A Countable-Type Branching Process Model for the Tug-of-War Cancer Cell Dynamics.

We consider a time-continuous Markov branching process of proliferating cells with a countable collection of types. Among-type transitions are inspired by the Tug-of-War process introduced by McFarland et al. (Proc Natl Acad Sci 111(42):15138-15143, 2014) as a mathematical model for competition of advantageous driver mutations and deleterious passenger mutations in cancer cells. We introduce a version of the model in which a driver mutation pushes the type of the cell L-units up, while a passenger mutation pulls it 1-unit down. The distribution of time to divisions depends on the type (fitness) of cell, which is an integer. The extinction probability given any initial cell type is strictly less than 1, which allows us to investigate the transition between types (type transition) in an infinitely long cell lineage of cells. The analysis leads to the result that under driver dominance, the type transition process escapes to infinity, while under passenger dominance, it leads to a limit distribution. Implications in cancer cell dynamics and population genetics are discussed.

The Lnc-ENST00000602558/IGF1 axis as a predictor of response to treatment with tripterygium glycosides in rheumatoid arthritis patients.

AIMS: Growing clinical evidence suggests that not all patients with rheumatoid arthritis (RA) benefit to the same extent by treatment with tripterygium glycoside (TG), which highlights the need to identify RA-related genes that can be used to predict drug responses. In addition, single genes as markers of RA are not sufficiently accurate for use as predictors. Therefore, there is a need to identify paired expression genes that can serve as biomarkers for predicting the therapeutic effects of TG tablets in RA. METHODS: A total of 17 pairs of co-expressed genes were identified as candidates for predicting an RA patient's response to TG therapy, and genes involved in the Lnc-ENST00000602558/GF1 axis were selected for that purpose. A partial-least-squares (PLS)-based model was constructed based on the expression levels of Lnc-ENST00000602558/IGF1 in peripheral blood. The model showed high efficiency for predicting an RA patient's response to TG tablets. RESULTS: Our data confirmed that genes co-expressed in the Lnc-ENST00000602558/IGF1 axis mediate the efficacy of TG in RA treatment, reduce tumor necrosis factor-α induced IGF1 expression, and decrease the inflammatory response of MH7a cells. CONCLUSION: We found that genes expressed in the Lnc-ENST00000602558/IGF1 axis may be useful for identifying RA patients who will not respond to TG treatment. Our findings provide a rationale for the individualized treatment of RA in clinical settings.

The crosstalk between macrophages and bone marrow mesenchymal stem cells in bone healing.

Bone injury plagues millions of patients worldwide every year, and it demands a heavy portion of expense from the public medical insurance system. At present, orthopedists think that autologous bone transplantation is the gold standard for treating large-scale bone defects. However, this method has significant limitations, which means that parts of patients cannot obtain a satisfactory prognosis. Therefore, a basic study on new therapeutic methods is urgently needed. The in-depth research on crosstalk between macrophages (Mϕs) and bone marrow mesenchymal stem cells (BMSCs) suggests that there is a close relationship between inflammation and regeneration. The in-depth understanding of the crosstalk between Mϕs and BMSCs is helpful to amplify the efficacy of stem cell-based treatment for bone injury. Only in the suitable inflammatory microenvironment can the damaged tissues containing stem cells obtain satisfactory healing outcomes. The excessive tissue inflammation and lack of stem cells make the transplantation of biomaterials necessary. We can expect that the crosstalk between Mϕs and BMSCs and biomaterials will become the mainstream to explore new methods for bone injury in the future. This review mainly summarizes the research on the crosstalk between Mϕs and BMSCs and also briefly describes the effects of biomaterials and aging on cell transplantation therapy.

Prognostic and therapeutic prediction by screening signature combinations from transcriptome-methylome interactions in oral squamous cell carcinoma.

DNA methylation pattern in oral squamous cell carcinoma (OSCC) remains poorly described. This study aimed to perform a genome-wide integrated analysis of the transcriptome and methylome and assess the efficacy of their prognostic signature model in patients with OSCC. We analyzed transcriptome and methylome data from 391 OSCC samples and 41 adjacent normal samples. A total of 8074 differentially expressed genes (DEGs) and 10,084 differentially expressed CpGs (DMCpGs) were identified. Then 241 DEGs with DMCpGs were identified. According to the prognostic analysis, the prognostic signature of methylation-related differentially expressed genes (mrDEGPS) was established. mrDEGPS consisted of seven prognostic methylation-related genes, including ESRRG, CCNA1, SLC20A1, COL6A6, FCGBP, CDKN2A, and ZNF43. mrDEGPS was a significant stratification factor of survival (P < 0.00001) irrespective of the clinical stage. The immune effector components, including B cells, CD4+ T cells, and CD8+ T cells, were decreased in the tumor environment of patients with high mrDEGPS. Immune checkpoint expressions, including CTLA-4, PD-1, LAG3, LGALS9, HAVCR2, and TIGHT, were comprehensively elevated (P < 0.001). The estimated half-maximal inhibitory concentration difference between low- and high-risk patients was inconsistent among chemotherapeutic drugs. In conclusion, the transcriptome-methylome interaction pattern in OSCC is complex. mrDEGPS can predict patient survival and responses to immunotherapy and chemotherapy and facilitate clinical decision-making in patients with OSCC.

Two-Step Approach Using Degradable Magnesium to Inhibit Surface Biofilm and Subsequently Kill Planktonic Bacteria.

Bacterial infection remains a great risk in medical implantation surgery. In this paper, we found that degradable metals may be a feasible alternative option of antibacterial implantation materials. It is known that the spalling mechanism of magnesium (Mg) during degradation leads to Mg ions-induced alkaline environment, which is harmful to planktonic bacteria. In this study, we showed that alkaline pH environment is almost harmless to those adhesive bacteria protected in well-formed biofilms. Moreover, experimental results demonstrated that the biofilm formed in the place where Mg spalls are destroyed, releasing the covered bacteria to be planktonic in the alkaline environment. As a result, the colonization of biofilms continues to shrink during the degradation of Mg. It implies that if degradable metal is employed as implantation material, even if bacterial infection occurs, it may be possibly cured without second surgery.

Assessment of the Multiphase Mechanical Properties of the Longmaxi Formation Shale Using Nanoindentation Tests.

Mechanical properties are some of the most important parameters for understanding well drilling and hydraulic fracturing designs in unconventional reservoir development. As an effective tool, nanoindentation has been used to determine the mechanical properties of rocks at the nanoscale. In this study, the Longmaxi Formation shale samples from the Yibin area of China were collected and analyzed to obtain the multiphase mechanical properties. The mineral compositions and organic geochemistry of the shale samples were studied using X-ray diffraction, energy-dispersive X-ray spectrometry, and a carbon/sulfur analyzer. The pore structures of the shale samples at the micro- and nanoscales were characterized by field-emission scanning electron microscopy. The mechanical parameters of the shale samples, such as the hardness and elastic modulus, were investigated using the nanoindentation method to identify three mineral phases: brittle minerals, soft matters, and complex minerals at the interfaces between brittle minerals and soft matters. The uncertainty characteristics of the mechanical parameters of the three mineral phases were evaluated using the Weibull model, and the factors interfering with the mechanical parameters were analyzed for the different shale samples. The results showed that the brittle minerals had the largest recovered elastic deformations and the smallest residual deformations, while the soft matters had the largest residual deformations and the smallest recovered elastic deformations. The analysis results of the coefficients of variation and the Weibull modulus both confirmed that the scatter of the hardness was higher than that of the elastic modulus because of the uncertain contact area, and the hardness and elastic modulus of the soft matters had the highest uncertainty among the three mineral phases. The elastic modulus increased nonlinearly with increasing hardness according to a power function for the whole shale sample. The elastic modulus and hardness both had a favorable linear relationship with the total organic carbon (TOC) content, illustrating that the TOC content was one of the significant factors that affected the mechanical parameters of the shale samples.

Simulating galactic cosmic ray effects: Synergy modeling of murine tumor prevalence after exposure to two one-ion beams in rapid sequence.

Health risks from galactic cosmic rays (GCR) in space travel above low earth orbit remain a concern. For many years accelerator experiments investigating space radiation induced prevalence of murine Harderian gland (HG) tumorigenesis have been performed to help estimate GCR risks. Most studies used acute, relatively low fluence, exposures. Results on a broad spectrum of individual ions and linear energy transfers (LETs) have become available. However, in space, the crew are exposed simultaneously to many different GCR. Recent upgrades at the Brookhaven NASA Space Radiation Laboratory (NSRL) now allow mixtures in the form of different one-ion beams delivered in rapid sequence. This paper uses the results of three two-ion mixture experiments to illustrate conceptual, mathematical, computational, and statistical aspects of synergy analyses and also acts as an interim report on the mixture experiments' results. The results were interpreted using the following: (a) accumulated data from HG one-ion accelerator experiments; (b) incremental effect additivity synergy theory rather than simple effect additivity synergy theory; (c) parsimonious models for one-ion dose-effect relations; and (d), computer-implemented numerical methods encapsulated in freely available open source customized software. The main conclusions are the following. As yet, the murine HG tumorigenesis experimental studies show synergy in only one case out of three. Moreover, some theoretical arguments suggest GCR-simulating mixed beams are not likely to be synergistic. However, more studies relevant to possible synergy are needed by various groups that are studying various endpoints. Especially important is the possibility of synergy among high-LET radiations, since individual high-LET ions have large relative biological effectiveness for many endpoints. Selected terminology, symbols, and abbreviations. DER - dose-effect relation; E(d) - DER of a one-ion beam, where d is dose; HG prevalence p - in this paper, p is the number of mice with at least one Harderian gland tumor divided by the number of mice that are at risk of developing Harderian gland tumors (so that in this paper prevalence p can never, conceptually speaking, be greater than 1); IEA - incremental effect additivity synergy theory; synergy level - a specification, exemplified in Fig. 5, of how clear-cut an observed synergy is; mixmix principle - a consistency condition on a synergy theory which insures that the synergy theory treats mixtures of agent mixtures in a mathematically self-consistent way; NTE - non-targeted effect(s); NSNA - neither synergy nor antagonism; SEA - simple effect additivity synergy theory; TE - targeted effect(s); ß* - ion speed relative to the speed of light, with 0 < ß* < 1; SLI - swift light ion(s).

Napabucasin Attenuates Resistance of Breast Cancer Cells to Tamoxifen by Reducing Stem Cell-Like Properties.

BACKGROUND Tamoxifen (TAM) is the first-line drug for estrogen receptor-positive (ER+) breast cancer (BC) treatment. However, its resistance is a main obstacle in clinical practice. Thus, new therapeutic agents are urgently needed to fight TAM resistance. MATERIAL AND METHODS Here, we constructed TAM-resistant ER+BC cells with TAM resistance, named MCF-7-R. Western blot, quantitative real-time PCR (qRT-PCR), ALDH1 activity analysis, and spheroid-forming detection were used to detect the stemness of cells and the effects of napabucasin (NP) on BC cell stemness. Cell counting kit-8 (CCK8) assay was used to evaluate the effects of NP on cell viability. RESULTS MCF-7-R cells exhibited higher stemness compared with the parental MCF-7 cells, which was evident by the increased spheroid formation ability at diluted concentration, aldehyde dehydrogenase (ALDH) activity, and expression of stemness critical biomarkers (Oct4, Nanog, and Sox2). Additionally, it was found that napabucasin (NP) specifically killed MCF-7-T cells, characterized by remarkably decreased IC50 value. Notably, NP reduced MCF-7-R cell stemness, which was evident as the decreased stemness marker expression, spheroid-forming capacity, and ALDH1 activity. Importantly, NP attenuated TAM resistance of MCF-7-R cells and enhanced sensitivity of MCF-7 cells to TAM. Mechanistic study showed that NP inhibited STAT3 activation, and overexpression of STAT3 rescued NP-mediated inhibition of the stemness-like characteristics of MCF-7-R cells. CONCLUSIONS NP might be used as an adjuvant therapy for ER+ BC patients with TAM resistance.

Enhanced Oil Recovery by a Suspension of Core-Shell Polymeric Nanoparticles in Heterogeneous Low-Permeability Oil Reservoirs.

Polymeric nanoparticle suspension is a newly developed oil-displacing agent for enhanced oil recovery (EOR) in low-permeability reservoirs. In this work, SiO2/P(MBAAm-co-AM) polymeric nanoparticles were successfully synthesized by a simple distillation-precipitation polymerization method. Due to the introduction of polymer, the SiO2/P(MBAAm-co-AM) nanoparticles show a favorable swelling performance in aqueous solution, and their particle sizes increase from 631 to 1258 nm as the swelling times increase from 24 to 120 h. The apparent viscosity of SiO2/P(MBAAm-co-AM) suspension increases with an increase of mass concentration and swelling time, whereas it decreases as the salinity and temperature increase. The SiO2/P(MBAAm-co-AM) suspension behaves like a non-Newtonian fluid at lower shear rates, yet like a Newtonian fluid at shear rates greater than 300 s-1. The EOR tests of the SiO2/P(MBAAm-co-AM) suspension in heterogeneous, low-permeability cores show that SiO2/P(MBAAm-co-AM) nanoparticles can effectively improve the sweep efficiency and recover more residual oils. A high permeability ratio can result in a high incremental oil recovery in parallel cores. With an increase of the permeability ratio of parallel cores from 1.40 to 15.49, the ratios of incremental oil recoveries (low permeability/high permeability) change from 7.69/4.61 to 23.61/8.46. This work demonstrates that this SiO2/P(MBAAm-co-AM) suspension is an excellent conformance control agent for EOR in heterogeneous, low-permeability reservoirs. The findings of this study can help to further the understanding of the mechanisms of EOR using SiO2/P(MBAAm-co-AM) suspension in heterogeneous, low-permeability reservoirs.

Association of body mass index and prostate cancer mortality.

OBJECTIVES: Inconsistent evidence exists on whether obesity is associated with an increased risk of prostate cancer death post-radical prostatectomy. We examined data from three large health plans to evaluate if an increased body mass index (BMI) at prostate cancer diagnosis is related to prostate cancer mortality SUBJECTS AND METHODS: This population-based case-control study included 751 men with prostate cancer who underwent radical prostatectomy. Cases were men who died due to prostate cancer (N=323) and matched controls (N=428). We used multivariable logistic regression models to assess the association between BMI at diagnosis and prostate cancer mortality, adjusted for Gleason score, PSA, tumour characteristics, and matching factors. RESULTS: Study subjects were classified into the following BMI (kg/m2) categories: healthy (18.5-24.9), overweight (25-29.9) and obese (≥30). Nearly 43% of the participants had a BMI ≥25 at diagnosis. A higher fraction of cases (30%) were obese compared to controls (22%). Overall, obese men had more than a 50% increase in prostate cancer mortality (adjusted odds ratio=1.50 [95% CI, 1.03-2.19]) when compared to men with healthy BMI. After stratifying by Gleason score, the odds of mortality generally rose with increasing BMI. The strongest effect was observed in the Gleason score 8+ category (2.37, 95% CI: 1.11-5.09). These associations persisted after adjusting for PSA at diagnosis and other tumour characteristics. CONCLUSIONS: These results suggest that BMI at diagnosis is strongly correlated with prostate cancer mortality, and that men with aggressive disease have a markedly greater odds of death if they are overweight or obese.

Androgen deprivation therapy for treatment of localized prostate cancer and risk of second primary malignancies.

BACKGROUND: While androgen deprivation therapy (ADT) is a common treatment for prostate cancer, little is known regarding its long-term health effects, particularly as it relates to the development of second primary malignancies. Therefore, the goal of this study was to assess the association between ADT use and second primary malignancies among men diagnosed with localized prostate cancer. METHODS: We assessed whether use of ADT (specifically, gonadotropin-releasing hormone agonists) was associated with the development of second primary malignancies in a retrospective cohort of 24,038 men ages more than 18 years who were diagnosed with localized prostate cancer between 1998 and 2007, and followed through 2009. We used proportional hazards regression to estimate the risk of developing a second primary cancer among men who were treated with ADT compared with men who were not. RESULTS: Men who were treated with ADT were not more likely to develop any second primary malignancy compared with those who were not treated with ADT after adjustment for age, race, date of diagnosis, utilization, clinical stage, Gleason score, and radiation therapy [HR, 1.10; 95% confidence interval (CI), 0.98-1.22)]. Radiotherapy, diabetes, and obesity did not modify the association between ADT use and second primary cancer risk. CONCLUSION: Our results suggest that among men with localized prostate cancer, ADT is not associated with an increased risk of second primary malignancies. IMPACT: When evaluating the risks and benefits of using ADT as a treatment for localized prostate cancer, considering the risk of second primary malignancies may not be clinically important.

Genome sequence of foxtail millet (Setaria italica) provides insights into grass evolution and biofuel potential.

Foxtail millet (Setaria italica), a member of the Poaceae grass family, is an important food and fodder crop in arid regions and has potential for use as a C(4) biofuel. It is a model system for other biofuel grasses, including switchgrass and pearl millet. We produced a draft genome (∼423 Mb) anchored onto nine chromosomes and annotated 38,801 genes. Key chromosome reshuffling events were detected through collinearity identification between foxtail millet, rice and sorghum including two reshuffling events fusing rice chromosomes 7 and 9, 3 and 10 to foxtail millet chromosomes 2 and 9, respectively, that occurred after the divergence of foxtail millet and rice, and a single reshuffling event fusing rice chromosome 5 and 12 to foxtail millet chromosome 3 that occurred after the divergence of millet and sorghum. Rearrangements in the C(4) photosynthesis pathway were also identified.

A sex-specific association between a 15q25 variant and upper aerodigestive tract cancers.

BACKGROUND: Sequence variants located at 15q25 have been associated with lung cancer and propensity to smoke. We recently reported an association between rs16969968 and risk of upper aerodigestive tract (UADT) cancers (oral cavity, oropharynx, hypopharynx, larynx, and esophagus) in women (OR = 1.24, P = 0.003) with little effect in men (OR = 1.04, P = 0.35). METHODS: In a coordinated genotyping study within the International Head and Neck Cancer Epidemiology (INHANCE) consortium, we have sought to replicate these findings in an additional 4,604 cases and 6,239 controls from 10 independent UADT cancer case-control studies. RESULTS: rs16969968 was again associated with UADT cancers in women (OR = 1.21, 95% CI = 1.08-1.36, P = 0.001) and a similar lack of observed effect in men [OR = 1.02, 95% CI = 0.95-1.09, P = 0.66; P-heterogeneity (P(het)) = 0.01]. In a pooled analysis of the original and current studies, totaling 8,572 UADT cancer cases and 11,558 controls, the association was observed among females (OR = 1.22, 95% CI = 1.12-1.34, P = 7 × 10(-6)) but not males (OR = 1.02, 95% CI = 0.97-1.08, P = 0.35; P(het) = 6 × 10(-4)). There was little evidence for a sex difference in the association between this variant and cigarettes smoked per day, with male and female rs16969968 variant carriers smoking approximately the same amount more in the 11,991 ever smokers in the pooled analysis of the 14 studies (P(het) = 0.86). CONCLUSIONS: This study has confirmed a sex difference in the association between the 15q25 variant rs16969968 and UADT cancers. IMPACT: Further research is warranted to elucidate the mechanisms underlying these observations.

Genetic variants and risk of lung cancer in never smokers: a genome-wide association study.

BACKGROUND: Lung cancer in individuals who have never smoked tobacco products is an increasing medical and public-health issue. We aimed to unravel the genetic basis of lung cancer in never smokers. METHODS: We did a four-stage investigation. First, a genome-wide association study of single nucleotide polymorphisms (SNPs) was done with 754 never smokers (377 matched case-control pairs at Mayo Clinic, Rochester, MN, USA). Second, the top candidate SNPs from the first study were validated in two independent studies among 735 (MD Anderson Cancer Center, Houston, TX, USA) and 253 (Harvard University, Boston, MA, USA) never smokers. Third, further replication of the top SNP was done in 530 never smokers (UCLA, Los Angeles, CA, USA). Fourth, expression quantitative trait loci (eQTL) and gene-expression differences were analysed to further elucidate the causal relation between the validated SNPs and the risk of lung cancer in never smokers. FINDINGS: 44 top candidate SNPs were identified that might alter the risk of lung cancer in never smokers. rs2352028 at chromosome 13q31.3 was subsequently replicated with an additive genetic model in the four independent studies, with a combined odds ratio of 1.46 (95% CI 1.26-1.70, p=5.94x10(-6)). A cis eQTL analysis showed there was a strong correlation between genotypes of the replicated SNPs and the transcription level of the gene GPC5 in normal lung tissues (p=1.96x10(-4)), with the high-risk allele linked with lower expression. Additionally, the transcription level of GPC5 in normal lung tissue was twice that detected in matched lung adenocarcinoma tissue (p=6.75x10(-11)). INTERPRETATION: Genetic variants at 13q31.3 alter the expression of GPC5, and are associated with susceptibility to lung cancer in never smokers. Downregulation of GPC5 might contribute to the development of lung cancer in never smokers. FUNDING: US National Institutes of Health; Mayo Foundation.

[Screen of early indicators for renal damage in mercury workers].

OBJECTIVE: To study the early indicators for renal damages in mercury workers and the clinical significance. METHODS: Eighty-five mercury workers were divided into 2 experimental groups: the normal & subject-under-surveillance group and the mercury-poisoning group. Sixty-five healthy adults with no mercury exposure history were assigned as the control group. Any subjects with history of renal diseases or concurrent renal diseases were excluded. The results from physical examinations and measurements of HgU, B-Cr, U-Cr, BUN, N-acetyl-beta-D-glucosaminidase (NAG), beta2-microglobulin (beta2-MG), urinary alpha1-microglobulin (alpha1-MG), and retinol-binding protein (RBP) in all the groups were analyzed. RESULTS: The levels of HgU, NAG, alpha1-MG, beta2-MG, and RBP were significantly higher in the experimental groups than in the control group. The levels of NAG, beta2-MG and RBP were significantly higher in the nomal & subject-under-surveillance group than in the control group. However, there was no statistically significant difference between the levels of B-Cr and BUN in the experimental groups and those of the control group. CONCLUSIONS: Long-term exposure to mercury can cause renal damages. The level of NAG, alpha1-MG, beta2-MG, and RBP can be used as sensitive indicators for detecting early renal damages caused by mercury.

Osmium Complexes of 1,4,7-Triazacyclononane (tacn) and 1,4,7-Trimethyl-1,4,7-triazacyclononane (Me(3)tacn) and the X-ray Crystal Structure of [(Me(3)tacn)Os(eta(6)-C(6)H(5)BPh(3))]BPh(4).CH(3)CN.

The complexes of osmium with tacn (1,4,7-triazacyclononane) and Me(3)tacn (1,4,7-trimethyl-1,4,7-triazacyclononane), [LOs (eta(6)-C(6)H(6))](PF(6))(2) (L = tacn) and LOsCl(3) (L = tacn, Me(3)tacn), have been prepared by substitution of L on [Os(eta(6)-C(6)H(6))Cl(2)](2) or [Os(2)Cl(8)](2)(-), respectively. Reaction of LOsCl(3) with neat triflic acid leads to partial replacement of chloride and formation of the binuclear Os(III)-Os(III) complexes [LOs(&mgr;-Cl(3))OsL](PF(6))(3) (L = tacn, Me(3)tacn). The binuclear nature was established by NMR spectroscopy and elemental analysis and, for L = tacn, a partially refined X-ray crystal structure which shows the Os-Os separation to be 2.667 Å, indicative of significant metal-metal bonding. Reduction of [LOs(&mgr;-Cl(3))OsL](3+) over zinc amalgam in either aqueous or non-aqueous solution yields the intensely colored Os(II)-Os(III) mixed-valence ions [LOs(&mgr;-Cl(3))OsL](2+). Electrochemical measurements on [LOs(&mgr;-Cl(3))OsL](3+) in CH(3)CN reveal the reversible formation of the mixed valence ions. These are further reduced at lower potential to the Os(II)-Os(II) binuclear species, reversibly for L = Me(3)tacn. (Me(3)tacn)OsCl(3) is oxidized by persulfate ion to give [(Me(3)tacn)OsCl(3)](+); zinc amalgam reduction in an aqueous solution at high concentration produces the binuclear complex [(Me(3)tacn)Os(&mgr;-Cl(3))Os(Me(3)tacn)](3+) or, at low concentration, a solution containing an air sensitive osmium(II) species. Addition of BPh(4)(-) results in the eta(6)-arene zwitterion [(Me(3)tacn)Os(eta(6)-C(6)H(5)BPh(3))](+), which was characterized by X-ray diffraction on the BPh(4)(-) salt. The compound crystallizes in the triclinic space group P1 with a = 11.829(2) Å, b = 12.480(3) Å, c = 17.155(4) Å, alpha = 84.42(2) degrees, beta = 83.52(2) degrees, gamma = 71.45(2) degrees, V = 2380(2) Å(3), Z = 2, and R = 7.62%, and R(w) = 7.39%.