Long-term information collection with energy harvesting wireless sensors: a multi-armed bandit based approach Abstract This paper reports on the development of a multi-agent approach to long-term information collection in networks of energy harvesting wireless sensors. In particular, we focus on developing energy management and data routing policies that adapt their behaviour according to the energy that is harvested, in order to maximise the amount of information collected given the available energy budget. In so doing, we introduce a new energy management technique, based on multi-armed bandit learning, that allows each agent to adaptively allocate its energy budget across the tasks of data sampling, receiving and transmitting. By using this approach, each agent can learn the optimal energy budget settings that give it efficient information collection in the long run. Then, we propose two novel decentralised multi-hop algorithms for data routing. The first proveably maximises the information throughput in the network, but can sometimes involve high communication cost. The second algorithm provides near-optimal performance, but with reduced computational and communication costs. Finally, we demonstrate that, by using our approaches for energy management and routing, we can achieve a 120% improvement in long-term information collection against state-of-the-art benchmarks. Due to their flexibility, low cost and ease of deployment, networks of wireless sensors are being used in a wide variety of applications ranging from environmental, habitat and traffic monitoring, to object tracking and military field observations [11, 40, 47, 48] . Specifically, in this context, a wireless sensor network (WSN) is viewed as a network of small, densely deployed, spatially decentralised autonomous sensor devices (referred to hereafter as "nodes") communicating through a wireless communication network, whose task is monitoring physical or environmental conditions including, but not limited to, temperature, sound, vibration, pressure, seismic, infrared, magnetic and motion information [5, 30, 51] .. These networks are typically deployed for collecting information from a heterogeneous and dynamically changing environment (i.e. the characteristics may vary over both space and time), and are typically required to operate over an extended period of time (covering months or even years). Within this paper, we typically focus on environmental changes such as varying occurrence of the observed phenomena, varying distribution of collectable information (both in space and time), or network topology changes during operation time. The information collected is then typically forwarded to a base station (B S) (also referred to as a sink or gateway). 1 Information that arrives at the B S is then processed or transmitted outside the sensor network to end-users for further analysis, fulfilling the specific goals of the WSN deployment.. Note that some real-world WSNs requires newest data only, and thus, the value of information that is sampled in the past rapidly decays as time passes by. Such WSNs are typically deployed for real-time target tracking or real-time object localisation [23, 51] . Within these networks, a fundamental goal is to send collected data to the B S as fast as possible (i.e. the data has a strict delivery time constraint). On the other hand, other networks focus on collecting information within a non real-time manner. That is, the deployed network continuously collects information from the surrounding environment, without having the aforementioned strict delivery time constraint (i.e. the collected information can be delayed for a longer time before it is delivered to the B S). Since most of the WSN applications are deployed to fulfil the latter type of monitoring [11, 40, 47] , here we focus on networks where the goal is to collect information over a period of time, in a non real-time manner.. Since the energy capacity of sensor nodes is typically limited, the total operation time of WSNs is often heavily restricted [2, 47] . In particular, limited energy capacity implies rapid depletion of the sensor batteries, which may lead to insufficient data collection from the network. Given this, in order to extend the operation time of sensor networks, a number of recent research works have proposed energy harvesting sensors, which have the capability of scavenging ambient energy from their surrounding environment, using solar, vibration, temperature, and radioactive sources [6, 56, 62] . Within such settings, sensor nodes typically seek to comply with the concept of energy-neutrality, in which the energy consumption of a node should be equal to its harvested energy [33, 57] . The advantage of such approaches is that sensors can indefinitely extend their life span, which is especially important when information collection has to operate over a prolonged period of time. Given this background, in this paper, we focus in particular on the challenges associated with efficient long-term information collection in networks of sensors with rechargeable batteries. That is, we aim to maximise the total information value collected and delivered to the B S in a given extended time interval of operation, or over the entire lifetime of the network, where the nodes follow the concept of energy-neutrality. Now, to forward data to the B S, sensor nodes can use single-hop (i.e. sensors directly send data to the B S) or multi-hop (i.e. data is forwarded towards the B S via relay nodes) routing scenarios. The former needs no coordination and cooperation between the nodes. However, due the limited communication range of the sensor nodes, this scenario is only feasible when the nodes are deployed in a small area (since the B S needs to be within the communication range of all the nodes). Since WSNs typically cover a significantly larger area, the multihop routing scenario is more desirable in such networks. However, this demands an efficient control mechanism that coordinates the nodes to collect information. In particular, this mechanism dictates the information collecting and forwarding actions of the sensor nodes, so that the objective of the network deployment can be achieved [25, 32] . Against this background, this paper focuses on the control side of the WSN; that is, we propose a sensory task control mechanism that sensor nodes can use in order to maximise the total amount of information collected within a prolonged period of time.. Such control mechanisms fall into two broad categories: centralised and decentralised. In the former, a single controller receives information from all the nodes, and then determines the actions of each node indicating how they should sample, receive, forward, and route data. Within this approach, however, the central controller is required to perform a large number of computations in order to find each node's optimal actions. Thus, it often represents a significant computational bottleneck, especially in large networks. Furthermore, since the controller needs to collect all the information from the nodes, there is typically a delay in time before it can start determining the nodes' actions. Given this, the centralised approach may not respond well to the environmental changes, and thus, it can suffer from a lack of ability to efficiently adapt to those changes. In contrast, in decentralised control regimes such a central controller does not exist. Instead, the nodes are autonomous and each decides its individual actions based on its own local state and observations, and those of its neighbouring nodes. Thus, the aforementioned disadvantages disappear within the decentralised control regime [7, 58] . Therefore, in this work, we focus on decentralised control mechanism for WSNs. However, this approach raises several new challenges. Specifically, to achieve system-wide goals, the nodes must typically coordinate their actions with their neighbours (e.g. to forward data or to track objects). In addition, since the nodes typically operate in a dynamically changing environment, they must be able to autonomously adapt their behaviour, without having global information about the system, in order to achieve the long-term global goals (e.g. maximal information collection or optimal coverage) [9] . Such issues naturally lend themselves to a multi-agent system (MAS) perspective [36, 45, 52] , in which each sensor is represented by an agent, which autonomously and cooperatively acts, in order to achieve system-wide objectives [29] .. Against this background, the information collection problem that we address consists of a set of energy harvesting sensor agents (i.e. nodes), collecting information from a dynamic environment over an extended period of time, without the aid of a centralised controller. However, due to the limited energy harvesting capacity of the agents [31] , energy efficiency is perhaps the most important issue within the information collection problem [11, 53] . In particular, since the agents follow the concept of energy-neutrality, their energy consumption cannot exceed the amount of energy that they can harvest. Given this, it is important to wisely manage the energy consumption of the agents, such that they can decide whether to allocate more of this scarce resource to the tasks of sampling, receiving, or transmitting data, in order to achieve maximal long-term information collection. In addition, we also need to develop routing techniques in order to deliver the data to the B S, and thus, to maximise the amount of information collected in the network. Given this, in this paper, we focus in particular on the challenges of energy management and data routing. However, tackling this joint problem of energy management and routing is hard. In particular, each agent has a number of options to allocate amounts of energy to its sensory tasks. In addition, it needs to decide which packet it has to send, and to whom among its neighbouring agents. These options together result in a large task combination space (i.e. the space of combined tasks of energy allocation and packet transmission/receiving), from which the agent has to determine an optimal one (i.e. the task combination that leads to the desired goal of the network). This task combination space is typically exponential, compared to the size of the network, so the joint problem quickly becomes infeasible in terms of complexity. Thus, to simplify the complexity of the original joint problem, we separate the energy management and data routing problems. However, as we will show, by using the solutions of the separated problems, efficient information collection can be still achieved.. In more detail, the decomposition of the original problem can be described as follows. It is based on the observation that by adaptively setting the value of the energy budgets allocated to the various sensory tasks, the agents should achieve better performance in dynamic environments than systems without the ability to adapt in this fashion. However, in order to determine which energy budget allocation combinations are optimal (exploitation), the agent first has to learn the performance of all the combinations (exploration). Thus, it has to balance between exploration and exploitation. Given this, within the energy management problem, we seek for an efficient learning method that finds a trade-off between exploring and exploiting the energy budget allocation combinations, in order to achieve optimal performance of long-term information collection. Now, suppose that all the agents have already set their energy budget value for sampling, receiving, and transmitting tasks. In this case, to maximise the value of the total collected information, it is obvious that we need to maximise the total information value of data sampled or relayed by agents that are one hop from the B S. The latter, however, is equal to data that is sampled or relayed by agents that are two hops from the B S, and so on. Thus, it is also important to maximise the information throughput (i.e. the total transmitted information value) between neighbouring layers of agents (i.e. the group of agents that are the same distance from the B S) by using efficient routing techniques. This forms the routing problem we aim to solve within our paper.. To solve the energy management problem, we propose a multi-armed bandit learning (MAB) based energy management model for each agent within the network. In particular, within the MAB model, each agent chooses from its action set (i.e. set of energy budget allocations) at each round, and, based on this choice, it gets a reward. The goal of the agent is simply to maximise its total reward over a given time period. For the routing problem, we propose two simple decentralised routing algorithms. The first is proveably optimal, but can sometimes use a large number of communication messages to coordinate the routing. The second algorithm is near-optimal, but its communication cost is significantly lower. By using one of the proposed routing algorithms, our approach can calculate the total amount of information throughput that the routing algorithm produces within that particular time step. This amount of information then forms the reward value that the MAB model gets by using the chosen energy budget allocation combination (see Sect. 4 for more details). With this reward value, the MAB model gets the feedback about the efficiency of the chosen energy allocation combination, and thus, it can learn which combinations are more efficient ones.. Given this context, this work advances the-state-of-the-art in the following specific ways:. -We introduce the first integrated model for WSNs that considers energy neutrality, adaptability, information content valuation techniques and long-term efficiency.. -We devise the first multi-armed bandit learning based energy budget allocation approach, called MAB/EM. Based on this, we show how efficient energy management can be sustained in the long term, by using this approach. -We propose two simple decentralised routing algorithms, MITRA and MITRA τ . The former is the first to proveably maximise the total information throughput between layers of agents, whilst the latter has a near-optimal performance (it achieves, on average, 98% of the optimal solution), but with a reduced communication cost. -We empirically evaluate the performance of these algorithms through extensive simulations and show that information collection is increased by up to 120%, by applying the proposed algorithms, compared to that of USAC, a state-of-the-art method (see Sect. 2 for more details of USAC). Furthermore, we show that the communication cost of our approaches are low, compared to the cost of real data transmission.. The remainder of this paper is organised as follows. First, we present related work in this area in Sect. 2, and detail why it does not meet all our requirements. Following this, we give the formal descriptions of our network model and research objectives in Sect. 3. We then discuss our approach for efficient long-term data collection, which includes the MAB learning based energy management method (Sect. 4), and routing algorithms (Sect. 5), respectively. Our approach is then empirically evaluated in Sect. 6. Finally, Sect.7 concludes. In this paper, we studied long-term information collection in the WSN domain. In particular, first we looked at previous on work energy management and data routing in WSNs. These are the perspectives from which efficient information collection can be achieved. Following this, we introduced our model for WSNs that includes the aforementioned perspectives, and we formalised our main objective of maximising the total amount of collected information at the base station over a given finite time interval.. In a review of the relevant literature, we demonstrated that none of the state-of-the-art algorithms in the aforementioned perspectives meets all of our research requirements for long-term information collection. Given this, we developed a novel model that enables learning and adapting to the environmental changes. In particular, we focused on adaptive energy management and routing, whilst we assumed that the data sampling and information content valuation parts of the model use state-of-the-art techniques. In so doing, we decomposed the original problem into two sub-problems, namely: (i) energy management; and (ii) maximal information throughput routing.. Against this background, we proposed a multi-armed bandit based approach called MAB/EM for the energy management problem. In particular, we first introduced the MAB model, which forms the foundation of our approach. Then we reduced the energy management problem into a MAB problem, by defining the actions and the reward functions for the agents. Following this, we described in more detail a state-of-the-art MAB algorithm, Exp3, that can be used to efficiently deal with the energy management problem.. For the maximal information throughput routing problem, we devised two decentralised routing algorithms, MITRA (for maximal information throughput routing algorithm), and MITRA τ , respectively. We proved that MITRA provides the optimal solution for the maximal information throughput routing problem. Furthermore, we also provided an upper bound for the number of communication rounds that MITRA needs to use within a time slot. Since the total number of communication rounds that MITRA uses may be large, we modified MITRA so that the number of communication rounds is reduced. The modification resulted in the introduction of MITRA τ .. Following this, we demonstrated the efficiency of our approach (i.e. MAB/EM combined with MITRA τ , where τ = 8) through extensive simulation results. In particular, to measure the efficiency of our approach, we compared with a state-of-the-art non-learning information collection algorithm, USAC. Moreover, to measure the performance surplus that MAB/EM adds to our approach, we also used a non-learning algorithm, that solely uses MITRA, as a benchmark method. Both comparisons showed that MAB/EM with MITRA τ together are efficient in terms of long-term information collection, since it can adapt to the environmental changes. In particular, we demonstrated that, within systems with high values of information discount factor, our approach outperforms USAC. However, we also showed that as the discount factor is decreased, the performance of our approach also decreases. In addition, we also empirically showed that by choosing small values of τ , near-optimal routing performance can still be achieved, whilst the number of communication rounds is significantly reduced. Given this, the integrated model and the proposed algorithms are particularly useful for non-real time monitoring systems (i.e. the information discount factor is high), in which the environment has to be monitored over a prolonged time interval, and unpredicted, important events should be distinguished from the other events.. In our WSN model, we assumed that agents can harvest energy over the whole period of their operation time, and thus, they can follow the concept of energy-neutrality. In particular, we assumed that the energy budget that each agent can use at each time slot is fixed over time. This indicates that the agent's action set does not change over time either. However, there are systems in which this assumption does not hold. In particular, for example, sensor agents with solar energy collectors may not perform well in energy harvesting if they are deployed in environments with cloudy weather. In these cases, agents may fail to comply with the concept of energy-neutrality. Given this, we aim to extend our work to systems in which energy harvesting is either not efficient or not feasible. More precisely, within these systems, agents need to decide whether to follow the concept of energy-neutrality, and thus, they should be able to save energy for time slots when energy harvesting is not possible, in order to achieve efficient long-term information collection. However, this implies that the current MAB model is not suitable for such systems, since the action set of each agent is not fixed over time. Given this, we need to modify the MAB concept so that this extended model can be efficiently tackled as well.

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 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 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 B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O 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 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The Formula One tire changing robot (F1-TCR) Abstract:BRIEF MECHANICAL APPROACHOur proposed robotic system consists of 5 manipulators: one for each of the tires, and a fifth one for the fuel tank. To preserve the environment of the pit stop and to assure the comfort of the team we implement suspended manipulators. The support of the 5 arms will allow a sliding motion of each arm and will not create any obstacles or driving difficulties for the pilot. The support has 2 double longitudinal branches on which the arms are to be suspended. The sliding mechanism of the arms is essential for the end effector positioning. The material used has to be resistant, of low elasticity and capable of sustaining the mass of the arms. Each of the tires of a Formula One car is fixed to the body with a single central screw (Figure 3 ). This design allows a flexible end -effector with decent power and mass requirements. The main advantage introduced by the system proposed here is the low-variance pit-stop time difference. Once a prototype is ready, further work will allow minimization of this time (currently estimated at 10 seconds). A second advantage is the elimination of human risks. The 5 manipulators are able not only to change the tires of a car and refuel without assistance, but also to obtain critical parameters of the car and interpret them in real-time. Future work will address the refueling manipulator and complete the integration of the entire system within the FIA restrictions.

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Solid-State Disk with Double Data Rate DRAM Interface for High-Performance PCs We propose a Solid-State Disk (SSD) with a Double Data Rate (DDR) DRAM interface for high-performance PCs. Traditional SSDs simply inherit the interface protocol of Hard Disk Drives (HDD) such as Parallel Advanced Technology Attachment (PATA) or Serial-ATA (SATA) for maintaining the compatibility. However, SSD itself provides much higher performance than HDD, hence the interface also needs to be enhanced. Unlike the traditional SSDs, the proposed SSD with DDR DRAM interface is placed in the North Bridge which provides two or more DDR DRAM interface ports in high-performance PCs. The novelty of our work is on DQS signaling scheme which allows arbitrary Column Address Strobe (CAS) latency unlike typical DDR DRAM interface scheme. The experimental results show that the proposed SSD maximally outperforms the traditional SSD by 8.7 times in read mode, by 1.5 times in write mode. Also, for synthetic workloads, the proposed scheme shows performance improvement over the conventional architecture by a factor of 1.6 times. SSD is a massive storage device based on NAND Flash memories. It is gradually replacing mechanical HDDs thanks to its non-volatile, low-power, silent, and shockresistant features in mobile and desktop PCs. Compared to HDDs, the major disadvantage of SSD is its cost. However, its cost is rapidly decreasing, since NAND Flash memory technology is continuously evolving. Over the past decade, the density of NAND Flash memory has doubled on every 12 month according to Hwang's law, hence SSD will lead the massive storage market in the near future. Even though modern SSDs outperform HDDs, many research works continue to pursue further increases in their performance from the architectural perspective. Lee et al. proposed a new NAND Flash memory package with smart buffer cache for exploiting the spatial and temporal localities [1] . Park et al. proposed an energy aware demand paging using Clean First LRU algorithm which minimizes the number of write or erase operations [2] . Kang et al. proposed a multi-channel architecture using I/O parallelism such as striping, interleaving and pipelining [3] . The authors in [4] host interface and NAND Flash memory interface. Also, the authors in [5] enhanced data throughput using multi-channel and way interleaving schemes. However, all of these works focused on the internal architecture of SSD. On the contrary, we focus on the interface scheme of SSD, since it would be a performance bottleneck according to Amdahl's law when the internal architecture of SSD is continuously improved. Table 1 shows a summary of high-performance interface schemes which are recognized as future SSD interface candidates in industry. Among those interface schemes, DDR DRAM interface delivers the highest bandwidth in the same generation. For this reason, we investigate an SSD with DDR DRAM interface for high-performance PCs in this work. The interface is well tailored to an SSD for arbitrary length of burst data transfer with arbitrary CAS latency which are not necessary for conventional DDR DRAMs. Such an enhanced SSD greatly improves the PC performance when it transfers massive data to and from the SSD. The block diagram of the enhanced PC architecture is shown in Fig. 2 (b) . The SSD is connected to North Bridge through the DDR DRAM interface. The major advantages of this architecture are two folds. First, DDR DRAM interface provides higher bandwidth than SATA interface. Second, South Bridge is eliminated in a data path between main memory and SSD, hence the arbitration overhead is reduced. By eliminating the South Bridge, the following changes are required. The SATA controller is no longer necessary, while the DRAM controller is extended for supporting the proposed SSD. CPU issues a DMA command to the DRAM controller in North Bridge, PRD fetching and the data transfer between DRAM and SSD are also performed by DMA in DRAM controller. In case of read operation, transfer operation sequence is 'A→C→D→B→E'. And the operation sequence 'C→D→B→E' is repeated to complete data transfer. In write operation, the operation sequence is 'A→B→E→D→C'. The operation sequence 'B→E→D→C' is repeated as in read operation. As the price of NAND Flash memories is decreasing, the demand for high performance SSDs will increase. However, the conventional SSD interface scheme can be a performance bottleneck of a high performance SSD. The proposed interface scheme shows the significant performance improvements in both write and read modes of an SSD. The experimental results showed that the proposed SSD maximally outperforms the traditional SSD by 8.7 times in read mode, by 1.5 times in write mode. Also, for synthetic workloads, the proposed scheme shows performance improvement over the conventional architecture by a factor of 1.6 times. Furthermore, the impact of our improvement will become larger as SSD itself becomes faster as shown in the experimental results of two extreme read cases.

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Encoding and decoding of analog signals with a population of neurons Abstract-In this paper, we discuss how The, field of computational neuroscience has experienced a tremendous expansion over the last several decades. Ever since the fundamental work of Hodgkin and Huxley [I] in the early 1950s that established computational neuroscience as a discipline, scientists have been trying to attach a meaning to the process of neural "computation". Even though, the "exact" mechanism of information processing at the level of neurons is still arguable, there have emerged several viable theories. One of them proposes that the information is encoded in a spike train, where in response to an excitatory synaptic stimulus, the neuron fires a series of action potentials [2] . Others claim that not all neurons are equipped with a spike generating mechanism! and even if they are, they fire very few action potentials, suggesting, therefore, that such a sparse representation cannot be Typeset by AMS-TF)( viewed as a frequency code. This theory proposes that the timing of spike occurrence, together with a synchronization (simultaneous or correlated firing of a group of neurons), is responsible for encoding and information processing [3] . Finally, a recently developed theory suggests that it is a nonlinear action at the level of a neuron dendritic tree that is responsible for a rich class of information processing [4] . Even though these theories do not necessarily contradict each other, this article will focus only on the first one.. The fact that neurons can encode analog, time-dependent signals into spike trains has been known for several decades [5] . Roughly speaking, a current input into the membrane of a neuron produces a "spiky" signal of the membrane potential.. Moreover, the frequency of the spikes increases monotonically with the amplitude of the injected current. Therefore, an analog input signal gets encoded (modulated) into a spike train, and this is often referred to as rate coding [2] . For a constant current input 5 to a neuron, the membrane potential has a constant frequency of spiking, which we shall denote by e(x). This quantity we shall refer to as the activity of a neuron, although other names are also commonly used, e.g., response tuning curve [6] . A typical activity curve is shown in Figure 1 . Note that a neuron produces spikes if the amplitude of the current exceeds the threshold Zth. Since a single neuron can only encode signals whose amplitudes exceed the threshold, for encoding signals taking both positive and negative values, we use the concept of on/off cells [7] , where on cells are primarily responsible for encoding the positive part of the signal and 08 cells are encoding the negative part of the signal. The activity curve of an on/o8 pair is shown in Figure 1 . Note that the two activity curves are shifted by a bias, indicating that the neurons can fire even if no external stimulus is applied. This common biological concept is called tonic activity or background firing rate. To conclude the section, we shall point out that the signal can be decoded (recovered) once it is encoded in a single on/o8 pair. For a more elaborate discussion on this subject, we refer to [8]. In this paper, we have described, in fairly complete details, how a population of neurons can encode analog signals. The basic idea of signal encoding is extended from a single neuron and on/off pair to a population of neurons. We demonstrate how such a population can be utilized for a specific computational task, viz., a function representation and solving a differential equation. Despite the nonlinear encoding process, we introduce the decoding rule which is linear. The concept of linear decoding represents a basis for solving differential equations using neurons, a process of transferring the dynamics from the space of external variables to the space internal variables-the activities of neurons. In this process, a further generalization of the population concept is introduced, i.e., the discussion includes a population of spiking neurons and the use of a low-pass filter. Finally, we investigate how these ideas can be implemented in a framework of biologically realistic neural networks, where the role of filters has to be replaced by a synapse. We propose a new constrained optimization scheme that gives rise to a set of synaptic weights that will preserve the information about the input at the level of presynaptic layer in a two layered BNN. Such a network can be utilized in building a memory, and the simulations have successfully been implemented in GENESIS, indicating a certain number of stationary points or distince values that can be memorized

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ADVANCES IN KNOWLEDGE ACQUISITION AND REPRESENTATION The articles in this special issue represent advances in several areas of knowledge acquisition and knowledge representation. In this article we attempt to place these advances in the context of a fundamental challenge in AI; namely, the automated acquisition of knowledge from data and the representation of this knowledge to support understanding and reasoning. We observe that while this work does indeed advance the field in important areas, the need exists to integrate these components into an end-to-end system and begin to extract general methodologies for this challenge. At the heart of this integration is the need for performance feedback throughout the process to guide the selection of alternative methods, the support for human interaction in the process, and the definition of general metrics and testbeds to evaluate progress. One of the fundamental challenges of AI is the automated acquisition of knowledge from data along with the representation of this knowledge to support reasoning and understanding. The articles in this issue span the spectrum of this challenge from feature selection for learning to new formalisms of knowledge representation to support for specific reasoning capabilities. In this article we attempt to place these advancements in the context of the aforementioned fundamental challenge and discuss future directions in the field. In this article we set out to describe the articles in this issue in the context of one of AI's grand challenges: the automated acquisition of knowledge from data along with the representation of this knowledge to support reasoning and understanding. While the articles lie on the cutting edge of the pursuit of this challenge, they represent only a small subset of the work on this challenge, which encompasses the fields of machine learning, knowledge representation and reasoning, automated theorem proving, search, uncertainty, natural language processing, and domains ranging from medical informatics to security and sociology. Still, we can draw some observations and generalizations from this work. First, most of the components of this challenge exist, and in many cases, multiple approaches exist for each phase of the challenge. While several domain-specific, end-toend approaches have been implemented, general methodologies for solving this challenge are still under investigation. Second, as with the knowledge discovery process 7 , this challenge requires an iterative approach, adapting and refining based on performance feedback and supporting human interaction and guidance. While such feedback has been incorporated into approaches to individual phases, feedback over the process as a whole is an open issue. Third, evaluation of approaches to this challenge requires new benchmark datasets or testbeds. Datasets would need to specify not only the initial data from which knowledge is acquired, but also the types of knowledge desired, alternatives for its representation, and goals for reasoning over this knowledge. Likewise, testbeds akin to games and simulators are necessary to exercise and evaluate the various components of the challenge. One possible evaluation testbed is the automated acquisition of semantic knowledge from the world-wide web to support natural language, semantic-based (rather than keyword-based) querying of and reasoning about the web content knowledge. Such evaluations will drive the field toward integration of methods rather than just parallel pursuit of complementary sub-problems, with the ultimate goal of addressing the grand challenge of knowledge acquisition, representation and reasoning.

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Strategies in Combined Learning via Logic Programs We discuss the adoption of a three-valued setting for inductive concept learning. Distinguishing between what is true, what is false and what is unknown can be useful in situations where decisions have to be taken on the basis of scarce, ambiguous, or downright contradictory information. In a three-valued setting, we learn a definition for both the target concept and its opposite, considering positive and negative examples as instances of two disjoint classes. To this purpose, we adopt Extended Logic Programs (ELP) under a Well-Founded Semantics with explicit negation (WFSX) as the representation formalism for learning, and show how ELPs can be used to specify combinations of strategies in a declarative way also coping with contradiction and exceptions.Explicit negation is used to represent the opposite concept, while default negation is used to ensure consistency and to handle exceptions to general rules. Exceptions are represented by examples covered by the definition for a concept that belong to the training set for the opposite concept.Standard Inductive Logic Programming techniques are employed to learn the concept and its opposite. Depending on the adopted technique, we can learn the most general or the least general definition. Thus, four epistemological varieties occur, resulting from the combination of most general and least general solutions for the positive and negative concept. We discuss the factors that should be taken into account when choosing and strategically combining the generality levels for positive and negative concepts.In the paper, we also handle the issue of strategic combination of possibly contradictory learnt definitions of a predicate and its explicit negation.All in all, we show that extended logic programs under well-founded semantics with explicit negation add expressivity to learning tasks, and allow the tackling of a number of representation and strategic issues in a principled way.Our techniques have been implemented and examples run on a state-of-the-art logic programming system with tabling which implements WFSX. Most work on inductive concept learning considers a two-valued setting. In such a setting, what is not entailed by the learned theory is considered false, on the basis of the Closed World Assumption (CWA) (Reiter, 1978) . However, in practice, it is more often the case that we are confident about the truth or falsity of only a limited number of facts, and are not able to draw any conclusion about the remaining ones, because the available information is too scarce. Like it has been pointed out in (De Raedt & Bruynooghe, 1990; De Raedt, 1992) , this is typically the case of an autonomous agent that, in an incremental way, gathers information from its surrounding world. Such an agent needs to distinguish between what is true, what is false and what is unknown, and therefore needs to learn within a richer setting.. To this purpose, we adopt the class of Extended Logic Programs (ELP, for short, in the sequel) as the representation language for learning in a three-valued setting. ELP contains two kinds of negation: default negation plus a second form of negation, called explicit, whose combination has been recognized elsewhere as a very expressive means of knowledge representation. The adoption of ELP allows one to deal directly in the language with incomplete and contradictory knowledge, with exceptions through default negation, as well as with truly negative information by means of explicit negation (Pereira & Alferes, 1992; Alferes & Pereira, 1996; Alferes, Damásio, & Pereira, 1998) . For instance, in (Alferes & Pereira, 1996; Baral & Gelfond, 1994; Damásio & Pereira, 1998; Leite & Pereira, 1998) it is shown how ELP is applicable to such diverse domains of knowledge representation as concept hierarchies, reasoning about actions, belief revision, counterfactuals, diagnosis, updates and debugging.. In this work, we show, that various approaches and strategies can be adopted in Inductive Logic Programming (ILP, henceforth) for learning with ELP under an extension of wellfounded semantics. As in (Inoue & Kudoh, 1997; Inoue, 1998) , where answer-sets semantics is used, the learning process starts from a set of positive and negative examples plus some background knowledge in the form of an extended logic program. Positive and negative information in the training set are treated equally, by learning a definition for both a positive concept p and its (explicitly) negated concept ¬ p. Coverage of examples is tested by adopting the SLX interpreter for ELP under the Well-Founded Semantics with explicit negation (WFSX) defined in (Alferes & Pereira, 1996; , and valid for its paraconsistent version (Damásio & Pereira, 1998) .. Default negation is used in the learning process to handle exceptions to general rules. Exceptions are examples covered by the definition for the positive concept that belong to the training set for the negative concept or examples covered by the definition for the negative concept that belong to the training set for the positive concept.. In this work, we adopt standard ILP techniques to learn a concept and its opposite. Depending on the technique adopted, one can learn the most general or the least general definition for each concept. Accordingly, four epistemological varieties occur, resulting from the mutual combination of most general and least general solutions for the positive and negative concepts. These possibilities are expressed via ELP, and we discuss some of the factors that should be taken into account when choosing the level of generality of each, and their combination, to define a specific learning strategy, and how to cope with contradictions. (In the paper, we concentrate on single predicate learning, for the sake of simplicity.) Indeed, separately learned positive and negative concepts may conflict and, in order to handle possible contradiction, contradictory learned rules are made defeasible by making the learned definition for a positive concept p depend on the default negation of the negative concept ¬ p, and vice-versa, i.e., each definition is introduced as an exception to the other. This way of coping with contradiction can be even generalized for learning n disjoint classes, or modified in order to take into account preferences among multiple learning agents or information sources (see Lamma, Riguzzi, & Pereira, 1999) .. The paper is organized as follows. We first motivate the use of ELP as target and background language in Section 2, and introduce the new ILP framework in Section 3. We then examine, in Section 4, factors to be taken into account when choosing the level of generality of learned theories. Section 5 proposes how to combine the learned definitions within ELP in order to avoid inconsistencies on unseen atoms and their opposites, through the use of mutually defeating ("non-deterministic") rules, and how to incorporate exceptions through negation by default. A description of our algorithm for learning ELP follows next, in Section 6, and the overall system implementation in Section 7. Section 8 evaluates the obtained classification accuracy. Finally, we examine related works in Section 9. The two-valued setting that has been adopted in most work on ILP and Inductive Concept Learning in general is not sufficient in many cases where we need to represent real world data. This is for example the case of an agent that has to learn the effect of the actions it can perform on the domain by performing experiments. Such an agent needs to learn a definition for allowed actions, forbidden actions and actions with an unknown outcome, and therefore it needs to learn in a richer three-valued setting.. In order to achieve that in ILP, the class of extended logic programs under the wellfounded semantics with explicit negation (WFSX) is adopted by us as the representation language. This language allows two kinds of negation, default negation plus a second form of negation called explicit, that is mustered in order to explicitly represent negative information. Adopting extended logic programs in ILP prosecutes the general trend in Machine Learning of extending the representation language in order to overcome the recognized limitations of existing systems.. The programs that are learned will contain a definition for the concept and its opposite, where the opposite concept is expressed by means of explicit negation. Standard ILP techniques can be adopted to separately learn the definitions for the concept and its opposite. Depending on the adopted technique, one can learn the most general or the least general definition.. The two definitions learned may overlap and the inconsistency is resolved in a different way for atoms in the training set and for unseen atoms: atoms in the training set are considered exceptions, while unseen atoms are considered unknown. The different behaviour is obtained by employing negation by default in the definitions: default abnormality literals are used in order to consider exceptions to rules, while non-deterministic rules are used in order to obtain an unknown value for unseen atoms. We have shown how the adoption of extended logic programs in ILP allows to tackle both learning in a three-valued setting and specify the combination of strategies in a declarative way, also coping with contradiction and exceptions in the process.. The system LIVE (Learning in a three-Valued Environment) has been developed to implement the above mentioned techniques. 6 In particular, the system learns a definition for both the concept and its opposite and is able to identify exceptions and treat them through default negation. The system is parametric in the procedure used for learning each definition: it can adopt either a top-down algorithm, using beam-search and a heuristic necessity stopping criterion, or a bottom-up algorithm, that exploits the GOLEM system. The adoption of negation in learning has been investigated by many authors. Many propositional learning systems learn a definition for both the concept and its opposite. For example, systems that learn decision trees, as c4.5 (Quinlan, 1993) , or decision rules, as the AQ family of systems (Michalski, 1973) , are able to solve the problem of learning a definition for n classes, which generalizes the problem of learning a concept and its opposite. However, in most cases the definitions learned are assumed to cover the whole universe of discourse: no undefined classification is produced, any instance is always classified as belonging to one of the classes. Instead, we classify as undefined the instances for which the learned definitions do not give a unanimous response.. When learning multiple concepts, it may be the case that the descriptions learned are overlapping. We have considered this case as non-desirable: this is reasonable when learning a concept and its opposite but it may not be the case when learning more than two concepts (see (Drobnic & Gams, 1993) ). As it has been pointed out by (Michalski, 1984) , in some cases it is useful to produce more than one classification for an instance: for example if a patient has two diseases, his symptoms should satisfy the descriptions of both diseases. A subject for future work will be to consider classes of paraconsistent logic programs where the overlap of definitions for p and ¬ p (and, in general, multiple concepts) is allowed.. The problems raised by negation and uncertainty in concept-learning, and Inductive Logic Programming in particular, were pointed out in some previous work (e.g. (Bain & Muggleton, 1992; De Raedt & Bruynooghe, 1990; De Raedt, 1992) (De Raedt & Bruynooghe, 1990) proposed to use a three-valued logic (later on formally defined in (De Raedt, 1992) ) and an explicit definition of the negated concept in concept learning. This technique has been integrated within the CLINT system, an interactive concept-learner. In the resulting system, both a positive and a negative definition are learned for a concept (predicate) p, stating, respectively, the conditions under which p is true and those under which it is false. The definitions are learned so that they do not produce an inconsistency on the examples. Furthermore, CLINT does not produce inconsistencies also on unseen examples because of its constraint handling mechanism, since it would assert the constraint p, not p → false, and take care that it is never violated. Distinctly from this system, we make sure that the two definitions do not produce inconsistency on unseen atoms by making learned rules non-deterministic. This way, we are able to learn definitions for exceptions to both concepts so that the information about contradiction is still available. Another difference is that we cope with and employ simultaneously two kinds of negation, the explicit one, to state what is false, and the default (defeasible) one, to state what can be assumed false.. The system LELP (Learning Extended Logic Programs) (Inoue & Kudoh, 1997) learns ELPs under answer-set semantics. LELP is able to learn non-deterministic default rules with a hierarchy of exceptions. Hierarchical learning of exceptions can be easily introduced in our system (see Lamma, Riguzzi, & Pereira, 1988) ). From the viewpoint of the learning problems that the two algorithms can solve, they are equivalent when the background is a stratified extended logic program, because then our and their semantics coincide. All the examples shown in (Inoue & Kudoh, 1997) are stratified and therefore they can be learned by our algorithm and, viceversa, example in Section 5 can be learned by LELP. However, when the background is a non-stratified extended logic program, the adoption of a well-founded semantics gives a number of advantages with respect to the answer-set semantics. For non-stratified background theories, answer-sets semantics does not enjoy the structural property of relevance (Dix, 1995) , like our WFSX does, and so they cannot employ any top-down proof procedure. Furthermore, answer-set semantics is not cumulative (Dix, 1995) i.e., if you add a lemma then the semantics can change, and thus the improvement in efficiency given by tabling cannot be obtained. Moreover, by means of WFSX, we have introduced a method to choose one concept when the other is undefined which they cannot replicate because in the answer-set semantics one has to compute eventually all answer-sets to find out if a literal is undefined. The structure of the two algorithms is similar: LELP first generates candidate rules from a concept using an ordinary ILP framework. Then exceptions are identified (as covered examples of the opposite set) and rules specialized through negation as default and abnormality literals, which are then assumed to prevent the coverage of exceptions. These assumptions can be, in their turn, generalized to generate hierarchical default rules. One difference between us and (Inoue & Kudoh, 1997) is in the level of generality of the definitions we can learn. LELP learns a definition for a concept only from positive examples of that concept and therefore it can only employ a bottom-up ILP technique and learn the LGS. Instead, we can choose whether to adopt a bottom-up or a top-down algorithm, and we can learn theories of different generality for different target concepts by integrating, in a declarative way, the learned definitions into a single ELP. Another difference consists in that LELP learns a definition only for the concept that has the highest number of examples in the training set. It learns both positive and negative concepts only when the number of positive examples is close to that of negative ones (in 60%-40% range), while we always learn both concepts.. Finally, many works have considered multi-strategy learners or multi-source learners. A multi-strategy learner combines learning strategies to produce effective hypotheses (see (Jenkins, 1993) ). A multi-source learner implements an algorithm for integrating knowledge produced by the separate learners. Multi-strategy learning has been adopted, for instance, for the improvement of classification accuracy (Drobnic & Gams, 1993) , and to equip an autonomous agent with capabilities to survive in an hostile environment (De Raedt et al., 1993) .. Our approach considers two separate concept-based learners, in order to learn a definition for a concept and its opposite. Multiple (opposite) target concepts constitute part of the learned knowledge base, and each learning element is able to adopt a bottom-up or a top-down strategy in learning rules. This can be easily generalized to learn definitions for n disjoint classes of concepts or for multiple agent learning (see our (Lamma, Riguzzi, & Pereira, 1999) ). Very often, the hypothesis can be more general than what is required. The second step of our approach, devoted to the application of strategies for eliminating learned contradictions, can be seen as a multi-source learner (Jenkins, 1993) or a meta-level one (Chan & Stolfo, 1993) , where the learned definitions are combined to obtain a non-contradictory extended logic program. ELPs are used to specify combinations of strategies in a declarative way, and to recover, in the the process, the consistency of the learned theory. A top-down ILP algorithm (cf. (Lavrač & Džeroski, 1994) ) has been integrated with the procedure SLX for testing the coverage in order to learn the most general solutions. The specialization loop of the top-down system consists of a beam search in the space of possible clauses. At each step of the loop, the system removes the best clause from the beam and generates refinements. They are then evaluated according to an accuracy heuristic function, and their refinements covering at least one positive example are added to the beam. The best clause found so far is also separately stored: this clause is compared with each refinement and is replaced if the refinement is better. The specialization loop stops when either the best clause in the beam is consistent or the beam becomes empty. Then the system returns the best clause found so far. The beam may become empty before a consistent clause is found and in this case the system will return an inconsistent clause.. In order to find least general solutions, the GOLEM (Muggleton & Feng, 1990 ) system is employed. The finite well-founded model is computed, through SLX, and is transformed by replacing literals of the form ¬A with new predicate symbols of the form neg A. Then GOLEM is called with the computed model as background knowledge. The output of GOLEM is then parsed in order to extract the clauses generated by rlgg before they are post-processed by dropping literals. Thus, the clauses that are extracted belong to the least general solution. In fact, they are obtained by randomly picking couples of examples, computing their rlgg and choosing the consistent one that covers the largest number of positive examples. This clause is further generalized by choosing randomly new positive examples and computing the rlgg of the previously generated clause and each of the examples. The consistent generalization that covers more examples is chosen and further generalized until the clause starts covering some negative examples. An inverse model transformation is then applied to the rules thus obtained by substituting each literal of the form neg A with the literal ¬A.

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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 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 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 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 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 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 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 B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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Feature normalization based on non-extensive statistics for speech recognition Most compensation methods to improve the robustness of speech recognition systems in noisy environments such as spectral subtraction, CMN, and MVN, rely on the fact that noise and speech spectra are independent. However, the use of limited window in signal processing may introduce a cross-term between them, which deteriorates the speech recognition accuracy. To tackle this problem, we introduce the q-logarithmic (q-log) spectral domain of non-extensive statistics and propose q-log spectral mean normalization (q-LSMN) which is an extension of log spectral mean normalization (LSMN) to this domain. The recognition experiments on a synthesized noisy speech database, the Aurora-2 database, showed that q-LSMN was consistently better than the conventional normalization methods, CMN, LSMN, and MVN. Furthermore, q-LSMN was even more effective when applied to a real noisy environment in the CENS-REC-2 database. It significantly outperformed ETSI AFE front-end. Current automatic speech recognition (ASR) systems are able to achieve good performance in quiet environments. However, their performance significantly degrades in noisy environments. The speech features are altered in the presence of noise. This causes a mismatch between quiet training conditions and recognition conditions, which are noisy. Environmental noises are classified into two categories: additive noise and convolutive noise. Examples of additive noise are street noise, train noise, computer fan, and the voice of other persons. Examples of convolutive noise are reverberation and channel distortions.. Robust speech recognition against noise has been an active area of research for the last few decades. A number of methods have been developed in this field. Their examples are spectral subtraction (Boll, 1979) , vector Taylor series (VTS) (Moreno et al., 1996) and parallel model combination (Gales and Young, 1996) . All these methods are based on an extensive statistics in which additivity holds.. Common features used for speech recognition, such as Mel frequency cepstral coefficient (MFCC) and perceptual linear prediction (PLP), are derived from short-time power spectra of speech. In short-time processing such as shorttime Fourier transform (STFT), the speech signal is processed in blocks over which speech is assumed to be stationary. This block of speech is called a frame. The length of a frame is usually between 5 and 30 ms. In the time domain, the relation between noisy speech yðtÞ, clean speech sðtÞ, additive noise nðtÞ and convolutive noise hðtÞ can be written as the following:. yðtÞ ¼ sðtÞ Ã hðtÞ þ nðtÞ: . where k is the index of frequency bin (a total frequency components K ¼ 256) and m is the frame index and:. X ðm; kÞ ¼ jX ðm; kÞj exp jh X ðm; kÞ ð Þ ; ð4Þ N ðm; kÞ ¼ jN ðm; kÞj exp jh N ðm; kÞ ð Þ : ð5Þ jX ðm; kÞj, jN ðm; kÞj are the magnitude spectra, and h X ðm; kÞ, h N ðm; kÞ are the phase spectra of filtered speech, i.e. the clean speech signal affected by convolutive noise only, and additive noise respectively. From (3), we obtain the power spectral representation of noisy speech as follows: . where N Ã ðm; kÞ is the complex conjugate of N ðm; kÞ. Substituting (4) and (5) into (6), we obtain: jYðm; kÞj 2 ¼ jXðm; kÞj 2 þ jNðm; kÞj 2 þ 2jXðm; kÞjjNðm; kÞj cos h X ðm; kÞ À h N ðm; kÞ ð Þ ;. where h X ðm; kÞ À h N ðm; kÞ is the phase difference between X ðm; kÞ and N ðm; kÞ. The last term of Eq. (7) is called a cross-term, which depends on the phase difference between speech and noise. This cross-term is ignored in most robust speech recognition methods under the assumption that speech and noise are uncorrelated. Although this assumption is generally valid since speech and noise are statistically independent, it does not hold when applying a short-time window (20-30 ms) . Several studies have shown that the cross-term does exist in short-time power spectra (Kadambe and Boudreaux-Bartels, 1992; Jeong and Williams, 1992) . The cross-term has been shown to significantly degrade the performance of speech recognition (Deng et al., 2004; Faubel et al., 2008) . In addition, it is well known that a speech pattern is a complex system. In a speech pattern, various long-term correlations exist among its different spectral components in complex ways in various time scales. As a consequence, the additive relation between speech components and convolutive noise may not hold in the log spectral domain. It is common to combine additive noise removal methods such as spectral subtraction with feature normalization methods such as cepstral mean normalization (CMN) (Furui, 1981) to remove both additive and convolutive noise. But as previously explained, speech and convolutive noise are not additive in general, and thus the cross term exist even when the additive noise spectra are completely removed.. In this paper, we propose q-log spectral mean normalization (q-LSMN) (Pardede and Shinoda, 2011) , which is an extension of the log spectral mean normalization (LSMN) (Avendano and Hermansky, 1997) to the q-log spectral domain. We further investigate the effect of q-LSMN in various conditions and analyze its property in more detail in this paper.. A few studies have already employed the non-extensive statistics for speech recognition. Rufiner et al. (2004) added Tsallis entropy, which is defined in non-extensive statistics, and its relative change to the standard MFCC features for capturing the dynamics of speech signals. Kobayashi and Imai (1984) employed the q-log function as the spectral smoother for speech features so that they are more robust especially in lower frequency regions. Ito et al. (2000) also implemented the q-log function to provide a forward masking scale for the dynamic cepstrums. In contrast to these studies, we use the q-log function to model non-additivity in noisy speech features.. The remainder of this paper is organized as follows: In Section 2, we describe some previous studies of robust speech recognition related to our study. In Section 3, we explain the influence of the cross-term in the speech features. In Section 4, we briefly review non-extensive statistics and its q-log function. In Section 5, we explain our proposed method. In Section 6, we describe the details of spectral subtraction which we implemented to remove additive noise. In Section 7, we describe the experimental setup to evaluate our proposed method. In Section 8, we present and discuss our experimental results. Section 9 concludes this paper. We propose q-LSMN, a feature normalization method in the q-log spectral domain. The use of the q-log function enables us to represent nonadditivity of speech features, which exists when noise and speech are correlated. Our evaluation using two types of databases, Aurora-2 and CENSREC-2 databases, showed the effectiveness of our approach. q-LSMN was better than CMN and MVN in both databases. Our method outperformed ETSI AFE on the CENSREC-2 database, where we gained up to 26.1% relative improvement. This result may indicate that our method is more effective in real environments. The combination of spectral subtraction with q-LSMN was also better than the combination of spectral subtraction with CMN or MVN. We believe that our method can be used complementary to any noise removal methods other than spectral subtraction.. We should say that our non-extensive approach can not provide a clear solution to the problems of non-extensivity of the noisy speech features, but does provide an alternative approach to them. In some q -1, it provides a better solution than the original extensive ones such as CMN and LSMN from the viewpoint of efficiency and/or performance.. Our q-LSMN is based on non-extensive statistics. While it has been shown to be successful in interpreting some physical phenomena that cannot be fully explained by extensive statistics, the physical meaning of the q-value has not yet been explored much. While we proved that the use of q different from 1 is effective in robust speech recognition, the meaning of q in speech processing is still not clear and should be investigated in future.. The optimal q-value may be different in different frequency bands since noise affects each frequency band differently. While we used the same values for all the bands in this study, the optimization of q-values to each band might be promising. Another interesting topic would be the implementation of other compensation methods in the q-log domain. Aurora-2 CENSREC-2 Table 3 The word accuracy (%) of q-LSMN and the other methods after spectral subtraction for the Aurora-2 task and the CENSREC-2 task.

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


On the Stability of Dynamic Diffusion Load Balancing We consider the problem of dynamic load balancing in arbitrary (connected) networks on n nodes. Our load generation model is such that during each round, n tasks are generated on arbitrary nodes, and then (possibly after some balancing) one task is deleted from every non-empty node. Notice that this model fully saturates the resources of the network in the sense that we generate just as many new tasks per round as the network is able to delete. We show that even in this situation the system is stable, in that the total load remains bounded (as a function of n alone) over time. Our proof only requires that the underlying "communication" graph be connected. (It of course also works if we generate less than n new tasks per round, but the major contribution of this paper is the fully saturated case.) We further show that the upper bound we obtain is asymptotically tight (up to a moderate multiplicative constant) by demonstrating a corresponding lower bound on the system load for the particular example of a linear array (or path). We also show some simple negative results (i.e., instability) for work-stealing based diffusion-type algorithms in this setting. The use of parallel and distributed computing is established in many areas of science, technology, and business. One of the most crucial parameters of parallel machines is the efficient utilization of resources. Of greatest importance here is an even distribution of the workload among the processors. In particular applications exposing some kind of "irregularity" require the use of a load balancing mechanism.. A well known and much studied load balancing approach is the so-called diffusion load balancing, first introduced by Cybenko and Boillat [10, 11] . The algorithm works in synchronized rounds. The basic idea is that in every round, every processor p balances load with all its neighbors (independently, i.e., pair-wise). Let p be the load of p and q the load of some of p's neighbor q, and let d p denote the degree of the vertex p. One popular method in the discrete setting has p transferring max{0, ( p − q )/(max{d p , d q } + 1) } tasks to q in a given round. Some of many advantages of diffusion-type algorithms are the locality (no global knowledge regarding the overall load situation, or, in fact, anything except the strict neighborhood of any vertex is needed), its simplicity, and its neighborhood preservation (tasks tend to stay close to the processors where they are generated, which may help to maintain small communication overhead).. The diffusion load balancing algorithm has been thoroughly analyzed for static scenarios, where each processor has some initial number of tasks, and the objective is to distribute this load evenly among the processors as quickly as possible. Much work has been done under the assumption that every edge is only allowed to forward one task per round [15, 17, 21] or when a constant number of tasks can be passed by each processor [16] . We refer to these scenarios as token distribution problems. In addition, [12, 14] have studied the diffusion algorithm where tasks can be split arbitrarily, while [13] assumes that they are indivisible. Muthukrishnan, Ghosh, and Schultz [19] examined first-and second-order schemes for "coarse" load balancing (the goal being to reduce large discrepancies between the loads on vertices). Rabani, Sinclair, and Wanka [22] also considered the problem of coarse balancing. They model the load balancing process by a suitable Markov chain, and show this model is accurate until a certain threshold discrepancy is reached.. In contrast to the static case of load balancing and token distribution, in the dynamic setting during each round new tasks are generated (in some manner) on the set of processors, load is balanced amongst neighbors, then tasks are deleted from non-empty processors.. Much past work has studied the dynamic token distribution problem. Muthukrishnan and Rajaraman [20] studied a dynamic version where processors can forward a single task in each round. They assume an adversarial load generation model. The adversary is allowed to generate and to delete tokens from the network in every round. The simple and elegant algorithm they consider is due to [1] : A node sends a task to its neighbor if the load difference between them is at least 2 + 1, where is the maximum degree of the underlying graph. They show that the system is stable if the load change in every subset S of the nodes minus a|S| is at most (1 − )e(S) for > 0. Here e(S) is the number of outgoing edges of S and a is the change in the average load. Their system is said to be stable if the deviation of the load of any processor from the average load can be bounded. Muthukrishnan and Rajaraman left open the question whether the system is also stable for = 0.. Anshelevich, Kempe, and Kleinberg [4] gave a positive result for token distribution when = 0. They showed that under the above load generation model no processor has more than average load ±(2 + 1) · n. Anshelevich et al. also showed how their result can be generalized for edges that can forward c tokens per time step. A node sends min{c, ρ} tasks to its neighbor if the load difference is at least 2 c + ρ. In this setting no processor has more than average load ±(2 + 1)c · n as long as the load change in every subset S of the nodes minus a|S| is at most c · e(S). Additionally, they showed that a generalization of the algorithm is stable for two distinct types of jobs, and they extended their results to related flow problems.. In [6, 7] Awerbuch and Leighton use a variant of the token distribution model under the assumption that tokens can be split into arbitrarily sized parts. They use a "balancing" algorithm to approximate the multi-commodity flow problem with capacitated edges. Their method is an iterative approach where flow is queued at the vertices of the graph. In each step, the commodity which has the largest excess is shipped from one vertex to another, and then new flow is injected into the system. In this balancing process, edge capacities must always be respected. These edge capacities are analogous to the restrictions on the number of tasks that can be passed over any single edge in the token distribution problems. Furthermore, their model does not actually allow full use of those edge capacities, which is similar to the case in [20] where > 0 was required to ensure stability. The work in [2] and [5] expands the results of Awerbuch and Leighton for packet routing, but again in these cases only a constant number of tasks can be moved across any edge in a single time step.. Clearly the condition that processors can forward only a single task (or a constant number) per edge in each round significantly restricts the number and distribution of tasks that can be generated on (or deleted from) processors in each round and still obtain a stability result. Thus, in the results of [20] and [4] some dependence on the quantity e(S) (or some measure of the "edge expansion") is to be expected.. Anagnostopoulos, Kirsch, and Upfal [3] consider the setting where there are no restrictions on the number of tasks balanced between processors in a time step, and they allow a broad range of injection models. Their protocol is similar to that studied in [16] for a static setting, but is not the typical diffusion load balancing procedure. In their setting, in each step nodes are matched randomly with adjacent neighbors and matched nodes equalize their load. Hence, every processor is only involved in a single load balancing action. They show that the system is stable as long as at most wnλ tasks (in expectation) are generated in a time interval of length w, where λ < 1. Their proof method unfortunately cannot be generalized to the case of full saturation when λ = 1, which is the main focus of this paper.. In a different approach in the dynamic setting, Berenbrink, Friedetzky, and Mayr [9] consider a load balancing scheme that uses a "collision protocol" (see also [18] ) to resolve load balancing requests amongst lightly-and heavily-loaded processors. They show stability with this balancing protocol and a variety of random-ized task generation models where each processor receives, in expectation, strictly less than one newly generated task per round.

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