1,745 research outputs found
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
with a geometric collection . We define the notion of regularity of a
coherent sheaf \cF on with respect to . 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} ( 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
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