S1S^{1}-invariant symplectic hypersurfaces in dimension 66 and the Fano condition

We prove that any symplectic Fano $6$-manifold $M$ with a Hamiltonian $S^1$-action is simply connected and satisfies $c_1 c_2(M)=24$. This is done by showing that the fixed submanifold $M_{\min}\subseteq M$ on which the Hamiltonian attains its minimum is diffeomorphic to either a del Pezzo surface, a $2$-sphere or a point. In the case when $\dim(M_{\min})=4$, we use the fact that symplectic Fano $4$-manifolds are symplectomorphic to del Pezzo surfaces. The case when $\dim(M_{\min})=2$ involves a study of $6$-dimensional Hamiltonian $S^1$-manifolds with $M_{\min}$ diffeomorphic to a surface of positive genus. By exploiting an analogy with the algebro-geometric situation we construct in each such $6$-manifold an $S^1$-invariant symplectic hypersurface ${\cal F}(M)$ playing the role of a smooth fibre of a hypothetical Mori fibration over $M_{\min}$. This relies upon applying Seiberg-Witten theory to the resolution of symplectic $4$-orbifolds occurring as the reduced spaces of $M$.Comment: Exposition improve

Advances in Repurposing and Recycling of Post-Vehicle-Application Lithium-Ion Batteries

Increased electrification of vehicles has increased the use of lithium-ion batteries for energy storage, and raised the issue of what to do with post-vehicle-application batteries. Three possibilities have been identified: 1) remanufacturing for intended reuse in vehicles; 2) repurposing for non-vehicle, stationary storage applications; and 3) recycling, extracting the precious metals, chemicals and other byproducts. Advances in repurposing and recycling are presented, along with a mathematical model that forecasts the manufacturing capacity needed for remanufacturing, repurposing, and recycling. Results obtained by simulating the model show that up to a 25% reduction in the need for new batteries can be achieved through remanufacturing, that the sum of repurposing and remanufacturing capacity is approximately constant across various scenarios encouraging the sharing of resources, and that the need for recycling capacity will be significant by 2030. A repurposing demonstration shows the use of post-vehicle-application batteries to support a semi-portable recycling platform. Energy is collected from solar panels, and dispensed to electrical devices as required. Recycling may be complicated: lithium-ion batteries produced by different manufacturers contain different active materials, particularly for the cathodes. In all cases, however, the collecting foils used in the anodes are copper, and in the cathodes are aluminum. A common recycling process using relatively low acid concentrations, low temperatures, and short time periods was developed and demonstrated

Hamiltonian S1S^1-actions on complete intersections

We study the problem of determining which diffeomorphism classes of K\"{a}hler manifolds admit a Hamiltonian circle action. Our main result is the following: Let $M$ be a closed symplectic manifold, diffeomorphic to a complete intersection with complex dimension $4k$, having a Hamiltonian circle action such that each component of the fixed point set is an isolated fixed point or has dimension $2 \mod 4$. Then $M$ is diffeomorphic to $\mathbb{CP}^{4k}$, a quadric $Q \subset \mathbb{CP}^{4k+1}$ or an intersection of two quadrics $Q_1 \cap Q_2 \subset \mathbb{CP}^{4k+2}$.Comment: Accepted version, to appear in Bulletin of the London Mathematical Society. 7 Page

Exotic almost complex circle actions on 6-manifolds

Jang has proven a remarkable classification of $6$-dimensional manifolds having an almost complex circle action with $4$ fixed points. Jang classifies the weights and associated multigraph into six cases, leaving the existence of connected manifolds fitting into three of the cases unknown. We show that one of the unknown cases may be constructed by a surgery construction of Kustarev, and the underlying manifold is diffeomorphic to $S^4 \times S^2$. We show that the action is not equivariantly diffeomorphic to a linear one, thus giving a new exotic $S^1$-action of on a product of spheres that preserves an almost complex structure. We also prove a uniqueness statement for the almost complex structures produced by Kustarev's construction and prove some topological applications of Jang's classification.Comment: 13 pages. Comments welcome

A Correlative Study of Epidemiological Mortality and Morbidity Rates: Appalachian vs Non-Appalachian Counties within Kentucky

In this study, differences in mortality rates were statistically analyzed between Kentucky Appalachian County Populations (KACP) and Kentucky Non-Appalachian County Populations (KnACP) for 2013. Health – risk factors and socio – economic conditions were also assessed to determine if they put KACP at a higher risk of the five most common causes of death in Kentucky. Estill County, a KACP, was also specifically examined for its mortality and health – risk factor rates. By examining the 2013 database provided by the Kentucky Department for Public Health (KDPH) and the Center for Disease Control and Prevention (CDC), it was determined that there is a significant increase in mortality rates of malignant neoplasms and heart disease in the KACP population compared to KnACP. The KACP population also has significantly increased rates of hypertension, diabetes, smoking, and obesity; all of which contribute to the significance of KACP mortality rates. Subsequently, socio – economic factors such as median house – hold income showed a significant decrease for KACP compared to KnACP which indirectly affects the mortality rates of KACP. Estill County also showed an increase in mortality rates, as well as, health-risk factors compared to KACP. These findings indicate that the populations of KACP are at higher risk of dying from malignant neoplasms and heart disease due to a significant increase in hypertension, smoking, diabetes, and obesity. To correct this overwhelming health issue, improving the quality of and access to healthcare for the KACP’s needs to be a focus. Projects including government resources such as more funding for free clinics, as well as community based efforts to reduce smoking, etc. is of utmost importance

The Long-Run Impacts of Same-Race Teachers

Black primary-school students matched to a same-race teacher perform better on standardized tests and face more favorable teacher perceptions, yet little is known about the long-run, sustained impacts of student-teacher demographic match. We show that assigning a black male to a black teacher in the third, fourth, or fifth grades significantly reduces the probability that he drops out of high school, particularly among the most economically disadvantaged black males. Exposure to at least one black teacher in grades 3-5 also increases the likelihood that persistently low-income students of both sexes aspire to attend a four-year college. These findings are robust across administrative data from two states and multiple identification strategies, including an instrumental variables strategy that exploits within-school, intertemporal variation in the proportion of black teachers, family fixed-effects models that compare siblings who attended the same school, and the random assignment of students and teachers to classrooms created by the Project STAR class-size reduction experiment

ACL RUPTURE IN COLLEGIATE WRESTLER

Objective: To educate others on unique Anterior Cruciate Ligament tears and percentage of usage of the ACL in normal daily function. Background: Patient is an eighteen year old male participating in wrestling and football at the time of the injury. Patient now only participates in wrestling. No previous knee or chronic injuries were reported prior to this injury. Patient was playing football during the time of injury. The patient stated that he planted his foot down and was tackled at the same time when the injury occurred. The patient felt his knee twist and buckle. Patient complained of clicking inside the knee and had minimal swelling. He also complained of it being difficult to bear weight at the time. The patient did not seek further treatment until two months after the injury occurred when he received an MRI. His MRI showed a positive finding for an Anterior Cruciate Ligament rupture. His previous Athletic Trainer could not find a positive diagnosis for the patient prior to the MRI. Differential Diagnosis: Possible meniscal or ACL injury. Treatment: Doctors officially diagnosed the injury as a complete rupture of the ACL. The patient did not receive surgery immediately. Doctors have stated that he only uses about 50% of his ACL on a daily basis compared to a normal person who uses about 95% of their ACL daily. Because of this, the patient played on his rupture for seven months before receiving surgery. He played a whole season of high school football and a whole season of wrestling his senior year with the ACL ruptured. The patient only used a brace for better comfort during the seven months. The patient then received reconstructive surgery to repair the rupture. A hamstring tendon graft was used to repair the ruptured ACL. Because a tendon was taken from the hamstring, patient experienced a tight ACL and hamstring of the left leg post-surgery. The patient participated in Physical Therapy for five months to strengthen and stretch the new ACL and hamstring. After completing five months of physical therapy, the patient joined a college wrestling team in August 2013. The athletic training staff at the university started him on a quadriceps and hamstring strengthening rehabilitation program for about one month. The staff also worked on continuous flexion and extension of the knee to where the patient could feel comfortable with doing activities with his knee. The patient continues to participate in daily stretching and strengthening protocols for his quadriceps and hamstring bilaterally. Deviation from the Expected/Uniqueness: The patient still participated on a fully ruptured ACL for seven months with just complaining of minimal pain and discomfort. The athlete chose to complete two seasons of activities instead of receiving surgery immediately. The ratio of people who rupture their ACL is about 5 in every 100,000 people. It is interesting that the high school clinician could not diagnose the injury until the patient received an MRI two months post-injury. The patient was also told by doctors that he only uses about 50% of his ACL on a daily basis compared to anyone else who uses their ACL about 95%. The patient felt comfortable with the ACL ruptured and changed any discomfort by just wearing a brace. Conclusions: Not many people can play on a ruptured ACL for seven months before receiving any surgical repairs. We need to keep this in mind as Athletic Trainers so we are not sending our athletes back on the field and possibly causing them more damage. The athlete continues stretching protocols daily. Key Words: rupture, ACL, Anterior Cruciate Ligamen

Development of Comprehensive Theoretical Morphospaces for Canine Cranial Morphology

Throughout the evolution of the family Canidae, there is a continuous belief that canines have an exceptional olfactory system which allows them to have a heightened sense of smell. Because of this olfactory sophistication, canines have become prevalent as detection animals in the military, homeland security, law enforcement, forensics, and civilian applications. However, while the trait is highly regarded, the exact role of nasal morphology is understudied. We aim to investigate the influences of nasal cavity and internal structure morphology in odor detection. However, nasal structure is a sophisticated morphological target and requires innovative solutions to capture the key variables in the system and isolate the effects when single parameters are altered. To develop this method, we will employ three Computerized Tomography (CT) scans; a Golden Retriever (Mesocephalic), Chihuahua (Mesocephalic), and English Bulldog (Brachiocephalic). From these we create 3D models of these skulls within SlicerMorph to retrieve morphometric parameters for incorporation into a Principal Components Analysis (PCA). We then use the subsequent morphospace in tandem with Blender to build out theoretical morphotypes that can be used to measure how varying parameters individually influences functional outcomes. The value of this method\u27s development study is the creation of a procedural workflow to populate a theoretical morphospace. Using canid skulls as a case study, the development of this workflow can lead to possible automation allowing for quick and efficient creation of large theoretical morphology data sets to examine structure-function interactions at high resolution. In the future, we will expand our data set with CT scans from the LA County Natural History Museum and integrate them into computational fluid dynamics analyses to assess shape-olfaction interactions