Hardness Transitions of Star Colouring and Restricted Star Colouring

We study how the complexity of the graph colouring problems star colouring and restricted star colouring vary with the maximum degree of the graph. Restricted star colouring (in short, rs colouring) is a variant of star colouring. For $k\in \mathbb{N}$, a $k$-colouring of a graph $G$ is a function $f\colon V(G)\to \mathbb{Z}_k$ such that $f(u)\neq f(v)$ for every edge $uv$ of $G$. A $k$-colouring of $G$ is called a $k$-star colouring of $G$ if there is no path $u,v,w,x$ in $G$ with $f(u)=f(w)$ and $f(v)=f(x)$. A $k$-colouring of $G$ is called a $k$-rs colouring of $G$ if there is no path $u,v,w$ in $G$ with $f(v)>f(u)=f(w)$. For $k\in \mathbb{N}$, the problem $k$-STAR COLOURABILITY takes a graph $G$ as input and asks whether $G$ admits a $k$-star colouring. The problem $k$-RS COLOURABILITY is defined similarly. Recently, Brause et al. (Electron. J. Comb., 2022) investigated the complexity of 3-star colouring with respect to the graph diameter. We study the complexity of $k$-star colouring and $k$-rs colouring with respect to the maximum degree for all $k\geq 3$. For $k\geq 3$, let us denote the least integer $d$ such that $k$-STAR COLOURABILITY (resp. $k$-RS COLOURABILITY) is NP-complete for graphs of maximum degree $d$ by $L_s^{(k)}$ (resp. $L_{rs}^{(k)}$). We prove that for $k=5$ and $k\geq 7$, $k$-STAR COLOURABILITY is NP-complete for graphs of maximum degree $k-1$. We also show that $4$-RS COLOURABILITY is NP-complete for planar 3-regular graphs of girth 5 and $k$-RS COLOURABILITY is NP-complete for triangle-free graphs of maximum degree $k-1$ for $k\geq 5$. Using these results, we prove the following: (i) for $k\geq 4$ and $d\leq k-1$, $k$-STAR COLOURABILITY is NP-complete for $d$-regular graphs if and only if $d\geq L_s^{(k)}$; and (ii) for $k\geq 4$, $k$-RS COLOURABILITY is NP-complete for $d$-regular graphs if and only if $L_{rs}^{(k)}\leq d\leq k-1$

Star Colouring of Bounded Degree Graphs and Regular Graphs

A $k$-star colouring of a graph $G$ is a function $f:V(G)\to\{0,1,\dots,k-1\}$ such that $f(u)\neq f(v)$ for every edge $uv$ of $G$, and every bicoloured connected subgraph of $G$ is a star. The star chromatic number of $G$, $\chi_s(G)$, is the least integer $k$ such that $G$ is $k$-star colourable. We prove that $\chi_s(G)\geq \lceil (d+4)/2\rceil$ for every $d$-regular graph $G$ with $d\geq 3$. We reveal the structure and properties of even-degree regular graphs $G$ that attain this lower bound. The structure of such graphs $G$ is linked with a certain type of Eulerian orientations of $G$. Moreover, this structure can be expressed in the LC-VSP framework of Telle and Proskurowski (SIDMA, 1997), and hence can be tested by an FPT algorithm with the parameter either treewidth, cliquewidth, or rankwidth. We prove that for $p\geq 2$, a $2p$-regular graph $G$ is $(p+2)$-star colourable only if $n:=|V(G)|$ is divisible by $(p+1)(p+2)$. For each $p\geq 2$ and $n$ divisible by $(p+1)(p+2)$, we construct a $2p$-regular Hamiltonian graph on $n$ vertices which is $(p+2)$-star colourable. The problem $k$-STAR COLOURABILITY takes a graph $G$ as input and asks whether $G$ is $k$-star colourable. We prove that 3-STAR COLOURABILITY is NP-complete for planar bipartite graphs of maximum degree three and arbitrarily large girth. Besides, it is coNP-hard to test whether a bipartite graph of maximum degree eight has a unique 3-star colouring up to colour swaps. For $k\geq 3$, $k$-STAR COLOURABILITY of bipartite graphs of maximum degree $k$ is NP-complete, and does not even admit a $2^{o(n)}$-time algorithm unless ETH fails

Randomized, Noncomparative, Phase II Trial of Early Switch From Docetaxel to Cabazitaxel or Vice Versa, With Integrated Biomarker Analysis, in Men With Chemotherapy-Naïve, Metastatic, Castration-Resistant Prostate Cancer

Purpose The TAXYNERGY trial ( ClinicalTrials.gov identifier: NCT01718353) evaluated clinical benefit from early taxane switch and circulating tumor cell (CTC) biomarkers to interrogate mechanisms of sensitivity or resistance to taxanes in men with chemotherapy-naïve, metastatic, castration-resistant prostate cancer. Patients and Methods Patients were randomly assigned 2:1 to docetaxel or cabazitaxel. Men who did not achieve ≥ 30% prostate-specific antigen (PSA) decline by cycle 4 (C4) switched taxane. The primary clinical endpoint was confirmed ≥ 50% PSA decline versus historical control (TAX327). The primary biomarker endpoint was analysis of post-treatment CTCs to confirm the hypothesis that clinical response was associated with taxane drug-target engagement, evidenced by decreased percent androgen receptor nuclear localization (%ARNL) and increased microtubule bundling. Results Sixty-three patients were randomly assigned to docetaxel (n = 41) or cabazitaxel (n = 22); 44.4% received prior potent androgen receptor-targeted therapy. Overall, 35 patients (55.6%) had confirmed ≥ 50% PSA responses, exceeding the historical control rate of 45.4% (TAX327). Of 61 treated patients, 33 (54.1%) had ≥ 30% PSA declines by C4 and did not switch taxane, 15 patients (24.6%) who did not achieve ≥ 30% PSA declines by C4 switched taxane, and 13 patients (21.3%) discontinued therapy before or at C4. Of patients switching taxane, 46.7% subsequently achieved ≥ 50% PSA decrease. In 26 CTC-evaluable patients, taxane-induced decrease in %ARNL (cycle 1 day 1 v cycle 1 day 8) was associated with a higher rate of ≥ 50% PSA decrease at C4 ( P = .009). Median composite progression-free survival was 9.1 months (95% CI, 4.9 to 11.7 months); median overall survival was not reached at 14 months. Common grade 3 or 4 adverse events included fatigue (13.1%) and febrile neutropenia (11.5%). Conclusion The early taxane switch strategy was associated with improved PSA response rates versus TAX327. Taxane-induced shifts in %ARNL may serve as an early biomarker of clinical benefit in patients treated with taxanes

Gene expression profiling reveals different pathways related to Abl and other genes that cooperate with c-Myc in a model of plasma cell neoplasia

<p>Abstract</p> <p>Background</p> <p>To elucidate the genes involved in the neoplastic transformation of B cells, global gene expression profiles were generated using Affymetrix U74Av2 microarrays, containing 12,488 genes, for four different groups of mouse B-cell lymphomas and six subtypes of pristane-induced mouse plasma cell tumors, three of which developed much earlier than the others.</p> <p>Results</p> <p>Unsupervised hierarchical cluster analysis exhibited two main sub-clusters of samples: a B-cell lymphoma cluster and a plasma cell tumor cluster with subclusters reflecting mechanism of induction. This report represents the first step in using global gene expression to investigate molecular signatures related to the role of cooperating oncogenes in a model of Myc-induced carcinogenesis. Within a single subgroup, e.g., ABPCs, plasma cell tumors that contained typical T(12;15) chromosomal translocations did not display gene expression patterns distinct from those with variant T(6;15) translocations, in which the breakpoint was in the <it>Pvt-1 </it>locus, 230 kb 3' of c-<it>Myc</it>, suggesting that c-<it>Myc </it>activation was the initiating factor in both. When integrated with previously published Affymetrix array data from human multiple myelomas, the IL-6-transgenic subset of mouse plasma cell tumors clustered more closely with MM1 subsets of human myelomas, slow-appearing plasma cell tumors clustered together with MM2, while plasma cell tumors accelerated by v-Abl clustered with the more aggressive MM3-MM4 myeloma subsets. Slow-appearing plasma cell tumors expressed <it>Socs1 </it>and <it>Socs2 </it>but v-<it>Abl</it>-accelerated plasma cell tumors expressed 4–5 times as much. Both v-<it>Abl</it>-accelerated and non-v-<it>Ab</it>l-associated tumors exhibited phosphorylated STAT 1 and 3, but only v-Abl-accelerated plasma cell tumors lost viability and STAT 1 and 3 phosphorylation when cultured in the presence of the v-Abl kinase inhibitor, STI-571. These data suggest that the Jak/Stat pathway was critical in the transformation acceleration by v-Abl and that v-Abl activity remained essential throughout the life of the tumors, not just in their acceleration. A different pathway appears to predominate in the more slowly arising plasma cell tumors.</p> <p>Conclusion</p> <p>Gene expression profiling differentiates not only B-cell lymphomas from plasma cell tumors but also distinguishes slow from accelerated plasma cell tumors. These data and those obtained from the sensitivity of v-Abl-accelerated plasma cell tumors and their phosphorylated STAT proteins indicate that these similar tumors utilize different signaling pathways but share a common initiating genetic lesion, a c-<it>Myc</it>-activating chromosome translocation.</p

Lack of Wdr13 Gene in Mice Leads to Enhanced Pancreatic Beta Cell Proliferation, Hyperinsulinemia and Mild Obesity

WD-repeat proteins are very diverse, yet these are structurally related proteins that participate in a wide range of cellular functions. WDR13, a member of this family, is conserved from fishes to humans and localizes into the nucleus. To understand the in vivo function(s) of Wdr13 gene, we have created and characterized a mutant mouse strain lacking this gene. The mutant mice had higher serum insulin levels and increased pancreatic islet mass as a result of enhanced beta cell proliferation. While a known cell cycle inhibitor, p21, was downregulated in the mutant islets, over expression of WDR13 in the pancreatic beta cell line (MIN6) resulted in upregulation of p21, accompanied by retardation of cell proliferation. We suggest that WDR13 is a novel negative regulator of the pancreatic beta cell proliferation. Given the higher insulin levels and better glucose clearance in Wdr13 gene deficient mice, we propose that this protein may be a potential candidate drug target for ameliorating impaired glucose metabolism in diabetes

Altitudinal variation in soil organic carbon stock in coniferous subtropical and broadleaf temperate forests in Garhwal Himalaya

<p>Abstract</p> <p>Background</p> <p>The Himalayan zones, with dense forest vegetation, cover a fifth part of India and store a third part of the country reserves of soil organic carbon (SOC). However, the details of altitudinal distribution of these carbon stocks, which are vulnerable to forest management and climate change impacts, are not well known.</p> <p>Results</p> <p>This article reports the results of measuring the stocks of SOC along altitudinal gradients. The study was carried out in the coniferous subtropical and broadleaf temperate forests of Garhwal Himalaya. The stocks of SOC were found to be decreasing with altitude: from 185.6 to 160.8 t C ha^-1and from 141.6 to 124.8 t C ha^-1in temperature (<it>Quercus leucotrichophora</it>) and subtropical (<it>Pinus roxburghii</it>) forests, respectively.</p> <p>Conclusion</p> <p>The results of this study lead to conclusion that the ability of soil to stabilize soil organic matter depends negatively on altitude and call for comprehensive theoretical explanation</p

Overhead tank is the potential breeding habitat of Anopheles stephensi in an urban transmission setting of Chennai, India

Background: Wells and overhead tanks (OHT) are the major breeding sources of the local malaria vector, Anopheles stephensi in the Indian city of Chennai; they play a significant role in vector breeding, and transmission of urban malaria. Many other man-made breeding habitats, such as cemented cisterns/containers, barrels or drums, sumps or underground tanks, and plastic pots/containers are maintained to supplement water needs, temporarily resulting in enhanced mosquito/vector breeding. Correlating breeding habitats with immature vector abundance is important in effective planning to strengthen operational execution of vector control measures. Methods: A year-long, weekly study was conducted in Chennai to inspect available clear/clean water mosquito breeding habitats. Different breeding features, such as instar-wise, immature density and co-inhabitation with other mosquito species, were analysed. The characteristics of breeding habitats, i.e., type of habitat, water temperature and presence of aquatic organisms, organic matter and green algal remnants on the water surface at the time of inspection, were also studied. Immature density of vector was correlated with presence of other mosquito species, malaria prevalence, habitat characteristics and monthly/seasonal fluctuations. All the data collected from field observations were analysed using standard statistical tools. Results: When the immature density of breeding habitats was analysed, using one-way ANOVA, it was observed that the density did not change in a significant way either across seasons or months. OHTs contributed significantly to the immature population when compared to wells and other breeding habitats of the study site. The habitat positivity of wells and OHTs was significantly associated with the presence of aquatic organisms, organic matter and algal remnants. Significant correlations of malaria prevalence with monthly immature density, as well as number of breeding habitats with immature vector mosquitoes, were also observed. Conclusions: The findings that OHTs showed fairly high and consistent immature density of An. stephensi irrespective of seasons indicates the potentiality of the breeding habitat in contributing to vector density. The correlation between vector breeding habitats, immature density and malaria prevalence indicates the proximity of these habitats to malaria cases, proving its role in vector abundance and local malaria transmission. The preference of An. stephensi to breed in OHTs calls for intensified, appropriate and sustained intervention measures to curtail vector breeding and propagation to shrink malaria to pre-elimination level and beyond

Resting and feeding preferences of Anopheles stephensi in an urban setting, perennial for malaria

Background: The Indian city of Chennai is endemic for malaria and the known local malaria vector is Anopheles stephensi. Plasmodium vivax is the predominant malaria parasite species, though Plasmodium falciparum is present at low levels. The urban ecotype of malaria prevails in Chennai with perennial transmission despite vector surveillance by the Urban Malaria Scheme (UMS) of the National Vector Borne Disease Control Programme (NVBDCP). Understanding the feeding and resting preferences, together with the transmission potential of adult vectors in the area is essential in effective planning and execution of improved vector control measures. Methods: A yearlong survey was carried out in cattle sheds and human dwellings to check the resting, feeding preferences and transmission potential of An. stephensi. The gonotrophic status, age structure, resting and host seeking preferences were studied. The infection rate in An. stephensi and Anopheles subpictus were analysed by circumsporozoite ELISA (CS-ELISA). Results: Adult vectors were found more frequently and at higher densities in cattle sheds than human dwellings. The overall Human Blood Index (HBI) was 0.009 indicating the vectors to be strongly zoophilic. Among the vectors collected from human dwellings, 94.2% were from thatched structures and the remaining 5.8% from tiled and asbestos structures. 57.75% of the dissected vectors were nulliparous whereas, 35.83% were monoparous and the rest 6.42% biparous. Sporozoite positivity rate was 0.55% (4/720) and 1.92% (1/52) for An. stephensi collected from cattle sheds and human dwellings, respectively. One adult An. subpictus (1/155) was also found to be infected with P. falciparum. Conclusions: Control of the adult vector populations can be successful only by understanding the resting and feeding preferences. The present study indicates that adult vectors predominantly feed on cattle and cattle sheds are the preferred resting place, possibly due to easy availability of blood meal source and lack of any insecticide or repellent pressure. Hence targeting these resting sites with cost effective, socially acceptable intervention tools, together with effective larval source management to reduce vector breeding, could provide an improved integrated vector management strategy to help drive down malaria transmission and assist in India's plan to eliminate malaria by 2030