A Distributive Lattice Connected with Arithmetic Progressions of Length Three

Let $\mathcal{T}$ be a collection of 3-element subsets $S$ of $\{1, \ldots,n\}$ with the property that if $i<j<k$ and $a<b<c$ are two 3-element subsets in $S$, then there exists an integer sequence $x_1 < x_2 < \cdots < x_n$ such that $x_i, x_j, x_k$ and $x_a, x_b, x_c$ are arithmetic progressions. We determine the number of such collections $\mathcal{T}$ and the number of them of maximum size. These results confirm two conjectures of Noam Elkies.Comment: 25 pages, 1 figure. To appear in the Ramanujan Journa

The Lecture Hall Parallelepiped

The s-lecture hall polytopes P_s are a class of integer polytopes defined by Savage and Schuster which are closely related to the lecture hall partitions of Eriksson and Bousquet-M\'elou. We define a half-open parallelopiped Par_s associated with P_s and give a simple description of its integer points. We use this description to recover earlier results of Savage et al. on the \delta-vector (or h^*-vector) and to obtain the connections to s-ascents and s-descents, as well as some generalizations of these results.Comment: 14 pages. To appear in Annals of Combinatoric

Graphene oxide-Au nano particle coated quartz crystal microbalance biosensor for the real time analysis of carcinoembryonic antigen

A label-free quartz crystal microbalance (QCM) biosensor was developed for the selective and real-time estimation of carcinoembryonic antigen (CEA) through the present study. Graphene oxide-Au nanoparticles (GO-AuNPs) was in situ synthesised on the surface of the QCM electrode and the antibody of CEA (monoclonal anti-CEA from mouse) was covalently immobilized on this layer as the bioreceptor for CEA. Mercaptoacetic acid–EDC–NHS reaction mechanism was used for anti-CEA immobilization. The effect of oxygen plasma treatment of the QCM electrode surface before bioreceptor preparation on the performance of the biosensor was tested and was found promising. CEA solutions with various concentrations were analysed using the bioreceptors to estimate the sensitivity and detection limit of the biosensor. The biosensors selectively recognized and captured CEA biomolecules with a detection limit of 0.06 and 0.09 ng mL−1 of CEA for oxygen plasma-treated (E2) and untreated (E1) bioreceptors, respectively. The sensitivity was estimated at 102 and 79 Hz, respectively, for E2 and E1. Clinical serum samples were analysed and the results were found in good agreement with the ELISA analysis. Long term stability was also found to be excellent. Langmuir adsorption isotherm was also conducted using the experimental results

A Class of Embedded DG Methods for Dirichlet Boundary Control of Convection Diffusion PDEs

We investigated an hybridizable discontinuous Galerkin (HDG) method for a convection diffusion Dirichlet boundary control problem in our earlier work [SIAM J. Numer. Anal. 56 (2018) 2262-2287] and obtained an optimal convergence rate for the control under some assumptions on the desired state and the domain. In this work, we obtain the same convergence rate for the control using a class of embedded DG methods proposed by Nguyen, Peraire and Cockburn [J. Comput. Phys. vol. 302 (2015), pp. 674-692] for simulating fluid flows. Since the global system for embedded DG methods uses continuous elements, the number of degrees of freedom for the embedded DG methods are smaller than the HDG method, which uses discontinuous elements for the global system. Moreover, we introduce a new simpler numerical analysis technique to handle low regularity solutions of the boundary control problem. We present some numerical experiments to confirm our theoretical results

Applying MCI-062, A Novel Pan-RAS Inhibitor, To Treat KRAS-Mutant Lung Cancer

RAS is a prevalent oncogene that is mutated in 27% of human cancers. Gain-of-function RAS mutations activate multiple downstream pathways, including the RAS-RAF-MEK-ERK and PI3K/AKT/mTOR pathways, which are critical in tumorigenesis and cancer cell proliferation. RAS proteins such as KRAS, a member of the RAS protein family, and their downstream effectors are attractive targets for cancer therapy since their mutations act as frequent drivers in lung, colorectal, and pancreatic cancers. However, RAS proteins have relatively smooth surfaces that lack traditional binding pockets, making inhibitors specific to RAS difficult to create. Recently, a novel small molecule pan-RAS inhibitor named MCI-062 was developed in Dr. Gary Piazza\u27s Drug Discovery Research Center at the Mitchell Cancer Institute. As a potential pan-RAS inhibitor, MCI-062 is hypothesized to serve as a targeted therapy for RAS-mutant cancers regardless of mutation isoform, including all types of KRAS-mutant lung cancers. The inhibitory effects of MCI-062 were tested on the growth and proliferation of two non-small cell lung cancer cell lines, A549 and H358, using colony formation assays. The cells were plated onto 12-well plates, treated with varying concentrations of MCI-062, and then digitally imaged and analyzed. A549 cells have a KRASG13D mutation, while H358 cells have a KRASG12C mutation. The results indicate that MCI-062 effectively suppresses the growth and proliferation of both A549 and H358 cells despite their differing mutation isoforms, suggesting that MCI-062 successfully functions as a pan-RAS inhibitor

Applying MCI-062, a Novel Pan-RAS Inhibitor, to Treat KRAS-Mutant Lung Cancer.

Honors thesis poster presentation. RAS, one of the most prevalent oncogenes, is mutated in 27% of human cancers. Gainof- function RAS mutations activate multiple downstream pathways, including the RASRAF- MEK-ERK and PI3K/AKT/mTOR pathways, which are critical in tumorigenesis and cancer cell proliferation. The RAS proteins KRAS, HRAS, and NRAS along with their downstream effectors are attractive targets for cancer therapy since they act as frequent drivers in lung, colorectal, and pancreatic cancers. However, RAS proteins have relatively smooth surfaces that lack traditional binding pockets, making inhibitors specific to RAS difficult to create. Recently, a novel small molecule pan-RAS inhibitor named MCI-062 was developed in Dr. Gary Piazza\u27s Drug Discovery Research Center at the Mitchell Cancer Institute. As a pan-RAS inhibitor, MCI-062 is hypothesized to serve as a targeted therapy for RAS-mutant cancers regardless of mutation isoform, including all types of KRAS-mutant lung cancers. The inhibitory effects of MCI-062 were tested on the growth and proliferation of two non-small cell lung cancer cell lines, A549 and H358, using colony formation assays. The cells were plated onto 12-well plates, treated with varying concentrations of MCI-062 in duplicate, and then digitally imaged and analyzed. A549 cells have a KRASG13D mutation, while H358 cells have a KRASG12C mutation. The results indicate that MCI-062 effectively suppresses the growth and proliferation of both A549 and H358 cells despite their differing mutation isoforms, suggesting that MCI-062 successfully functions as a pan-RAS inhibitor.https://jagworks.southalabama.edu/honors_college_posters/1003/thumbnail.jp

A Covert Data Transport Protocol

Both enterprise and national firewalls filter network connections. For data forensics and botnet removal applications, it is important to establish the information source. In this paper, we describe a data transport layer which allows a client to transfer encrypted data that provides no discernible information regarding the data source. We use a domain generation algorithm (DGA) to encode AES encrypted data into domain names that current tools are unable to reliably differentiate from valid domain names. The domain names are registered using (free) dynamic DNS services. The data transmission format is not vulnerable to Deep Packet Inspection (DPI).Comment: 8 pages, 10 figures, conferenc