•Multiobjective optimization problems with uncertainty can easily be robustified.•The concept of the robust Pareto front is introduced.•Applications to Markowitz portfolio optimization are described ...in detail.
Motivated by Markowitz portfolio optimization problems under uncertainty in the problem data, we consider general convex parametric multiobjective optimization problems under data uncertainty. For the first time, this uncertainty is treated by a robust multiobjective formulation in the gist of Ben-Tal and Nemirovski. For this novel formulation, we investigate its relationship to the original multiobjective formulation as well as to its scalarizations. Further, we provide a characterization of the location of the robust Pareto frontier with respect to the corresponding original Pareto frontier and show that standard techniques from multiobjective optimization can be employed to characterize this robust efficient frontier. We illustrate our results based on a standard mean–variance problem.
Mutations in NR5A1 have been reported as a frequent cause of 46,XY disorders of sex development (DSD) associated to a broad phenotypic spectrum ranging from infertility, ambiguous genitalia, anorchia ...to gonadal dygenesis and female genitalia. Here we present the clinical follow up of four 46,XY DSD patients with three novel heterozygous mutations in the NR5A1 gene leading to a p.T40P missense mutation and a p.18DKVSG22del nonframeshift deletion in the DNA-binding domain and a familiar p.Y211Tfs*83 frameshift mutation. Functional analysis of the missense and nonframeshift mutation revealed a deleterious character with loss of DNA-binding and transactivation capacity. Both, the mutations in the DNA-binding domain, as well as the familiar frameshift mutation are associated with highly variable endocrine values and phenotypic appearance. Phenotypes vary from males with spontaneous puberty, substantial testosterone production and possible fertility to females with and without Müllerian structures and primary amenorrhea. Exome sequencing of the sibling's family revealed TBX2 as a possible modifier of gonadal development in patients with NR5A1 mutations.
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Dostopno za:
DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, SIK, UILJ, UKNU, UL, UM, UPUK
Duplications at the Xp21.2 locus have previously been linked to 46,XY gonadal dysgenesis (GD), which is thought to result from gene dosage effects of
(
), but the exact disease mechanism remains ...unknown.
Patients with 46,XY GD were analysed by whole genome sequencing. Identified structural variants were confirmed by array CGH and analysed by high-throughput chromosome conformation capture (Hi-C).
We identified two unrelated patients: one showing a complex rearrangement upstream of
and a second harbouring a 1.2 Mb triplication, including
. Whole genome sequencing and Hi-C analysis revealed the rewiring of a topological-associated domain (TAD) boundary close to
associated with neo-TAD formation and may cause enhancer hijacking and ectopic
expression. Modelling of previous Xp21.2 structural variations associated with isolated GD support our hypothesis and predict similar neo-TAD formation as well as TAD fusion.
Here we present a general mechanism how deletions, duplications or inversions at the
locus can lead to partial or complete GD by disrupting the cognate TAD in the vicinity of
. This model not only allows better diagnosis of GD with copy number variations (CNVs) at Xp21.2, but also gives deeper insight on how spatiotemporal activation of developmental genes can be disrupted by reorganised TADs causing impairment of gonadal development.
•Framework for regret optimization in multiobjective optimization under uncertainty.•No limitation to linear objectives nor to finite or interval uncertainty sets.•Continuity analysis of the robust ...objective functions with respect to uncertainty.
Consider a multiobjective decision problem with uncertainty in the objective functions, given as a set of scenarios. In the single-criterion case, robust optimization methodology helps to identify solutions which remain feasible and of good quality for all possible scenarios. A well-known alternative method in the single-objective case is to compare possible decisions under uncertainty with the optimal decision with the benefit of hindsight, i.e. to minimize the (possibly scaled) regret of not having chosen the optimal decision. In this contribution, we extend the concept of regret from the single-objective case to the multiobjective setting and introduce a proper definition of multivariate (robust) (relative) regret. In contrast to the few existing ideas that mix scalarization and optimization, we clearly separate the modelling of multiobjective (robust) regret from its numerical solution. Moreover, our approach is not limited to a finite uncertainty set or interval uncertainty and furthermore, computations or at least approximations remain tractable in several important special cases. We illustrate all approaches based on a biobjective shortest path problem under uncertainty.
Inactivating mutations within the AR gene are present in only ~40% of individuals with clinically and hormonally diagnosed androgen insensitivity syndrome (AIS). Previous studies revealed the ...existence of an AR gene mutation-negative group of patients with AIS who have compromised androgen receptor (AR) function (AIS type II).
To investigate whether AIS type II can be due to epigenetic repression of AR transcription.
Quantification of AR mRNA and AR proximal promoter CpG methylation levels in genital skin-derived fibroblasts (GFs) derived from patients with AIS type II and control individuals.
University hospital endocrine research laboratory.
GFs from control individuals (n = 11) and patients with AIS type II (n = 14).
Measurement of AR mRNA and AR promoter CpG methylation as well as activity of AR proximal promoter in vitro.
Fifty-seven percent of individuals with AIS type II (n = 8) showed a reduced AR mRNA expression in their GFs. A significant inverse correlation was shown between AR mRNA abundance and methylation at two consecutive CpGs within the proximal AR promoter. Methylation of a 158-bp-long region containing these CpGs was sufficient to severely reduce reporter gene expression. This region was bound by the runt related transcription factor 1 (RUNX1). Ectopic expression of RUNX1 in HEK293T cells was able to inhibit reporter gene expression through this region.
Aberrant CpGs methylation within the proximal AR promoter plays an important role in the control of AR gene expression and may result in AIS type II. We suggest that transcriptional modifiers, such as RUNX1, could play roles therein offering new perspectives for understanding androgen-mediated endocrine diseases.
A subset of patients with monogenic disorders lacks disease causing mutations in the protein coding region of the corresponding gene. Here we describe a recurrent germline mutation found in two ...unrelated patients with complete androgen insensitivity syndrome (CAIS) generating an upstream open reading frame (uORF) in the 5' untranslated region (5'-UTR) of the androgen receptor (AR) gene. We show in patient derived primary genital skin fibroblasts as well as in cell-based reporter assays that this mutation severely impacts AR function by reducing AR protein levels without affecting AR mRNA levels. Importantly, the newly generated uORF translates into a polypeptide and the expression level of this polypeptide inversely correlates with protein translation from the primary ORF of the AR thereby providing a model for AR-5'UTR mediated translational repression. Our findings not only add a hitherto unrecognized genetic cause to complete androgen insensitivity but also underline the importance of 5'UTR mutations affecting uORFs for the pathogenesis of monogenic disorders in general.
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Dostopno za:
DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, SIK, UILJ, UKNU, UL, UM, UPUK
A region of 160 kb at Xp21.2 has been defined as dosage-sensitive sex reversal (DSS) and includes the
gene, considered to be the candidate gene involved in XY gonadal dysgenesis if overexpressed. We ...describe a girl with 46,XY partial gonadal dysgenesis carrying a 297 kb duplication at Xp21.2 upstream of
initially detected by chromosomal microarray analysis. Fine mapping of the breakpoints by whole-genome sequencing showed a tandem duplication of
,
and partially
, upstream of
. This is the first description of an Xp21.2 duplication upstream of
associated with 46,XY partial gonadal dysgenesis.
The replicating portfolio approach is a well-established approach carried out by many life insurance companies within their Solvency II framework for the computation of risk capital. In this note we ...elaborate on one specific formulation of a replicating portfolio problem. In contrast to the two most popular replication approaches, it does not yield an analytic solution (if, at all, a solution exists and is unique). Further although convex, the objective function seems to be non-smooth and hence a numerical solution might thus be much more demanding than for the two most popular formulations. Especially for the second reason, this formulation did not (yet) receive much attention in practical applications, in contrast to the other two formulations. In the following, we will demonstrate that the (potential) non-smoothness can be avoided due to an equivalent reformulation as a linear second order cone program (SOCP). This allows for a numerical solution by efficient second order methods like interior point methods or similar. We also show that - under weak assumptions - existence and uniqueness of the optimal solution can be guaranteed. We additionally prove that - under a further similarly weak condition - the fair value of the replicating portfolio equals the fair value of liabilities. Based on these insights, we argue that this unloved stepmother child within the replication problem family indeed represents an equally good formulation for practical purposes.
Transition matrices, containing credit risk information in the form of ratings based on discrete observations, are published annually by rating agencies. A substantial issue arises, as for higher ...rating classes practically no defaults are observed yielding default probabilities of zero. This does not always reflect reality. To circumvent this shortcoming, estimation techniques in continuous-time can be applied. However, raw default data may not be available at all or not in the desired granularity, leaving the practitioner to rely on given one-year transition matrices. Then, it becomes necessary to transform the one-year transition matrix to a generator matrix. This is known as the embedding problem and can be formulated as a nonlinear optimization problem, minimizing the distance between the exponential of a potential generator matrix and the annual transition matrix. So far, in credit risk-related literature, solving this problem directly has been avoided, but approximations have been preferred instead. In this paper, we show that this problem can be solved numerically with sufficient accuracy, thus rendering approximations unnecessary. Our direct approach via nonlinear optimization allows one to consider further credit risk-relevant constraints. We demonstrate that it is thus possible to choose a proper generator matrix with additional structural properties.
The group of disorders known as 46,XY gonadal dysgenesis (GD) is characterized by anomalies in testis determination, including complete and partial GD (PGD) and testicular regression syndrome (TRS). ...Several genes are known to be involved in sex development pathways, however approximately 50% of all cases remain elusive. Recent studies have identified variants in
, a gene encoding a putative RNA helicase essential in ribosome biogenesis and previously associated with neurodevelopmental disorders, as a cause of PGD and TRS. To investigate the potential role of
in disorders of sexual development (DSD), 25 individuals with 46,XY DSD were analyzed and putative pathogenic variants were found in four of them. WES analyses were performed on these patients. In
, the variant p.(Arg308Gln), recurrent associated with DSD, was identified in one patient; the p.(Leu467Val), predicted to be deleterious, was found together with an
loss-of-function variant in patient 2; and, the p.(Val999Met) was identified in two unrelated patients, one of whom (patient 3) also carried a pathogenic
variant. For both patients carrying
and
pathogenic variants, a digenic inheritance is suggested. Our findings support the importance of
variants as a cause of disorders of sex development, implying a role in testis development.
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