Group Strategyproof Pareto-Stable Marriage with Indifferences via the Generalized Assignment Game

We study the variant of the stable marriage problem in which the preferences of the agents are allowed to include indifferences. We present a mechanism for producing Pareto-stable matchings in stable marriage markets with indifferences that is group strategyproof for one side of the market. Our key technique involves modeling the stable marriage market as a generalized assignment game. We also show that our mechanism can be implemented efficiently. These results can be extended to the college admissions problem with indifferences

Prophet Inequalities for IID Random Variables from an Unknown Distribution

A central object in optimal stopping theory is the single-choice prophet inequality for independent, identically distributed random variables: given a sequence of random variables X1, . . . , Xn drawn independently from a distribution F , the goal is to choose a stopping time τ so as to maximize α such that for all distributions F we have E[Xτ ] ≥ α · E[maxt Xt ]. What makes this problem challenging is that the decision whether τ = t may only depend on the values of the random variables X1, . . . , Xt and on the distribution F . For a long time the best known bound for the problem had been α ≥ 1 − 1/e ≈ 0.632, but quite recently a tight bound of α ≈ 0.745 was obtained. The case where F is unknown, such that the decision whether τ = t may depend only on the values of the random variables X1, . . . , Xt , is equally well motivated but has received much less attention. A straightforward guarantee for this case of α ≥ 1/e ≈ 0.368 can be derived from the solution to the secretary problem, where an arbitrary set of values arrive in random order and the goal is to maximize the probability of selecting the largest value. We show that this bound is in fact tight. We then investigate the case where the stopping time may additionally depend on a limited number of samples from F , and show that even with o(n) samples α ≤ 1/e. On the other hand, n samples allow for a significant improvement, while O(n2) samples are equivalent to knowledge of the distribution: specifically, with n samples α ≥ 1 − 1/e ≈ 0.632 and α ≤ ln(2) ≈ 0.693, and with O(n2) samples α ≥ 0.745 − ε for any ε > 0

Regulation of early steps of GPVI signal transduction by phosphatases: a systems biology approach

We present a data-driven mathematical model of a key initiating step in platelet activation, a central process in the prevention of bleeding following Injury. In vascular disease, this process is activated inappropriately and causes thrombosis, heart attacks and stroke. The collagen receptor GPVI is the primary trigger for platelet activation at sites of injury. Understanding the complex molecular mechanisms initiated by this receptor is important for development of more effective antithrombotic medicines. In this work we developed a series of nonlinear ordinary differential equation models that are direct representations of biological hypotheses surrounding the initial steps in GPVI-stimulated signal transduction. At each stage model simulations were compared to our own quantitative, high-temporal experimental data that guides further experimental design, data collection and model refinement. Much is known about the linear forward reactions within platelet signalling pathways but knowledge of the roles of putative reverse reactions are poorly understood. An initial model, that includes a simple constitutively active phosphatase, was unable to explain experimental data. Model revisions, incorporating a complex pathway of interactions (and specifically the phosphatase TULA-2), provided a good description of the experimental data both based on observations of phosphorylation in samples from one donor and in those of a wider population. Our model was used to investigate the levels of proteins involved in regulating the pathway and the effect of low GPVI levels that have been associated with disease. Results indicate a clear separation in healthy and GPVI deficient states in respect of the signalling cascade dynamics associated with Syk tyrosine phosphorylation and activation. Our approach reveals the central importance of this negative feedback pathway that results in the temporal regulation of a specific class of protein tyrosine phosphatases in controlling the rate, and therefore extent, of GPVI-stimulated platelet activation

Target dependence of chick retinal ganglion cells during embryogenesis: cell survival and dendritic development

The survival of retinal ganglion cells and the dendritic development were investigated a) in normal chick embryos, b) in embryos whose primordial optic lobes and adjacent areas were removed (target reduced embryos), and c) in embryos whose optic nerves were transected (target deprived embryos) in order to study the influences of central targets on developing ganglion cells. The ganglion cells were stained postmortem with the carbocyanine dye DiI. Cell body and dendritic field diameters were measured in whole-mounted retinae before and after the period of cell death at embryonic day 10 (E10) and E16. The cell densities within the ganglion cell layer were counted in cresyl violet/thionine stained retinae. The central retinal projection in target reduced embryos was studied with the anterogradely transported fluorescent marker rhodamine-B-isothiocyanate (RITC). In normal embryos, the earliest dendritic processes were observed at E6 in the central retina, whereas at E10 elaborate dendritic branching was found across the retina. Different morphological types of ganglion cells could be identified at E16. In both, target reduced embryos and target deprived embryos, the initial dendritic growth and pattern of ramification were indistinguishable from those of normal embryos up to E10. Cell body diameters, dendritic tree diameters, and cell densities were not significantly different. At the end of the naturally occurring cell death period (E16), the ganglion cell density was strongly reduced in both experimental groups compared to controls. In particular, when the optic nerve was transected, it resulted in the almost complete degeneration of ganglion cells. In target reduced embryos, a small population (about 5% of the normal number) of ganglion cells survived. The proportion of large cells was increased within the total population compared to normal retinae. Displaced ganglion cells were not affected by partial target removal but strongly affected by transection of the optic nerve. Anterograde labelling from the retina revealed that in target reduced embryos the remaining ganglion cells innervated non-tectal primary visual nuclei. The present results suggest the following: a) Before the onset of the cell death period, the growth and ramification of ganglion cell dendrites occur independently of central visual targets. b) In target reduced embryos, a small population of ganglion cells survives, namely, those cells that project to remaining central areas. Complete disconnection from central targets by transecting the optic nerve leads to the degeneration of almost all ganglion cells. c) The surviving ganglion cell population consists mainly of large ganglion cells

Patient preference and tolerability of a DPP-4 inhibitor a GLP-1 analog in patients with type 2 diabetes mellitus inadequately controlled with metformin: a 24-week, randomized, multicenter, crossover study

Objective: The present study aimed to assess the patient preference and tolerability of oral dipeptidyl peptidase-4 inhibitor (vildagliptin) versus injectable glucagon-like peptide-1 analog (liraglutide) in patients with type 2 diabetes mellitus inadequately controlled with metformin monotherapy. Methods: This 24-week, randomized, multicenter, crossover study, patients with type 2 diabetes mellitus inadequately controlled on metformin monotherapy with hemoglobin A1c (HbA 1c ) ⩾6.5% and ⩽9.0% were randomized in a crossover manner to receive either vildagliptin/metformin single-pill combination (SPC) 50/1000 mg twice daily ( n = 32) or 1.2 mg liraglutide as an add-on to metformin (0.6 mg [weeks 0–1] followed by 1.2 mg [weeks 2–12] once daily/1000 mg twice daily) ( n = 30) for the first 12 weeks. Results: Patient preference at week 24 was similar, with 51.7% ( n = 31) patients preferring vildagliptin/metformin SPC compared with 48.3% ( n = 29) preferring liraglutide as an add-on to metformin therapy ( p = 0.449). Post hoc analyses showed that more elderly patients (⩾65 years) preferred vildagliptin (65%; n = 13) over liraglutide (35%; n = 7) therapy. Liraglutide was associated with better improvement in fasting plasma glucose (–21.5 mg/dl versus –3.4 mg/dl) and HbA 1c (–0.5% versus –0.3%) levels. Fewer adverse events were reported with vildagliptin/metformin SPC ( n = 16) compared with liraglutide as add-on to metformin treatment ( n = 46). Conclusions: In this pilot study, although both vildagliptin and liraglutide therapies were preferred similarly by the patients and showed effective control of glycemia over 12 weeks, vildagliptin was associated with fewer adverse events and was preferred more by elderly patients

Partial respecification of nasotemporal polarity in double-temporal chick and chimeric chick-quail eyes

In chick embryos, naso-temporal polarity of the retina becomes established before Hamburger-Hamilton stage 10. To examine the plasticity of the early eye anlage, double-temporal eyes were made using stage 10-11 (E1.5) chick embryos and stage 8-9 quail embryos. In vivo and in vitro experiments revealed that these double-temporal compound eyes were not completely temporal but nasal in a large peripheral part of the graft. Four hours after transplantation, the nasal-specific fork head transcription factor CBF1 was not expressed in double-temporal eyes but was clearly detectable 24 h later. This suggests that in the peripheral part of the graft, temporal positional values were changed into nasal positional values by a respecification process

The EphA4 receptor tyrosine kinase is necessary for the guidance of nasal retinal ganglion cell axons in vitro

The retinotectal projection serves as a model system for the study of topographic projections. It has been shown in the past few years that members of the Eph family are strongly involved in establishing this projection. The analysis so far has focused on a characterization of Ephrin ligands which are expressed in a gradient in both the tectum and the retina. Here we investigate the role of one of the multiple EphA receptors expressed on retinal ganglion cell axons, EphA4, which is uniformly expressed on nasal and temporal axons. We have adopted both a dominant negative approach and a method using neutralizing monoclonal antibodies in order to inactivate this receptor. The results of these in vitro experiments suggest that EphA4 is crucially involved in the repulsive guidance of nasal but not of temporal axons