A negative answer to a question of Bass

In this companion paper to arXiv:0802.1928 we provide an example of an isolated surface singularity $R$ over a number field such that $K_0(R) = K_0(R[t])$ but $K_0(R) \neq K_0(R[t_1,t_2])$. This answers, negatively, a question of Bass.Comment: The paper was previously part of arXiv:0802.192

Equivalence, reduction and minimization of finite fuzzy-automata

AbstractA new algebraic approach to the problem of equivalence, reduction and minimization of some kinds of fuzzy-automata is given. A system of necessary and sufficient conditions for equivalence of weakly initial fuzzy-automata is formulated. Some algorithms considering the equivalence for two fuzzy-automata are constructed

Endoscopic placental laser coagulation in dichorionic and monochorionic triplet pregnancies

Objective: To report outcome of monochorionic (MC) and dichorionic (DC) triamniotic (TA) triplet pregnancies treated with endoscopic laser coagulation of communicating placental vessels for severe fetofetal transfusion syndrome (FFTS) and selective fetal growth restriction (sFGR). Methods: Laser surgery was performed at 18 (15-24) weeks gestation in 11 MCTA and 33 DCTA pregnancies complicated by FFTS and 14 DCTA pregnancies complicated by sFGR. Data from our study and previous reports were pooled using meta-analytic techniques. Results: Survival of at least one baby and survival among all fetuses was 97.0% and 72.7% in DCTA pregnancies with FFTS, 78.6% and 52.4% in DCTA pregnancies with sFGR and 81.8% and 39.4% in MCTA pregnancies with FFTS. In the combined data from our study and previous reports, the pooled survival rates in 132 DCTA pregnancies with FFTS were 94.4% and 76.1% and in 29 MCTA pregnancies with FFTS were 80.6% and 57.5%. Conclusions: Survival after laser surgery is higher in DC triplets with FFTS than those with sFGR and in DC than MC triplets with FFTS

Regularity of prime ideals

We answer several natural questions which arise from a recent paper of McCullough and Peeva providing counterexamples to the Eisenbud\u2013Goto Regularity Conjecture. We give counterexamples using Rees algebras, and also construct counterexamples that do not rely on the Mayr\u2013Meyer construction. Furthermore, examples of prime ideals for which the difference between the maximal degree of a minimal generator and the maximal degree of a minimal first syzygy can be made arbitrarily large are given. Using a result of Ananyan-Hochster we show that there exists an upper bound on regularity of prime ideals in terms of the multiplicity alone

A simple remark on a flat projective morphism with a Calabi-Yau fiber

If a K3 surface is a fiber of a flat projective morphisms over a connected noetherian scheme over the complex number field, then any smooth connected fiber is also a K3 surface. Observing this, Professor Nam-Hoon Lee asked if the same is true for higher dimensional Calabi-Yau fibers. We shall give an explicit negative answer to his question as well as a proof of his initial observation.Comment: 8 pages, main theorem is generalized, one more remark is added, mis-calculation and typos are corrected etc

The absence of serotonin in the brain alters acute stress responsiveness by interfering with the genomic function of the glucocorticoid receptors

Alterations in serotonergic transmission have been related to a major predisposition to develop psychiatric pathologies, such as depression. We took advantage of tryptophan hydroxylase (TPH) 2 deficient rats, characterized by a complete absence of serotonin in the brain, to evaluate whether a vulnerable genotype may influence the reaction to an acute stressor. In this context, we investigated if the glucocorticoid receptor (GR) genomic pathway activation was altered by the lack of serotonin in the central nervous system. Moreover, we analyzed the transcription pattern of the clock genes that can be affected by acute stressors. Adult wild type (TPH2(+/+)) and TPH2-deficient (TPH2(-/-)) male rats were sacrificed after exposure to one single session of acute restraint stress. Protein and gene expression analyses were conducted in the prefrontal cortex (PFC). The acute stress enhanced the translocation of GRs in the nucleus of TPH2(+/+) animals. This effect was blunted in TPH2(-/-) rats, suggesting an impairment of the GR genomic mechanism. This alteration was mirrored in the expression of GR-responsive genes: acute stress led to the up-regulation of GR-target gene expression in TPH2(+/+), but not in TPH2(-/-) animals. Finally, clock genes were differently modulated in the two genotypes after the acute restraint stress. Overall our findings suggest that the absence of serotonin within the brain interferes with the ability of the HPA axis to correctly modulate the response to acute stress, by altering the nuclear mechanisms of the GR and modulation of clock genes expression