Search for: All records

Abstract We consider a Gatenby–Gawlinski-type model of invasive tumors in the presence of an Allee effect. We describe the construction of bistable one-dimensional traveling fronts using singular perturbation techniques in different parameter regimes corresponding to tumor interfaces with, or without, an acellular gap. By extending the front as a planar interface, we perform a stability analysis to long wavelength perturbations transverse to the direction of front propagation and derive a simple stability criterion for the front in two spatial dimensions. In particular we find that in general the presence of the acellular gap indicates transversal instability of the associated planar front, which can lead to complex interfacial dynamics such as the development of finger-like protrusions and/or different invasion speeds. 

Abstract Evidence implicating theta rhythms in declarative memory encoding and retrieval, together with the notion that both retrieval and consolidation involve memory reinstatement or replay, suggests that post-learning theta rhythm modulation can promote early consolidation of newly formed memories. Building on earlier work employing theta neurofeedback, we examined whether theta-frequency transcranial alternating stimulation (tACS) can engender effective consolidation of newly formed episodic memories, compared with beta frequency stimulation or sham control conditions. We compared midline frontal and posterior parietal theta stimulation montages and examined whether benefits to memory of theta upregulation are attributable to consolidation rather than to retrieval processes by using a washout period to eliminate tACS after-effects between stimulation and memory assessment. Four groups of participants viewed object pictures followed by a free recall test during three study-test cycles. They then engaged in tACS (frontal theta montage/parietal theta montage/frontal beta montage/sham) for a period of 20 min, followed by a 2-h break. Free recall assessments were conducted after the break, 24 h later, and 7 days later. Frontal midline theta-tACS induced significant off-line retrieval gains at all assessment time points relative to all other conditions. This indicates that theta upregulation provides optimal conditions for the consolidation of episodic memory, independent of mental-state strategies.