Serotonin (5-HT) neurons in the dorsal raphe nucleus (DRN) are implicated in mediating learned helplessness (LH) behaviors, such as poor escape responding and expression of exaggerated conditioned ...fear, induced by acute exposure to uncontrollable stress. DRN 5-HT neurons are hyperactive during uncontrollable stress, resulting in desensitization of 5-HT type 1A (5-HT1A) inhibitory autoreceptors in the DRN. 5-HT1A autoreceptor downregulation is thought to induce transient sensitization of DRN 5-HT neurons, resulting in excessive 5-HT activity in brain areas that control the expression of learned helplessness behaviors. Habitual physical activity has antidepressant/anxiolytic properties and results in dramatic alterations in physiological stress responses, but the neurochemical mediators of these effects are unknown. The current study determined the effects of 6 weeks of voluntary freewheel running on LH behaviors, uncontrollable stress-induced activity of DRN 5-HT neurons, and basal expression of DRN 5-HT1A autoreceptor mRNA. Freewheel running prevented the shuttle box escape deficit and the exaggerated conditioned fear that is induced by uncontrollable tail shock in sedentary rats. Furthermore, double c-Fos/5-HT immunohistochemistry revealed that physical activity attenuated tail shock-induced activity of 5-HT neurons in the rostral-mid DRN. Six weeks of freewheel running also resulted in a basal increase in 5-HT1A inhibitory autoreceptor mRNA in the rostral-mid DRN. Results suggest that freewheel running prevents behavioral depression/LH and attenuates DRN 5-HT neural activity during uncontrollable stress. An increase in 5-HT1A inhibitory autoreceptor expression may contribute to the attenuation of DRN 5-HT activity and the prevention of LH in physically active rats.
For strongly connected, pure
n
-dimensional regular CW-complexes, we show that
evenness
(each
(
n
-
1
)
-cell is contained in an even number of
n
-cells) is equivalent to generalizations of both ...cycle decomposition and traversability.
Any graph
admits a neighborhood multiset 𝒩(
) = {
) |
∈
(
)} whose elements are precisely the open neighborhoods of
. We say
is neighborhood reconstructible if it can be reconstructed from 𝒩(
), ...that is, if
≅
whenever 𝒩 (
) = 𝒩(
) for some other graph
. This note characterizes neighborhood reconstructible graphs as those graphs
that obey the exponential cancellation
≅
⇒
≅=
A New View of Hypercube Genus Hammack, Richard H.; Kainen, Paul C.
The American mathematical monthly,
01/2021, Letnik:
128, Številka:
4
Journal Article
Recenzirano
Odprti dostop
Beineke, Harary, and Ringel discovered a formula for the minimum genus of a torus in which the n-dimensional hypercube graph can be embedded. We give a new proof of the formula by building this ...surface as a union of certain faces in the hypercube's 2-skeleton. For odd dimension n, the entire 2-skeleton decomposes into
copies of the surface, and the intersection of any two copies is the hypercube graph.
Graph Bases and Diagram Commutativity Hammack, Richard H.; Kainen, Paul C.
Graphs and combinatorics,
07/2018, Letnik:
34, Številka:
4
Journal Article
Recenzirano
Given two cycles
A
and
B
in a graph, such that
A
∩
B
is a non-trivial path, the
connected sum
A
+
^
B
is the cycle whose edges are the symmetric difference of
E
(
A
) and
E
(
B
). A special kind of ...cycle basis for a graph, a
connected sum basis
, is defined. Such a basis has the property that a hierarchical method, building successive cycles through connected sum, eventually reaches all the cycles of the graph. It is proved that every graph has a connected sum basis. A property is said to be
cooperative
if it holds for the connected sum of two cycles when it holds for the summands. Cooperative properties that hold for the cycles of a connected sum basis will hold for all cycles in the graph. As an application, commutativity of a groupoid diagram follows from commutativity of a connected sum basis for the underlying graph of the diagram. An example is given of a noncommutative diagram with a (non-connected sum) basis of cycles which do commute.
In 1971 Lovász proved the following cancellation law concerning the direct product of digraphs. If A, B and C are digraphs, and C admits no homomorphism into a disjoint union of directed cycles, then ...A×C≅B×C implies A≅B. On the other hand, if such a homomorphism exists, then there are pairs A⁄≅B for which A×C≅B×C. This gives exact conditions on C that govern whether cancellation is guaranteed to hold or fail.
Left unresolved was the question of what conditions on A (or B) force A×C≅B×C⟹A≅B, or, more generally, what relationships between A and C (or B and C) guarantee this. Even if C has a homomorphism into a collection of directed cycles, can there still be restrictions on A and C that guarantee cancellation? We characterize the exact conditions.
We use a construction called the factorialA! of a digraph A. Given digraphs A and C, the digraph A! carries information that determines the complete set of solutions X to the digraph equation A×C≅X×C. We state the exact conditions under which there is only one solution X (namely X≅A) and that is the situation in which cancellation holds.
The direct product of graphs obeys a limited cancellation property. Lovász proved that if
C
has an odd cycle then
A
×
C
≅
B
×
C
if and only if
A
≅
B
, but cancellation can fail if
C
is bipartite. ...This note investigates the ways cancellation can fail. Given a graph
A
and a bipartite graph
C
, we classify the graphs
B
for which
A
×
C
≅
B
×
C
. Further, we give exact conditions on
A
that guarantee
A
×
C
≅
B
×
C
implies
A
≅
B
. Combined with Lovász’s result, this completely characterizes the situations in which cancellation holds or fails.
Proper Connection Of Direct Products Hammack, Richard H.; Taylor, Dewey T.
Discussiones Mathematicae. Graph Theory,
01/2017, Letnik:
37, Številka:
4
Journal Article
Recenzirano
Odprti dostop
The proper connection number of a graph is the least integer k for which the graph has an edge coloring with k colors, with the property that any two vertices are joined by a properly colored path. ...We prove that given two connected non-bipartite graphs, one of which is (vertex) 2-connected, the proper connection number of their direct product is 2.
Several variants of hypergraph products have been introduced as generalizations of the strong and direct products of graphs. Here we show that only some of them are associative. In addition to the ...Cartesian product, these are the minimal rank preserving direct product, and the normal product. Counter-examples are given for the strong product as well as the non-rank-preserving and the maximal rank preserving direct product.
We are motivated by the following question concerning the direct product of graphs. If
A
×
C
≅
B
×
C
, what can be said about the relationship between
A
and
B
? If cancellation fails, what properties ...must
A
and
B
share? We define a structural equivalence relation
∼
(called similarity) on graphs, weaker than isomorphism, for which
A
×
C
≅
B
×
C
implies
A
∼
B
. Thus cancellation holds, up to similarity. Moreover, if
C
is bipartite, then
A
×
C
≅
B
×
C
if and only if
A
∼
B
. We conjecture that the prime factorization of connected bipartite graphs is unique up to similarity of factors, and we offer some results supporting this conjecture.
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