Fractional quantum Hall states with variational Projected Entangled-Pair States: a study of the bosonic Harper-Hofstadter model

An important class of model Hamiltonians for investigation of topological phases of matter consists of mobile, interacting particles on a lattice subject to a semi-classical gauge field, as exemplified by the bosonic Harper-Hofstadter model. A unique method for investigations of two-dimensional quantum systems are the infinite projected-entangled pair states (iPEPS), as they avoid spurious finite size effects that can alter the phase structure. However, due to no-go theorems in related cases this was often conjectured to be impossible in the past. In this letter, we show that upon variational optimization the infinite projected-entangled pair states can be used to this end, by identifying fractional Hall states in the bosonic Harper-Hofstadter model. The obtained states are characterized by showing exponential decay of bulk correlations, as dictated by a bulk gap, as well as chiral edge modes via the entanglement spectrum

variPEPS -- a versatile tensor network library for variational ground state simulations in two spatial dimensions

Tensor networks capture large classes of ground states of phases of quantum matter faithfully and efficiently. Their manipulation and contraction has remained a challenge over the years, however. For most of the history, ground state simulations of two-dimensional quantum lattice systems using (infinite) projected entangled pair states have relied on what is called a time-evolving block decimation. In recent years, multiple proposals for the variational optimization of the quantum state have been put forward, overcoming accuracy and convergence problems of previously known methods. The incorporation of automatic differentiation in tensor networks algorithms has ultimately enabled a new, flexible way for variational simulation of ground states and excited states. In this work, we review the state of the art of the variational iPEPS framework. We present and explain the functioning of an efficient, comprehensive and general tensor network library for the simulation of infinite two-dimensional systems using iPEPS, with support for flexible unit cells and different lattice geometries

Effects of nonspatial selective and divided visual attention on fMRI BOLD responses

Using an uncertainty paradigm and functional magnetic resonance imaging (fMRI) we studied the effect of nonspatial selective and divided visual attention on the activity of specific areas of human extrastriate visual cortex. The stimuli were single ovals that differed from an implicit standard oval in either colour or width. The subjects’ task was to classify the current stimulus as one of two possible alternatives per stimulus dimension. Three different experimental conditions were conducted: “colour-certainty”, “shape-certainty” and “uncertainty”. In all experimental conditions, the stimulus differed in only one stimulus dimension per trial. In the two certainty conditions, the subjects knew in advance which dimension this would be. During the uncertainty condition they had no such previous knowledge and had to monitor both dimensions simultaneously. Statistical analysis of the fMRI data (with SPM2) revealed a modest effect of the attended stimulus dimension on the neural activity in colour sensitive area V4 (more activity during attention to colour) and in shape sensitive area LOC (more activity during attention to shape). Furthermore, cortical areas known to be related to attention and working memory processes (e.g., lateral prefrontal and posterior parietal cortex) exhibit higher activity during the condition of divided attention (“uncertainty”) than during that of selective attention (“certainty”)

The study of expanded tri-lobed flap in a rabbit model: possible flap model in ear reconstruction?

BACKGROUND: Local flaps are widely used in reconstructive surgery. Tri-lobed skin flap is a relatively new flap and there has been no experimental model of this flap. This flap can be used for repair of full thickness defects in the face, ears and alar region. Based on the size of ears in a rabbit, we designed a model of ear reconstruction using expanded tri-lobed flap. Local flaps are more advantageous in that they provide excellent color and texture matching up with those of the face, adequately restore ear contour, place scars in a favorable location and ideally accomplish these goals in a single stage with minimal donor site morbidity. METHODS: Eight adult New Zealand rabbits were divided into two groups. 50 ml round tissue expander were implanted to four rabbits. After completion of the expansion, a superiorly based tri-lobed flap was elevated and a new ear was created from the superior dorsal skin of each rabbit. Scintigraphy with Technetium-99m pertecnetate was performed to evaluate flap viability. RESULTS: Subtotal flap necrosis was seen in all animals in non-expanded group. New ear in dimensions of the original ear was created in expanded group without complication. Perfusion and viability of the flaps were proved by Technetium-99m pertecnetate scintigraphy. CONCLUSION: According to our knowledge this study is the first to demonstrate animal model in tri-lobed flap. Also, our technique is the first application of the trilobed flap to the possible ear reconstruction. We speculated that this flap may be used mastoid based without hair, in human. Also, tri-lobed flap may be an alternative in reconstruction of cylindrical organs such as penis or finger

Variable expressivity of FGF3 mutations associated with deafness and LAMM syndrome

<p>Abstract</p> <p>Background</p> <p>Recessive mutations of fibroblast growth factor 3 (FGF3) can cause LAMM syndrome (OMIM 610706), characterized by fully penetrant complete labyrinthine aplasia, microtia and microdontia.</p> <p>Methods</p> <p>We performed a prospective molecular genetic and clinical study of families segregating hearing loss linked to <it>FGF3 </it>mutations. Ten affected individuals from three large Pakistani families segregating <it>FGF3 </it>mutations were imaged with CT, MRI, or both to detect inner ear abnormalities. We also modeled the three dimensional structure of FGF3 to better understand the structural consequences of the three missense mutations.</p> <p>Results</p> <p>Two families segregated reported mutations (p.R104X and p.R95W) and one family segregated a novel mutation (p.R132GfsX26) of <it>FGF3</it>. All individuals homozygous for p.R104X or p.R132GfsX26 had fully penetrant features of LAMM syndrome. However, recessive p.R95W mutations were associated with nearly normal looking auricles and variable inner ear structural phenotypes, similar to that reported for a Somali family also segregating p.R95W. This suggests that the mild phenotype is not entirely due to genetic background. Molecular modeling result suggests a less drastic effect of p.R95W on FGF3 function compared with known missense mutations detected in fully penetrant LAMM syndrome. Since we detected significant intrafamilial variability of the inner ear structural phenotype in the family segregating p.R95W, we also sequenced <it>FGF10 </it>as a likely candidate for a modifier. However, we did not find any sequence variation, pointing out that a larger sample size will be needed to map and identify a modifier. We also observed a mild to moderate bilateral conductive hearing loss in three carriers of p.R95W, suggesting either a semi-dominant effect of this mutant allele of <it>FGF3</it>, otitis media, or a consequence of genetic background in these three family members.</p> <p>Conclusions</p> <p>We noted a less prominent dental and external ear phenotype in association with the homozygous p.R95W. Therefore, we conclude that the manifestations of recessive <it>FGF3 </it>mutations range from fully penetrant LAMM syndrome to deafness with residual inner ear structures and, by extension, with minimal syndromic features, an observation with implications for cochlear implantation candidacy.</p