Complementary action of chemical and electrical synapses to perception

Acknowledgements This study was possible by partial financial support from the following agencies: Fundação Araucária, EPSRC-EP/I032606/1, CNPq No. 441553/2014-1, CAPES No. 17656-12-5 and Science Without Borders Program— Process Nos. 17656125, 99999.010583/2013-00 and 245377/2012-3.Peer reviewedPostprin

Alterations in brain connectivity due to plasticity and synaptic delay

Brain plasticity refers to brain's ability to change neuronal connections, as a result of environmental stimuli, new experiences, or damage. In this work, we study the effects of the synaptic delay on both the coupling strengths and synchronisation in a neuronal network with synaptic plasticity. We build a network of Hodgkin-Huxley neurons, where the plasticity is given by the Hebbian rules. We verify that without time delay the excitatory synapses became stronger from the high frequency to low frequency neurons and the inhibitory synapses increases in the opposite way, when the delay is increased the network presents a non-trivial topology. Regarding the synchronisation, only for small values of the synaptic delay this phenomenon is observed

Random interactions and spin-glass thermodynamic transition in the hole-doped Haldane system Y2−x_{2-x}Cax_xBaNiO5_5

Magnetization, DC and AC bulk susceptibility of the $S$=1 Haldane chain system doped with electronic holes, Y$_{2-x}$Ca$_x$BaNiO$_5$ (0$\leq$x$\leq$0.20), have been measured and analyzed. The most striking results are (i) a sub-Curie power law behavior of the linear susceptibility, $\chi (T)$$\sim$ $T$$^{-\alpha}$, for temperature lower than the Haldane gap of the undoped compound (x=0) (ii) the existence of a spin-glass thermodynamic transition at $T$$_g$ = 2-3 K. These findings are consistent with (i) random couplings within the chains between the spin degrees of freedom induced by hole doping, (ii) the existence of ferromagnetic bonds that induce magnetic frustration when interchain interactions come into play at low temperature.Comment: 4 pages, 4 figures, to appear in Phys. Rev.

Generalized Jordan-Wigner Transformations

We introduce a new spin-fermion mapping, for arbitrary spin $S$ generating the SU(2) group algebra, that constitutes a natural generalization of the Jordan-Wigner transformation for $S=1/2$. The mapping, valid for regular lattices in any spatial dimension $d$, serves to unravel hidden symmetries in one representation that are manifest in the other. We illustrate the power of the transformation by finding exact solutions to lattice models previously unsolved by standard techniques. We also present a proof of the existence of the Haldane gap in $S=$1 bilinear nearest-neighbors Heisenberg spin chains and discuss the relevance of the mapping to models of strongly correlated electrons. Moreover, we present a general spin-anyon mapping for the case $d \leq 2$.Comment: 5 pages, 1 psfigur

Pathways to Mathematics College Readiness in Maine

The goal of this study was to examine the pathways to being college ready in mathematics. Students who enter high school already having demonstrated mathematics proficiency on a standardized test in the 8th grade have already taken a significant step towards being college ready. The best scenario is to enter high school proficient in mathematics and having already completed Algebra I, then to complete at least Algebra II and Calculus before graduating from high school. Students completing this pathway are virtually guaranteed to be college ready in mathematics. There also is an alternative path to being college ready. Being proficient entering high school, and then completing a course sequence that includes at least Algebra I, Algebra II, and pre-Calculus significantly increased students\u27 chances of being college ready in mathematics. Thus, it appears 8th grade proficiency is key to becoming college ready in mathematics. It affords opportunities for students to complete Algebra I before entering high school and then take higher level mathematics courses in high school. Alternatively, even if students wait to take Algebra I in high school, if they are proficient and complete at least pre-Calculus, they have a high likelihood of being college ready. The key is 8th grade mathematics proficiency. It opens the gate to a successful high school and college experience in mathematics. The typical sequence of courses completed by most high school students is Algebra I, Geometry, and Algebra II. The Common Core State Standards Initiative (2012) has endorsed this three course sequence as preparing students for college. However, the evidence from this study does not support this endorsement. Completing Geometry does not substantially ensure college readiness, nor does completing Algebra II ensure college readiness. Students also need to successfully complete either a pre-Calculus or Calculus course in high school to be college ready