Linear independence of Gamma values in positive characteristic

We investigate the arithmetic nature of special values of Thakur's function field Gamma function at rational points. Our main result is that all linear independence relations over the field of algebraic functions are consequences of the known relations of Anderson and Thakur arising from the functional equations of the Gamma function.Comment: 51 page

The Randomized Shortened Dental Arch Study: Tooth Loss

The evidence concerning the management of shortened dental arch (SDA) cases is sparse. This multi-center study was aimed at generating data on outcomes and survival rates for two common treatments, removable dental prostheses (RDP) for molar replacement or no replacement (SDA). The hypothesis was that the treatments lead to different incidences of tooth loss. We included 215 patients with complete molar loss in one jaw. Molars were either replaced by RDP or not replaced, according to the SDA concept. First tooth loss after treatment was the primary outcome measure. This event occurred in 13 patients in the RDP group and nine patients in the SDA group. The respective Kaplan-Meier survival rates at 38 months were 0.83 (95% CI: 0.74-0.91) in the RDP group and 0.86 (95% CI: 0.78-0.95) in the SDA group, the difference being non-significant

Group 2 ITI Consensus Report: Technological developments in implant prosthetics

Objectives Group‐2 reviewed the scientific evidence in the field of «Technology». Focused research questions were: (1) additive versus subtractive manufacturing of implant restorations; (2) survival, complications, and esthetics comparing prefabricated versus customized abutments; and (3) survival of posterior implant‐supported multi‐unit fixed dental prostheses.Materials and MethodsLiterature was systematically screened, and 67 publications could be critically reviewed following PRISMA guidelines, resulting in three systematic reviews. Consensus statements were presented to the plenary where after modification, those were accepted.ResultsAdditively fabricated implant restorations of zirconia and polymers were investigated for marginal/internal adaptation and mechanical properties without clear results in favor of one technology or material. Titanium base abutments for screw‐retained implant single crowns compared to customized abutments did not show significant differences concerning 1‐year survival. PFM, veneered and monolithic zirconia implant‐supported multi‐unit posterior fixed dental prostheses demonstrated similar high 3‐year survival rates, whereas veneered restorations exhibited the highest annual ceramic fracture and chipping rates.ConclusionsFor interim tooth‐colored implant single crowns both additive and subtractive manufacturing are viable techniques. The clinical performance of additively produced restorations remains to be investigated. Implant single crowns on titanium base abutments show similar clinical performance compared to other type of abutments; however, long‐term clinical data from RCTs are needed. The abutment selection should be considered already during the planning phase. Digital planning facilitates 3D visualization of the prosthetic design including abutment selection. In the posterior area, monolithic zirconia is recommended as the material of choice for multi‐unit implant restorations to reduce technical complications

A Sodium Leak Current Regulates Pacemaker Activity of Adult Central Pattern Generator Neurons in Lymnaea Stagnalis

The resting membrane potential of the pacemaker neurons is one of the essential mechanisms underlying rhythm generation. In this study, we described the biophysical properties of an uncharacterized channel (U-type channel) and investigated the role of the channel in the rhythmic activity of a respiratory pacemaker neuron and the respiratory behaviour in adult freshwater snail Lymnaea stagnalis. Our results show that the channel conducts an inward leak current carried by Na+ (ILeak-Na). The ILeak-Na contributed to the resting membrane potential and was required for maintaining rhythmic action potential bursting activity of the identified pacemaker RPeD1 neurons. Partial knockdown of the U-type channel suppressed the aerial respiratory behaviour of the adult snail in vivo. These findings identified the Na+ leak conductance via the U-type channel, likely a NALCN-like channel, as one of the fundamental mechanisms regulating rhythm activity of pacemaker neurons and respiratory behaviour in adult animals

Spontaneous Local Gamma Oscillation Selectively Enhances Neural Network Responsiveness

Synchronized oscillation is very commonly observed in many neuronal systems and might play an important role in the response properties of the system. We have studied how the spontaneous oscillatory activity affects the responsiveness of a neuronal network, using a neural network model of the visual cortex built from Hodgkin-Huxley type excitatory (E-) and inhibitory (I-) neurons. When the isotropic local E-I and I-E synaptic connections were sufficiently strong, the network commonly generated gamma frequency oscillatory firing patterns in response to random feed-forward (FF) input spikes. This spontaneous oscillatory network activity injects a periodic local current that could amplify a weak synaptic input and enhance the network's responsiveness. When E-E connections were added, we found that the strength of oscillation can be modulated by varying the FF input strength without any changes in single neuron properties or interneuron connectivity. The response modulation is proportional to the oscillation strength, which leads to self-regulation such that the cortical network selectively amplifies various FF inputs according to its strength, without requiring any adaptation mechanism. We show that this selective cortical amplification is controlled by E-E cell interactions. We also found that this response amplification is spatially localized, which suggests that the responsiveness modulation may also be spatially selective. This suggests a generalized mechanism by which neural oscillatory activity can enhance the selectivity of a neural network to FF inputs

Intense Synaptic Activity Enhances Temporal Resolution in Spinal Motoneurons

In neurons, spike timing is determined by integration of synaptic potentials in delicate concert with intrinsic properties. Although the integration time is functionally crucial, it remains elusive during network activity. While mechanisms of rapid processing are well documented in sensory systems, agility in motor systems has received little attention. Here we analyze how intense synaptic activity affects integration time in spinal motoneurons during functional motor activity and report a 10-fold decrease. As a result, action potentials can only be predicted from the membrane potential within 10 ms of their occurrence and detected for less than 10 ms after their occurrence. Being shorter than the average inter-spike interval, the AHP has little effect on integration time and spike timing, which instead is entirely determined by fluctuations in membrane potential caused by the barrage of inhibitory and excitatory synaptic activity. By shortening the effective integration time, this intense synaptic input may serve to facilitate the generation of rapid changes in movements

Bursts and Isolated Spikes Code for Opposite Movement Directions in Midbrain Electrosensory Neurons

Directional selectivity, in which neurons respond strongly to an object moving in a given direction but weakly or not at all to the same object moving in the opposite direction, is a crucial computation that is thought to provide a neural correlate of motion perception. However, directional selectivity has been traditionally quantified by using the full spike train, which does not take into account particular action potential patterns. We investigated how different action potential patterns, namely bursts (i.e. packets of action potentials followed by quiescence) and isolated spikes, contribute to movement direction coding in a mathematical model of midbrain electrosensory neurons. We found that bursts and isolated spikes could be selectively elicited when the same object moved in opposite directions. In particular, it was possible to find parameter values for which our model neuron did not display directional selectivity when the full spike train was considered but displayed strong directional selectivity when bursts or isolated spikes were instead considered. Further analysis of our model revealed that an intrinsic burst mechanism based on subthreshold T-type calcium channels was not required to observe parameter regimes for which bursts and isolated spikes code for opposite movement directions. However, this burst mechanism enhanced the range of parameter values for which such regimes were observed. Experimental recordings from midbrain neurons confirmed our modeling prediction that bursts and isolated spikes can indeed code for opposite movement directions. Finally, we quantified the performance of a plausible neural circuit and found that it could respond more or less selectively to isolated spikes for a wide range of parameter values when compared with an interspike interval threshold. Our results thus show for the first time that different action potential patterns can differentially encode movement and that traditional measures of directional selectivity need to be revised in such cases