Identities in twisted Brauer monoids

We show that it is co-NP-hard to check whether a given semigroup identity holds in the twisted Brauer monoid $\mathcal{B}^\tau_n$ with $n\ge5$.Comment: 20 pages, 5 figures. In v2, several typos and inaccuracies are corrected, and a few suggestions by the anonymous referee are implemente

Digitalization of the agro-industrial complex in the Russian Federation: Current status and development prospects

The article is concerned with the current state of digitalisation of the agro-industrial complex (AIC) in the Russian Federation. It lists a number of legal instruments that have been approved by the legislative authorities and establish the digitalisation trends of the agro-industrial complex at the federal and regional level

Does Banque de France control inflation and unemployment?

We re-estimate statistical properties and predictive power of a set of Phillips curves, which are expressed as linear and lagged relationships between the rates of inflation, unemployment, and change in labour force. For France, several relationships were estimated eight years ago. The change rate of labour force was used as a driving force of inflation and unemployment within the Phillips curve framework. The set of nested models starts with a simplistic version without autoregressive terms and one lagged term of explanatory variable. The lag is determined empirically together with all coefficients. The model is estimated using the Boundary Element Method (BEM) with the least squares method applied to the integral solutions of the differential equations. All models include one structural break might be associated with revisions to definitions and measurement procedures in the 1980s and 1990s as well as with the change in monetary policy in 1994-1995. For the GDP deflator, our original model provided a root mean squared forecast error (RMSFE) of 1.0% per year at a four-year horizon for the period between 1971 and 2004. The rate of CPI inflation is predicted with RMSFE=1.5% per year. For the naive (no change) forecast, RMSFE at the same time horizon is 2.95% and 3.3% per year, respectively. Our model outperforms the naive one by a factor of 2 to 3. The relationships for inflation were successfully tested for cointegration. We have formally estimated several vector error correction (VEC) models for two measures of inflation. At a four year horizon, the estimated VECMs provide significant statistical improvements on the results obtained by the BEM: RMSFE=0.8% per year for the GDP deflator and ~1.2% per year for CPI. For a two year horizon, the VECMs improve RMSFEs by a factor of 2, with the smallest RMSFE=0.5% per year for the GDP deflator.Comment: 25 pages, 12 figure

Basin-scale approach to integration of agro- and hydrogeological monitoring for sustainable environmental management: a case study of Belgorod oblast, European Russia

Some integrated indicators of agroecological (on the watershed surface) and hydroecological (in river water flow) monitoring are proposed to improve basin environmental management projects. Six-year monitoring showed the effectiveness of water quality control measures on an example of a decrease in the concentrations of five major pollutants in river water

A mutational analysis of the globotriaosylceramide-binding sites of verotoxin VT1.

Escherichia coli verotoxin, also known as Shiga-like toxin, binds to eukaryotic cell membranes via the glycolipid Gb(3) receptors which present the P(k) trisaccharide Galalpha(1-4)Galbeta(1-4)Glcbeta. Crystallographic studies have identified three P(k) trisaccharide (P(k)-glycoside) binding sites per verotoxin 1B subunit (VT1B) monomer while NMR studies have identified binding of P(k)-glycoside only at site 2. To understand the basis for this difference, we studied binding of wild type VT1B and VT1B mutants, defective at one or more of the three sites, to P(k)-glycoside and pentavalent P(k) trisaccharide (pentaSTARFISH) in solution and Gb(3) presented on liposomal membranes using surface plasmon resonance. Site 2 was the key site in terms of free trisaccharide binding since mutants altered at sites 1 and 3 bound this ligand with wild type affinity. However, effective binding of the pentaSTARFISH molecule also required a functional site 3, suggesting that site 3 promotes pentavalent binding of linked trisaccharides at site 1 and site 2. Optimal binding to membrane-associated Gb(3) involved all three sites. Binding of all single site mutants to liposomal Gb(3) was weaker than wild type VT1B binding. Site 3 mutants behaved as if they had reduced ability to enter into high avidity interactions with Gb(3) in the membrane context. Double mutants at site 1/site 3 and site 2/site 3 were completely inactive in terms of binding to liposomal Gb(3,) even though the site 1/site 3 mutant bound trisaccharide with almost wild type affinity. Thus site 2 alone is not sufficient to confer high avidity binding to membrane-localized Gb(3). Cytotoxic activity paralleled membrane glycolipid binding. Our data show that the interaction of verotoxin with the Gb(3) trisaccharide is highly context dependent and that a membrane environment is required for biologically relevant studies of the interaction