Constructing Tumor Progression Pathways and Biomarker Discovery with Fuzzy Kernel Kmeans and DNA Methylation Data

Constructing pathways of tumor progression and discovering the biomarkers associated with cancer is critical for understanding the molecular basis of the disease and for the establishment of novel chemotherapeutic approaches and in turn improving the clinical efficiency of the drugs. It has recently received a lot of attention from bioinformatics researchers. However, relatively few methods are available for constructing pathways. This article develops a novel entropy kernel based kernel clustering and fuzzy kernel clustering algorithms to construct the tumor progression pathways using CpG island methylation data. The methylation data which come from tumor tissues diagnosed at different stages can be used to distinguish epigenotype and phenotypes the describe the molecular events of different phases. Using kernel and fuzzy kernel kmeans, we built tumor progression trees to describe the pathways of tumor progression and find the possible biomarkers associated with cancer. Our results indicate that the proposed algorithms together with methylation profiles can predict the tumor progression stages and discover the biomarkers efficiently. Software is available upon request

Reentrant Non-Hermitian Skin Effect in Coupled Non-Hermitian and Hermitian Chains with Correlated Disorder

The interplay of non-Hermiticity and disorder dramatically influences system's localization properties, giving rise to intriguing quantum phenomena. Although the intrinsic non-Hermitian skin effect (NHSE) is robust against the weak disorder even in a one-dimensional system, it becomes Anderson localization under strong disorder. Here, we study a localization-delocalization transition by coupling a strongly disordered Hatano-Nelson (HN) chain to a disordered Hermitian chain with its disorder correlated to that of HN chain. Regardless of the disorder strength, as the coupling strength between HN and Hermitian chain increases, a delocalization transition occurs. This leads to a reentrant NHSE due to the interplay of non-Hermiticity and correlated disorder. We reveal the underlying mechanism for the reentrant NHSE under correlated disorder. Moreover, the localization-delocalization transition is well captured by the real-space winding number.Comment: 7 pages, 5 figure

Non-Hermitian Skin Effect In Periodically-Driven Dissipative Ultracold Atoms

The non-Hermitian skin effect (NHSE), featured by the collapse of bulk-band eigenstates into the localized boundary modes of the systems, is one of most striking properties in the fields of non-Hermitian physics. Unique physical phenomena related to the NHSE have attracted a lot of interest, however, their experimental realizations usually require nonreciprocal hopping, which faces a great challenge in ultracold-atom systems. In this work, we propose to realize the NHSE in a 1D optical lattice by periodically-driven ultracold atoms in the presence of staggered atomic loss. By studying the effective Floquet Hamiltonian in the high-frequency approximation, we reveal the underlying mechanism for the periodic-driving-induced the NHSE. We found that the robust NHSE can be tuned by driving phase, which is manifested by the dynamical localization. Most remarkably, we uncover the periodic-driving-induced critical skin effect for two coupled chains with different driving phases, accompanied by the appearance of size-dependent topological in-gap modes. Our studies provide a feasible way for observing the NHSE and exploring corresponding unique physical phenomena due to the interplay of non-Hermiticity and many-body statistics in ultracold-atom systems.Comment: 10 pages, 9 figure

Explicit solutions for a class of nonlinear backward stochastic differential equations and their nodal sets

In this paper, we investigate a class of nonlinear backward stochastic differential equations (BSDEs) arising from financial economics, and give specific information about the nodal sets of the related solutions. As applications, we are able to obtain the explicit solutions to an interesting class of nonlinear BSDEs including the k-ignorance BSDE arising from the modeling of ambiguity of asset pricing

Attrition of methanol to olefins catalyst in a jet cup

Attrition of catalyst in a fluidized bed reactor is an inevitable issue especially in a commercial unit. Methanol to olefins (MTO) is becoming one of the main stream technologies for light olefins production. The attrition of MTO catalyst, however, received little attention. This study is focused on the attrition behavior of MTO catalyst in jet cup at high temperature. The influence of test time, inlet gas velocity, and temperature on MTO catalyst attrition was studied. It is found that the Gwyn formulation can well represent the relation between attrition index and test time. Our results show that jet cup can retrieve results quantitatively comparable to high velocity gas jets method while significantly shortening test time. It is also found that the inlet gas velocity has considerable influence on the MTO catalyst attrition, and the relation between inlet gas velocities and attrition index can be described by a power index of 3.7. Similar to high velocity gas jets experiments the attrition index manifests a maximum with the increase of temperature. But the temperature corresponding to the maximum attrition index shifts from 300 degrees C in high velocity jets tests to 100 degrees C in jet cup experiments. An analysis based on SEM pictures indicates that the transition of attrition mechanism is responsible for this shift. An empirical correlation has been presented for MTO catalyst attrition in jet cup, which shows good agreement with experimental data for inlet gas velocity from 88 to 158 m/s, and temperature from 100 to 500 degrees C. (C) 2017 Elsevier B.V. All rights reserved

Persistence of nonautonomous logistic system with time-varying delays and impulsive perturbations

In this paper, we develop the impulsive control theory to nonautonomous logistic system with time-varying delays. Some sufficient conditions ensuring the persistence of nonautonomous logistic system with time-varying delays and impulsive perturbations are derived. It is shown that the persistence of the considered system is heavily dependent on the impulsive perturbations. The proposed method of this paper is completely new. Two examples and the simulations are given to illustrate the proposed method and results

Clinical application of CT-guided 125I seed interstitial implantation for local recurrent rectal carcinoma

<p>Abstract</p> <p>Purpose</p> <p>The present study aimed to explore the safety profile and clinical efficacy of CT-guided radioactive seed implantation in treating local recurrent rectal carcinoma.</p> <p>Materials and methods</p> <p>CT-guided ¹²⁵I seed implantation was carried out in 20 patients with locally recurrent rectal carcinoma. 14 of the 20 patient had prior adjuvant external-beam radiation therapy (EBRT). The treatment planning system (TPS) was used preoperatively to reconstruct three dimensional images of the tumor and to calculate the estimated seed number and distribution. The median matched peripheral dose (MPD) was 120 Gy (range, 100-160 Gy).</p> <p>Results</p> <p>Of the 20 patients, 12 were male, 8 were female, and ages ranged from 38 to 78, with a median age of 62. Duration of follow-up was 3-34 months. The response rate of pain relief was 85% (17/20). Repeat CT scan 2 months following the procedure revealed complete response (CR) of the tumor in 2 patients, partial response (PR) in 13 patients, stable disease (SD) in 3 patients, and progressive disease (PD) in 2 patients. 75% of patients had either CR or PR. Median survival time was 18.8 months (95% CI: 3.5-22.4 months). 1 and 2 year survival rates were 75% and 25%, respectively. 4 patients died of recurrent tumor; 4 patients died of distant metastases; 9 patients died of recurrent tumor and distant metastases. 3 patients survived after 2 year follow up. Two patients were found to have mild hematochezia, which was reversible with symptomatic management.</p> <p>Conclusion</p> <p>CT-guided ¹²⁵I seed implantation appeared to be a safe, useful and less complicated interventional treatment option for local recurrent rectal carcinoma.</p