Ranking with Submodular Valuations

We study the problem of ranking with submodular valuations. An instance of this problem consists of a ground set $[m]$, and a collection of $n$ monotone submodular set functions $f^1, \ldots, f^n$, where each $f^i: 2^{[m]} \to R_+$. An additional ingredient of the input is a weight vector $w \in R_+^n$. The objective is to find a linear ordering of the ground set elements that minimizes the weighted cover time of the functions. The cover time of a function is the minimal number of elements in the prefix of the linear ordering that form a set whose corresponding function value is greater than a unit threshold value. Our main contribution is an $O(\ln(1 / \epsilon))$-approximation algorithm for the problem, where $\epsilon$ is the smallest non-zero marginal value that any function may gain from some element. Our algorithm orders the elements using an adaptive residual updates scheme, which may be of independent interest. We also prove that the problem is $\Omega(\ln(1 / \epsilon))$-hard to approximate, unless P = NP. This implies that the outcome of our algorithm is optimal up to constant factors.Comment: 16 pages, 3 figure

Bribeproof mechanisms for two-values domains

Schummer (Journal of Economic Theory 2000) introduced the concept of bribeproof mechanism which, in a context where monetary transfer between agents is possible, requires that manipulations through bribes are ruled out. Unfortunately, in many domains, the only bribeproof mechanisms are the trivial ones which return a fixed outcome. This work presents one of the few constructions of non-trivial bribeproof mechanisms for these quasi-linear environments. Though the suggested construction applies to rather restricted domains, the results obtained are tight: For several natural problems, the method yields the only possible bribeproof mechanism and no such mechanism is possible on more general domains.Comment: Extended abstract accepted to SAGT 2016. This ArXiv version corrects typos in the proofs of Theorem 7 and Claims 28-29 of prior ArXiv versio

Predictors of Success of Repeated Injections of Single-dose Methotrexate Regimen for Tubal Ectopic Pregnancy

The purpose of this study is to evaluate predictors of success of repeated injections of methotrexate in the single-dose regimen for the treatment of tubal ectopic pregnancy. All patients who had ectopic tubal pregnancy and were treated with a single dose regimen were retrospectively identified. 126 patients were treated with methotrexate. Among them, 39 patients were adequate for this study. 33 were treated with the 2nd dose and 27 were successfully cured. Additionally, 6 who were injected with the 3rd dose were all cured as well. Therefore, in our study, the success rate for the repeated injections of methotrexate was found to be 84.6% (33/39). The mean initial β-hCG level was significantly lower in patients who were successfully treated than in patients who failed (3915.3±3281.3 vs. 8379.7±2604.4 IU/mL, p<0.05). The success rate is 96% when the β-hCG level is less than 6,000 IU/mL and is 58% when β-hCG is greater than 6,000 IU/mL (OR=18.57, 95% CI 1.86-185.89). The initial β-hCG level is the only factor that has significant meaning as predictor of success of repeated injections of methotrexate in the single-dose regimen. Repeated injections of methotrexate may be particularly effective when the initial β-hCG level is below 6,000 IU/mL

Contact Force and Scanning Velocity during Active Roughness Perception

Haptic perception is bidirectionally related to exploratory movements, which means that exploration influences perception, but perception also influences exploration. We can optimize or change exploratory movements according to the perception and/or the task, consciously or unconsciously. This paper presents a psychophysical experiment on active roughness perception to investigate movement changes as the haptic task changes. Exerted normal force and scanning velocity are measured in different perceptual tasks (discrimination or identification) using rough and smooth stimuli. The results show that humans use a greater variation in contact force for the smooth stimuli than for the rough stimuli. Moreover, they use higher scanning velocities and shorter break times between stimuli in the discrimination task than in the identification task. Thus, in roughness perception humans spontaneously use different strategies that seem effective for the perceptual task and the stimuli. A control task, in which the participants just explore the stimuli without any perceptual objective, shows that humans use a smaller contact force and a lower scanning velocity for the rough stimuli than for the smooth stimuli. Possibly, these strategies are related to aversiveness while exploring stimuli