Critical frontier of the Potts and percolation models in triangular-type and kagome-type lattices I: Closed-form expressions

We consider the Potts model and the related bond, site, and mixed site-bond percolation problems on triangular-type and kagome-type lattices, and derive closed-form expressions for the critical frontier. For triangular-type lattices the critical frontier is known, usually derived from a duality consideration in conjunction with the assumption of a unique transition. Our analysis, however, is rigorous and based on an established result without the need of a uniqueness assumption, thus firmly establishing all derived results. For kagome-type lattices the exact critical frontier is not known. We derive a closed-form expression for the Potts critical frontier by making use of a homogeneity assumption. The closed-form expression is new, and we apply it to a host of problems including site, bond, and mixed site-bond percolation on various lattices. It yields exact thresholds for site percolation on kagome, martini, and other lattices, and is highly accurate numerically in other applications when compared to numerical determination.Comment: 22 pages, 13 figure

On the generalized continuity equation

A generalized continuity equation extending the ordinary continuity equation has been found using quanternions. It is shown to be compatible with Dirac, Schrodinger, Klein-Gordon and diffusion equations. This generalized equation is Lorentz invariant. The transport properties of electrons are found to be governed by Schrodinger-like equation and not by the diffusion equation.Comment: 9 Latex pages, no figure

Variational method and duality in the 2D square Potts model

The ferromagnetic q-state Potts model on a square lattice is analyzed, for q>4, through an elaborate version of the operatorial variational method. In the variational approach proposed in the paper, the duality relations are exactly satisfied, involving at a more fundamental level, a duality relationship between variational parameters. Besides some exact predictions, the approach is very effective in the numerical estimates over the whole range of temperature and can be systematically improved.Comment: 20 pages, 5 EPS figure

Theory of d-density wave viewed from a vertex model and its implications

The thermal disordering of the $d$-density wave, proposed to be the origin of the pseudogap state of high temperature superconductors, is suggested to be the same as that of the statistical mechanical model known as the 6-vertex model. The low temperature phase consists of a staggered order parameter of circulating currents, while the disordered high temperature phase is a power-law phase with no order. A special feature of this transition is the complete lack of an observable specific heat anomaly at the transition. There is also a transition at a even higher temperature at which the magnitude of the order parameter collapses. These results are due to classical thermal fluctuations and are entirely unrelated to a quantum critical point in the ground state. The quantum mechanical ground state can be explored by incorporating processes that causes transitions between the vertices, allowing us to discuss quantum phase transition in the ground state as well as the effect of quantum criticality at a finite temperature as distinct from the power-law fluctuations in the classical regime. A generalization of the model on a triangular lattice that leads to a 20-vertex model may shed light on the Wigner glass picture of the metal-insulator transition in two-dimensional electron gas. The power-law ordered high temperature phase may be generic to a class of constrained systems and its relation to recent advances in the quantum dimer models is noted.Comment: RevTex4, 10 pages, 11 figure

Gene-specific repair of Pt/DNA lesions and induction of apoptosis by the oral platinum drug JM216 in three human ovarian carcinoma cell lines sensitive and resistant to cisplatin

JM216, an oral platinum drug entering into phase III clinical trial, exhibited comparable cytotoxicity to cisplatin in three human ovarian carcinoma cell lines: the sensitive (CH1), acquired resistant (CH1cisR) and intrinsically resistant (SKOV-3). Platinum accumulation and binding to DNA were similar in each of the three cell lines at equimolar doses, indicating that the resistant cell lines could tolerate higher intracellular platinum levels and platinum bound to DNA at IC50 concentrations of drug. Comparison with cisplatin demonstrated that intracellular platinum levels were marginally higher with JM216, but that platinum binding to DNA was similar for the two drugs in each of the cell lines. Each of the cell lines exhibited an ability to repair JM216 induced platinum/DNA lesions in the N-ras gene (gene-specific repair) at equitoxic concentrations of drug. However, this occurred to a greater extent in the two resistant cell lines such that by 24 h the CH1cisR and SKOV-3 had removed 72% and 67% respectively compared with approximately 32% for the CH1. Reduced gene-specific repair capacity in CH1 cells was also seen following incubation with 25 μM (or 5 μM – 2 × IC50) cisplatin, whereas the CH1cisR and SKOV-3 cell lines were repair proficient. JM216 induced apoptosis in the three cell lines following a 2h incubation with 2 × the IC50 of drug. Fluorescent microscopy of cells stained with propidium iodide showed that the detached cell population displayed typical apoptotic nuclei. Furthermore, field inversion gel electrophoresis demonstrated the presence of DNA fragments approximately 23–50 kb in size, indicative of apoptosis, in the detached cells. JM216 induced an S phase slow down in each of the three cell lines accompanied by a G2 block in the CH1 pair. Incubation with this concentration of JM216 also resulted in the induction of p53 in the CH1 and CH1cisR. These studies suggest that the relative sensitivity of the CH1 cell line to cisplatin and JM216 is at least partly attributable to a deficiency in gene-specific repair. The oral platinum drug, JM216, exerts its cytotoxic effects through the induction of apoptosis following a slow-down in S phase in both the sensitive and resistant lines. © 1999 Cancer Research Campaig

Organometallic iridium(III) anticancer complexes with new mechanisms of action: NCI-60 screening, mitochondrial targeting, and apoptosis

Platinum complexes related to cisplatin, cis-[PtCl2(NH3)2], are successful anticancer drugs; however, other transition metal complexes offer potential for combating cisplatin resistance, decreasing side effects, and widening the spectrum of activity. Organometallic half-sandwich iridium (IrIII) complexes [Ir(Cpx)(XY)Cl]+/0 (Cpx = biphenyltetramethylcyclopentadienyl and XY = phenanthroline (1), bipyridine (2), or phenylpyridine (3)) all hydrolyze rapidly, forming monofunctional G adducts on DNA with additional intercalation of the phenyl substituents on the Cpx ring. In comparison, highly potent complex 4 (Cpx = phenyltetramethylcyclopentadienyl and XY = N,N-dimethylphenylazopyridine) does not hydrolyze. All show higher potency toward A2780 human ovarian cancer cells compared to cisplatin, with 1, 3, and 4 also demonstrating higher potency in the National Cancer Institute (NCI) NCI-60 cell-line screen. Use of the NCI COMPARE algorithm (which predicts mechanisms of action (MoAs) for emerging anticancer compounds by correlating NCI-60 patterns of sensitivity) shows that the MoA of these IrIII complexes has no correlation to cisplatin (or oxaliplatin), with 3 and 4 emerging as particularly novel compounds. Those findings by COMPARE were experimentally probed by transmission electron microscopy (TEM) of A2780 cells exposed to 1, showing mitochondrial swelling and activation of apoptosis after 24 h. Significant changes in mitochondrial membrane polarization were detected by flow cytometry, and the potency of the complexes was enhanced ca. 5× by co-administration with a low concentration (5 μM) of the γ-glutamyl cysteine synthetase inhibitor L-buthionine sulfoximine (L-BSO). These studies reveal potential polypharmacology of organometallic IrIII complexes, with MoA and cell selectivity governed by structural changes in the chelating ligands

The Next Generation of Platinum Drugs: Targeted Pt(II) Agents, Nanoparticle Delivery, and Pt(IV) Prodrugs

The platinum drugs, cisplatin, carboplatin, and oxaliplatin, prevail in the treatment of cancer, but new platinum agents have been very slow to enter the clinic. Recently, however, there has been a surge of activity, based on a great deal of mechanistic information, aimed at developing nonclassical platinum complexes that operate via mechanisms of action distinct from those of the approved drugs. The use of nanodelivery devices has also grown, and many different strategies have been explored to incorporate platinum warheads into nanomedicine constructs. In this Review, we discuss these efforts to create the next generation of platinum anticancer drugs. The introduction provides the reader with a brief overview of the use, development, and mechanism of action of the approved platinum drugs to provide the context in which more recent research has flourished. We then describe approaches that explore nonclassical platinum(II) complexes with trans geometry or with a monofunctional coordination mode, polynuclear platinum(II) compounds, platinum(IV) prodrugs, dual-threat agents, and photoactivatable platinum(IV) complexes. Nanoparticles designed to deliver platinum(IV) complexes will also be discussed, including carbon nanotubes, carbon nanoparticles, gold nanoparticles, quantum dots, upconversion nanoparticles, and polymeric micelles. Additional nanoformulations, including supramolecular self-assembled structures, proteins, peptides, metal–organic frameworks, and coordination polymers, will then be described. Finally, the significant clinical progress made by nanoparticle formulations of platinum(II) agents will be reviewed. We anticipate that such a synthesis of disparate research efforts will not only help to generate new drug development ideas and strategies, but also will reflect our optimism that the next generation of approved platinum cancer drugs is about to arrive.National Cancer Institute (U.S.) (CA034992

Initial agronomic benefits of enhanced weathering using basalt: a study of spring oat in a temperate climate

Addressing soil nutrient degradation and global warming requires novel solutions. Enhanced weathering using crushed basalt rock is a promising dual-action strategy that can enhance soil health and sequester carbon dioxide. This study examines the short-term effects of basalt amendment on spring oat (Avena sativa L.) during the 2022 growing season in NE England. The experimental design consisted of four blocks with control and basalt-amended plots, and two cultivation types within each treatment, laid out in a split plot design. Basalt (18.86 tonnes ha−1) was incorporated into the soil during seeding. Tissue, grain and soil samples were collected for yield, nutrient, and pH analysis. Basalt amendment led to significantly higher yields, averaging 20.5% and 9.3% increases in direct drill and ploughed plots, respectively. Soil pH was significantly higher 256 days after rock application across cultivation types (direct drill: on average 6.47 vs. 6.76 and ploughed: on average 6.69 vs. 6.89, for control and basalt-amended plots, respectively), likely due to rapidly dissolving minerals in the applied basalt, such as calcite. Indications of growing season differences in soil pH are observed through direct measurement of lower manganese and iron uptake in plants grown on basalt-amended soil. Higher grain and tissue potassium, and tissue calcium uptake were observed in basalt-treated crops. Notably, no accumulation of potentially toxic elements (arsenic, cadmium, chromium, nickel) was detected in the grain, indicating that crops grown using this basaltic feedstock are safe for consumption. This study indicates that basalt amendments can improve agronomic performance in sandy clay-loam agricultural soil under temperate climate conditions. These findings offer valuable insights for producers in temperate regions who are considering using such amendments, demonstrating the potential for improved crop yields and environmental benefits while ensuring crop safety

Genomic copy number and expression patterns in testicular germ cell tumours

Testicular germ cell tumours of adults and adolescents (TGCT) include seminomas (SE) and nonseminomas (NS), with spermatocytic seminomas (SSE) representing a distinct entity in older men. SE and NS have gain of 12p material in all cases, whereas SSE are associated with overrepresentation of chromosome 9. Here, we compare at the chromosomal level, copy number imbalances with global expression changes, identified by comparative expressed sequence hybridisation analyses, in seven SE, one combined tumour, seven NS and seven cell lines. Positive correlations were found consistent with copy number as a main driver of expression change, despite reported differences in methylation status in SE and NS. Analysis of chromosomal copy number and expression data could not distinguish between SE and NS, in-keeping with a similar genetic pathogenesis. However, increased expression from 4q22, 5q23.2 and 9p21 distinguished SSE from SE and NS and decreased copy number and expression from 2q36–q37 and 6q24 was a specific feature of NS-derived cell lines. Our analysis also highlights 19 regions with both copy number and expression imbalances in greater than 40% of cases. Mining available expression array data identified genes from these regions as candidates for involvement in TGCT development. Supplementary data is available at http://www.crukdmf.icr.ac.uk/array/array.html