Use of active RFID and environment-embedded sensors for indoor object location estimation This paper describes a method for localizing objects in an actual living environment. We have developed this method by using a complementary combination of 1) received signal strength indicators (RSSIs) and vibration data acquired from active RFID tags, and 2) human behavior detected from various types of sensors embedded in the environment. Regarding the former, we use a pattern recognition method to select a feature appeared in SSIs received by several radio frequency (RF) readers at different places and to classify them into a particular location. In our work, we regard the estimated location as the most probable location where the object is placed. As for the latter, we use the detected human behavior to support the estimation based on the analysis of RSSIs. Experiment results showed that the proposed method improved the estimation performance from about 50 to 95% compared with using only RSSIs to localize objects. Moreover, the results also suggested that we can estimate object location indoors without sensors for detecting human position. This indoor object localization method can contribute for constructing an indoor object management system that improves living comfort. Indoor object localization system has become more and more important in various fields these days. For example, people not only feel stress but also waste precious time when they cannot find what they want in the expected place. If we can provide people with information about the object location, people will save lots of time and lead a comfortable daily life.. Furthermore, if we can detect object movement and estimate object location online, we will be able to know life patterns of people by analyzing the behavior of objects in everyday life. Efficient online object localization system should be able to identify the object a user wants and to determine its location. In our work, we focus on not 3-dimensional "position" of the object, but its "location" in living environment, because we think the only object location is sufficient to achieve our application. Various technologies have been used to construct such systems up-to-date, but most of them have difficulty in recognition of the objects. Against this problem, many studies have focused on using radio frequency identification (RFID) due to its strong identification ability [1] [2] . Because RFID tag has a property to communicate with RF reader by RF signals, it is superior to other technologies for identifying objects. RFID can be divided into two types, one is called passive RFID, and the other is called active RFID. Passive RFID is widely used in many fields nowadays. Suica, a rechargeable contactless smart card used as a fare card on train lines in Japan, is the best example of passive RFID. When people hold Suica up over the prescribed place, RF reader embedded at the place will energize and activate the passive RFID tag by electromagnetic waves. Then the reader receives traffic information of users from the activated RFID tag. The main characteristic of passive one is that it uses reader's energy to transmit its information. For this reason, the transmission range of passive RFID is short, 1 meter at best. In contrast, because active RFID has a battery inside, it can use its own energy to communicate with RF reader. This characteristic enables active RFID to have longer transmission range than passive one. Active RFID has another significant characteristic that deserves our attention. Signal strength indicator (SSI) received by RF reader depends on the distance between a tag and reader. This dependency can be used as a clue about object location [3] [4] .. We choose active RFID rather than passive RFID as our key technology for the following reasons. The first one is for the long transmission range. Because our purpose is to develop an indoor object localization method, long transmission range is more convenient than short one. Another reason is for the number of RF readers required in object Session 3: Human Analysis. Paper No. 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, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. IUCS '09, December 3-4, 2009 location estimation. As the transmission range of active RFID is much longer than that of passive RFID, the necessary number of active RFID readers is much less than that of passive ones. This advantage of active RFID plays a great role in reducing the total introduction cost of the system. The other reason is for the potential of active RFID tag. One remarkable characteristic of active RFID tag compared with passive one is that active RFID tag can attach sensors inside. In fact, every active RFID tag, which we used in our work, contains a vibration sensor to detect object motion. It is certain that users have to exchange battery of active RFID tags regularly in about one year or so. However, the battery itself is inexpensive and the benefits provided by the system are much greater than the exertion spared for the exchange.. A great number of researchers have focused on developing indoor localization methods based on active RFID up-todate. For example, Hightower [3] applied triangulation algorithm to the SSIs received by several RF readers to estimate the 3-dimensional position of tag indoors. This estimation method works well under the condition that few obstacles exist in the environment, however it fails to localize objects once too often in the environment where various obstacles exist like actual human living space. The main reason for the failures is that received SSI, which we call RSSI, is quite sensitive to environmental factors such as the presence and the location of people and furniture because the radio waves are weak against those factors. To reduce the environmental influences on RSSI, some researches introduced the concept of reference tags as an indicator of object position [4] [5] . It is certain that reference tags are useful for reducing the influences on RSSI to a certain extent, still it cannot be evaluated as the perfect solution to indoor object localization. In those researches, the authors also conducted some experiments in the environment where obstacles exist to show the robustness of their methods. However, the complexity of their experimental environment is far from that of our target environment. Human living space is full of various obstacles not only static ones such as furniture, but also dynamic ones such as human beings. To estimate object location robustly in such an environment, we have to confront with more difficult problems than those researches.. To improve the robustness of object location estimation, our previous work [2] focused on the idea that any kinds of motion of objects must be caused by human. Therefore in the previous work, we introduced floor sensors to detect human position in the environment. Floor sensors are pretty effective for the detection of human position, however they also have some serious problems. One is that accurate human position detection requires quite a lot of floor sensors embedded in the environment. Actually, we installed 356 pressure sensors to cover the whole environment. Because the unit price of a floor sensor is not cheap, the total cost for installing all the floor sensors is highly expensive. Besides, because floor sensors are supposed to be buried under the floor, they need not only heavy labor but also long time to install. It must be troublesome to repair those floor sensors when some of them go out of order.. To reduce the cost and maintenance burden caused by floor sensors, we have combined active RFID technology with some simple sensors such as table sensor, sofa sensor, and Figure 1 : Dependency of RSSI on Distance switch sensors. The main advantage of these sensors against floor sensors is that they are inexpensive and easy to install into home. In addition, as these kinds of sensors usually have other uses such as monitoring human daily life to predict human behavior, it is quite natural to have these sensors embedded in human living space. Substitution of simple sensors for floor sensors makes it difficult to detect human position accurately in the environment, which will cause in a drop in estimation accuracy of object location. To solve this problem, we use an integrated algorithm in compensation for the lack of human position information. By taking this approach, we have proposed a method for indoor object location estimation based on active RFID and simple environment-embedded sensors, which achieves sufficient accuracy even without using any costly sensors designed for detecting human position. In conclusion, we have developed an indoor object localizing method by using active RFID tags and simple sensors embedded in the environment. Our system uses 1) a pattern recognition method to classify the RSSIs collected by several RF readers into particular location and 2) the information detected by vibration sensor and environmentembedded sensors to improve the robustness of the method. Although floor sensors used in our previous work can detect accurate human position in the environment, we attempted to eliminate them because of their disadvantages by combining simple sensors such as table sensor, sofa sensor, and switch sensors. The results show that our method can be used to estimate the location of daily objects with sufficient accuracy without the use of floor sensor.. One of future work is to reduce the number of RF readers. In our work, we use five active RFID readers placed at different locations so as to cover the whole environment. However, because the unit cost of RF readers is quite expensive, we have to reduce the number of RF readers to ease the economical burden on introducing our system without lowering the performance of object location estimation. The results shown in Table. 1 suggest two things in particular. One is that the pattern recognition method used has little effect on the location estimation accuracy. Although we used three kinds of methods such as k-nearest neighbor (KNN), distance-weighted k-nearest neighbor (DKNN), and three-layered neural network (NN), none of them achieved sufficient accuracy in object localization. The main cause of estimation mistakes we suppose is that the object location is far from all the RF readers. As the radio wave is sensitive to environmental noises, the further the distance between tag and reader is, the more unreliable RSSI becomes.. The other thing which we noticed from the results is that the lack of estimation accuracy caused by not using floor sensor data can be approximately compensated for by using the proposed algorithms and other simple sensors instead of floor sensors. Although floor sensors can detect human position accurately, they are costly and require complicated maintenance. To reduce the cost and maintenance burden, we estimated object location by using only the RSSI data and data from other simple sensors (table, sofa, and switch sensors). The results indicate that data from a combination of these sensors can achieve accuracy almost equal to that of using floor sensors. We classified the estimation results by the pattern recognition method used for the localization and by the types of information used for the estimation, as shown in Table. 1. There was little difference in the results among the pattern recognition method used: KNN, DKNN, and three-layered NN algorithm. There was a substantial difference in the results among the pattern recognition methods used for the estimation. Localization accuracy with only RSSI of the active RFID was 50% at best, whereas when we combined these two approaches followed our proposed estimation algorithm, the accuracy reached 97.0% regardless of the pattern recognition method. With the three-layered NN algorithm, it reached 98.6% at best. Although we used floor sensors for the estimation in the best case, the system still recorded 95.3% even without floor sensors as shown in the table. In this section, we describe the design of our experiments to evaluate the proposed system effectively and the conditions which we used throughout the experiments.

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


Modeling learned categorical perception in human vision A long standing debate in cognitive neuroscience has been the extent to which perceptual processing is influenced by prior knowledge and experience with a task. A converging body of evidence now supports the view that task does influence perceptual processing, leaving us with the challenge of understanding the locus of, and mechanisms underpinning, these influences. An exemplar of this influence is learned categorical perception (CP), in which there is superior perceptual discrimination of stimuli that are placed in different categories. Psychophysical experiments on humans have attempted to determine whether early cortical stages of visual analysis change as a result of learning a categorization task. However, while some results indicate that changes in visual analysis occur, the extent to which earlier stages of processing are changed is still unclear. To explore this issue, we develop a biologically motivated neural model of hierarchical vision processes consisting of a number of interconnected modules representing key stages of visual analysis, with each module learning to exhibit desired local properties through competition. With this system level model, we evaluate whether a CP effect can be generated with task influence to only the later stages of visual analysis. Our model demonstrates that task learning in just the later stages is sufficient for the model to exhibit the CP effect, demonstrating the existence of a mechanism that requires only a high-level of task influence. However, the effect generalizes more widely than is found with human participants, suggesting that changes to earlier stages of analysis may also be involved in the human CP effect, even if these are not fundamental to the development of CP. The model prompts a hybrid account of task-based influences on perception that involves both modifications to the use of the outputs from early perceptual analysis along with the possibility of changes to the nature of that early analysis itself. Understanding and modeling human vision is a highly challenging area of computational intelligence given the complexity and scale of the processing involved. One key question regarding vision is to what extent does prior knowledge and experience with a given task influence perceptual processing? Evidence suggests that such task influences happen as early as the primary visual cortex for visual discrimination (Li, Piëch, & Gilbert, 2004; Sowden & Schyns, 2006) , and earlier for other activities including multi-sensory integration in the superior colliculus (Stein, 2005) , cortical moderation of fear responses in the amygdala (Shi & Davis, 2001) , and decision making in visual tasks with the basal ganglia (Bogacz & Gurney, 2007) . What is interesting about this feedback is that it is between functional areas, is adaptive, and often changes as a function of task. It is therefore clear that feedback is a key component of visual analysis, but what is its compu-tational role (Olshausen & Field, 2005) and at what stage does it occur in order to produce observed behavior?. Work on visual categorization has been one fruitful area for exploring the links between task and visual perception. For instance, psychophysical work suggests that the spatial frequency analysis carried out in the initial cortical stages of visual processing varies as a function of the categorization task that an individual is trying to perform (Sowden & Schyns, 2006) . Categorization is a fundamental mechanism for dealing with the infinite variation in stimulation from our environment. By quickly identifying the category to which a visual stimulus belongs, we can rapidly access information about the likely properties of that stimulus and how we might interact with it. Without such abstracted knowledge we would have to deal with each visual event as entirely new, losing the benefit of previous learning about other similar stimuli.. In order to make rapid and consistent categorizations it is helpful if members of a category share many features in common that have low overlap with members of other categories. One approach is to attempt to 'carve nature at its joints' (Harnad, 1987) finding natural discontinuities in the dimensions of visual stimulation along which stimuli vary. However, in many cases there will be no ready joints at which to separate visual stimuli into distinct and functional categories. It has been argued that in such circumstances, an individual learns to place stimuli which vary along such a dimension(s) into separate categories, with the relevant dimension(s) of variation becoming warped. This warping is such that stimuli that are placed into the same category come to appear more similar, while stimuli that are placed into different categories become less similar. This warping process marks an important difference between semantic categorization processes and the categorization of visual stimuli. Whereas semantic categories are defined by the abstract relations between objects (e.g. 'desk' and 'computer' are both members of the category of equipment used for academic work) visual categories are defined by the perceptual relationships between stimuli and only these categories acquire changes in the perception of physical stimulus properties through experience, resulting in the phenomenon of categorical perception (CP).. Behaviorally, learned CP effects are shown as more accurate and rapid discrimination of stimuli that are placed in different categories compared to discrimination of equally different (on some physical metric) stimuli that are placed in the same category. Put simply between category discrimination is superior to within category discrimination. CP therefore provides a key example of how task can influence perceptual analysis. By exploring how and where neural processing changes in order to facilitate the sharpening of the distinction between categories, we can improve our understanding of the feedback that occurs between neural circuits.. So where is the locus of change in visual CP? Evidence points to a wide range of brain areas involved in visual categorization and therefore potentially CP. It is known that cells in the pre-frontal cortex form strong categorical representations (Freedman, Riesenhuber, Poggio, & Miller, 2001 , 2003 ; that patterns of activity in the inferotemporal cortex code for different object categories (Freedman, Riesenhuber, Poggio, & Miller, 2006; Kiani, Esteky, Mirpour, & Tanaka, 2007; Op de Beeck, Deutsch, Vanduffel, Kanwisher, & DiCarlo, 2008) ; and that cells there become tuned along diagnostic category dimensions (Sigala & Logothetis, 2002) . Further, changes to early visual analysis in the occipital lobe could serve to amplify/attenuate differences in basic visual properties that serve to distinguish members of different categories. Any or all of these sites could be involved in the development of CP effects, from pre-cortical areas, through the occipital lobe, to ventral visual processing and beyond. Notman, Sowden, &Özgen (2005) attempted to determine the possible neural locus of the CP effect. They trained human observers to categorize Gabor patch stimuli that varied in spatial phase and measured their ability to discriminate within and between category differences before and after training. They found that a CP effect developed as a result of training and that it did not generalize to exactly the same stimuli rotated to a different visual orientation. Because it is known that cells in the primary visual cortex are highly selective for stimulus orientation, Notman et al. deduced that the pattern of specificity of CP to stimulus orientation was consistent with changes to the processing conducted in these initial cortical visual processing stages. These may be implemented as dynamic task specific changes to the strengths of connections in these areas driven through feedback connections from later categorical processing stages. However, another possibility is that later stages in the visual processing hierarchy learn to make better use of the information being fed forwards from these initial processing stages (Mollon & Danilova, 1996; Petrov, Dosher, & Lu, 2005) .. In this paper, our hypothesis is that only changes to the later stages of processing are required to induce CP; that is, feedback to initial cortical processing is not required. In order to evaluate this hypothesis, we need to develop a sufficiently plausible model of vision that demonstrates key properties needed for categorization, namely feature selection through localized receptive fields, and categorization through a global combination of features. There have been many attempts at building models of such aspects of visual analysis as well as those that model the combination of different visual functions (for example, von der Malsburg, 1973; Grossberg, 1976; Kohonen, 1982; Linsker, 1988; Jacobs, Jordan, & Barto, 1991; Miikkulainen, Bednar, Choe, & Sirosh, 2005; Serre, Oliva, & Poggio, 2007) . Some common attributes of these models include hierarchical modules performing successive visual analysis, and self-organization through competition.. An exemplar of hierarchical vision is the modular model of early visual cortical processing developed by Itti, Koch, & Braun (1999) , which exhibited equivalent psychophysically observed results. Their model consisted of layers representing orientation columns in V1, connected together to represent the interactions between feature selectors, which then fed a decision process. While the later stages are loosely based on mechanisms thought to occur in the brain, the model parameters are estimated by minimizing the error to the training data, rather than a more concrete understanding of the processing. However, this model does show that a simple modular architecture can demonstrate known psychophysical phenomena through the interaction of the different layers. Furthermore, it has been extended to explore task-driven attention, albeit using representations for long term and working memory (Navalpakkam & Itti, 2005) . Although these models successfully demonstrate the properties we are looking for, we are motivated to find a more biologically plausible approach to modeling the modular nature of vision that uses neuronal principles to learn, and which can encode the influence of task. One such model is reported by Deco & Zihl (2001) , which is a hierarchical model of visual attention which uses a recurrent network for feedback to guide attention. Other similar models have also been proposed (Spratling & Johnson, 2004; Hamker, 2007) . Each of these builds on biological principles to provide a system level model of attention that compares well with behavioral data. Spratling & Johnson (2006) go one step further and explore feedback in perceptual learning. By using a biologically plausible model of feedforward and feedback 'cortical regions', they demonstrated how task influence could induce a simple CP effect. However, while showing that feedback can induce a CP effect, they did not explore the interaction between different stages of visual analysis and task influence.. How do we model visual analysis so that we can test for an induced CP effect? One possible modular architecture which is both biologically motivated and encodes task training has been developed by Armony et al. (1995) . While their approach is much simpler than the attentional models that have been developed, their uniform architecture of layers of identical, interconnected neurons uses Hebbian adaptation (Hebb, 1949) with lateral inhibition through competition (Rumelhart & Zipser, 1986) to train neurons to become sensitive to different, overlapping patterns. Similar competitive architectures built on biological principles have proven effective at modeling vision (Linsker, 1988; Miikkulainen et al., 2005) , but have not been used for task training. Armony et al. (1995) used the competitive principle to model sub-cortical and cortical auditory pathways leading to the amygdala, the response from which could be adapted through the use of a conditioning signal. The idea of conditioning being used for category learning has been applied by Gluck & Bower (1988) . In Armony et al.'s model, the conditioning signal is applied as an additional input to selected modules, modifying the response from their neurons as well as subsequently connected modules. While each module is formed by a single layer of neurons only, each learns to exhibit desired local properties (feature selection) as well as the whole model exhibiting the required global properties (conditioned responses).. Of particular interest to us is that the architecture defined by Armony et al. has been used to make biological processing predictions, which have subsequently been tested (Armony, Servan-Schreiber, Cohen, & LeDoux, 1997a; Armony, Servan-Schreiber, Romanski, Cohen, & LeDoux, 1997b) , thereby validating the model and closing the circle between computational modeling and neuroscience. For us, this model provides a way in which different stages of vision can be modeled (modules) with task influence (categorization) being learned through association (conditioning). Both the local properties of the modules (feature detectors) and the global properties (categorization) can then be analyzed and compared with observed human data, building upon the successful use of such approaches before to model aspects of visual, cortical processing (Linsker, 1988; Miikkulainen et al., 2005) . This approach for the first time therefore allows us to build a model of the different stages of visual analysis so that we can explore whether CP emerges as a result of changes to later stages of visual processing only, comparing this with relevant behavioral experiments.. In this paper we present an adaptive model of hierarchical vision processes (section 2) that is trained to perform a categorization task. This model is based upon the work by Armony et al. (1995) , and hence we model hierarchical vision at a system level, and include task training to generate a CP effect. This work is novel because we are 1) evaluating whether an abstract, system level model of visual processing can sufficiently model early visual analysis such that it exhibits both local (feature detection) and global (categorization) behavior, 2) whether a CP effect can be induced through task influence to the later stages of processing, and 3) comparing our results systematically with behavioral experiments. This will allow us to provide computational evidence for the extent to which task influence is required through later or earlier stages of visual analysis in humans for categorical perception to arise. To achieve this, we execute the experiments conducted by Notman et al. (2005) on the model. These experiments tested whether early visual analysis changed as a result of learning a categorization. Our results show that the model is capable of reproducing the desired visual analysis behavior (section 3). We then go on to show that task influence is only needed in the highest level of analysis that we model (ventral visual processing), rather than at early stages of analysis as hypothesized in humans. However, while our model shows an existence proof for CP without early perceptual changes, we note that this effect does not fully replicate the specificity of the human data to stimulus orientation, suggesting that some other change at early stages of analysis (for example, see Furmanski et al., 2004; Schoups et al., 2001; Yang & Maunsell, 2004) may be needed to fine-tune the CP effect. In this paper we have provided computational evidence for the way in which prior knowledge of a task can influence perceptual processing. We have done this by presenting an adaptive model of hierarchical vision processes trained on a visual categorization task. In defining the model and establishing our experimental method, we have attempted to provide an equivalence between the model and human vision. To achieve this we have used biological inspiration in our choice of architecture and algorithm, systematically parameterized the model, executed equivalent experimental steps to that of the human experiments, and finally, rigorously analyzed the results using statistical approaches applied in psychophysics.. Contrary to current debate on the influence of task on visual analysis, our results demonstrate that a visual CP effect can be established with only task influence to the latter stages of analysis that we have modeled: ventral visual processing. However, our model also shows that the developed CP effect is less specific to the stimulus orientation than found in humans. So, while we propose that a basic CP effect may arise in later stages of processing learning to make better use of the phase selective outputs from early stages, a more complex form of CP may still require changes to perceptual processing in these earlier stages.. We have drawn this conclusion based upon the evidence that the model provides. Here, we find that the strength of the CP effect observed in VV is not affected by replacing the after category-training connection weights in PC, EC or both with their pre-training values. The phase selective outputs, which are present following pre-training and before any category training takes place, appear to be sufficient for CP when coupled with the learning that takes place in VV following application of the category signal. This proposal is consistent with late selection models of CP and perceptual learning (Mollon & Danilova, 1996; Petrov, Dosher, & Lu, 2005) . However, this basic CP effect shows far less specificity to the orientation of the visual stimulus than is the case for the human data implying that some additional changes to perceptual analysis, possibly localized to earlier stages of processing, are involved in the human CP effect in line with the conclusions of Notman et al. (2005) and the Reverse Hierarchy Theory of Ahissar & Hochstein (2004) . Such modifications might include changes to the strengths of intra-cortical connections (i.e. within module) under the influence of feedback connections from later stages of analysis Gilbert, Sigman, & Crist, 2001) .. Our results prompt further human experiments to test the hybrid account of CP effects proposed above involving both early and late stage modifications to perceptual analysis. For example, Transcranial Magnetic Stimulation designs might be used to selectively disrupt the processing at different stages of visual analysis at the point in time when task feedback is provided, and the effects of this on CP observed. Our model might predict that disruptions to early visual analysis could increase the generalization of CP effects across stimulus dimensions such as orientation.. However, in drawing these conclusions, we recognize that the model suffers from a number of limitations. For example, more capable models of vision may be built by considering the role of inter-module feedback, temporal coding (pulse coded networks) and the use of more sophisticated techniques to decrease the levels of abstraction (better models of receptive fields and the implementation of earlier stages of visual processing). Work on this has already started with, for example, the inclusion of topographic properties within the modules (Pavlou & Casey, 2009) . Despite these limitations, the model does have a sufficient level of plausibility and replication of behavior to provide an existence proof that the CP effect can develop with only simple feedback to later stages of visual analysis. The set of eight images used for the human experiments, each constructed from two sets of Gaussian windowed compound gratings (Notman et al., 2005 • }. For convenience, each image is numbered (clockwise from 1 to 8), and also each image pair (again clockwise from 9 to 16). During discrimination testing, images are presented as pairs, in random order, with either the same image on the left and right visual field (1 to 8), or pairs made up of consecutive images (9 to 16), noting the difference in within (9, 11, 12, 13, 15, 16) (Notman et al., 2005) . (Notman et al., 2005) . Table 2 : Results from analysis of variance to explore A scores for within and between category discriminations, in each visual area as a function of training. Here, we show analyses for five different variants of the model (after pre-training, after category training, then with the PC, EC and the PC and EC replaced), the three different modules in each processing stream (PC, EC and VV) and the category position (within and between). The Mauchley Sphericity Test showed that the assumption of sphericity was violated for all effects. Consequently, the Greenhouse Geisser correction was made to the degrees of freedom in every case. In all cases, p < 0.0000001 and the observed statistical power is very high (1.0) because each model was run a large number of times (100). With such high power even a very small difference will be statistically significant. A separate question is whether the difference is meaningful. An indication of this is given by measures of effect size such as partial η 2 . Values for this can range between 0 and 1 with larger values indicating a bigger effect and a value of less than 0.2 a very small effect. In the present case most effects were moderate to large in size and importantly, this is true of the crucial interactions with category position. Previous models of CP have tended to focus on speech, such as vowel (Anderson, Silverstein, & Ritz, 1977) and phoneme categorization (McClelland & Elman, 1986) , and speech production (Kröger, Birkholz, Kannampuzha, & Neuschaefer-Rube, 2007) . However, Goldstone, Steyvers, & Larimer (1996) explored categorization of visual stimuli in the form of Bezier curves, Padgett & Cottrell (1998) facial expressions and Spratling & Johnson (2006) a simple square of nine, joined dots. Our model falls somewhere between these two approaches by using visual stimuli, but which are represented in an abstract form to present phase information only from the Gabor patterns.. In addition to the types of task that have been modeled, various different architectures have been used to simulate CP. In the simulations conducted by Anderson et al. (1977) , CP was modeled using Hebbian learning for positive feedback (the brain-state-in-a-box model). McClelland & Elman (1986) focused on using excitatory and inhibitory connections between neurons, whereas Kröger et al. (2007) used self-organizing maps. The model developed by Spratling & Johnson (2006) is perhaps the most plausible so far presented in that it consists of interacting layers of 'cortical regions' based on pyramidal neurons. In contrast to these simulations, which have some degree of biological plausibility in that they are each based around competitive learning or similar, other less plausible architectures have been used, such as Padgett & Cottrell (1998) , who used an ensemble of multi-layered perceptrons trained using backpropagation.. In this paper we have gone beyond these existing models of CP. We have developed a biologically motivated model of the key stages of visual analysis that is capable of exhibiting local properties in each layer (feature selection) and global properties of the whole system (category learning). While this is similar to other models of hierarchical vision and categorization (Deco & Zihl, 2001; Spratling & Johnson, 2004; Hamker, 2007) , our approach is novel because we then went on to demonstrate how the model can exhibit a CP effect as a result of sequential stages of visual analysis. These stages convert the input data into a form which can be categorized by our model of VV processing, which is coupled with a category signal as feedback.. In addition to developing a biologically inspired model of visual CP, we have also followed an equivalent training and testing regimen to that of a set of psychophysics experiments. Despite using simple neural structures and an abstract image representation, the results have both demonstrated a CP effect and its orientation specificity which compares well with human data. Here, our simple neural model applied a category signal only to the VV module, representing ventral visual processing, despite evidence from human data suggesting that the CP effect occurs as a result of changes at earlier stages of processing (for example, V1). If we treat our model as sufficiently plausible, our results provide evidence for the CP effect to occur as a result of changes to ventral processing only, although with some variation in the observed values and, in particular, the orientation bandwidth of the effect. These two different aspects of our findings may reconcile two different views of perceptual learning and categorical perception effects. One view, consistent with our finding that CP can arise from modifications to VV alone, posits that learning effects arise primarily because later stages of analysis learn to make better use of the fine grained information coming from early visual analysis (cf. Mollon & Danilova, 1996; Petrov et al., 2005) . However, a second view proposes that learning more difficult tasks, or equivalently fine-tuning performance to a high degree, recruits successively earlier stages of analysis (cf. Ahissar & Hochstein, 2004) . This latter view is consistent with the failure of our model to achieve the same degree of orientation tuning that is observed for the human data implying that, in humans, modifications are also driven to earlier stages of visual analysis to achieve this fine tuning.. Evidence in support of the likely involvement of early cortical stages of visual analysis in tasks involving orientation specific learning has come from perceptual learning research, which has sought to identify the neural correlates of such learning. For instance, Furmanski et al. (2004) showed that practice improved observers' ability to detect low contrast gratings in an orientation specific way and that activity in V1 in response to the practiced grating orientation increased following training. Further, Schoups et al. (2001) showed that in monkeys, practising orientation identification narrowed the tuning of orientation selective V1 neurons for practised orientations. In addition, Yang & Maunsell (2004) reported that practicing orientation discrimination produced narrower orientation tuning curves for units in V4 responding to the practised orientation at the practised stimulus location.. However, we must recognize that our model has three main limitations that we must consider along with this evidence. First, we must acknowledge that the model is an abstraction of a complex neural hierarchy, with arbitrary labels delineating broadly different stages of processing. What we have shown is that these three successive stages of processing can exhibit behavior which can be mapped to human data through the tuning of parameters, and that this behavior can be modified by the application of a category signal. The model also abstracts temporal information through the use of a rate coding architecture. However, despite these limiting factors, what the results have shown is that modeling can be used to explore complex biological processes and, more importantly, can be used to make predictions about these processes, namely that the CP effect appears to be possible without changes to early perceptual processing.. Second, in order to test orientation specificity, we paired orientations to keep the size of the input vectors small. While this is a valid and often used strategy for psychophysics experiments, humans are capable of processing multiple orientations at once. Tests that included all orientations in the input to our model did demonstrate the CP effect, but they did not show a decreasing profile of orientation generalization, with all orientations gaining the same A (B) values instead. This suggests that the model cannot adequately cope with significantly increased input dimensions (perhaps the curse of dimensionality being felt).. Third, one striking result is that we could not find parameters that would sufficiently tune the orientation bandwidth to the desired 6.5. • . While we could dismiss this as a result of a fundamental limit of the architecture, this could also suggest that the model does not sufficiently represent the underlying biology. Here, the role of feedback connections underlying the CP effect is thought to be important to enable changes to be made to perceptual processing (for example, although not explicitly for CP, Gilbert, Sigman, & Crist, 2001 ). In our model, connections between modules are feedforward only; feedback connections may be important in achieving a smaller orientation bandwidth by modulating activation within layers as a result of category learning. This remains an important goal for future work.

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


An analysis of multi-sampled issue and no-replacement tournament selection Standard tournament selection samples individuals with replacement. The sampling-with-replacement strategy has its advantages but also has issues. One of the commonly recognised issues is that it is possible to have the same individual sampled multiple times in a tournament. Although the impact of this multi-sampled issue on genetic programming is not clear, some researchers believe that it may lower the probability of some good individuals being sampled or selected. One solution is to use an alternative tournament selection (no-replacement tournament selection), which samples individuals in a tournament without replacement. This paper analyses no-replacement tournament selection to investigate the impact of the scheme and the importance of the issue. Theoretical simulations show that when common tournament sizes and population sizes are used, noreplacement tournament selection does not make the selection behaviour significantly different from that in the standard one and that the multi-sampled issue seldom occurs. In general, the issue is not crucial to the selection behaviour of standard tournament selection. Tournament selection is one of the commonly used parent selection schemes in Evolutionary Algorithms (EAs) and is 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. GECCO'08, July 12-16, 2008 , Atlanta, Georgia, USA. Copyright 2008 ACM 978-1-60558-130-9/08/07 ...$5.00.. very popular in Genetic Programming (GP) [10] . According to the description given by Goldberg and Deb [8] , the initial study of tournament selection can be traced back to the early 1980s [5] . One form of the conventional tournament selections introduced in [5] has became the standard. Standard tournament selection randomly samples k individuals with replacement from the current population of size N into a tournament of size k and selects the one with the best fitness from the tournament. Because individuals in a tournament are sampled from the population with replacement, standard tournament selection is simple to code and efficient for both non-parallel and parallel architectures [14] . Standard tournament selection has been widely studied theoretically since the 1990s [1, 2, 3, 14, 17] , while many alternative implementations have been developed [7, 9, 11, 12, 19] .. One commonly recognised issue in standard tournament selection is that it is possible to have the same individual sampled multiple times in a single tournament (the multisampled issue). Although the impact of this multi-sampled issue on GP is not clear, some researchers believe that it may lower the probability of some good individuals being sampled or selected. One solution is to use an alternative tournament selection in which individuals are sampled without replacement into a tournament, then, after the winner is determined, all individuals in the tournament are returned to the population. According to [8] , tournament selection using the sampling-without-replacement strategy is the other conventional tournament selection. We abbreviate it as noreplacement tournament selection. It is not clear why noreplacement tournament selection is less commonly used in EAs.. From the literature, it is not clear whether the samplingwithout-replacement strategy makes the selection behaviour significantly different from that in the standard one and whether the multi-sampled issue is crucial to the selection behaviour in standard tournament selection. Although researchers may have an intuition that the two methods are not significantly different, this view has not yet been well proved. Standard tournament selection samples individuals with replacement, which causes the multi-sampled issue. The multi-sampled issue can be overcame by no-replacement tournament selection. Through theoretical analyses and simulations of the two tournament selection schemes, the paper showed that when common tournament sizes and population sizes are used, the sampling-without-replacement strategy does not make the selection behaviour significantly different from that in standard tournament selection. The multisampled issue seldom occurs in standard tournament selection. Therefore, in general, the issue is not crucial to the selection behaviour in standard tournament selection.. This work was conducted with intention for GP, however the theoretical analyses are very general so that the results could be applied to any other EAs.

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


Solution of the Simultaneous Pose and Correspondence Problem Using Gaussian Error Model The use of hypothesis veri cation is recurrent in the model-based recognition literature. Veri cation consists in measuring how many model features transformed by a pose coincide with some image features. When data involved in the computation of the pose are noisy, the pose is inaccurate and di cult to verify, especially when the objects are partially occluded. To address this problem, the noise in image features is modeled by a Gaussian distribution. A probabilistic framework allows the evaluation of the probability o f a matching, knowing that the pose belongs to a rectangular volume of the pose space. It involves quadratic programming, if the transformation is a ne. This matching probability is used in an algorithm computing the best pose. It consists in a recursive m ultiresolution exploration of the pose space, discarding outliers in the match data while the search is progressing. Numerous experimental results are described. They consist of 2D and 3D recognition experiments using the proposed algorithm. Despite recent advances in computer vision the recognition and localization of 3D objects from a 2D image of a cluttered scene is still a key problem. The reason for the di culty to progress mainly lies in the combinatorial aspect of the problem.. This di culty can be bypassed if the location of the objects in the image is known. In that case, the problem is to compare e ciently a region of the image to a viewer-centered object database. (See Fig. 1 for the gures used in our experiments.) Recent proposed solutions are, for example, based on principal component analysis 1, 2], modal matching 3], or template matching 4].. But Grimson 5] emphasized that the hard part of the recognition problem is in separating out subsets of correct data from the spurious data that arise from a single object.. Recent research e s i n t h i s e l d h a ve focused on the various components of the recognition problem: which features are invariant and discriminant 6], how it is possible to group features into salient parts 7], how to index models 8], how t o i d e n tify sets of data feature/model feature pairings consistent w i t h a n object 9], or which similarity measures are relevant 10] .. From this previous research, we can note that most of the proposed strategies can be described in terms of predictionveri cation schemes. In a pre-processing stage, model feature groups having invariant properties are stored in a hash table. Recognition rst consists in grouping image features into salient parts. Index keys obtained from these small groups select objects in the model base, producing sets of pairings from indexed models to data features. The transformation aligning a model with the image is usually referred to as the pose of the object. Poses obtained by this method are treated as hypotheses realizing a few feature-to-feature correspondences. These hypotheses have t o b e v eri ed by transforming the remaining model features and by trying to match them with image features. Transformations are generally assumed to be a ne.. However errors in data usually make the pose incorrect and the veri cation becomes more di cult (see Fig. 2 for an illustration).. In that case, as pointed out by Gandhi and Camps 11 ] the noise in the data will propagate into the pose and will decrease the quality of the correspondences obtained in the veri cation stage.. This noise e ect has been studied assuming bounded error models. Grimson et al. 12 ] gave a precise analysis of a ne point matching under uncertainty. They obtained an expression for the set of a ne-invariant v alues consistent with a set of four points, where each data point lies in a small disk. Alter and Jacobs 13] modeled the error by assuming that a detected feature point i s n o m o r e t h a n pixels from the location of the true point. They proposed an expression for the error in the computed image position of a 4th point (and nth point)when three matching pairs of image and model points are assumed. Gandhi and Camps 11] proposed an algorithm to select the next feature to be matched, after the pose has been computed with a small number of correspondences. Their aim is to nd the subset of n model points so that the e ect of the data uncertainty in the estimation of the pose will be minimized.. Some authors use the Gaussian error model. Sarachik and Grimson 14] analytically derived the probability of false positive and negative as a function of the number of model features, image features, and occlusions, under the assumption of 2D Gaussian noise.. Beveridge and Riseman 15] presented a model-based recognition system using 3D pose recovery during matching. Their algorithm is based on a random local search to nd the globally optimal correspondence between image and model, with a high probability of success. A current set of correspondences is modi ed, using the neighboring sets. The neighborhood is de ned as sets obtained by adding or removing a single pair from the current correspondences set.. In spite of all this research activity, h ypothesis veri cation remains a di cult problem. In this article, we h a ve proposed a robust solution to the pose veri cation problem. It allows the management of recognition applications in which a s m a l l n umber of noisy correspondences is used to hypothesize a pose.. It consists in re ning a set of possible poses. At the end of this process a pose is computed so that the probability that a k n o wn object is aligned with some image features is maximal. This is done by dividing recursively an initial \box" of the pose space, which is obtained by initial correspondences. This performs a multiresolution pose search. We h a ve s h o wn that the search for the best pose involves quadratic programming, supposing that the normal distribution is used to model the data error and supposing that the transformation is a ne. The search s i m ultaneously explores several boxes therefore, it is not stopped by local minima. Furthermore, the implementation of this algorithm is very straightforward.. This algorithm has been integrated in two di erent recognition applications: 2D recognition and 3D recognition with line segments. However, it can be directly used with di erent features and di erent recognition strategies.. We h a ve experimentally proved that it is quick and reliable despite data noise and occlusions. The robustness is due to the probabilistic framework used to describe data-to-model correspondences and also to the way the search is performed.. The performances and the robustness of the described algorithm allow it to be used for tracking applications, as shown in the 3D examples. Pose veri cation has connections with several other related areas such as pose determination, robust estimation, object tracking, error models, MAP matching, or object recognition. Let us see the advantages of our algorithm against recent related algorithms from these other domains.. Hel-Or and Werman 24] proposed a method for fusing 2D (viewed as 3D with in nite uncertainty) and 3D measurements for pose estimation. This method assumes that an initial estimate of the pose is provided, which can be obtained by utilizing a s m a l l n umber of correspondences. Despite its ability to deal with data noise, this method is not suitable for our problem, since it does not tolerate outliers and assumes that the correspondences between points of the model and measured points are known.. There are two major sets of techniques for handling outliers. The rst one consists of detecting outliers and computing robust estimates simultaneously. The technique used by Kumar and Hanson 25] to address the problem of estimating a pose when outliers are present i n t h e m a t c h data is of this kind. They have analyzed the results obtained with Mestimates (maximum likehood type estimate) and L-estimates (linear combination of order statistics). They report that the M-estimate is extremely sensitive to initial estimations. This is due to the presence of multiple local minima in the objective function minimized. L-estimation (median LMS) does not have this drawback but involves combinatorial methods. From our point of view, our method is more e cient, because it can be viewed as a M-estimation operating simultaneously around several multiple local minima of the objective function. Local minima are obtained by a recursive s e a r c h w h i c h a c t s a s a multiresolution search. The proposed algorithm does not guarantee to nd the best solution because it only explores a nite number of branches simultaneously. But our experimental results show that satisfactory solutions are, however, generally obtained, even in severe conditions. The other set of techniques for handling outliers attempts to detect outliers before forming a robust estimate. For example Lowe 26] proposed to use an iterative probabilistic selection. The described iterative matching procedure, based on the treatment of matching and measurement errors, allows the most reliable matches to improve the probability of correctly matching other features. Propagation of noise in the data into the pose has been also studied by Gandhi and Camps 11] . However, we have observed, in agreement with Kumar and Hanson 25] , that techniques attempting to detect outliers before forming the estimate often failed when the noise in the data is severe if there is a great number of outliers.. Instead of trying to minimize an objective function in spite of outliers, Cass 27] proposed to generate all feasible interpretations of the data in a polynomial time. He argued that there is only a nite number of equivalence classes of transformation to consider, assuming that the error model of correspondences is bounded. For the case of 3D planar objects under rotation and translation, there are k 6 M 6 N 6 equivalence classes to evaluate, where M is the number of model features, N is the number of data features, and k is the number of constraints in the pairing. If k = 8 M= 30, and N = 100, the size of the set of arrangements is 8 6 30 6 100 6 , w h i c h i s t o o l a r g e t o b e exhaustively treated. Cass also points out that bounded error methods can also provide a discrete approximation to Gaussian error. A drawback is that it increases k, and, as a consequence, the number of equivalence classes is also increased.. The appropriateness of Gaussian distribution for modeling feature uctuations has been studied by s e v eral authors 14, 26]. Wells 28] was motivated by this evidence and developed a maximum likehood and MAP recognition formulation, which are based on normal feature models. Our formulation is close to the Wells one. However, we formulate the objective function in the pose space and not in the image space. In this way, the objective function becomes a quadratic form which can be easily used in a pose estimation algorithm. The knowledge base includes about 600 2D views of the 10 objects (from 50 to 80 views per object). A view is a collection of line segments. During these experiments, each image contains one or several di culties: the image is cluttered, objects are occluded, or objects are strongly a ected by the perspective e ect.. We h a ve made no assumption either on the pose or on the object(s) occurring in the image. Recognition times are measured on an HP-700 workstation (see Fig. 6 ).. First results. The rst results (see Fig.7 ) illustrate the method. Polygonal approximation of edges (b) is computed from image (a). Two h undred segments are detected. From these 200 segments, 60 groups of coterminating segments are built, leading to about 800 group-to-group correspondences (image/knowledge base). It means that 800 poses have t o b e veri ed. The best pose (the one giving the highest model correspondence probability i n t h e v eri cation stage) is displayed in (c). Less than 4.4 s were necessary to verify the 800 poses. Paired data features are represented in (d). Image (e) represents the group that has produced the best pose, and the corresponding initial pose is shown in (f). Other results. We h a ve tested our veri cation algorithm on several hundred images similar to those given Figure 7 .

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


From sockets and RMI to web services Traditional coverage of network programming techniques in a computer networking course addresses sockets, remote procedure call, and object-oriented remote procedure call. We propose two innovations to that coverage. The first is to emphasize the historical development of those techniques as a sequence with each technique evolving from the previous one. The second innovation is to extend the historical development and the techniques to the important current technique of web services. The Final Report on Computer Science Curricula of the Joint Task Force [1] identifies Net-Centric Computing as one of the top-level topics in the Computer Science Body of Knowledge. There are excellent textbooks introducing computer networking available. Consequently, our approach requires a computer networking textbook [5] but to cover network programming and distributed applications by a series of programming projects.. Our projects include detailed handouts to cover the needed concepts. This past year we introduced a significant change in the series of programming projects by adding a project involving web services. How we introduce web services as an evolution from other approaches to network programming is noteworthy and is the subject of this paper. In prior work, Gagne [3] has also reported a course that includes socket and RMI-based projects, but not the historical evolution approach nor the extension to web services. Interestingly, the more recent papers on integrating web services have focused on CS1/CS2 [7] and on a first year graduate course [4] instead of on the computer networking course.. In the next section we illustrate how the course teaches network programming techniques as an historical evolution. Section Two covers the historical sequence taught prior to this semester. Section Three explains the programming projects we have developed that follow that historical development. Section Four explains how web services are a natural next step both in terms of the historical development of network programming and in terms of pedagogy. Section Five discusses the web services project and the software infrastructure it requires. Section Six reports on our experiences with that project. We conclude in Section Seven. In distributed applications, one of the most important current approaches is web services. In this paper we have outlined how we are doing that in a current course. The course integrates a computer network protocol course with a course on network programming techniques for developing distributed applications. We argue that organizing the course's content and programming projects around the historical development of those techniques offers a number of advantages. This paper explains how the course does that including the novel extension to web services.

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


The Green500 list: escapades to exascale Abstract Energy efficiency is now a top priority. The first four years of the Green500 have seen the importance of energy efficiency in supercomputing grow from an afterthought to the forefront of innovation as we approach a point where systems become increasingly constrained by power consumption. Even so, the landscape of energy efficiency in supercomputing continues to shift-with new trends emerging and unexpected shifts in previous predictions.This paper offers an in-depth analysis of the new and shifting trends in the Green500. In addition, the analysis offers early indications of the path that we are taking towards exascale and what an exascale machine in 2018 is likely to look like. Lastly, we discuss the emerging efforts and collaborations toward designing and establishing better metrics, methodologies, and workloads for the measurement and analysis of energy-efficient supercomputing. As with all the great races in modern history, the supercomputing race has been myopically focused on a single metric of success. With the space race, the metric was which country could reach the moon first. In supercomputing, the race is more open-ended, but it has focused on maximum achievable performance. This persistent drive toward more speed at any cost has brought about an age of supercomputers that consume enormous quantities of energy, resulting in the need for extensive and costly cooling facilities to operate these supercomputers [1, 2, 12] .. In 2007, we created the Green500 [7] to bring awareness to this issue and to provide a venue for supercomputers to compete on energy efficiency as a complement to the TOP500's focus on speed [13] . Since that time, many milestones have been achieved, most notably, (1) the first petaflop supercomputer and (2) the first GFLOP/watt supercomputer. Concurrently, energy efficiency has entered the consciousness of the supercomputing community at large and is now a primary concern in the design of new supercomputers. In this paper, we -Explore the emergence of green high-performance computing (HPC). -Track trends across the past four years of the Green500.. -Discuss the results of the shift toward thinking green.. -Investigate the implications of the above as we move into the future.. Of particular interest are the implications of past and current trends on the feasibility of exascale computing systems in the timeframe discussed in the DARPA IPTO exascale study [3] . The study itself indicates that power will be the determining factor in the success or failure of any exascale program. Past trends in the Green500 have led us to believe that at least one of the targets listed in the study may be feasible, but as we look at the progression in total power use and the aggregate progression of the list, some questions are raised as to whether the optimistic figure of 20 megawatts (MW) will be possible by 2018.. The rest of the paper is organized as follows. First, Sect. 2 discusses the background of and motivation behind the Green500. Section 3 offers a high-level analysis of efficiency, along with power, and a more in-depth analysis of the efficiency characteristics of the different types of machines that achieve high energy efficiency. Projections from current and past lists to exascale are discussed along with their implications in Sect. 4. Section 5 presents the innovations and collaborations behind the continuing evolution of the Green500 as well as directions for future growth. Finally, Sect. 6 presents concluding remarks along with future work. Large-scale, high-performance computing (HPC) has reached a turning point. Prior to 2001, the cost of purchasing a 1U server exceeded the annualized infrastructure and energy (I&E) cost for that server, as depicted in Fig. 1 . By 2001, this annualized I&E cost for a server matched the cost of purchasing the server. By 2004, the annualized infrastructure cost by itself matched the cost of purchasing the server, and by 2008, the annualized energy cost by itself matched the cost of purchasing the server. Ignoring power and energy efficiency to pursue performance at any cost is no longer feasible. Data centers and HPC centers are already feeling the pinch across the industry from Yahoo! [9] to Google [12] to the National Security Agency [4, 10] .. The supercomputing community has been particularly guilty of seeking speed at the exclusion of all else. When the first Green500 in November 2007 was released, the computers that resulted from the event known colloquially as Com- Fig. 1 Annual amortized costs in the data center [2] , data projected after 2007 putenik, were still in the TOP500, namely the Earth Simulator supercomputer from Japan and ASCI Q from the US. The former far outstripped the performance of the latter by five-fold. Furthermore, the Earth Simulator had an efficiency of only 5.60 MFLOPS/W while ASCI Q had an even lower efficiency of 3.65 MFLOPS/W.. In 2004, the first US machine to regain the number one position on the TOP500 was an IBM BlueGene/L prototype. It delivered two orders of magnitude better energy efficiency than the Earth Simulator and ASCI Q and debuted at 205 MFLOPS/W on the first Green500. Clearly, there was an inkling of the need for efficiency to achieve the greatest possible performance, but even so, it continues to be an uphill battle.. The original goal of the Green500 was to raise awareness of the state of energy efficiency in supercomputing and bring the importance of energy efficiency to be on par with the importance of performance. In order to measure and rank supercomputers in terms of their energy efficiency, the Green500 employs the LINPACK benchmark, as provided by the TOP500 list, combined with power measurements. LINPACK solves a problem in dense linear algebra that uses LU factorization and backward substitution. It is designed and tuned for load balancing and scalability.. While the Green500 remains a ranking of the energy efficiency of the 500 fastest supercomputers in the world, we launched three additional lists in 2009, based on feedback from the HPC community: the Little Green500, the HPCC Green500 and the Open Green500. As of now, the HPCC Green500 and Open Green500 have been discontinued due in part to lack of participation and interest from the community. The Little Green500 continues to operate and broadens the definition of a supercomputer to help guide purchasing decisions for smaller institutions. To be eligible for the Little Green500, a supercomputer must be as "fast" as the 500th-ranked supercomputer on the TOP500 list 18 months prior to the release of the Little Green500.

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


On the query complexity of finding a local maximum point We calculate the minimal number of queries sufficient to find a local maximum point of a function on a discrete interval, for a model with M parallel queries, M 1. Matching upper and lower bounds are obtained. The bounds are formulated in terms of certain Fibonacci type sequences of numbers. Query complexity has been extensively studied in the context of decision trees, sorting and searching problems (see, e.g., [7, 8, 4] ) as well as in recursion theory [5] . It is relevant in the situation, where one has costly access to (parts of) the input data, whereas the time and space costs of the computation can be ignored. If the input is given in the form of a finite function f and as the model of computation one considers, say, oracle Turing machines that may ask questions of the form f (x) = ?, the natural query complexity measure means the minimal number of oracle queries necessary to solve a given problem (depending on the size of the domain of f ).. This paper deals with one particular problem of the above kind. Given a finite function f : {0, . . ., n} → N the task is to find a local maximum point (lmp) of f , that is, a point x such that the value of f at x exceeds those at the neighbors of x. (The neighbors of x are x − 1 and x + 1, if 0 < x < n, and the points 0 and n each have only one neighbor, 1 and n − 1, respectively.). A similar problem can also be formulated in the continuous case, when the function f has real arguments and values, the local maximum points of f being defined as usual. Here one cannot hope for an exact determination of a local maximum point. Rather, one is interested in localizing such a point within a small interval of uncertainty and minimizing the number of necessary queries depending on the length of the uncertainty interval. From the point of view of the query search the discrete and the continuous cases are quite similar, but in this paper we only deal with the discrete problem.. The problem of finding a maximum point of a function belongs to classical mathematical problems and numerous search methods are known. However, in this paper we study very restricted, in a sense, search procedures that are only based on querying the values of the function. This kind of procedures are practically important when no additional regularity conditions on the function, such as the existence of derivatives, etc., are being postulated. Such functions often arise, for example, from sets of experimentally collected data. Thus, query search for a maximum has many applications in statistics, optimal control, engineering and economics.. As just one example the reader may think about an oil refinery and making probes to determine certain parameters of the product. Such probes are being done in practice in order to optimize (in real time) the refining process. Every single probe is quite costly, which makes it important to minimize the total amount of probes. This brings the problem, theoretically speaking, to the realm of query complexity.. As early as in the '50s the problem of finding a maximum point of a unimodal function (that is, the function with a single local maximum on a given interval) attracted the attention of analysts in the continuous case. In [6] the now well-known Fibonacci search technique was proposed and shown to be optimal (see also [1] ). The same technique applies in the discrete case for a model with dependent queries. It yields that log α (n) queries (up to a small additive constant) are sufficient to find a local maximum point of a function on an interval of length n, where α =. is the 'golden ratio'. It can be extracted from Kiefer's result that this number of queries is worst case optimal. Rather than doing this we give another more transparent proof in Theorem 2.. In the present paper a more general situation is considered, when our computing device can ask M queries simultaneously, the model with parallel queries. We obtain matching upper and lower bounds on the number of such M-queries needed to find a local maximum point of a discrete function. This leads to a family of search procedures that generalize Fibonacci and binary search (respectively, for odd and even M).. Finally, we note that our own interest in local maximum search came from a completely different direction: applications of query complexity in logic and formal arithmetic. In the papers [2, 3] , query complexity lower bounds were applied to separate some fragments of Peano arithmetic. In particular, in [3] a logarithmic lower bound on the query complexity of the problem of computing a lmp of a discrete function 2 was used to show the independence of the schema of induction for decidable predicates I ∆ 1 from the set of all true arithmetical Π 2 -sentences.. Of course, the exact bounds and concrete constants dealt with in this paper are not very relevant to such theoretical applications. But, as indicated above, they might be practically important. Besides, such results are mathematically attractive because of their relation to the remarkable sequence of Fibonacci numbers. As a corollary of the previous theorems we obtain. Note that α 1 is the 'golden ratio'.

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