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

Metabolic consequences of the water we drink: a study based on field evidence and animal model experimentation

The effect of the chronic consumption of water contaminated with residual concentrations of DDT’s metabolites (DDD—dichlorodiphenyldichloroethane and DDE—dichlorodiphenyldichloroethylene) found in the environment were evaluated on the biometric, hematological and antioxidant system parameters of the hepatic, muscular, renal and nervous tissues of Wistar rats. The results showed that the studied concentrations (0.002 mg.L−1 of DDD plus 0.005 mg.L−1 of DDE) could not cause significant changes in the hematological parameters. However, the tissues showed significant alteration in the activity of the antioxidant system represented by the increase in the activity of the enzymes gluthathione S-transferases in the liver, superoxide dismutase in the kidney, gluthathione peroxidase in the brain, and several changes in enzymatic activity in muscle (SOD, GPx and LPO). The enzymes alanine aminotransaminase (ALT) and aspartate aminotransaminase (AST) were also evaluated for the amino acids’ metabolism in the liver, with ALT showing a significant increase in the exposed animals. In the integrative analysis of biomarkers (Permanova and PCOA), the studied concentrations showed possible metabolic changes and damage to cellular structures evidenced by increased oxidative stress and body weight gain among the treated animals. This study highlights the need for further studies on the impact of banned pesticides still present in soils that may induce adverse effects in organisms that may prevail in future generations and the environment

A pp-adic Approach to the Weil Representation of Discriminant Forms Arising from Even Lattices

Suppose that $M$ is an even lattice with dual $M^{*}$ and level $N$. Then the group $Mp_{2}(\mathbb{Z})$, which is the unique non-trivial double cover of $SL_{2}(\mathbb{Z})$, admits a representation $\rho_{M}$, called the Weil representation, on the space $\mathbb{C}[M^{*}/M]$. The main aim of this paper is to show how the formulae for the $\rho_{M}$-action of a general element of $Mp_{2}(\mathbb{Z})$ can be obtained by a direct evaluation which does not depend on ``external objects'' such as theta functions. We decompose the Weil representation $\rho_{M}$ into $p$-parts, in which each $p$-part can be seen as subspace of the Schwartz functions on the $p$-adic vector space $M_{\mathbb{Q}_{p}}$. Then we consider the Weil representation of $Mp_{2}(\mathbb{Q}_{p})$ on the space of Schwartz functions on $M_{\mathbb{Q}_{p}}$, and see that restricting to $Mp_{2}(\mathbb{Z})$ just gives the $p$-part of $\rho_{M}$ again. The operators attained by the Weil representation are not always those appearing in the formulae from 1964, but are rather their multiples by certain roots of unity. For this, one has to find which pair of elements, lying over a matrix in $SL_{2}(\mathbb{Q}_{p})$, belong to the metaplectic double cover. Some other properties are also investigated.Comment: 29 pages, shortened a lo

PirB regulates a structural substrate for cortical plasticity

Experience-driven circuit changes underlie learning and memory. Monocular deprivation (MD) engages synaptic mechanisms of ocular dominance (OD) plasticity and generates robust increases in dendritic spine density on L5 pyramidal neurons. Here we show that the paired immunoglobulin-like receptor B (PirB) negatively regulates spine density, as well as the threshold for adult OD plasticity. In PirB(-/-) mice, spine density and stability are significantly greater than WT, associated with higher-frequency miniature synaptic currents, larger long-term potentiation, and deficient long-term depression. Although MD generates the expected increase in spine density in WT, in PirB(-/-) this increase is occluded. In adult PirB(-/-), OD plasticity is larger and more rapid than in WT, consistent with the maintenance of elevated spine density. Thus, PirB normally regulates spine and excitatory synapse density and consequently the threshold for new learning throughout life

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