PY352 FINAL EXAM- 12, 14, 15
Moral Development
Morality has 3 components emotional, cognitive, behavioral
Biological perspective on moral development
1) Evolutionary, genetic heritage
2) Brain areas
Psychoanalytic
1) Freud: superego and guilt
2) Today:
178 Chapter 3. Discrete Stochastic Processes
can't be analytic in A in a point Ao of the support of dk which is the
spectrum
of
Z,
the
claim
follows.
Remark. We have seen that the matrix L defines a spectral measure pe on
the real line. It can be defined
3.13.
Discrete
Dirichlet
problem
181
the Cayley graph by putting V([k,k]) = V(k) and V([kJ]) = 0 for k j- I,
we can define exp(/7 V) as the product Uti V([ycfw_i)Mi + !)]) Then
(Lnu)(0) = E[exp(/ V)u(7(n)]
Jo
which is formally the Feynman-Kac formula.
In
182 Chapter 3. Discrete Stochastic Processes
where ei,., e<* is the standard basis in Zd.
Definition. A bounded region D in Zd is a finite subset of Zd. Two points
are connected in D if they are connected in Z3. The boundary 5D of D
consists of all lattic
3.12.
A
discrete
Feynman-Kac
formula
179
Random walks and Laplacian can be defined on any graph. The spectrum
of the Laplacian on a finite graph is an invariant of the graph but there are
non-isomorphic graphs with the same spectrum. There are known infin
3.13. Discrete Dirichlet problem
183
Proof. Use induction. By definition, Lxz is l/(2d) if there is a path from x
to z. The integer Ly is the number of paths of length n from x to y.
Figure, /"ere is an example of a
problem where D C Z2 /ms i0
4L =
0 0 0
value
254
K-x
K
2
(K - L) (x/L)-2r/
K
Stock price
x
value
Figure 25.2: Value of perpetual American put
C3 x
-2r/ 2
C2 x
C1 x
-2r/ 2
Stock price
Figure 25.3: Curves.
-2r/ 2
x
PY 352 Final Exam Review (Chapters 12, 14 and 15)
Moral Development
Biological Approach
o
Morally relevant behaviors and emotions have roots in our evolutionary history
Aiding others in turn helps yourself in the long run
o
Humans biased to aid family mem
Temperament
o
Temperament- early appearing, stable individual differences in reactivity and selfregulation
o
Reactivity- refers to quickness and intensity of emotional arousal,
attention and motor action
Self-regulation: refers to strategies that modify
PSYCHOLOGY 352 TEST 2
Passive correlation: parents pass on genes and provide the environment
Evocative correlation: children evoke responses from others, influenced by
heredity
Active correlation: seek environments that fit with genetic tendencies; nic
PY352 Test #3
PIAGETS COGNITIVE- DEVELOPMENTAL THEORY
Piagets Constructivist approach assumes that children discover knowledge
through their own activity, moving though four invariant, universal stages
a) Newborn infants have little in the way of built
180 Chapter 3. Discrete Stochastic Processes
Here is a discrete version of the Feynman-Kac formula:
Definition. The Schrodinger equation with discrete time is defined as
i(ut+e -ut) = eLut ,
where e > 0 is fixed. We get the evolution
ut+ne = (1 - ieL)nut