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Concept: Ratio distribution


The fair division of a surplus is one of the most widely examined problems. This paper focuses on bargaining problems with fixed disagreement payoffs where risk-neutral agents have reached an agreement that is the Nash-bargaining solution (NBS). We consider a stochastic environment, in which the overall return consists of multiple pies with uncertain sizes and we examine how these pies can be allocated with fairness among agents. Specifically, fairness is based on the Aristotle’s maxim: “equals should be treated equally and unequals unequally, in proportion to the relevant inequality”. In this context, fairness is achieved when all the individual stochastic surplus shares which are allocated to agents are distributed in proportion to the NBS. We introduce a novel algorithm, which can be used to compute the ratio of each pie that should be allocated to each agent, in order to ensure fairness within a symmetric or asymmetric NBS.

Concepts: Game theory, Ratio, Agent, Ratio distribution, Nash bargaining game, Bargaining, Pie, Cooperative games


Although printed circuit boards (PCBs) contain various elements, only the major elements (i.e., those with content levels in wt% or over grade) of and precious metals (e.g., Ag, Au, and platinum groups) contained within PCBs can be recycled. To recover other elements from PCBs, the PCBs should be properly disassembled as the first step of the recycling process. The recovery of these other elements would be beneficial for efforts to conserve scarce resources, reuse electric/electronic components (EECs), and eliminate environmental problems. This paper examines the disassembly of EECs from wasted PCBs (WPCBs) and the physical separation of these EECs using a self-designed disassembling apparatus and a 3-step separation process of sieving, magnetic separation, and dense medium separation. The disassembling efficiencies were evaluated by using the ratio of grinding area (E(area)) and the weight ratio of the detached EECs (E(weight)). In the disassembly treatment, these efficiencies were improved with an increase of grinder speed and grinder height. 97.7% (E(area)) and 98% (E(weight)) could be accomplished ultimately by 3 repetitive treatments at a grinder speed of 5500rpm and a grinder height of 1.5mm. Through a series of physical separations, most groups of the EECs (except for the diode, transistor, and IC chip groups) could be sorted at a relatively high separation efficiency of about 75% or more. To evaluate the separation efficiency with regard to the elemental composition, the distribution ratio (R(dis)) and the concentration ratio (R(conc)) were used. 15 elements could be separated with the highest R(dis) and R(conc) in the same separated division. This result implies that the recyclability of the elements is highly feasible, even though the initial content in EECs is lower than several tens of mg/kg.

Concepts: Ratio, Integrated circuit, Recycling, Printed circuit board, Breadboard, Electronic component, Multi-Chip Module, Ratio distribution


Large-scale data from social media have a significant potential to describe complex phenomena in the real world and to anticipate collective behaviors such as information spreading and social trends. One specific case of study is represented by the collective attention to the action of political parties. Not surprisingly, researchers and stakeholders tried to correlate parties' presence on social media with their performances in elections. Despite the many efforts, results are still inconclusive since this kind of data is often very noisy and significant signals could be covered by (largely unknown) statistical fluctuations. In this paper we consider the number of tweets (tweet volume) of a party as a proxy of collective attention to the party, identify the dynamics of the volume, and show that this quantity has some information on the election outcome. We find that the distribution of the tweet volume for each party follows a log-normal distribution with a positive autocorrelation of the volume over short terms, which indicates the volume has large fluctuations of the log-normal distribution yet with a short-term tendency. Furthermore, by measuring the ratio of two consecutive daily tweet volumes, we find that the evolution of the daily volume of a party can be described by means of a geometric Brownian motion (i.e., the logarithm of the volume moves randomly with a trend). Finally, we determine the optimal period of averaging tweet volume for reducing fluctuations and extracting short-term tendencies. We conclude that the tweet volume is a good indicator of parties' success in the elections when considered over an optimal time window. Our study identifies the statistical nature of collective attention to political issues and sheds light on how to model the dynamics of collective attention in social media.

Concepts: Volume, Ratio, Normal distribution, Brownian motion, Logarithm, Ratio distribution, Political party, Political faction


There is a perception that women are under-represented as speakers at emergency medicine (EM) conferences. We aimed to evaluate the ratio of male to female speakers and the proportion of presenting time by gender at major international EM conferences.

Concepts: Male, Female, Gender, Sex, Ratio, Woman, Gamete, Ratio distribution


We aimed to compare empirically the treatment effects measured by the hazard ratio (HR) and by the difference (and ratio) of restricted mean survival times (RMST) in oncology randomized trials.

Concepts: Comparison, Epidemiology, Randomized controlled trial, Ratio, Comparisons, Ratio distribution


Given increasing efforts to use resting-state fMRI (rfMRI) as a biomarker of disease progression in multiple sclerosis (MS) we here explored the reproducibility of longitudinal rfMRI over three months in patients with clinically and radiologically stable MS. To pursue this aim, two approaches were applied in nine rfMRI networks: First, the intraclass correlation coefficient (ICC 3,1) was assessed for the mean functional connectivity maps across the entire network and a region of interest (ROI). Second, the ratio of overlap between Z-thresholded connectivity maps for each network was assessed. We quantified between-session functional reproducibility of rfMRI for 20 patients with stable MS and 14 healthy controls (HC). Nine rfMRI networks (RSNs) were examined at baseline and after 3 months of follow-up: three visual RSNs, the default-mode network, sensorimotor-, auditory-, executive control, and the left and right fronto-parietal RSN. ROI analyses were constrained to thresholded overlap masks for each individual (Z>0) at baseline and follow-up.In both stable MS and HC mean functional connectivity across the entire network did not reach acceptable ICCs for several networks (ICC<0.40) but we found a high reproducibility of ROI ICCs and of the ratio of overlap. ROI ICCs of all nine networks were between 0.98 and 0.99 for HC and ranged from 0.88 to 0.99 in patients with MS, respectively. The ratio of overlap for all networks was similar for both groups, ranging from 0.60 to 0.75.Our findings attest to a high reproducibility of rfMRI networks not only in HC but also in patients with stable MS when applying ROI analysis. This supports the utility of rfMRI to monitor functional changes related to disease progression or therapeutic interventions in MS.

Concepts: Multiple sclerosis, Ratio, Arithmetic mean, Correlation and dependence, Covariance and correlation, Computer network, Intraclass correlation, Ratio distribution


Development of tamarind seed gum (TSG)-hydrolyzed polymethacrylamide-g-gellan (h-Pmaa-g-GG) composite beads for extended release of diclofenac sodium using 32full factorial design is the main purpose of this study. The ratio of h-Pmaa-g-GG and TSG and concentration of cross-linker CaCl2were taken as independent factors with three different levels of each. Effects of polymer ratio and CaCl2on drug entrapment efficiency (DEE), drug release, bead size and swelling were investigated. Responses such as DEE and different drug release parameters were statistically analyzed by 32full factorial design using Design-Expert software and finally the formulation factors were optimized to obtain USP-reference release profile. Drug release rate was found to decrease with decrease in the ratio of h-Pmaa-g-GG:TSG and increase in the concentration of Ca2+ions in cross-linking medium. The optimized formulation showed DEE of 93.25% and an extended drug release profile over a period of 10 h with f2 = 80.13. Kinetic modeling unveiled case-I-Fickian diffusion based drug release mechanism.

Concepts: Ratio, Diclofenac, Seed, Cross-link, Bead, Ratio distribution


To evaluate the prognostic value of fluid-attenuated inversion recovery (FLAIR) signal intensity of postoperative cavity on progression free survival (PFS) and overall survival (OS) in patients with high-grade gliomas (HGG). This study retrospectively enrolled 45 consecutive HGG patients. These patients had chemoradiotherapy after gross-total resection of tumors. Quantitative analysis of the FLAIR signal intensity in postoperative cavity and background was made. We evaluated the threshold value, accuracy, sensitivity, specificity, and survival state with this technique. The patients who progressed and patients who did not progress were 33 and 12 cases separately. The ratio of postoperative cavity and background (C-B) on FLAIR sequence in patients who progressed was higher than that of patients who did not progress (P = 0.014). The PFS of the patients who progressed was shorter than that of patients who did not progress (P = 0.008). The area under ROC curve, threshold, sensitivity, specificity of C-B ratio for predicting tumor progression were 0.875, 62.3, 69.7, 0.84, and 0.50% respectively. The PFS of lower signal group was much longer than that of higher signal group (P = 0.004). The OS of the patients with higher signal was shorter than that of patients with lower signal (P = 0.034). The increase of gray value of FLAIR in postoperative cavity may be used as an imaging marker for predicting tumor progression.

Concepts: Sensitivity and specificity, Brain tumor, Tumor, Ratio, Prognosis, Work in progress, Binary classification, Ratio distribution


Mössbauer reflectivity spectra and nuclear resonance reflectivity (NRR) curves have been measured using the Synchrotron Mössbauer Source (SMS) for a [57Fe/Cr]30periodic multilayer, characterized by the antiferromagnetic interlayer coupling between adjacent57Fe layers. Specific features of the Mössbauer reflectivity spectra measured with π-polarized radiation of the SMS near the critical angle and at the `magnetic' maximum on the NRR curve are analyzed. The variation of the ratio of lines in the Mössbauer reflectivity spectra and the change of the intensity of the `magnetic' maximum under an applied external field has been used to reveal the transformation of the magnetic alignment in the investigated multilayer.

Concepts: Electron, Ionizing radiation, Magnetism, Ratio, Curve, Nuclear weapon, Ratio distribution, Blend modes


We demonstrate the generation of counter-rotating cavity solitons in a silicon nitride microresonator using a fixed, single-frequency laser. We demonstrate a dual three-soliton state with a difference in the repetition rates of the soliton trains that can be tuned by varying the ratio of pump powers in the two directions. Such a system enables a highly compact, tunable dual comb source that can be used for applications such as spectroscopy and distance ranging.

Concepts: Fluid dynamics, Ratio, Silicon, Boron nitride, Ratio distribution, Soliton