A PTAS for planar group Steiner tree via spanner bootstrapping and prize collecting

We present the first polynomial-time approximation scheme (PTAS), i.e., (1 + ϵ)-approximation algorithm for any constant ϵ > 0, for the planar group Steiner tree problem (in which each group lies on a boundary of a face). This result improves on the best previous approximation factor of O(logn(loglogn)O(1)). We achieve this result via a novel and powerful technique called spanner bootstrapping, which allows one to bootstrap from a superconstant approximation factor (even superpolynomial in the input size) all the way down to a PTAS. This is in contrast with the popular existing approach for planar PTASs of constructing lightweight spanners in one iteration, which notably requires a constant-factor approximate solution to start from. Spanner bootstrapping removes one of the main barriers for designing PTASs for problems which have no known constant-factor approximation (even on planar graphs), and thus can be used to obtain PTASs for several difficult-to-approximate problems. Our second major contribution required for the planar group Steiner tree PTAS is a spanner construction, which reduces the graph to have total weight within a factor of the optimal solution while approximately preserving the optimal solution. This is particularly challenging because group Steiner tree requires deciding which terminal in each group to connect by the tree, making it much harder than recent previous approaches to construct spanners for planar TSP by Klein [SIAM J. Computing 2008], subset TSP by Klein [STOC 2006], Steiner tree by Borradaile, Klein, and Mathieu [ACM Trans. Algorithms 2009], and Steiner forest by Bateni, Hajiaghayi, and Marx [J. ACM 2011] (and its improvement to an efficient PTAS by Eisenstat, Klein, and Mathieu [SODA 2012]. The main conceptual contribution here is realizing that selecting which terminals may be relevant is essentially a complicated prize-collecting process: we have to carefully weigh the cost and benefits of reaching or avoiding certain terminals in the spanner. Via a sequence of involved prize-collecting procedures, we can construct a spanner that reaches a set of terminals that is sufficient for an almost-optimal solution. Our PTAS for planar group Steiner tree implies the first PTAS for geometric Euclidean group Steiner tree with obstacles, as well as a (2 + ϵ)-approximation algorithm for group TSP with obstacles, improving over the best previous constant-factor approximation algorithms. By contrast, we show that planar group Steiner forest, a slight generalization of planar group Steiner tree, is APX-hard on planar graphs of treewidth 3, even if the groups are pairwise disjoint and every group is a vertex or an edge

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

Covering problems in edge- and node-weighted graphs

This paper discusses the graph covering problem in which a set of edges in an edge- and node-weighted graph is chosen to satisfy some covering constraints while minimizing the sum of the weights. In this problem, because of the large integrality gap of a natural linear programming (LP) relaxation, LP rounding algorithms based on the relaxation yield poor performance. Here we propose a stronger LP relaxation for the graph covering problem. The proposed relaxation is applied to designing primal-dual algorithms for two fundamental graph covering problems: the prize-collecting edge dominating set problem and the multicut problem in trees. Our algorithms are an exact polynomial-time algorithm for the former problem, and a 2-approximation algorithm for the latter problem, respectively. These results match the currently known best results for purely edge-weighted graphs.Comment: To appear in SWAT 201

Sexual Function and Factors Affecting Menopause: A Systematic Review

The purpose of this review study is to evaluate sexual function and its effective factors in menopause. A systematic review was conducted according to the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines. The key words of "menopause," "postmenopause," "postmenopausal," "premenopause," "pre-menopausal period," "sexual function," "sexual health," "sexuality," "sexual and gender disorders," "sexual development," "sexual dysfunction," "sexual disorders," "sexual behavior and "sexual activity" were used in combination with the Boolean operators OR and AND. After reviewing the selected articles, 27 papers were selected based on the criteria for entering the study and the goals set. The results of the reviewed articles showed that, in the physical domain, the factors affecting sexual function can be mentioned, age, hormonal changes, medical problems and reproductive history. Sexual disorders in menopause can be affected by some of the individual and social characteristics and psychological problems. Considering the fact that many psychological and social injuries occur in this period following sexual disorders; therefore, policies and programs for improving the quality of life of women in menopause should be aimed at eliminating sexual dysfunction, correcting attitudes and negative emotions and help to women for more comfortable in menopause

Solving Multi-choice Secretary Problem in Parallel: An Optimal Observation-Selection Protocol

The classical secretary problem investigates the question of how to hire the best secretary from $n$ candidates who come in a uniformly random order. In this work we investigate a parallel generalizations of this problem introduced by Feldman and Tennenholtz [14]. We call it shared $Q$-queue $J$-choice $K$-best secretary problem. In this problem, $n$ candidates are evenly distributed into $Q$ queues, and instead of hiring the best one, the employer wants to hire $J$ candidates among the best $K$ persons. The $J$ quotas are shared by all queues. This problem is a generalized version of $J$-choice $K$-best problem which has been extensively studied and it has more practical value as it characterizes the parallel situation. Although a few of works have been done about this generalization, to the best of our knowledge, no optimal deterministic protocol was known with general $Q$ queues. In this paper, we provide an optimal deterministic protocol for this problem. The protocol is in the same style of the $1\over e$-solution for the classical secretary problem, but with multiple phases and adaptive criteria. Our protocol is very simple and efficient, and we show that several generalizations, such as the fractional $J$-choice $K$-best secretary problem and exclusive $Q$-queue $J$-choice $K$-best secretary problem, can be solved optimally by this protocol with slight modification and the latter one solves an open problem of Feldman and Tennenholtz [14]. In addition, we provide theoretical analysis for two typical cases, including the 1-queue 1-choice $K$-best problem and the shared 2-queue 2-choice 2-best problem. For the former, we prove a lower bound $1-O(\frac{\ln^2K}{K^2})$ of the competitive ratio. For the latter, we show the optimal competitive ratio is $\approx0.372$ while previously the best known result is 0.356 [14].Comment: This work is accepted by ISAAC 201

A digitally-augmented ground space with timed visual cues for facilitating forearm crutches’ mobility

Persuasive technologies for physical rehabilitation have been pro posed in a number of different health interventions such as post-stroke gait rehabilitation. We propose a new persuasive system, called Augmented Crut ches, aimed at helping people to walk with crutches. People with injuries, or with any sort of mobility problem typically use assistive devices such as crut ches, walkers or canes in order to be able to walk more independently. However, walking with crutches is a learning skill that needs continuous repetition and constant attention to detail in order to walk correctly with them and without suffering negative consequences, such as falls or injuries. In close collaboration with therapists, we identify the main issues that patients face when walking with crutches. These vary from person to person, but the most common and hardest challenges are the position and coordination of the crutches. Augmented Crut ches studies human behavior aspects in these situations and augments the ground space around the user with digital visual cues where timing is the most important factor, without the need for a constant therapist providing manual help. This is performed through a mini-projector connected to a smartphone, worn by the user in a portable, lightweight manner. Our system helps people to learn how to walk using crutches with increased self-confidence and motivation. Additionally, our work identifies timing, controllability and awareness as the key design dimensions for the successful creation of persuasive, interactive experiences for learning how to walk with crutches.info:eu-repo/semantics/publishedVersio

Wet deposition of hydrocarbons in the city of Tehran-Iran

Air pollution in the city of Tehran has been a major problem for the past three decades. The direct effects of hydrocarbon contaminants in the air are particularly important such as their carcinogenic, mutagenic, and teratogenic effects which can be transported to other environments via dry and wet deposition. In the present study, rainwater samples were collected and analyzed for 16 polycyclic aromatic hydrocarbons (PAHs), benzene, toluene, ethyl benzene, and xylene (BTEX) as well as fuel fingerprints in two ranges of gasoline (C5–C11) and diesel fuel (C12–C20) using a gas chromatograph equipped with a flame ionization detector (GC/FID). Mean concentrations of ∑16 PAHs varied between 372 and 527 µg/L and for BTEX was between 87 and 188 µg/L with maximum of 36 µg/L for toluene. Both gasoline range hydrocarbons (GRH) and diesel range hydrocarbons (DRH) were also present in the collected rainwater at concentrations of 190 and 950 µg/L, respectively. Hydrocarbon transports from air to soil were determined in this wet deposition. Average hydrocarbon transportation for ∑PAHs, BTEX, GRH, and DRH was 2,747, 627, 1,152, and 5,733 µg/m2, respectively

Assessment of personal care and medical robots from older adults' perspective

Demographic reports indicate that population of older adults is growing significantly over the world and in particular in developed nations. Consequently, there are a noticeable number of demands for certain services such as health-care systems and assistive medical robots and devices. In today's world, different types of robots play substantial roles specifically in medical sector to facilitate human life, especially older adults. Assistive medical robots and devices are created in various designs to fulfill specific needs of older adults. Though medical robots are utilized widely by senior citizens, it is dramatic to find out into what extent assistive robots satisfy their needs and expectations. This paper reviews various assessments of assistive medical robots from older adults' perspectives with the purpose of identifying senior citizen's needs, expectations, and preferences. On the other hand, these kinds of assessments inform robot designers, developers, and programmers to come up with robots fulfilling elderly's needs while improving their life quality

Evolutionary dynamics of tumor-stroma interactions in multiple myeloma

Cancer cells and stromal cells cooperate by exchanging diffusible factors that sustain tumor growth, a form of frequency-dependent selection that can be studied in the framework of evolutionary game theory. In the case of multiple myeloma, three types of cells (malignant plasma cells, osteoblasts and osteoclasts) exchange growth factors with different effects, and tumor-stroma interactions have been analysed using a model of cooperation with pairwise interactions. Here we show that a model in which growth factors have autocrine and paracrine effects on multiple cells, a more realistic assumption for tumor-stroma interactions, leads to different results, with implications for disease progression and treatment. In particular, the model reveals that reducing the number of malignant plasma cells below a critical threshold can lead to their extinction and thus to restore a healthy balance between osteoclast and osteoblast, a result in line with current therapies against multiple myeloma

The use of the Nintendo Wii in motor rehabilitation for virtual reality interventions:a literature review

Several review articles have been published on the use of Virtual Reality (VR) in motor rehabilitation. The majority of these focus on the effectiveness of VR on improving motor function using relatively expensive commercial tools and technologies including robotics, cybergloves, cybergrasps, joysticks, force sensors and motion capture systems. However, we present the case in this chapter that game sensors and VR technologies which can be customized and reconfigured, such as the Nintendo Wii, provide an alternative and affordable VR intervention for rehabilitation. While the performance of many of the Wii based interventions in motor rehabilitation are currently the focus of investigation by researchers, an extensive and holistic discussion on this subject does not yet exist. As such, the purpose of this chapter is to provide readers with an understanding of the advantages and limitations of the Nintendo Wii game sensor device (and its associated accessories) for motor rehabilitation and in addition, to outline the potential for incorporating these into clinical interventions for the benefit of patients and therapists