On the full automorphism group of a Hamiltonian cycle system of odd order

It is shown that a necessary condition for an abstract group G to be the full automorphism group of a Hamiltonian cycle system is that G has odd order or it is either binary, or the affine linear group AGL(1; p) with p prime. We show that this condition is also sufficient except possibly for the class of non-solvable binary groups.Comment: 11 pages, 2 figure

Involvement of fast-spiking cells in ictal sequences during spontaneous seizures in rats with chronic temporal lobe epilepsy

Epileptic seizures represent altered neuronal network dynamics, but the temporal evolution and cellular substrates of the neuronal activity patterns associated with spontaneous seizures are not fully understood. We used simultaneous recordings from multiple neurons in the hippocampus and neocortex of rats with chronic temporal lobe epilepsy to demonstrate that subsets of cells discharge in a highly stereotypical sequential pattern during ictal events, and that these stereotypical patterns were reproducible across consecutive seizures. In contrast to the canonical view that principal cell discharges dominate ictal events, the ictal sequences were predominantly composed of fast-spiking, putative inhibitory neurons, which displayed unusually strong coupling to local field potential even before seizures. The temporal evolution of activity was characterized by unique dynamics where the most correlated neuronal pairs before seizure onset displayed the largest increases in correlation strength during the seizures. These results demonstrate the selective involvement of fast spiking interneurons in structured temporal sequences during spontaneous ictal events in hippocampal and neocortical circuits in experimental models of chronic temporal lobe epilepsy

On pyramidal groups whose number of involutions is a prime power

A Kirkman Triple System $\Gamma$ is called $m$-pyramidal if there exists a subgroup $G$ of the automorphism group of $\Gamma$ that fixes $m$ points and acts regularly on the other points. Such group $G$ admits a unique conjugacy class $C$ of involutions (elements of order $2$) and $|C|=m$. We call groups with this property $m$-pyramidal. We prove that, if $m$ is an odd prime power $p^k$, then every $m$-pyramidal group is solvable if and only if either $m=9$ or $k$ is odd. The primitive permutation groups play an important role in the proof. We also determine the orders of the $m$-pyramidal groups when $m$ is a prime number.Comment: 19 page

Altered Expression of the CB1 Cannabinoid Receptor in the Triple Transgenic Mouse Model of Alzheimer's Disease

The endocannabinoid system has gained much attention as a new potential pharmacotherapeutic target in various neurodegenerative diseases, including Alzheimer's disease (AD). However, the association between CB1 alterations and the development of AD neuropathology is unclear and often contradictory. In this study, brain CB1 mRNA and CB1 protein levels were analyzed in 3 × Tg-AD mice and compared to wild-type littermates at 2, 6 and 12 months of age, using in-situ hybridization and immunohistochemistry, respectively. Semiquantitative analysis of CB1 expression focused on the prefrontal cortex (PFC), prelimbic cortex, dorsal hippocampus (DH), basolateral amygdala complex (BLA), and ventral hippocampus (VH), all areas with high CB1 densities that are strongly affected by neuropathology in 3 × Tg-AD mice. At 2 months of age, there was no change in CB1 mRNA and protein levels in 3 × Tg-AD mice compared to Non-Tg mice in all brain areas analyzed. However, at 6 and 12 months of age, CB1 mRNA levels were significantly higher in PFC, DH, and BLA, and lower in VH in 3 × Tg-AD mice compared to wild-type littermates. CB1 immunohistochemistry revealed that CB1 protein expression was unchanged in 3 × Tg-AD at 2 and 6 months of age, while a significant decrease in CB1 receptor immunoreactivity was detected in the BLA and DH of 12-month-old 3 × Tg-AD mice, with no sign of alteration in other brain areas. The altered CB1 levels appear, rather, to be age-and/or pathology-dependent, indicating an involvement of the endocannabinoid system in AD pathology and supporting the ECS as a potential novel therapeutic target for treatment of AD

Steiner systems and configurations of points

The aim of this paper is to make a connection between design theory and algebraic geometry/commutative algebra. In particular, given any Steiner System S(t, n, v) we associate two ideals, in a suitable polynomial ring, defining a Steiner configuration of points and its Complement. We focus on the latter, studying its homological invariants, such as Hilbert Function and Betti numbers. We also study symbolic and regular powers associated to the ideal defining a Complement of a Steiner configuration of points, finding its Waldschmidt constant, regularity, bounds on its resurgence and asymptotic resurgence. We also compute the parameters of linear codes associated to any Steiner configuration of points and its Complement

Exploring adult hippocampal neurogenesis using optogenetics

In the 1980s, it was widely accepted that new neurons are continuously generated in the dentate gyrus of the mammalian hippocampus. Since its acceptance, researchers have employed various techniques and behavioral paradigms to study the proliferation, differentiation, and functional role of adult-born neurons. This literature thesis aims to discuss how optogenetics is able to overcome the limitations of past techniques and provide the field with new insights into the functional role of neurogenesis. We will review the current knowledge on both adult hippocampal neurogenesis and optogenetics, present representative studies using optogenetics to investigate neurogenesis and discuss potential limitations and concerns involved in using optogenetics