Solving the KO Labyrinth

The KO Labyrinth is a colorful spherical puzzle with 26 chambers, some of which can be connected via holes through which a small ball can pass when the chambers are aligned correctly. The puzzle can be realigned by performing physical rotations of the sphere in the same way one manipulates a Rubik’s Cube, which alters the configuration of the puzzle. The goal is to navigate the ball from the entrance chamber to the exit chamber. We find the shortest path through the puzzle using Dijkstra’s algorithm and explore questions related to connectivity of puzzle with the adjacency matrix, distance matrix, and first passage time analysis. We show that the shortest path through the maze takes only 10 moves, whereas a random walk through the maze requires, on average, about 340 moves before reaching the end. We pose an analogue of the gambler’s ruin problem and separately consider whether we are able to solve the puzzle if certain chambers are off limits. We conclude with comments and questions for future investigation

The Effects of 24 weeks of Resistance Training with Simultaneous Elastic and Free Weight Loading on Muscular Performance of Novice Lifters

The purpose of this investigation was to assess the effectiveness of variable resistance as provided through elastic plus free weight techniques in college aged males and females. Twenty novice lifters were randomly assigned to a traditional free weight only (6 males and 5 females) or elastic band plus free weight group (5 males and 5 females) and 9 more normally active controls (5 males and 4 females), were recruited to maintain normal activity for the duration of the study. No differences existed between control, free weight and elastic band at baseline for age, body height, body mass, body mass index, and body fat percentage. One-repetition maximums were performed for squat and bench press while both strength and power were assessed using isokinetic dynamometry. Elastic groups and free-weight groups completed 24 weeks of whole body, periodized, high intensity resistance (65-95% of one-repetition maximum) training three times/week. Training programs were identical except that the elastic group trained the barbell squat, bench press and stiff-legged deadlift with 20-35% of their total prescribed training loads coming from band resistance (assessed at the top of the range of motion) with the remainder from free weight resistance. A mixed-model analysis revealed that peak torque, average power and one-repetition maximums for squat were significantly greater after training for the elastic group compared to the control (p\u3c0.05). In addition, the free weight group also showed significantly greater improvements over the control in peak torque and one-repetition maximums for squat and bench press. No significant differences were observed between the elastic band and free weight groups. Combined variable elastic band plus free weight exercises are effective at increasing strength and power similar to free-weights alone in novice college aged males and females. However, due to complexity in set-up and load assignment elastic adoption by novice lifters in an unsupervised situation is not advised

Spark-induced Sparks as a Mechanism of Intracellular Calcium Alternans in Cardiac Myocytes

Rationale: Intracellular calcium (Ca) alternans has been widely studied in cardiac myocytes and tissue, yet the underlying mechanism remains controversial. Objective: In this study, we used computational modeling and simulation to study how randomly occurring Ca sparks interact collectively to result in whole-cell Ca alternans. Methods and Results: We developed a spatially-distributed intracellular Ca cycling model in which Ca release units (CRUs) are locally coupled by Ca diffusion throughout the myoplasm and sarcoplasmic reticulum (SR) network. Ca sparks occur randomly in the CRU network when periodically paced with a clamped voltage waveform, but Ca alternans develops as the pacing speeds up. Combining computational simulation with theoretical analysis, we show that Ca alternans emerges as a collective behavior of Ca sparks, determined by three critical properties of the CRU network from which Ca sparks arise: randomness (of Ca spark activation), refractoriness (of a CRU after a Ca spark), and recruitment (Ca sparks inducing Ca sparks in adjacent CRUs). We also show that the steep nonlinear relationship between fractional SR Ca release and SR Ca load arises naturally as a collective behavior of Ca sparks, and Ca alternans can occur even when SR Ca is held constant. Conclusions: We present a general theory for the mechanisms of intracellular Ca alternans, which mechanistically links Ca sparks to whole-cell Ca alternans, and is applicable to Ca alternans in both physiological and pathophysiological conditions

Period-doubling Bifurcation in an Array of Coupled Stochastically-excitable Elements Subjected to Global Periodic Forcing

The collective behaviors of coupled, stochastically-excitable elements subjected to global periodic forcing are investigated numerically and analytically. We show that the whole system undergoes a period-doubling bifurcation as the driving period decreases, while the individual elements still exhibit random excitations. Using a mean-field representation, we show that this macroscopic bifurcation behavior is caused by interactions between the random excitation, the refractory period, and recruitment (spatial cooperativity) of the excitable elements

Sled-pull Training Improves Maximal Horizontal Velocity in Collegiate Male and Female Soccer Players

The force velocity profile (FvP), which details the capacity to sprint and accelerate, is a determinant of success in soccer. To date, no data exist that details the FvP of male and female collegiate Division I soccer players. Further, there is limited insight on how training interventions may modify the FvP of either males or females. PURPOSE: The aim of this investigation was to compare FvP between collegiate male and female athletes and assess the efficacy of a 12-week sled pull training intervention. METHODS: 17 male (20.17 ± 1.38 yrs) and 12 female (19.75 ± 1.05 yrs) soccer players participated in a 12-week sled pull training intervention. FvP was measured prior, during, and after training using a 30m sprint to assess maximal horizontal force (F0), maximal horizontal speed (V0), and maximal power output (Pmax). RESULTS: The intervention improved 30m sprint times of men by 11.86% (pre: 4.35 ± 0.17s, post: 4.27 ± 0.17, p0 in both men (pre: 7.98 ± 0.36 m/s, post: 8.09 ± 0.35 m/s, p0 or Pmax. CONCLUSION: This is the first study to detail FvP in both male and female collegiate soccer players. A 12-week sled pull training intervention improves 30m sprint times and V0 in both male and female collegiate athletes, but does not improve F0 and Pmax. Thus, the sled pull intervention should be modified or paired with other training that specifically targets force and power development

Beyond Formulas: A Collaboration between Liberal Arts Honors Underclassmen and Senior Math Majors

“Congratulations! Sony Pictures producers have hired you as a scientific consultant to assist them in producing a remake of the classic film Gone With The Seabreeze, which chronicles the founding of the Westchester campus of Loyola University in 1929. The original film features shots of various old buildings that can still be found across campus today. The producers wish to recreate these shots, but need to know where to position the camera, which they have tasked you with finding.” Thus began the month-long, collaborative project at Loyola Marymount University between the honors underclassmen in HNRS 140, On Motion and Mechanics, taught by Alissa S. Crans, and the senior applied mathematics majors in MATH 495, Mathematical Modeling, taught by Robert Rovetti. During a period of four weeks, six teams of freshman and sophomore liberal arts honors students, each led by a senior math major, set out to reconstruct an old photograph using a mathematical technique based on straightforward geometry. Along the way they would run into inaccessible landscapes, blocked views, and busy schedules, but ultimately they emerged with both a finished product and a clearer understanding of what it means to apply a theoretical method to a real-world problem. We begin by describing the courses and the assigned project itself, and then we reflect on the pedagogical goals of the project and various observations made by both students and instructors

The Effects of 24 weeks of Resistance Training with Simultaneous Elastic and Free Weight Loading on Muscular Performance of Novice Lifters

The purpose of this investigation was to assess the effectiveness of variable resistance as provided through elastic plus free weight techniques in college aged males and females. Twenty novice lifters were randomly assigned to a traditional free weight only (6 males and 5 females) or elastic band plus free weight group (5 males and 5 females) and 9 more normally active controls (5 males and 4 females), were recruited to maintain normal activity for the duration of the study. No differences existed between control, free weight and elastic band at baseline for age, body height, body mass, body mass index, and body fat percentage. One-repetition maximums were performed for squat and bench press while both strength and power were assessed using isokinetic dynamometry. Elastic groups and free-weight groups completed 24 weeks of whole body, periodized, high intensity resistance (65–95% of one-repetition maximum) training three times/week. Training programs were identical except that the elastic group trained the barbell squat, bench press and stiff-legged deadlift with 20–35% of their total prescribed training loads coming from band resistance (assessed at the top of the range of motion) with the remainder from free weight resistance. A mixed-model analysis revealed that peak torque, average power and one-repetition maximums for squat were significantly greater after training for the elastic group compared to the control (p<0.05). In addition, the free weight group also showed significantly greater improvements over the control in peak torque and one-repetition maximums for squat and bench press. No significant differences were observed between the elastic band and free weight groups. Combined variable elastic band plus free weight exercises are effective at increasing strength and power similar to free-weights alone in novice college aged males and females. However, due to complexity in set-up and load assignment elastic adoption by novice lifters in an unsupervised situation is not advised