Quiver GIT for varieties with tilting bundles

In the setting of a variety X admitting a tilting bundle T we consider the problem of constructing X as a quiver GIT quotient of the algebra A:=EndX(T)opA:=EndX(T)op . We prove that if the tilting equivalence restricts to a bijection between the skyscraper sheaves of X and the closed points of a quiver representation moduli functor for A=EndX(T)opA=EndX(T)op then X is indeed a fine moduli space for this moduli functor, and we prove this result without any assumptions on the singularities of X. As an application we consider varieties which are projective over an affine base such that the fibres are of dimension 1, and the derived pushforward of the structure sheaf on X is the structure sheaf on the base. In this situation there is a particular tilting bundle on X constructed by Van den Bergh, and our result allows us to reconstruct X as a quiver GIT quotient for an easy to describe stability condition and dimension vector. This result applies to flips and flops in the minimal model program, and in the situation of flops shows that both a variety and its flop appear as moduli spaces for algebras produced from different tilting bundles on the variety. We also give an application to rational surface singularities, showing that their minimal resolutions can always be constructed as quiver GIT quotients for specific dimension vectors and stability conditions. This gives a construction of minimal resolutions as moduli spaces for all rational surface singularities, generalising the G-Hilbert scheme moduli space construction which exists only for quotient singularities

Just One? Solo Dining, Gender and Temporal Belonging in Public Spaces

In recent years, various lifestyle websites have offered tips on eating out alone as well as lists of the best restaurants for solo dining in major cities of the world. Utilising the theoretical concepts of participation units, territories of the self (Goffman 1972[1971]) and belonging (Author B2011, 2013), this paper explores the challenges that spatio-temporal conventions pose for women solo diners in particular. Through the lens of solo dining, we explore being alone and belonging in shared public spaces, and the gendered nature of aloneness and respectability. The papercontributes to existing theory by examining the influence that time has on a woman solo diner’s ‘single’ participation unit, her ability to lay claim to public space and her relationship with the surrounding social environment. The paper concludes by exploring what the new trend of solo dining can offer and the consequences this has for how sociologists conceptualise sociality inpublic spaces

Tailoring electromechanical properties of natural rubber vitrimers by cross-linkers

The growing demand for smart polymeric transducers such as dielectric elastomer actuators and energy harvesters has urged the use of sustainable and recyclable elastomeric materials. Vitrimer chemistry has shed light on future reprocessable and recyclable thermosets and elastomers. In this work, epoxidized natural rubber (ENR) vitrimers were prepared using diacid or triacid cross-linkers and formed covalently cross-linking networks via thermally triggered reversible β-hydroxy ester bonds. The cross-linked ENR elastomers exhibited Arrhenius-type viscoelastic behavior with a complete stress relaxation between 140 and 160 °C, that is, vitrimer characteristics, which were highly dependent on the cross-linking temperature. The mechanical and dielectric properties of the ENR vitrimers can be tuned by varying the molecular structure and concentration of the cross-linkers. Among the diacid and triacid cross-linkers, Pripol 1017 fatty polyacid (P1017) and 3,3′-dithiopropionic acid (DTPA) had similar effects on the cross-linking density and mechanical properties of the ENR vitrimers. The highest tensile strength of 8.70 ± 1.9 or 15.6 ± 2.6 MPa was obtained at 6 mol % of P1017 or DTPA, respectively. While for diamide-based diacid cross-linker (DME), 8 mol % was needed to reach the highest tensile strength of 13.1 ± 2.7 MPa for the elastomer. The three ENR vitrimers showed increased relative permittivity ε′ = 5∼7 at 1 kHz while maintaining low dielectric losses compared to traditional dicumyl peroxide-cured ENR, with ε′ = 3.57 at 1 kHz. With the optimized acidic cross-linker concentrations of P1017 at 6 mol %, DTPA at 6 mol %, and DME at 8 mol %, the ENR vitrimers exhibited improved actuation capabilities at lower electrical fields. Utilizing dynamic cross-linkers to tune the electromechanical properties of dielectric elastomers and the reversibly cross-linked polymer networks will open new opportunities for smart and sustainable dielectric elastomer devices

The GL(2, C) McKay correspondence

In this paper we show that for any affine complete rational surface singularity the quiver of the reconstruction algebra can be determined combinatorially from the dual graph of the minimal resolution. As a consequence the derived category of the minimal resolution is equivalent to the derived category of an algebra whose quiver is determined by the dual graph. Also, for any finite subgroup G of GL(2,C)GL(2,C), it means that the endomorphism ring of the special CM CC [[x, y]]G-modules can be used to build the dual graph of the minimal resolution of C2/GC2/G, extending McKay’s observation (McKay, Proc Symp Pure Math, 37:183–186, 1980) for finite subgroups of SL(2,C)SL(2,C) to all finite subgroups of GL(2,C)GL(2,C)

Clinical improvement and radiological progression in a girl with early onset scoliosis (EOS) treated conservatively – a case report

BACKGROUND: Chêneau-Brace treatment of a certain standard reduces the rate of surgery, prevents progression and in a certain patient population leads to marked improvement of Cobb angle and cosmetic appearance. During the last two years a patient refusing surgery with a double major curvature of initially 60° showed a clear cosmetic improvement and a clear radiological progression at the same time. The findings of this patient have been reviewed in order to find out how cosmetic appearance and Cobb angle can develop differently. METHODS: The patient entered conservative treatment at the age of 13 years, premenarchial with Tanner II and a Cobb angle of 60° thoracic and 59° lumbar. The angle of trunk rotation (ATR; Scoliometer) was 13° thoracic and 13° lumbar. We have documented the findings of this patient (Surface topography, ATR, Cobb angles and angles of vertebral rotation (according to Raimondi) during the treatment period (27 Month) until 2 years after the onset of menarche. RESULTS: After a treatment time of 27 Month the Cobb angle increased to 74° thoracic and 65° lumbar. The angles of vertebral rotation according to Raimondi increased slightly from 26° thoracic and 28° lumbar to 30° thoracic and 28° lumbar. The ATR improved to 12° thoracic and 5° lumbar while Lateral deviation improved from 22,4 mm to 4,6 mm and average surface rotation improved from 10,6° to 6°. In the X-rays a reduction of decompensation was visible. The patient felt comfortable with the cosmetic result. CONCLUSION: Conservative treatment may improve cosmetic appearance while the curve progresses radiologically. This could be explained by assuming that (1) the Rigo Chêneau brace is able to improve cosmetic appearance by changing the shape of the thorax when the curve itself is too stiff to be corrected by a brace, that (2) reduction of decompensation leads to significant cosmetical improvements or (3) that the patient gained weight and therefore the deformation is masked. However, the weight the patient gained cannot explain the cosmetical improvement in this case. Conservative treatment with a certain standard of quality seems a viable alternative for patients with Cobb angles of > 60° when surgical treatment is refused. Specialists in scoliosis management should be aware of the fact that curve progression can occur even if the clinical measurements show an improvement

Whiteness and diasporic Irishness: nation, gender and class

Whiteness is often detached from the notion of diaspora in the recent flurry of interest in the phenomenon, yet it is a key feature of some of the largest and oldest displacements. This paper explores the specific contexts of white racial belonging and status over two centuries in two main destinations of the Irish diaspora, the USA and Britain. Its major contribution is a tracing of the untold story of ‘How the Irish became white in Britain’ to parallel and contrast with the much more fully developed narrative in the USA. It argues that, contrary to popular belief, the racialisation of the Irish in England did not fade away at the end of the nineteenth century but became transmuted in new forms which have continued to place the ‘white’ Irish outside the boundaries of the English nation. These have been strangely ignored by social scientists, who conflate Irishness and working-class identities in England without acknowledging the distinctive contribution of Irish backgrounds to constructions of class difference. Gender locates Irish women and men differently in relation to these class positions, for example allowing mothers to be blamed for the perpetuation of the underclass. Class and gender are also largely unrecognised dimensions of Irish ethnicity in the USA, where the presence of ‘poor white’ neighbourhoods continues to challenge the iconic story of Irish upward mobility. Irishness thus remains central to the construction of mainstream ‘white’ identities in both the USA and Britain into the twenty-first century

Direct detection and measurement of wall shear stress using a filamentous bio-nanoparticle

The wall shear stress (WSS) that a moving fluid exerts on a surface affects many processes including those relating to vascular function. WSS plays an important role in normal physiology (e.g. angiogenesis) and affects the microvasculature's primary function of molecular transport. Points of fluctuating WSS show abnormalities in a number of diseases; however, there is no established technique for measuring WSS directly in physiological systems. All current methods rely on estimates obtained from measured velocity gradients in bulk flow data. In this work, we report a nanosensor that can directly measure WSS in microfluidic chambers with sub-micron spatial resolution by using a specific type of virus, the bacteriophage M13, which has been fluorescently labeled and anchored to a surface. It is demonstrated that the nanosensor can be calibrated and adapted for biological tissue, revealing WSS in micro-domains of cells that cannot be calculated accurately from bulk flow measurements. This method lends itself to a platform applicable to many applications in biology and microfluidics