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The wide application of molecular beacon probes in specific DNA detection, especially in the fast prototyping of pathogen DNA detection kits in point-of-care diagnostics, has been hindered by the nonflexible choice of target sequences and the unstable fluorophore output. We developed an in vitro DNA detection system consisting of a pair of dCas9 proteins linked to split halves of luciferase, named the Paired dCas9 (PC) reporter. Co-localization of the reporter pair to a ~46 bp target sequence defined by two single guide RNAs (sgRNAs) activated luciferase which subsequently generated highly intensified luminescent signals. Combined with an array design and statistical analyses, the PC reporter system could be programmed to access sequence information across the entire genome of the pathogenic Mycobacterium tuberculosis H37Rv strain. These findings suggest great potential for the PC reporter in effective and affordable in vitro nucleic acid detection technologies. In this article we highlighted the systems design from our previous research work on the PC reporter (Zhang et al, 2015) with a focus on methodology.

We study integer-valued matrices with bounded determinants. Such matrices appear in the theory of integer programs (IP) with bounded determinants. For example, Artmann et al. showed that an IP can be solved in strongly polynomial time if the constraint matrix is bimodular, that is, the determinants are bounded in absolute value by two. Determinants are also used to bound the $\ell_1$-distance between IP solutions and solutions of its linear relaxation. One of the first works to quantify the complexity of IPs with bounded determinants was that of Heller, who identified the maximum number of differing columns in a totally unimodular matrix. Each extension of Heller's bound to general determinants has been super-polynomial in the determinants or the number of equations. We provide the first column bound that is polynomial in both values. For integer programs with box constraints, our result gives the first $\ell_1$-distance bound that is polynomial in the determinants and the number of equations. Our result can also be used to derive a bound on the height of Graver basis elements that is polynomial in the determinants and the number of equations. Furthermore, we show a tight bound on the number of differing columns in a bimodular matrix; this is the first tight bound since Heller. Our analysis reveals combinatorial properties of bimodular IPs that may be of independent interest., Fixed typo and accepted for journal publication

We study MINLO (mixed-integer non-linear optimization) formulations of the disjunction x ∈{0}∪ [l, u], where z is a binary indicator of x ∈ [l, u] (0 ≤ l 1.

We study MINLO (mixed-integer nonlinear optimization) formulations of the disjunction $x\in\{0\}\cup[\ell,u]$, where $z$ is a binary indicator of $x\in[\ell,u]$ ($0 \leq \ell 1$.

Fundamental in matrix algebra and its applications, a \emph{generalized inverse} of a real matrix $A$ is a matrix $H$ that satisfies the Moore-Penrose (M-P) property $AHA=A$. If $H$ also satisfies the additional useful M-P property, $HAH=H$, it is called a \emph{reflexive generalized inverse}. Reflexivity is equivalent to minimum rank, so we are particularly interested in reflexive generalized inverses. We consider aspects of symmetry related to the calculation of a \emph{sparse} reflexive generalized inverse of $A$. As is common, and following Lee and Fampa (2018) for calculating sparse generalized inverses, we use (vector) 1-norm minimization for inducing sparsity and for keeping the magnitude of entries under control. When $A$ is symmetric, we may naturally desire a symmetric $H$; while generally such a restriction on $H$ may not lead to a 1-norm minimizing reflexive generalized inverse. We investigate a block construction method to produce a symmetric reflexive generalized inverse that is structured and has guaranteed sparsity. We provide a theoretically-efficient and practical local-search algorithm to block-construct an approximate 1-norm minimizing symmetric reflexive generalized inverse. Another aspect of symmetry that we consider relates to another M-P property: $H$ is \emph{ah-symmetric} if $AH$ is symmetric. The ah-symmetry property is the key one for solving least-squares problems using $H$. Here we do not assume that $A$ is symmetric, and we do not impose symmetry on $H$. We investigate a column block construction method to produce an ah-symmetric reflexive generalized inverse that is structured and has guaranteed sparsity. We provide a theoretically-efficient and practical local-search algorithm to column block construct an approximate 1-norm minimizing ah-symmetric reflexive generalized inverse.

We developed an in vitro DNA detection system using a pair of dCas9 proteins linked to split halves of luciferase. Luminescence was induced upon colocalization of the reporter pair to a ∼44 bp target sequence defined by sgRNAs. We used the system to detect Mycobacterium tuberculosis DNA with high specificity and sensitivity. The reprogrammability of dCas9 was further leveraged in an array design that accesses sequence information across the entire genome.

In the context of global optimization of mixed-integer nonlinear optimization formulations, we consider smoothing univariate functions $f$ that satisfy $f(0)=0$, $f$ is increasing and concave on $[0,+\infty)$, $f$ is twice differentiable on all of $(0,+\infty)$, but $f'(0)$ is undefined or intolerably large. The canonical examples are root functions $f(w):=w^p$, for $00$, then replacing the part of $f$ on $[0,\delta]$ with the unique homogeneous cubic, matching $f$, $f'$ and $f''$ at $\delta$. The parameter $\delta$ is used to control (i.e., upper bound) the derivative at 0 (which controls it on all of $[0,+\infty)$ when $g$ is concave). Our main results: (i) we weaken an earlier sufficient condition to give a necessary and sufficient condition for the piecewise function $g$ to be increasing and concave; (ii) we give a general sufficient condition for $g'(0)$ to be decreasing in the smoothing parameter $\delta$; under the same condition, we demonstrate that the worst-case error of $g$ as an estimate of $f$ is increasing in $\delta$; (iii) we give a general sufficient condition for $g$ to underestimate $f$; (iv) we give a general sufficient condition for $g$ to dominate the simple `shift smoothing' $h(w):=f(w+\lambda)-f(\lambda)$ ($\lambda>0$), when the parameters $\delta$ and $\lambda$ are chosen `fairly' --- i.e., so that $g'(0)=h'(0)$. In doing so, we solve two natural open problems of Lee and Skipper (2016), concerning (iii) and (iv) for root functions.