Promotion/Inhibition Effects in Networks: A Model with Negative Probabilities

Biological networks often encapsulate promotion/inhibition as signed edge-weights of a graph. Nodes may correspond to genes assigned expression levels (mass) of respective proteins. The promotion/inhibition nature of co-expression between nodes is encoded in the sign of the corresponding entry of a sign-indefinite adjacency matrix, though the strength of such co-expression (i.e., the precise value of edge weights) cannot typically be directly measured. Herein we address the inverse problem to determine network edge-weights based on a sign-indefinite adjacency and expression levels at the nodes. While our motivation originates in gene networks, the framework applies to networks where promotion/inhibition dictates a stationary mass distribution at the nodes. In order to identify suitable edge-weights we adopt a framework of ``negative probabilities,'' advocated by P.\ Dirac and R.\ Feynman, and we set up a likelihood formalism to obtain values for the sought edge-weights. The proposed optimization problem can be solved via a generalization of the well-known Sinkhorn algorithm; in our setting the Sinkhorn-type ``diagonal scalings'' are multiplicative or inverse-multiplicative, depending on the sign of the respective entries in the adjacency matrix, with value computed as the positive root of a quadratic polynomial.Comment: 6 page

Lasso formulation of the shortest path problem

The shortest path problem is formulated as an $l_1$-regularized regression problem, known as lasso. Based on this formulation, a connection is established between Dijkstra's shortest path algorithm and the least angle regression (LARS) for the lasso problem. Specifically, the solution path of the lasso problem, obtained by varying the regularization parameter from infinity to zero (the regularization path), corresponds to shortest path trees that appear in the bi-directional Dijkstra algorithm. Although Dijkstra's algorithm and the LARS formulation provide exact solutions, they become impractical when the size of the graph is exceedingly large. To overcome this issue, the alternating direction method of multipliers (ADMM) is proposed to solve the lasso formulation. The resulting algorithm produces good and fast approximations of the shortest path by sacrificing exactness that may not be absolutely essential in many applications. Numerical experiments are provided to illustrate the performance of the proposed approach.Comment: 17 page

Monge-Kantorovich Optimal Transport Through Constrictions and Flow-rate Constraints

We consider the problem to transport resources/mass while abiding by constraints on the flow through constrictions along their path between specified terminal distributions. Constrictions, conceptualized as toll stations at specified points, limit the flow rate across. We quantify flow-rate constraints via a bound on a sought probability density of the times that mass-elements cross toll stations and cast the transportation scheduling in a Kantorovich-type of formalism. Recent work by our team focused on the existence of Monge maps for similarly constrained transport minimizing average kinetic energy. The present formulation in this paper, besides being substantially more general, is cast as a (generalized) multi-marginal transport problem - a problem of considerable interest in modern-day machine learning literature and motivated extensive computational analyses. An enabling feature of our formalism is the representation of an average quadratic cost on the speed of transport as a convex constraint that involves crossing times.Comment: 8 pages, 6 figure

A novel IgE epitope-specific antibodies-based sandwich ELISA for sensitive measurement of immunoreactivity changes of peanut allergen Ara h 2 in processed foods

BackgroundPeanut is an important source of dietary protein for human beings, but it is also recognized as one of the eight major food allergens. Binding of IgE antibodies to specific epitopes in peanut allergens plays important roles in initiating peanut-allergic reactions, and Ara h 2 is widely considered as the most potent peanut allergen and the best predictor of peanut allergy. Therefore, Ara h 2 IgE epitopes can serve as useful biomarkers for prediction of IgE-binding variations of Ara h 2 and peanut in foods. This study aimed to develop and validate an IgE epitope-specific antibodies (IgE-EsAbs)-based sandwich ELISA (sELISA) for detection of Ara h 2 and measurement of Ara h 2 IgE-immunoreactivity changes in foods.MethodsDEAE-Sepharose Fast Flow anion-exchange chromatography combining with SDS-PAGE gel extraction were applied to purify Ara h 2 from raw peanut. Hybridoma and epitope vaccine techniques were employed to generate a monoclonal antibody against a major IgE epitope of Ara h 2 and a polyclonal antibody against 12 IgE epitopes of Ara h 2, respectively. ELISA was carried out to evaluate the target binding and specificity of the generated IgE-EsAbs. Subsequently, IgE-EsAbs-based sELISA was developed to detect Ara h 2 and its allergenic residues in food samples. The IgE-binding capacity of Ara h 2 and peanut in foods was determined by competitive ELISA. The dose-effect relationship between the Ara h 2 IgE epitope content and Ara h 2 (or peanut) IgE-binding ability was further established to validate the reliability of the developed sELISA in measuring IgE-binding variations of Ara h 2 and peanut in foods.ResultsThe obtained Ara h 2 had a purity of 94.44%. Antibody characterization revealed that the IgE-EsAbs recognized the target IgE epitope(s) of Ara h 2 and exhibited high specificity. Accordingly, an IgE-EsAbs-based sELISA using these antibodies was able to detect Ara h 2 and its allergenic residues in food samples, with high sensitivity (a limit of detection of 0.98 ng/mL), accuracy (a mean bias of 0.88%), precision (relative standard deviation < 16.50%), specificity, and recovery (an average recovery of 98.28%). Moreover, the developed sELISA could predict IgE-binding variations of Ara h 2 and peanut in foods, as verified by using sera IgE derived from peanut-allergic individuals.ConclusionThis novel immunoassay could be a user-friendly method to monitor low level of Ara h 2 and to preliminary predict in vitro potential allergenicity of Ara h 2 and peanut in processed foods

Exploiting an Allosteric Binding Site of PRMT3 Yields Potent and Selective Inhibitors

Protein arginine methyltransferases (PRMTs) play an important role in diverse biological processes. Among the nine known human PRMTs, PRMT3 has been implicated in ribosomal biosynthesis via asymmetric dimethylation of the 40S ribosomal protein S2 and in cancer via interaction with the DAL-1 tumor suppressor protein. However, few selective inhibitors of PRMTs have been discovered. We recently disclosed the first selective PRMT3 inhibitor, which occupies a novel allosteric binding site and is noncompetitive with both the peptide substrate and cofactor. Here we report comprehensive structure-activity relationship studies of this series, which resulted in the discovery of multiple PRMT3 inhibitors with submicromolar potencies. An X-ray crystal structure of compound 14u in complex with PRMT3 confirmed that this inhibitor occupied the same allosteric binding site as our initial lead compound. These studies provide the first experimental evidence that potent and selective inhibitors can be created by exploiting the allosteric binding site of PRMT3

Motivations of women who organized others for prostitution: Evidence from a female prison in China

This article discusses women’s involvement in sex work management – an offence defined under section 358 of the 1997 Chinese Criminal Law and one of the re-emerged areas of illegality following the economic reforms since 1978. It first provides the historical context, legislative background and relevant sections of the Chinese vice laws so as to help make sense of the data obtained. Then it discusses the methodological issues before presenting the empirical findings to explore the socio-demographic profile of the incarcerated female sex work organizers who participated in this study and their motivations for organizing others for prostitution. Based on empirical data, this article explores the impact of social conditions on female offenders in China’s reform era and also the effects of the anti-prostitution policy in the country. Moreover, through a Chinese case study, it makes contributions to broader scholarship on the sex trade regulation. It concludes with a couple of implications for policy and practice

Non-Standard Errors

In statistics, samples are drawn from a population in a data-generating process (DGP). Standard errors measure the uncertainty in estimates of population parameters. In science, evidence is generated to test hypotheses in an evidence-generating process (EGP). We claim that EGP variation across researchers adds uncertainty: Non-standard errors (NSEs). We study NSEs by letting 164 teams test the same hypotheses on the same data. NSEs turn out to be sizable, but smaller for better reproducible or higher rated research. Adding peer-review stages reduces NSEs. We further find that this type of uncertainty is underestimated by participants