  Motivated by recent experiments in neuroscience which indicate that neuronal
avalanches exhibit scale invariant behavior similar to self-organized critical
systems, we study the role of noisy (non-conservative) local dynamics on the
critical behavior of a sandpile model which can be taken to mimic the dynamics
of neuronal avalanches. We find that despite the fact that noise breaks the
strict local conservation required to attain criticality, our system exhibit
true criticality for a wide range of noise in various dimensions, given that
conservation is respected \textit{on the average}. Although the system remains
critical, exhibiting finite-size scaling, the value of critical exponents
change depending on the intensity of local noise. Interestingly, for
sufficiently strong noise level, the critical exponents approach and saturate
at their mean-field values, consistent with empirical measurements of neuronal
avalanches. This is confirmed for both two and three dimensional models.
However, addition of noise does not affect the exponents at the upper critical
dimension ($D=4$). In addition to extensive finite-size scaling analysis of our
systems, we also employ a useful time-series analysis method in order to
establish true criticality of noisy systems. Finally, we discuss the
implications of our work in neuroscience as well as some implications for
general phenomena of criticality in non-equilibrium systems.
