Escape regimes of biased random walks on Galton-Watson trees

The confirmation bias is the tendency to focus on information that confirms our existing beliefs and ignore information that is inconsistent with our expectations. For example, if you think that your professor is not very nice, you notice all of the instances of rude behavior exhibited by the professor while ignoring the countless pleasant interactions he is involved in on a daily basis. Have you ever fallen prey to the confirmation bias, either as the source or target of such bias?

Hindsight bias leads you to believe that the event you just experienced was predictable, even though it really wasn’t. In other words, you knew all along that things would turn out the way they did. Can you relate this to the phrase "Hindsight is 20/20" now? 

The “tree of life” describes the evolution of life and the evolutionary relationships between organisms. The root of the tree is the common ancestor to all life on Earth. All other species radiate from this point, much like the branches of a tree. The numerous tips of these branches on the tree of life represent every living, or extant, species. Extinct species, which are species that no longer exist, can be found towards the center of the tree. Currently, these organisms, both...

The escape velocity of an object is defined as the minimum initial velocity that it requires to escape the surface of another object to which it is gravitationally bound and never to return. For example, what would be the minimum velocity at which a satellite should be launched from the Earth's surface such that it just escapes the Earth's gravitational field?
To calculate the escape velocity, it is assumed that no energy is lost to any frictional forces. In practice, a satellite...

Bias refers to any tendency that prevents a question from being considered unprejudiced. In research, bias occurs when one outcome or answer is selected or encouraged over others in sampling or testing. Bias can occur during any research phase, including study design, data collection, analysis, and publication.
In statistics, a sampling bias is created when a sample is collected from a population, and some members of the population are not as likely to be chosen as others (remember, each member...

To escape the Earth's gravity, an object near the top of the atmosphere at an altitude of 100 km must travel away from Earth at 11.1 km/s. This speed is called the escape velocity. The temperature at which gas molecules attain the rms speed, which is equal to the escape velocity, can be estimated by using the equation for the average kinetic energy of the gas molecules. According to the kinetic theory of gas, the average kinetic energy of the gas molecules is proportional to its...