The Laplacian Eigenvalues and Invariants of Graphs

In this paper, we investigate some relations between the invariants (including vertex and edge connectivity and forwarding indices) of a graph and its Laplacian eigenvalues. In addition, we present a sufficient condition for the existence of Hamiltonicity in a graph involving its Laplacian eigenvalues.Comment: 10 pages,Filomat, 201

Increase in neuroexcitability of unmyelinated C-type vagal ganglion neurons during initial postnatal development of visceral afferent reflex functions

BACKGROUND: Baroreflex gain increase up closely to adult level during initial postnatal weeks, and any interruption within this period will increase the risk of cardiovascular problems in later of life span. We hypothesize that this short period after birth might be critical for postnatal development of vagal ganglion neurons (VGNs). METHODS: To evaluate neuroexcitability evidenced by discharge profiles and coordinate changes, ion currents were collected from identified A- and C-type VGNs at different developmental stages using whole-cell patch clamping. RESULTS: C-type VGNs underwent significant age-dependent transition from single action potential (AP) to repetitive discharge. The coordinate changes between TTX-S and TTX-R Na(+) currents were also confirmed and well simulated by computer modeling. Although 4-AP or iberiotoxin age dependently increased firing frequency, AP duration was prolonged in an opposite fashion, which paralleled well with postnatal changes in 4-AP- and iberiotoxin-sensitive K(+) current activity, whereas less developmental changes were verified in A-types. CONCLUSION: These data demonstrate for the first time that the neuroexcitability of C-type VGNs increases significantly compared with A-types within initial postnatal weeks evidenced by AP discharge profiles and coordinate ion channel changes, which explain, at least in part, that initial postnatal weeks may be crucial for ontogenesis in visceral afferent reflex function

Fermion sign bounds theory in quantum Monte Carlo simulation

Sign problem in fermion quantum Monte Carlo (QMC) simulation appears to be an extremely hard problem. Traditional lore passing around for years tells people that when there is a sign problem, the average sign in QMC simulation approaches zero exponentially fast with the space-time volume of the configurational space. We, however, analytically show this is not always the case and manage to find physical bounds for the average sign. Our understanding is based on a direct connection between the sign bounds and a well-defined partition function of reference system and could distinguish when the bounds have the usual exponential scaling, and when they are bestowed on an algebraic scaling at low temperature limit. We analytically explain such algebraic sign problems found in flat band moir\'e lattice models at low temperature limit. At finite temperature, a domain size argument based on sign bounds also explains the connection between sign behavior and finite temperature phase transition. Sign bounds, as a well-defined observable, may have ability to ease or even make use of the sign problem.Comment: 11 pages, 3 figure