Recent advances in optimization techniques for statistical tabular data protection One of the main services of National Statistical Agencies (NSAs) for the current Information Society is the dissemination of large amounts of tabular data, which is obtained from microdata by crossing one or more categorical variables. NSAs must guarantee that no confidential individual information can be obtained from the released tabular data. Several statistical disclosure control methods are available for this purpose. These methods result in large linear, mixed integer linear, or quadratic mixed integer linear optimization problems. This paper reviews some of the existing approaches, with an emphasis on two of them: cell suppression problem (CSP) and controlled tabular adjustment (CTA). CSP and CTA have concentrated most of the recent research in the tabular data protection field. The particular focus of this work is on methods and results of practical interest for end-users (mostly, NSAs). Therefore, in addition to the resulting optimization models and solution approaches, computational results comparing the main optimization techniques-both optimal and heuristic-using real-world instances are also presented. National Statistical Agencies (NSAs) store information about individuals or respondents (persons, companies, etc.) in microdata files. A microdata file V of s individuals and t P 1 P 2 P 3 P 4 P variables is a s × t matrix where v ij is the value of variable j for individual i. Formally, it can be defined as a function. that maps individuals of set I to an array of t values for variables V 1 ,. . . , V t , D() being the domain of those variables. According to this domain, variables can be classified as numerical (e.g., "age", "net profit") or categorical ("sex","economy sector"). From those microdata files, tabular data is obtained by crossing one or more categorical variables. For instance, assuming a microdata file with information of inhabitants of some region, crossing variables "profession" and "municipality" the two-dimensional frequency table of Figure 1 may be obtained. Instead, the table could provide information about a third variable; these tables are named magnitude tables. For instance, the table of Figure 2 shows the overall salary for each profession and municipality. Formally, a table is a function. l being the number of categorical variables that were crossed. The result of function T (cell values) belongs to N for a frequency table, and to R for a magnitude table.. Although tabular data show aggregated information, there is a risk of disclosing individual information. For instance, if the two tables of Figures 1 and 2 are published, then any attacker knows that the salary of the unique respondent of cell (M 2 , P 3 ) is 22000e. This is named an external attacker. If there were two respondents in that cell, then any of them could deduce the other's salary, becoming an internal attacker. Even if there was a larger number of respondents, e.g. 5, if one of them had a salary of, e.g. 18000e, there would be a disclosure risk, since the contribution of the largest respondent could exceed some predefined can be obtained, and how they are modeled; this background is needed for the subsequent sections. Section 3 introduces tabular data protection methods. Sections 4 and 5 focus on two of the most widely used protection techniques, the cell suppression and the controlled tabular adjustment, both describing the optimization models and outlining the main solution approaches. This paper presented some of the techniques for tabular data protection, focusing on CSP and CTA. It also outlined the main successful optimization approaches currently being applied. They are used in real-world by NSAs for the protection of released tables. All of those approaches share, at different degrees, the same computational drawbacks: they result in large difficult MILP optimization problems. Current research for improving the solution of these MILPs is being undertaken, mainly for the most recent method, CTA. There are other alternative protection methods, like interval protection or partial cell suppression which result in a very large, even massive, linear programming problem. However, being a continuous optimization problem, recent specialized interior-point methods for structured problems (Castro, 2007b; Castro and Cuesta, 2010) are expected to be a very efficient alternative. This is research to be conducted in the near future. Adding to current CSP methods the solutions outlined in Section 4 to deal with the singleton problem is also part of the work to be done in this challenging field.

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


Threshold Group Testing on Inhibitor Model In classical group testing, one is given a population N and an unknown subset D & N of positive items, and the goal is to determine D by testing subsets of N . Threshold group testing is a generalization of classical group testing, where the outcome of a group test is determined by the number of positive items in the test. In group testing on inhibitor model, inhibitors are the third type of item that dictate the test outcome to be negative regardless of how many positives are in the test. The threshold group testing on k-inhibitor model is a natural combination of threshold group testing and inhibitor model. In this article, we provide nonadaptive algorithms to conquer the threshold group testing on k-inhibitor model where error-tolerance is considered. Furthermore, we provide a two-stage algorithm to identify all inhibitors and find a g-approximate set.

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


Uncovering distinct protein-network topologies in heterogeneous cell populations


Intermedia Synchronization Protocol for Continuous Media Using MPEG-4 in Mobile Distributed Systems The preservation of temporal dependencies among a group of processes that exchange continuous media at runtime is a key issue for emerging mobile distributed systems (MDS), such as monitoring of biosignals and interactive multiuser games. Although several works are oriented to satisfy temporal dependencies, most of them are not suitable for MDSs. In general, an MDS is characterized by the absence of global references (e.g. shared memory and wall clock), host mobility, limited processing and storage capabilities in mobile hosts, and limited bandwidth on wireless communication channels. This paper proposes an asymmetric synchronization protocol to be used at runtime in an MDS without using a common reference. One main aspect of our synchronization protocol is that it translates temporal constraints to causal dependencies of the continuous media data as seen by the mobile hosts. We simulate the protocol by considering a cellular network environment and by using MPEG-4 encoders. The simulation results show that our protocol is effective in reducing the synchronization error. In addition, the protocol is efficient in terms of processing and storage costs at the mobile devices, as well as in the overhead attached per message across the wired and wireless channels. The development of mobile distributed systems (MDS) that exchange continuous media at runtime among a group of processes has become a relevant research field. Examples of these systems include remote monitoring of biosignals for telemedicine networks and interactive multiuser games [1] [2] . An important characteristic that the MDS must fulfill is the synchronization of continuous media data in multi-party environments. The problem of synchronization in this context concerns the preservation of temporal dependencies among the continuous data (e.g. audio and video) from the time of generation to the time of presentation at the group of processes.. Numerous works have proposed mechanisms to carry out the synchronization at runtime [2] [3] [4] [5] [6] . Nevertheless, these works cannot be applied in mobile distributed systems due to the fact that they do not consider the inherent characteristics of such systems, such as: absence of global references (e.g. shared memory and wall clock), host mobility, limited processing and storage capabilities in mobile hosts, and limited bandwidth on wireless communication channels.. In this work, we propose an asymmetric and distributed synchronization protocol to be used at runtime among a group of processes in an MDS. The synchronization protocol avoids the use of a common reference by using the logical mapping model (LMM) presented in [6] . Based on the LMM our protocol translates temporal constraints to causal dependencies of the continuous media data transmitted in an MDS. The protocol satisfies temporal constrains by ensuring data causal delivery dependencies when possible. One important aspect of our work is that the temporal constraints are satisfied according to the view of the end mobile hosts and not according to some intermediate element (e.g. proxy).. We did the simulation of the protocol considering a cellular network environment and by using MPEG-4 encoders. We show in this paper that our protocol is effective in reducing the synchronization error in an MDS without requiring previous knowledge of the system nor global references.. The rest of this paper is organized as follows. In section 2, we review the related work. Section 3 presents some preliminaries. In section 4, we describe the synchronization protocol. Section 5 presents the simulation results. Finally, some conclusions are presented in Section 6. We have presented a distributed synchronization protocol for continuous media to be used at runtime among a group of processes in an MDS. The protocol avoids the use of a global reference (e.g. wall clock) by executing temporal dependencies according to the causal dependencies of the continuous media data as viewed by the end mobile hosts. To demonstrate the effectiveness and efficiency of the synchronization protocol, we carried out the simulation of the protocol considering a group of processes, a cellular network architecture and MPEG-4 encoders. The simulation results show that our protocol reduces in all cases the synchronization error at the message delivery. Such correction in most of the cases gives as a result a tolerable error according to the maximum synchronization error supported. Furthermore, the simulation results show that the protocol is efficient in terms of processing and storage cost at the mobile devices, as well as is in the overhead attached per message across the wired and wireless channels. Many works have proposed mechanisms to achieve the synchronization between streams [7] [8] [9] [10] [11] [12] . We organize these works into three categories according to the design principle used: end-to-end, proxy and asymmetric. The end-to-end mechanisms were developed for distributed systems considering "smart" static hosts and wired communication channels [7] [8] .. The second category considers "dumb" communicant end hosts and for this reason, introduces a logical entity, called proxy, that carries out the main activities of the end hosts. The works in this category at an MDS reduce the overhead sent at wireless communication channels. However, these works introduce extra delays during the delivery of messages (known as unnecessary inhibition), and they cannot reflect the behavior seen of the mobile hosts because they accomplish the message delivery at and according to the view of the communication service points (e.g. base stations) [ 9] [10].. The last category uses the asymmetric design principle [11] [12] . Asymmetric protocols also discharge some tasks of the mobile hosts towards logical or physical entities, which are assumed to have more capacity. The main difference between this category and the previous one is that a direct logical channel is considered to exist between the end hosts [13] [14] . This characteristic is important since it allows a communication and interaction according to the view of the mobile hosts. Our work is classified in this category. To the best of our knowledge, our work is the first asymmetric protocol to synchronize continuous media with causality control at mobile distributed systems.

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


Model-free reconfiguration mechanism for fault tolerance The problem of fault tolerant control is studied from the behavioral point of view. In this mathematical framework, the concept of interconnection among the variables describing the system is a key point. The problem is that the behavior we intend to control is not known. Therefore, we are interested in designing a fault accommodation scheme for an unknown behavior through an appropriate behavioral interconnection. Here we deal simply with the trajectories that are generated by the system in real time. These trajectories determine the behavior of a system in various (faulty/healthy) modes. Based on the desired interconnected behavior, only the trajectories that obey certain laws are selected. These laws, representing the desired behavior, can indeed be achieved by a regular interconnection. Thus, when the trajectories do not belong to a certain desired behavior, it is considered to be due to the occurrence of a fault in the system. The vantage point is that the fault tolerant control problem now becomes completely a model-free scheme. Moreover, no explicit fault diagnosis module is required in our approach. The proposed fault tolerance mechanism is illustrated on an aircraft during the landing phase. A fault represents an unexpected change in the system dynamics that tends to degrade the overall system performance and can lead to system instability as well. Generally, a Fault Tolerant Control (FTC) system includes two modules: the Fault Diagnosis (FD) module and the Fault Accommodation (FA) module (see Fig. 1 ). The former is a monitoring module that is used to detect faults and diagnose their location and significance in a system. The module with a fault estimation sub-module is very often regarded as Fault Detection and Isolation (FDI). The latter is a Fault-recovery module that controls the faulty system in a specific way, such that the system still achieves the objectives which were met by the healthy system before the occurrence of fault.. The general block diagram of a fault tolerant control is shown in Fig. 1 . The main controller activities occur on the execution level. In the faultless case, the nominal controller attenuates the disturbance d and ensures set-point following and other requirements on the closed loop system on the execution level. On the supervision level, the diagnosis block simply recognizes that the closed-loop system is faultless and no change of the control law is necessary. If a fault occurs, the supervision level makes the control loop fault-tolerant. The diagnostic block identifies the fault and gives this information as D to the fault accommodation block. The FA module adjusts the controller to the new situation, such that the closed loop satisfies the performance specifications (Jain et al., 2010; Zhang and Jiang, 1999) .. The problem of fault tolerant control is often handled in two ways, namely, using a model-based approach and a model-free approach. In the former the full information of the actual plant is known a priori. Accordingly, a subsystem (state observer, output observer, Kalman's filter, etc.) is built, which reconstructs the plant output and diagnoses the fault. The fault is then accommodated using the FA module. On the other hand, generally, in the so-called model-free approaches in the existing literature, the model of the plant is estimated. Nevertheless, the plant knowledge is required during estimation in real-time as well. Hence, the knowledge of a plant model is mandatory at any time to achieve fault tolerance either by assuming the plant model to be known or to be estimated. This entails the model mismatching issue that can generate false alarms, even in the faultless situation. r is a reference signal, u is the control signal, y is the output signal, f is a fault signal, d is a disturbance, D is the diagnosis information and C is the controller redesign information.. involves some dynamics of the fault in the faulty mode that have not been accommodated entirely. Therefore, the fault diagnosis module must be adaptive with respect to the fault accommodation module so that the further modeling issue can be averted. Otherwise, it will again result in a false alarm.. As we have seen, FTC requires two distinctive modules that operate sequentially to accommodate the fault. These two modules involve their respective time delays, particularly, known as fault detection delay and fault accommodation delay. Significant attention has to be paid while handling these time delays. In the time interval between the occurrence of a fault and its accommodation, the stability aspects of any FTC scheme become a concern. In addition, due to historical reasons and the complexity of the problem, most of the research on FD and FA was carried out in two directions. Specifically, most of the FDI techniques are developed as a diagnostic or monitoring tool, rather than an integral part of FTC systems. As a result, some existing FD methods may not satisfy the need of controller reconfiguration in the FA module. On the other hand, most of the research on reconfigurable controls is carried out assuming the availability of a perfect FD. Little attention has been paid to the analysis and design with the overall system structure and interaction between FD and FA modules (Zhang and Jiang, 2008) .. Seeing these shortcomings, the objective of this work is to develop a generic method for fault tolerant control based on real trajectories from the system subjected to faults. The main aim of the paper is to formulate a modelfree approach to FTC that does not require any information about the plant in real-time. Unlike in the so-called subspace approach for FTC by Ding et al. (2009) , we do not focus on designing an FDI module that implicitly requires the knowledge of the plant parameters. On the contrary, our approach does not include any explicit FD module. The idea here is to choose an appropriate control law such that the system in any (faulty/healthy) mode Estimator n achieves the performance specifications without the need for a plant model. We employed the mathematical framework of behavioral systems for the proposed approach. In the last decade, the behavioral point of view has received increasingly broader acceptance as an approach for modeling dynamic systems, and now it is generally viewed as a cogent framework for system analysis (Zerz, 2008) . The proposed FTC mechanism is illustrated on an aircraft during the landing phase. In this paper, the fault tolerant control problem has been formalized in the behavioral setting using the concept of system interconnection. This results in a model-free reconfiguration scheme in real-time that is solely based upon the input-output trajectories. In fact, the concept of interconnection among the variables describing the system is regulated by the closed-loop performance evaluation. A cost-detectable "performance functional" captures the control objectives effectively and plays the role of a detector for any abnormal situation or faults in the closed-loop system. On detecting this undesired behavior of the closed loop, an appropriate interconnection is made in real-time without using an explicit model of the plant so that the control objective is satisfied at any time. A novel feature of this scheme is that it does not require any FDI unit. This clearly rules out the issues of generating false or missed alarms associated with standard FDI units, and thus increases the reliability of the FTC system.

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


Growth optimal investment in discrete-time markets with proportional transaction costs We investigate how and when to diversify capital over assets, i.e., the portfolio selection problem, from a signal processing perspective. To this end, we first construct portfolios that achieve the optimal expected growth in i.i.d. discrete-time two-asset markets under proportional transaction costs. We then extend our analysis to cover markets having more than two stocks. The market is modeled by a sequence of price relative vectors with arbitrary discrete distributions, which can also be used to approximate a wide class of continuous distributions. To achieve the optimal growth, we use threshold portfolios, where we introduce a recursive update to calculate the expected wealth. We then demonstrate that under the threshold rebalancing framework, the achievable set of portfolios elegantly form an irreducible Markov chain under mild technical conditions. We evaluate the corresponding stationary distribution of this Markov chain, which provides a natural and efficient method to calculate the cumulative expected wealth. Subsequently, the corresponding parameters are optimized yielding the growth optimal portfolio under proportional transaction costs in i.i.d. discrete-time two-asset markets. As a widely known financial problem, we also solve the optimal portfolio selection problem in discrete-time markets constructed by sampling continuous-time Brownian markets. For the case that the underlying discrete distributions of the price relative vectors are unknown, we provide a maximum likelihood estimator that is also incorporated in the optimization framework in our simulations. The problem of how and when an investor should diversify capital over various assets, whose future returns are yet to be realized, is extensively studied in various different fields from signal processing [1, 2, 12, [28] [29] [30] 33, 35] and financial engineering [25, 26] to machine learning [13, 34] and information theory [9] . Naturally, this is one of the most important financial applications due to the amount of money involved. However, the recent financial crisis demonstrated that there is a significant room for improvement in this field by sound signal processing methods [12, 30] , which is the main goal of this paper. In this paper, we investigate how and when to diversify capital over assets, i.e., the portfolio selection problem, from a signal processing perspective and provide portfolio selection strategies that maximize the expected cumula-* Corresponding author. tive wealth in discrete-time markets under proportional transaction costs.. In particular, we study an investment problem in markets that allows trading at discrete periods, where the discrete period is arbitrary, e.g., it can be seconds, minutes or days [24] . Furthermore, the market levies transaction fees for both selling and buying an asset proportional to the volume of trading at each transaction, which accurately models a broad range of financial markets [3, 24] . In our discussions, we first consider markets with two assets. Twostock markets are extensively studied in financial literature and are shown to accurately model a wide range of financial applications [24] such as the well-known "Stock and Bond Market" [24] . We then extend our analysis to markets having more than two assets, i.e., m-stock markets, where m is arbitrary.. Following the extensive literature [9, 19, [24] [25] [26] 33] , the market is modeled by a sequence of price relative vectors, say {X(n)} n≥1 , X (n) ∈ [0, ∞) m , where each entry of X(n), i.e., X i (n) ∈ [0, ∞), is the ratio of the closing price to the opening price of the ith stock per investment period. Hence, each entry of X(n) quantifies the gain (or the loss) of that asset at each investment period. crete" distribution [24] [25] [26] 33] , however, the discrete distributions on the vector of price relatives are arbitrary. In this sense, the corresponding discrete distributions can approximate a wide class of continuous distributions on the price relatives that satisfy certain regularity conditions by appropriately increasing the size of the discrete sample space. We first assume that the discrete distributions on the price relative vectors are known and then extend our analysis to cover the case, where the underlying distributions are unknown. We emphasize that the i.i.d. assumption on the sequence of price relative vectors is shown to hold in most realistic markets [14, 24] . At each investment period, the diversification of the capital over the assets is represented by a portfolio vector b(n), where ∀i ∈ {1, . . . , m}, b i (n) represents the ratio of the capital invested in the ith asset at investment period n, i.e., we have. As an example, if we invest using b(n), we earn (or lose) b T (n)X(n) at the nth investment period, after X (n) is revealed. Given that we start with one dollar, after an investment period of N days, we have the wealth growth. Under this general market model, we provide algorithms that maximize the expected growth over any period N by using "threshold rebalanced portfolios" (TRPs), which are shown to yield optimal growth in general i.i.d. discrete-time markets [14] .. In [9] , Cover et al. showed that the portfolio that achieves the maximal growth is a constant rebalanced portfolio (CRP) in i.i.d. discrete-time markets, under certain assumptions on the sequence of price relatives and without any transaction costs. A CRP is a portfolio investment strategy, where the fraction of wealth invested in each stock is kept constant at each investment period. A problem extensively studied in this framework is to find sequential portfolios that asymptotically achieve the wealth of the best CRP tuned to the underlying sequence of price relatives. Several sequential algorithms are introduced to achieve the performance of the best CRP (such as [9, 13, 16, 34] ) with different convergence rates and different performances on historical data sets. In [3], sequential algorithms that achieve the performance of the best CRP under transaction costs are introduced. However, we emphasize that keeping a CRP may require extensive trading due to a possible rebalancing at each investment period which deems CRPs (even the best CRP) ineffective in realistic markets even under mild transaction costs [19] .. In continuous-time markets, however, it has been shown that under transaction costs, the optimal portfolios that achieve the maximal wealth are certain class of "no-trade zone" portfolios [7, 11, 32] . In simple terms, a no-trade zone portfolio has a compact closed set and a rebalancing occurs if the current portfolio breaches this set, otherwise no rebalancing occurs. Clearly, such a no-trade zone portfolio may avoid hefty transaction costs since it can limit excessive rebalancing by defining appropriate no-trade zones. Analogous to continuous time markets, it has been shown in [14] that in two-asset i.i.d. markets under proportional transaction costs, compact no-trade zone portfolios are optimal such that they achieve the maximal growth under certain assumptions on the sequence of price relatives. In two-asset markets, the compact no-trade zone is represented by thresholds, e.g., if at investment period n, the portfolio is given by However, how to construct the no-trade zone portfolio, i.e., how to select the thresholds that achieve the maximal growth, has not yet been solved except in elementary scenarios [14] . In [15], a universal algorithm that asymptotically achieves the performance of the best TRP tuned to the underlying sequence of price relatives is introduced. This algorithm leverages Bayesian type weighting from [9] inspired from universal source coding and requires no statistical assumptions on the sequence of price relatives. In similar lines, various different universal algorithms are introduced that achieve the performance of the best expert in different competition classes in [1, 2, [17] [18] [19] [20] . Although the performance guarantees in [1, 2, 15, 18, 19] ) are derived without any stochastic assumptions, these methods are highly conservative due to the worst case scenario optimization, i.e., they are only optimal in an asymptotical sense. However, the order of such performance upper bounds may not be negligible in actual financial markets [6, 20] , even though they may be neglected in source coding applications (where these algorithms are inspired from). We demonstrate that our algorithm readily outperforms these universal methods over historical data.. Our main contributions are as follows. We first consider twoasset markets and recursively evaluate the expected achieved wealth of a threshold portfolio for any b and over any investment period. We then extend this analysis to markets having more than two-stocks. We next demonstrate that under the threshold rebalancing framework, the achievable set of portfolios form an irreducible Markov chain under mild technical conditions. We evaluate the corresponding stationary distribution of this Markov chain, which provides a natural and efficient method to calculate the cumulative expected wealth. Subsequently, the corresponding parameters are optimized using a brute force approach yielding the growth optimal investment portfolio under proportional transaction costs in i.i.d. discrete-time two-asset markets. We note that for the case with the irreducible Markov chain, which covers practically all scenarios in the realistic markets, the optimization of the parameters is offline and carried out only once. However, for the case with recursive calculations, the algorithm has an exponential computational complexity in terms of the number of states. However, in our simulations, we observe that a reduced complexity form of the recursive algorithm that keeps only a constant number of states by appropriately pruning certain states provides nearly identical results with the "optimal" algorithm. Furthermore, as a well studied problem, we also solve optimal portfolio selection in discrete-time markets constructed by sampling continuous-time Brownian markets [24] . When the underlying discrete distributions of the price relative vectors are unknown, we provide a maximum likelihood estimator to estimate the corresponding distributions that is incorporated in the optimization framework in the Simulations section. For all these approaches, we also provide the corresponding complexity bounds.. The organization of the paper is as follows. In Section 2, we briefly describe our discrete-time stock market model with discrete price relatives and symmetric proportional transaction costs. In Section 3, we start to investigate TRPs, where we first introduce a recursive update in Section 3.1 for a market having twostocks. Generalization of the iterative algorithm to the m-asset market case is provided in Section 3.2. We then show that the TRP framework can be analyzed using finite state Markov chains in Section 3.4 and Section 3.5. The special Brownian market is analyzed in Section 3.6. The maximum likelihood estimator is derived in Section 4. We simulate the performance of our algorithms in Section 5 and conclude the paper with certain remarks in Section 6.

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


An investigation into two bin packing problems with ordering and orientation implications This paper considers variants of the one-dimensional bin packing (and stock cutting) problem in which both the ordering and orientation of items in a container influences the validity and quality of a solution. Two new real-world problems of this type are introduced, the first that involves the creation of wooden trapezoidal-shaped trusses for use in the roofing industry, the second that requires the cutting and scoring of rectangular pieces of cardboard in the construction of boxes. To tackle these problems, two variants of a local search-based approximation algorithm are proposed, the first that attempts to determine item ordering and orientation via simple heuristics, the second that employs more accurate but costly branch-and-bound procedures. We investigate the inevitable trade-off between speed and accuracy that occurs with these variants and highlight the circumstances under which each scheme is advantageous. Many problems arising in mathematics, computer science and operational research require the partitioning of a discrete set of entities into an exhaustive collection of mutually exclusive subsets, subject to specific constraints. Though simple to define, such "grouping" problems often pose significant challenges in practical settings because it is not always easy to judge whether the imposed constraints can be satisfied. Indeed many such problems including those concerning graph partitioning (Hertz et al., 2008; Isomoto et al., 1993; Jensen and Toft, 1994; Nakano1 et al., 1995) , school and university timetabling (Lewis, 2008; McCollum et al., 2010) , sports fixture scheduling (de Werra, 1988; Kendall et al., 2010; Rasmussen and Trick, 2008) , load balancing (Falkenauer, 1998) , and frequency assignment (Aardel et al., 2002; Valenzuela, 2001) , are known to be NP-hard (Garey and Johnson, 1979; Karp, 1972) , implying that we cannot hope to establish polynomially bounded algorithms for solving them in the general sense.. An important class of grouping problem common in various commercial operations such as the clothing and construction industries are packing and cutting problems. Such problems involve determining the way in which a pre-defined set of "items" should be "packed" into "bins" (respectively "cut" from "stocks") such that wastage (or spare capacity) is minimised. In this paper we focus on a subclass of these, what Wäscher et al. (2007) have termed fixed-dimension input-minimisation problems: given a set of items I (where |I| = n), construct a set of "groups" S = {S 1 , S 2 , . . . , S |S| }, where:. such that the number of groups |S| is minimised.. In the above, each group S i ∈ S defines the items that will be packed into the same bin (respectively, cut from the same stock), and conditions (1) and (2) specify that each item should be assigned to exactly one of the |S| groups. Condition (3), meanwhile, indicates that each of these groups should be feasible: thus the set F denotes the set of all feasible subsets of I. The contents of F are affected by the constraints of the specific problem being considered, and will also vary on an instance-by-instance basis. For non-trivial instances, F will also usually be too large to be constructed directly since the number of possible groups (subsets) of items to be checked rises exponentially with respect to n.. Perhaps the most widely known examples in this class of problem are the one-dimensional stock cutting problem (SCP) and the one-dimensional bin packing problem (BPP). In both cases each item j ∈ I has a size s j , and the aim is to partition the items into groups such that ∀S i ∈ S, ∑ j∈S i s j ≤ C, where C is some constant defined as part of the problem. According to the taxonomy of Wäscher et al. (2007) the main distinction between these problems is that in the BPP the items are strongly heterogeneous (i.e. of many different sizes), whereas in the SCP items are only weakly heterogeneous (that is, many items have the same size). Though rather subjective, this difference is important to note as, historically, it has brought about quite different solution approaches for the two problems (Falkenauer, 1998; Haessler and Sweeny, 1991; Liang et al., 2002; Martello and Toth, 1990b; Lewis, 2009) .. Although the SCP and BPP are both NP-hard (Garey and Johnson, 1979) , it is noticeable that the sub-problem of determining whether S i ∈ F in these cases is trivial, since we need only sum the sizes of the items assigned to S i . The commutativity of this operation also implies that the order in which items occur in a bin/on a stock is irrelevant since all of the |S i |! permutations of items in a group will result in the same total. In many practical circumstances however, things can be more complicated and factors beyond the total size of the items might also need to be considered for determining membership of F. In this paper we will examine two such problems where both the ordering and orientation of items is significant in the sub-problem of deciding whether S i ∈ F. We will observe that in both cases these underlying sub-problems are NP-complete, adding an extra degree of complexity to the grouping problem. Having noted these features we propose a local search-based method for these problems and examine the effects of tackling the underlying sub-problems using fast but approximate heuristics, and also using more accurate but expensive branch-and-bound procedures.. The problems considered in this paper involve the creation of wooden trusses for use in the roofing industry, and the cutting and scoring of rectangular pieces of cardboard for use in the construction of packing boxes. In the next section we begin by describing the overall algorithmic framework used for both of these problems. In Sections 3 and 4, we then conduct an analysis of each problem in turn and describe the operators that are used in conjunction with this framework, presenting empirical evidence on the subsequent performances. In general, we tend to refer these problems as bin packing variants, since this seems the most appropriate classification according to the taxonomy of Wäscher et al. (2007) ; thus we will often speak of items being "packed" into "bins" (though in the real industrial processes, what is actually required is for items to be cut from stocks). Finally, Section 5 concludes the paper and makes some suggestions for further work on these new problems.

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


Computing intersection numbers between abelian varieties associated to subspaces of modular forms We state a result and describe an algorithm for computing the intersection number between abelian varieties associated to complementary subspaces of the space of cuspidal modular forms. Let N > 5 to be an integer. If g is a newform of level N g dividing N, then let [g] denote its Galois conjugacy class. Denote by S ([g],C) the subspace in S 2 (Γ 0 (N), C) generated by degeneracy map images of forms in [g] . Denote by S ([g],Q) the Qvector space of all such forms with rational Fourier coefficients. Then S 2 (Γ 0 (N), Q) = ⊕ [g] S ([g],Q) where the sum is over the Galois conjugacy classes of newforms at levels that divide N. Let X 0 (N) denote the modular curve over Q associated to Γ 0 (N), and let J 0 (N) be its Jacobian, which is an abelian variety over Q. Let T denote the subring of endomorphisms of J 0 (N) generated by the Hecke operators (usually denoted T for N and U p for p | N). If X = ⊕ [g] S ([g],C) and Y = ⊕ [ f ] S ([ f ],C) are two subpaces of S 2 (Γ 0 (N), C) with trivial intersection, then the intersection number between X and Y is the order of intersection between the two associated abelian varieties (J 0 (N)/Ann T (X)J 0 (N)) ∨ and (J 0 (N)/Ann T (Y )J 0 (N)) ∨ , where the superscript ∨ denotes the dual abelian variety, and the intersection is taken inside J 0 (N) ∨ (which is isomorphic to J 0 (N)).. One reason for studying intersection numbers between such spaces X and Y is as a means to study congruence primes between X and Y , since [ARS12, Thm. 3.6] shows that the primes that divide the intersection number are congruence primes, and a congruence prime whose square does not divide the level N divides the intersection number. Another reason for studying the intersection number is that it plays a role in the second part of the Birch and Swinnerton-Dyer conjecture: for example, if the level N is prime and X is associated to a single newform, then it is shown in [Aga10] (see equation (2) and Lemma 4.4 in loc. cit.) that a certain intersection number divides the Birch and Swinnerton-Dyer conjectural order of the Shafarevich-Tate group of the abelian variety associated to the newform.. We now prepare to state the main theorem of this article. Let g denote the genus of X 0 (N). Given a basis B = {s 1 , . . . , s 2g } for S 2 (Γ 0 (N), C), the matrix for the Hecke operator t relative to the basis B is the unique matrix M that satisfies. If M is a matrix with rational entries, then let d denote the least common multiple of all of the denominators of entries of M. We denote by M int the matrix given by d · M, the integer matrix produced by clearing denominators in M. If M is an m × n matrix with integer coefficients, we define the torsion order of M to be the product of the diagonal entries of the Smith Normal Form of M. We denote the torsion order of M as tors(M). The torsion order of M is so called because it is the order of the torsion part of the group Z m /Col(M) where Col(M) the denotes subgroup of Z m generated by the columns of M. Given a set of m × n matrices, {M 1 , . . . , M k }, we denote by M 1 . . . M k the m × (nk) matrix produced by the horizontal augmentation of the {M i }.. We have the following result.. , where the sums are over two complementary subsets of the set of Galois conjugacy classes of newforms at levels that divide N. Let {t 1 , . . . ,t m } and {r 1 , . . . , r m } be generators for the annihilator ideals in T⊗Q of X and Y respectively. Let {T 1 , . . . , T m } and {R 1 , . . . , R n } be matrices for {t 1 , . . . ,t m } and {r 1 , . . . r n } respectively relative to some basis of S 2 (Γ 0 (N)). Then the intersection number between X and Y is. In Section 2, we present an algorithm for computing intersection numbers based on the theorem above, and in section 3, we give the proof of Theorem 1.. We remark that the key idea in this paper is that the annihilator ideals in the theorem above and in the algorithm can be computed over Q. The ideals are more naturally defined over Z and there is a simpler formula analogous to the one in the theorem above over Z; however doing linear algebra over the integers takes too long. Replacing the ideals over Z by their tensor over Q speeds up the process significantly.

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


Planning the location and rating of distributed energy storage in LV networks using a genetic algorithm with simulated annealing Abstract In light of the expansion of domestic photovoltaic (PV) systems in the UK, there are concerns of voltage rise within LV networks. Consequently, network operators are interested in the costs and benefits of different technologies to manage their assets. This paper examines the particular case for distributed energy storage. A heuristic planning tool is developed using a genetic algorithm with simulated annealing to investigate the problem of locating and sizing energy storage within LV networks. This is applied to investigate the configuration and topologies of storage to solve voltage rise problems as a result of increased penetration of PV. Under a threshold PV penetration, it is shown that distributed storage offers a financially viable alternative to reconductoring the LV network. Further, it is shown that a configuration of single phase storage located within the customer home can solve the voltage problem using less energy than a three phase system located on the street. This paper presents a heuristic planning tool for locating distributed electrical energy storage in LV networks. Below a particular penetration of PV, distributed storage is shown to offer a lower capital cost method of resolving a voltage rise problem when compared with network reconductoring. Single phase storage at customer premises provides solutions that require overall lower power and energy ratings than three phase storage located on the street. Locating storage in homes can offer benefits to customers by storing self-generated energy and reducing the consumer bill, owing to the structure of the Feed-in-Tariff. This provides additional revenue to offset the cost storage.

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Fence methods for backcross experiments Model search strategies play an important role in finding simultaneous susceptibility genes that are associated with a trait. More particularly, model selection via the information criteria, such as the BIC with modifications, have received considerable attention in quantitative trait loci mapping. However, such modifications often depend upon several factors, such as sample size, prior distribution, and the type of experiment, for example, backcross, intercross. These changes make it difficult to generalize the methods to all cases. The fence method avoids such limitations with a unified approach, and hence can be used more broadly. In this article, this method is studied in the case of backcross experiments throughout a series of simulation studies. The results are compared with those of the modified BIC method as well as some of the most popular shrinkage methods for model selection. Unravelling the genetic influence on phenotypic differences in human is often difficult due to the genetic and cultural heterogeneity of the populations. One approach to the problem has been to use appropriate animal models to pinpoint candidate genes for more focused further investigations. For example, the mouse model has been extensively used in quantitative trait loci (QTL) mapping. Mouse is relatively inexpensive to maintain and breed. In addition, it has a high rate of reproduction. The importance of mice in genetic studies has been established through the work of Lucien Cuénot, a French geneticist, who demonstrated Mendelian inheritance in mammals using the inheritance of coat colours in mice [1] . Castle and Allen [2] often earned a credit for this success from their work published in 1903. Lucien Cuénot later on also demonstrated that a gene has multiple alleles [3] and that some alleles can be lethal, using the yellow allele of the agouti gene A" [4] . Castle and Little [5] confirmed this observation through their work and gave an explanation in 1910. Nowadays, developed mouse strains serve as primary models for many studies in human diseases, such as obesity, diabetes and cancer.. Ideally, the objective of the experiment is to identify susceptibility genes that contribute to the variation of a phenotype. However, in practice, such an ambitious aim is often reduced to identifying the genomic regions in which attributed genes are lying. Therefore, it is desirable to form an association between the phenotypic variation and such informative genomic regions. Classical methods of QTL mapping includes interval mapping [6] , composite interval mapping [7, 8] , and multiple QTL mapping [9, 10] . Recently, model-selection methods via the information criteria, for example, AIC [11] , BIC [12] have received considerable attention in QTL mapping [13] [14] [15] [16] [17] [18] [19] [20] . In particular, Broman and Speed [14] proposed a modification of the BIC criterion, called BIC δ to overcome the overestimation of the number of QTLs when using the traditional BIC. However, the modification depends on the sample size. Namely, the authors obtained an appropriate value of δ via extensive Monte Carlo simulations, whose value changes with the sample size. In other words, unless the sample size of the study coincides with one that has already been considered, the Monte Carlo simulations have to be carried out again in order to determine the value of δ. Bogdan et al. [19] proposed another version of BIC modification, called mBIC, which includes an extra penalty term that depends on the number of markers and the choice of prior on the QTL numbers. Baierl et al. [20] modified the mBIC by adjusting its penalty and applied the method to intercross experiments. In short, all of the BIC modifications depend on several factors, such as sample size, prior distribution, and the type of experiment; thus, it is not easy to adopt a unified approach along these lines that can apply to all the cases.. The fence method [21, 22] was motivated by the limitations of the information criteria when applied to non-conventional situations, even though the method has been shown to be very competitive to traditional methods in the conventional settings as well. In particular, the adaptive fence procedure is a data driven procedure to determine an optimal tuning parameter. In terms of QTL mapping, once a parsimonious model is determined, the corresponding QTL number and locations can be identified. This method does not suffer from the limitations of the above-mentioned methods based on BIC modifications. For example, although it is beyond the scope of this study, the method is potentially useful to human genetics, in which selection of the variance components can be essential.. It should be pointed out that there are a number of differences between the model-selection approach to QTL mapping and the traditional regression variable selection. First, the regressors used in the QTL mapping, namely, the genotype indicators corresponding to the markers, are usually correlated (typically a Markov chain). Such correlations are expected to have an impact on the variable selection (here, the variables correspond to the markers) in that if a marker is identified as a QTL, its neighbouring markers also have a (good) chance to be selected, due to the correlation, especially when the distance between markers is small. Second, the signals at the true QTLs are typically fairly weak, for example, heritability of 50% or less. Finally, the number of potential markers to be examined is typically fairly large, leading to a large number of evaluations for the all-subset selection. For example, Broman and Speed [14] considered QTL mapping in a backcross experiment with nine chromosomes, each with 11 markers. This led to a (conditional) linear regression model with 99 candidate variables, one corresponding to each marker. In fact, these difficulties have led the authors to modify the traditional BIC criterion for regression variable selection in order to apply it to QTL mapping problems (see below for more details).. We similarly treat the QTL mapping as a model-selection problem, but our approach is based on the fence method, which is attractive in this situation due to its flexibility and data-driven optimality [21, 22] . On the other hand, the fence, especially the adaptive fence, encounters computational difficulties when applied to QTL mapping due to the potentially large number of markers, as mentioned above. For example, in the aforementioned backcross experiment considered in [14] , the fence would require up to 2 99 evaluations of the measures of lack-of-fit, and the adaptive fence would need to do the same for every bootstrap sample. (1) For the candidate variables. Apply the SAF (stage 1) using the measure of lack-of-fit (4) to select the variables among x j , j ∈ S 1 . The SAF consists of the following steps: (i) Estimating the parameters under the restricted full model (= {x j , j ∈ S 1 }). Example 1 In the backcross experiment considered in [14] , J is the total number of markers, that is, J = 99. We may let T 1 be the subset of the first six markers on chromosome 1, T 2 be the subset of the last five markers on chromosome 1, T 3 be the subset of the first six markers on chromosome 2, and so on. Thus, q = 18 in this case. In step (2), S 1 = T 1 consists of six markers, and S 2 is the rest of the 99 − 6 = 93 markers. Then, in Step (3), S 1 = T 2 and S 2 is the rest of the markers; thus, S 1 , S 2 consist of five markers and 99 − 5 = 94 markers, respectively, and so on.

O 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 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


Dimensionality reduction of electropalatographic data using latent variable models We consider the problem of obtaining a reduced dimension representation of electropalatographic (EPG) data. An unsupervised learning approach based on latent variable modelling is adopted, in which an underlying lower dimension representation is inferred directly from the data. Several latent variable models are investigated, including factor analysis and the generative topographic mapping (GTM). Experiments were carried out using a subset of the EUR-ACCOR database, and the results indicate that these automatic methods capture important, adaptive structure in the EPG data. Nonlinear latent variable modelling clearly outperforms the investigated linear models in terms of log-likelihood and reconstruction error and suggests a substantially smaller intrinsic dimensionality for the EPG data than that claimed by previous studies. A two-dimensional representation is produced with applications to speech therapy, language learning and articulatory dynamics. The technique of electropalatography (EPG) is well established as a relatively noninvasive, conceptually simple and easy-to-use tool for the investigation of lingual activity in both normal and pathological speech. Qualitative and quantitative data about patterns of lingual contacts with the hard palate during continuous speech may be obtained using EPG, and the technique has been used in studies of descriptive phonetics, coarticulation, and diagnosis and treatment of disordered speech (Hardcastle et al., 1991a; Hardcastle et al., 1989) . Typically, the subject wears an artificial palate moulded to fit the upper palate with a number of electrodes mounted on the surface to detect lingual contact (62 in the Reading EPG system (Hardcastle et al., 1991a) ). The EPG signal is sampled at 100-200 Hz. Thus, for a given utterance, the sequence of raw EPG data consists of a stream of binary vectors with both spatial and temporal structure.. Potentially the tongue has many degrees of freedom owing to its lack of skeleton (Stone, 1991) ; however, a number of studies suggest that tongue movements in speech may be appropriately modelled using a few elementary articulatory parameters (e.g. (Nguyen et al., 1994; Nguyen et al., 1996) and references therein). Spatial redundancy arises due to the limited number of possible tongue configurations-only a tiny fraction of the potential 2 62 ≈ 4.6 · 10 18 EPG patterns can be produced by the articulatory system. Temporal redundancy arises due to the correlations between neighbouring frames: the position of the tongue (and thereby the EPG signal) changes slowly with time, compared to the acoustic signal. If the appropriate constraints were known, then it would be possible to represent the EPG signal using fewer dimensions.. In this paper we approach the problem of finding such a dimensionality reduction mapping, not from a physical point of view, but from a machine learning one. That is, we consider a data set consisting of a number of EPG patterns and try to learn a mapping into a low-dimensional space from the data, without any a priori assumption about it (other than a specific, but quite general, form) and using methods well-known in the statistics and pattern recognition fields. Our approach will be that of latent variable modelling, in which the data is assumed to have been generated stochastically from a small number of hidden variables. In common with most work on EPG data reduction we will concentrate on dimensionality reduction at the spatial level only, thus ignoring the constraints arising from coarticulation and other dynamics of the articulatory system.. The primary advantage of dimensionality reduction for EPG data is that it makes a sequence of EPG data more amenable to analysis, since direct manipulation of the raw EPG sequence is cumbersome due to its high dimensionality (Hardcastle et al., 1991b) . A reduced-dimension representation in terms of a few variables can be inspected, plotted against time or against each other, etc. more easily. Additional advantages are the consequent reductions in storage space and data transmission rate-albeit of little relevance, since the EPG data has relatively low requirements for them.. The resultant dimensionality reduction may suggest a value for the intrinsic dimensionality of the EPG data, i.e., the number of degrees of freedom of the tongue-palate system in what concerns the generation of EPG patterns. It may also give some insight into the problem of the acoustic-to-articulatory mapping (Schroeter and Sondhi, 1994) , in which values for articulatory parameters such as vocal tract area functions, lip positions and jaw dynamics are determined from the acoustic signal. Note that the EPG signal alone is an incomplete articulatory description, omitting such details as nasalisation and vocalisation. Hence, the mapping from phonemes to EPG patterns is not one-to-one since certain phonemes (e.g.. ¢ ¡ £ and ¥ ¤ ¦ ) can produce the same EPG patterns.. The rest of the paper is organised as follows. Section 2 explains the advantages that unsupervised learning methods (in particular latent variable models) for EPG data have over fixed data reduction methods. Section 3 introduces the latent variable modelling framework. Section 4 describes the data set employed for the experiments. These experiments are described in sections 5, 6, 7 and 8. The paper is completed with a discussion of the results in section 9 and a conclusion in section 10. We have shown that latent variable models, owing to their ability to produce a reduced-dimension representation of a data set, can be useful to present the relatively high-dimensional information contained in the EPG sequence in a way which is easier to understand and handle, e.g.:. • The loading vectors and principal component vectors of factor analysis and PCA, respectively, can be used as conventional EPG data reduction indices, with the advantage of adapting better to the database under consideration.. • A two-dimensional latent space representation can be used for the analysis of EPG sequences in several applications, such as speech therapy, language learning and articulatory dynamics. This is a significant advantage over general probability models and mixtures of them, which are suitable for classification or clustering but not for dimensionality reduction. The superior performance of a two-dimensional GTM model over the other methods indicates that the EPG data may be appropriately accounted for with a very small number of degrees of freedom as long as a nonlinear, complex model is used.

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


The dynamic factory pattern The DYNAMIC FACTORY pattern describes a factory that can create product instances based on concrete type definitions stored as external metadata. This facilitates adding new products to a system without having to modify code in the factory class. The DYNAMIC FACTORY pattern describes a factory that can create product instances based on concrete type definitions stored as external metadata. This facilitates adding new products to a system without having to modify code in the factory class. This paper presented the ABSTRACT FACTORY pattern, which allows for dynamic creation of product instances based on the interpretation of externally stored metadata. Variants of this pattern support the creation of a family of products, improve performance, or support Adaptive-Object Model implementations.. We used as an example the creation of rules for a workflow system. Since rules can be added frequently, applying this pattern provides the capability to dynamically create rule instances based on the interpretation of externally stored metadata descriptions.

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Efficient methods for computing observation impact in 4D-Var data assimilation Abstract This paper presents a practical computational approach to quantify the effect of individual observations in estimating the state of a system. Such a methodology can be used for pruning redundant measurements and for designing future sensor networks. The mathematical approach is based on computing the sensitivity of the analyzed model states (unconstrained optimization solution) with respect to the data. The computational cost is dominated by the solution of a linear system, whose matrix is the Hessian of the cost function, and is only available in operator form. The right-hand side is the gradient of a scalar cost function that quantifies the forecast error of the numerical model. The use of adjoint models to obtain the necessary first-and secondorder derivatives is discussed. We study various strategies to accelerate the computation, including matrix-free iterative solvers, preconditioners, and an in-house multigrid solver. Experiments are conducted on both a small-size shallow-water equations model and on a large-scale numerical weather prediction model, in order to illustrate the capabilities of the new methodology. Data assimilation is the process that combines prior information, numerical model predictions, observational data, and the corresponding error statistics, to produce a better estimate of the state of a physical system. In this paper, we consider the four-dimensional variational (4D-Var) approach, which formulates data assimilation as a nonlinear optimization problem constrained by the numerical model. The initial conditions (as well as boundary conditions, forcings, or model parameters) are adjusted such as to minimize the discrepancy between the model trajectory and a set of time-distributed observations. In real-time operations, the analysis is performed in cycles: observations within an assimilation time window are used to obtain an optimal trajectory, which provides the initial condition for the next time window, and the process is repeated. Data assimilation is an important application of data-driven application systems (DDDAS, or InfoSymbiotic systems) where measurements of the real system are used to constrain simulation results.. The quality and availability of observational data have a considerable impact on the accuracy of the resulting analysis (optimal initial conditions). We are interested to quantify rigorously the impact that different observations have on the result of data assimilation. The assessment of contributions of observations has important applications such as detecting erroneous data (e.g., due to faulty sensors), pruning redundant or unimportant data, and finding the most important locations where future sensors should be deployed.. Early studies of observation impact were concerned with quantifying the predictability of the numerical model, using breeding vectors, potential vorticity, and singular vectors [1, 2] . It was assumed that observations in areas of high uncertainty would significantly improve the data assimilation, which led to the concept of targeted and adaptive observations. Later research developed specialized methods such as ensemble transformation techniques [3, 4] and adjoint-based model sensitivity [5, 6] . Some of this research was validated through Observing System Simulation Experiments (OSSEs) [7] [8] [9] . Recent research shifted focus from the numerical model to studying the entire data assimilation system for ensemble-based methods [10] , 3D-Var [11] , nonlinear 4D-Var [12, 13] , and incremental 4D-Var [14] . Important alternative approaches to assess the importance of observations are based on statistical design [15] and information theory [16, 17] .. The focus of this work is on the sensitivity of the 4D-Var analysis to observations. The sensitivity equations are derived rigorously in the theoretical framework of optimal control and optimization [18] [19] [20] . Sensitivity analysis reveals subsets of data and areas in the computational domain, which have a large contribution in reducing (or increasing) the forecast error. The solution of the 4D-Var sensitivity equations involves the solution of a linear system, whose system matrix is the Hessian of the 4D-Var cost function. This matrix is typically very large and available only in the form of matrix-vector products.. This work addresses two challenges associated with computing sensitivities to observations. The first challenge is the computation of the required first-and second-order derivatives. The solution discussed herein is based on firstand second-order adjoint models. The second challenge is obtaining an accurate solution of the large linear system that defines the sensitivities.. Computational time is an important consideration, especially in applications where the solution is needed in real time. Several solutions are proposed in this work. A set of preconditioners is selected and tested to speed up the convergence of Krylov solvers. A multigrid strategy is also considered. Tests are conducted using two numerical models. The first one is the 2D shallow-water equations, for which all the derivatives can be computed very accurately. The second test is the Weather Research and Forecast (WRF) model, widely used in numerical weather prediction. The experimental results illustrate the potential of the proposed computational approaches to speed up observation impact calculations in real-life applications.. The paper is organized as follows: Section 2 reviews the 4D-Var data assimilation approach. Section 3 covers the theoretical framework of sensitivity analysis in the context of 4D-Var and derives the equations for the sensitivities to observations. Section 4 discusses practical computational algorithms and their application to the shallow-water equations along with visual results for experimental tests. Section 5 presents the results obtained with the large-scale WRF model. Conclusions are drawn in Section 6, and several directions of future research are highlighted. In data assimilation, the sensitivity of a forecast aspect to observations provides a quantitative metric of the impact each data point has on reducing forecast uncertainty. This metric can be used in hindsight to prune redundant data, to identify faulty measurements, and to improve the parameters of the data assimilation system. The metric can also be used in foresight to adaptively configure and deploy sensor networks for future measurements. This work provides a systematic study of computational strategies to obtain sensitivities to observations in the context of 4D-Var data assimilation. Solution efficiency is of paramount importance since the models of interest in practice are large-scale and the computational cost of sensitivities is considerable; moreover, in an operational setting, the sensitivities have to be solved in faster than real time (e.g., for dynamically deploying new sensors).. The cost of computing sensitivities to observations is dominated by the solution of a large-scale linear system, whose matrix is the Hessian of the 4D-Var cost function. In practice, this matrix is available only in operator form (i.e., matrix-vector products obtained via second-order adjoint models).. The main contributions of this paper are to formulate the computational challenges associated with sensitivities to observations and to present solutions to address them. We consider a set of matrix-free linear solvers, build specific preconditioners, and compare their performance on two numerical models. For the SWE test, the results are very promising: certain preconditioners as well as the multigrid approach lead to significant efficiency improvements in the solution of the linear system. The results for the WRF test are less clear-cut: preconditioning brings only a modest improvement, and we attribute this to the limited accuracy with which derivatives are computed by the (currently incomplete) WRF adjoint model. Future work with WRF should focus both on finding better preconditioners and on developing a more accurate adjoint model.

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


Rapid prototype of a hardware emulator for a SIMD processor array The rapid prototype provides full functionality, allowing any design errors or beneficial modifications to the design to be identified. the need for costly design modifications, and delay of delivery of the final system. This paper presents the rapid prototyping of a custom chip set implementing a Single Instruction Multiple Data (SIMD) architecture [2] . The rapid prototype was designed using automated CADKAE development tools, and was implemented using off the shelf parts and FPGAs.First, an overview of the target SIMD architecture is presented. The design methodology used for developing the rapid prototype is then discussed, followed by description of the prototype design and implementation. 391 1066-1409/95 $4.00 Q 1995 IEEE This paper presented an overview of a methodology and design of a rapid prototype SIMD embedded processor developed at the University of Arkansas. The prototype is a scaled version of the final processor, implementing the same instructions, and containing the same interface. The prototype was built to allow development of the parallel debugging software for programmers, and to validate the design. Validation of the design included both operational verification of assembler instructions and microcode, and verification of all data and control paths. This low level verification was not possible by discrete event simulation, and required a hardware emulator. The prototype will also serve as an economical development platform for software developers. The prototype is implemented in FPGAs, PLDs, and other off the shelf nonprogrammable parts. The FPGA's have provided a fast development cycle, and the flexibility to alter the design for bug fixes and functional enhancements. The CAD development environment provided the framework and support for performing a quick turnaround of the prototype.. The prototype has been successfully used to verify the assembler instruction set, and circuit timing of the overall system. The emulator has been used to verify the board to board interfaces, as well as board level timing.. Several modifications were made to the final VLSI SPAR design based on the prototype evaluation. These modifications were necessary for the correct operation of the system, and were not identified during discrete level simulations.

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