Four generated, squarefree, monomial ideals

Let $I\supsetneq J$ be two squarefree monomial ideals of a polynomial algebra over a field generated in degree $\geq d$, resp. $\geq d+1$ . Suppose that $I$ is either generated by three monomials of degrees $d$ and a set of monomials of degrees $\geq d+1$, or by four special monomials of degrees $d$. If the Stanley depth of $I/J$ is $\leq d+1$ then the usual depth of $I/J$ is $\leq d+1$ too.Comment: to appear in "Bridging Algebra, Geometry, and Topology", Editors Denis Ibadula, Willem Veys, Springer Proceed. in Math. and Statistics, 96, 201

Linear resolutions of powers and products

The goal of this paper is to present examples of families of homogeneous ideals in the polynomial ring over a field that satisfy the following condition: every product of ideals of the family has a linear free resolution. As we will see, this condition is strongly correlated to good primary decompositions of the products and good homological and arithmetical properties of the associated multi-Rees algebras. The following families will be discussed in detail: polymatroidal ideals, ideals generated by linear forms and Borel fixed ideals of maximal minors. The main tools are Gr\"obner bases and Sagbi deformation

State of Harmonization of 24 Serum Albumin Measurement Procedures and Implications for Medical Decisions

BACKGROUND: Measurements of serum and plasma albumin are widely used in medicine, including as indicators of quality of patient care in renal dialysis centers. METHODS: Pools were prepared from residual patient serum (n = 50) and heparin plasma (n = 48) from patients without renal disease, and serum from patients with kidney failure before hemodialysis (n = 53). Albumin was measured in all samples and in ERM-DA470k/IFCC reference material (RM) by 3 immunochemical, 9 bromcresol green (BCG), and 12 bromcresol purple (BCP) methods. RESULTS: Two of 3 immunochemical procedures, 5 of 9 BCG, and 10 of 12 BCP methods recovered the RM value within its uncertainty. One immunochemical and 3 BCG methods were biased vs the RM value. Random error components were small for all measurement procedures. The Tina-quant immunochemical method was chosen as the reference measurement procedure based on recovery and results of error analyses. Mean biases for BCG vs Tina-quant were 1.5% to 13.9% and were larger at lower albumin concentrations. BCP methods\u27 mean biases were -5.4% to 1.2% irrespective of albumin concentration. Biases for plasma samples were generally higher than for serum samples for all method types. For most measurement procedures, biases were lower for serum from patients on hemodialysis vs patients without kidney disease. CONCLUSIONS: Significant differences among immunochemical, BCG, and BCP methods compromise interpretation of serum. albumin results. Guidelines and calculations for clinical management of kidney and other diseases must consider the method used for albumin measurement until harmonization can be achieved

Sparsity of integer solutions in the average case

We examine how sparse feasible solutions of integer programs are, on average. Average case here means that we fix the constraint matrix and vary the right-hand side vectors. For a problem in standard form with m equations, there exist LP feasible solutions with at most m many nonzero entries. We show that under relatively mild assumptions, integer programs in standard form have feasible solutions with O(m) many nonzero entries, on average. Our proof uses ideas from the theory of groups, lattices, and Ehrhart polynomials. From our main theorem we obtain the best known upper bounds on the integer Carathéodory number provided that the determinants in the data are small

Fungi isolated from Miscanthus and sugarcane: biomass conversion, fungal enzymes, and hydrolysis of plant cell wall polymers.

BackgroundBiofuel use is one of many means of addressing global change caused by anthropogenic release of fossil fuel carbon dioxide into Earth's atmosphere. To make a meaningful reduction in fossil fuel use, bioethanol must be produced from the entire plant rather than only its starch or sugars. Enzymes produced by fungi constitute a significant percentage of the cost of bioethanol production from non-starch (i.e., lignocellulosic) components of energy crops and agricultural residues. We, and others, have reasoned that fungi that naturally deconstruct plant walls may provide the best enzymes for bioconversion of energy crops.ResultsPreviously, we have reported on the isolation of 106 fungi from decaying leaves of Miscanthus and sugarcane (Appl Environ Microbiol 77:5490-504, 2011). Here, we thoroughly analyze 30 of these fungi including those most often found on decaying leaves and stems of these plants, as well as four fungi chosen because they are well-studied for their plant cell wall deconstructing enzymes, for wood decay, or for genetic regulation of plant cell wall deconstruction. We extend our analysis to assess not only their ability over an 8-week period to bioconvert Miscanthus cell walls but also their ability to secrete total protein, to secrete enzymes with the activities of xylanases, exocellulases, endocellulases, and beta-glucosidases, and to remove specific parts of Miscanthus cell walls, that is, glucan, xylan, arabinan, and lignin.ConclusionThis study of fungi that bioconvert energy crops is significant because 30 fungi were studied, because the fungi were isolated from decaying energy grasses, because enzyme activity and removal of plant cell wall components were recorded in addition to biomass conversion, and because the study period was 2 months. Each of these factors make our study the most thorough to date, and we discovered fungi that are significantly superior on all counts to the most widely used, industrial bioconversion fungus, Trichoderma reesei. Many of the best fungi that we found are in taxonomic groups that have not been exploited for industrial bioconversion and the cultures are available from the Centraalbureau voor Schimmelcultures in Utrecht, Netherlands, for all to use

Fermat hypersurfaces and Subcanonical curves

We extend the classical Enriques-Petri Theorem to $s$-subcanonical projectively normal curves, proving that such a curve is $(s+2)$-gonal if and only if it is contained in a surface of minimal degree. Moreover, we show that any Fermat hypersurface of degree $s+2$ is apolar to an $s$-subcanonical $(s+2)$-gonal projectively normal curve, and vice versa.Comment: 18 pages; AMS-LaTe

The amalgamated duplication of a ring along a multiplicative-canonical ideal

After recalling briefly the main properties of the amalgamated duplication of a ring $R$ along an ideal $I$, denoted by R\JoinI, we restrict our attention to the study of the properties of R\JoinI, when $I$ is a multiplicative canonical ideal of $R$ \cite{hhp}. In particular, we study when every regular fractional ideal of $R\Join I$ is divisorial