A Note on Knights, Knaves, and Truth Tables

Student and teacher (in the order above) have taken on a project of trying to understand something about Boolean algebra, logic circuits, and applications with the aid of Mathematica. We quickly recognized that the logical puzzles popularized by Raymond Smullyan that involve Knights (truth tellers) and Knaves (liars) are ideally suited for analysis by Boolean methods and truth tables. with a big boost from Mathematica. Not only is there a lot of mathematics to be learned, there is a great deal of fun to be had. The topic seems to us to be an ideal vehicle for exposing young high school and undergraduate college students to wonderful mathematics outside of the standard Advanced Placement Calculus stream

Effect of jumping style on the performance of large and medium elite agility dogs

Dog agility is a rapidly progressing sport worldwide. Consequentially, research and methods to improve technique and performance are becoming highly sought after. Video data were collected of elite agility dogs during a training session, with downstream analysis examining differences in apparent topline angle and jumping speed of large and medium dogs as well as collie breeds and non-collie breeds. The study further examined any correlations between topline angle and jumping speed. Findings suggest that there is a difference between the jump kinematics of large and medium dogs (P=0.001) and between collie breeds and non-collie breeds (P<0.001) with collie breeds jumping faster than non-collie breeds (P=0.013). This information could be used to inform future training regimes and competitive strategies in a breed and size specific way, with the aim to improve long-term health and welfare of canine participants, whilst also ensuring that training and competitive expectations are within biological capabilities

Mathematical modeling of the flow field and particle motion in a rotating bioreactor at unit gravity and microgravity

The biotechnology group at NASA Johnson Space Center is developing systems for culturing mammalian cells that stimulate some aspect of microgravity and provide a low shear environment for microgravity-based studies on suspension and anchorage dependent cells. The design of these vessels for culturing cells is based on the need to suspend cells and aggregates of cells and microcarrier beads continually in the culturing medium. The design must also provide sufficient circulation for adequate mass transfer of nutrients to the cells and minimize the total force on the cells. Forces, resulting from sources such as hydrodynamic fluid shear and collisions of cells and walls of the vessels, may damage delicate cells and degrade the formation of three dimensional structures. This study examines one particular design in both unit gravity and microgravity based on two concentric cylinders rotating in the same direction at different speeds to create a Couette flow between them. A numerical simulation for the flow field and the trajectories of particles in the vessel. The flow field for the circulation of the culturing medium is modeled by the Navier-Stokes equations. The forces on a particle are assumed to be drag from the fluid's circulation, buoyancy from the gravitational force and centrifugal force from the rotation of the vessel. The problem requires first solving the system of partial differential equations for the fluid flow by a finite difference method and then solving the system of ordinary differential equations for the trajectories by Gear's stiff method. Results of the study indicate that the trajectories in unit gravity and microgravity are very similar except for small spatial deviations on the fast time scale in unit gravity. The total force per unit cross sectional area on a particle in microgravity, however, is significantly smaller than the corresponding value in unit gravity, which is also smaller than anticipated. Hence, this study indicates that this design for a bioreactor with optimal rates of rotation can provide a good environment for culturing cells in microgravity with adequate circulation and minimal force on the cells

Understanding the role of technology in the commercial sexual exploitation of children: the perspective of law enforcement.

This exploratory study was conducted to better assess how technology can be used in criminal investigations; it is important to get a better understanding of how technology is currently employed in child sex trafficking as well as the approaches and needs of law enforcement. 144 investigators from Internet Crimes Against Children (ICAC) Task Forces and affiliate agencies responded to an online semi‐structured survey, including 45 investigators with experience conducting investigations of the commercial sexual exploitation of children (CSEC) that involved technology. Participants included investigators working in local, county, and state law enforcement agencies in the United States. The discussion suggested a great deal of variation in perspectives and experiences surrounding the problem of CSEC and technology. Investigators were able to highlight both benefits and obstacles. Benefits included the availability of digital evidence instead of relying on personal accounts, the monitoring capabilities of police, and the ability to conduct extensive undercover operations. Obstacles tended to focus on financial concerns, the continual need for training and technical assistance, and the rapidly changing technological environment. Findings highlight the vast complexity and variability in these crimes. There is still quite a bit of the unknown when it comes to investigating CSEC – technology changes rapidly and avenues for marketing and communicating are vast. Continual education, training and technical assistance are central to investigators’ needs in this area

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