Dynamics of living cells in a cytomorphological state space.

Cells are nonequilibrium systems that exchange matter and energy with the environment to sustain their metabolic needs. The nonequilibrium nature of this system presents considerable challenges to developing a general theory describing its behavior; however, when studied at appropriate spatiotemporal scales, the behavior of ensembles of nonequilibrium systems can resemble that of a system at equilibrium. Here we apply this principle to a population of cells within a cytomorphological state space and demonstrate that cellular transition dynamics within this space can be described using equilibrium formalisms. We use this framework to map the effective energy landscape underlying the cytomorphological state space of a population of mouse embryonic fibroblasts (MEFs) and identify topographical nonuniformity in this space, indicating nonuniform occupation of cytomorphological states within an isogenic population. The introduction of exogenous apoptotic agents fundamentally altered this energy landscape, inducing formation of additional energy minima that correlated directly with changes in sensitivity to apoptosis induction. An equilibrium framework allows us to describe the behavior of an ensemble of single cells, suggesting that although cells are complex nonequilibrium systems, the application of formalisms derived from equilibrium thermodynamics can provide insight into the basis of nongenetic heterogeneities within cell populations, as well as the relationship between cytomorphological and functional heterogeneity

Olfactory Orientation and Navigation in Humans.

Although predicted by theory, there is no direct evidence that an animal can define an arbitrary location in space as a coordinate location on an odor grid. Here we show that humans can do so. Using a spatial match-to-sample procedure, humans were led to a random location within a room diffused with two odors. After brief sampling and spatial disorientation, they had to return to this location. Over three conditions, participants had access to different sensory stimuli: olfactory only, visual only, and a final control condition with no olfactory, visual, or auditory stimuli. Humans located the target with higher accuracy in the olfaction-only condition than in the control condition and showed higher accuracy than chance. Thus a mechanism long proposed for the homing pigeon, the ability to define a location on a map constructed from chemical stimuli, may also be a navigational mechanism used by humans

Mapping Ohio's Compassion

This report gives an overview of the state of the nonprofit sector in Ohio

Faulhaber's Theorem on Power Sums

We observe that the classical Faulhaber's theorem on sums of odd powers also holds for an arbitrary arithmetic progression, namely, the odd power sums of any arithmetic progression $a+b, a+2b, ..., a+nb$ is a polynomial in $na+n(n+1)b/2$. While this assertion can be deduced from the original Fauhalber's theorem, we give an alternative formula in terms of the Bernoulli polynomials. Moreover, by utilizing the central factorial numbers as in the approach of Knuth, we derive formulas for $r$-fold sums of powers without resorting to the notion of $r$-reflexive functions. We also provide formulas for the $r$-fold alternating sums of powers in terms of Euler polynomials.Comment: 12 pages, revised version, to appear in Discrete Mathematic