We give a generating set of the generalized Reidemeister moves for oriented singular links. We then introduce an algebraic structure arising from the axiomatization of Reidemeister moves on oriented singular knots. We give some examples, including some non-isomorphic families of such structures over non-abelian groups. We show that the set of colorings of a singular knot by this new structure is an invariant of oriented singular knots and use it to distinguish some singular links.2000 Mathematics Subject Classification. Primary 57M25.

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Abstract. The tail of a sequence {Pn(q)} n∈N of formal power series in Z [[q]] is the formal power series whose first n coefficients agree up to a common sign with the first n coefficients of Pn. This paper studies the tail of a sequence of admissible trivalent graphs with edges colored n or 2n. We use local skein relations to understand and compute the tail of these graphs. We also give product formulas for the tail of such trivalent graphs. Furthermore, we show that our skein theoretic techniques naturally lead to a proof for the Andrews-Gordon identities for the two variable Ramanujan theta function as well to corresponding identities for the false theta function.

This study introduces a machine learning model for near-crash prediction from observed vehicle kinematics data. The main hypothesis is that vehicles tend to experience discernible turbulence in their kinematics shortly before involvement in near-crashes. To test this hypothesis, the SHRP2 NDS vehicle kinematics data (speed, longitudinal acceleration, lateral acceleration, yaw rate, and pedal position) are utilized. Several machine learning algorithms are trained and comparatively analyzed including K nearest neighbor (KNN), random forest, support vector machine (SVM), decision trees, Gaussian naïve Bayes (Gaussian NB), and adaptive boost (AdaBoost). Sensitivity analysis is performed to determine the optimal prediction horizon length (the time period before the occurrence of a near-crash) and the turbulence horizon length (the time period during which near-crash related changes in vehicle kinematics take place). The results indicate that optimal prediction performance can be achieved at a 1 s prediction horizons and a 3 s turbulence horizon. At these values, the AdaBoost model outperforms all other models in relation to its recall (100%), precision (98%), and F1-score (99%). These values imply that the near-crash prediction model is highly efficient in predicting most instances of near-crashes with minimal false near-crash predictions. This promising prediction performance offers a viable tool for supporting crash avoidance systems in the emerging connected/autonomous vehicle technology.

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