In [k]n = [k]×[k]× · · ·×[k], a line consists of the collection of points where all but one coordinate is fixed and the unfixed coordinate varies over all possibilities. We consider the problem of marking (or designating) one point on each line in [k]n so that each point in [k]n is marked either a or b times, for some fixed a or b. This is equivalent to forming a strategy for a hat guessing gam...

We study a cooperative game in which each member of a team of N players, wearing coloured hats and situated at the vertices of the cycle graph CN , is guessing their own hat colour merely on the basis of observing the hats worn by their two neighbours without exchanging the information. Each hat can have one of three colours. A predetermined guessing strategy is winning if it guarantees at leas...

T he handheld umbrella (HU) is a commonly employed method of sun protection by women in many countries in Asia (45% in China) and the Middle East. In Turkey, hats and umbrellas were found to be the most common photoprotection accessories. The HU was standard outdoor attire for women of the 18th and 19th centuries in the United States. In the next century, sunscreen, hats, and sun-protective clo...

Histone acetyltransferases (HATs) and histone deacetylases (HDACs) promote histone posttranslational modifications, which lead to an epigenetic alteration in gene expression. Aberrant regulation of HATs and HDACs in neuronal cells results in pathological consequences such as neurodegeneration. Alzheimer's disease is the most common neurodegenerative disease of the brain, which has devastating e...

We consider a popular game puzzle, called Hats-on-a-line, wherein a warden has n prisoners, each one wearing a randomly assigned black or white hat, stand in a line. Thus each prisoner can see the colors of all hats before him, but not his or of those behind him. Everyone can hear the answer called out by each prisoner. Based on this information and without any further communication, each priso...

Many models of cortical function assume that local lateral connections are specific with respect to the preferred features of the interacting cells and that they are organized in a Mexican-hat pattern with strong "center" excitation flanked by strong "surround" inhibition. However, anatomical data on primary visual cortex indicate that the local connections are isotropic and that inhibition has...

SCIENCE sciencemag.org significance that each can reduce cases and deaths. But efficacy in a carefully managed, tightly monitored study does not equal effectiveness in the messiness of the real world. Confusing matters further still, weather patterns, an economic upswing, or improved housing can also have a big impact on disease. The CGD researchers are part of a growing movement that seeks har...