Random and exhaustive generation of permutations and cycles

In 1986 S. Sattolo introduced a simple algorithm for uniform random generation of cyclic permutations on a fixed number of symbols. This algorithm is very similar to the standard method for generating a random permutation, but is less well known. We consider both methods in a unified way, and discuss their relation with exhaustive generation methods. We analyse several random variables associated with the algorithms and find their grand probability generating functions, which gives easy access to moments and limit laws.Comment: 9 page

Observations of the atmosphere and surface state over Terra Nova Bay, Antarctica, using unmanned aerial systems

In September 2012 five Aerosonde unmanned aircraft were used to make measurements of the atmospheric state over the Terra Nova Bay polynya, Antarctica, to explore the details of air–sea ice–ocean coupling. A total of 14 flights were completed in September 2012. Ten of the flight missions consisted of two unmanned aerial systems (UAS) sampling the atmosphere over Terra Nova Bay on 5 different days, with one UAS focusing on the downwind evolution of the air mass and a second UAS flying transects roughly perpendicular to the low-level winds. The data from these coordinated UAS flights provide a comprehensive three-dimensional data set of the atmospheric state (air temperature, humidity, pressure, and wind) and surface skin temperature over Terra Nova Bay. The remaining UAS flights during the September 2012 field campaign included two local flights near McMurdo Station for flight testing, a single UAS flight to Terra Nova Bay, and a single UAS flight over the Ross Ice Shelf and Ross Sea polynya. A data set containing the atmospheric and surface data as well as operational aircraft data have been submitted to the United States Antarctic Program Data Coordination Center (USAP-DCC)

Structure of the first representative of Pfam family PF04016 (DUF364) reveals enolase and Rossmann-like folds that combine to form a unique active site with a possible role in heavy-metal chelation.

The crystal structure of Dhaf4260 from Desulfitobacterium hafniense DCB-2 was determined by single-wavelength anomalous diffraction (SAD) to a resolution of 2.01 Å using the semi-automated high-throughput pipeline of the Joint Center for Structural Genomics (JCSG) as part of the NIGMS Protein Structure Initiative (PSI). This protein structure is the first representative of the PF04016 (DUF364) Pfam family and reveals a novel combination of two well known domains (an enolase N-terminal-like fold followed by a Rossmann-like domain). Structural and bioinformatic analyses reveal partial similarities to Rossmann-like methyltransferases, with residues from the enolase-like fold combining to form a unique active site that is likely to be involved in the condensation or hydrolysis of molecules implicated in the synthesis of flavins, pterins or other siderophores. The genome context of Dhaf4260 and homologs additionally supports a role in heavy-metal chelation

Structure of a putative NTP pyrophosphohydrolase: YP_001813558.1 from Exiguobacterium sibiricum 255-15.

The crystal structure of a putative NTPase, YP_001813558.1 from Exiguobacterium sibiricum 255-15 (PF09934, DUF2166) was determined to 1.78 Å resolution. YP_001813558.1 and its homologs (dimeric dUTPases, MazG proteins and HisE-encoded phosphoribosyl ATP pyrophosphohydrolases) form a superfamily of all-α-helical NTP pyrophosphatases. In dimeric dUTPase-like proteins, a central four-helix bundle forms the active site. However, in YP_001813558.1, an unexpected intertwined swapping of two of the helices that compose the conserved helix bundle results in a `linked dimer' that has not previously been observed for this family. Interestingly, despite this novel mode of dimerization, the metal-binding site for divalent cations, such as magnesium, that are essential for NTPase activity is still conserved. Furthermore, the active-site residues that are involved in sugar binding of the NTPs are also conserved when compared with other α-helical NTPases, but those that recognize the nucleotide bases are not conserved, suggesting a different substrate specificity

Structure of the γ-D-glutamyl-L-diamino acid endopeptidase YkfC from Bacillus cereus in complex with L-Ala-γ-D-Glu: insights into substrate recognition by NlpC/P60 cysteine peptidases.

Dipeptidyl-peptidase VI from Bacillus sphaericus and YkfC from Bacillus subtilis have both previously been characterized as highly specific γ-D-glutamyl-L-diamino acid endopeptidases. The crystal structure of a YkfC ortholog from Bacillus cereus (BcYkfC) at 1.8 Å resolution revealed that it contains two N-terminal bacterial SH3 (SH3b) domains in addition to the C-terminal catalytic NlpC/P60 domain that is ubiquitous in the very large family of cell-wall-related cysteine peptidases. A bound reaction product (L-Ala-γ-D-Glu) enabled the identification of conserved sequence and structural signatures for recognition of L-Ala and γ-D-Glu and, therefore, provides a clear framework for understanding the substrate specificity observed in dipeptidyl-peptidase VI, YkfC and other NlpC/P60 domains in general. The first SH3b domain plays an important role in defining substrate specificity by contributing to the formation of the active site, such that only murein peptides with a free N-terminal alanine are allowed. A conserved tyrosine in the SH3b domain of the YkfC subfamily is correlated with the presence of a conserved acidic residue in the NlpC/P60 domain and both residues interact with the free amine group of the alanine. This structural feature allows the definition of a subfamily of NlpC/P60 enzymes with the same N-terminal substrate requirements, including a previously characterized cyanobacterial L-alanine-γ-D-glutamate endopeptidase that contains the two key components (an NlpC/P60 domain attached to an SH3b domain) for assembly of a YkfC-like active site

The structure of BVU2987 from Bacteroides vulgatus reveals a superfamily of bacterial periplasmic proteins with possible inhibitory function.

Proteins that contain the DUF2874 domain constitute a new Pfam family PF11396. Members of this family have predominantly been identified in microbes found in the human gut and oral cavity. The crystal structure of one member of this family, BVU2987 from Bacteroides vulgatus, has been determined, revealing a β-lactamase inhibitor protein-like structure with a tandem repeat of domains. Sequence analysis and structural comparisons reveal that BVU2987 and other DUF2874 proteins are related to β-lactamase inhibitor protein, PepSY and SmpA_OmlA proteins and hence are likely to function as inhibitory proteins

Toward verification of the Riemann hypothesis: Application of the Li criterion

We substantially apply the Li criterion for the Riemann hypothesis to hold. Based upon a series representation for the sequence \{\lambda_k\}, which are certain logarithmic derivatives of the Riemann xi function evaluated at unity, we determine new bounds for relevant Riemann zeta function sums and the sequence itself. We find that the Riemann hypothesis holds if certain conjectured properties of a sequence \eta_j are valid. The constants \eta_j enter the Laurent expansion of the logarithmic derivative of the zeta function about s=1 and appear to have remarkable characteristics. {\em On our conjecture}, not only does the Riemann hypothesis follow, but an inequality governing the values \lambda_n and inequalities for the sums of reciprocal powers of the nontrivial zeros of the zeta function.Comment: to appear in Math. Physics, Analysis and Geometry; 1 figur

Structure of an essential bacterial protein YeaZ (TM0874) from Thermotoga maritima at 2.5 Å resolution

The crystal structure of an essential bacterial protein, YeaZ, from T. maritima identifies an interface that potentially mediates protein–protein interaction