178 research outputs found
Irreducible triangulations of surfaces with boundary
A triangulation of a surface is irreducible if no edge can be contracted to
produce a triangulation of the same surface. In this paper, we investigate
irreducible triangulations of surfaces with boundary. We prove that the number
of vertices of an irreducible triangulation of a (possibly non-orientable)
surface of genus g>=0 with b>=0 boundaries is O(g+b). So far, the result was
known only for surfaces without boundary (b=0). While our technique yields a
worse constant in the O(.) notation, the present proof is elementary, and
simpler than the previous ones in the case of surfaces without boundary
Hamiltonian submanifolds of regular polytopes
We investigate polyhedral -manifolds as subcomplexes of the boundary
complex of a regular polytope. We call such a subcomplex {\it -Hamiltonian}
if it contains the full -skeleton of the polytope. Since the case of the
cube is well known and since the case of a simplex was also previously studied
(these are so-called {\it super-neighborly triangulations}) we focus on the
case of the cross polytope and the sporadic regular 4-polytopes. By our results
the existence of 1-Hamiltonian surfaces is now decided for all regular
polytopes.
Furthermore we investigate 2-Hamiltonian 4-manifolds in the -dimensional
cross polytope. These are the "regular cases" satisfying equality in Sparla's
inequality. In particular, we present a new example with 16 vertices which is
highly symmetric with an automorphism group of order 128. Topologically it is
homeomorphic to a connected sum of 7 copies of . By this
example all regular cases of vertices with or, equivalently, all
cases of regular -polytopes with are now decided.Comment: 26 pages, 4 figure
Diffusion MRI of Structural Brain Plasticity Induced by a Learning and Memory Task
Background: Activity-induced structural remodeling of dendritic spines and glial cells was recently proposed as an important factor in neuroplasticity and suggested to accompany the induction of long-term potentiation (LTP). Although T1 and diffusion MRI have been used to study structural changes resulting from long-term training, the cellular basis of the findings obtained and their relationship to neuroplasticity are poorly understood. Methodology/Principal Finding: Here we used diffusion tensor imaging (DTI) to examine the microstructural manifestations of neuroplasticity in rats that performed a spatial navigation task. We found that DTI can be used to define the selective localization of neuroplasticity induced by different tasks and that this process is age-dependent in cingulate cortex and corpus callosum and age-independent in the dentate gyrus. Conclusion/Significance: We relate the observed DTI changes to the structural plasticity that occurs in astrocytes and discuss the potential of MRI for probing structural neuroplasticity and hence indirectly localizing LTP
Differential Regulation of the Variations Induced by Environmental Richness in Adult Neurogenesis as a Function of Time: A Dual Birthdating Analysis
Adult hippocampal neurogenesis (AHN) augments after environmental enrichment (EE) and it has been related to some of the anxiolytic, antidepressant and neuroprotective effects of EE. Indeed, it has been suggested that EE specifically modulates hippocampal neurogenic cell populations over the course of time. Here we have used dual-birthdating to study two subpopulations of newborn neuron in mice (Mus musculus): those born at the beginning and at the end of enrichment. In this way, we demonstrate that while short-term cell survival is upregulated after an initial 1 week period of enrichment in 2 month old female mice, after long-term enrichment (2 months) neither cell proliferation nor the survival of the younger newly born cell populations are distinguishable from that observed in non-enriched control mice. In addition, we show that the survival of older newborn neurons alone (i.e. those born at the beginning of the enrichment) is higher than in controls, due to the significantly lower levels of cell death. Indeed, these parameters are rapidly adjusted to the sudden cessation of the EE conditions. These findings suggest both an early selective, long-lasting effect of EE on the neurons born in the initial stages of enrichment, and a quick response when the environment again becomes impoverished. Therefore, EE induces differential effects on distinct subpopulations of newborn neurons depending on the age of the immature cells and on the duration of the EE itself. The interaction of these two parameters constitutes a new, specific regulation of these neurogenic populations that might account for the long-term enrichment's behavioral effects
Effects of Enriched Physical and Social Environments on Motor Performance, Associative Learning, and Hippocampal Neurogenesis in Mice
We have studied the motor abilities and associative learning capabilities of adult mice placed in different enriched environments. Three-month-old animals were maintained for a month alone (AL), alone in a physically enriched environment (PHY), and, finally, in groups in the absence (SO) or presence (SOPHY) of an enriched environment. The animals' capabilities were subsequently checked in the rotarod test, and for classical and instrumental learning. The PHY and SOPHY groups presented better performances in the rotarod test and in the acquisition of the instrumental learning task. In contrast, no significant differences between groups were observed for classical eyeblink conditioning. The four groups presented similar increases in the strength of field EPSPs (fEPSPs) evoked at the hippocampal CA3-CA1 synapse across classical conditioning sessions, with no significant differences between groups. These trained animals were pulse-injected with bromodeoxyuridine (BrdU) to determine hippocampal neurogenesis. No significant differences were found in the number of NeuN/BrdU double-labeled neurons. We repeated the same BrdU study in one-month-old mice raised for an additional month in the above-mentioned four different environments. These animals were not submitted to rotarod or conditioned tests. Non-trained PHY and SOPHY groups presented more neurogenesis than the other two groups. Thus, neurogenesis seems to be related to physical enrichment at early ages, but not to learning acquisition in adult mice
Absence of Ca2+-stimulated adenylyl cyclases leads to reduced synaptic plasticity and impaired experience-dependent fear memory
Ca2+-stimulated adenylyl cyclase (AC) 1 and 8 are two genes that have been shown to play critical roles in fear memory. AC1 and AC8 couple neuronal activity and intracellular Ca2+ increases to the production of cyclic adenosine monophosphate and are localized synaptically, suggesting that Ca2+-stimulated ACs may modulate synaptic plasticity. Here, we first established that Ca2+-stimulated ACs modulate protein markers of synaptic activity at baseline and after learning. Primary hippocampal cell cultures showed that AC1/AC8 double-knockout (DKO) mice have reduced SV2, a synaptic vesicle protein, abundance along their dendritic processes, and this reduction can be rescued through lentivirus delivery of AC8 to the DKO cells. Additionally, phospho-synapsin, a protein implicated in the regulation of neurotransmitter release at the synapse, is decreased in vivo 1 h after conditioned fear (CF) training in DKO mice. Importantly, additional experiments showed that long-term potentiation deficits present in DKO mice are rescued by acutely replacing AC8 in the forebrain, further supporting the idea that Ca2+-stimulated AC activity is a crucial modulator of synaptic plasticity. Previous studies have demonstrated that memory is continually modulated by gene–environment interactions. The last set of experiments evaluated the effects of knocking out AC1 and AC8 genes on experience-dependent changes in CF memory. We showed that the strength of CF memory in wild-type mice is determined by previous environment, minimal or enriched, whereas memory in DKO mice is unaffected. Thus, overall these results show that AC1 and AC8 modulate markers of synaptic activity and help integrate environmental information to modulate fear memory
Retinoic Acid Restores Adult Hippocampal Neurogenesis and Reverses Spatial Memory Deficit in Vitamin A Deprived Rats
A dysfunction of retinoid hippocampal signaling pathway has been involved in the appearance of affective and cognitive disorders. However, the underlying neurobiological mechanisms remain unknown. Hippocampal granule neurons are generated throughout life and are involved in emotion and memory. Here, we investigated the effects of vitamin A deficiency (VAD) on neurogenesis and memory and the ability of retinoic acid (RA) treatment to prevent VAD-induced impairments. Adult retinoid-deficient rats were generated by a vitamin A-free diet from weaning in order to allow a normal development. The effects of VAD and/or RA administration were examined on hippocampal neurogenesis, retinoid target genes such as neurotrophin receptors and spatial reference memory measured in the water maze. Long-term VAD decreased neurogenesis and led to memory deficits. More importantly, these effects were reversed by 4 weeks of RA treatment. These beneficial effects may be in part related to an up-regulation of retinoid-mediated molecular events, such as the expression of the neurotrophin receptor TrkA. We have demonstrated for the first time that the effect of vitamin A deficient diet on the level of hippoccampal neurogenesis is reversible and that RA treatment is important for the maintenance of the hippocampal plasticity and function
Fluoxetine Counteracts the Cognitive and Cellular Effects of 5-Fluorouracil in the Rat Hippocampus by a Mechanism of Prevention Rather than Recovery
5-Fluorouracil (5-FU) is a cytostatic drug associated with chemotherapy-induced cognitive impairments that many cancer patients experience after treatment. Previous work in rodents has shown that 5-FU reduces hippocampal cell proliferation, a possible mechanism for the observed cognitive impairment, and that both effects can be reversed by co-administration of the antidepressant, fluoxetine. In the present study we investigate the optimum time for administration of fluoxetine to reverse or prevent the cognitive and cellular effects of 5-FU
Environmental Enrichment Induces Behavioral Recovery and Enhanced Hippocampal Cell Proliferation in an Antidepressant-Resistant Animal Model for PTSD
Background: Post traumatic stress disorder (PTSD) can be considered the result of a failure to recover after a traumatic experience. Here we studied possible protective and therapeutic aspects of environmental enrichment (with and without a running wheel) in Sprague Dawley rats exposed to an inescapable foot shock procedure (IFS). Methodology/Principal Findings: IFS induced long-lasting contextual and non-contextual anxiety, modeling some aspects of PTSD. Even 10 weeks after IFS the rats showed reduced locomotion in an open field. The antidepressants imipramine and escitalopram did not improve anxiogenic behavior following IFS. Also the histone deacetylase (HDAC) inhibitor sodium butyrate did not alleviate the IFS induced immobility. While environmental enrichment (EE) starting two weeks before IFS did not protect the animals from the behavioral effects of the shocks, exposure to EE either immediately after the shock or one week later induced complete recovery three weeks after IFS. In the next set of experiments a running wheel was added to the EE to enable voluntary exercise (EE/VE). This also led to reduced anxiety. Importantly, this behavioral recovery was not due to a loss of memory for the traumatic experience. The behavioral recovery correlated with an increase in cell proliferation in hippocampus, a decrease in the tissue levels of noradrenalin and increased turnover of 5-HT in prefrontal cortex and hippocampus. Conclusions/Significance: This animal study shows the importance of (physical) exercise in the treatment of psychiatri
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