Pricing in Social Networks with Negative Externalities

We study the problems of pricing an indivisible product to consumers who are embedded in a given social network. The goal is to maximize the revenue of the seller. We assume impatient consumers who buy the product as soon as the seller posts a price not greater than their values of the product. The product's value for a consumer is determined by two factors: a fixed consumer-specified intrinsic value and a variable externality that is exerted from the consumer's neighbors in a linear way. We study the scenario of negative externalities, which captures many interesting situations, but is much less understood in comparison with its positive externality counterpart. We assume complete information about the network, consumers' intrinsic values, and the negative externalities. The maximum revenue is in general achieved by iterative pricing, which offers impatient consumers a sequence of prices over time. We prove that it is NP-hard to find an optimal iterative pricing, even for unweighted tree networks with uniform intrinsic values. Complementary to the hardness result, we design a 2-approximation algorithm for finding iterative pricing in general weighted networks with (possibly) nonuniform intrinsic values. We show that, as an approximation to optimal iterative pricing, single pricing can work rather well for many interesting cases, but theoretically it can behave arbitrarily bad

Pricing Multi-Unit Markets

We study the power and limitations of posted prices in multi-unit markets, where agents arrive sequentially in an arbitrary order. We prove upper and lower bounds on the largest fraction of the optimal social welfare that can be guaranteed with posted prices, under a range of assumptions about the designer's information and agents' valuations. Our results provide insights about the relative power of uniform and non-uniform prices, the relative difficulty of different valuation classes, and the implications of different informational assumptions. Among other results, we prove constant-factor guarantees for agents with (symmetric) subadditive valuations, even in an incomplete-information setting and with uniform prices

Approximating Node-Weighted k-MST on Planar Graphs

We study the problem of finding a minimum weight connected subgraph spanning at least $k$ vertices on planar, node-weighted graphs. We give a (4+\eps)-approximation algorithm for this problem. We achieve this by utilizing the recent LMP primal-dual $3$-approximation for the node-weighted prize-collecting Steiner tree problem by Byrka et al (SWAT'16) and adopting an approach by Chudak et al. (Math.\ Prog.\ '04) regarding Lagrangian relaxation for the edge-weighted variant. In particular, we improve the procedure of picking additional vertices (tree merging procedure) given by Sadeghian (2013) by taking a constant number of recursive steps and utilizing the limited guessing procedure of Arora and Karakostas (Math.\ Prog.\ '06). More generally, our approach readily gives a (\nicefrac{4}{3}\cdot r+\eps)-approximation on any graph class where the algorithm of Byrka et al.\ for the prize-collecting version gives an $r$-approximation. We argue that this can be interpreted as a generalization of an analogous result by K\"onemann et al. (Algorithmica~'11) for partial cover problems. Together with a lower bound construction by Mestre (STACS'08) for partial cover this implies that our bound is essentially best possible among algorithms that utilize an LMP algorithm for the Lagrangian relaxation as a black box. In addition to that, we argue by a more involved lower bound construction that even using the LMP algorithm by Byrka et al.\ in a \emph{non-black-box} fashion could not beat the factor \nicefrac{4}{3}\cdot r when the tree merging step relies only on the solutions output by the LMP algorithm

Mobility, Balance and Falls in Persons with Multiple Sclerosis

BACKGROUND: There is a lack of information concerning the relation between objective measures of gait and balance and fall history in persons with MS (PwMS). This investigation assessed the relation between demographic, clinical, mobility and balance metrics and falls history in persons with multiple sclerosis (MS). METHODS: 52 ambulatory persons with MS (PwMS) participated in the investigation. All persons provided demographic information including fall history over the last 12 months. Disease status was assessed with Expanded Disability Status Scale (EDSS). Walking speed, coordination, endurance and postural control were quantified with a multidimensional mobility battery. RESULTS: Over 51% of the participants fell in the previous year with 79% of these people being suffering recurrent falls. Overall, fallers were older, had a greater prevalence of assistive devices use, worse disability, decreased walking endurance, and greater postural sway velocity with eyes closed compared to non-fallers. Additionally, fallers had greater impairment in cerebellar, sensory, pyramidal, and bladder/bowel subscales of the EDSS. CONCLUSIONS: The current observations suggest that PwMS who are older, more disabled, utilize an assistive device, have decreased walking coordination and endurance and have diminished balance have fallen in the previous year. This suggests that individuals who meet these criteria need to be carefully monitored for future falls. Future research is needed to determine a prospective model of falls specific to PwMS. Additionally, the utility of interventions aimed at reducing falls and fall risk in PwMS needs to be established

Automated postural responses are modified in a functional manner by instruction.

Contains fulltext : 70025.pdf (publisher's version ) (Open Access)The restoration of upright balance after a perturbation relies on highly automated and, to a large extent, stereotyped postural responses. Although these responses occur before voluntary control comes into play, previous research has shown that they can be functionally modulated on the basis of cognitive set (experience, advanced warning, instruction, etc.). It is still unknown, however, how the central nervous system deals with situations in which the postural response is not necessarily helpful in the execution of a task. In the present study, the effects of instruction on automated postural responses in neck, trunk, shoulder, and leg muscles were investigated when people were either instructed to recover balance after being released from an inclined standing posture [balance recovery (BR) trials], or not to recover at all and fall onto a safety mattress in the most comfortable way [fall (F) trials], in both backward and leftward directions. Participants were highly successful in following the instructions, consistently exhibiting stepping responses for balance recovery in BR trials, and suppressing stepping in the F trials. Yet EMG recordings revealed similar postural responses with onset latencies between 70 and 130 ms in both BR and F trials, with slightly delayed responses in F trials. In contrast, very pronounced and early differences were observed between BR and F trials in response amplitudes, which were generally much higher in BR than in F trials, but with clear differentiation between muscles and perturbation directions. These results indicate that a balance perturbation always elicits a postural response, irrespective of the task demands. However, when a specific balance recovery response is not desired after a perturbation, postural responses can be selectively downregulated and integrated into the motor output in a functional and goal-oriented way