Negative selection algorithms on strings with efficient training and linear-time classification

A string-based negative selection algorithm is an immune-inspired classifier that infers a partitioning of a string space Σ^? into “normal” and “anomalous” partitions from a training set S containing only samples from the “normal” partition. The algorithm generates a set of patterns, called “detectors”, to cover regions of the string space containing none of the training samples. Strings that match at least one of these detectors are then classified as “anomalous”. A major problem with existing implementations of this approach is that the detector generating step needs exponential time in the worst case. Here we show that for the two most widely used kinds of detectors, the r-chunk and r-contiguous detectors based on partial matching to substrings of length r, negative selection can be implemented more efficiently by avoiding generating detectors altogether: for each detector type, training set S⊆Σ^? and parameter r≤? one can construct an automaton whose acceptance behaviour is equivalent to the algorithm’s classification outcome. The resulting runtime is O(|S|?r|Σ|) for constructing the automaton in the training phase and O(?) for classifying a string.     

Model-free Q-learning designs for linear discrete-time zero-sum games with application to H-infinity control

In this paper, the optimal strategies for discrete-time linear system quadratic zero-sum games related to the H-infinity optimal control problem are solved in forward time without knowing the system dynamical matrices. The idea is to solve for an action dependent value function Q(x,u,w) of the zero-sum game instead of solving for the state dependent value function V(x) which satisfies a corresponding game algebraic Riccati equation (GARE). Since the state and actions spaces are continuous, two action networks and one critic network are used that are adaptively tuned in forward time using adaptive critic methods. The result is a Q-learning approximate dynamic programming (ADP) model-free approach that solves the zero-sum game forward in time. It is shown that the critic converges to the game value function and the action networks converge to the Nash equilibrium of the game. Proofs of convergence of the algorithm are shown. It is proven that the algorithm ends up to be a model-free iterative algorithm to solve the GARE of the linear quadratic discrete-time zero-sum game. The effectiveness of this method is shown by performing an H-infinity control autopilot design for an F-16 aircraft.     

A necessary and sufficient condition for parameter insensitive disturbance-rejection problem with state feedback

In this paper a necessary and sufficient condition for a parameter insensitive disturbance-rejection problem with state feedback which was pointed out as an open problem by Bhattacharyya to be solvable is proved. A constructive algorithm of simultaneously (A,B)-invariant subspaces for a finite-number of linear systems and a relationship between simultaneously (A,B)-invariant subspaces and generalized (A,B)-invariant subspaces play an important role to prove the main result.     

Improved deterministic algorithms for weighted matching and packing problems

Based on the method of (n,k)-universal sets, we present a deterministic parameterized algorithm for the weighted rd-matching problem with time complexity O^∗(4^{(r−1)k+o(k)}), improving the previous best upper bound O^∗(4^rk+o(k)). In particular, the algorithm applied to the unweighted 3d-matching problem results in a deterministic algorithm with time O^∗(16^k+o(k)), improving the previous best result O^∗(21.26^k). For the weighted r-set packing problem, we present a deterministic parameterized algorithm with time complexity O^∗(2^{(2r−1)k+o(k)}), improving the previous best result O^∗(2^2rk+o(k)). The algorithm, when applied to the unweighted 3-set packing problem, has running time O^∗(32^k+o(k)), improving the previous best result O^∗(43.62^k+o(k)). Moreover, for the weighted r-set packing and weighted rd-matching problems, we give a kernel of size O(k^r), which is the first kernelization algorithm for the problems on weighted versions.     

Modelling series of studies with a common structure

Consider the situation where the Structuration des Tableaux à Trois Indices de la Statistique (STATIS) methodology is applied to a series of studies, each study being represented by data and weight matrices. Relations between studies may be captured by the Hilbert-Schmidt product of these matrices. Specifically, the eigenvalues and eigenvectors of the Hilbert-Schmidt matrix S may be used to obtain a geometrical representation of the studies. The studies in a series may further be considered to have a common structure whenever their corresponding points lie along the first axis. The matrix S can be expressed as the sum of a rank 1 matrix λuu^T with an error matrix E. Therefore, the components of the vector are sufficient to locate the points associated to the studies. Former models for S where vec(E) are mathematically tractable and yet do not take into account the symmetry of the matrix S. Thus a new symmetric model is proposed as well as the corresponding tests for a common structure. It is further shown how to assess the goodness of fit of such models. An application to the human immunodeficiency virus (HIV) infection is used for assessing the proposed model.     

Split Bregman method for large scale fused Lasso

Ordering of regression or classification coefficients occurs in many real-world applications. Fused Lasso exploits this ordering by explicitly regularizing the differences between neighboring coefficients through an ?₁ norm regularizer. However, due to nonseparability and nonsmoothness of the regularization term, solving the fused Lasso problem is computationally demanding. Existing solvers can only deal with problems of small or medium size, or a special case of the fused Lasso problem in which the predictor matrix is the identity matrix. In this paper, we propose an iterative algorithm based on the split Bregman method to solve a class of large-scale fused Lasso problems, including a generalized fused Lasso and a fused Lasso support vector classifier. We derive our algorithm using an augmented Lagrangian method and prove its convergence properties. The performance of our method is tested on both artificial data and real-world applications including proteomic data from mass spectrometry and genomic data from array comparative genomic hybridization (array CGH). We demonstrate that our method is many times faster than the existing solvers, and show that it is especially efficient for large p, small n problems, where p is the number of variables and n is the number of samples.     

Online computation with advice

We consider a model for online computation in which the online algorithm receives, together with each request, some information regarding the future, referred to as advice. The advice is a function, defined by the online algorithm, of the whole request sequence. The advice provided to the online algorithm may allow an improvement in its performance, compared to the classical model of complete lack of information regarding the future. We are interested in the impact of such advice on the competitive ratio, and in particular, in the relation between the size b of the advice, measured in terms of bits of information per request, and the (improved) competitive ratio. Since b=0 corresponds to the classical online model, and b=⌈log∣A∣⌉, where A is the algorithm’s action space, corresponds to the optimal (offline) one, our model spans a spectrum of settings ranging from classical online algorithms to offline ones.In this paper we propose the above model and illustrate its applicability by considering two of the most extensively studied online problems, namely, metrical task systems (MTS) and the k-server problem. For MTS we establish tight (up to constant factors) upper and lower bounds on the competitive ratio of deterministic and randomized online algorithms with advice for any choice of 1≤b≤Θ(logn), where n is the number of states in the system: we prove that any randomized online algorithm for MTS has competitive ratio Ω(log(n)/b) and we present a deterministic online algorithm for MTS with competitive ratio O(log(n)/b). For the k-server problem we construct a deterministic online algorithm for general metric spaces with competitive ratio k^O(1/b) for any choice of Θ(1)≤b≤logk.     

Noncausal linear periodically time-varying scaling for robust stability analysis of discrete-time systems: Frequency-dependent scaling induced by static separators

This article is concerned with robust stability analysis of discrete-time systems and introduces a novel and powerful technique that we call noncausal linear periodically time-varying (LPTV) scaling. Based on the discrete-time lifting together with the conventional but general scaling approach, we are led to the notion of noncausal LPTV scaling for LPTV systems, and its effectiveness is demonstrated with a numerical example. To separate the effect of noncausal and LPTV characteristics of noncausal LPTV scaling to see which is a more important source leading to the effectiveness, we then consider the case of LTI systems as a special case. Then, we show that even static noncausal LPTV scaling has an ability of inducing frequency-dependent scaling when viewed in the context of the conventional LTI scaling, while causal LPTV scaling fails to do so. It is further discussed that the effectiveness of noncausal characteristics leading to the frequency-domain interpretation can be exploited even for LPTV systems by considering the νN-lifted transfer matrices of N-periodic systems.     

Three results on frequency assignment in linear cellular networks

In the frequency assignment problem we are given a graph representing a wireless network and a sequence of requests, where each request is associated with a vertex. Each request has two more attributes: its arrival and departure times, and it is considered active from the time of arrival to the time of departure. We want to assign frequencies to all requests so that at each time step any two active requests associated with the same or adjacent vertices use different frequencies. The objective is to minimize the number of frequencies used.We focus exclusively on the special case of the problem when the underlying graph is a linear network (path). For this case, we consider both the offline and online versions of the problem, and we present three results. First, in the incremental online case, where the requests arrive over time, but never depart, we give an algorithm with an optimal (asymptotic) competitive ratio . Second, in the general online case, where the requests arrive and depart over time, we improve the current lower bound on the (asymptotic) competitive ratio to . Third, we prove that the offline version of this problem is NP-complete.     

Filter design for LPV systems using quadratically parameter-dependent Lyapunov functions

This paper considers design problems of robust gain-scheduled H_∞ and H₂ filters for linear parameter-varying (LPV) systems whose state-space matrices are represented as parametrically affine matrices, using quadratically parameter-dependent Lyapunov functions, and proposes methods of filter design via parametrically affine linear matrix inequalities (LMIs). For robust filters, our design methods theoretically encompass those that use constant Lyapunov functions. Several numerical examples are included that demonstrate the effectiveness of gain-scheduled and robust filters using our proposed methods compared with robust filters using existing methods.     

Hamiltonian connectivity and globally 3∗-connectivity of dual-cube extensive networks

In 2000, Li et al. introduced dual-cube networks, denoted by DC_n for n?1, using the hypercube family Q_n and showed the vertex symmetry and some fault-tolerant hamiltonian properties of DC_n. In this article, we introduce a new family of interconnection networks called dual-cube extensive networks, denoted by DCEN(G). Given any arbitrary graph G, DCEN(G) is generated from G using the similar structure of DC_n. We show that if G is a nonbipartite and hamiltonian connected graph, then DCEN(G) is hamiltonian connected. In addition, if G has the property that for any two distinct vertices u,v of G, there exist three disjoint paths between u and v such that these three paths span the graph G, then DCEN(G) preserves the same property. Furthermore, we prove that the similar results hold when G is a bipartite graph.     

Robust model selection with flexible trimming

The forward search provides data-driven flexible trimming of a C_p statistic for the choice of regression models that reveals the effect of outliers on model selection. An informed robust model choice follows. Even in small samples, the statistic has a null distribution indistinguishable from an F distribution. Limits on acceptable values of the C_p statistic follow. Two examples of widely differing size are discussed. A powerful graphical tool is the generalized candlestick plot, which summarizes the information on all forward searches and on the choice of models. A comparison is made with the use of M-estimation in robust model choice.     

Three-dimensional beta shapes

The Voronoi diagram of a point set has been extensively used in various disciplines ever since it was first proposed. Its application realms have been even further extended to estimate the shape of point clouds when Edelsbrunner and Mücke introduced the concept of α-shape based on the Delaunay triangulation of a point set.In this paper, we present the theory of β-shape for a set of three-dimensional spheres as the generalization of the well-known α-shape for a set of points. The proposed β-shape fully accounts for the size differences among spheres and therefore it is more appropriate for the efficient and correct solution for applications in biological systems such as proteins.Once the Voronoi diagram of spheres is given, the corresponding β-shape can be efficiently constructed and various geometric computations on the sphere complex can be efficiently and correctly performed. It turns out that many important problems in biological systems such as proteins can be easily solved via the Voronoi diagram of atoms in proteins and β-shapes transformed from the Voronoi diagram.     

Worst case control of uncertain jumping systems with multi-state and input delay information

In this paper, the problem of worst case (also called H_∞) Control for a class of uncertain systems with Markovian jump parameters and multiple delays in the state and input is investigated. The jumping parameters are modelled as a continuous-time, discrete-state Markov process and the parametric uncertainties are assumed to be real, time-varying and norm-bounded that appear in the state, input and delayed-state matrices. The time-delay factors are unknowns and time-varying with known bounds. Complete results for instantaneous and delayed state feedback control designs are developed which guarantee the weak-delay dependent stochastic stability with a prescribed H_∞-performance. The solutions are provided in terms of a finite set of coupled linear matrix inequalities (LMIs). Application of the developed theory to a typical example has been presented.     

A comparative runtime analysis of heuristic algorithms for satisfiability problems

The satisfiability problem is a basic core NP-complete problem. In recent years, a lot of heuristic algorithms have been developed to solve this problem, and many experiments have evaluated and compared the performance of different heuristic algorithms. However, rigorous theoretical analysis and comparison are rare. This paper analyzes and compares the expected runtime of three basic heuristic algorithms: RandomWalk, (1+1) EA, and hybrid algorithm. The runtime analysis of these heuristic algorithms on two 2-SAT instances shows that the expected runtime of these heuristic algorithms can be exponential time or polynomial time. Furthermore, these heuristic algorithms have their own advantages and disadvantages in solving different SAT instances. It also demonstrates that the expected runtime upper bound of RandomWalk on arbitrary k-SAT (k?3) is O(n(k−1)), and presents a k-SAT instance that has Θ(n(k−1)) expected runtime bound.     

Shortest hop multipath algorithm for wireless sensor networks

Shortest hop or distance path is one of the most common methods used for relaying messages in a wide variety of networks. It provides an efficient message relaying to destination in terms of energy and time. There are many algorithms for constructing shortest hop or distance path. However, according to our knowledge, no algorithm for constructing a shortest hop multipath for wireless sensor networks (WSNs) has yet been proposed in the literature. In this paper, we propose a novel distributed shortest hop multipath algorithm for WSNs in order to generate energy efficient paths for data dissemination or routing. The proposed algorithm generates shortest hop braided multipath to be used for fault-tolerance or load-balancing. It guarantees the BFS tree and generates near optimal paths in O(V.D+V) message complexity and O(D²) time complexity regarding the communication costs towards the sink after termination of algorithm.     

Two-machine flow-shop scheduling with rejection

We study a scheduling problem with rejection on a set of two machines in a flow-shop scheduling system. We evaluate the quality of a solution by two criteria: the first is the makespan and the second is the total rejection cost. We show that the problem of minimizing the makespan plus total rejection cost is NP-hard and for its solution we provide two different approximation algorithms, a pseudo-polynomial time optimization algorithm and a fully polynomial time approximation scheme (FPTAS). We also study the problem of finding the entire set of Pareto-optimal points (this problem is NP-hard due to the NP-hardness of the same problem variation on a single machine [20]). We show that this problem can be solved in pseudo-polynomial time. Moreover, we show how we can provide an FPTAS that, given that there exists a Pareto optimal schedule with a total rejection cost of at most R and a makespan of at most K, finds a solution with a total rejection cost of at most (1+?)R and a makespan value of at most (1+?)K. This is done by defining a set of auxiliary problems and providing an FPTAS algorithm to each one of them.     

On using prototype reduction schemes to enhance the computation of volume-based inter-class overlap measures

In most pattern recognition (PR) applications, it is advantageous if the accuracy (or error rate) of the classifier can be evaluated or bounded prior to testing it in a real-life setting. It is also well known that if the two class-conditional distributions have a large overlapping volume (almost all the available work on “overlapping of classes” deals with the case when there are only two classes), the classification accuracy is poor. This is because if we intend to use the classification accuracy as a criterion for evaluating a PR system, the points within the overlapping volume tend to lead to maximal misclassification. Unfortunately, the computation of the indices which quantify the overlapping volume is expensive. In this vein, we propose a strategy of using a prototype reduction scheme (PRS) to approximately, but quickly, compute the latter. In this paper, we demonstrate, first of all, that this is an extremely expedient proposition. Indeed, we show that by completely discarding (we are not aware of any reported scheme which discards “irrelevant” sample (training) points, and which simultaneously attains to an almost-comparable accuracy) the points not included by the PRS, we can obtain a reduced set of sample points, using which, in turn, the measures for the overlapping volume can be computed. The value of the corresponding figures is comparable to those obtained with the original training set (i.e., the one which considers all the data points) even though the computations required to obtain the prototypes and the corresponding measures are significantly less. The proposed method has been rigorously tested on artificial and real-life datasets, and the results obtained are, in our opinion, quite impressive—sometimes faster by two orders of magnitude.     

Channel assignment via fast zeta transform

We show an O^?(n(?+1))-time algorithm for the channel assignment problem, where ? is the maximum edge weight. This improves on the previous O^?(n(?+2))-time algorithm by Král (2005) [1], as well as algorithms for important special cases, like L(2,1)-labeling. For the latter problem, our algorithm works in O^?(n³) time. The progress is achieved by applying the fast zeta transform in combination with the inclusion-exclusion principle.     

A new global optimization strategy for coordinated multi-robot exploration: Development and comparative evaluation

This paper proposes a new multi-robot coordinated exploration algorithm that applies a global optimization strategy based on K-Means clustering to guarantee a balanced and sustained exploration of big workspaces. The algorithm optimizes the on-line assignment of robots to targets, keeps the robots working in separate areas and efficiently reduces the variance of average waiting time on those areas. The latter ensures that the different areas of the workspace are explored at a similar speed, thus avoiding that some areas are explored much later than others, something desirable for many exploration applications, such as search & rescue. The algorithm leads to the lowest variance of regional waiting time (WTV) and the lowest variance of regional exploration percentages (EPV). Both features are presented through a comparative evaluation of the proposed algorithm with different state-of-the-art approaches.