Towards computational Morse-Floer homology: forcing results for connecting orbits by computing relative indices of critical points

To make progress towards better computability of Morse-Floer homology, and thus enhance the applicability of Floer theory, it is essential to have tools to determine the relative index of equilibria. Since even the existence of nontrivial stationary points is often difficult to accomplish, extracting their index information is usually out of reach. In this paper we establish a computer-assisted proof approach to determining relative indices of stationary states. We introduce the general framework and then focus on three example problems described by partial differential equations to show how these ideas work in practice. Based on a rigorous implementation, with accompanying code made available, we determine the relative indices of many stationary points. Moreover, we show how forcing results can be then used to prove theorems about connecting orbits and traveling waves in partial differential equations.Comment: 30 pages, 4 figures. Revised accepted versio

Parallel Sparse LU Decomposition on a Mesh Network of Transputers

A parallel algorithm is presented for the LU decomposition of a general sparse matrix on a distributed-memory MIMD multiprocessor with a square mesh communication network. In the algorithm, matrix elements are assigned to processors according to the grid distribution. Each processor represents the nonzero elements of its part of the matrix by a local, ordered, two-dimensional linked-list data structure. The complexity of important operations on this data structure and on several others is analysed. At each step of the algorithm, a parallel search for a set of m compatible pivot elements is performed. The Markowitz counts of the pivot elements are close to minimum, to preserve the sparsity of the matrix. The pivot elements also satisfy a threshold criterion, to ensure numerical stability. The compatibility of the m pivots enables the simultaneous elimination of m pivot rows and m pivot columns in a rank-m update of the reduced matrix. Experimental results on a network of 400 transputers are presented for a set of test matrices from the Harwell–Boeing sparse matrix collection

Alpha-gliadin genes from the A, B, and D genomes of wheat contain different sets of celiac disease epitopes

BACKGROUND: Bread wheat (Triticum aestivum) is an important staple food. However, wheat gluten proteins cause celiac disease (CD) in 0.5 to 1% of the general population. Among these proteins, the α-gliadins contain several peptides that are associated to the disease. RESULTS: We obtained 230 distinct α-gliadin gene sequences from severaldiploid wheat species representing the ancestral A, B, and D genomes of the hexaploid bread wheat. The large majority of these sequences (87%) contained an internal stop codon. All α-gliadin sequences could be distinguished according to the genome of origin on the basis of sequence similarity, of the average length of the polyglutamine repeats, and of the differences in the presence of four peptides that have been identified as T cell stimulatory epitopes in CD patients through binding to HLA-DQ2/8. By sequence similarity, α-gliadins from the public database of hexaploid T. aestivum could be assigned directly to chromosome 6A, 6B, or 6D. T. monococcum (A genome) sequences, as well as those from chromosome 6A of bread wheat, almost invariably contained epitope glia-α9 and glia-α20, but never the intact epitopes glia-α and glia-α2. A number of sequences from T. speltoides, as well as a number of sequences fromchromosome 6B of bread wheat, did not contain any of the four T cell epitopes screened for. The sequences from T. tauschii (D genome), as well as those from chromosome 6D of bread wheat, were found to contain all of these T cell epitopes in variable combinations per gene. The differences in epitope composition resulted mainly from point mutations. These substitutions appeared to be genome specific. CONCLUSION: Our analysis shows that α-gliadin sequences from the three genomes of bread wheat form distinct groups. The four known T cell stimulatory epitopes are distributed non-randomly across the sequences, indicating that the three genomes contribute differently to epitope content. A systematic analysis of all known epitopes in gliadins and glutenins will lead to better understanding of the differences in toxicity among wheat varieties. On the basis of such insight, breeding strategies can be designed to generate less toxic varieties of wheat which may be tolerated by at least part of the CD patient population

Non Existence Theorems for Systems of Quasilinear Partial Differential Equations

this paper we shall investigate the non existence of ground states of quasilinear systems of the for

DAVINC3I : Towards Collaborative Responsive Logistics Networks in Floriculture

Today most flowers physically pass through the Dutch auction houses on their fixed routes from growers located all over the world to European customers. Physical presence is necessary to allow for inspection, quality control and break-bulk activities. Several developments, such as increased internationalization and virtualization, stimulate the sector to develop an efficient European hub distribution network, in which cut flowers, plants and other products are delivered to detail, retail and e-tail (i.e. webshop) customers using different logistics concepts. The DaVinc3i project has had the objective to strengthen the international leading competitive position of the Dutch horticulture sector in a global, virtualized trade network by researching the opportunities for new logistics coordination, consolidation and collaboration concepts in extended international trade park networks. In the last years over 30 case studies with business partners have been conducted within the DaVinc3i project. In this chapter we highlight the main research advances and lessons learned when moving towards collaborative responsive logistics network designs for perishables, illustrated with five case studies

Parallel Sparse LU Decomposition on a Mesh Network of Transputers

A parallel algorithm is presented for the LU decomposition of a general sparse matrix on a distributed-memory MIMD multiprocessor with a square mesh communication network. In the algorithm, matrix elements are assigned to processors according to the grid distribution. Each processor represents the nonzero elements of its part of the matrix by a local, ordered, two-dimensional linked-list data structure. The complexity of important operations on this data structure and on several others is analysed. At each step of the algorithm, a parallel search for a set of m compatible pivot elements is performed. The Markowitz counts of the pivot elements are close to minimum, to preserve the sparsity of the matrix. The pivot elements also satisfy a threshold criterion, to ensure numerical stability. The compatibility of the m pivots enables the simultaneous elimination of m pivot rows and m pivot columns in a rank-m update of the reduced matrix. Experimental results on a network of 400 transputers are presented for a set of test matrices from the Harwell–Boeing sparse matrix collection

Towards a close computed tomography monitoring approach for screen detected subsolid pulmonary nodules?

Pulmonary subsolid nodules (SSNs) have a high likelihood of malignancy, but are often indolent. A conservative treatment approach may therefore be suitable. The aim of the current study was to evaluate whether close follow-up of SSNs with computed tomography may be a safe approach. The study population consisted of participants of the Dutch-Belgian lung cancer screening trial (Nederlands Leuvens Longkanker Screenings Onderzoek; NELSON). All SSNs detected during the trial were included in this analysis. Retrospectively, all persistent SSNs and SSNs that were resected after first detection were segmented using dedicated software, and maximum diameter, volume and mass were measured. Mass doubling time (MDT) was calculated. In total 7135 volunteers were included in the current analysis. 264 (3.3%) SSNs in 234 participants were detected during the trial. 147 (63%) of these SSNs in 126 participants disappeared at follow-up, leaving 117 persistent or directly resected SSNs in 108 (1.5%) participants available for analysis. The median follow-up time was 95 months (range 20-110 months). 33 (28%) SSNs were resected and 28 of those were (pre-) invasive. None of the non-resected SSNs progressed into a clinically relevant malignancy. Persistent SSNs rarely developed into clinically manifest malignancies unexpectedly. Close follow-up with computed tomography may be a safe option to monitor changes