule concentration. This AHL signal enters one well in an array of several nanofabricated wells. Each well contains a bistable genetic switch that can be toggled by the signal. This switch can help to amplify the signal and aid in its propagation through the array of wells. However, optimal signal propagation is realized when a particular level of noise is present in the system. This phenomenon is referred to as stochastic resonance and is further described in Section 2.. Our study demonstrates the rich potential of harnessing biological components for engineered nanocommunication networks. We also demonstrate the importance of considering the role of noise in nanoscale systems, and we show that function can actually be improved by tuning the level of noise. Furthermore, the use of nanofabricated structures enables the flexible, robust, and well-defined layout of communication channels.. Since our proposed system connects several different fields of research, we discuss background information and related work in Section 2. We describe our proposed system for stochastic resonance in Section 3 and detail materials and methods in Section 4. We present the model for our system in Section 5, and the modeling results in Section 6 demonstrate functional stochastic resonance for a variety of different conditions. In Section 7, we discuss these results and present concluding remarks.

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


Exploiting path diversity in the link layer in wireless ad hoc networks We develop an anycast mechanism at the link layer for wireless ad hoc networks. It is well-known that in wireless ad hoc networks, the "link" between two nodes is a "soft" entity [7] . From basic communication theory, its existence is governed by whether the signal to interference plus noise power ratio (SINR) at the receiver exceeds a given threshold (called the receive threshold ). is determined by the the data rate, the modulation technique, receiver design, and the target bit error rate (BER) the receiver is able to withstand (i.e., able to correct using coding techniques). SINR is again influenced by transient factors such as transmit power, distance between the transmitter and receiver, multipath fading, and interference and noise powers reaching the receiver. Multipath fading [20] is caused by different components of the transmitted signal being reflected by the surrounding objects, and reaching the receiver via paths of different lengths, and combining either constructively or destructively. Interference is caused by signals from other, unintended nearby transmitters. Both fading and interference could be time varying.. Significant changes in fading and interference levels (beyond that can be masked by changes in sending data rate [21, 10] ) 1 may lead to transient "loss" of a link. This loss is often sufficient for many common routing and transport protocols to react -either to repair routes or to bring down the offered load. This leads to various operational inefficiencies, given that this loss is transient. Thus, there is a need to incorporate mechanisms that can "withstand" this loss of link at shorter time-scales.. Assume that multiple routing paths have been computed from the source and also from the intermediate nodes to the destination. Typically, the routing layer decides which of the several paths should be used for data forwarding and then the MAC layer is responsible to deliver the packet to the next hop along the chosen path. A better, alternative approach would be, for the link layer, to choose the next hop by observing the channel conditions on all possible next hop links. This "channel state-based" anycasting should improve performance, requiring very little operational coordination between the routing and MAC layers.. The goal of this paper is to develop an anycast MAC layer protocol to do this "channel state-based" next hop selection. The rest of the paper is organized as follows. In Section 2, we provide an overview of the 802.11 MAC protocol operation and describe the properties of a fading channel. In Section 3, we describe our extension of 802.11 that implements anycasting to do the channel state based next hop link selection. We also describe the essentials of the the multipath routing layer. Section 4 is devoted to performance evaluation. We analyze the performance of the anycast mechanism for a grid network via analytical mod- 1 Note that while physical layer techniques can mask effect of fading and interference, this work does not target physical layer techniques. Here, the interest is working on beyond physical layer capabilities, by exploring alternative paths.. eling, and an experimental testbed using Berkeley motes, and proceed to detailed simulation-based evaluations using the ns-2 simulator. We describe the related work in Section 5 and conclude in Section 6. We have proposed an anycast mechanism at the link layer that forwards packets to the best suitable next hop link to enable efficient packet forwarding on a multihop route. This mechanism is dependent on the availability of multiple next hops, which could be computed by a multipath routing protocol. We have designed the link layer protocol as an extension of the popular IEEE Standard 802.11 and carried out an extensive performance evaluation using both an experimental testbed and detailed simulation modeling. The anycast protocol provides a significantly better packet delivery relative to 802.11 in a variety of ad hoc network models, both regular and random, stationary and mobile. The performance differential was observed to increase when path lengths increase. In [13] , a combination of forwarding and MAC layer protocol called selection diversity forwarding has been proposed. Here, the data frame is multicast to a set of candidate nodes, each of which send back ACK control packets. Then only one node is chosen from this set by the forwarding node and issued a forwarding order control packet, which is again acknowledged. This is the node that will forward the data packet further; and others will discard the packet. Selection diversity forwarding has been shown to perform better than fixed forwarding mechanisms, such as NFP (nearest with forward progress) or MFR (most forward with fixed radius) for Rayleigh fading channels.. Several recent articles build on the 802.11 standard to estimate the channel condition and automatically adapt the sending bit rate to match the channel conditions. However, they still use single next hop, and use the unicast forwarding model in 802.11. In the RBAR protocol [10] , the receiver estimates the channel condition by the physical layer analysis of the RTS packet and determines the best rate to send the data frame. The control packets are sent using the base (lowest) rate so that they are always successfully delivered. The OAR protocol [21] extends this idea to send multiple back-to-back packets when the channel condition is determined to be good.. In [19] an adaptive transmission protocol is used that adjusts the power and code rate of the transmitted signal to adapt to the channel conditions. But this scheme does not work when a poor quality link has not been used by the routing protocol for some time. The work suggests an alternate forwarding technique dependent on multipath routing that alters routing paths to discover links that may have improved recently.. Three recent papers also motivate use of anycasting in the MAC layer. In [5] authors motivate anycast as a generalpurpose MAC layer method to take decisions on packet forwarding in short time scales. They describe potential use of anycast from the point of view of improving spatial reuse and reducing interference. In the same forum, an "opportunistic" routing mechanism is presented [3] , which is very similar in spirit to the selection diversity forwarding work described earlier. Another protocol called GeRaF [25] also contains similar ideas, but has been specifically applied for geographic forwarding. Here, the interest is more on modeling, rather than a practical implementation.. Two recent studies [12, 22] used a protocol similar to ours in spirit, however, for a different goal. 4 These protocols exploit multiuser diversity in the context of an access point-based system. Similar exploitation of multiuser diversity was also explored earlier in channel state based scheduling [2] protocols. In contrast, we exploit path diversity.

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


Multiobjective genetic rule selection as a data mining postprocessing procedure In this paper, we show the usefulness of multiobjective genetic rule selection as a postprocessing procedure in data mining for pattern classification problems. First we extract a prespecified number of rules using a data mining technique. Then we apply multiobjective genetic rule selection to the extracted rules. Experimental results show that multiobjective genetic rule selection significantly decreases the number of extracted rules while improving their classification accuracy. Evolutionary multiobjective optimization (EMO) is a very active research area in the field of evolutionary computation [2] . The main advantage of EMO algorithms is that multiple tradeoff solutions are simultaneously obtained by their single run. Recently EMO algorithms have been employed in some studies on modeling and classification. For example, an EMO algorithm was used to generate multiple neural networks on a receiver operating characteristic curve [8] . Gonzalez et al. [5] generated multiple radial basis function networks of different sizes. In [9] , an EMO algorithm was used in Pittsburgh-style learning classifier systems. In some studies on fuzzy systems [1] , [6] , [7] , EMO algorithms were used to analyze the tradeoff structure between the accuracy and the interpretability of fuzzy rule-based systems. In this paper, we examine the usefulness of multiobjective genetic rule selection as a postprocessing procedure in data mining. In this paper, we demonstrated that multiobjective genetic rule selection improved the accuracy-complexity tradeoff curve of heuristically extracted classification rules. This improvement was observed in our computational experiments on all the six data sets for training patterns and the five data sets for test patterns except for the Cleveland heart disease data. Since a large number of rules are usually extracted in data mining, multiobjective genetic rule selection seems to play a significant role as a postprocessing procedure to decrease the complexity of extracted rules.. This work was partially supported by Japan Society for the Promotion of Science (JSPS) through Grand-in-Aid for Scientific Research (B): KAKENHI (17300075).

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Human Motion Tracking by Registering an Articulated Surface to 3D Points and Normals Abstract-We address the problem of human motion tracking by registering a surface to 3D data. We propose a method that iteratively computes two things: maximum likelihood estimates for both the kinematic and free-motion parameters of a kinematic human-body representation, as well as probabilities that the data are assigned either to a body part or to an outlier class. We introduce a new metric between observed points and normals on one side and a parameterized surface on the other side, the latter being defined as a blending over a set of ellipsoids. We claim that this metric is well suited when one deals with either visual-hull or visualshape observations. We illustrate the method by tracking human motions using sparse visual-shape data (3D surface points and normals) gathered from imperfect silhouettes. WE address the problem of recovering articulated human-motion parameters using 3D data gathered from multiple image sequences. We advocate that this type of data has several advantages over 2D data: It is less ambiguous and it is less sensitive to selfocclusions. Three-dimensional features may be obtained by stereo [5] , [6] , [12] . Alternatively, one can capitalize on 3D shape from silhouettes. In general, 2D silhouettes are explicitly associated with a 3D smooth surface [9] , [10] , [12] . Another way to use silhouettes is to infer volumetric representations and to fit articulated models to the voxels thus obtained [4] , [13] or to extract skeletal representations from these voxels [3] . It is also possible to infer 3D surfaces from silhouettes, namely, the visual hull [2] or the visual shape [8] . The advantage of surface-from-silhouettes is that it allows the recovery of both 3D surface points and surface normals. Moreover, there is no matching process associated with the reconstruction algorithm. Visual-hull algorithms have been proven to be extremely useful for recovering 3D meshes, which, in turn, are very useful for surface rendering. The drawback is that they need perfect silhouettes. Alternatively, visual-shape methods (such as the one described in [8] ) produce sparse surface descriptions (points and normals) and can operate on imperfect silhouettes.. In this paper, we present a new method for tracking human motion based on fitting an articulated implicit surface to 3D points and normals. There are two important contributions. First, we introduce a new distance between an observation (a point and a normal) and an ellipsoid. We show that this can be used to define an implicit surface as a blending over a set of ellipsoids that are linked together to form a kinematic chain. Second, we exploit the analogy between the distance from a set of observations to the implicit surface and the negative log-likelihood of a mixture of Gaussian distributions. This allows us to cast the problem of implicit surface fitting into the problem of maximum likelihood (ML) estimation with hidden variables. We argue that outliers are best described by a uniform component that is added to the mixture and we formally derive the associated expectationmaximization (EM) algorithm.. Casting the data-to-model association problem into ML with hidden variables has already been addressed in the past within the framework of point registration [14] , [11] , [6] . In [5] , observations are deterministically and iteratively assigned to each individual body part. We appear to be the first to apply a probabilistic datato-model association framework to the problem of fitting a blending of ellipsoids to a set of 3D observations and to explicitly model outliers within this context.. The remainder of this paper is organized as follows: Section 2 describes how to compute a distance between a 3D observation (point and normal) and an ellipsoid, and how to build an implicit articulated surface based on this distance. Finally, it introduces the concept of a probabilistic implicit surface. Section 3 describes the formal derivation of the EM algorithm in the case of implicit surface fitting. Section 4 describes experiments with simulated data and with multiple-camera video data. In this paper, we have described a method for tracking articulated motion with several cameras. We have introduced a new metric that measures the discrepancy between observations (composed of both 3D points and 3D normals) and an articulated implicit surface. This metric is more powerful than previously used distance functions because it allows for less ambiguous associations between the data and the model. Moreover, it is well suited when one deals with either visual-hull or visual-shape representations of the data.. We cast the data-to-model fitting process into a robust probabilistic framework. We showed that there is a strong similarity between the mathematical representation of an implicit surface and a mixture of Gaussian distributions. We explored this similarity and we showed that the articulated motion tracking problem can be formulated as ML with hidden variables. We added a uniform component to the mixture to account for outliers. We formally derived an algorithm that computes ML estimates for the motion parameters within the framework of EM. Therefore, the tracker may well be interpreted in the framework of robust data clustering, where the observations are assigned to one of the ellipsoids or to an outlier component.. There are many questions that remain open and that we plan to investigate in the near future: The algorithm may be trapped in local minima if it is not properly initialized; there are some similarities between our robust tracker and the use of M-estimators and these similarities deserve further investigation. There are other interesting issues such as a thorough and quantitative evaluation of the results and their comparison with marker-based motion capture systems and the possibility to capture several articulated motions at once.

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


Characterization of Glushkov automata Glushkov algorithm computes a nondeterministic nite automaton without -transition and with n + 1 states from a simple regular expression having n occurrences of letters. The aim of this paper is to give a set of necessary and su cient conditions characterizing this automaton. Our characterization theorem is formulated in terms of directed graphs. Moreover these conditions allow us to produce an algorithm of conversion of a Glushkov automaton into a regular expression of small size. During the last forty years, the synthesis of automaton The best known property of Glushkov automata is certainly the fact that a given state is always reached using the same letter. However this property is not su cient to have an automaton be a Glushkov one. Our aim is to study structural properties of Glushkov automata and to establish a characterization of these automata. Beyond its theoretical interest this study yields an algorithm computing a regular expression from a Glushkov automaton. This expression is particularly \short" (it contains n?1 occurrences of letters if the initial Glushkov automaton has n states). Let us notice that our characterization is entirely formulated in terms of graphs. Section 2 aims at de ning the notion of Glushkov automaton; it is made up of theoretical recalls on words, languages, automata and regular expressions. The third section gathers de nitions and notations we use for the characterization in terms of graphs. Section 4 enumerates necessary conditions to have an automaton be a Glushkov one. The last section establishes the characterization theorem. Let be a nite set of symbols called the alphabet. Elements of are denoted by a; b; c; ::: and are called letters. A word over the alphabet ; denoted by u; v; w; ::: is a nite sequence (a 1 ; a 2 ; :::; a n ) of symbols of , which can be written a 1 a 2 :::a n . The empty word is denoted by ": The length of a word u, denoted by juj is the number of symbols in which are in u. If u = a 1 a 2 :::a n and v = b 1 b 2 :::b m are two words on , their concatenation uv is the word a 1 a 2 :::a n b 1 b 2 :::b m . The set of all words over is denoted by . With the operation of concatenation, is the free monoid generated by . + is the free semigroup generated by , which is exactly ? f"g. A language over is a part L of . The empty language is denoted by ;. De nition 2.1 Let L and L 0 be two languages over . We can de ne several operations on these languages. We have : De nition 2.2 (regular languages) The set Reg( ) of regular languages over is the smallest set of languages over that veri es the following conditions :. 1. Reg( ) contains ;; f"g and fag, for all a 2 , 2. Reg( ) is closed under union, concatenation product and Kleene closure. Kleene has characterized the class Reg( ) of regular languages in terms of (simple) regular expressions.. De nition 2.3 Regular expressions over an alphabet are recursively de ned as follows:. ; is the regular expression that denotes the empty language, " is the regular expression that denotes the language f"g, a is the regular expression that denotes the language fag where a 2 , if E and F are regular expressions representing the languages L(E) and L(F), then the following expressions are regular : Q is a nite set called set of states, is an alphabet, I Q is the set of initial states, F Q is the set of nal states, Q Q is the set of arrows. An automaton is represented by a labeled graph in which the vertices are the states of the automaton and the edges are the labeled arrows.. De nition 2.5 An automaton M = (Q; ; I; F; ) is deterministic (DFA) if and only if there is only one initial state : I = fs I g, and, for all (q; a) 2 Q there is at most one state p such that (q; a; p) 2 .. A path of length n in M is a sequence c = f 1 f 2 :::f n of n consecutive arrows f i = (p i ; a i ; q i+1 ) with i = 1; :::; n, and p i = q i for i = 2; :::; n. The label of a path c, is the word a 1 a 2 :::a n . A word w = a 1 a 2 :::a n is recognized by the automaton Our study of structural properties of Glushkov automata leads to a theorem of characterization for theses automata. We intend to use this characterization in order to simplify the expression computed by classical methods of conversion of an automaton into an expression. We draw your attention on the fact that the Maple package "Automap" developped by P. Caron Ca96a] Ca96b] proves to be an e cient tool to undertake this type of survey.

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


Convolution operations arising from Vandermonde matrices Abstract-Different types of convolution operations involving large Vandermonde matrices are considered. The convolutions parallel those of large Gaussian matrices and additive and multiplicative free convolution. First additive and multiplicative convolution of Vandermonde matrices and deterministic diagonal matrices are considered. After this, several cases of additive and multiplicative convolution of two independent Vandermonde matrices are considered. It is also shown that the convergence of any combination of Vandermonde matrices is almost sure. We will divide the considered convolutions into two types: those which depend on the phase distribution of the Vandermonde matrices, and those which depend only on the spectra of the matrices. A general criterion is presented to find which type applies for any given convolution. A simulation is presented, verifying the results. Implementations of all considered convolutions are provided and discussed, together with the challenges in making these implementations efficient. The implementation is based on the technique of Fourier-Motzkin elimination, and is quite general as it can be applied to virtually any combination of Vandermonde matrices. Generalizations to related random matrices, such as Toeplitz and Hankel matrices, are also discussed. Certain random matrices have in the large dimensional limit a deterministic behavior of the eigenvalue distributions, meaning that one can compute the eigenvalue distributions of AB and A + B based only on the individual eigenvalue distributions of A and B, when the matrices are independent and large. The process of computing theses eigenvalues is called convolution, or de-convolution when one would like to compute the inverse operation. Gaussian-like matrices fit into this setting, and the concept which can be used to find the eigenvalue distribution from that of the component matrices in this case is called freeness [1] . Free probability theory [1] , which uses the concept of freeness, is not a new tool but has grown into an entire field of research since the pioneering work of Voiculescu in the 1980's ( [2] , [3] , [4] , [5] ). However, the basic definitions of free probability are quite abstract and this has hinged a burden on its actual practical use. The original goal was to introduce an analogy to independence in classical probability that can be used for non-commutative random variables like matrices. These more general random This work was supported by Alcatel-Lucent within the Alcatel-Lucent Chair on flexible radio at SUPELEC Øyvind Ryan is with the Centre of Mathematics for Applications, University of Oslo, P.O. Box 1053 Blindern, NO-0316 Oslo, Norway, oyvindry@ifi.uio.no. Mérouane Debbah is with SUPELEC, Gif-sur-Yvette, France, merouane.debbah@supelec.fr variables are elements of what is called a noncommutative probability space. The convolution/deconvolution techniques used are various. The classical ones are either analytic (using R and S transforms [6] , [1] ) or based on moments [7] , [8] , [9] , [10] . Recent deconvolution techniques based on statistical eigen-inference methods using large Wishart matrices [11] , random Matrix theory [12] or other deterministic equivalentsà la Girko [13] , [14] , [15] , [16] were proposed and are possible alternatives. Each one has its advantages and drawbacks. Unfortunately, although successfully applied [17] , [18] , all these techniques can only treat very simple models i.e. the case where one of the considered matrices is unitarily invariant. This invariance has a special meaning in wireless networks and supposes that there is some kind of symmetry in the problem to be analyzed. The moments technique, which will be the focus of this work, is very appealing and powerful in order to derive the exact asymptotic moments of "nonfree matrices", for which we still do not have a general framework. It requires combinatorial skills and can be used for a large class of random matrices. The main drawback of the technique (compared to other tools such as the Stieltjes transform method [19] ) is that it can rarely provide the exact eigenvalue distribution. However, in many applications, one needs only a subset of the moments depending on the number of parameters to be estimated.. Recently [20] , Vandermonde matrices (which do not fall within the free probability framework) were shown to be a case of high interest in wireless communications. Such matrices have various applications in signal reconstruction [21] , cognitive radio [22] , physical layer security [23] , and MIMO channel modeling [24] . A Vandermonde matrix with entries on the unit circle is on the form . V will in this paper always denote a Vandermonde matrix, and its dimension will be denoted N × L. The ω 1 ,...,ω L , also called phase distributions, will be assumed i.i.d., taking values in [0, 2π). We will also assume, as in many applications, that N and L go to infinity at the same rate, and write c = lim N →∞ L N for the aspect ratio. If necessary, we will write V ω to emphasize the actual phase distribution, or V ω,c to also emphasize the aspect ratio. In [20] , the limit eigenvalue distributions of combinations of V H V and diagonal matrices D(N ) were shown to be dependent on only the limit eigenvalue distributions of the two matrices. Important combinations are the multiplicative and additive models,. In the large N -limit, (2) thus gives rise to two convolution operations, 1). which thus depend only on the input spectra. Here lim is used to denote the limit of the eigenvalue distribution of the considered matrix, in an appropriate metric. However, it is not clear from [20] how 1) can be computed algorithmically, as only sketches for this were provided. We also have the operations 2) lim N →∞ D(N )VV for which it is unknown whether the result only depends on the spectra. This case happens in practical scenarios (for cognitive applications [22] as well as secure transmissions [23] ) when a Vandermonde precoder V is used in a given Toeplitz channel matrix D(N ) independent from V. One can then compute cognitive and secrecy rates. When we replace with independent Vandermonde matrices V 1 and V 2 which may or may not have the same phase distributions, it is also unknown if the convolution operations 3). and lim N →∞ (. , only depend on the spectra of V 1 and V 2 . These cases are important for the recovery of the distribution of sensors (which are deployed in a clustered manner with different mean positions) and in the case of MIMO multi-fold scattering [25] .. Expressions such as 4), when different types of matrices are multiplied, will in the following be called mixed moments.. In this contribution we explain which of the above operations depend only on the spectra of the matrices, state expressions for those convolutions (in fact, we also state expressions for the cases where the result can not be written in terms of the spectra), explain how these expressions have been obtained algorithmically, and explain an accompanying software implementation [26] , [27] of the corresponding algorithms. We also attempt to complete the analysis started in [20] , by stating a very general criterion for when the mixed moments of (many) Vandermonde matrices and deterministic matrices depend only the input spectra:. If there are no terms on the form V H 1 V 2 in a mixed moment, with V 1 and V 2 independent and with different phase distributions, the mixed moment will depend only on the spectra of the input matrices. In all other cases, we can't expect dependence on just the spectra of the input matrices, and the mixed moment can depend on the entire phase distributions of the input matrices.. The software implementation can in fact be extended to handle all cases which meet this criterion, as well as cases where knowledge of the phase distribution also is required. In this way it is an indispensable tool, as it automates the very tedious computations inherent in the presented formulas, for which no simple expressions are known.. Concluding from the criterion, 1) will depend only on the spectra (as shown in [20] ), as does 3). 4) may not depend on only the spectra when the two phase distributions are different. Despite this, 4) is interesting in its own right, since it has a geometric interpretation in terms of phase distributions, and is therefore handled separately. For case 2), we state more generally that when the pattern D(N )V appears in a mixed moment, we can not expect dependence only on the spectrum.. It turns out that other types of random matrices can use the same methods as for Vandermonde matrices to compute their moments, such as Toeplitz matrices and Hankel matrices. We will explain how the software implementation has been extended to handled these matrices as well.. The paper is organized as follows. Section II provides background essentials on random matrix theory needed for the main results, which are stated in III. The results include the precise statement of the criterion above for when we only have dependence on the spectra of the matrices, results on the convolution operations 1)-4), and extensions to related random matrices such as Toeplitz and Hankel matrices. A generalization of our results to almost sure convergence of matrices is also made. All presented formulas are obtained from the implementation, and the major pieces in this implementation are gone through in Section IV, such as partition iteration, and Fourier-Motzkin elimination [28] . Section V presents a simulation which verifies the results.

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


Location leakage in distance bounding: Why location privacy does not work In many cases, we can only have access to a service by proving we are sufficiently close to a particular location (e.g., in automobile or building access control). In these cases, proximity can be guaranteed through signal attenuation. However, by using additional transmitters an attacker can relay signals between the prover and the verifier. Distance-bounding protocols are the main countermeasure against such attacks; however, such protocols may leak information regarding the location of the prover and/or the verifier who run the distance-bounding protocol.In this paper, we consider a formal model for location privacy in the context of distance-bounding. In particular, our contributions are threefold: we first define a security game for location privacy in distance bounding; secondly, we define an adversarial model for this game, with two adversary classes; finally, we assess the feasibility of attaining location privacy for distance-bounding protocols. Concretely, we prove that for protocols with a beginning or a termination, it is theoretically impossible to achieve location privacy for either of the two adversary classes, in the sense that there always exists a polynomially-bounded adversary winning the security game. However, for so-called limited adversaries, who cannot see the location of arbitrary provers, carefully chosen parameters do, in practice, enable computational location privacy. Often, our location is critical in order to gain access to places and/or services. For instance, in applications such as automobile access control the key (prover) needs to be close enough to the car lock (verifier) in order to unlock it [17] . In some cases, unlocking the car may in fact also start the car (in passive keyless entry and start (PKES) systems [18] ). If the proximity check is performed through signal attenuation, an adversary may easily perform man-in-the-middle attacks by relaying messages between the communicating parties (provers and verifiers), while these parties are situated far from each other. Thus, in the automobile example, an adversary may unlock the car even if the car key (the prover) is located very far. This type of attack (called mafia fraud [11] ) can also be mounted against bankcards [13] , mobile phones [19] , proximity cards [20] , and wireless ad-hoc networks [21, 27] .. Distance-bounding (DB) protocols are meant to counteract man-in-themiddle relay attacks in authentication schemes. They are challenge-response authentication protocols, that allow the verifier, by measuring the time-offlight of the messages exchanged, to calculate an upper bound on the prover's distance (as well as checking the validity of the responses which usually ensure authentication). DB protocols were first introduced by Brands and Chaum [6] to preclude relay attacks in ATM systems. Subsequently, numerous DB protocols were proposed [22, 30, 9] and many attacks against them have been published [2, 3, 15] . DB protocols have also been analysed for the case of noisy channels [23] and the optimal setting of security parameters [12, 25] . To the best of our knowledge [4, 5] describes the latest most secure distance-bounding protocol against all known attack modes. Another provably-secure protocol attaining quite strong terrorist-fraud resistance requirements has been recently published in [16] .. Location privacy was introduced in the context of distance bounding by Rasmussen andČapkun [28] , who noted that distance-bounding protocols may leak further location-related information than just the fact that the prover is within the maximum allowed distance from the verifier. This information leakage follows from the measurement of the messages' arrival times.. To combat this, Rasmussen andČapkun [28] proposed a privacy-preserving distance-bounding protocol (denoted here as the RČ protocol). Though the M A N U S C R I P T A C C E P T E D protocol in [28] claims to preserve location privacy, we note that location privacy has never been formalized in the literature. Additionally, the RČ protocol has been shown to be susceptible to a non-polynomial dictionary attack which may reveal the prover's and verifier's locations [1] as well as to a mafia fraud attack [24] . Mitrokotsa et al. [24] have proposed a new distancebounding protocol called Location-Private Distance Bounding (LPDB) that improves the basic construction of the RČ protocol and renders it secure against the latter attack.. Distance bounding can also be extended to location verification [32] (also known as secure positioning [31] ), where multiple verifiers interact with a single prover. In that case the location of the prover can be determined using the intersection of the bounding spheres surrounding each verifier. This approach is also taken under consideration in the recent work regarding position-based cryptography [10] . Our approach here is different as we consider a single verifier and many provers, and we thus only achieve distance bounding, and not secure positioning. Moreover, in position-based cryptography all the adversaries have the same knowledge as the prover, including the secret key. However, in our model, we do not allow the adversary knowledge of the secret key, as that would allow it to trivially distinguish between the two provers in the location privacy game, without actually requiring any location data.. We also mention the recent work on localisation privacy by Burmester [7, 8] , where location is used in a steganographic sense (such that provers are convinced that verifier-generated challenges are honest, and they do not reveal their presence to adversaries). However, very notably the constructions in [8] require provers to be aware of their position/location, which is a strong assumption in generic authentication/distance-bounding scenarios. In this case, location is used as a part of the verifier's challenge, and the prover verifies that the location is sufficiently close to its own location.. Contributions: In this paper, we address precisely the topics of location privacy in distance-bounding. Our contributions are threefold:. 1. We first define a classical left-or-right indistinguishability game for location privacy in distance-bounding protocols. In this game, the adversary knows its distance to the verifier V and can create provers P at arbitrary distances from itself and V.. 2. For this location privacy game, we consider two main adversarial classes: omniscient and limited adversaries. Omniscient adversaries capture an M A N U S C R I P T

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The controller placement problem Network architectures such as Software-Defined Networks (SDNs) move the control logic off packet processing devices and onto external controllers. These network architectures with decoupled control planes open many unanswered questions regarding reliability, scalability, and performance when compared to more traditional purely distributed systems. This paper opens the investigation by focusing on two specific questions: given a topology, how many controllers are needed, and where should they go? To answer these questions, we examine fundamental limits to control plane propagation latency on an upcoming Internet2 production deployment, then expand our scope to over 100 publicly available WAN topologies. As expected, the answers depend on the topology. More surprisingly, one controller location is often sufficient to meet existing reaction-time requirements (though certainly not fault tolerance requirements). Historically, control plane functions in packet networks have been tightly coupled to the data plane. That is, the boxes that decide where and how to forward packets have Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. also performed the actual packet forwarding. A more recent trend is to decouple the forwarding and control planes. While the details vary, the common change is moving the control-plane logic to a set of dedicated control-plane-only boxes -controllers -that each manage one or more simplified packet-forwarding boxes. This trend is highlighted by a range of industry products and academic prototypes: BGP Route Reflectors [2] , RCP [7] , MPLS Path Computation Elements with Label-Switched Routers [5] , enterprise wireless controllers with CAPWAP access points [3] , the planes of 4D [9, 22] , Ethane [8] , and in Software-Defined Networks, OpenFlow-based switches and controllers [12, 16, 18] .. However, the performance characteristics of these decoupled architectures are largely unstudied, and the debate is not always data-driven. Proponents claim that controllerbased architectures simplify control-plane design, improve convergence, and yield a flexible, evolvable network; detractors raise concerns about decision latency, scalability, and availability. To inform this debate and quantify performance concerns, we narrow our focus to two essential questions:. (1) How many controllers are needed? (2) Where in the topology should they go?. This design choice, the controller placement problem, influences every aspect of a decoupled control plane, from state distribution options to fault tolerance to performance metrics. In long-propagation-delay WANs, it places fundamental limits on availability and convergence time. It has practical implications for software design, affecting whether controllers can respond to events in real-time, or whether they must push forwarding actions to forwarding elements in advance. Furthermore, controller placement has immediate relevance: Internet2 is constructing a 34-node SDN [4] and must place the controllers in this production network.. Our contributions are to (1) motivate the controller placement problem and (2) more importantly, quantify the impacts of placement on real topologies. Our goal is not to find optimal minimum-latency placements at scale -theorists have already done that, and we can solve it offline anyway -but instead, to present our initial analysis of a fundamental design problem that is worth further study.. After motivating the problem in §2, introducing example users in §3, and defining the metrics in §4, our analysis begins in §5 with an in-depth look at controller placements in the Internet2 OS3E topology, along with their tradeoffs. We then quantify the impacts of controller placement in §6 for over 100 publicly available network topologies from the Internet Topology Zoo [15] . Lastly, in §7 we summarize our findings and describe future extensions to the analysis. In this paper, we showed that the answer to where and how many controllers to deploy depends on desired reaction bounds, metric choice(s), and the network topology itself. Most networks show diminishing returns from each added controller, along with tradeoffs between metrics. Surprisingly, in many medium-size networks, the latency from every node to a single controller can meet the response-time goals of existing technologies, such as SONET ring protection ( §6.1). Natural extensions for this analysis include:. Availability: Intuition suggests that fully distributed control planes are more resilient to failures than decoupled control planes, but issues of route flapping [17] , BGP "wedgies" [10] , and protracted route convergence times [11] undermine this belief. On the other hand, decoupled network control planes exchange these concerns for other failure modes such as controller failure or disconnection. One could place controllers to maximize fault tolerance; or, one could minimize the distance to the n thclosest controller, called the α-neighbor k-centers problem, which considers up to n − 1 controller failures. State Distribution: Decoupling potentially enables stateoriented methods such as Distributed Hash Tables and Paxos to replace more traditional message-oriented approaches in wide-area network control planes [16] . One could place controllers not for latency bounds, but to optimize for full event-to-response delays, given a controller communication model.. Controller Selection: Decoupling the data and control planes opens the question of how to maintain a map of forwarding devices to controllers. One could place controllers to minimize latency, as a starting point, then use another algorithm to (possibly dynamically) balance switches among available controllers.. We believe that this exploration of the controller placement problem provides useful guidance for SDN operators and application designers. However, there appear to be no placement rules that apply to every network. Whenever an operator wants to add controllers, they should use the methods shown in this paper to determine their own best controller placement; full code to generate and analyze placements is available at github.com/brandonheller/cpp.git.

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