The duality between color and kinematics present in scattering amplitudes of Yang-Mills theory strongly suggest the existence of a hidden kinematic Lie algebra that controls the gauge theory. While associated BCJ numerators are known on closed forms to any multiplicity at tree level, the kinematic algebra has only been partially explored for the simplest of four-dimensional amplitudes: up to the MHV sector. In this paper we introduce a framework that allows us to characterize the algebra beyond the MHV sector. This allows us to both constrain some of the ambiguities of the kinematic algebra, and better control the generalized gauge freedom that is associated with the BCJ numerators. Specifically, in this paper, we work in dimension-agnostic notation and determine the kinematic algebra valid up to certain O (ε i ·ε j ) 2 terms that in four dimensions compute the next-to-MHV sector involving two scalars. The kinematic algebra in this sector is simple, given that we introduce tensor currents that generalize standard Yang-Mills vector currents. These tensor currents controls the generalized gauge freedom, allowing us to generate multiple different versions of BCJ numerators from the same kinematic algebra. The framework should generalize to other sectors in Yang-Mills theory.1 Cubic interactions are obtained by the replacement Tr([A µ , A ν ] 2 ) → − 1 2 (B µν ) 2 +Tr([A µ , A ν ]B µν ).

Optical scattering coefficient from ex vivo unfixed normal and malignant ovarian tissue was quantitatively extracted by fitting optical coherence tomography (OCT) A-line signals to a single scattering model. 1097 average A-line measurements at a wavelength of 1310 nm were performed at 108 sites obtained from 18 ovaries. The average scattering coefficient obtained from the normal tissue group consisted of 833 measurements from 88 sites was 2.41 mm(-1) (± 0.59), while the average coefficient obtained from the malignant tissue group consisted of 264 measurements from 20 sites was 1.55 mm(-1) (± 0.46). The malignant ovarian tissue showed significant lower scattering than the normal group (p < 0.001). The amount of collagen within OCT imaging depth was analyzed from the tissue histological section stained with Sirius Red. The average collagen area fraction (CAF) obtained from the normal tissue group was 48.4% (± 12.3%), while the average CAF obtained from the malignant tissue group was 11.4% (± 4.7%). A statistical significance of the collagen content was found between the two groups (p < 0.001). These results demonstrated that quantitative measurements of optical scattering coefficient from OCT images could be a potential powerful method for ovarian cancer detection.

Ovarian cancer has the lowest survival rate of the gynecologic cancers because it is predominantly diagnosed in Stages III or IV due to the lack of reliable symptoms, as well as the lack of efficacious screening techniques. Detection before the malignancy spreads or at the early stage would greatly improve the survival and benefit patient health. In this report, we present an integrated optical coherence tomography (OCT), ultrasound (US) and photoacoustic imaging (PAI) prototype endoscopy system for ovarian tissue characterization. The overall diameter of the prototype endoscope is 5 mm which is suitable for insertion through a standard 5-12.5mm endoscopic laparoscopic port during minimally invasive surgery. It consists of a ball-lensed OCT sample arm probe, a multimode fiber having the output end polished at 45 degree angle so as to deliver the light perpendicularly for PAI, and a high frequency ultrasound transducer with 35MHz center frequency. System characterizations of OCT, US and PAI are presented. In addition, results obtained from ex vivo porcine and human ovarian tissues are presented. The optical absorption contrast provided by PAI, the high resolution subsurface morphology provided by OCT, and the deeper tissue structure imaged by US demonstrate the synergy of the combined endoscopy and the superior performance of this hybrid device over each modality alone in ovarian tissue characterization.

We extend the Operator Product Expansion for Null Polygon Wilson loops to the MasonSkinner-Caron-Huot super loop dual to non MHV gluon amplitudes. We explain how the known tree level amplitudes can be promoted into an infinite amount of data at any loop order in the OPE picture. As an application, we re-derive all one loop NMHV six gluon amplitudes by promoting their tree level expressions. We also present some new all loops predictions for these amplitudes.

We study three-point correlation functions of local operators in planar N = 4 SYM at weak coupling using integrability. We consider correlation functions involving two scalar BPS operators and an operator with spin, in the so called SL(2) sector. At tree level we derive the corresponding structure constant for any such operator. We also conjecture its one loop correction. To check our proposals we analyze the conformal partial wave decomposition of known four-point correlation functions of BPS operators. In perturbation theory, we extract from this decomposition sums of structure constants involving all primaries of a given spin and twist. On the other hand, in our integrable setup these sum rules are computed by summing over all solutions to the Bethe equations. A perfect match is found between the two approaches.