Anti-lecture Hall Compositions and Overpartitions

We show that the number of anti-lecture hall compositions of n with the first entry not exceeding k-2 equals the number of overpartitions of n with non-overlined parts not congruent to $0,\pm 1$ modulo k. This identity can be considered as a refined version of the anti-lecture hall theorem of Corteel and Savage. To prove this result, we find two Rogers-Ramanujan type identities for overpartition which are analogous to the Rogers-Ramanjan type identities due to Andrews. When k is odd, we give an alternative proof by using a generalized Rogers-Ramanujan identity due to Andrews, a bijection of Corteel and Savage and a refined version of a bijection also due to Corteel and Savage.Comment: 16 page

The Rogers-Ramanujan-Gordon Theorem for Overpartitions

Let $B_{k,i}(n)$ be the number of partitions of $n$ with certain difference condition and let $A_{k,i}(n)$ be the number of partitions of $n$ with certain congruence condition. The Rogers-Ramanujan-Gordon theorem states that $B_{k,i}(n)=A_{k,i}(n)$. Lovejoy obtained an overpartition analogue of the Rogers-Ramanujan-Gordon theorem for the cases $i=1$ and $i=k$. We find an overpartition analogue of the Rogers-Ramanujan-Gordon theorem in the general case. Let $D_{k,i}(n)$ be the number of overpartitions of $n$ satisfying certain difference condition and $C_{k,i}(n)$ be the number of overpartitions of $n$ whose non-overlined parts satisfy certain congruences condition. We show that $C_{k,i}(n)=D_{k,i}(n)$. By using a function introduced by Andrews, we obtain a recurrence relation which implies that the generating function of $D_{k,i}(n)$ equals the generating function of $C_{k,i}(n)$. We also find a generating function formula of $D_{k,i}(n)$ by using Gordon marking representations of overpartitions, which can be considered as an overpartition analogue of an identity of Andrews for ordinary partitions.Comment: 26 page

Generalized Toffoli gates using qudit catalysis

We present quantum networks for a n-qubit controlled gate C^{n-1}(U) which use a higher dimensional (qudit) ancilla as a catalyser. In its simplest form the network has only n two-particle gates (qubit-qudit) -- this is the minimum number of two-body interactions needed to couple all n+1 subsystems (n qubits plus one ancilla). This class of controlled gates includes the generalised Toffoli gate C^{n-1}(X) on n qubits, which plays an important role in several quantum algorithms and error correction. A particular example implementing this model is given by the dispersive limit of a generalised Jaynes-Cummings Hamiltonian of an effective spin-s interacting with a cavity mode.Comment: 5 pages, 3 fig

Progressive Failure And Life Prediction of Ceramic and Textile Composites

An engineering approach to predict the fatigue life and progressive failure of multilayered composite and textile laminates is presented. Analytical models which account for matrix cracking, statistical fiber failures and nonlinear stress-strain behavior have been developed for both composites and textiles. The analysis method is based on a combined micromechanics, fracture mechanics and failure statistics analysis. Experimentally derived empirical coefficients are used to account for the interface of fiber and matrix, fiber strength, and fiber-matrix stiffness reductions. Similar approaches were applied to textiles using Repeating Unit Cells. In composite fatigue analysis, Walker's equation is applied for matrix fatigue cracking and Heywood's formulation is used for fiber strength fatigue degradation. The analysis has been compared with experiment with good agreement. Comparisons were made with Graphite-Epoxy, C/SiC and Nicalon/CAS composite materials. For textile materials, comparisons were made with triaxial braided and plain weave materials under biaxial or uniaxial tension. Fatigue predictions were compared with test data obtained from plain weave C/SiC materials tested at AS&M. Computer codes were developed to perform the analysis. Composite Progressive Failure Analysis for Laminates is contained in the code CPFail. Micromechanics Analysis for Textile Composites is contained in the code MicroTex. Both codes were adapted to run as subroutines for the finite element code ABAQUS and CPFail-ABAQUS and MicroTex-ABAQUS. Graphic user interface (GUI) was developed to connect CPFail and MicroTex with ABAQUS

Cell-free measurements of brightness of fluorescently labeled antibodies

Validation of imaging contrast agents, such as fluorescently labeled imaging antibodies, has been recognized as a critical challenge in clinical and preclinical studies. As the number of applications for imaging antibodies grows, these materials are increasingly being subjected to careful scrutiny. Antibody fluorescent brightness is one of the key parameters that is of critical importance. Direct measurements of the brightness with common spectroscopy methods are challenging, because the fluorescent properties of the imaging antibodies are highly sensitive to the methods of conjugation, degree of labeling, and contamination with free dyes. Traditional methods rely on cell-based assays that lack reproducibility and accuracy. In this manuscript, we present a novel and general approach for measuring the brightness using antibody-avid polystyrene beads and flow cytometry. As compared to a cell-based method, the described technique is rapid, quantitative, and highly reproducible. The proposed method requires less than ten microgram of sample and is applicable for optimizing synthetic conjugation procedures, testing commercial imaging antibodies, and performing high-throughput validation of conjugation procedures

Fractal atomic-level percolation in metallic glasses

Metallic glasses are metallic alloys that exhibit exotic material properties. They may have fractal structures at the atomic level, but a physical mechanism for their organization without ordering has not been identified. We demonstrated a crossover between fractal short-range (<2 atomic diameters) and homogeneous long-range structures using in situ x-ray diffraction, tomography, and molecular dynamics simulations. A specific class of fractal, the percolation cluster, explains the structural details for several metallic-glass compositions. We postulate that atoms percolate in the liquid phase and that the percolating cluster becomes rigid at the glass transition temperature

Inhibiting the oncogenic translation program is an effective therapeutic strategy in multiple myeloma

Published in final edited form as: Sci Transl Med. 2017 May 10; 9(389). https://doi.org/10.1126/scitranslmed.aal2668.Multiple myeloma (MM) is a frequently incurable hematological cancer in which overactivity of MYC plays a central role, notably through up-regulation of ribosome biogenesis and translation. To better understand the oncogenic program driven by MYC and investigate its potential as a therapeutic target, we screened a chemically diverse small-molecule library for anti-MM activity. The most potent hits identified were rocaglate scaffold inhibitors of translation initiation. Expression profiling of MM cells revealed reversion of the oncogenic MYC-driven transcriptional program by CMLD010509, the most promising rocaglate. Proteome-wide reversion correlated with selective depletion of short-lived proteins that are key to MM growth and survival, most notably MYC, MDM2, CCND1, MAF, and MCL-1. The efficacy of CMLD010509 in mouse models of MM confirmed the therapeutic relevance of these findings in vivo and supports the feasibility of targeting the oncogenic MYC-driven translation program in MM with rocaglates