Finding the Minimum-Weight k-Path

Given a weighted $n$-vertex graph $G$ with integer edge-weights taken from a range $[-M,M]$, we show that the minimum-weight simple path visiting $k$ vertices can be found in time \tilde{O}(2^k \poly(k) M n^\omega) = O^*(2^k M). If the weights are reals in $[1,M]$, we provide a $(1+\varepsilon)$-approximation which has a running time of \tilde{O}(2^k \poly(k) n^\omega(\log\log M + 1/\varepsilon)). For the more general problem of $k$-tree, in which we wish to find a minimum-weight copy of a $k$-node tree $T$ in a given weighted graph $G$, under the same restrictions on edge weights respectively, we give an exact solution of running time \tilde{O}(2^k \poly(k) M n^3) and a $(1+\varepsilon)$-approximate solution of running time \tilde{O}(2^k \poly(k) n^3(\log\log M + 1/\varepsilon)). All of the above algorithms are randomized with a polynomially-small error probability.Comment: To appear at WADS 201

Social media addiction and poor mental health: examining the mediating roles of internet addiction and phubbing

Many researchers have examined the potential detrimental role of problematic social media use (often referred as ‘social media addiction’) on mental health. The present study investigated how social media addiction is associated with three components of mental health: depression, anxiety, and stress. In addition, structural equation modeling was used to test the mediating roles of internet addiction and phubbing among a sample of young adults (N = 603). Results showed that social media addiction was associated with poorer mental health via internet addiction and phubbing. More specifically, associations between social media addiction and stress, and social media addiction and anxiety were explained by both internet addiction and phubbing. The association between social media addiction and depression was explained by internet addiction only. These results remained consistent after controlling for gender, age, frequency of internet use, frequency of social media use, and frequency of smartphone use. These findings extend the extant literature by providing evidence for the dual roles of internet addiction and phubbing in explaining the relationship between social media addiction and poor mental health. Social media addiction did not directly influence poorer mental health but did via internet addiction and phubbing. Therefore, greater awareness of the inter-relationships between technology-based behaviors and their impact on mental health is needed among a wide range of stakeholders, and these inter-relationships need considering in the prevention and treatment of technology-based disorders

Which morphological abnormalities better define the elongation of transverse aortic arch: a magnetic resonance angiography study

Background: The aim of the study is to investigate the relation between morphological abnormalities that might indicate elongation of transverse aortic arch (ETA) and various aortic and thoracic measurements, and to determine which morphological criteria define the elongated transverse arch better.Materials and methods: Patients under 40 years of age who underwent contrast enhanced thoracic magnetic resonance angiography were included in the study. Images were evaluated for the presence of morphological arch abnormalities such as late take off (LTO) of left subclavian artery (LSA), flattening of the arch, and kinking at the posterior or anterior contour of the lesser curvature. Various aortic and thoracic measurements, including the distance between the orifices of the left common carotid artery (LCCA) and LSA, were made. Statistical relation between morphological abnormalities and these measurements was analysed. The effect of morphological abnormalities and their combinations on the distance between LCCA and LSA orifices was evaluated by linear regression analysis.Results: Ninety three cases were included in the study. All morphological abnormalities and most of their combinations show statistically significant relation with longer LCCA to LSA distance. The parameters that most affected this distance were combination of flattening with LTO of LSA, anterior kinking and combination of anterior kinking with both flattening and LTO, respectively.Conclusions: Our study showed that the finding which best defines ETA is the combination of LTO and arch flattening. Therefore, we recommend using this combination in the diagnosis of ETA instead of the classical diagnostic criteria including combination of LTO and posterior kinking

Spectra of Modular and Small-World Matrices

We compute spectra of symmetric random matrices describing graphs with general modular structure and arbitrary inter- and intra-module degree distributions, subject only to the constraint of finite mean connectivities. We also evaluate spectra of a certain class of small-world matrices generated from random graphs by introducing short-cuts via additional random connectivity components. Both adjacency matrices and the associated graph Laplacians are investigated. For the Laplacians, we find Lifshitz type singular behaviour of the spectral density in a localised region of small $|\lambda|$ values. In the case of modular networks, we can identify contributions local densities of state from individual modules. For small-world networks, we find that the introduction of short cuts can lead to the creation of satellite bands outside the central band of extended states, exhibiting only localised states in the band-gaps. Results for the ensemble in the thermodynamic limit are in excellent agreement with those obtained via a cavity approach for large finite single instances, and with direct diagonalisation results.Comment: 18 pages, 5 figure

On the critical level-curvature distribution

The parametric motion of energy levels for non-interacting electrons at the Anderson localization critical point is studied by computing the energy level-curvatures for a quasiperiodic ring with twisted boundary conditions. We find a critical distribution which has the universal random matrix theory form ${\bar P}(K)\sim |K|^{-3}$ for large level-curvatures $|K|$ corresponding to quantum diffusion, although overall it is close to approximate log-normal statistics corresponding to localization. The obtained hybrid distribution resembles the critical distribution of the disordered Anderson model and makes a connection to recent experimental data.Comment: 4 pages, 3 figure

A preferential attachment model with random initial degrees

In this paper, a random graph process ${G(t)}_{t\geq 1}$ is studied and its degree sequence is analyzed. Let $(W_t)_{t\geq 1}$ be an i.i.d. sequence. The graph process is defined so that, at each integer time $t$, a new vertex, with $W_t$ edges attached to it, is added to the graph. The new edges added at time t are then preferentially connected to older vertices, i.e., conditionally on $G(t-1)$, the probability that a given edge is connected to vertex i is proportional to $d_i(t-1)+\delta$, where $d_i(t-1)$ is the degree of vertex $i$ at time $t-1$, independently of the other edges. The main result is that the asymptotical degree sequence for this process is a power law with exponent $\tau=\min\{\tau_{W}, \tau_{P}\}$, where $\tau_{W}$ is the power-law exponent of the initial degrees $(W_t)_{t\geq 1}$ and $\tau_{P}$ the exponent predicted by pure preferential attachment. This result extends previous work by Cooper and Frieze, which is surveyed.Comment: In the published form of the paper, the proof of Proposition 2.1 is incomplete. This version contains the complete proo

Vascular Wall-Resident CD44+ Multipotent Stem Cells Give Rise to Pericytes and Smooth Muscle Cells and Contribute to New Vessel Maturation

Here, we identify CD44(+)CD90(+)CD73(+)CD34(−)CD45(−) cells within the adult human arterial adventitia with properties of multipotency which were named vascular wall-resident multipotent stem cells (VW-MPSCs). VW-MPSCs exhibit typical mesenchymal stem cell characteristics including cell surface markers in immunostaining and flow cytometric analyses, and differentiation into adipocytes, chondrocytes and osteocytes under culture conditions. Particularly, TGFß1 stimulation up-regulates smooth muscle cell markers in VW-MPSCs. Using fluorescent cell labelling and co-localisation studies we show that VW-MPSCs differentiate to pericytes/smooth muscle cells which cover the wall of newly formed endothelial capillary-like structures in vitro. Co-implantation of EGFP-labelled VW-MPSCs and human umbilical vein endothelial cells into SCID mice subcutaneously via Matrigel results in new vessels formation which were covered by pericyte- or smooth muscle-like cells generated from implanted VW-MPSCs. Our results suggest that VW-MPSCs are of relevance for vascular morphogenesis, repair and self-renewal of vascular wall cells and for local capacity of neovascularization in disease processes

Genome-wide patterns of promoter sharing and co-expression in bovine skeletal muscle

Background: Gene regulation by transcription factors (TF) is species, tissue and time specific. To better understand how the genetic code controls gene expression in bovine muscle we associated gene expression data from developing Longissimus thoracis et lumborum skeletal muscle with bovine promoter sequence information.Results: We created a highly conserved genome-wide promoter landscape comprising 87,408 interactions relating 333 TFs with their 9,242 predicted target genes (TGs). We discovered that the complete set of predicted TGs share an average of 2.75 predicted TF binding sites (TFBSs) and that the average co-expression between a TF and its predicted TGs is higher than the average co-expression between the same TF and all genes. Conversely, pairs of TFs sharing predicted TGs showed a co-expression correlation higher that pairs of TFs not sharing TGs. Finally, we exploited the co-occurrence of predicted TFBS in the context of muscle-derived functionally-coherent modules including cell cycle, mitochondria, immune system, fat metabolism, muscle/glycolysis, and ribosome. Our findings enabled us to reverse engineer a regulatory network of core processes, and correctly identified the involvement of E2F1, GATA2 and NFKB1 in the regulation of cell cycle, fat, and muscle/glycolysis, respectively.Conclusion: The pivotal implication of our research is two-fold: (1) there exists a robust genome-wide expression signal between TFs and their predicted TGs in cattle muscle consistent with the extent of promoter sharing; and (2) this signal can be exploited to recover the cellular mechanisms underpinning transcription regulation of muscle structure and development in bovine. Our study represents the first genome-wide report linking tissue specific co-expression to co-regulation in a non-model vertebrate