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The orbits of stars near massive black holes precess very slowly. As a result the (secular) interactions of stars in such an environment are strongly correlated over time, leading to enhanced angular momentum evolution. I will describe a framework that accommodates both secular and two-body effects, and allows the study of such orbits over very long times. We have calibrated the free parameters of this "ARMA" model with extensive N-body simulations. With these simulations, we also found that energy relaxation occurs on a far slower rate than is usually assumed in the literature. We have applied our simulations to the Galactic center. Our main findings are that (1) there is probably not enough time to reach steady state within a Hubble time; (2) even if steady state is reached, stars are tidally disrupted faster than they are replaced by energy disruption, so that instead of a cusp there is a a depression in the stellar density near the black hole; (3) the currently observed eccentricity distribution of S-stars is not consistent with the popular formation mechanisms.

The eating disorders anorexia nervosa (AN) and bulimia nervosa (BN) are serious psychiatric disorders characterized by disturbed eating behavior and characteristic psychopathology, and in the case of AN, very low weight. The mortality of AN is the highest of any psychiatric disorder. The etiology of AN and BN are multidetermined; there are factors biologically, psychologically and socioculturallly that predispose an individual to an eating disorder. Biologically, genes contribute significantly to the risk for eating disorders. Studies have shown that the risk of anorexia nervosa in first degree relatives if one parent has AN is between 8-10%.compraed to the general population risk of 1%. The concordance rate for MZ twins in AN is close to 70%. Approximately 70% of the variance in AN is attributable to genetic effects whereas about 30% is attributable to unique environmental effects. For BN, approximately 60% of the variance in BN is attributable to genetic effects whereas about 40% is attributable to unique environmental effects. Eating disorders do not map on to one chromosome Instead there are dimensions that are genetic, such as risk of obesity, anxiety, and temperament such as perfectionism and obssessionality that are inherited and place an individual at risk for an eating disorder

Gender is also a genetic risk factor for an eating disorder. Being female is a risk factor for an eating disorder, not just because females are more sensitive to cultural pressure than males. Females are more commonly affected by eating disorders because female brains are much more sensitive to dietary manipulation than male brains related to the effects of estrogen and progesterone on serotonin metabolism. Tryptophan depletion does not significantly affect levels of brain serotonin in males but dramatically reduces levels of serotonin produced in females’ brains. Dieting, especially restricting carbohydrates lowers the level of blood tryptophan available to cross the blood brain and be available to be synthesized to serotonin. Patients are at risk for an eating disorder will reduce the levels of serotonin produced in their brains by dieting and restricting carbohydrates, leading to changes in satiety and mood and increasing the likelihood of an eating disorder developing . There are those who believe that binge eating develops in response to a hyposerotonergic state in an attempt to restore tryptophan available for brain serotonin synthesis

I have been involved in several large multi site genetic studies of eating disorders over the past 15 years. In a linkage analysis of affected relative AN pairs, when only restricting anorexics were included in the analyses, a significant signal was found on the long arm of chromosome 1. Candidate genes that have been found in that area of chromosome 1 include the serotonin 1D receptor gene, the opiod delta gene, and the dopamine D2 receptor gene. In a linkage analyses on a sample of affected relative pairs with BN, a significant signal was found on chromosome 10 when the sample included only subjects who vomited. I am currently involved in a whole genome wide association study ( GWAS) of 4000 AN cases and 4000 female controls which will hopefully elucidate which specific genes contribute to the risk for AN.

Future genetic studies we are involved in will focus on why patients with AN are able to drop their weight to dangerously low levels, whereas patients with bulimia nervosa (BN) with similar psychopathology and dysfunctional eating behaviors are protected from extreme weight loss and do not develop AN. So far, research on genes that are important for appetite and weight regulation, such as the leptin receptor (LEPR), ghrelin (GHRL), melanocortin 4 receptor (MC4R), and brain derived neurotrophic factor (BDNF), has yielded conflicting findings in AN and BN, while related genes with potential in the same genetic systems have not been sufficiently studied. Considering that AN in adults tends to follow a chronic course and currently does not have any evidence-based treatments, determining the role of genetic factors in the vulnerability to achieve low weight in AN patients could be an important first step toward improved treatment.

For centuries, scientists have attempted to identify and document analytical laws that underlie physical phenomena in nature. Despite the prevalence of computing power, the process of finding natural laws and their corresponding equations has resisted automation. A key challenge to finding analytic relations automatically is defining algorithmically what makes a correlation in observed data important and insightful. By seeking dynamical invariants and symmetries, we show how we can go from finding just predictive models to finding deeper conservation laws. We demonstrated this approach by automatically searching motion-tracking data captured from various physical systems, ranging from simple harmonic oscillators to chaotic double-pendula. Without any prior knowledge about physics, kinematics, or geometry, the algorithm discovered Hamiltonians, Lagrangians, and other laws of geometric and momentum conservation. The discovery rate accelerated as laws found for simpler systems were used to bootstrap explanations for more complex systems, gradually uncovering the “alphabet” used to describe those systems. Application to modeling physical and biological systems will be shown.