Standard Young Tableaux and Colored Motzkin Paths

In this paper, we propose a notion of colored Motzkin paths and establish a bijection between the $n$-cell standard Young tableaux (SYT) of bounded height and the colored Motzkin paths of length $n$. This result not only gives a lattice path interpretation of the standard Young tableaux but also reveals an unexpected intrinsic relation between the set of SYTs with at most $2d+1$ rows and the set of SYTs with at most 2d rows.Comment: 21 page

The Metastasectomy and Timing of Pulmonary Metastases on the Outcome of Osteosarcoma Patients

Background The author intended to clarify the therapeutic effect and prognostic factors of metastasectomy and timing of pulmonary metastases in osteosarcoma patents. Methods Data was obtained retrospectively on all consecutive osteosarcoma patients from 1985 to 2005 in author's institute. Fifty-two patients with pulmonary nodules were identified, including 24 patients undergoing pulmonary metastasectomy treatment. These patients were categorized into four groups: group 1, patients with lung metastases at the initial presentation; group 2, lung metastases identified during the period of pre-operative chemotherapy; group 3, lung metastases identified during period of the post-operative chemotherapy; group 4, lung metastases identified after therapy for the primary osteosarcoma completed. Results In our study, the 2-, 3-, and 5-year overall survival rates for 52 patients were 49%, 39% and 20%. The 2-year overall survival rates were 18% for group 1, 32% for group 3, and 70% for group 4 (p < 0.001). The 5-year overall survival rate was 34% for group 4. Patients who underwent metastesectomy showed a better survival outcome as compared with the patients not undergoing metastasectomy (p = 0.003). The 2-year and 5-year overall survival rates of only one lung metastatic nodule were 62% and 50%, and for initially multiple lung metastatic nodules, 45% and 5%, respectively. In addition, the patients presented with lung metastases had a worse prognosis as compared with those without initial lung metastases (p = 0.0001). Conclusions The patients having single metastatic nodule showed a better prognosis than those with multiple lung nodules. Furthermore, those patients who underwent metastasectomy survived longer than those not undergoing metastasectomy. Patients who had late metastases after complete chemotherapy had a better prognosis; whereas those who had metastases identified at the initial presentation predicted a poor prognosis

Clustering Multiple Sclerosis Medication Sequence Data with Mixture Markov Chain Analysis with covariates using Multiple Simplex Constrained Optimization Routine (MSiCOR)

Multiple sclerosis (MS) is an autoimmune disease of the central nervous system that causes neurodegeneration. While disease-modifying therapies (DMTs) reduce inflammatory disease activity and delay worsening disability in MS, there are significantly varying treatment responses across people with MS (pwMS). pwMS often receive serial monotherapies of DMTs. Here, we propose a novel method to cluster pwMS according to the sequence of DMT prescriptions and associated clinical features (covariates). This is achieved via a mixture Markov chain analysis with covariates, where the sequence of prescribed DMTs for each patient is modeled as a Markov chain. Given the computational challenges to maximize the mixture likelihood on the constrained parameter space, we develop a pattern search-based global optimization technique which can optimize any objective function on a collection of simplexes and shown to outperform other related global optimization techniques. In simulation experiments, the proposed method is shown to outperform the Expectation-Maximization (EM) algorithm based method for clustering sequence data without covariates. Based on the analysis, we divided MS patients into 3 clusters: inferon-beta dominated, multi-DMTs, and natalizumab dominated. Further cluster-specific summaries of relevant covariates indicate patient differences among the clusters. This method may guide the DMT prescription sequence based on clinical features

Soliton Solutions on Noncommutative Orbifold $ T^2/Z_4

In this paper, we explicitly construct a series of projectors on integral noncommutative orbifold $T^2/Z_4$ by extended $GHS$ constrution. They include integration of two arbitary functions with $Z_4$ symmetry. Our expressions possess manifest $Z_{4}$ symmetry. It is proved that the expression include all projectors with minimal trace and in their standard expansions, the eigen value functions of coefficient operators are continuous with respect to the arguments $k$ and $q$. Based on the integral expression, we alternately show the derivative expression in terms of the similar kernal to the integral one.Since projectors correspond to soliton solutions of the field theory on the noncommutative orbifold, we thus present a series of corresponding solitons.Comment: 18 pages, no figure; referrences adde

catena-Poly[[bis­(nitrato-κO)cobalt(II)]-bis­[μ-1,4-bis­(pyridin-3-ylmeth­oxy)benzene-κ2 N:N′]]

In the title compound, [Co(NO3)2(C18H16N2O2)2]n, the CoII ion is located on an inversion center and is six-coordinated in an octa­hedral environment defined by four N atoms of the pyridine rings and two O atoms of the nitrate anions. The ligands link the CoII ions into a linear chain running along [201]. One O atom of the nitrate ligand is disordered over two positions with site-occupancy factors of 0.59 (4) and 0.41 (4)

Simple one-pot fabrication of ultra-stable core-shell superparamagnetic nanoparticles for potential application in drug delivery

Ultrastable superparamagnetic core-shell nanoparticles of average diameter 80 nm have been fabricated via a simple one-pot method involving superparamagnetic iron oxide nanoparticles (SPIONs) core ([similar]50 nm in diameter) and lipid bilayer shell by high energy ultrasonication. The surface charges (zeta potentials) were measured to be between −15 mV and + 16 mV depending on the batch composition. Anticancer drug mitomycin C (MMC) was loaded into four different samples of variable surface charges in aqueous solution (pH = 6.8) and released in PBS buffer (pH = 7.2) at room temperature. The kinetics of drug loading and releasing data indicated that the stable lipid bilayer coated SPIONs (LBCSPIONs) of nearly neutral surface exhibited the highest loading (10.9 μg of MMC/mg of materials), whereas uncoated or partially coated SPIONs of positive zeta potential exhibited the lowest loading (2.8 and 3.5 μg MMC/mg of materials, respectively). The release behavior of MMC was observed to be highest (5.8 μg MMC/mg of materials) from materials of negative zeta potential compared to materials of near neutral surfaces (3.68 μg MMC/mg of materials). The plausible mechanism of MMC loading and releasing behavior has been explained based on the electrostatic interaction and diffusion through the lipid bilayers. To ensure biocompatibility, the interaction of the prepared SPIONs with human cervical cancer cell line (HeLa) was also investigated using an MTT (3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide) assay and ROS (reactive oxygen species) production assay and the results confirmed the super-compatibility of LBCSPIONs