A short introduction is given about direct variational methods and their relation to Galerkin and moment methods, all flexible and powerful approaches for finding approximate solutions to difficult physicalequations. An application of these methods is given in the form of the variational problem of minimizing the discomfort experienced during different journeys, between two fixed horizontal points while keeping the travel time constant. The analysis is shown to provide simple, yet accurate, approximate solutions of the problem and illustrates the usefulness and the power of direct variational and moment methods. It also demonstrates the problem of a priori assessing the accuracy of the approximate solutions and illustrates that the variational solution does not necessarily provide a more accurate solution than that obtained by moment methods.

Machine learning algorithms utilizing gradient descent to identify concepts or more general learnables hint at a so-far ignored possibility, namely that local and global minima represent any vocabulary as a landscape against which evaluation of the results can take place. A simple example to illustrate this idea would be a potential surface underlying gravitation. However, to construct a gravitation-based representation of, e.g., word meaning, only the distance between localized items is a given in the vector space, whereas the equivalents of mass or charge are unknown in semantics. Clearly, the working hypothesis that physical fields could be a useful metaphor to study word and sentence meaning is an option but our current representations are incomplete in this respect.For a starter, consider that an RBF kernel has the capacity to generate a potential surface and hence create the impression of gravity, providing one with distance-based decay of interaction strength, plus a scalar scaling factor for the interaction, but of course no term masses. We are working on an experiment design to change that. Therefore, with certain mechanisms in neural networks that could host such quasi-physical fields, a novel approach to the modeling of mind content seems plausible, subject to scrutiny.Work in progress in another direction of the same idea indicates that by using certain algorithms, already emerged vs. still emerging content is clearly distinguishable, in line with Aristotle’s Metaphysics. The implications are that a model completed by “term mass” or “term charge” would enable the computation of the specific work equivalent of sentences or documents, and that via replacing semantics by other modalities, vector fields of more general symbolic content could exist as well. Also, the perceived hypersurface generated by the dynamics of language use may be a step toward more advanced models, for example addressing the Hamiltonian of expanding semantic systems, or the relationship between reaction paths in quantum chemistry vs. sentence construction by gradient descent.

Solutions of the nonlinear Schrodinger equation for initial conditions in the form of two separated sech-shaped in-phase pulsed,; are analyzed. It is found that; this initial condition, with appropriate amplitude, may give rise to, not; only stationary solitons, but also to symmetrically separating solitons, if the initial distance of separation is large enough. The condition for the generation of a separating soliton pair is derived from the Zakharov-Shabat eigenvalue problem using a variational approach.

The significant potential for so-called “smart textiles” in the design of the next generation of devices that measure pressure, tension, moisture, and heat at the humanehorse interface is discussed in this article. Research techniques from theoretical and experimental physics laboratories, combined with wireless technology, can be readily adapted to measure and store metrics for numerous variables in equine structure and function. Activities, such as breathing, the extension and flexion of joints, limb kinematics, and cardiac function, can be logged as indicators of physiological and behavioral conditioning (training). Such metrics may also, one day, support veterinary diagnostics but also play a role in safeguarding sporthorse welfare, especially in elite contexts where the horse may be pushed to its functional limits. As such, they are likely to emerge as an area of great interest to equitation and welfare scientists. It is important to note that smart textiles sense and react to exogenous stimuli via integrated sensors. So, beyond the equitation science laboratory, the emergence of polymers and smart materials may enhance the effectiveness of, or challenge us to completely rethink, traditional items of saddlery, thus improving equitation. The integration of smart textiles in all sorts of extant and emergent equipment for everyday equestrians could, in the future, lead to equipment that responds appropriately to the demands of equitation in its various forms. Rethinking equitation through physics and the use of smart textiles seems to have merit in that it is a novel means of both investigating and addressing problems that compromise the welfare and performance of horses. The purpose of this article is to envision the use of smart textiles in research, clinical, equestrian, and horse care contexts.