On the intersection of ACM curves in \PP^3

Bezout's theorem gives us the degree of intersection of two properly intersecting projective varieties. As two curves in P^3 never intersect properly, Bezout's theorem cannot be directly used to bound the number of intersection points of such curves. In this work, we bound the maximum number of intersection points of two integral ACM curves in P^3. The bound that we give is in many cases optimal as a function of only the degrees and the initial degrees of the curves

Time to pregnancy : a computational method for using the duration of non-conception for predicting conception

An important problem in reproductive medicine is deciding when people who have failed to become pregnant without medical assistance should begin investigation and treatment. This study describes a computational approach to determining what can be deduced about a couple's future chances of pregnancy from the number of menstrual cycles over which they have been trying to conceive. The starting point is that a couple's fertility is inherently uncertain. This uncertainty is modelled as a probability distribution for the chance of conceiving in each menstrual cycle. We have developed a general numerical computational method, which uses Bayes' theorem to generate a posterior distribution for a couple's chance of conceiving in each cycle, conditional on the number of previous cycles of attempted conception. When various metrics of a couple's expected chances of pregnancy were computed as a function of the number of cycles over which they had been trying to conceive, we found good fits to observed data on time to pregnancy for different populations. The commonly-used standard of 12 cycles of non-conception as an indicator of subfertility was found to be reasonably robust, though a larger or smaller number of cycles may be more appropriate depending on the population from which a couple is drawn and the precise subfertility metric which is most relevant, for example the probability of conception in the next cycle or the next 12 cycles. We have also applied our computational method to model the impact of female reproductive ageing. Results indicate that, for women over the age of 35, it may be appropriate to start investigation and treatment more quickly than for younger women. Ignoring reproductive decline during the period of attempted conception added up to two cycles to the computed number of cycles before reaching a metric of subfertility

Consent agreements for cryopreserved embryos : the case for choice

Under current UK law, an embryo cannot be transferred to a woman’s uterus without the consent of both of its genetic parents, that is both of the people from whose gametes the embryo was created. This consent can be withdrawn at any time before the embryo transfer procedure. Withdrawal of consent by one genetic parent can result in the other genetic parent losing the opportunity to have their own genetic children. We argue that offering couples only one type of consent agreement, as happens at present, is too restrictive. An alternative form of agreement, in which one genetic parent agrees to forego the right to future withdrawal of consent, should be available alongside the current form of agreement. Giving couples such a choice will better enable them to store embryos under a consent agreement that is appropriate for their circumstances. Allowing such a choice, with robust procedures in place to ensure the validity of consent, is the best way to respect patient autonomy

Apoptosis in mouse fetal and neonatal oocytes during meiotic prophase one

Background The vast majority of oocytes formed in the fetal ovary do not survive beyond birth. Possible reasons for their loss include the elimination of non-viable genetic constitutions arising through meiosis, however, the precise relationship between meiotic stages and prenatal apoptosis of oocytes remains elusive. We studied oocytes in mouse fetal and neonatal ovaries, 14.5–21 days post coitum, to examine the relationship between oocyte development and programmed cell death during meiotic prophase I. Results Microspreads of fetal and neonatal ovarian cells underwent immunocytochemistry for meiosis- and apoptosis-related markers. COR-1 (meiosis-specific) highlighted axial elements of the synaptonemal complex and allowed definitive identification of the stages of meiotic prophase I. Labelling for cleaved poly-(ADP-ribose) polymerase (PARP-1), an inactivated DNA repair protein, indicated apoptosis. The same oocytes were then labelled for DNA double strand breaks (DSBs) using TUNEL. 1960 oocytes produced analysable results. . Oocytes at all stages of meiotic prophase I stained for cleaved PARP-1 and/or TUNEL, or neither. Oocytes with fragmented (19.8%) or compressed (21.2%) axial elements showed slight but significant differences in staining for cleaved PARP-1 and TUNEL to those with intact elements. However, fragmentation of axial elements alone was not a good indicator of cell demise. Cleaved PARP-1 and TUNEL staining were not necessarily coincident, showing that TUNEL is not a reliable marker of apoptosis in oocytes. Conclusions Our data indicate that apoptosis can occur throughout meiotic prophase I in mouse fetal and early postnatal oocytes, with greatest incidence at the diplotene stage. Careful selection of appropriate markers for oocyte apoptosis is essential

Consent agreements for cryopreserved embryos : the case for choice

Under current UK law, an embryo cannot be transferred to a woman’s uterus without the consent of both of its genetic parents, that is both of the people from whose gametes the embryo was created. This consent can be withdrawn at any time before the embryo transfer procedure. Withdrawal of consent by one genetic parent can result in the other genetic parent losing the opportunity to have their own genetic children. We argue that offering couples only one type of consent agreement, as happens at present, is too restrictive. An alternative form of agreement, in which one genetic parent agrees to forego the right to future withdrawal of consent, should be available alongside the current form of agreement. Giving couples such a choice will better enable them to store embryos under a consent agreement that is appropriate for their circumstances. Allowing such a choice, with robust procedures in place to ensure the validity of consent, is the best way to respect patient autonomy

An inclusion result for dagger closure in certain section rings of abelian varieties

We prove an inclusion result for graded dagger closure for primary ideals in symmetric section rings of abelian varieties over an algebraically closed field of arbitrary characteristic.Comment: 11 pages, v2: updated one reference, fixed 2 typos; final versio

Geometric collections and Castelnuovo-Mumford Regularity

The paper begins by overviewing the basic facts on geometric exceptional collections. Then, we derive, for any coherent sheaf \cF on a smooth projective variety with a geometric collection, two spectral sequences: the first one abuts to \cF and the second one to its cohomology. The main goal of the paper is to generalize Castelnuovo-Mumford regularity for coherent sheaves on projective spaces to coherent sheaves on smooth projective varieties $X$ with a geometric collection $\sigma$. We define the notion of regularity of a coherent sheaf \cF on $X$ with respect to $\sigma$. We show that the basic formal properties of the Castelnuovo-Mumford regularity of coherent sheaves over projective spaces continue to hold in this new setting and we show that in case of coherent sheaves on \PP^n and for a suitable geometric collection of coherent sheaves on \PP^n both notions of regularity coincide. Finally, we carefully study the regularity of coherent sheaves on a smooth quadric hypersurface Q_n \subset \PP^{n+1} ($n$ odd) with respect to a suitable geometric collection and we compare it with the Castelnuovo-Mumford regularity of their extension by zero in \PP^{n+1}.Comment: To appear in Math. Proc. Cambridg

Introduction to derived categories of coherent sheaves

In these notes, an introduction to derived categories and derived functors is given. The main focus is the bounded derived category of coherent sheaves on a smooth projective variety.Comment: 24 pages, minor changes, same content as published versio

D-modules on 1|1 Supercurves

It is known that to every 1|1 dimensional supercurve X there is associated a dual supercurve \hat{X}, and a superdiagonal \Delta in their product. We establish that the categories of D-modules on X, \hat{X}, and \Delta are equivalent. This follows from a more general result about D-modules and purely odd submersions. The equivalences preserve tensor products, and take vector bundles to vector bundles. Line bundles with connection are studied, and examples are given where X is a superelliptic curve.Comment: 18 page

Psych verbs, the linking problem, and the acquisition of language

In acquiring language, children must learn to appropriately place the different participants of an event (e.g., causal agent, affected entity) into the correct syntactic positions (e.g., subject, object) so that listeners will know who did what to whom. While many of these mappings can be characterized by broad generalizations, both within and across languages (e.g., semantic agents tend to be mapped onto syntactic subjects), not all verbs fit neatly into these generalizations. One particularly striking example is verbs of psychological state: The experiencer of the state can appear as either the subject (Agnes fears/hates/loves Bartholomew) or the direct object (Agnes frightens/angers/delights Bartholomew). The present studies explore whether this apparent variability in subject/object mapping may actually result from differences in these verbs’ underlying meanings. Specifically, we suggest that verbs like fear describe a habitual attitude towards some entity whereas verbs like frighten describe an externally caused emotional episode. We find that this distinction systematically characterizes verbs in English, Mandarin, and Korean. This pattern is generalized to novel verbs by adults in English, Japanese, and Russian, and even by English-speaking children who are just beginning to acquire psych verbs. This results support a broad role for systematic mappings between semantics and syntax in language acquisition