I/O-efficient computation of water flow across a terrain Consider rain falling at a uniform rate onto a terrain T represented as a triangular irregular network. Over time, water collects in the basins of T , forming lakes that spill into adjacent basins. Our goal is to compute, for each terrain vertex, the time this vertex is flooded (covered by water). We present an I/O-efficient algorithm that solves this problem using O(sort(X) log(X/M ) + sort(N )) I/Os, where N is the number of terrain vertices, X is the number of pits of the terrain, sort(N ) is the cost of sorting N data items, and M is the size of the computer's main memory. Our algorithm assumes that the volumes and watersheds of the basins of T have been precomputed using existing methods. An important problem in terrain analysis is the prediction of water flow across a terrain. Traditional approaches focus on computing the river network of the terrain under the assumption that water does not collect in the basins of the terrain. In reality, water does collect in the terrain's basins, particularly during heavy rainfall. This may cause basins to spill into adjacent basins, changing the river network of the terrain as a result. Thus, to model the flow of water across a terrain over time, it is necessary to compute the times at which the basins of the terrain spill. In this paper, we solve the more general problem of computing, for every vertex v of a terrain T , the time tv at which it is flooded. We assume the terrain T is represented as a triangular irregular network (TIN) and the amount of rain is uniform across the terrain.. The accuracy of predictions of natural phenomena, such as flooding, depends on the precision of the data used in these predictions. High-resolution elevation models even of fairly small geographic regions often exceed the size of a computer's main memory. Current GIS tools cannot handle data sets of this size efficiently and therefore need to work with models of lower resolutions. This sacrifices accuracy because lower-resolution models do not capture all terrain features. For example, in experiments we conducted to predict the flooding of coastal regions of Denmark due to rising sea levels, an elevation model with one data point every 10m failed to capture a dike around an island, and the island was predicted to be flooded if the sea rises by 2m, while the dike can in fact withstand 2m higher sea levels. Using a higherresolution model with one data point every 2m, we obtained the correct prediction, but storing elevation data for Denmark alone requires 500GB of space at this resolution, an input size well beyond the size of main memory and beyond the reach of current GIS tools.. To process data sets beyond the size of main memory efficiently, it is necessary to develop I/O-efficient algorithms, that is, algorithms that focus on minimizing the number of disk accesses they perform to swap data between disk and internal memory, as a disk access is orders of magnitude slower than an internal-memory computation step. In this paper, we propose an I/O-efficient algorithm for computing the flooding times of all vertices of a terrain T .. The core of the problem is computing the spill times of all basins of T . A simple method to compute these spill times is to simulate the entire sequence of spill events of the basins of T and maintain the watersheds of all basins that yet have to spill, as well as predicted spill times for these basins based on their current watersheds. An internal-memory solution based on this idea has been presented in [14] . In Section 3.2, we discuss an O(N log N ) time implementation of this approach using a priority queue and a union-find structure. This simulation approach does not translate into an I/Oefficient algorithm, as the only known I/O-efficient unionfind structure [1] requires the sequence of Union operations to be known in advance. In simulating the sequence of spill events, the set of Union operations is known, but their order depends on the spill times of the basins. Using an internal-memory union-find structure and an I/O-efficient priority queue (e.g., [3, 12] ), a cost of O(Xα(X) + sort(N )) disk accesses can be achieved, where α(·) is the inverse of Ackermann's function, sort(N ) ≪ N is the I/O complexity of sorting N data items (see next section), and X is the number of pits of the terrain. In contrast, the algorithm presented in this paper achieves an I/O complexity of O(sort(X) log(X/M ) + sort(N )) disk accesses.. In the remainder of this section, we formally define the computational model we use, discuss previous work, and give an overview of our algorithm. Section 2 introduces the terminology and notation we use throughout the paper. Section 3 discusses our algorithm for computing the spill times of the terrain's basins and the flooding times of all terrain vertices. This algorithm makes use of an I/O-efficient meldable priority queue, which we discuss in Section 4. To prove the correctness of all priority queue operations, we need to verify that the heap property is maintained at all times. This is little more than an exercise and is therefore omitted.. It is easy to see that every Create, Insert, DeleteMin, and Meld operation makes only O(1) changes to the buffer stack and thus has an amortized cost of O(1/B) I/Os, excluding the manipulations performed by the Flush, Fill, Merge, and Heapify operations they trigger. The following two lemmas bound the cost of all Flush, Fill, Merge, and Heapify operations performed during a sequence of N priority queue operations. Due to lack of space, their proofs are omitted. Due to its importance, the problem of computing water flow across a terrain (usually in the form of a river network) has been studied extensively. Most existing methods for computing river networks assume that once water flows into a small basin of the terrain, it never flows out-in other words, basins do not spill. Therefore, to avoid water getting caught in small local basins, most flow modelling approaches first remove all basins by flooding the terrain, that is, conceptually pouring water onto the terrain until all basins are filled [4, 13, 15] . However, this often leads to unrealistic flow patterns, since many important geographical features are removed. Recent papers [1, 5] suggested partial flooding algorithms that flood only "small" basins, where the size of a basin can be defined using different measures, such as height, volume or area. Agarwal, Arge and Yi [1] described an O(sort(N )) I/O partial flooding algorithm that removes all basins of small height. This is done by computing the topological persistence [10, 11] of each basin and removing the ones with persistence below a small threshold.. The key to obtaining an O(sort(N )) I/O solution to this problem is an algorithm that can process a sequence of N Union and Find operations using O(sort(N )) I/Os, assuming the entire sequence of operations is provided in advance. Arge and Revsbaek [5] extended the result of [1] to removing basins based on different geometric measures, including volume and area.. Partial flooding methods provide a basis only for approximate solutions to flow modelling, as the underlying assumption is that all "small" basins are flooded at a certain time, while all "big" basins are not. This assumption may not be true, as the spill time of a basin depends on its volume and its watershed, and the watershed of a basin may grow over time as a result of other basins spilling into it; in particular, the watershed of a big basin may grow to a size far exceeding the size of the watershed of a small basin and, thus, the big basin may spill before the small basin. To model the flow network at time t accurately, it is necessary to compute the times the basins of T fill and remove the basins that are full at time t. This is much harder than the partial flooding approaches discussed above, as the above methods are based on local measures associated with each basin, while the computation of the actual spill time of each basin β depends on the spill times of other basins that spill into β. As mentioned in the introduction, Liu and Snoeyink [14] presented an internal-memory algorithm for computing actual spill times and used it for flow prediction. While the paper does not present the algorithm in detail, we discuss an efficient implementation using a union-find structure and a priority queue in Section 3.2; this implementation is needed as part of our I/O-efficient algorithm.. We also require a tree structure that represents the nesting of the basins of T . This tree has been termed the merge tree of T in [7, 8] (also see Section 2) and can be computed using O(sort(N )) I/Os using the topological persistence algorithm of [1] . This algorithm is easily augmented to compute the lowest saddle on the boundary of each basin and, as shown in [5] , the volume of each basin.. Computing the watershed sizes of all basins of T is harder. The watershed sizes of all basins of T are easily computed from the watershed sizes of all pits by summing watershed sizes bottom up in the merge tree. However, the only I/Oefficient algorithm for computing the watersheds of all pits of a terrain exactly is the one of [9] . This algorithm performs O(sort(N + S)) I/Os for fat terrains, where S is the size of the terrain's strip map. The size of the strip map of a fat terrain is Θ(N 2 ) in the worst case [9] , in which case the exact computation of watersheds becomes infeasible. An approach often taken in practice [16] [17] [18] is to assume that water flows only along terrain edges, allowing the computation of watersheds using O(sort(N )) I/Os. While this may lead to poor approximations of the watersheds for irregular terrains [9] , TIN's derived from LIDAR data, for example, are rather regular, and the computed watersheds match the real watersheds rather closely.

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Not just another focus group: making the case for the nominal group technique in criminology Background: The Nominal Group Technique (NGT) is seldom applied in criminological research. This article explores the potential of NGT as a tool for criminological research. NGT is a highly structured technique combining characteristics of an individual survey and a focus group. Its structure limits researcher influence and influence from group dynamics. It increases the likelihood of equal participation for all group members and equal influence of (conflicting) values and ideas. NGT can be used in an exploratory (phase of a) study, can be used to generate hypotheses about topics which are relatively unfamiliar to the researcher, or to become familiar with the ideas found to be relevant to a research population that is socially and culturally different from the researcher. NGT is particularly relevant in applied research as a decisionmaking tool and as a consensus method. Its purpose is to gain insight into the problems or issues of importance and to identify solutions for these problems and issues. Since NGT limits the influence of group members with perceived high status, the technique is also valuable in research where participants have different levels of power.

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Kinematic Models for Manoeuvring and Seakeeping of Marine Vessels The motion of marine vessels has traditionally been studied using two different approaches: manoeuvring and seakeeping. These two approaches use different reference frames and coordinate systems to describe the motion. This paper derives the kinematic models that characterize the transformation of motion variables (position, velocity, accelerations) and forces between the different coordinate systems used in these theories. The derivations hereby presented are done in terms of the formalism adopted in robotics. The advantage of this formulation is the use of matrix notation and operations. As an application, the transformation of linear equations of motion used in seakeeping into body-fixed coordinates is considered for both zero and forward speed. The study of ship dynamics has traditionally been covered by two main theories: Manoeuvring and Seakeeping. Manoeuvring refers to the study of ship motion in the absence of wave excitation (calm water). Seakeeping, on the other hand, refers to the study of motion when there is wave excitation and while the vessel keeps its course and its speed constant (which includes the case of zero speed). Although both areas are concerned with the same issues: study of motion, stability and control, the separation allows making different assumptions that simplify the study in each case. A chief distinguishing characteristic of these theories is the use of different coordinates and reference systems to express the equations of motion.. In manoeuvring, the equations of motion are described relative to a coordinate system fixed to the vessel (a body-fixed coordinate system), whereas in seakeeping the motion is described relative to a coordinate system fixed to an equilibrium virtual vessel that moves at a constant speed and heading corresponding the average motion of the actual vessel. Most hydrodynamic programs compute radiation and wave excitation forces in this equilibrium frame.. When time-domain simulations and motion control system designs are considered, it is necessary to use a unified framework, and a body-fixed coordinate system is a natural choice. This calls for kinematic models that characterize the transformation of motion variables (position, velocity and accelerations) and forces between different coordinate systems. For the case of a vessel operating at zero forward speed, the equilibrium coordinate system can be considered fixed to the earth. The kinematic models then describe the traditional transformation between body-and earth-fixed coordinates used in robotics and aeronautics. For the case of forward speed, transformations between earthfixed, body-fixed and equilibrium (or seakeeping) coordinates are different. Details of the latter transfor-mations are often only outlined or considered for small angles in the literature-see, for example, Bishop and Price (1981) ; Lloyd (1989) ; Graham (1990) ; Faltinsen (2005) .. Therefore, this paper reviews the kinematic models commonly used in both theories and provides a complete derivation of the transformations that link these descriptions. In recent years, there has been a significant interest of these models in relation to the timedomain models for simulation and control system design based on data obtained from seakeeping programs, and unified models for manoeuvring and seakeepingsee Bailey et al. (1997) ; Fossen and Smogeli (2004) ; Fossen (2005) ; Smogeli et al. (2005) ; Perez (2005) ; Perez and Fossen (2006) . In this paper, the kinematic models most commonly used for the description of ship motion were derived using the formalism of the robotics literature. The classical transformation used in ship manoeuvring, which relates the body-fixed linear and angular velocity to the position and orientation in local geographical coordinates was revisited. The kinematic models used in seakeeping, together with the simplifying assumptions that lead to them, were considered with a notation consistent with that used in manoeuvring. Transformation between variables were derived, and the results were applied to expressing the seakeeping equations of motion in terms of manoeuvring variables. The latter provides the basis for models that can be used in guidance and motion control systems.

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Absolute Conductivity Reconstruction in Magnetic Induction Tomography Using a Nonlinear Method Abstract-Magnetic induction tomography (MIT) attempts to image the electrical and magnetic characteristics of a target using impedance measurement data from pairs of excitation and detection coils. This inverse eddy current problem is nonlinear and also severely ill posed so regularization is required for a stable solution. A regularized Gauss-Newton algorithm has been implemented as a nonlinear, iterative inverse solver. In this algorithm, one needs to solve the forward problem and recalculate the Jacobian matrix for each iteration. The forward problem has been solved using an edge based finite element method for magnetic vector potential A and electrical scalar potential , a so called A AA theoretical study of the general inverse eddy current problem and a derivation, paying special attention to the boundary conditions, of an adjoint field formula for the Jacobian is given. This efficient formula calculates the change in measured induced voltage due to a small perturbation of the conductivity in a region. This has the advantage that it involves only the inner product of the electric fields when two different coils are excited, and these are convenient computationally. This paper also shows that the sensitivity maps change significantly when the conductivity distribution changes, demonstrating the necessity for a nonlinear reconstruction algorithm. The performance of the inverse solver has been examined and results presented from simulated data with added noise. We presented an edge-based FEM for the forward problem, a sensitivity formula to calculate the changes in induced voltages due to a small change in the conductivity of a region, and an image reconstruction scheme for MIT. The image reconstruction method has been tested on various examples with conductivity ranges encountered in medical applications. Although a linear approximation may work for some simple conductivity distributions the general case requires a nonlinear approach. This paper demonstrates the advantages of nonlinear method both in terms of locating of inclusions and reconstruction of the absolute conductivity values. It is clear from this work that a nonlinear algorithm including an updated forward model and recalculated Jacobian offers improvements over equivalent linear reconstructions with simulated data. However, the application of this method to in vitro or in vivo experimental biomedical data requires a sufficiently accurate measurement system and forward model to justify the computational effort. If a linear algorithm fits the measured data to within the precision of measurement and model a nonlinear algorithm is unlikely to offer any improvement. In an industrial setting, with fixed and simple geometry and large conductivity contrasts, we have already demonstrated that nonlinear reconstruction is worthwhile for experimental data [32] . In a previous paper [32] , we considered high conductivity of metal objects relevant to industrial tomography problems. In the low contrasts typical of medical problems treated in this paper, better absolute reconstruction could be obtained. The application to experimental data from biomedical problems is the subject of our continuing efforts.

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Equivalence and Reduction of Delay-Differential Systems A new direct method is presented which reduces a given high-order representation of a control system with delays to a firstorder form that is encountered in the study of neutral delay-differential systems. Using the polynomial system description (PMD) setting due to Rosenbrock, it is shown that the transformation connecting the original PMD with the first-order form is Fuhrmann's strict system equivalence. This type of system equivalence leaves the transfer function and other relevant structural properties of the original system invariant. One of the most basic procedures in control systems theory is to transform a given system of differential or difference equations into a low-order form which is simpler but equivalent to the original system. The objective is to make identification, analysis and synthesis easier. The transformation involved, however, must preserve the relevant system properties such as controllability, observability and minimality if the conclusions about the reduced system are to remain valid about the original one. For systems described by ordinary differential or difference equations, Rosenbrock (1970) introduced the concept of polynomial matrix description (PMD). The resulting matrix has elements which are polynomials in a single indeterminate. He also introduced the notion of strict-system-equivalence between polynomial system matrices. However, a more general definition of strict-system-equivalence was given by Fuhrmann (1977) and this may be regarded mathematically as the equivalence of two polynomial system matrices through the multiplication of zero coprime matrices. For delay-differential control systems, the resulting PMD is a two-variable polynomial matrix, i.e. it has elements which are polynomials in two indeterminates. In fact, over the recent years, multivariate polynomial matrices have found many applications in n-D circuits, systems, controls, signal processing and other areas.. The problem of reducing a two-variable PMD to a first order form describing delay-differential systems was first studied by Pugh et al. (1998a) . Their method involves the construction of certain block polynomial matrices from which factors have to be removed to ensure that the resulting transformations are polynomial. Furthermore, the equivalence transformation involved could not be set out directly in terms of the given initial polynomial matrix. A two-stage method for the reduction of a two-variable polynomial matrix to first order form used in the study of singular Roesser type 2-D discrete systems was given by Pugh et al. (2005a) , and for singular Fornasini-Marchesini type 2-D discrete systems a direct method was given by Boudellioua (2006) . In this paper, a new direct method similar to the one given in (Pugh et al., 2005a; Boudellioua, 2006 ) is proposed for a class of delay-differential systems. The resulting PMD is one which arises in the theory of neutral delay-differential systems as studied by Byrnes et al. (1984) . The transformation connecting the original and final PMDs is shown to be that of Fuhrmann's strict system equivalence (F-SSE). This type of equivalence, also referred to as zero coprime system equivalence, was studied in the context of multidimensional systems by Levy (1981) , Johnson (1993) and Pugh et al. (1996) , and was shown to preserve many of the relevant original system properties. Furthermore, it was shown by Pugh et al. (1998b; 2005a) and Boudellioua (2006) that this transformation plays an important role in a number of areas of multidimensional systems theory.

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


Prediction of novel drug indications using network driven biological data prioritization and integration Background: With the rapid development of high-throughput genomic technologies and the accumulation of genome-wide datasets for gene expression profiling and biological networks, the impact of diseases and drugs on gene expression can be comprehensively characterized. Drug repositioning offers the possibility of reduced risks in the drug discovery process, thus it is an essential step in drug development. Results: Computational prediction of drug-disease interactions using gene expression profiling datasets and biological networks is a new direction in drug repositioning that has gained increasing interest. We developed a computational framework to build disease-drug networks using drug-and disease-specific subnetworks. The framework incorporates protein networks to refine drug and disease associated genes and prioritize genes in disease and drug specific networks. For each drug and disease we built multiple networks using gene expression profiling and text mining. Finally a logistic regression model was used to build functional associations between drugs and diseases. Conclusions: We found that representing drugs and diseases by genes with high centrality degree in gene networks is the most promising representation of drug or disease subnetworks.The development of many methods that enable the isolation and study of individual cells and molecules has revolutionized the process of drug discovery from being at the physiological level to more the accurate molecular level. This revolution was all due to the genome sequencing project that provides a complete list of genes and gene products and enables the simultaneous monitoring of the expression of the whole genome. Consequently, this technology has shed light on possible computational techniques for investigating new therapeutic applications for already approved drugs or other safe drug candidates in what is called drug repositioning. By definition, drug repositioning techniques ignore the first testing phases, The presented results in this work demonstrates that defining robust gene signatures for diseases and drugs from expression profiles and literature and using protein networks to refine and prioritize genes is valuable and have potential in clinical pharmacogenomics research. The results can significantly accelerate the translation into the clinics of known compounds for novel therapeutic uses. Drug repositioning is one of the most important techniques that is being used to improve drug discovery process. Drug repositioning most attractive feature is its ability to reduce costs and provide shorter paths to approval compared to the daunting traditional techniques. Most of the proposed techniques for drug repositioning tend to use a specific source of data to predict drugdisease interactions. In this work we integrated data from three major sources into a single paradigm to predict some novel drug-disease interactions. More precisely, microarray expression profiles, text-mining and biological networks were all integrated to build a drug-disease network. Comparing the proposed paradigm with a drugdisease gold standard demonstrated the robustness of the integrative paradigm in predicting drug-disease interactions. More specifically, the AUC showed that selecting hub genes from combined network, microarray and text mining, would be more representative than selecting these genes from either of these sources independently. These findings, shown in Figure 4 , were validated with considering hub genes in three centrality contexts: degree, betweenness and closeness. The results were consistent in all these centrality measures; hub genes using a combined network were more representative than hub genes using a single data source network. Finally we wanted to check for biological meaning for some of the predicted associations. More specifically we focused on some prostate cancer-drug associations and browsed the scientific literature for biological sense. Azacitidine is a pyrimidine nucleoside analogue that inhibits DNA methyltransferase, impairing DNA methylation [24] . Azacitidine is used for treatment of patients with myelodysplastic syndrome subtypes; refractory anemia with ringed or excess blasts or acute myleogenous leukemia [24] . Azacitidine is believed to exert its effect by causing hypomethylation of DNA on abnormal hematopoitic cells in the bone marrow. According to our study, Azacitidine was found to have a role in prostate cancer treatment. In an experiment to study the effect of Azacitidine in aggressive prostate cancer models, it improved the anti-tumor effect of Docetaxel and cisplatin drugs. The authors suggested using Azacitidine as a chemosensitizing agent in chemoresistant tumors [32] . In another experiment [33] , Azacitidine was found to have anti-proliferative activities when administrated chronically. This treatment resulted in a marked decrease in tumor cell proliferation with significant increases in androgen and PSA protein levels. Another interesting association predicted by our suggested model was Berberine and prostate cancer. In many experiments Berberine was found to have antitumor activities on prostate cancer cell lines [34, 35] , and found to induce G1 arrest at low concentration [34] . In addition, at high concentration it has been found to efficiently abrogate G2/M arrest. The results suggest that combined administration of Berberine and caffeine may http://www.jcheminf.com/content/6/1/1 Figure 7 Protein network of the 34 prostate genes and cancer genes. This figure shows the functional protein network of the 34 prostate genes predicted by our model and other cancer related protein partners. Most of the genes in this network are oncogenes and tumor suppressors in addition to other keys players in cancer development.. accelerate the killing of cancer cells. Berberine suppresses AR, which is known to be activated in cancer signaling and suggests that Berberine presents a promising agent for the prevention and/or treatment of prostate cancer [35] . Paclitaxel is an antineoplastic agent indicated as a first-line and subsequent therapy for the treatment of advanced carcinoma of the ovary and other various cancers including breast cancer [24] . According to our model, Paclitaxel was found to have a strong association score with prostate cancer. Indeed, the anti-neoplastic activity of Paclitaxel on prostate cancer was detected in many experiments [36, 37] . The findings suggest that Paclitaxel induces nuclear translocation and activation of PKC-Ît', which in turn causes Golgi-Cdk1 activation. Golgimediated signaling cascades facilitate mitochondria involved apoptotic pathways, the thing that might explain the anti-tumor activity of Paclitaxel. Surface modified tumor cells may have potential clinical benefit for patients with prostate cancer when it is combined with paclitaxel [35] . With the consideration that immunochemotherapy must depend on careful selection of paclitaxel dosage and the sequence of paclitaxel/vaccine administration.

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


Neuromodulation of STDP through short-term changes in firing causality Abstract Spike timing dependent plasticity (STDP) likely plays an important role in forming and changing connectivity patterns between neurons in our brain. In a unidirectional synaptic connection between two neurons, it uses the causal relation between spiking activity of a presynaptic input neuron and a postsynaptic output neuron to change the strength of this connection. While the nature of STDP benefits unsupervised learning of correlated inputs, any incorporation of value into the learning process needs some form of reinforcement. Chemical neuromodulators such as Dopamine or Acetylcholine are thought to signal changes between external reward and internal expectation to many brain regions, including the basal ganglia. This effect is often modelled through a direct inclusion of the level of Dopamine as a third factor into the STDP rule. While this gives the benefit of direct control over synaptic modification, it does not account for observed instantaneous effects in neuronal activity on application of Dopamine agonists. Specifically, an instant facilitation of neuronal excitability in the striatum can not be explained by the only indirect effect that dopamine-modulated STDP has on a neuron's firing pattern. We therefore propose a model for synaptic transmission where the level of neuromodulator does not directly influence synaptic plasticity, but instead alters the relative firing causality between preand postsynaptic neurons. Through the direct effect on postsynaptic activity, our rule allows indirect modulation of the learning outcome even with unmodulated, two-factor STDP. However, it also does not prohibit joint operation together with three-factor STDP rules. Recent experiments have indicated that Dopamine may directly influence the spiking activity of prefrontal neurons by increasing signal-to-noise ratio (Kroener et al. 2009 ) or gain (Thurley et al. 2008 ) during synaptic transmission. These studies suggest that an instant effect of Dopamine may only be present during additional synaptic input and that Dopamine may not be capable of eliciting a synaptic response on its own in this case.. While the influence of varying Dopamine on synaptic learning processes has been recognized and modelled in a large number of publications (Farries and Fairhall 2007; Izhikevich 2007; Morrison et al. 2008; Potjans et al. 2009; Reynolds and Wickens 2002) , this has usually been done by directly adapting the STDP rule to include an additional third factor signalling dopaminergic reinforcement, beside inclusion of the pre-and postsynaptic activities. The requested synaptic weight change defined by STDP would often be multiplied by a reinforcement factor in the interval [-1,1] , yielding no synaptic learning for baseline levels of Dopamine (zero reinforcement) and inverted, or ''antihebbian'', learning for negative values of reinforcement.. Postsynaptic activity would be only indirectly affected by Dopamine in these models, through the gradual synaptic weight change induced by reinforced STDP.. However, there have been modelling studies incorporating experimental evidence on increased postsynaptic facilitation under Dopamine exposure (Chorley and Seth 2011) , albeit by affecting the neuron-wide recovery function of the postsynaptic model neuron. To our knowledge, no previous modelling studies of dopaminergic influence on synaptic transmission with an only indirect effect on the synaptic learning process have been published. We chose to investigate the possible network level implications of a (Dopamine-like) neuromodulator purely affecting synaptic transmission on a local scale. As any postsynaptic activity is highly dependent on the received synaptic input, changes to this input directly affect the postsynaptic neuron's spiking activity as the second factor in usual STDP rules (Bi and Poo 2001) . Any neuromodulation of synaptic transmission is therefore in principle able to affect the learning outcome of STDP, even when no direct involvement of the modulator in the actual weight adjustment process is present.. There are in theory two ways of affecting the amount of synaptic input a neuron receives. The first would need sufficient control over the spiking activity of presynaptic neurons, which is difficult to provide for inputs arriving from distant brain areas such as the axonal endings arriving in the basal ganglia's striatum from all parts of the cortex. The second possibility would be to introduce a short-term, reversible effect on the actual process of synaptic transmission, which regulates the amount of input arriving at a postsynaptic neuron through the synaptic connection when a presynaptic neuron fires. If a neuromodulator were to influence the short-term transmission efficacy of synaptic connections, it would temporarily be changing the effective weight of those synaptic connections for all intents and purposes.. We therefore modulate only synaptic transmission in our model, and show that we can still influence the learning outcome with an unchanged STDP rule. Without any direct reference to existing chemical neuromodulators, we coincidentally call our neuromodulatory reinforcement factor DA. However, simply multiplying the existing baseline weight with the current DA level to form an effective weight would be problematic: Whenever the applied reinforcement would reach a value around zero, all synaptic transmission would stop, which is unwanted behaviour for a neuromodulated synapse. Instead, we use a power law relationship between baseline weights and the current level of DA to form the effective synaptic weights used for transmission. We define a threshold value h that divides the baseline weights into strong and weak weights and shifts the strong weights above 1 before applying the power law (Eqs. 1, 2). For low DA, all effective weights now become more similar to h. For high DA, all effective weights move away from h, towards the extremes of the defined weight range. We call h the generalisation threshold for low levels of the reinforcement signal and the sparsification threshold for high levels. Due to the shape of our effective weights rule (Fig. 1) , no strong baseline weight ever has an effective value below h, and no weak baseline weight ever has an effective value above h. Also, as the effective weight curves for low DA mirror those for high DA around the unmodulated weights line (DA = 1, shown in green), the overall postsynaptic firing rate remains unaffected under reinforcement for uniformly distributed baseline weights. For a possible chemical interpretation of h, see ''Conclusion''. In this article, we demonstrated how we can influence the learning outcome of a spiking network simply by applying some global reinforcement during synaptic transmission. All synaptic modification is only dependent on the pre-and postsynaptic spiking activity, and no third (modulatory) factor is used during spike-timing dependent plasticity. Through controlling a global level of neuromodulator concentration, we are able to influence the effective range of synaptic efficacies, and thereby the discriminability of trained vs. untrained inputs arriving at a postsynaptic neuron. This change in synaptic efficacy is computed locally in each synapse, using only the current synaptic strength and the current global neuromodulator concentration.. A variable neuron-wide threshold h may be used in future work as a homeostatic slow parameter that automatically updates to retain normal excitability on varying neuromodulator levels for non-uniform weight distributions. The size of h would likely come to be far below 0.5 in an automatically adopting implementation.. Applying modulation by locally affecting synaptic transmission instead of direct manipulation of the STDP rule gives the advantage of direct control over the causal firing relationship between selected presynaptic and postsynaptic neurons, which can instantly be observed as the modulation factor changes. In terms of network learning, the reinforcement signal does not directly increase or decrease active synapses, but instead leads to a temporary sparsification of effective weights for high reinforcement and a generalisation around h for low reinforcement.. As the modulatory factor needs to be present during the arrival of inputs, we do not approach the distal reward problem (Izhikevich 2007) through our model, but assume for the case of delayed reward an involvement of hippocampus and cortical working memory instead of direct application of delayed reward into an STDP rule. Instead, we hope to provide a possible explanation for experimentally observed (Kroener et al. 2009; Thurley et al. 2008) instantaneous effects during neuromodulator application. Assuming the process of novelty detection by subcortical sensory nuclei performs faster than or equally fast as the semantic processing of some signals in the cortex (Trimmer et al. 2008) , our model may also be useful for learning the short-latency novelty portion (Redgrave and Gurney 2006) of the nigral reinforcement signal (Schultz et al. 1997 ).. Although we have until now only been studying pairwise rules of STDP, there is no reason to assume that the proposed modulation rule should not be combinable with STDP learning based on triplets of spikes (Pfister and Gerstner 2006) . Specific examination of this combination is not focus of the current article.. Our model presents some interesting questions for biological validation: It is currently unclear if and how exactly Dopamine affects signal transmission locally at single synapses. Little is known about the exact local concentrations of dopaminergic receptors across a neuron's membrane (Reynolds and Wickens 2002; Shen et al. 2008; Surmeier et al. 2007 ). Also, it might be useful to look for a biological analogy to our theoretical sparsification/generalisation threshold h, as this may explain many of the observed instant effects of Dopamine or related substances.. A chemical prediction by our proposed rule may start at the ratio between D1-type and D2-type receptors on a Dopamine-modulated synapse of a D1-dominant postsynaptic neuron. While a neuron-wide baseline ratio of dopaminergic receptors may represent a homeostatic default configuration similar to h in our model, any strengthening synaptic connection may be found to also increase the local concentration of D1-type receptors towards a higher excitability on raised levels of Dopamine. Similarly, a weakening synaptic connection may reduce the local concentration of D1-type receptors, allowing the existing D2-type receptors to become locally dominant in controlling the synapse's reaction to drops in global Dopamine concentration. Although the actual curve of h-dependent neuromodulation of synaptic efficacy would be up for experimental refinement, such a weight-dependent dynamic reconfiguration of D1-type/D2-type receptor ratio might allow for fast Dopamine-dependent modulation of synaptic transmission to take place. Similarly, on D2-dominant neurons, the concentration of D2-type dopaminergic receptors may be locally increased with a strengthening of synapses, leading to a supposed opposite behaviour on application of Dopamine.. While both D1-type and D2-type receptors seem to be evenly distributed across the main striatal target areas of dopaminergic projections, it is currently unknown whether local concentrations among and within neurons diverge from this general ratio or if neurons tend towards skewed distribution of receptor ratio depending on synaptic strength and projection target area.. An additional effect of the increased efficacy of weak synapses on D1-type neurons for low DA is that as these synapses tend to be more active, any neurons that have nearly all weights close to zero and may never fire, have a new chance of becoming active to the current inputs. This opens the chance of recovering muted model neurons that would previously never fire, given useful values for h.. Low DA may inherently support exploration through D1-type neurons in our model, while high DA may inherently support exploitation, with opposite behaviour for D2-type neurons (compare recent work of Humphries et al. 2012) . We performed two stages of tests with our proposed new method of modulation. During the first stage, we examined the direct effect on postsynaptic activity for a typical distribution of fixed weights, while on-line synaptic modification using spike timing dependent plasticity was incorporated during the second stage of tests.

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


A review of computer assisted detection/diagnosis (CAD) in breast thermography for breast cancer detection Abstract Breast cancer is the leading type of cancer diagnosed in women. For years human limitations in interpreting the thermograms possessed a considerable challenge, but with the introduction of computer assisted detection/diagnosis (CAD), this problem has been addressed. This review paper compares different approaches based on neural networks and fuzzy systems which have been implemented in different CAD designs. The greatest improvement in CAD systems was achieved with a combination of fuzzy logic and artificial neural networks in the form of FALCON-AART complementary learning fuzzy neural network (CLFNN). With a CAD design based on FALCON-AART, it was possible to achieve an overall accuracy of near 90%. This confirms that CAD systems are indeed a valuable addition to the efforts for the diagnosis of breast cancer. Lower cost and high performance of new infrared systems combined with accurate CAD designs can promote the use of thermography in many breast cancer centres worldwide.

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The degree resistance distance of cacti Graph invariants, based on the distances between the vertices of a graph, are widely used in theoretical chemistry. The degree resistance distance of a graph G is defined asis the degree of the vertex u, and R(u, v) the resistance distance between the vertices u and v. Let Cact(n; t) be the set of all cacti possessing n vertices and t cycles. The elements of Cact(n; t) with minimum degree resistance distance are characterized. The graphs considered in this paper are finite, loopless, and contain no multiple edges. Given a graph G, let V (G) and E(G) be, respectively, its vertex and edge sets. The ordinary distance d(u, v) = d G (u, v) between the vertices u and v of the graph G is the length of the shortest path between u and v.. The Wiener index W (G) is the sum of ordinary distances between all pairs of vertices, that is,. It is the oldest and one of the most thoroughly studied distance-based graph invariants [8, 9, 25] .

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Integrating human observer inferences into robot motion planning Our goal is to enable robots to produce motion that is suitable for human-robot collaboration and coexistence. Most motion in robotics is purely functional, ideal when the robot is performing a task in isolation. In collaboration, however, the robot's motion has an observer, watching and interpreting the motion. In this work, we move beyond functional motion, and introduce the notion of an observer into motion planning, so that robots can generate motion that is mindful of how it will be interpreted by a human collaborator. We formalize predictability and legibility as properties of motion that naturally arise from the inferences in opposing directions that the observer makes, drawing on action interpretation theory in psychology. We propose models for these inferences based on the principle of rational action, and derive constrained functional trajectory optimization techniques for planning motion that is predictable or legible. Finally, we present experiments that test our work on novice users, and discuss the remaining challenges in enabling robots to generate such motion online in complex situations. In this paper, we explore the problem where a robot and a human are collaborating side by side to perform a tightly coupled physical task together, like clearing a table (a running example in our paper).. The task amplifies the burden on the robot's motion. Most motion in robotics is purely functional: industrial robots move to package parts, vacuuming robots move to suck dust, and personal robots move to clean up a dirty table. This type of motion is ideal when the robot is performing a task in isolation.. Collaboration, however, does not happen in isolation. In collaboration, the robot's motion has an observer, watching and interpreting the motion.. In this work, we move beyond functional motion, and introduce the notion of an observer and their inferences into motion planning, so that robots can generate motion that is mindful of how it will be interpreted by a human collaborator.. When we collaborate, we make two inferences ( Fig. 1 , lower center) about our collaborator (Vesper et al. 2010; Tomasello et al. 2004; Csibra and Gergely 2007) : (1) we infer their goal based on their ongoing action (action-to-goal), and (2) if we know their goal, we infer their future action from it (goal-to-action). Our work formalizes the two properties of motion that enable these two inferences: predictability and legibility.. Legibility stems from the first inference, and is about conveying intent-moving in a manner that makes the robot's goal clear to observer. Predictability stems from the second inference, and is about matching the observer's expectation-matching the motion they predict when they know the robot's goal.. Predictable and legible motion can be correlated. For example, in an unambiguous situation, where an actor's Fig. 1 Above A predictable and legible trajectory of a robot's hand for the same task of grasping the green object. Center Predictability and legibility stem from inferences in opposing directions. Below The legibility optimization process for a reaching task. By exaggerating to the right, the robot is more clear about its intent to grasp the object on the right observed motion matches what is expected for a given intent (i.e. is predictable), then this intent can be used to explain the motion. If this is the only intent which explains the motion, the observer can immediately infer the actor's intent, meaning that the motion is also legible. This is why we tend to assume that predictability implies legibility-that if the robot moves in an expected way, then its intentions will automatically be clear (Beetz et al. 2010; Kruse et al. 2012) .. The writing domain, however, clearly distinguishes the two. The word legibility, traditionally an attribute of written text (Tinker et al. 1963) , refers to the quality of being easy to read. When we write legibly, we try consciously, and with some effort, to make our writing clear and readable to someone else. The word predictability, on the other hand, refers to the quality of matching expectation. When we write predictably, we fall back to old habits, and write with minimal effort.. As a consequence, our legible and predictable writings are different: our friends do not expect to open our diary and see our legible writing style. They rightfully assume the diary will be written for us, and expect our usual, day-today style. In this paper, by formalizing predictability and legibility as directly stemming from the two inferences in opposing directions, goal-to-action and action-to-goal, we show that the two are different in motion as well: Our formalism emphasizes the difference between legibility and predictability in theory: they stem from inferences in opposing directions (from trajectories to goals vs. from goals to trajectories), with strong parallels in the theory of action interpretation. Table 1 shows a summary. Predictability In line with our hypothesis, a factorial ANOVA revealed a significant main effect for the trajectory: subjects rated the predictable trajectory ξ P as matching what they expected better than ξ L , F(1, 310) = 21.88, p < .001, with a difference in the mean rating of 0.8, but small effect size (η 2 =.02). The main effect of the character was only marginally significant, F(2, 310) = 2, 91, p = .056. The interaction effect was significant however, with F(2, 310) = 10.24, p < .001. The post-hoc analysis using Tukey corrections for multiple comparisons revealed, as Fig. 11a shows, that our hypothesis holds for the point robot (adjusted p < .001) and for the human (adjusted p = 0.28), but not for HERB.. The trajectories the subjects drew confirm this (Fig. 12) : while for the point robot and the human the trajectory they expected is, much like the predictable one, a straight line, for HERB the trajectory they expected splits between straight lines and trajectories looking more like the legible one.. For HERB, ξ L was just as (or even more) predictable than ξ P . We conducted an exploratory follow-up study with novice subjects from a local pool (with no technical background) to help understand this phenomenon. We asked them to describe the trajectory they would expect HERB to take in the same scenario, and asked them to motivate it. Surprisingly, all 5 subjects imagined a different trajectory, motivating it with a different reason.. Two subjects thought HERB's hand would reach from the right side because of the other object: one thought HERB's hand is too big and would knock over the other object, and the other thought the robot would be more careful than a human. This brings up an interesting possible correlation between legibility and obstacle avoidance. However, as Fig. 7 shows, a legible trajectory still exaggerates motion away from the other candidate objects even in if it means getting closer to a static obstacle.. Another subject expected HERB to not be flexible enough to reach straight towards the goal in a natural way, like a human would, and thought HERB would follow a trajectory made out of two straight line segments joining on a point on the right. She expected HERB to move one joint at a time. We often saw this in the drawn trajectories with the original set of subjects as well (Fig. 12, HERB, Expected) .. The other subjects came up with interesting strategies: one thought HERB would grasp the bottle from above because that would work better for HERB's hand, while the other thought HERB would use the other object as a prop and push against it in order to grasp the bottle.. Overall, that ξ P was not more predictable than ξ L despite what the theory suggested because the cost function we assumed did not correlate to the cost function the subjects actually expected. What is more, every subject expected a different cost function, indicating that a predictable robot would have to adapt to the particulars of a human observer.. Legibility We collected from each subject the time at which they stopped the trajectory and their guess of the goal. Figure 11b (above) shows the cumulative percent of the total number of subjects assigned to each condition that made a correct prediction as a function of time along the trajectory. With the legible trajectories, more of the subjects tend to make correct predictions faster.. To compare the trajectories statistically, we unified time and correctness into a typical score inspired by the Guttman structure (e.g. Bergersen et al. 2011) : guessing wrong gets a score of 0, and guessing right gets a higher score if it happens earlier. A factorial ANOVA predicting this score revealed, in line with our hypothesis, a significant effect for trajectory: the legible trajectory had a higher score than the predictable one, F(1, 241) = 5.62, p = .019. The means were 6.75 and 5.73, much higher than a random baseline of making a guess independent of the trajectory at uniformly distributed time, which would result in a mean of 2.5-the subjects did not act randomly. The effect size was small, η 2 = .02. No other effect in the model was significant. Although a standard way to combine timing and correctness information, this score rewards subjects that gave an incorrect answer 0 reward. This is equivalent to assuming that the subject would keep making the incorrect prediction. However, we know this not to be the case. We know that at the end (time T ), every subject would know the correct answer. We also know that at time 0, subjects have a probability of 0.5 of guessing correctly. To account for that, we computed an approximate probability of guessing correctly given the trajectory so far as a function of time-see Fig. 11b (below). Each subject's contribution propagates (linearly) to 0.5 at time 0 and 1 at time T. The result shows that indeed, the probability of making a correct inference is higher for the legible trajectory at all times.. This effect is strong for the point robot and for HERB, and not as strong for the human character. We believe that this might be a consequence of the strong bias humans have about human motion-when a human moves even a little unpredictably, confidence in goal prediction drops. This is justified by the fact that subjects did have high accuracy when they responded, but responded later compared to other conditions. Thus, legible human trajectories would need a stronger emphasis on optimality w.r.t. C (i.e. smaller trust region parameter β in (20)).. An ANOVA using β as a factor supported H1, showing that the factor had a significant effect on legibility (F(6, 290) = 12.57, p < 0.001), with a medium-large effect size, η 2 = .2. Figure 13 (left) shows the means and standard errors for each condition.. An all-pairs post-hoc analysis with Tukey corrections for multiple comparisons revealed that all trajectories with β ≥ 20 were significantly more legible than the predictable trajectory (β = 0), all with p < 0.001, the maximum being reached at β = 40. This supports the first part of H2, that legibility significantly increases with β at first: there is no practical need to become more unpredictable beyond this point. The post-hoc analysis also revealed that the trajectories with β =20, 40, 80, or 320 were significantly more legible than the trajectory with β = 10 ( p = .003, p < .001, p = .004, and p = .002 respectively).. The maximum mean legibility was the trajectory with β = 40. Beyond this value, the mean legibility stopped increasing. Contrary to our expectation, it did not significantly decrease. In fact, the difference in score between β = 40 and β = 320 is in fact significantly less than 2.81 (t (84) = 1.67, p = 0.05). At a first glance, the robot's overly unpredictable behavior seems to not have caused any confusion as to what its intent was.. Analyzing the score histograms (Fig. 14) for different β values, we observed that for higher βs, the wide majority of users stopped the trajectory in the beginning. The consequence is that our legibility measure failed to capture whether the mid-part of the trajectory becomes illegible: the end of the trajectory conveys the goal because it reaches it, but what happens in between the beginning and end? Thus, we ran a follow-up study to verify that legibility in this region does decrease at β = 320 as compared to our β * = 40, in which we explicitly measured the legibility in the middle of the trajectory. This paper studied motion planning in the presence of an observer who is watching the motion and making inferences about it.. We first formalized predictability and legibility based on the inferences that the observer makes, which have opposing directionality. We then proposed mathematical models for these inferences in order to arrive at predictability and legibility scores that a robot can evaluate. Finally, we derived functional gradient optimization methods for generating predictable or legible motion, as well as a constrained optimization method for optimizing for legibility in a trust region of predictability.. Our studies on novice users provided some support for our models-trajectories more predictable according to the model were overall more predictable in practice, and trajec- tories more legible according to the model were overall more legible in practice while inside a trust region of predictability. However, three main challenges remain in planning such motions for complex cases (i.e. high-dimensional spaces and non-convex C):. 11.1 Challenge I: finding C If the human observer expects human-like motion, cues from animation or biomechanics (Lasseter 1987; Witkin and Kass 1988; Flash and Hogan 1985; can help provide good approximations for C. However, our studies suggest that efficiency of robot motion has different meanings for different observers (see follow-up experiment in Sect. 10.1).. A possibility is to learn from demonstrations provided by the observer. Here, the robot can learn a C that explains the demonstrations (Argall et al. 2009 ), using tools like Inverse Optimal Control (IOC) (Abbeel and Ng 2004; Ratliff et al. 2006; Ziebart et al. 2008) . However, extending these tools to higher dimensions is an open problem (Ratliff et al. 2006) , and recent work focuses on learning costs that make the demonstrations locally optimal (Levine and Koltun 2012; Kalakrishnan et al. 2013) , or on restricting the space of trajectories to one in which optimization is tractable (Jain et al. 2013) .. Aside from investigating the extension of IOC to highdimensional spaces, we also propose a second thread of research: the idea of familiarizing users to robot behavior. Can users be taught a particular C over time? Our preliminary results suggest that familiarization helps for the motion generated by the C from (19), but that it suffers from severe limitations, especially on less natural choices of C. One possibility is that motion for nonanthropomorphic arms is complex enough that we cannot rely solely on the user to do all the learning, suggesting that the two threads of research-familiarization and learning from demonstration-are complementary.

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


Estimation of Distribution Algorithms as Logistic Regression Regularizers of Microarray Classifiers Objectives: The "large k (genes), small N (samples)" phenomenon complicates the problem of microarray classification with logistic regression. The indeterminacy of the maximum likelihood solutions, multicollinearity of predictor variables and data over-fitting cause unstable parameter estimates. Moreover, computational problems arise due to the large number of predictor (genes) variables. Regularized logistic regression excels as a solution. However, the difficulties found here involve an objective function hard to be optimized from a mathematical viewpoint and a careful required tuning of the regularization parameters. Methods: Those difficulties are tackled by introducing a new way of regularizing the logistic regression. Estimation of distribution algorithms (EDAs), a kind of evolutionary algorithms, emerge as natural regularizers. Obtaining the regularized estimates of the logistic classifier amounts to maximizing the likelihood function via our EDA, without having to be penalized. Likelihood penalties add a number of difficulties to the resulting optimization problems, which vanish in our case. Simulation of new estimates during the evolutionary process of EDAs is performed in such a way that guarantees their shrinkage while maintaining their probabilistic dependence relationships learnt. The EDA process is embedded in an adapted recursive feature elimination procedure, thereby providing the genes that are best markers for the classification.The consistency with the literature and excellent classification performance achieved with our algorithm are illustrated on four microarray data sets: Breast, Colon, Leukemia and Prostate. Details on the last two data sets are available as supplementary material.We have introduced a novel EDA-based logistic regression regularizer. It implicitly shrinks the coefficients during EDA evolution process while optimizing the usual likelihood function. The approach is combined with a gene subset selection procedure and automatically tunes the required parameters. Empirical results on microarray data sets provide sparse models with confirmed genes and performing better in classification than other competing regularized methods. The development of DNA microarray technology allows screening of gene expression levels from different tissue samples (e.g. cancerous and normal). The resulting gene expression data help explore gene interactions, discover gene functions and classify individual cancerous/normal samples, using different supervised learning techniques [1, 2] .. Among these techniques, logistic regression [3] is widely used because it provides explicit probabilities of class membership, interpretation of the regression coefficients of predictor variables and it avoids gaussianity or correlation structure assumptions.. Microarray classification is a challenging task since these data typically involve extremely high dimensionality (thousands of genes) and small sample sizes (less than one hundred cases). This is the so-called "large k (variables), small N (samples) problem" or the "curse of dimensionality". This may cause a number of statistical problems for estimating parameters properly. First, a large number of parameters have to be estimated using a very small number of samples. Therefore, an infinite number of solutions is possible as the problem is undetermined. Second, multicollinearity largely exists. The likelihood of some gene profiles being linear combinations of other gene profiles grows as more and more variables are introduced into the model, thereby supplying no new information. Third, over-fitting may occur, i.e. the model may fit the training data well but perform badly on new samples. These problems yield unstable parameter estimates. Furthermore, there are also computational problems due to the large number of predictor variables. Traditional numerical algorithms for finding the estimates, like Newton-Raphson's method [4] , require prohibitive computa -tions to invert a huge, sometimes singular matrix, at each iteration.. To alleviate this situation within the context of logistic regression, many authors use techniques of dimensionality reduction and feature (or variable) selection [5] . Feature selection methods yield parsimonious models which reduce information costs, are easier to explain and understand, and increase model applicability and robustness. The goodness of a proposed gene subset may be assessed via an initial screening process where genes are selected in terms of some univariate or multivariate scoring metric (filter approach [6] ). By contrast, wrapper approaches search for good gene subsets using the classifier itself as part of their function evaluation [7] . A performance estimate of the classifier trained with each subset assesses the merit of this subset.. Imposing a penalty on the size of logistic regression coefficients is another different solution. Finding a maximum likelihood estimate subject to spherical restrictions on the logistic regression parameters leads to ridge or quadratic (penalized) logistic regression [8] . Therefore, the ridge estimator is a restricted maximum likelihood estimator (MLE). Shrinking the coefficients towards zero and allowing a little bias provide more stable estimates with smaller variance.. Apart from ridge penalization, there are other penalties within the more general framework of regularization methods. All of them aim at balancing the fit to the data and the stability of the estimates. These methods are much more efficient computationally than wrapper methods with the similar performance. Furthermore, regularization methods are more continuous than usual discrete processes of retaining-or-discarding features thereby not suffering as much from high variability.. Here we introduce estimation of distribution algorithms (EDAs) as natural regularizers within the logistic regression context. EDAs are a recent optimization heuristic included in the class of stochastic populationbased search methods [9] . EDAs work by constructing an explicit probability model from a set of selected solutions, which is then conveniently used to generate new promising solutions in the next iteration of the evolutionary process. An optimization heuristic is an appropriate tool since shaping the logistic classifier means estimating its parameters, which in turn entails solving a maximization problem. Unlike traditional numerical methods, EDAs do not require derivative information or matrix inversions. Moreover, used as fitness functions, EDAs could similarly maximize penalized likelihoods to tackle the k >> N problem. This would just reveal the potential of a heuristic (EDA) against a numerical (Newton-Raphson) method. In this paper we will show that the EDA framework is so general that, under certain parameterizations, it obtains the regularized estimates in a natural way, without penalizing the original likelihood. EDAs receive the unrestricted likelihood equations as inputs and they generate the restricted MLEs as outputs. The high interest of combining a regularization with a dimension-reduction step to enhance classifier efficiency has been pointed out elsewhere [31] . Combined with a gene subset selection procedure that adapts the RFE and automatically tunes the required parameters, we have introduced a novel EDAbased logistic regression regularizer. It includes the shrinkage of the coefficients implicitly during EDA evolution process while optimizing the usual likelihood function. The Unlike the traditional procedures for finding maximum likelihood β i parameters, the EDA approach is able to use any optimization objective, regardless of its complexity or the non-existence of an explicit formula for its expression. In this respect, our framework could find parameters that maximize the AUC objective (a difficult problem [41] ) or it would also fit the search for parameters of any regularized logistic regression. The inclusion of interaction terms among (possibly coregulated) genes in η j of expression (1) would also be feasible as other future direction to explore.

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