A census of cubic fourfolds over 𝔽₂

In this article we give a systematic treatment of Newton polygons of exponential sums. The Newton polygon is a nice way to describe p-adic values of the zeroes or poles of zeta functions and L functions. Our main objective is to show that the Adolphson-Sperber conjecture 12], which asserts that under a simple condition the generic Newton polygon of L functions coincides with its lower bound, is false in its full form, but true in a slightly weaker form. We also show that the full form is true in various important special cases. For example, we show that for a generic projective hypersurface of degree d, the Newton polygon of the interesting part of the zeta function coincides with its lower bound (the Hodge polygon). This gives a p-adic proof of a recent theorem of Illusie, conjectured by Dwork and Mazur. For more examples, let us consider the family of affine hypersurfaces of degree d or the family of affine hypersurfaces defined by polynomials f(xi, . . ., x7n) of degree di with respect to xi (1 < i < n), where the di are fixed positive integers. Then, for all large prime numbers p, the generic Newton polygon for the zeta functions of each of the two families of hypersurfaces coincides with its lower bound. We obtain our main results, namely several decomposition theorems, using certain maximizing functions from linear programming. Our work suggests a possible connection between Newton polygons and the resolution of singularities of toric varieties. Let p be a prime, q = pa, and let Fq be the finite field of q elements and Fqm its extension of degree m. Fix a nontrivial additive character qP of Fp. For any Laurent polynomial f(xi, . . ., xn) E Fq[xl, xj1,.. . ., x, xi1] we form

In tropical regions, rampant land-use conversion for agriculture threatens biodiversity hotspots. Forests are vanishing, and taxonomic diversity is severely affected by the transformation on a large scale. For mitigating the impacts of these land-use changes and reconciling human needs with biological conservation, we require effective and standardized biodiversity monitoring methods. Along with the biodiversity decline, functional diversity is also believed to suffer great losses, affecting ecosystem functions and their resilience. This also poses the question how ecosystem services will be affected. Focusing on the province of Jambi in Sumatra, Indonesia, I present results from studies on aboveground biodiversity, concentrating on birds. I investigated four different land-use systems: lowland rainforest, jungle rubber, rubber monocultures, and oil palm monocultures. The performance of autonomous acoustic sampling of birds was compared with classical bird point counts using a systematic review and meta-analysis, as well as field data. For the first time, I present methods for measuring the sound detection space: the sampling area of acoustic recorders, an important pre-requisite of any diversity comparison. I then document the changes in diversity of birds associated with the conversion of forests to plantations, and show how bird communities and feeding guilds are affected. The functional dimension of these changes is expanded next, when we analyse the relationship between species richness and functional diversity, and subsequently analyse the change in ecological function of birds, arboreal ants, and leaf-litter invertebrates using single-trait and multi-trait indices. Finally I demonstrate the role of birds and bats, as well as ants, on ecosystem functions and yield in a long-term and large-scale full-factorial exclusion experiment situated in young oil palm plantations. My results show that autonomous sound recordings systems are at least equal to traditional avian survey methods, generating datasets of indistinguishable completeness. However, acoustic sampling is superior to bird point counts in many other ways, not the least a lack of observer bias and guaranteed verifiability of results. Importantly, I show that the sound detection space of sound recorders is measurable and has a strong impact on any measure of diversity obtained from acoustic data. Using traditional bird point counts, we also confirm previous research, presenting strong declines in bird diversity and large differences in their communities, which also impact feeding guilds differently in our two study regions. The more general study of bird, ant, and invertebrate function demonstrates that multi-trait indices can mask trends that are better assessed with single-trait indices. Nevertheless, species diversity was strongly correlated with functional diversity and their relationship indicated low functional redundancy, as well as a shift towards lower trophic levels for all taxa and towards more mobile species in birds and ants. Contrary to our expectations, these functional changes did not seem to affect ecosystem functions or oil palm yield in our exclusion experiment: we found that the bird and ant exclusion only affected arthropod predators, but left ecosystem functions and yield untouched. I recommend promoting the use of autonomous acoustic sampling methods for their many advantages over traditional survey methods based on human observation. These methods still need to be developed and standardized, and I provide first elements of response by deriving sound detection spaces of acoustic recorders. However overall, acoustic sampling bears strong potential and could become a method of choice for assessing multiple animal taxa with one tool. In the discussion I further show that results from acoustic data are equivalent to those obtained from point counts, confirming that the taxonomic biodiversity losses we observed are robust and real. We can assert that land-use conversion detrimentally affects frugivores, possibly also insectivores, and positively affects omnivores. Also, the low functional redundancy we observed across all taxa predicts dire consequences of biodiversity loss for ecosystem functioning and resilience. Although we could not demonstrate a positive role of birds and ants on oil palm, we believe the observed trends to be specific to the region, which still experiences very low pest damage. However, we need to link animals to their function more directly with individual-based dietary data, and straightforward measurements of birds’ ecosystem functions. We also call for examining animal movement more thoroughly to reveal the true picture of the functional transformation associated with land-use change.

We developed sampling methods to characterize the participation of bird species in foraging flocks led by the Eastern Tufted Titmouse (Baeolophus bicolor) in North-central Florida during winter, because standard field methods, developed primarily for permanent resident Neotropical flocks, were intractable in our system. During January–February 2004 and November 2004–March 2005, we observed 55 mixed-species flocks, recorded 40 potential flocking species [mean of 12.4 species (SD = 3.8; range 3–20), 26.3 individuals (SD = 12.2; range 8–60), and 3.1 titmice (SD = 1.4; range 1–7), per flock]. Twenty-six species were observed frequently enough (>10% of observations) to be included in analyses. We paired 60-min flock observations with 10-min point counts conducted in locations used by flocks, but after flocks had moved more than 100 m away. This method yielded a measure of flocking propensity: the ratio of the number of individuals observed in the flock versus during the point count for each species. We used regression tree (RT) analysis to classify species into groupings according to their levels of flock participation, and to investigate relationships between flocking propensity and various environmental and social factors that we measured. Our analysis identified three clear species groups; “Nuclear/Regular Associate” (12 spp.; high/moderate), “Occasional Associate” (four spp.; moderate/low), and “Non-joiner/Accidental” (ten spp.; low/no flocking propensity). Groupings were similar to schemes produced via more time-intensive field methods. In order to contextualize grouping categories, we conducted a review of flocking group definitions and relevant autecological information (e.g., interspecific sociality) about our study species. We found this method to be useful for geographically extensive sampling of species’ participation in mixed-species flocks, despite high inter-flock variability in species composition and limited labor.

In this paper, we study τ -tilting modules over right 2-Nakayama algebras. Let Λ be a right 2-Nakayama algebra. We give a criterion for indecomposable Λ -modules to be τ -rigid. We characterize τ -tilting Λ -modules and establish a bijection between the set of isomorphism classes of τ -tilting Λ -modules and the set of isomorphism classes of τ -tilting Λ / 〈 e 〉 -modules for certain primitive idempotents e of Λ . It turns out that all (support) τ -tilting Λ -modules can be obtained through an iterative process using this bijection. We also establish a bijection between the set of isomorphism classes of τ -tilting Λ -modules and the set of isomorphism classes of support τ -tilting Λ -modules without nonzero projective direct summands.

DOI: 10.17014/ijog.3.1.29-51Stratified sampling of coal seams for petrographic analysis using block samples is a viable alternative to standard methods of channel sampling and particulate pellet mounts. Although petrographic analysis of particulate pellets is employed widely, it is both time consuming and does not allow variation within sampling units to be assessed - an important measure in any study whether it be for paleoenvironmental reconstruction or in obtaining estimates of industrial attributes. Also, samples taken as intact blocks provide additional information, such as texture and botanical affinity that cannot be gained using particulate pellets. Stratified sampling can be employed both on ‘fine’ and ‘coarse’ grained coal units. Fine-grained coals are defined as those coal intervals that do not contain vitrain bands greater than approximately 1 mm in thickness (as measured perpendicular to bedding). In fine-grained coal seams, a reasonable sized block sample (with a polished surface area of ~3 cm2) can be taken that encapsulates the macroscopic variability. However, for coarse-grained coals (vitrain bands &gt;1 mm) a different system has to be employed in order to accurately account for the larger particles. Macroscopic point counting of vitrain bands can accurately account for those particles&gt;1 mm within a coal interval. This point counting method is conducted using something as simple as string on a coal face with marked intervals greater than the largest particle expected to be encountered (although new technologies are being developed to capture this type of information digitally). Comparative analyses of particulate pellets and blocks on the same interval show less than 6% variation between the two sample types when blocks are recalculated to include macroscopic counts of vitrain. Therefore even in coarse-grained coals, stratified sampling can be used effectively and representatively.

Problems of deleterious effects in food are mainly caused by two groups of microbial agents including food pathogenic or spoilage microorganisms. The presence and contamination of those microorganisms in food can lead to the adverse impacts for both consumer health and food business operators around the world. To overcome such microbial risk in food or food-processing environments, one of control measures which food business operators can apply is to monitor or evaluate those relevant microorganisms by using specific, sensitive, and reliable detection, identification, or enumeration methods. Therefore, this chapter aims to basically emphasize on the brief principles and applications of standard culturing methods (reference methods) and rapid methods (alternative methods) as analysis tools for detection, identification, or enumeration of foodborne microorganisms. These methods are generally classified into two major categories: culture-dependent and culture-independent assays. Additionally, their major advantages and disadvantages are described.KeywordsFoodborne microorganismsContaminationStandard methodsRapid methodsDetection

We study the robustness of complete sets for various complexity classes. A complete set A is robust if for any f(n)-dense set S /spl isin/ P, A - S is still complete, where f(n) ranges from log(n), polynomial, to subexponential. We show that robustness can be used to separate complexity classes: For every /spl les//sub m//sup p/-complete set A for EXP and any subexponential dense sets S /spl isin/ P, A - S is still Turing complete and under a reasonable hardness assumption even /spl les//sub m//sup p/-complete. For EXP and the delta levels of the exponential hierarchy we show that for every Turing complete set A and any log-dense set S /spl isin/ P, A - S is still Turing complete. There exists a 3-truth-table complete set A for EEXPSPACE, and a log-dense set S /spl isin/ P such that A - S is not Turing complete. This implies that settling this issue for EEXP will either separate P from PSPACE or PUfrom EXP. We show that the robustness results for EXP and the delta levels of the exponential hierarchy do not relativize.

We consider a Krull–Schmidt, Hom-finite, 2-Calabi–Yau triangulated category with a basic rigid object T, and show a bijection between the set of isomorphism classes of basic rigid objects in the finite presented category pr T of T and the set of isomorphism classes of basic τ-rigid pairs in the module category of the endomorphism algebra Endc(T) op . As a consequence, basic maximal objects in pr T are one-to-one correspondence to basic support τ-tilting modules over End c (T) op . This is a generalization of correspondences established by Adachi–Iyama–Reiten.

Let H be the upper half plane and T a discrete subgroup of AutH.Suppose that H mod Y is of finite measure.This work stems from the question whether there is an algebraic interpretation for the moduli of unitary representations of T similar to the case whenWe show that this is indeed the case via the moduli of vector bundles on the compactification of H mod r, provided with some additional structures which we propose to call parabolic structures.The idea of parabolic structures is inspired from A. Weil's work [6,§2, Chapter I, p. 56].Let Xbe a smooth, irreducible, projective curve defined, say, over an algebraically closed field k.By vector bundles on X we understand algebraic vector bundles.DEFINITION 1.Let V be a vector bundle on X and Q G X. Then a quasiparabolic structure of Vat Q is giving a flag on the fibre VQ of Fat Ô, i.e., giving linear subspaces F*VQ of VQ,We call I = (l l9 . . .9 l r ) the type (or flag type) of the quasi-parabolic structure.Let k x = l x -/ 2 , k 2 = l 2 -/ 3 , . . ., fc fWl = /,._! -l r , k r = l r \ then k t are called the multiplicities of the quasi-parabolic structure.DEFINITION 2. Let V be a vector bundle on X and Q G X. Then a parabolic structure of V at Q is giving (i) a quasi-parabolic structure of V at Q; say I = (l t , . . ., l r ) is its type and {k.} its multiplicities, and(ii) constants a = (a 1 , . . ., a n ) called the weights of the parabolic structure such that 0 < a x < a 2 < • • • < ot n < 1 and there are r distinct elements among a, say a' = (o^, . . ., Û£), 0 < a\ < a 2 < • • • < a r < 1, such that OL\ occurs k x times, a 2 occurs k 2 times, . . ., a r occurs k r times among a.We call a. the weight ofF l V Q .Note that l x = « = rkV.Let F, H> be vector bundles on X with quasi-parabolic structures at Q.An isomorphism ƒ: F -• W of vector bundles is said to be a quasi-parabloic isomorphism if the types of V, W at Q are the same and fçiF'Vç) = F 1 WQ (/^:

ϕ-Coordinated modules for quantum vertex algebras and associative algebras

Congruence classes of presentations for the complex reflection groups G( m, 1, n) and G( m, m, n)

Here we give an upper bound for the number of irreducible components of the moduli scheme of stable rank r torsion-free sheaves of fixed degree on the integral curve X. This bound depends only on r, Sing(X),pa(X) and the corresponding number for the rank 1 case. Let X be an integral complete curve of arithmetic genus Pa and geometric genus g. For all integers r, d with r > 1 let M(X, r, d) (or just M(r, d)) be the moduli scheme of stable rank r torsion-free sheaves on X with degree d. For general background on stable vector bundles and sheaves on curves and their moduli schemes, see [N] or [S]. The number of irreducible components of M (r, d) does not depend on d, but only on X and r (see Theorem 1.2). Let n(r, X) (or just n(r)) be the number of irreducible components of M(r, d). Here we want to give upper bounds on n(r) depending only on the singularities of X, the integer r and n(l). This is given by Theorem 0.1 (see the discussion in the last part of Remark 1.4). To state Theorem 0.1 (our main result) we need to introduce a few concepts (e.g. measures for the singularities of X) and fix some notation. Let 7r: C -* X be the normalization (hence g = pa(C)). Set 6 := Pa g. Set o:= Ox. For any x C Sing(X), set Ox := Ox,x and let mx be the maximal ideal of Ox; set kx := Ox/mx. Set fx := dimK(Ext1(kx,Ox)) and f := max{fx}xEsirlg(x). For example, we have fx = 1 if and only if Ox is Gorenstein (see e.g. [Co], Lemma 2.1.4). Let ex be the multiplicity of X at x; set := max(ex) and e := Ex ex. Let F be a rank r torsion-free sheaf on X; the set of all formal isomorphism classes of the germs {FX}xEsirlg(x) will be called the formal isomorphism class of F. The set W of all possible isomorphism classes for rank r torsion-free sheaves around Sing(X) has in a natural way a scheme structure; for any reduced subscheme Q of W, let M(r, d, Q) be the reduced subscheme of M(r, d)r.eci parametrizing sheaves with formal isomorphism type in Q. Let n(r, Q) (or n(r, d, Q)) be the number of irreducible components of M(r, d, Q). By Theorem 1.2 this integer does not depend on d. Our main interest is when Q is an irreducible component of Wr.ec. Here is our main result. Received by the editors November 28, 1994. 1991 Mathematics Subject Classification. Primary 14H60, 14D20, 14B99. This research was partially supported by MURST and GNSAGA of CNR (Italy). The author is a member of Europroj (and its group Vector bundles on curves). ?)1997 Arnericari Mathernatical Society

Let F ( G ) \mathcal {F}(G) denote the set of isomorphism classes of finite homomorphic images of a group G. We say that groups G and H have isomorphic finite quotients if F ( G ) = F ( H ) \mathcal {F}(G) = \mathcal {F}(H) . Let H \mathcal {H} denote the class of finite extensions of finitely generated nilpotent groups. In this paper we show that if G is in H \mathcal {H} , then the groups H in H \mathcal {H} for which F ( G ) = F ( H ) \mathcal {F}(G) = \mathcal {F}(H) lie in only finitely many isomorphism classes.

A new design for a small growth container which was used for investigation of the microbiota of the White Sea littoral and sublittoral sediments is presented. These chambers made it possible to observe development of fungal mycelium under conditions of a natural ecotope (marine sediments) and to isolate this mycelium as pure cultures. The mycobiota isolated from the containers was compared to that obtained by standard plating method of the same sediments. The mycelium developed in 10% of the containers installed. Intensity of growth was found to be lower in the sublittoral than in the littoral. Most fungi isolated from the containers did not produce spores in pure cultures. Apart from non-sporulating cultures, colonies of marine species Paradendryphiellasalina and Acremoniumfuci were obtained. Standard plating of the sediments often resulted in isolation of Penicillium and Tolypocladium species, while the share of sterile isolates was considerably lower than in the case of isolation using growth containers.

In this paper we investigate the structure of sets which are complete for various classes. We show, for example, that sets complete for deterministic time classes contain infinite polynomial time recognizable subsets, thus showing that they are not complex almost everywhere. We show by a related technique that any set complete for NEXP_TIME contains an infinite subset in DEXP_TIME, thereby showing that these sets do not require the use of non-determinism almost everywhere. Furthermore, we show that complete sets for deterministic time classes have effective I.O. speed-up to a polynomial; this strengthens a result of Stockmeyer.