Approximately Stable Matchings with Budget Constraints

This paper considers two-sided matching with budget constraints where one side (firm or hospital) can make monetary transfers (offer wages) to the other (worker or doctor). In a standard model, while multiple doctors can be matched to a single hospital, a hospital has a maximum quota: the number of doctors assigned to a hospital cannot exceed a certain limit. In our model, a hospital instead has a fixed budget: the total amount of wages allocated by each hospital to doctors is constrained. With budget constraints, stable matchings may fail to exist and checking for the existence is hard. To deal with the nonexistence of stable matchings, we extend the "matching with contracts" model of Hatfield and Milgrom, so that it handles approximately stable matchings where each of the hospitals' utilities after deviation can increase by factor up to a certain amount. We then propose two novel mechanisms that efficiently return such a stable matching that exactly satisfies the budget constraints. In particular, by sacrificing strategy-proofness, our first mechanism achieves the best possible bound. Furthermore, we find a special case such that a simple mechanism is strategy-proof for doctors, keeping the best possible bound of the general case.Comment: Accepted for the 32nd AAAI Conference on Artificial Intelligence (AAAI2018). arXiv admin note: text overlap with arXiv:1705.0764

Z-score-based modularity for community detection in networks

Identifying community structure in networks is an issue of particular interest in network science. The modularity introduced by Newman and Girvan [Phys. Rev. E 69, 026113 (2004)] is the most popular quality function for community detection in networks. In this study, we identify a problem in the concept of modularity and suggest a solution to overcome this problem. Specifically, we obtain a new quality function for community detection. We refer to the function as Z-modularity because it measures the Z-score of a given division with respect to the fraction of the number of edges within communities. Our theoretical analysis shows that Z-modularity mitigates the resolution limit of the original modularity in certain cases. Computational experiments using both artificial networks and well-known real-world networks demonstrate the validity and reliability of the proposed quality function.Comment: 8 pages, 10 figure

Additive Approximation Algorithms for Modularity Maximization

The modularity is a quality function in community detection, which was introduced by Newman and Girvan (2004). Community detection in graphs is now often conducted through modularity maximization: given an undirected graph $G=(V,E)$, we are asked to find a partition $\mathcal{C}$ of $V$ that maximizes the modularity. Although numerous algorithms have been developed to date, most of them have no theoretical approximation guarantee. Recently, to overcome this issue, the design of modularity maximization algorithms with provable approximation guarantees has attracted significant attention in the computer science community. In this study, we further investigate the approximability of modularity maximization. More specifically, we propose a polynomial-time $\left(\cos\left(\frac{3-\sqrt{5}}{4}\pi\right) - \frac{1+\sqrt{5}}{8}\right)$-additive approximation algorithm for the modularity maximization problem. Note here that $\cos\left(\frac{3-\sqrt{5}}{4}\pi\right) - \frac{1+\sqrt{5}}{8} < 0.42084$ holds. This improves the current best additive approximation error of $0.4672$, which was recently provided by Dinh, Li, and Thai (2015). Interestingly, our analysis also demonstrates that the proposed algorithm obtains a nearly-optimal solution for any instance with a very high modularity value. Moreover, we propose a polynomial-time $0.16598$-additive approximation algorithm for the maximum modularity cut problem. It should be noted that this is the first non-trivial approximability result for the problem. Finally, we demonstrate that our approximation algorithm can be extended to some related problems.Comment: 23 pages, 4 figure

The Densest Subgraph Problem with a Convex/Concave Size Function

we propose a linear-programming-based polynomial-time exact algorithm. It should be emphasized that this algorithm obtains not only an optimal solution to the problem but also subsets of vertices corresponding to the extreme points of the upper convex hull of {(|S|, w(S)) | S subseteq V }, which we refer to as the dense frontier points. We also propose a flow-based combinatorial exact algorithm for unweighted graphs that runs in O(n^3) time. Finally, we propose a nearly-linear-time 3-approximation algorithm

Stochastic Solutions for Dense Subgraph Discovery in Multilayer Networks

Network analysis has played a key role in knowledge discovery and data mining. In many real-world applications in recent years, we are interested in mining multilayer networks, where we have a number of edge sets called layers, which encode different types of connections and/or time-dependent connections over the same set of vertices. Among many network analysis techniques, dense subgraph discovery, aiming to find a dense component in a network, is an essential primitive with a variety of applications in diverse domains. In this paper, we introduce a novel optimization model for dense subgraph discovery in multilayer networks. Our model aims to find a stochastic solution, i.e., a probability distribution over the family of vertex subsets, rather than a single vertex subset, whereas it can also be used for obtaining a single vertex subset. For our model, we design an LP-based polynomial-time exact algorithm. Moreover, to handle large-scale networks, we also devise a simple, scalable preprocessing algorithm, which often reduces the size of the input networks significantly and results in a substantial speed-up. Computational experiments demonstrate the validity of our model and the effectiveness of our algorithms.Comment: Accepted to WSDM 202

EFFECTS OF FASTING ON PRAVASTATIN DISPOSITION IN PERFUSED RAT LIVER

Objective: Various nutrients such as glucose and cholesterol affect the expression of hepatic transporters. Although the pharmacokinetics of some drugs is affected by fasting, the fasting effects on drug hepatic disposition via alterations in transporters are unclear. Organic anion-transporting polypeptides and multidrug resistance-associated protein 2 (Mrp2/Abcc2) expressed in the liver are involved in hepatic disposition of pravastatin.Methods: An in situ perfused rat liver system was established. The mRNA and protein levels of transporters in the liver were examined by real-time reverse transcription PCR and western blotting. The localization of Mrp2 in hepatocytes was determined by immunostaining.Results: Pravastatin was rapidly eliminated from the perfusate. The cumulative biliary excretion amounts of pravastatin in fasting rats were significantly lower from 10 min compared with control. In fasting rats, the area under the plasma concentration-time curve (AUC)0‒∞ of pravastatin in the perfusate was significantly decreased, and hepatic clearance (CLh) and hepatic corrected clearance (CLcor) were significantly increased. The biliary clearance (CLbile) in fasting rats tended to decrease compared with that in control rats. Protein expression levels of transporters were unchanged after fasting. Confocal microscopy revealed a disruption of Mrp2 and ZO-1 colocalization in the liver of fasting rats.Conclusion: The biliary excretion of pravastatin was inhibited by fasting via decreased Mrp2 localization on the canalicular membrane

Spatially Resolved Spectral Imaging by A THz-FEL

Using the unique characteristics of the free-electron-laser (FEL), we successfully performed high-sensitivity spectral imaging of different materials in the terahertz (THz) and far-infrared (FIR) domain. THz imaging at various wavelengths was achieved using in situ spectroscopy by means of this wavelength tunable and monochromatic source. In particular, owing to its large intensity and directionality, we could collect high-sensitivity transmission imaging of extremely low-transparency materials and three-dimensional objects in the 3–6 THz range. By accurately identifying the intrinsic absorption wavelength of organic and inorganic materials, we succeeded in the mapping of spatial distribution of individual components. This simple imaging technique using a focusing optics and a raster scan modality has made it possible to set up and carry out fast spectral imaging experiments on different materials in this radiation facility

Identification of a novel intronic enhancer responsible for the transcriptional regulation of musashi1 in neural stem/progenitor cells

<p>Abstract</p> <p>Background</p> <p>The specific genetic regulation of neural primordial cell determination is of great interest in stem cell biology. The Musashi1 (Msi1) protein, which belongs to an evolutionarily conserved family of RNA-binding proteins, is a marker for neural stem/progenitor cells (NS/PCs) in the embryonic and post-natal central nervous system (CNS). Msi1 regulates the translation of its downstream targets, including <it>m-Numb </it>and <it>p21 </it>mRNAs. <it>In vitro </it>experiments using knockout mice have shown that Msi1 and its isoform Musashi2 (Msi2) keep NS/PCs in an undifferentiated and proliferative state. Msi1 is expressed not only in NS/PCs, but also in other somatic stem cells and in tumours. Based on previous findings, Msi1 is likely to be a key regulator for maintaining the characteristics of self-renewing stem cells. However, the mechanisms regulating <it>Msi1 </it>expression are not yet clear.</p> <p>Results</p> <p>To identify the DNA region affecting <it>Msi1 </it>transcription, we inserted the fusion gene <it>ffLuc</it>, comprised of the fluorescent <it>Venus </it>protein and firefly <it>Luciferase</it>, at the translation initiation site of the mouse <it>Msi1 </it>gene locus contained in a 184-kb bacterial artificial chromosome (BAC). Fluorescence and Luciferase activity, reflecting the <it>Msi1 </it>transcriptional activity, were observed in a stable BAC-carrying embryonic stem cell line when it was induced toward neural lineage differentiation by retinoic acid treatment. When neuronal differentiation was induced in embryoid body (EB)-derived neurosphere cells, reporter signals were detected in Msi1-positive NSCs and GFAP-positive astrocytes, but not in MAP2-positive neurons. By introducing deletions into the BAC reporter gene and conducting further reporter experiments using a minimized enhancer region, we identified a region, "D5E2," that is responsible for <it>Msi1 </it>transcription in NS/PCs.</p> <p>Conclusions</p> <p>A regulatory element for <it>Msi1 </it>transcription in NS/PCs is located in the sixth intron of the <it>Msi1 </it>gene. The 595-bp D5E2 intronic enhancer can transactivate <it>Msi1 </it>gene expression with cell-type specificity markedly similar to the endogenous Msi1 expression patterns.</p