Gorensteinness and iteration of Cox rings for Fano type varieties

We show that finitely generated Cox rings are Gorenstein. This leads to a refined characterization of varieties of Fano type: they are exactly those projective varieties with Gorenstein canonical quasicone Cox ring. We then show that for varieties of Fano type and Kawamata log terminal quasicones X, iteration of Cox rings is finite with factorial master Cox ring. In particular, even if the class group has torsion, we can express such X as quotients of a factorial canonical quasicone by a solvable reductive group.

An Approach to the Construction of a Recursive Argument of Polynomial Evaluation in the Discrete Log Setting

Succinct Non-interactive Arguments of Knowledge (SNARks) are receiving a lot of attention as a core privacy-enhancing technology for blockchain applications. Polynomial commitment schemes are important building blocks for the construction of SNARks. Polynomial commitment schemes enable the prover to commit to a secret polynomial of the prover and convince the verifier that the evaluation of the committed polynomial is correct at a public point later. Bünz et al. recently presented a novel polynomial commitment scheme with no trusted setup in Eurocrypt’20. To provide a transparent setup, their scheme is built over an ideal class group of imaginary quadratic fields (or briefly, class group). However, cryptographic assumptions on a class group are relatively new and have, thus far, not been well-analyzed. In this paper, we study an approach to transpose Bünz et al.’s techniques in the discrete log setting because the discrete log setting brings a significant improvement in efficiency and security compared to class groups. We show that the transposition to the discrete log setting can be obtained by employing a proof system for the equality of discrete logarithms over multiple bases. Theoretical analysis shows that the transposition preserves security requirements for a polynomial commitment scheme.

Genomic Insights into the Diversity of Non-Coding RNAs in Bacillus Cereus Sensu Lato.

Bacillus cereus sensu lato is a group of bacteria of medical and agricultural importance in different ecological niches and with controversial taxonomic relationships. Studying the composition of non-coding RNAs (ncRNAs) in several bacterial groups has been an important tool for identifying genetic information. However, to date, no comparative genomics study of ncRNA has been performed in this group. Thus, this study aimed to identify and characterize the set of ncRNAs from 132 strains of Bacillus cereus, Bacillus thuringiensis and Bacillus anthracis to obtain an overview of the diversity and distribution of these genetic elements in these species. We observed that the number of ncRNAs differs in the chromosomes of the three species, but not in the plasmids, when species or phylogenetic clusters were compared. The prevailing functional/structural category was Cis-reg and the most frequent class was Riboswitch. However, in plasmids, the class Group II intron was the most frequent. Also, nine ncRNAs were selected for validation in the strain B. thuringiensis 407 by RT-PCR, which allowed to identify the expression of the ncRNAs. The wide distribution and diversity of ncRNAs in the B. cereus group, and more intensely in B. thuringiensis, may help improve the abilities of these species to adapt to various environmental changes.

Galois covers of ℙ1 and number fields with large class groups

For each finite subgroup [Formula: see text] of [Formula: see text], and for each integer [Formula: see text] coprime to [Formula: see text], we construct explicitly infinitely many Galois extensions of [Formula: see text] with group [Formula: see text] and whose ideal class group has [Formula: see text]-rank at least [Formula: see text]. This gives new [Formula: see text]-rank records for class groups of number fields.

Internalisasi nilai-nilai Pancasila dalam upaya mencegah radikalisme

As the basis of the Indonesian state, Pancasila has positive values that can embody in all aspects of community life, including the younger generation who will continue the leadership of the Indonesian nation. It must consider because of the exposure to radicalism that is currently targeting the younger generation. The younger generation is seeing as individuals who have great potential to commit harmful actions against their nation. That is why educational institutions need to instill the noble values of Pancasila in their students as early as possible so that the values of togetherness and unity that they are holding are not intolerant. Therefore, it is necessary to integrate the values of Pancasila students in the STT Bethel Indonesia environment. The method used to reveal this fact is a case study that portrays social interactions through intensive in-depth surveys. The results of the study state that STT Bethel Indonesia institutionally and individually practices the values of Pancasila by respecting the differences that exist, both ethnicity, race, and class. STT Bethel Indonesia instills the value of Pancasila students for each student through religious and educational activities. Every morning before the start of the teaching and learning class, group prayer is holding to increase the value of student religiosity. In addition, the narrative that is building for students is to love each other because it is a mandate that God has given to humans to do.