Infinite Transitivity on Affine Varieties

In this note we survey recent results on automorphisms of affine algebraic varieties, infinitely transitive group actions and flexibility. We present related constructions and examples, and discuss geometric applications and open problems.

Implicit task sequence learning in patients with Parkinson's disease, frontal lesions and amnesia: The critical role of fronto–striatal loops

The purpose of this study was to investigate the role of the fronto–striatal system for implicit task sequence learning. We tested performance of patients with compromised functioning of the fronto–striatal loops, that is, patients with Parkinson's disease and patients with lesions in the ventromedial or dorsolateral prefrontal cortex. We also tested amnesic patients with lesions either to the basal forebrain/orbitofrontal cortex or to thalamic/medio-temporal regions. We used a task sequence learning paradigm involving the presentation of a sequence of categorical binary-choice decision tasks. After several blocks of training, the sequence, hidden in the order of tasks, was replaced by a pseudo-random sequence. Learning (i.e., sensitivity to the ordering) was assessed by measuring whether this change disrupted performance. Although all the patients were able to perform the decision tasks quite easily, those with lesions to the fronto–striatal loops (i.e., patients with Parkinson's disease, with lesions in the ventromedial or dorsolateral prefrontal cortex and those amnesic patients with lesions to the basal forebrain/orbitofrontal cortex) did not show any evidence of implicit task sequence learning. In contrast, those amnesic patients with lesions to thalamic/medio-temporal regions showed intact sequence learning. Together, these results indicate that the integrity of the fronto–striatal system is a prerequisite for implicit task sequence learning.

Analysis of Pressure Head-Flow Loops of Pulsatile Rotodynamic Blood Pumps

The clinical importance of pulsatility is a recurring topic of debate in mechanical circulatory support. Lack of pulsatility has been identified as a possible factor responsible for adverse events and has also demonstrated a role in myocardial perfusion and cardiac recovery. A commonly used method for restoring pulsatility with rotodynamic blood pumps (RBPs) is to modulate the speed profile, synchronized to the cardiac cycle. This introduces additional parameters that influence the (un)loading of the heart, including the timing (phase shift) between the native cardiac cycle and the pump pulses, and the amplitude of speed modulation. In this study, the impact of these parameters upon the heart-RBP interaction was examined in terms of the pressure head-flow (HQ) diagram. The measurements were conducted using a rotodynamic Deltastream DP2 pump in a validated hybrid mock circulation with baroreflex function. The pump was operated with a sinusoidal speed profile, synchronized to the native cardiac cycle. The simulated ventriculo-aortic cannulation showed that the level of (un)loading and the shape of the HQ loops strongly depend on the phase shift. The HQ loops displayed characteristic shapes depending on the phase shift. Increased contribution of native contraction (increased ventricular stroke work [WS ]) resulted in a broadening of the loops. It was found that the previously described linear relationship between WS and the area of the HQ loop for constant pump speeds becomes a family of linear relationships, whose slope depends on the phase shift.

New Constraints on Dark Matter Effective Theories from Standard Model Loops

We consider an effective field theory for a gauge singlet Dirac dark matter particle interacting with the standard model fields via effective operators suppressed by the scale Λ≳1  TeV. We perform a systematic analysis of the leading loop contributions to spin-independent Dirac dark matter–nucleon scattering using renormalization group evolution between Λ and the low-energy scale probed by direct detection experiments. We find that electroweak interactions induce operator mixings such that operators that are naively velocity suppressed and spin dependent can actually contribute to spin-independent scattering. This allows us to put novel constraints on Wilson coefficients that were so far poorly bounded by direct detection. Constraints from current searches are already significantly stronger than LHC bounds, and will improve in the near future. Interestingly, the loop contribution we find is isospin violating even if the underlying theory is isospin conserving.