Standard Young Tableaux and Colored Motzkin Paths

In this paper, we propose a notion of colored Motzkin paths and establish a bijection between the $n$-cell standard Young tableaux (SYT) of bounded height and the colored Motzkin paths of length $n$. This result not only gives a lattice path interpretation of the standard Young tableaux but also reveals an unexpected intrinsic relation between the set of SYTs with at most $2d+1$ rows and the set of SYTs with at most 2d rows.Comment: 21 page

Efficient Spin-Orbit Torques in an Antiferromagnetic Insulator with Tilted Easy Plane

Electrical manipulation of spin textures inside antiferromagnets represents a new opportunity for developing spintronics with superior speed and high device density. Injecting spin currents into antiferromagnets and realizing efficient spin-orbit-torque-induced switching is however still challenging due to the complicated interactions from different sublattices. Meanwhile, because of the diminishing magnetic susceptibility, the nature and the magnitude of current-induced magnetic dynamics remain poorly characterized in antiferromagnets, whereas spurious effects further complicate experimental interpretations. In this work, by growing a thin film antiferromagnetic insulator, {\alpha}-Fe2O3, along its non-basal plane orientation, we realize a configuration where an injected spin current can robustly rotate the N\'eel vector within the tilted easy plane, with an efficiency comparable to that of classical ferromagnets. The spin-orbit torque effect stands out among other competing mechanisms and leads to clear switching dynamics. Thanks to this new mechanism, in contrast to the usually employed orthogonal switching geometry, we achieve bipolar antiferromagnetic switching by applying positive and negative currents along the same channel, a geometry that is more practical for device applications. By enabling efficient spin-orbit torque control on the antiferromagnetic ordering, the tilted easy plane geometry introduces a new platform for quantitatively understanding switching and oscillation dynamics in antiferromagnets.Comment: 21 pages, 5 figure

Renormalization group and perfect operators for stochastic differential equations

We develop renormalization group methods for solving partial and stochastic differential equations on coarse meshes. Renormalization group transformations are used to calculate the precise effect of small scale dynamics on the dynamics at the mesh size. The fixed point of these transformations yields a perfect operator: an exact representation of physical observables on the mesh scale with minimal lattice artifacts. We apply the formalism to simple nonlinear models of critical dynamics, and show how the method leads to an improvement in the computational performance of Monte Carlo methods.Comment: 35 pages, 16 figure

Advances in perturbative thermal field theory

The progress of the last decade in perturbative quantum field theory at high temperature and density made possible by the use of effective field theories and hard-thermal/dense-loop resummations in ultrarelativistic gauge theories is reviewed. The relevant methods are discussed in field theoretical models from simple scalar theories to non-Abelian gauge theories including gravity. In the simpler models, the aim is to give a pedagogical account of some of the relevant problems and their resolution, while in the more complicated but also more interesting models such as quantum chromodynamics, a summary of the results obtained so far are given together with references to a few most recent developments and open problems.Comment: 84 pages, 18 figues, review article submitted to Reports on Progress in Physics; v2, v3: minor additions and corrections, more reference

Piezo1 integration of vascular architecture with physiological force

The mechanisms by which physical forces regulate endothelial cells to determine the complexities of vascular structure and function are enigmatic¹⁻⁵. Studies of sensory neurons have suggested Piezo proteins as subunits of Ca²⁺-permeable non-selective cationic channels for detection of noxious mechanical impact⁶⁻⁸. Here we show Piezo1 (Fam38a) channels as sensors of frictional force (shear stress) and determinants of vascular structure in both development and adult physiology. Global or endothelial-specific disruption of mouse Piezo1 profoundly disturbed the developing vasculature and was embryonic lethal within days of the heart beating. Haploinsufficiency was not lethal but endothelial abnormality was detected in mature vessels. The importance of Piezo1 channels as sensors of blood flow was shown by Piezo1 dependence of shear-stress-evoked ionic current and calcium influx in endothelial cells and the ability of exogenous Piezo1 to confer sensitivity to shear stress on otherwise resistant cells. Downstream of this calcium influx there was protease activation and spatial reorganization of endothelial cells to the polarity of the applied force. The data suggest that Piezo1 channels function as pivotal integrators in vascular biology

A Zebrafish Model of Roberts Syndrome Reveals That Esco2 Depletion Interferes with Development by Disrupting the Cell Cycle

The human developmental diseases Cornelia de Lange Syndrome (CdLS) and Roberts Syndrome (RBS) are both caused by mutations in proteins responsible for sister chromatid cohesion. Cohesion is mediated by a multi-subunit complex called cohesin, which is loaded onto chromosomes by NIPBL. Once on chromosomes, cohesin binding is stabilized in S phase upon acetylation by ESCO2. CdLS is caused by heterozygous mutations in NIPBL or cohesin subunits SMC1A and SMC3, and RBS is caused by homozygous mutations in ESCO2. The genetic cause of both CdLS and RBS reside within the chromosome cohesion apparatus, and therefore they are collectively known as “cohesinopathies”. However, the two syndromes have distinct phenotypes, with differences not explained by their shared ontology. In this study, we have used the zebrafish model to distinguish between developmental pathways downstream of cohesin itself, or its acetylase ESCO2. Esco2 depleted zebrafish embryos exhibit features that resemble RBS, including mitotic defects, craniofacial abnormalities and limb truncations. A microarray analysis of Esco2-depleted embryos revealed that different subsets of genes are regulated downstream of Esco2 when compared with cohesin subunit Rad21. Genes downstream of Rad21 showed significant enrichment for transcriptional regulators, while Esco2-regulated genes were more likely to be involved the cell cycle or apoptosis. RNA in situ hybridization showed that runx1, which is spatiotemporally regulated by cohesin, is expressed normally in Esco2-depleted embryos. Furthermore, myca, which is downregulated in rad21 mutants, is upregulated in Esco2-depleted embryos. High levels of cell death contributed to the morphology of Esco2-depleted embryos without affecting specific developmental pathways. We propose that cell proliferation defects and apoptosis could be the primary cause of the features of RBS. Our results show that mutations in different elements of the cohesion apparatus have distinct developmental outcomes, and provide insight into why CdLS and RBS are distinct diseases