Multi-Degrees in Polynomial Optimization

We study structured optimization problems with polynomial objective function and polynomial equality constraints. The structure comes from a multi-grading on the polynomial ring in several variables. For fixed multi-degrees we determine the generic number of complex critical points. This serves as a measure for the algebraic complexity of the optimization problem. We also discuss computation and certification methods coming from numerical nonlinear algebra

Tropical Implicitization Revisited

Tropical implicitization means computing the tropicalization of a unirational variety from its parametrization. In the case of a hypersurface, this amounts to finding the Newton polytope of the implicit equation, without computing its coefficients. We present a new implementation of this procedure in Oscar.jl. It solves challenging instances, and can be used for classical implicitization as well. We also develop implicitization in higher codimension via Chow forms, and we pose several open questions.Comment: 18 pages, 3 figure

The algebraic degree of sparse polynomial optimization

In this paper we study a broad class of polynomial optimization problems whose constraints and objective functions exhibit sparsity patterns. We give two characterizations of the number of critical points to these problems, one as a mixed volume and one as an intersection product on a toric variety. As a corollary, we obtain a convex geometric interpretation of polar degrees, a classical invariant of algebraic varieties as well as Euclidean distance degrees. Furthermore, we prove BKK generality of Lagrange systems in many instances. Motivated by our result expressing the algebraic degree of sparse polynomial optimisation problems via Porteus' formula, in the appendix we answer a related question concerning the degree of sparse determinantal varieties.Comment: 29 page

Yield and Quality in Purple-Grained Wheat Isogenic Lines

Breeding programs for purple wheat are underway in many countries but there is a lack of information on the effects of Pp (purple pericarp) genes on agronomic and quality traits in variable environments and along the product chain (grain-flour-bread). This study was based on unique material: two pairs of isogenic lines in a spring wheat cv. Saratovskaya-29 (S29) background differing only in Pp genes and grain color. In 2017, seven experiments were conducted in Kazakhstan, Russia, and Turkey with a focus on genotype and environment interaction and, in 2018, one experiment in Turkey with a focus on grain, flour, and bread quality. The eect of environment was greater compared to genotype for the productivity and quality traits studied. Nevertheless, several important traits, such as grain color and anthocyanin content, are closely controlled by genotype, offering the opportunity for selection. Phenolic content in purple-grained lines was not significantly higher in whole wheat flour than in red-colored lines. However, this trait was significantly higher in bread. For antioxidant activities, no differences between the genotypes were detected in both experiments. Comparison of two sources of Pp genes demonstrated that the lines originating from cv. Purple Feed had substantially improved productivity and quality traits compared to those from cv. Purple

Lines on pp-adic and real cubic surfaces

We study lines on smooth cubic surfaces over the field of $p$-adic numbers, from a theoretical and computational point of view. Segre showed that the possible counts of such lines are $0,1,2,3,5,7,9,15$ or $27$. We show that each of these counts is achieved. Probabilistic aspects are also investigated by sampling both $p$-adic and real cubic surfaces from different distributions and estimating the probability of each count. We link this to recent results on probabilistic enumerative geometry. Some experimental results on the Galois groups attached to $p$-adic cubic surfaces are also discussed.Comment: 9 pages, 1 figur

Pertussis Circulation Has Increased T-Cell Immunity during Childhood More than a Second Acellular Booster Vaccination in Dutch Children 9 Years of Age

<div><p>Here we report the first evaluation of T-cell responses upon a second acellular pertussis booster vaccination in Dutch children at 9 years of age, 5 years after a preschool booster vaccination. Blood samples of children 9 years of age were studied longitudinally until 1 year after the second aP booster and compared with those after the first aP booster in children 4 and 6 years of age from a cross-sectional study. After stimulation with pertussis-vaccine antigens, Th1, Th2 and Th17 cytokine responses were measured and effector memory cells (CCR7-CD45RA-) were characterized by 8-colour FACS analysis. The second aP booster vaccination at pre-adolescent age in wP primed individuals did increase pertussis-specific Th1 and Th2 cytokine responses. Noticeably, almost all T-cell responses had increased with age and were already high before the booster vaccination at 9 years of age. The enhancement of T-cell immunity during the 5 year following the booster at 4 years of age is probably caused by natural boosting due to the a high circulation of pertussis. However, the incidence of pertussis is high in adolescents and adults who have only received the Dutch wP vaccine during infancy and no booster at 4 years of age. Therefore, an aP booster vaccination at adolescence or later in these populations might improve long-term immunity against pertussis and reduce the transmission to the vulnerable newborns.</p> <h3>Trial Registration</h3><p>Controlled-Trials.com <a href="http://www.controlled-trials.com/ISRCTN64117538/">ISRCTN64117538</a></p> </div

Differential T- and B-Cell Responses to Pertussis in Acellular Vaccine-Primed versus Whole-Cell Vaccine-Primed Children 2 Years after Preschool Acellular Booster Vaccination

<p>This study investigated long-term cellular and humoral immunity against pertussis after booster vaccination of 4-year-old children who had been vaccinated at 2, 3, 4, and 11 months of age with either whole-cell pertussis (wP) or acellular pertussis (aP) vaccine. Immune responses were evaluated until 2 years after the preschool booster aP vaccination. In a cross-sectional study (registered trial no. ISRCTN65428640), blood samples were taken from wP- and aP-primed children prebooster and 1 month and 2 years postbooster. Pertussis vaccine antigen-specific IgG levels, antibody avidities, and IgG subclasses, as well as T-cell cytokine levels, were measured by fluorescent bead-based multiplex immunoassays. The numbers of pertussis-specific memory B cells and gamma interferon (IFN-gamma)-producing T cells were quantified by enzyme-linked immunosorbent spot assays. Even 2 years after booster vaccination, memory B cells were still present and higher levels of pertussis-specific antibodies than prebooster were found in aP-primed children and, to a lesser degree, also in wP-primed children. The antibodies consisted mainly of the IgG1 subclass but also showed an increased IgG4 portion, primarily in the aP-primed children. The antibody avidity indices for pertussis toxin and pertactin in aP-primed children were already high prebooster and remained stable at 2 years, whereas those in wP-primed children increased. All measured prebooster T-cell responses in aP-primed children were already high and remained at similar levels or even decreased during the 2 years after booster vaccination, whereas those in wP-primed children increased. Since the Dutch wP vaccine has been replaced by aP vaccines, the induction of B-cell and T-cell memory immune responses has been enhanced, but antibody levels still wane after five aP vaccinations. Based on these long-term immune responses, the Dutch pertussis vaccination schedule can be optimized, and we discuss here several options.</p>