Optimization with multivariate conditional value-at-risk constraints

For many decision making problems under uncertainty, it is crucial to develop risk-averse models and specify the decision makers' risk preferences based on multiple stochastic performance measures (or criteria). Incorporating such multivariate preference rules into optimization models is a fairly recent research area. Existing studies focus on extending univariate stochastic dominance rules to the multivariate case. However, enforcing multivariate stochastic dominance constraints can often be overly conservative in practice. As an alternative, we focus on the widely-applied risk measure conditional value-at-risk (CVaR), introduce a multivariate CVaR relation, and develop a novel optimization model with multivariate CVaR constraints based on polyhedral scalarization. To solve such problems for finite probability spaces we develop a cut generation algorithm, where each cut is obtained by solving a mixed integer problem. We show that a multivariate CVaR constraint reduces to finitely many univariate CVaR constraints, which proves the finite convergence of our algorithm. We also show that our results can be naturally extended to a wider class of coherent risk measures. The proposed approach provides a flexible, and computationally tractable way of modeling preferences in stochastic multi-criteria decision making. We conduct a computational study for a budget allocation problem to illustrate the effect of enforcing multivariate CVaR constraints and demonstrate the computational performance of the proposed solution methods

Optimization with multivariate conditional value-at-risk constraints

For many decision making problems under uncertainty, it is crucial to develop risk-averse models and specify the decision makers' risk preferences based on multiple stochastic performance measures (or criteria). Incorporating such multivariate preference rules into optimization models is a fairly recent research area. Existing studies focus on extending univariate stochastic dominance rules to the multivariate case. However, enforcing multivariate stochastic dominance constraints can often be overly conservative in practice. As an alternative, we focus on the widely-applied risk measure conditional value-at-risk (CVaR), introduce a multivariate CVaR relation, and develop a novel optimization model with multivariate CVaR constraints based on polyhedral scalarization. To solve such problems for finite probability spaces we develop a cut generation algorithm, where each cut is obtained by solving a mixed integer problem. We show that a multivariate CVaR constraint reduces to finitely many univariate CVaR constraints, which proves the finite convergence of our algorithm. We also show that our results can be naturally extended to a wider class of coherent risk measures. The proposed approach provides a flexible, and computationally tractable way of modeling preferences in stochastic multi-criteria decision making. We conduct a computational study for a budget allocation problem to illustrate the effect of enforcing multivariate CVaR constraints and demonstrate the computational performance of the proposed solution methods

Bilinearity rank of the cone of positive polynomials and related cones

For a proper cone K ⊂ Rn and its dual cone K the complementary slackness condition xT s = 0 defines an n-dimensional manifold C(K) in the space { (x, s) | x ∈ K, s ∈ K^* }. When K is a symmetric cone, this manifold can be described by a set of n bilinear equalities. When K is a symmetric cone, this fact translates to a set of n linearly independent bilinear identities (optimality conditions) satisfied by every (x, s) ∈ C(K). This proves to be very useful when optimizing over such cones, therefore it is natural to look for similar optimality conditions for non-symmetric cones. In this paper we define the bilinearity rank of a cone, which is the number of linearly independent bilinear identities valid for the cone, and describe a linear algebraic technique to bound this quantity. We examine several well-known cones, in particular the cone of positive polynomials P2n+1 and its dual, the closure of the moment cone M2n+1, and compute their bilinearity ranks. We show that there are exactly four linearly independent bilinear identities which hold for all (x,s) ∈ C(P2n+1), regardless of the dimension of the cones. For nonnegative polynomials over an interval or half-line there are only two linearly independent bilinear identities. These results are extended to trigonometric and exponential polynomials

Bilinearity rank of the cone of positive polynomials and related cones

For a proper cone K ⊂ Rn and its dual cone K the complementary slackness condition xT s = 0 defines an n-dimensional manifold C(K) in the space { (x, s) | x ∈ K, s ∈ K^* }. When K is a symmetric cone, this manifold can be described by a set of n bilinear equalities. When K is a symmetric cone, this fact translates to a set of n linearly independent bilinear identities (optimality conditions) satisfied by every (x, s) ∈ C(K). This proves to be very useful when optimizing over such cones, therefore it is natural to look for similar optimality conditions for non-symmetric cones. In this paper we define the bilinearity rank of a cone, which is the number of linearly independent bilinear identities valid for the cone, and describe a linear algebraic technique to bound this quantity. We examine several well-known cones, in particular the cone of positive polynomials P2n+1 and its dual, the closure of the moment cone M2n+1, and compute their bilinearity ranks. We show that there are exactly four linearly independent bilinear identities which hold for all (x,s) ∈ C(P2n+1), regardless of the dimension of the cones. For nonnegative polynomials over an interval or half-line there are only two linearly independent bilinear identities. These results are extended to trigonometric and exponential polynomials

Complexity Results for Equistable Graphs and Related Classes

The class of equistable graphs is defined by the existence of a cost structure on the vertices such that the maximal stable sets are characterized by their costs. This graph class, not contained in any nontrivial hereditary class, has so far been studied mostly from a structural point of view; characterizations and polynomial time recognition algorithms have been obtained for special cases. We focus on complexity issues for equistable graphs and related classes. We describe a simple pseudo-polynomial-time dynamic programming algorithm to solve the maximum weight stable set problem along with the weighted independent domination problem in some classes of graphs, including equistable graphs. Our results are obtained within the wider context of Boolean optimization; corresponding hardness results are also provided. More specifically, we show that the above problems are APX-hard for equistable graphs and that it is co-NP-complete to determine whether a given cost function on the vertices of a graph defines an equistable cost structure of that graph.Germany. Federal Ministry of Education and ResearchAlexander von Humboldt-Stiftung (Sofja Kovalevskaja Award 2004

Staurosporine induces necroptotic cell death under caspase-compromised conditions in U937 cells

For a long time necrosis was thought to be an uncontrolled process but evidences recently have revealed that necrosis can also occur in a regulated manner. Necroptosis, a type of programmed necrosis is defined as a death receptor-initiated process under caspase-compromised conditions. The process requires the kinase activity of receptor-interacting protein kinase 1 and 3 (RIPK1 and RIPK3) and mixed lineage kinase domain-like protein (MLKL), as a substrate of RIPK3. The further downstream events remain elusive. We applied known inhibitors to characterize the contributing enzymes in necroptosis and their effect on cell viability and different cellular functions were detected mainly by flow cytometry. Here we report that staurosporine, the classical inducer of intrinsic apoptotic pathway can induce necroptosis under caspase-compromised conditions in U937 cell line. This process could be hampered at least partially by the RIPK1 inhibitor necrotstin-1 and by the heat shock protein 90 kDa inhibitor geldanamycin. Moreover both the staurosporine-triggered and the classical death ligand-induced necroptotic pathway can be effectively arrested by a lysosomal enzyme inhibitor CA-074-OMe and the recently discovered MLKL inhibitor necrosulfonamide. We also confirmed that the enzymatic role of poly(ADP-ribose)polymerase (PARP) is dispensable in necroptosis but it contributes to membrane disruption in secondary necrosis. In conclusion, we identified a novel way of necroptosis induction that can facilitate our understanding of the molecular mechanisms of necroptosis. Our results shed light on alternative application of staurosporine, as a possible anticancer therapeutic agent. Furthermore, we showed that the CA-074-OMe has a target in the signaling pathway leading to necroptosis. Finally, we could differentiate necroptotic and secondary necrotic processes based on participation of PARP enzyme

Estimation of CpG Coverage in Whole Methylome Next-Generation Sequencing Studies

Background Methylation studies are a promising complement to genetic studies of DNA sequence. However, detailed prior biological knowledge is typically lacking, so methylome-wide association studies (MWAS) will be critical to detect disease relevant sites. A cost-effective approach involves the next-generation sequencing (NGS) of single-end libraries created from samples that are enriched for methylated DNA fragments. A limitation of single-end libraries is that the fragment size distribution is not observed. This hampers several aspects of the data analysis such as the calculation of enrichment measures that are based on the number of fragments covering the CpGs. Results We developed a non-parametric method that uses isolated CpGs to estimate sample-specific fragment size distributions from the empirical sequencing data. Through simulations we show that our method is highly accurate. While the traditional (extended) read count methods resulted in severely biased coverage estimates and introduces artificial inter-individual differences, through the use of the estimated fragment size distributions we could remove these biases almost entirely. Furthermore, we found correlations of 0.999 between coverage estimates obtained using fragment size distributions that were estimated with our method versus those that were “observed” in paired-end sequencing data. Conclusions We propose a non-parametric method for estimating fragment size distributions that is highly precise and can improve the analysis of cost-effective MWAS studies that sequence single-end libraries created from samples that are enriched for methylated DNA fragments

Study on simplified model for estimating evaporation from reservoirs

In this study, the Linacre evaporation model was tested for its accuracy using daily, weekly and monthly records. The records were collected from class A evaporation pan installed at Algardabiya Reservoir, Sirt, Libya. The records for three years were used to calibrate and validate the model. Statistical tests show that the model gives a reasonable accuracy. The errors in the model prediction are 5.8%, 8% and 8.5% for weekly, monthly and daily prediction respectively. Thus, the Linacre model can be used when the available meteorological data is limited (air temperature only) and for all types of record such as daily, weekly and monthly

Increased activation of the pregenual anterior cingulate cortex to citalopram challenge in migraine: an fMRI study

Background The anterior cingulate cortex (ACC) is a key structure of the pain processing network. Several structural and functional alterations of this brain area have been found in migraine. In addition, altered serotonergic neurotransmission has been repeatedly implicated in the pathophysiology of migraine, although the exact mechanism is not known. Thus, our aim was to investigate the relationship between acute increase of brain serotonin (5-HT) level and the activation changes of the ACC using pharmacological challenge MRI (phMRI) in migraine patients and healthy controls. Methods Twenty-seven pain-free healthy controls and six migraine without aura patients participated in the study. All participant attended to two phMRI sessions during which intravenous citalopram, a selective serotonin reuptake inhibitor (SSRI), or placebo (normal saline) was administered. We used region of interest analysis of ACC to compere the citalopram evoked activation changes of this area between patients and healthy participants. Results Significant difference in ACC activation was found between control and patient groups in the right pregenual ACC (pgACC) during and after citalopram infusion compared to placebo. The extracted time-series showed that pgACC activation increased in migraine patients compared to controls, especially in the first 8-10 min of citalopram infusion. Conclusions Our results demonstrate that a small increase in 5-HT levels can lead to increased phMRI signal in the pregenual part of the ACC that is involved in processing emotional aspects of pain. This increased sensitivity of the pgACC to increased 5-HT in migraine may contribute to recurring headache attacks and increased stress-sensitivity in migraine

A clinical feasibility study to evaluate the safety and efficacy of PEOT/PBT implants for human donor site filling during mosaicplasty

Mosaicplasty has become a well-accepted treatment modality for articular cartilage lesions in the knee. Postoperative bleeding remains potentially concerning. This study evaluates the porous poly(ethylene oxide)terephthalate/poly(butylene terephthalate) (PEOT/PBT) implants used for donor site filling. Empty donor sites were the controls. After 9 months, MRI, macroscopical and histological analysis were carried out. Treated defects did not cause postoperative bleeding. No adverse events or inflammatory response was observed. PEOT/PBT implants were well integrated. Empty controls occasionally showed protrusion of repair tissue at the defect margins. Surface stiffness was minimally improved compared to controls. Existing polymer fragments indicated considerable biodegradation. Histological evaluation of the filled donor sites revealed congruent fibrocartilaginous surface repair with proteoglycan-rich domains and subchondral cancellous bone formation with interspersed fibrous tissue in all implanted sites. The PEOT/PBT implants successfully reduce donor site morbidity and postoperative bleeding after mosaicplasty