Generic Arrangements Research Articles

SPIDERweb: a neural network approach to spectral phase interferometry

Reliably characterized pulses are the starting point of any application of ultrafast techniques. Unfortunately, experimental constraints do not always allow for optimizing the characterization conditions. This dictates the need for refined analysis methods. Here we show that neural networks can provide a viable characterization when applied to data from interferometry for direct electric-field reconstruction (SPIDER). We have adopted a cascade of convolutional networks, addressing the multiparameter structure of the interferogram with a reasonable computing power. In particular, the necessity of precalibration is reduced, thus pointing toward the introduction of neural networks in more generic arrangements.

PLMP - Point-Line Minimal Problems in Complete Multi-View Visibility.

We present a complete classification of all minimal problems for generic arrangements of points and lines completely observed by calibrated perspective cameras. We show that there are only 30 minimal problems in total, no problems exist for more than 6 cameras, for more than 5 points, and for more than 6 lines. We present a sequence of tests for detecting minimality starting with counting degrees of freedom and ending with full symbolic and numeric verification of representative examples. For all minimal problems discovered, we present their algebraic degrees, i.e.the number of solutions, which measure their intrinsic difficulty. It shows how exactly the difficulty of problems grows with the number of views. Importantly, several new minimal problems have small degrees that might be practical in image matching and 3D reconstruction.

Evolutionary Algorithms for Multi‐Center Solutions

AbstractLarge classes of multi‐center supergravity solutions have been constructed in the study of supersymmetric black holes and their microstates. Many smooth multi‐center solutions have the same charges as supersymmetric black holes, with all centers deep inside a long black‐hole‐like throat. These configurations are constrained by regularity, absence of closed timelike curves, and charge quantization. Due to these constraints, constructing explicit solutions with several centers in generic arrangements, and with all parameters in physically relevant ranges, is a hard task. In this work, an optimization algorithm, based on evolutionary algorithms and Bayesian optimization is presented, that systematically constructs numerical solutions satisfying all constraints. Explicit examples of novel five‐center and seven‐center machine‐precision solutions are exhibited.

The mitogenomes of Leptographium aureum, Leptographium sp., and Grosmannia fruticeta: expansion by introns.

Many members of the Ophiostomatales are of economic importance as they are bark-beetle associates and causative agents for blue stain on timber and in some instances contribute towards tree mortality. The taxonomy of these fungi has been challenging due to the convergent evolution of many traits associated with insect dispersal and a limited number of morphological characters that happen to be highly pleomorphic. This study examines the mitochondrial genomes for three members of Leptographium sensu lato [Leptographium aureum (also known as Grosmannia aurea), Grosmannia fruticeta (also known as Leptographium fruticetum), and Leptographium sp. WIN(M)1376)]. Illumina sequencing combined with gene and intron annotations and phylogenetic analysis were performed. Sequence analysis showed that gene content and gene synteny are conserved but mitochondrial genome sizes were variable: G. fruticeta at 63,821 bp, Leptographium sp. WIN(M)1376 at 81,823 bp and L. aureum at 104,547 bp. The variation in size is due to the number of introns and intron-associated open reading frames. Phylogenetic analysis of currently available mitochondrial genomes for members of the Ophiostomatales supports currently accepted generic arrangements within this order and specifically supports the separation of members with Leptographium-like conidiophores into two genera, with L. aureum grouping with Leptographium and G. fruticeta aligning with Grosmannia. Mitochondrial genomes are promising sequences for resolving evolutionary relationships within the Ophiostomatales.

A Note on Bernstein–Sato Varieties for Tame Divisors and Arrangements

For strongly Euler-homogeneous, Saito-holonomic, and tame analytic germs, we consider general types of multivariate Bernstein–Sato ideals associated to arbitrary factorizations of our germ. We show that these ideals are principal, and the zero loci associated to different factorizations are related by a diagonal property. If, additionally, the divisor is a hyperplane arrangement, we obtain nice estimates for the zero locus of its Bernstein–Sato ideal for arbitrary factorizations and show that the Bernstein–Sato ideal attached to a factorization into linear forms is reduced. As an application, we independently verify and improve upon an estimate of Maisonobe regarding standard Bernstein–Sato ideals for reduced, generic arrangements: we compute the Bernstein–Sato ideal for a factorization into linear forms, and we compute its zero locus for other factorizations.

The missing piece of the puzzle: larval morphology of Xenohyla truncata (Anura: Hylidae: Dendropsophini) and its implication to the evolution of Dendropsophini tadpoles

Dendropsophini is a highly diverse clade with a controversial phylogenetic and taxonomic history. Different generic arrangements have been proposed and the monophyly of several clades supported or rejected. Previous evidence suggested that larval morphology could play an important role in our understanding of the evolution and diversification of Dendropsophini, although data are missing for most lineages, including the sister group of Dendropsophus, Xenohyla. Herein we describe the internal morphology of the tadpoles of X. truncata and compare our results with available information for members of Dendropsophini and closely related lineages. We propose that the presence of a fan-like papilla in the buccopharyngeal cavity, a single element suprarostral, and a triangular process at the base of the muscular process are synapomorphies for Dendropsophini; moreover, the presence of a divided m. subarcualis rectus II–IV seems to be a synapomorphy for Pseudini and, the nasal sac insertion of the m. levator lateralis could be a synapomorphy of Dendropsophini + Pseudini.

Immature stages and new host plant records for four satyrine species feeding on herbaceous bamboos in southeastern Peru (Lepidoptera: Nymphalidae: Satyrinae: Satyrini).

We here document the immature stages of three euptychiine butterflies, Nhambikuara mima (Butler, 1867), Splendeuptychia furina (Hewitson, 1862), and Paryphthimoides brixius (Godart, [1824]), all found feeding on a species of herbaceous bamboo, Taquara micrantha (Kunth) I.L.C.Oliveira R.P.Oliveira (Poaceae: Bambusoideae: Olyreae) in Madre de Dios, Peru. This study is the first to report the life history of these three taxa with their natural host plant. We provide illustrations of immatures, head capsules, and the host plant for each of these three species. The immature morphology of these taxa supports recent generic arrangements of these three species in comparison with their close relatives, namely Splendeuptychia furina to Nhambikuara mima and Paryphthimoides brixius to Paryphthimoides terrestris (Butler, 1867), a species documented in our successive study. Thus, the present study includes taxonomic implications based on immature stages by discovering putative synapomorphic characters of larvae and pupae. These pairs of closely related species occur in micro-sympatry at the study site in southeastern Peru, and our observations possibly suggest niche partitioning between sibling species. Additionally, we report two herbaceous bamboo species, Olyra latifolia L. and Taquara micrantha (Kunth) I.L.C.Oliveira R.P.Oliveira as the first known natural host plants for Magneuptychia harpyia (C. Felder R. Felder, 1867).

Filling the gaps: The mitogenomes of Afrotropical egg-guarding frogs based on historical type material and a re-assessment of the nomenclatural status of Alexteroon Perret, 1988 (Hyperoliidae)

The African reedfrog taxon Alexteroon consists of only three described species with rather restricted geographical ranges. Although the assignment to a distinct genus is supported by multiple evidence, its position within the larger African hyperoliid radiation has been disputed. Available molecular data are scarce and the geographic records are few and scattered. The partially formalin fixed type series were previously not accessible to molecular analyses. This changed only very recently with the advancement of Next Generation Sequencing and ancient DNA techniques. Here we provide a reassessment of the current distribution and identity of all known species in this taxon based on (a) historical and new records, (b) morphological reanalyses of the type material and newly collected specimens from Angola and Gabon, and (c) newly established, nearly complete mitochondrial genome data from historical type and modern non-type material. We also present a molecular phylogeny (five mitochondrial loci 12S, 16S, ND1, ND2, COI, Cytb) for 78 sequences from 75 different species of Hyperolius retrieved from GenBank and 14 newly established Alexteroon sequences. We demonstrate that Alexteroon is more widely distributed than previously thought with records from northern Angola representing major southern range extensions. Results of the quantitative morphometric analyses show that the group has a rather conserved general body plan. Therefore qualitative phenotypic features observable in live specimens appear to be more useful for ad hoc species delimitation. We found Alexteroon to be nested within Hyperolius, corroborating previous findings. However, the combination of molecular data and consistent differences observed in morphology and ecology provide strong support for the distinctiveness of this evolutionary lineage within Hyperolius sensu lato. We therefore treat Alexteroon as a subgenus of Hyperolius and argue that the large and diverse genus Hyperolius is in need of revision that may result in new generic arrangements.

Discriminantal arrangement, 3 × 3 minors of Plücker matrix and hypersurfaces in Grassmannian Gr(3,n)

We show that points in specific degree-2 hypersurfaces in the Grassmannian Gr(3,n) correspond to generic arrangements of n hyperplanes in C3 with associated discriminantal arrangement having intersections of multiplicity three in codimension two.

Female reproductive system of the tribe Galeritini (Coleoptera: Carabidae): structural features and evolution

ABSTRACT The female internal reproductive tract characters of the dryptite tribes Zuphiini, Dryptini and Galeritini (Coleoptera: Carabidae: Harpalinae) provide features useful for distinguishing taxa at various hierarchical levels. The details, in aggregate, support the generally accepted generic arrangements within the Dryptini and Galeritini. But within the genus Galerita Fabricius, characters of the genitalia support transfer of Galerita sulcipennis Reichardt from the nominotypical subgenus to subgenus Progaleritina Jeannel (new taxonomic placement). Within subgenus Galerita, the Eastern Hemisphere (Old World) taxa are better placed taxonomically in the perrieri species complex separate from the americana species complex of the Western Hemisphere. The striking loss of the digitate spermatheca 1 and its replacement with an independently derived large sac-like spermatheca 2 occurs within the basal genus Planetes Macleay (subtribe Planetina) and independently in the subtribe Galeritina (including Eunostus...

Conflicting molecular and morphological evidence of evolution within the Bryaceae (Bryopsida) and its implications for generic taxonomy

Phylogenetic analyses within the Bryaceae were performed based on DNA sequence data from three chloroplast genomic regions. Special emphasis was placed on sampling the small tuber-bearing species of Bryum ('Erythrocarpa') from Europe and those with axillary bulbils (B. dichotomum group). Multiple exemplars were studied for most of the species investigated. As in previous studies, the results demonstrate a pattern of evolutionary diversification that differs widely from that implied by traditional generic and subgeneric classifications. More recent generic arrangements based exclusively on morphological characters are also shown to seriously misrepresent phylogeny because of convergent evolution of morphology. Among the 'Erythrocarpa', for instance, the superficially similar B. rubens and B. subapiculatum emerge as only distant relatives, the former being close to B. capillare (treated in Ptychostomum here) whereas the latter is close to B. alpinum (placed in Imbribryum here). Likewise, using only morphological characters, B. dunense and B. versicolor [Bryum s.s.] may both be almost indistinguishable from some specimens of B. caespiticium [Ptychostomum]. On the other hand, rapid differentiation of morphology has occurred within some clades, notably of 'Plagiobryum' zieri from within Ptychostomum. Thus the argument is reiterated that 'classification of the Bryaceae based on morphological characters alone cannot be defended', since it leads to classifications which are incongruent with phylogeny and do not take account of all available information. Hence a generic classification is proposed here containing mainly those Bryaceae for which molecular data are available. Several nomenclatural questions that arise from this are resolved.

Logarithmic sheaves attached to arrangements of hyperplanes

A reduced divisor on a nonsingular variety defines the sheaf of logarithmic 1-forms. We introduce a certain coherent sheaf whose double dual coincides with this sheaf. It has some nice properties, for example, the residue exact sequence still holds even when the divisor is singular, and also it has a simple locally free resolution. We specialize to the case when the divisor is an arrangement of hyperplanes in projective space, and relate the properties of stability of the sheaf with the combinatorics of the arrangement. We also extend a Torelli type theorem to non generic arrangements which allows one to reconstruct an arrangement from the sheaf attached to it.

Optimal Intron Analyses in the Trimeresurus Radiation of Asian Pitvipers

Nuclear introns are commonly used as phylogenetic markers, but a number of issues related to alignment strategies, indel treatments, and the incorporation of length-variant heterozygotes (LVHs) are not routinely addressed when generating phylogenetic hypotheses. Topological congruence in relation to an extensive mitochondrial DNA multigene phylogeny (derived from 2,423 bp of 12S, 16S, ND4, and CYTB genes) of the Asian pitviper Trimeresurus radiation was used to compare combinations of "by eye" and edited and unedited ClustalX 1.8 alignments of two nuclear introns. Indels were treated as missing data, fifth character states, and assigned simple and multistate codes. Upon recovery of the optimal alignment and indel treatment strategy, a total evidence approach was used to investigate the phylogenetic utility of the indels and test new generic arrangements within Trimeresurus. Approximately one third of the intron data partitions exhibited LVHs, suggesting that they are common in introns. Furthermore, a simple concatenation approach can facilitate the incorporation of LVHs into phylogenetic analyses to make use of all available data and investigate mechanisms of molecular evolution. Analyses of ClustalX 1.8-assisted alignments were generally more congruent than the "by eye" alignment and the analysis of a simple coded, edited ClustalX 1.8 (gap opening cost 5, gap extension cost 1) alignment revealed the most congruent tree. The total evidence approach supported the new arrangements within Trimeresurus, suggesting that the phylogeny should be considered as a working benchmark in Asian pitviper systematics. Finally, a critical appraisal of the diverse array of indels (56 to 57 per intron, ranging from 1 to 151 bp in length) suggested that they are a combination of Hennigian and homoplasious events unrelated to indel size or location within the intron. [Alignment; indels; intron analysis; length-variant heterozygotes; Trimeresurus.].

Studying the deformation of arachnid slit sensilla by a fracture mechanical approach

Slit sensilla are sensory organs which measure strains in the exoskeleton of arachnids. They occur as isolated slits, in loose groups and in close parallel arrangements known as lyriform organs or compound slit sensilla. The deformations of the slits’ faces induced by far-field strains acting on groups of slits are studied using Kachanov's analytical approximations for the opening displacements of cracks, a method developed within the framework of fracture mechanics. The accuracy of the approach is assessed by comparisons with results obtained by finite element analysis. The limits of its applicability to slit sensilla are found to be reached when the lateral spacing between interacting slits is less than half their length, i.e., the method is suitable for studying single slits and loose groups but not lyriform organs. The influence of a number of geometrical parameters of slit sensilla on the deformation patterns of the faces of parallel slits in generic arrangements is studied, viz., spacing between slits, longitudinal shifts between slits, and slit length. The results are presented as opening distances along the length of the cracks and in terms of normalized diagrams that relate the opening distances at mid-length of the slits to the geometrical parameters. In addition, Kachanov's method is used to find a set of slit lengths that give rise to prescribed opening distances.

SUBSPACE ARRANGEMENTS DEFINED BY PRODUCTS OF LINEAR FORMS

The vanishing ideal of an arrangement of linear subspaces in a vector space is considered, and the paper investigates when this ideal can be generated by products of linear forms. A combinatorial construction (blocker duality) is introduced which yields such generators in cases with a great deal of combinatorial structure, and examples are presented that inspired the work. A construction is given which produces all elements of this type in the vanishing ideal of the arrangement. This leads to an algorithm for deciding if the ideal is generated by products of linear forms. Generic arrangements of points in P2 and lines in P3 are also considered.

Higher Homotopy Groups of Complements of Complex Hyperplane Arrangements

We generalize results of Hattori on the topology of complements of hyperplane arrangements, from the class of generic arrangements, to the much broader class of hypersolvable arrangements. We show that the higher homotopy groups of the complement vanish in a certain combinatorially determined range, and we give an explicit Zπ1-module presentation of πp, the first non-vanishing higher homotopy group. We also give a combinatorial formula for the π1-coinvariants of πp. For affine line arrangements whose cones are hypersolvable, we provide a minimal resolution of π2 and study some of the properties of this module. For graphic arrangements associated to graphs with no 3-cycles, the algorithm for computing π2 is purely combinatorial. The Fitting varieties associated to π2 may distinguish the homotopy 2-types of arrangement complements with the same π1, and the same Betti numbers in low degrees.

The Module of Logarithmic p-Forms of a Locally Free Arrangement

For an essential, central hyperplane arrangement A⊆V≃kn+1 we show that Ω1(A) (the module of logarithmic one forms with poles along A) gives rise to a locally free sheaf on Pn if and only if, for all X∈LA with rank X<dimV, the module Ω1(AX) is free. Motivated by a result of L. Solomon and H. Terao (1987, Adv. Math.64, 305–325), we give a formula for the Chern polynomial of a bundle E on Pn in terms of the Hilbert series of ⊕m∈ZH0(Pn,∧iE(m)). As a corollary, we prove that if the sheaf associated to Ω1(A) is locally free, then π(A,t) is essentially the Chern polynomial. If Ω1(A) has projective dimension one and is locally free, we give a minimal free resolution for Ωp and show that ΛpΩ1(A)≃Ωp(A), generalizing results of L. Rose and H. Terao (1991, J. Algebra136, 376–400) on generic arrangements.

Moiré strain analysis: An introduction, review and critique, including related techniques and future potential

The moire fringe method is described and reviewed with particular reference to its application in strain analysis. The theory is briefly dealt with, followed by a discussion of the common methods used to analyse the information that the fringes contain and then certain non-obvious limitations are discussed. The generic grid-preparation techniques and optical arrangements are described. Moire interferometry is dealt with at some greater length, and questions that are frequently raised concerning moire in comparison to somewhat similar methods are addressed. Specific difficulties are indicated and the work concludes with a consideration of some recent work that may influence future developments of the method. Of necessity, there is much reliance on reference to quoted works.

De Rham cohomology of logarithmic forms on arrangements of hyperplanes

The paper is devoted to computation of the cohomology of the complex of logarithmic differential forms with coefficients in rational functions whose poles are located on the union of several hyperplanes of a linear space over a field of characteristic zero. The main result asserts that for a vast class of hyperplane arrangements, including all free and generic arrangements, the cohomology algebra coincides with the Orlik-Solomon algebra. Over the field of complex numbers, this means that the cohomologies coincide with the cohomologies of the complement of the union of the hyperplanes. We also prove that the cohomologies do not change if poles of arbitrary multiplicity are allowed on some of the hyperplanes. In particular, this gives an analogue of the algebraic de Rham theorem for an arbitrary arrangement over an arbitrary field of zero characteristic.

A free resolution of the module of derivations for generic arrangements

Let Y be an I-dimensional vector space over an arbitrary field F and d an arrangement of n hyperplanes H,, . . . . i7,, in V. We always assume that n > I > 1. For each i, 1~ id ~1, we fix once and forever aj E V* such that ker(cl,) = Hi. The arrangement d is generic if its every I elements intersect only at 0 or equivalently every I functionals ai are linearly independent in V*. Let S be the symmetric algebra of V* and Der(S) = Der,(S, S) the S-module of derivations of S. The following graded S-module was introduced by H. Terao [4] and studied in many papers on arrangements: D = D(d) = (0 E Der(S) ( f3(ai) E Sa,, i= 1, . . . . n}. At the NSF-CBMS conference on “Arrangements of Hyperplanes” in 1988 the author conjectured that for a generic arrangement with II > 1 we have hd, D = 1 2. Soon after that L. Rose and H. Terao [2] proved this conjecture. Moreover they constructed minimal free resolutions of all modules of logarithmic forms with poles along d and used the fact that D is isomorphic to one of them. The aim of the present paper is to give another somewhat more straightforward construction of a minimal free resolution of D. More precisely we put Do= D,(d)= (BEDJO =O) and note that D= Does MO, where t$, is the Euler derivation defined by &,(a) = CI for every CI E V*. Then we construct a minimal free resolution of Do which of course has the same length as a minimal free resolution of D. The notation introduced above is used throughout the paper. Besides we denote by L the intersection lattice of & (including V as the unique minimal element of L), put Li=(X~L/dimX=i}, and for every XEL put cQzx= (Xn HiI X$ Hi}, viewing it as an arrangement in X Also for every XEL we put L~‘={YEL~(YcX), L,=(YEL(XC Y>, and a(X)=