A Finite Algorithm for the Linear Exchange Model

It is shown that Lemke’s algorithm can be used to compute, in a finite number of steps, an equilibrium or reduction for the pure exchange model with linear utilities

A Finite Algorithm for the Linear Exchange Model

It is shown that Lemke's algorithm can be used to compute, in a finite number of steps, an equilibrium or reduction for the pure exchange model with linear utilities.

Feasibility study of a randomised controlled trial to investigate the effectiveness of using a humanoid robot to improve the social skills of children with an Autism Spectrum Disorder (Kaspar RCT): A Study Protocol

This is an Open Access article distributed in accordance with the terms of the Creative Commons Attribution (CC BY 4.0) license, which permits others to distribute, remix, adapt and build upon this work, for commercial use, provided the original work is properly cited. See: http:// creativecommons. org/licenses/ by/ 4.0/Introduction: Interventions using robot-assisted therapy may be beneficial for the social skills development of children with autism spectrum disorder (ASD), however randomised controlled trials (RCTs) are lacking. The present research aims to assess the feasibility of conducting a RCT evaluating the effectiveness of a social skills intervention using the robot ‘Kaspar’ with children with ASD. Methods and analysis: Forty children will be recruited. Inclusion criteria are: aged 5-10 years, confirmed ASD diagnosis, IQ over 70, English language comprehension, a carer who can complete questionnaires in English, and no current participation in a private social communication intervention. Children will be randomised to receive an intervention with a therapist and Kaspar, or with the therapist only. They will receive two familiarisation sessions and six treatment sessions over eight weeks. They will be assessed at baseline, and at 10-weeks and 22-weeks after baseline. The primary outcome of this study is to evaluate whether the pre-determined feasibility criteria for a full-scale trial are met. The potential primary outcome measures for a full-scale trial are the Social Communication Questionnaire (SCQ) and the Social Skills Improvement System (SSIS). We will conduct a preliminary economic analysis. After the study has ended, a sample of twenty participants and their families will be invited to participate in semi-structured interviews to explore the feasibility and acceptability of the study’s methods and intervention. Ethics and dissemination: Parents/carers will provide informed consent, and children will give assent, where appropriate. Care will be taken to avoid pressure or coercion to participate. Aftercare is available from the recruiting NHS Trust and a phased withdrawal protocol will be followed if children become excessively attached to the robot. The results of the study will be disseminated to academic audiences and non-academic stakeholders, e.g. families of children with ASD, support groups, clinicians and charities. Registration details: ISRCTN14156001.Peer reviewe

ZNF703 is a common Luminal B breast cancer oncogene that differentially regulates luminal and basal progenitors in human mammary epithelium.

The telomeric amplicon at 8p12 is common in oestrogen receptor-positive (ER+) breast cancers. Array-CGH and expression analyses of 1172 primary breast tumours revealed that ZNF703 was the single gene within the minimal amplicon and was amplified predominantly in the Luminal B subtype. Amplification was shown to correlate with increased gene and protein expression and was associated with a distinct expression signature and poor clinical outcome. ZNF703 transformed NIH 3T3 fibroblasts, behaving as a classical oncogene, and regulated proliferation in human luminal breast cancer cell lines and immortalized human mammary epithelial cells. Manipulation of ZNF703 expression in the luminal MCF7 cell line modified the effects of TGFβ on proliferation. Overexpression of ZNF703 in normal human breast epithelial cells enhanced the frequency of in vitro colony-forming cells from luminal progenitors. Taken together, these data strongly point to ZNF703 as a novel oncogene in Luminal B breast cancer

Modification of BRCA1-associated breast cancer risk by HMMR overexpression

Breast cancer risk for carriers of BRCA1 pathological variants is modified by genetic factors. Genetic variation in HMMR may contribute to this effect. However, the impact of risk modifiers on cancer biology remains undetermined and the biological basis of increased risk is poorly understood. Here, we depict an interplay of molecular, cellular, and tissue microenvironment alterations that increase BRCA1-associated breast cancer risk. Analysis of genome-wide association results suggests that diverse biological processes, including links to BRCA1-HMMR profiles, influence risk. HMMR overexpression in mouse mammary epithelium increases Brca1-mutant tumorigenesis by modulating the cancer cell phenotype and tumor microenvironment. Elevated HMMR activates AURKA and reduces ARPC2 localization in the mitotic cell cortex, which is correlated with micronucleation and activation of cGAS-STING and non-canonical NF-kappa B signaling. The initial tumorigenic events are genomic instability, epithelial-to-mesenchymal transition, and tissue infiltration of tumor-associated macrophages. The findings reveal a biological foundation for increased risk of BRCA1-associated breast cancer. The effect of hyaluronan-mediated motility receptor (HMMR) expression in BRCA1-associated breast cancer risk remains unknown. Here, HMMR overexpression induces the activation of cGAS-STING and non-canonical NF-kappa B signalling, instigating an immune permissive environment for breast cancer development

Maria Cosway’s Hours: Cosmopolitan and Classical Visual Culture in Thomas Macklin’s Poets Gallery

Thomas Macklin’s Gallery of Poets opened at the Mitre Tavern in Fleet Street in 1788 with the aim to ‘display British Genius’ through ‘Prints Illustrative of the Most Celebrated British Poets’. Early newspaper coverage promised ‘a monument of the powers of the pencil in England, as the Vatican is at Rome’. The incongruous juxtaposition between Fleet Street and the Vatican spells out the cosmopolitan ambition of the literary gallery phenomenon through its real and imagined geographies of display. Through the format of the paper gallery of prints, Macklin’s Poets offered the inventions of British Poets as a repository of painting. This chapter examines how the cosmopolitan idiom of the paper gallery is negotiated in the first number of Macklin’s Poets. This essay examines the extent to which this ambition was achieved in the first Number of Macklin’s Poets which carried an engraving of Maria Cosway’s The Hours, originally a painting with an impressively European iconographic heritage. The painting was first exhibited at the Royal Academy in 1783, and was retroactively associated by Macklin with Thomas Gray’s ‘Ode on the Spring’. The trope of the Hours brought with it a weighty provenance derived from classical marble bas-relief, through the antiquarian pages of Pietro Santi Bartoli and Bernard de Montfaucon to Flaxman’s designs for Wedgwood plaques and vases. Cosway’s name also imported into Gray’s poem her reputation as a cosmopolitan, cultured woman who had completed the Grand Tour and who moved in elite circles including those of the Prince of Wales in London and the Duke of Orleans, Pierre d’Hancarville and Thomas Jefferson in Paris. The iconographies of the painting, the print, and the poem articulate a European cosmopolitan tradition for British Art

On Quadratic Programming

A procedure based on Lemke's algorithm is developed which either computes stationary points for general quadratic programs or else shows that the program has no optimum. If a general quadratic program has an optimum and satisfies a non-degeneracy condition then it is demonstrated that there are an odd number of stationary points.

The Linear Complementarity Problem

This study centers on the task of efficiently finding a solution of the linear complementarity problem: Ix - My = q, x \ge 0, y \ge 0, x \perp y. The main results are: (1) It is shown that Lemke's algorithm will solve (or show no solution exists) the problem for M \in L where L is a class of matrices, which properly includes (i) certain copositive matrices, (ii) certain matrices with nonnegative principal minors, (iii) matrices for bimatrix games. (2) If M \in L, if the system Ix - My = q, x \ge 0, y \ge 0 is feasible and nondegenerate, then the corresponding linear complementarity problem has an odd number of solutions. If M \in L and q > 0 then the solution is unique. (3) If for some M and every q \ge 0 the problem has a unique solution then M \in L and the problem has a solution for every q. (4) If M has nonnegative principal minors and if the linear complementarity with M and q has a nondegenerate complementary solution then the solution is unique. (5) If y TMy + y Tq is bounded below on y \ge 0 then the linear complementarity problem with M and q has a solution and Lemke's algorithm can be used to find such a solution. If, in addition, the problem is nondegenerate, then it has an odd number of solutions. (6) A procedure based on Lemke's algorithm is developed which either computes stationary points for general quadratic programs or else shows that the program has no optimum. (7) If a quadratic program has an optimum and satisfies a nondegeneracy condition then there are an odd number of stationary points.

A cellation of the Grassmann manifold

Motivated by the computation of equilibria in economic models with incomplete asset markets, a cellation of the Grassmann manifold is constructed by restricting a common atlas. The Grassmann manifold of m-planes in n-dimensional space is shown to be a union of n choose m congruent m(n - m)-dimensional topological disks whose interiors are disjoint.