ABJM amplitudes and the positive orthogonal grassmannian

A remarkable connection between perturbative scattering amplitudes of four-dimensional planar SYM, and the stratification of the positive grassmannian, was revealed in the seminal work of Arkani-Hamed et. al. Similar extension for three-dimensional ABJM theory was proposed. Here we establish a direct connection between planar scattering amplitudes of ABJM theory, and singularities there of, to the stratification of the positive orthogonal grassmannian. In particular, scattering processes are constructed through on-shell diagrams, which are simply iterative gluing of the fundamental four-point amplitude. Each diagram is then equivalent to the merging of fundamental OG_2 orthogonal grassmannian to form a larger OG_k, where 2k is the number of external particles. The invariant information that is encoded in each diagram is precisely this stratification. This information can be easily read off via permutation paths of the on-shell diagram, which also can be used to derive a canonical representation of OG_k that manifests the vanishing of consecutive minors as the singularity of all on-shell diagrams. Quite remarkably, for the BCFW recursion representation of the tree-level amplitudes, the on-shell diagram manifests the presence of all physical factorization poles, as well as the cancellation of the spurious poles. After analytically continuing the orthogonal grassmannian to split signature, we reveal that each on-shell diagram in fact resides in the positive cell of the orthogonal grassmannian, where all minors are positive. In this language, the amplitudes of ABJM theory is simply an integral of a product of dlog forms, over the positive orthogonal grassmannian.Comment: 52 pages: v2, typos corrected, published version in JHE

Spin chains and classical strings in rotating Rindler-AdS space

In this paper, we study the spin chain and string excitation in the rotating Rindler-$AdS_3$ proposed in [12]. We obtain a one-parameter deformed $SL(2)$ spin chain at the fast spin limit. Two-spin GKP-like solutions are studied at short and long string limits. General ansatz for the giant magnons and the spiky strings are analyzed in detail for various $\beta$. At last, we explore its counterpart in analytic continuation and pp-wave limit.Comment: 23pp, 8 figure

Multipotent vascular stem cells contribute to neurovascular regeneration of peripheral nerve.

BackgroundNeurovascular unit restoration is crucial for nerve regeneration, especially in critical gaps of injured peripheral nerve. Multipotent vascular stem cells (MVSCs) harvested from an adult blood vessel are involved in vascular remodeling; however, the therapeutic benefit for nerve regeneration is not clear.MethodsMVSCs were isolated from rats expressing green fluorescence protein (GFP), expanded, mixed with Matrigel matrix, and loaded into the nerve conduits. A nerve autograft or a nerve conduit (with acellular matrigel or MVSCs in matrigel) was used to bridge a transected sciatic nerve (10-mm critical gap) in rats. The functional motor recovery and cell fate in the regenerated nerve were investigated to understand the therapeutic benefit.ResultsMVSCs expressed markers such as Sox 17 and Sox10 and could differentiate into neural cells in vitro. One month following MVSC transplantation, the compound muscle action potential (CMAP) significantly increased as compared to the acellular group. MVSCs facilitated the recruitment of Schwann cell to regenerated axons. The transplanted cells, traced by GFP, differentiated into perineurial cells around the bundles of regenerated myelinated axons. In addition, MVSCs enhanced tight junction formation as a part of the blood-nerve barrier (BNB). Furthermore, MVSCs differentiated into perivascular cells and enhanced microvessel formation within regenerated neurovascular bundles.ConclusionsIn rats with peripheral nerve injuries, the transplantation of MVSCs into the nerve conduits improved the recovery of neuromuscular function; MVSCs differentiated into perineural cells and perivascular cells and enhanced the formation of tight junctions in perineural BNB. This study demonstrates the in vivo therapeutic benefit of adult MVSCs for peripheral nerve regeneration and provides insight into the role of MVSCs in BNB regeneration

Demarcating stable and turbulent regimes in Taiwan's stock market

Various trading rules involving derivatives have been widely applied by practitioners under a wide range of market conditions to date, however, few econometric models can provide a way to accurately decide when to apply those strategies. In this paper, we employ the Innovation Regime-Switching (IRS) model (Kuan, et al, 2005, JBES) to separate stock price sample periods into stable and turbulent regimes on the basis of their dynamic behaviors. Our results show that, based on regime identification, we can obtain satisfactory profits by implementing appropriate and timely derivative strategies.Bear market