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- Define the term Proof of the Chain Rule?Using the Tukey HSD test: what is the HSD for group 1 (ore dock) vs. group 2 (black rocks) ? What is the HSD for group 1 ( ore dock) vs. group 3 (barrel &beam) ? What is the HSD for group 2 vs. group 3 ?2.which of the ff.is the reverse process of chain rule?a additional rule b.product rule c.substitution rule d.division rule
- New "closed loop" (CL) devices have been developed to help to suppress overactive brain activity in patients with conditions such as Parkinson's disease and epilepsy.† The CL device is implanted directly into a specific area of the brain, and one of the key advantages is that it can immediately apply a treatment in reaction to heightened brain activity. This may help to reduce the duration of seizures and other periods of uncontrolled movement in patients. A study was conducted on the effectiveness of the CL device on brain activity in rats. First, each of seven rats was observed for 15 minutes with the CL device implanted but not activated (OFF). The percentage of the time that each rat was moving was recorded. Then, after each CL device was activated (CL), the percentage of the time that the rat was moving was recorded over another 15-minute period. The OFF and CL data values given in the accompanying table are approximated from a graph in the research article. The calculated…Researchers have noted a decline in cognitive functioning as people age (Bartus, 1990). However, the results from other research suggest that the antioxidant in foods such as blueberries can reduce and even reverse those age-related declines, at least in laboratory rats (Joseph,et al.,1999). Based on these results, one might theorize that the same antioxidants might benefit elderly humans. Suppose a researcher is interested in testing this theory. The researcher obtains a sample of n = 16 adults who are older than 65, and gives and gives each participant a daily dose of blueberry supplement that is very high in antioxidants. After taking the supplement for 6 months, the participants are given a standardized cognitive skills test and produce a mean score of M = 50.2. For the general population of elderly adults scores on the test average μ =45 and form a normal distribution with a σ = 9. Can the researchers conclude that the supplement significantly increases cognitive skills? Use a…Researchers have noted a decline in cognitive functioning as people age (Bartus, 1990). However, the results from other research suggest that the antioxidant in foods such as blueberries can reduce and even reverse those age-related declines, at least in laboratory rats (Joseph,et al.,1999). Based on these results, one might theorize that the same antioxidants might benefit elderly humans. Suppose a researcher is interested in testing this theory. The researcher obtains a sample of n = 16 adults who are older than 65, and gives and gives each participant a daily dose of blueberry supplement that is very high in antioxidants. After taking the supplement for 6 months, the participants are given a standardized cognitive skills test and produce a mean score of M = 50.2. For the general population of elderly adults scores on the test average μ =45 and form a normal distribution with a σ = 9. Can the researchers conclude that the supplement significantly increases cognitive skills? Use a…
- Normally when you look at something, your left and right eyes take in very similar images, and your brain blends them together, However, if totally different images are shown to each eye, the brain does something wild: it perceives one image for a brief time, then switches again and again. To model this process, we posit that there are two populations of neurons with average firing rates x1 and x2. These two populations battle for dominance, resulting in a model for neuronal competition: x'1 = -x1 + F(I - bx2) x'2 = -x2 + F(I - bx1) Here F(x) = 1/(1 + e-x) is a "gain function", I > 0 is the strength of the input stimulus, and b > 0 is the strength of the antagonism between neuron groups. a) Show that the Jacobian at this symmetric fixed point has delta = 1 - b2(x* - (x*)2)2 and Tau = -2. Argue that for large enough b the stability of the fixed points ches from a stable node to a saddle. b) Does this model exhibit the binocular rivalry switching behavior observed in experiments?Normally when you look at something, your left and right eyes take in very similar images, and your brain blends them together, However, if totally different images are shown to each eye, the brain does something wild: it perceives one image for a brief time, then switches again and again. To model this process, we posit that there are two populations of neurons with average firing rates x1 and x2. These two populations battle for dominance, resulting in a model for neuronal competition: x'1 = -x1 + F(I - bx2) x'2 = -x2 + F(I - bx1) Here F(x) = 1/(1 + e-x) is a "gain function", I > 0 is the strength of the input stimulus, and b > 0 is the strength of the antagonism between neuron groups. a) Interpret the terms in this model in words. b) Sketch phase portaits for the following values of I and b: I = 1, b = 2; I = 1, b = 4; I = 1, b = 8. Discuss what you observe. What type of bifurcation do you see? c) Show that there is always a symmetric fixed point at x* = x*1 = x*2 for any…Open water oil spills, such as the Deepwater Horizon spill of 2010, can wreak terrible consequences on the environment and be expensive to clean up. Many physical and biological methods have been developed to recover oil from water surfaces. In the article “Capacity of Straw for Repeated Binding of Crude Oil from Salt Water and Its Effect on Biodegradation” (J. Hazard. Toxic Radioact. Waste, 2012: 75–78), researchers examined how wheat straw could be used to extract crude oil from a water surface. An experiment was conducted in which crude oil (0 to 16.9 g) was added to 100 mL of saltwater in separate Petri dishes. Wheat straw (2 g) was then added to each dish and all dishes were shaken at 70 rpm overnight. The following data read from a graph is based on the amount of oil added (in g) and the corresponding amount of oil recovered (in g) from wheat straw. a. For each observation, determine the percentage of oil recovery by wheat straw. Is this percentage relatively…
- Researchers have noted a decline in cognitive functioning as people age (Bartus, 1990). However, theresults from other research suggest that the antioxidants in foods such as blueberries can reduce andeven reverse these age-related declines, at least inlaboratory rats (Joseph et al., 1999). Based on theseresults, one might theorize that the same antioxidants might also benefit elderly humans. Supposea researcher is interested in testing this theory. Theresearcher obtains a sample of n = 16 adults who areolder than 65, and gives each participant a daily doseof a blueberry supplement that is very high in antioxidants. After taking the supplement for 6 months, theparticipants are given a standardized cognitive skillstest and produce a mean score of M = 50.2. For thegeneral population of elderly adults, scores on the testaverage μ = 45 and form a normal distribution withσ = 9.a. Can the researcher conclude that the supplementhas a significant effect on cognitive skill? Use atwo-tailed test…Omega-3, finis Exercises 21 and 23 describe an experi-ment investigating the effectiveness of omega-3 fats in treating bipolar disorder. Suppose some of the 30 sub-jects were very active people who walked a lot or got vig-orous exercise several times a week, while others tended to be more sedentary, working office jobs and watchinga lot of TV. Why might researchers choose to block thesubjects by activity level before randomly assigning themto the omega-3 and placebo groups?hello, can you please solve this with chain rule ? thank you
