Group Synchronization on Grids

Group synchronization requires to estimate unknown elements $({\theta}_v)_{v\in V}$ of a compact group ${\mathfrak G}$ associated to the vertices of a graph $G=(V,E)$, using noisy observations of the group differences associated to the edges. This model is relevant to a variety of applications ranging from structure from motion in computer vision to graph localization and positioning, to certain families of community detection problems. We focus on the case in which the graph $G$ is the $d$-dimensional grid. Since the unknowns ${\boldsymbol \theta}_v$ are only determined up to a global action of the group, we consider the following weak recovery question. Can we determine the group difference ${\theta}_u^{-1}{\theta}_v$ between far apart vertices $u, v$ better than by random guessing? We prove that weak recovery is possible (provided the noise is small enough) for $d\ge 3$ and, for certain finite groups, for $d\ge 2$. Viceversa, for some continuous groups, we prove that weak recovery is impossible for $d=2$. Finally, for strong enough noise, weak recovery is always impossible.Comment: 21 page

Prenatal alcohol: Effect on Depression and Brain Derived Neurotrophic Factor (BDNF) levels

Fetal alcohol exposure poses a significant social problem. Conservative rates of Fetal alcohol syndrome and Alcohol-Related Neurodevelopmental Disorders (ARND) together have been estimated at 9.1/1000 live births (Sampson 1997). Prenatal ethanol exposure can produce subtle learning disabilities in children, which may not become apparent until a child is school-aged and can occur in the absence of other physical evidence of alcohol-related birth defects. Along with cognitive deficits, ARND has been associated with an increased risk of psychiatric disorders such as Major Depressive Disorder (MDD). Major Depressive Disorder (MDD) has been linked to polymorphisms in the Brian Derived Neurotrophic Factor (BDNF) gene and patients with MDD have low serum BDNF levels (Levinson 2005, Chen et al 2001). Also post-mortem depressed patients who were on anti-depressant drugs have shown increased levels of BDNF (Chen et al 2001). BDNF given to stressed animals can even produce an antidepressant-like effect through the antagonism of a model of depression called learned helplessness behavior (Karege 2002). Efforts to better understand how prenatal ethanol increases susceptibility to MDD and the mechanism(s) by which ethanol produces these defects will rely on the study of these effects in animal models of prenatal ethanol exposure. Recently, our laboratory developed a mouse Fetal Alcohol Exposure (FAE) model which displays neurochemical and learning deficits. This model was used to explore the relationship of FAE-induced learned helplessness and changes in BDNF in the adult brain. Prenatal alcohol exposure was shown to produce an increase in learned helplessness and this was associated with a decrease in BDNF levels in the brain. These findings support the hypothesis that ARND is associated with an increase in depressive behavior and that lower levels of BDNF following prenatal exposure to alcohol may be involved

The Weak Limit of Ising Models on Locally Tree-Like Graphs

We consider the Ising model with inverse temperature β and without external field on sequences of graphs G n which converge locally to the k-regular tree. We show that for such graphs the Ising measure locally weakly converges to the symmetric mixture of the Ising model with + boundary conditions and the − boundary conditions on the k-regular tree with inverse temperature β. In the case where the graphs G n are expanders we derive a more detailed understanding by showing convergence of the Ising measure conditional on positive magnetization (sum of spins) to the + measure on the tree

The Effects of SNAP-25 Deficits and Pre-Natal Nicotine in a Mouse and ADHD Model

It has been recognized that the foundation of most, if not all, complex disease processes, particularly neuropsychiatric disorders, is due to the interactions between subtle genetic deficits and environmental insults. One of the most studied neuropsychiatric disorders shown to contribute from both heritable-related factors and environmental stressor sensitivity is Attention Deficit Hyperactivity Disorder (ADHD). Of the heritable issues involved, meta-analysis of genetic linkage studies has shown that the SNARE protein SNAP-25, is one of many possible proteins that may provide answers to the genetic component. In contrast to this genetic factor, studies have shown that prenatal nicotine exposure causes a direct effect to the fetus and predisposes them to nicotine and substance abuse behavior. Finally, preliminary studies have shown that heterozygote SNAP-25 deficient mice following in-utero exposure to nicotine are, in fact, hyperactive compared to their wild type littermates. To study the relationship between SNAP-25 and prenatal nicotine exposure with locomotor activity, we compared wild type mice with and without nicotine exposure to SNAP-25 wild type mice with and without nicotine exposure. Additionally, this study also examined prenatal nicotine exposed SNAP-25 heterozygous mice with their wild type counterpart with intraperitoneal cocaine to see if the combination of factors increased the likelihood of substance abuse potential. The results demonstrated that prenatal nicotine exposed mice had greater locomoter activity and substance abuse behavior. Moreover the SNAP-25 heterozygous genotype compounded both of these affects and demonstrated greater results

Intranasal rapamycin ameliorates Alzheimer-like cognitive decline in a mouse model of Down syndrome

Background: Down syndrome (DS) individuals, by the age of 40s, are at increased risk to develop Alzheimer-like dementia, with deposition in brain of senile plaques and neurofibrillary tangles. Our laboratory recently demonstrated the disturbance of PI3K/AKT/mTOR axis in DS brain, prior and after the development of Alzheimer Disease (AD). The aberrant modulation of the mTOR signalling in DS and AD age-related cognitive decline affects crucial neuronal pathways, including insulin signaling and autophagy, involved in pathology onset and progression. Within this context, the therapeutic use of mTOR-inhibitors may prevent/attenuate the neurodegenerative phenomena. By our work we aimed to rescue mTOR signalling in DS mice by a novel rapamycin intranasal administration protocol (InRapa) that maximizes brain delivery and reduce systemic side effects. Methods: Ts65Dn mice were administered with InRapa for 12 weeks, starting at 6 months of age demonstrating, at the end of the treatment by radial arms maze and novel object recognition testing, rescued cognition. Results: The analysis of mTOR signalling, after InRapa, demonstrated in Ts65Dn mice hippocampus the inhibition of mTOR (reduced to physiological levels), which led, through the rescue of autophagy and insulin signalling, to reduced APP levels, APP processing and APP metabolites production, as well as, to reduced tau hyperphosphorylation. In addition, a reduction of oxidative stress markers was also observed. Discussion: These findings demonstrate that chronic InRapa administration is able to exert a neuroprotective effect on Ts65Dn hippocampus by reducing AD pathological hallmarks and by restoring protein homeostasis, thus ultimately resulting in improved cognition. Results are discussed in term of a potential novel targeted therapeutic approach to reduce cognitive decline and AD-like neuropathology in DS individuals

Disturbance of Redox Homeostasis in Down Syndrome: Role of Iron Dysmetabolism

Down syndrome (DS) is the most common genetic form of intellectual disability that leads in the majority of cases to development of early-onset Alzheimer-like dementia (AD). The neuropathology of DS has several common features with AD including alteration of redox homeostasis, mitochondrial deficits, and inflammation among others. Interestingly, some of the genes encoded by chromosome 21 are responsible of increased oxidative stress (OS) conditions that are further exacerbated by decreased antioxidant defense. Previous studies from our groups showed that accumulation of oxidative damage is an early event in DS neurodegeneration and that oxidative modifications of selected proteins affects the integrity of the protein degradative systems, antioxidant response, neuronal integrity and energy metabolism. In particular, the current review elaborates recent findings demonstrating the accumulation of oxidative damage in DS and we focus attention on specific deregulation of iron metabolism, which affects both the central nervous system and the periphery. Iron dysmetabolism is a well-recognized factor that contributes to neurodegeneration; thus we opine that better understanding how and to what extent the concerted loss of iron dyshomestastis and increased OS occur in DS could provide novel insights for the development of therapeutic strategies for the treatment of Alzheimer-like dementia