BACKGROUND:The clustering of immune repertoire data is challenging due to the computational cost associated with a very large number of pairwise sequence comparisons. To overcome this limitation, we developed Anchor Clustering, an unsupervised clustering method designed to identify similar sequences from millions of antigen receptor gene sequences. First, a Point Packing algorithm is used to identify a set of maximally spaced anchor sequences. Then, the genetic distance of the remaining sequences to all anchor sequences is calculated and transformed into distance vectors. Finally, distance vectors are clustered using unsupervised clustering. This process is repeated iteratively until the resulting clusters are small enough so that pairwise distance comparisons can be performed. RESULTS:Our results demonstrate that Anchor Clustering is faster than existing pairwise comparison clustering methods while providing similar clustering quality. With its flexible, memory-saving strategy, Anchor Clustering is capable of clustering millions of antigen receptor gene sequences in just a few minutes. CONCLUSIONS:This method enables the meta-analysis of immune-repertoire data from different studies and could contribute to a more comprehensive understanding of the immune repertoire data space.

Computational Intelligence (CI) provides a set of powerful tools to effectively tackle complex computational tasks: global optimization methods (e.g., evolutionary computation, swarm intelligence), machine learning (e.g., neural networks), fuzzy reasoning, and so on. While CI research generally focuses on the improvement of algorithms (e.g., faster convergence, higher accuracy, reduced error), another promising research direction concerns the representations and models in CI. This can be in the form of search space transformation, that is, dilating, shrinking, stretching, collapsing, or remapping the fitness landscape, leading to the simplified formulations of optimization problems. The use of surrogate modeling can further reduce the complexity – or the computational effort – of a CI task, by providing the optimization algorithm with a simplified or approximated version of the fitness landscape. Moreover, in discrete domains, the simplification of the problem can be obtained by embedding implicit or explicit assumptions into the structure of candidate solutions, so that the feasible search space can be explored by genetic operators in a “smarter” way, reducing the overall computational effort. In the contexts of machine learning or fuzzy modeling, the focus can be on interpretability and explainability, the two open issues that currently affect the trust in AI solutions and hamper the adoption of such techniques in some disciplines (in particular, biomedical applications).

Intrinsically disordered proteins (IDPs) are proteins that lack a stable 3D structure but maintain a biological function. It has been frequently suggested that IDPs are difficult to align because they tend to have fewer conserved residues compared to ordered proteins, but to our knowledge this has never been directly tested. To compare the alignments of ordered proteins to IDPs, their multiple sequence alignments (MSAs) were assessed using two different methods. The first compared the similarity between MSAs produced using the same sequences but created with Clustal Omega, MAFFT, and MUSCLE. The second assessed MSAs based on how well they recapitulated the species tree. These two methods measure the "correctness" of an MSA with two different approaches; the first method measures consistency while the second measures the underlying phylogenetic signal. Proteins that contained both regions of disorder and order were analyzed along with proteins that were fully disordered and fully ordered, using nucleotide, codon and peptide sequence alignments. We observed that IDPs had less similar MSAs than ordered proteins, which is most likely linked to the lower sequence conservation in IDPs. However, comparisons of tree distances found that trees from the ordered sequence MSAs were not significantly closer to the species tree than those inferred from disordered sequence MSAs. Our results show that it is correct to say that IDPs are difficult to align on the basis of MSA consistency, but that this does not equate with alignments being of poor quality when assessed by their ability to correctly infer a species tree.

Divide the dollar is a simplified version of a two player bargaining problem game devised by John Nash. The generalized divide the dollar game has n>2 players. Evolutionary algorithms can be used to evolve individual players for this generalized game but representation—i.e., a genome plus a move or search operator(s)—must be carefully chosen since it affects the search process. This paper proposes an entirely new representation called a demand matrix. Each individual in the evolving population now represents a collection of n players rather than just an individual player. Players use previous outcomes to decide their choices (bids) in the current round. The representation scales linearly with the number of players and the move operator is a variant of an evolution strategy. The results indicate that this proposed representation for the generalized divide the dollar game permits the efficient evolution of large player populations with high payoffs and fair demand sets.

A number of problems from specifiers for Boolean networks to programs for quantum computers can be encoded as matrices. The paper presents a novel family of linear, generative representations for evolving matrices. The matrices can be general or restricted within special classes of matrices like permutation matrices, Hermitian matrices, or other groups of matrices with particular algebraic properties. These classes include unitary matrices which encode quantum programs. This representation avoids the brittleness that arises in direct representations of matrices and permits the researcher substantial control of the part of matrix space being searched. The representation is demonstrated on a relatively simple matrix problem in automatic content generation as well as Boolean map induction and automatic quantum programming. The automatic content generation problem yields interesting results; the generative matrix representation yields worse fitness but a substantially greater variety of outcomes than a direct encoding, which is acceptable when generating content. The Boolean map experiments extend and confirm results that demonstrate that the generative encoding is superior to a direct encoding for the transition matrix of a Boolean map. The quantum programming results are generally quite good, with poor performance on the simplest problems in two of the families of programming tasks studied. The viability of the new representation for evolutionary matrix induction is well supported.

Divide the dollar is a simpler version of a game invented by John Nash to study the bargaining problem. The generalized divide the dollar game is an n-player version. Evolutionary algorithms can be used to evolve players for this game, but it has been previously shown representation has a profound effect on the success of the evolutionary search. Representation defines both the genome and the move (search) operator used by the evolutionary algorithm. This study investigates how well two representations for a 3-player generalized divide the dollar game, one using a differential evolution move operator and the other a CMA-ES move operator, can find good players implemented as neural networks. Our results indicate both representations can evolve very good player trios, but the CMA-ES representation tends to evolve fairer players.

In this study, the group of finite cyclic lamplighter states is reinterpreted as the novel lamplighter puzzle. The rules of the puzzle are outlined and related back to properties of the lamplighter group with specific interest placed upon the discussion of which puzzle instances are solvable. The paper shows that, through the use of algebra, many puzzle instances can be identified as solvable without the use of an exhaustive search algorithm. Solvability depends upon the creation of irregular generating sets for subgroups of the finite cyclic lamplighter group and the cosets formed by these subgroups. Further possible generalizations of the lamplighter puzzle are also discussed in closing.

Solving optimization problems is one of the most complex and widespread task in Computer Science. In many scenarios, finding the global optimum of a function is hampered by several features that characterize the fitness landscapes, such as noisiness, multi-modality, non-convexity, non-separability, and non-differentiability. In order to facilitate the optimization process, a variety of methods have been proposed to manipulate either the search space or the fitness landscape. Among these, Dilation Functions (DFs) were introduced to expand regions of the search space that are characterized by promising fitness values. In this work, we extend the family of DFs by introducing Local Bubble Dilation Functions (LBDFs), a novel approach that generates local distortions bounded by hyper-spheres. By performing an appropriate mapping of the search space, LBDFs can improve the optimization performance, since they expand and reveal the promising regions around the global optimum, while leaving the rest of the fitness landscape untouched. The additional advantage of LBDFs, with respect to DFs, is that different dilations can be applied to each dimension of the search space, which is useful in the case of asymmetric landscapes. In order to show the benefits of local dilations, we executed several tests on the Michalewicz benchmark function, with different settings for the LBDFs. Our results show that a properly designed LBDF can lead to statistically significant better results than using vanilla optimization. Finally, we investigated the use of LBDFs to facilitate the solution of the parameter estimation problem in Systems Biology by analyzing the landscape related to a stochastic model of enzyme kinetics.

Recent work in representation has developed small, evolvable structures called a complex string generator that generate infinite, aperiodic strings of characters. Such a string can be sectioned to provide an arbitrary list of parameters of indefinite length. Other work in evolving networks to model disease transmission has an issue common in many high-dimensional problems, evolution is less efficient when it must get a large number of parameter values correct. Specifying many parameters with a small evolvable object is a potential solution to this problem. In this study we compare three different implementations of representations, two of which employ complex string generators, to specify social contact graphs that plausibly explain the pattern of infection in a small epidemic. Representations that edit a starting network are found to have results that clump in network space while evolving the adjacency matrix provides increased diversity: none of the representations overlap in their results. The adjacency matrix based representation also generated outliers that outperform a baseline representation, probably because of its enhance diversity of solutions.

Divide the Dollar is a two-player simultaneous game derived from the bargaining game invented by John Nash. This game is interesting because its strategy space contains an entire subspace of Nash equilibria. The large number of moves in the game means that it is somewhat challenging to design agents to play the game. This study examines the problem of designing representations for divide the dollar playing agents and tests a number of representations. It was found that representation and resources allotted were significant factors affecting the agents' performance and that fitness and resources used appeared to be negatively correlated during evolution. This study places agents with different representations into direct competition and finds that there are representations with a strong competitive advantage. Both the choice of representation and the allocation of resources to that representation are found to impact the ability of agents to make bargains and to compete with one another.

This study refines and extends an earlier effort that demonstrated the utility of the do-whats-possible representation for laying out large numbers of rooms with connected adjacency for a level map. In this study, we continue development of the technique as well as adding doors to establish the connectedness of the rooms on a level, yielding a graph of the rooms and the connections between said rooms. Using complex string generators and an evolutionary algorithm, the diameter of three starting level maps is decreased to the best possible diameter using the least amount of doors. This produces maps which have a variety of features useful to developers and enjoyed by the players.

In this book, we’ve shown you several types of problem factories. The authors have been researching problem factories for several years now and the ones chosen for this book belong to a particular category. While we used computers to generate or check our examples, all of the problem factories in this book can be worked with pencil and paper and require only very modest sorts of computer code to generate or validate them. During our research, we also found a number of problem factories that require moderately powerful AI to generate or validate the problems. This does not mean they are not problem factories, but it does put them in a different category. This chapter is going to mention a few of these more complex problem factories and discuss plans for making these available in a future book.