$Herschel$ investigation of cores and filamentary structures in the
  Perseus molecular cloud
  Cores and filamentary structures are the prime birthplaces of stars, and play
key roles in the process of star formation. Latest advances in the methods of
multi-scale source and filament extraction, and in making high-resolution
column density map from $Herschel$ multi-wavelength observations enable us to
detect the filamentary network structures in highly complex molecular cloud
environments. The statistics for physical parameters shows that core mass
strongly correlates with core dust temperature, and $M/L$ strongly correlates
with $M/T$, which is in line with the prediction of the blackbody radiation,
and can be used to trace evolutionary sequence from unbound starless cores to
robust prestellar cores. Crest column densities of the filamentary structures
are clearly related with mass per unit length ($M_{\rm line}$), but are
uncorrelated by three orders ranging from $\sim 10^{20}$ to $\sim 10^{22}$ $
\rm cm^{-2}$ with widths. Full width at half maximum (FWHM) have a median value
of 0.15 pc, which is consistent with the 0.1 pc typical inner width of the
filamentary structures reported by previous research. We find $\sim $70\% of
robust prestellar cores (135/199) embedded in supercritical filaments with
$M_{\rm line}>16~M_{\odot}/{\rm pc}$, which implies that the gravitationally
bound cores come from fragmentation of supercritical filaments. And on the
basis of observational evidences that probability distribution function (PDF)
with power-law distribution in the Perseus south is flatter than north, YSO
number is significantly less than that in the north, and dust temperature
difference. We infer that south region is more gravitationally bound than north
region.
