A novel encoding element for robust pose estimation using planar fiducials.

Pose estimation in robotics is often achieved using images from known and purposefully applied markers or fiducials taken by a monocular camera. This low-cost system architecture can provide accurate and precise pose estimation measurements. However, to prevent the restriction of robotic movement and occlusions of features, the fiducial markers are often planar. While numerous planar fiducials exist, the performance of these markers suffers from pose ambiguities and loss of precision under frontal observations. These issues are most prevalent in systems with less-than-ideal specifications such as low-resolution detectors, low field of view optics, far-range measurements etc. To mitigate these issues, encoding markers have been proposed in literature. These markers encode an extra dimension of information in the signal between marker and sensor, thus increasing the robustness of the pose solution. In this work, we provide a survey of these encoding markers and show that existing solutions are complex, require optical elements and are not scalable. Therefore, we present a novel encoding element based on the compound eye of insects such as the Mantis. The encoding element encodes a virtual point in space in its signal without the use of optical elements. The features provided by the encoding element are mathematically equivalent to those of a protrusion. Where existing encoding fiducials require custom software, the projected virtual point can be used with standard pose solving algorithms. The encoding element is simple, can be produced using a consumer 3D printer and is fully scalable. The end-to-end implementation of the encoding element proposed in this work significantly increases the pose estimation performance of existing planar fiducials, enabling robust pose estimation for robotic systems.

Graphical Models in Reconstructability Analysis and Bayesian Networks.

Reconstructability Analysis (RA) and Bayesian Networks (BN) are both probabilistic graphical modeling methodologies used in machine learning and artificial intelligence. There are RA models that are statistically equivalent to BN models and there are also models unique to RA and models unique to BN. The primary goal of this paper is to unify these two methodologies via a lattice of structures that offers an expanded set of models to represent complex systems more accurately or more simply. The conceptualization of this lattice also offers a framework for additional innovations beyond what is presented here. Specifically, this paper integrates RA and BN by developing and visualizing: (1) a BN neutral system lattice of general and specific graphs, (2) a joint RA-BN neutral system lattice of general and specific graphs, (3) an augmented RA directed system lattice of prediction graphs, and (4) a BN directed system lattice of prediction graphs. Additionally, it (5) extends RA notation to encompass BN graphs and (6) offers an algorithm to search the joint RA-BN neutral system lattice to find the best representation of system structure from underlying system variables. All lattices shown in this paper are for four variables, but the theory and methodology presented in this paper are general and apply to any number of variables. These methodological innovations are contributions to machine learning and artificial intelligence and more generally to complex systems analysis. The paper also reviews some relevant prior work of others so that the innovations offered here can be understood in a self-contained way within the context of this paper.

Dynamics of prebiotic RNA reproduction illuminated by chemical game theory.

Many origins-of-life scenarios depict a situation in which there are common and potentially scarce resources needed by molecules that compete for survival and reproduction. The dynamics of RNA assembly in a complex mixture of sequences is a frequency-dependent process and mimics such scenarios. By synthesizing Azoarcus ribozyme genotypes that differ in their single-nucleotide interactions with other genotypes, we can create molecules that interact among each other to reproduce. Pairwise interplays between RNAs involve both cooperation and selfishness, quantifiable in a 2 × 2 payoff matrix. We show that a simple model of differential equations based on chemical kinetics accurately predicts the outcomes of these molecular competitions using simple rate inputs into these matrices. In some cases, we find that mixtures of different RNAs reproduce much better than each RNA type alone, reflecting a molecular form of reciprocal cooperation. We also demonstrate that three RNA genotypes can stably coexist in a rock-paper-scissors analog. Our experiments suggest a new type of evolutionary game dynamics, called prelife game dynamics or chemical game dynamics. These operate without template-directed replication, illustrating how small networks of RNAs could have developed and evolved in an RNA world.

Reconstructability analysis of epistasis.

The literature on epistasis describes various methods to detect epistatic interactions and to classify different types of epistasis. Reconstructability analysis (RA) has recently been used to detect epistasis in genomic data. This paper shows that RA offers a classification of types of epistasis at three levels of resolution (variable-based models without loops, variable-based models with loops, state-based models). These types can be defined by the simplest RA structures that model the data without information loss; a more detailed classification can be defined by the information content of multiple candidate structures. The RA classification can be augmented with structures from related graphical modeling approaches. RA can analyze epistatic interactions involving an arbitrary number of genes or SNPs and constitutes a flexible and effective methodology for genomic analysis.

Reconstructability analysis as a tool for identifying gene-gene interactions in studies of human diseases.

There are a number of common human diseases for which the genetic component may include an epistatic interaction of multiple genes. Detecting these interactions with standard statistical tools is difficult because there may be an interaction effect, but minimal or no main effect. Reconstructability analysis (RA) uses Shannon's information theory to detect relationships between variables in categorical datasets. We applied RA to simulated data for five different models of gene-gene interaction, and find that even with heritability levels as low as 0.008, and with the inclusion of 50 non-associated genes in the dataset, we can identify the interacting gene pairs with an accuracy of > or =80%. We applied RA to a real dataset of type 2 non-insulin-dependent diabetes (NIDDM) cases and controls, and closely approximated the results of more conventional single SNP disease association studies. In addition, we replicated prior evidence for epistatic interactions between SNPs on chromosomes 2 and 15.

The evolution of altruism: game theory in multilevel selection and inclusive fitness.

Although the prisoner's dilemma (PD) has been used extensively to study reciprocal altruism, here we show that the n-player prisoner's dilemma (NPD) is also central to two other prominent theories of the evolution of altruism: inclusive fitness and multilevel selection. An NPD model captures the essential factors for the evolution of altruism directly in its parameters and integrates important aspects of these two theories such as Hamilton's rule, Simpson's paradox, and the Price covariance equation. The model also suggests a simple interpretation of the Price selection decomposition and an alternative decomposition that is symmetrical and complementary to it. In some situations this alternative shows the temporal changes in within- and between-group selection more clearly than the Price equation. In addition, we provide a new perspective on strong vs. weak altruism by identifying their different underlying game structures (based on absolute fitness) and showing how their evolutionary dynamics are nevertheless similar under selection (based on relative fitness). In contrast to conventional wisdom, the model shows that both strong and weak altruism can evolve in periodically formed random groups of non-conditional strategies if groups are multigenerational. An integrative approach based on the NPD helps unify different perspectives on the evolution of altruism.

Unifying the theories of inclusive fitness and reciprocal altruism.

Inclusive fitness and reciprocal altruism are widely thought to be distinct explanations for how altruism evolves. Here we show that they rely on the same underlying mechanism. We demonstrate this commonality by applying Hamilton's rule, normally associated with inclusive fitness, to two simple models of reciprocal altruism: one, an iterated prisoner's dilemma model with conditional behavior; the other, a mutualistic symbiosis model where two interacting species differ in conditional behaviors, fitness benefits, and costs. We employ Queller's generalization of Hamilton's rule because the traditional version of this rule does not apply when genotype and phenotype frequencies differ or when fitness effects are nonadditive, both of which are true in classic models of reciprocal altruism. Queller's equation is more general in that it applies to all situations covered by earlier versions of Hamilton's rule but also handles nonadditivity, conditional behavior, and lack of genetic similarity between altruists and recipients. Our results suggest changes to standard interpretations of Hamilton's rule that focus on kinship and indirect fitness. Despite being more than 20 years old, Queller's generalization of Hamilton's rule is not sufficiently appreciated, especially its implications for the unification of the theories of inclusive fitness and reciprocal altruism.

Application of information-theoretic data mining techniques in a national ambulatory practice outcomes research network.

The Medical Quality Improvement Consortium data warehouse contains de-identified data on more than 3.6 million patients including their problem lists, test results, procedures and medication lists. This study uses reconstructability analysis, an information-theoretic data mining technique, on the MQIC data warehouse to empirically identify risk factors for various complications of diabetes including myocardial infarction and microalbuminuria. The risk factors identified match those risk factors identified in the literature, demonstrating the utility of the MQIC data warehouse for outcomes research, and RA as a technique for mining clinical data warehouses.

Strong altruism can evolve in randomly formed groups.

Although the conditions under which altruistic behaviors evolve continue to be vigorously debated, there is general agreement that altruistic traits involving an absolute cost to altruists (strong altruism) cannot evolve when populations are structured with randomly formed groups. This conclusion implies that the evolution of such traits depends upon special environmental conditions or additional organismic capabilities that enable altruists to interact with each other more than would be expected with random grouping. Here we show, using both analytic and simulation results, that the positive assortment necessary for strong altruism to evolve does not require these additional mechanisms, but merely that randomly formed groups exist for more than one generation. Conditions favoring the selection of altruists, which are absent when random groups initially form, can naturally arise even after a single generation within groups-and even as the proportion of altruists simultaneously decreases. The gains made by altruists in a second generation within groups can more than compensate for the losses suffered in the first and in this way altruism can ratchet up to high levels. This is true even if altruism is initially rare, migration between groups allowed, homogeneous altruist groups prohibited, population growth restricted, or kin selection precluded. Until now random group formation models have neglected the significance of multigenerational groups-even though such groups are a central feature of classic "haystack" models of the evolution of altruism. We also explore the important role that stochasticity (effectively absent in the original infinite models) plays in the evolution of altruism. The fact that strong altruism can increase when groups are periodically and randomly formed suggests that altruism may evolve more readily and in simpler organisms than is generally appreciated.