Comforting with Mathematics: A Case Study

Death by suicide often leaves behind grieving family members with unanswered questions. Of these concerns, fear that their loved one suffered or felt regret is common. When the method of suicide was jumping from height, that answer can easily be determined using basic kinematics. Despite the perception that mathematics is a cold, calculating field, it can provide a clear, definitive answer and comfort those left behind

Family-Expressed Emotion, Childhood-Onset Depression, and Childhood-Onset Schizophrenia Spectrum Disorders: Is Expressed Emotion a Nonspecific Correlate of Child Psychopathology or a Specific Risk Factor for Depression?

Expressed emotion (EE) was examined, using the brief Five Minute Speech Sample measure, in families of (1) children with depressive disorders, (2) children with schizophrenia spectrum disorders, and (3) normal controls screened for the absence of psychiatric disorder. Consistent with the hypothesis of some specificity in the association between EE and the form of child disorder, rates of EE were significantly higher among families of depressed children compared to families of normal controls and families of children with schizophrenia spectrum disorders. Within the depressed group, the presence of a comorbid disruptive behavior disorder was associated with high levels of critical EE, underscoring the need to attend to comorbid patterns and subtypes of EE in future research

Collective chemotactic dynamics in the presence of self-generated fluid flows

In micro-swimmer suspensions locomotion necessarily generates fluid motion, and it is known that such flows can lead to collective behavior from unbiased swimming. We examine the complementary problem of how chemotaxis is affected by self-generated flows. A kinetic theory coupling run-and-tumble chemotaxis to the flows of collective swimming shows separate branches of chemotactic and hydrodynamic instabilities for isotropic suspensions, the first driving aggregation, the second producing increased orientational order in suspensions of "pushers" and maximal disorder in suspensions of "pullers". Nonlinear simulations show that hydrodynamic interactions can limit and modify chemotactically-driven aggregation dynamics. In puller suspensions the dynamics form aggregates that are mutually-repelling due to the non-trivial flows. In pusher suspensions chemotactic aggregation can lead to destabilizing flows that fragment the regions of aggregation.Comment: 4 page

The theory of zeta functions of several complex variables, I

AbstractThe paper introduces a general class of Tate-like zeta functions and proves an analytic continuation and a general formula for the values of such zeta functions at negative integral arguments. In particular these zeta functions discussed include the Shintani zeta functions and the results generalize his formula for the value of such zeta functions at negative integral arguments