On the decomposition threshold of a given graph

We study the $F$-decomposition threshold $\delta_F$ for a given graph $F$. Here an $F$-decomposition of a graph $G$ is a collection of edge-disjoint copies of $F$ in $G$ which together cover every edge of $G$. (Such an $F$-decomposition can only exist if $G$ is $F$-divisible, i.e. if $e(F)\mid e(G)$ and each vertex degree of $G$ can be expressed as a linear combination of the vertex degrees of $F$.) The $F$-decomposition threshold $\delta_F$ is the smallest value ensuring that an $F$-divisible graph $G$ on $n$ vertices with $\delta(G)\ge(\delta_F+o(1))n$ has an $F$-decomposition. Our main results imply the following for a given graph $F$, where $\delta_F^\ast$ is the fractional version of $\delta_F$ and $\chi:=\chi(F)$: (i) $\delta_F\le \max\{\delta_F^\ast,1-1/(\chi+1)\}$; (ii) if $\chi\ge 5$, then $\delta_F\in\{\delta_F^{\ast},1-1/\chi,1-1/(\chi+1)\}$; (iii) we determine $\delta_F$ if $F$ is bipartite. In particular, (i) implies that $\delta_{K_r}=\delta^\ast_{K_r}$. Our proof involves further developments of the recent `iterative' absorbing approach.Comment: Final version, to appear in the Journal of Combinatorial Theory, Series

Monochromatic cycle partitions in random graphs

Erd\H{o}s, Gy\'arf\'as and Pyber showed that every $r$-edge-coloured complete graph $K_n$ can be covered by $25 r^2 \log r$ vertex-disjoint monochromatic cycles (independent of $n$). Here, we extend their result to the setting of binomial random graphs. That is, we show that if $p = p(n) = \Omega(n^{-1/(2r)})$, then with high probability any $r$-edge-coloured $G(n,p)$ can be covered by at most $1000 r^4 \log r$ vertex-disjoint monochromatic cycles. This answers a question of Kor\'andi, Mousset, Nenadov, \v{S}kori\'{c} and Sudakov.Comment: 16 pages, accepted in Combinatorics, Probability and Computin

Virtual volatility

We introduce the concept of virtual volatility. This simple but new measure shows how to quantify the uncertainty in the forecast of the drift component of a random walk. The virtual volatility also is a useful tool in understanding the stochastic process for a given portfolio. In particular, and as an example, we were able to identify mean reversion effect in our portfolio. Finally, we briefly discuss the potential practical effect of the virtual volatility on an investor asset allocation strategy.Comment: 15 pages, 2 figures, elsart.cls, Accepted to Physica A. Added few comments that clarify data used for empirical wor

Study protocol for a randomised controlled trial evaluating the effectiveness of strengths model case management (SMCM) with Chinese mental health service users in Hong Kong

Introduction Strengths-based approaches mobilise individual and environmental resources that can facilitate the recovery of people with mental illness. Strengths model case management (SMCM), developed by Rapp and Goscha through collaborative efforts at the University of Kansas, offers a structured and innovative intervention. As evidence of the effectiveness of strengths-based interventions come from Western studies, which lacked rigorous research design or failed to assure fidelity to the model, we aim to fill these gaps and conduct a randomised controlled trial (RCT) to test the effectiveness of SMCM for individuals with mental illness in Hong Kong. Methods and analysis This will be an RCT of SMCM. Assuming a medium intervention effect (Cohen’s d=0.60) with 30% missing data (including dropouts), 210 service users aged 18 years or above will be recruited from three community mental health centres. They will be randomly assigned to SMCM groups (intervention) or SMILE groups (control) in a 1:1 ratio. The SMCM groups will receive strengths model interventions from case workers, whereas the SMILE groups will receive generic care from case workers with an attention placebo. The case workers will all be embedded in the community centres and will be required to provide a session with service users in both groups at least once every fortnight. There will be two groups of case workers for the intervention and control groups, respectively. The effectiveness of the SMCM will be compared between the two groups of service users with outcomes at baseline, 6 and 12 months after recruitment. Functional outcomes will also be reported by case workers. Data on working alliances and goal attainment will be collected from individual case workers. Qualitative evaluation will be conducted to identify the therapeutic ingredients and conditions leading to positive outcomes. Trained outcome assessors will be blind to the group allocation. Ethics and dissemination Ethical approval from the Human Research Ethics Committee at the University of Hong Kong has been obtained (HRECNCF: EA1703078). The results will be disseminated to service users and their families via the media, to healthcare professionals via professional training and meetings and to researchers via conferences and publications

In vivo delivery of transcription factors with multifunctional oligonucleotides.

Therapeutics based on transcription factors have the potential to revolutionize medicine but have had limited clinical success as a consequence of delivery problems. The delivery of transcription factors is challenging because it requires the development of a delivery vehicle that can complex transcription factors, target cells and stimulate endosomal disruption, with minimal toxicity. Here, we present a multifunctional oligonucleotide, termed DARTs (DNA assembled recombinant transcription factors), which can deliver transcription factors with high efficiency in vivo. DARTs are composed of an oligonucleotide that contains a transcription-factor-binding sequence and hydrophobic membrane-disruptive chains that are masked by acid-cleavable galactose residues. DARTs have a unique molecular architecture, which allows them to bind transcription factors, trigger endocytosis in hepatocytes, and stimulate endosomal disruption. The DARTs have enhanced uptake in hepatocytes as a result of their galactose residues and can disrupt endosomes efficiently with minimal toxicity, because unmasking of their hydrophobic domains selectively occurs in the acidic environment of the endosome. We show that DARTs can deliver the transcription factor nuclear erythroid 2-related factor 2 (Nrf2) to the liver, catalyse the transcription of Nrf2 downstream genes, and rescue mice from acetaminophen-induced liver injury

Cyclical modulation of sphingosine-1-phosphate receptor 1 surface expression during lymphocyte recirculation and relationship to lymphoid organ transit

Sphingosine-1-phosphate receptor 1 (S1P1) was recently shown to be required for lymphocyte egress from lymphoid organs. Here we have examined the relationship between S1P1 abundance on the cell and egress efficiency. Using an integrin neutralization approach to separate the processes of entry and exit, we show that pertussis toxin treatment reduces lymphocyte egress from lymph nodes. Retrovirally mediated S1P1 overexpression is sufficient to reduce B cell accumulation in the splenic white pulp and to promote egress of activated T cells from lymph nodes, whereas S1P1+/−cells have reduced lymph node exit efficiency. Furthermore, lymphocyte S1P1 is down-regulated in the blood, up-regulated in lymphoid organs, and down-regulated again in the lymph. We propose that cyclical ligand-induced modulation of S1P1 on circulating lymphocytes contributes to establishing their lymphoid organ transit time

Assessing the Applicability of Hofstede\u27s Cultural Dimensions for Global 500 Corporations\u27 Facebook Profiles and Content

This research examines how Hofstede’s six cultural dimensions are reflected on the official corporate Facebook pages from 259 organizations on Fortune magazine’s Global 500 list. This research is grounded in original indices to measure the six dimensions across Facebook’s “About Us” section, the textual updates provided by the companies, as well as the media that they share (photographs and videos). This is the first attempt to create a conceptualization of Hofstede’s dimensions for organizational social media use. The results paint a mixed picture indicating that the global nature of these corporations is echoed in a somewhat similar overall presence on Facebook; but when the individual elements (About Us, updates, and media) are examined, statistical differences emerge in relation to the reflection of the cultural dimensions. Limitations and directions for future research are discussed