Topologically Twisted SUSY Gauge Theory, Gauge-Bethe Correspondence and Quantum Cohomology

We calculate partition function and correlation functions in A-twisted 2d $\mathcal{N}=(2,2)$ theories and topologically twisted 3d $\mathcal{N}=2$ theories containing adjoint chiral multiplet with particular choices of $R$-charges and the magnetic fluxes for flavor symmetries. According to Gauge-Bethe correspondence, they correspond to Heisenberg XXX and XXZ spin chain models. We identify the partition function as the inverse of the norm of the Bethe eigenstates. Correlation functions are identified as the coefficients of the expectation value of Baxter $Q$-operators. In addition, we consider correlation functions of 2d $\mathcal{N}=(2,2)^*$ theory and their relation to equivariant quantum cohomology and equivariant integration of cotangent bundle of Grassmann manifolds. Also, we study the ring relations of supersymmetric Wilson loops in 3d $\mathcal{N}=2^*$ theory and Bethe subalgebra of XXZ spin chain model.Comment: 33 page

Abelian arithmetic Chern-Simons theory and arithmetic linking numbers

Following the method of Seifert surfaces in knot theory, we define arithmetic linking numbers and height pairings of ideals using arithmetic duality theorems, and compute them in terms of n-th power residue symbols. This formalism leads to a precise arithmetic analogue of a 'path-integral formula' for linking numbers

Arithmetic Chern-Simons theory II

In this paper, we apply ideas of Dijkgraaf and Witten [6, 32] on 3 dimensional topological quantum field theory to arithmetic curves, that is, the spectra of rings of integers in algebraic number fields. In the first three sections, we define classical Chern–Simons actions on spaces of Galois representations. In the subsequent sections, we give formulas for computation in a small class of cases and point towards some arithmetic applications

In vivo study of optical speckle decorrelation time across depths in the mouse brain

The strong optical scattering of biological tissue confounds our ability to focus light deeply into the brain beyond depths of a few hundred microns. This challenge can be potentially overcome by exploiting wavefront shaping techniques which allow light to be focused through or inside scattering media. However, these techniques require the scattering medium to be static, as changes in the arrangement of the scatterers between the wavefront recording and playback steps reduce the fidelity of the focus that is formed. Furthermore, as the thickness of the scattering medium increases, the influence of the dynamic nature becomes more severe due to the growing number of scattering events experienced by each photon. In this paper, by examining the scattering dynamics in the mouse brain in vivo via multispeckle diffusing wave spectroscopy (MSDWS) using a custom fiber probe that simulates a point-like source within the brain, we investigate the relationship between this decorrelation time and the depth of the point-like light source inside the living mouse brain at depths up to 3.2 mm

Development of a clinical scoring system for appendicitis in children with presumed appendicitis

Purpose To develop a clinical scoring system for children with presumed appendicitis who visit the emergency department. Methods A registry based-retrospective study was conducted in the pediatric emergency department between September 2015 and December 2016. Patients aged 4 to 17 years who had a > 1 of 5 Likert scale for possibility of appendicitis were included. Multiple logistic regressions based on Akaike information criterion were performed using variables regarding clinical features and inflammatory markers to develop the clinical scoring system. Results A total of 233 patients were included, and 93 (39.9%) had the final diagnosis of appendicitis. The final model with the lowest Akaike information criterion (171.7) consisted of 5 variables, including vomiting (1 point), absence of watery diarrhea (1 point), duration of symptoms ≤ 3 days (1 point), rebound tenderness (1 point), and white blood cell count > 10.0 × 109/L (2 points). If the clinical score was ≥ 4 of 6 points, the area under the receiver operating characteristic curve was 0.78 (95% confidence interval, 0.71-0.86) with a 78.9% sensitivity, 66.7% specificity, positive and negative predictive values of 70.0% and 76.2%, respectively, and positive and negative likelihood ratios of 2.4 and 0.3, respectively. Conclusion The 5-item clinical scoring system shows a fair performance for prediction of pediatric appendicitis. This simple tool could be applied to predict the pediatric appendicitis, and to avoid the use of potentially unnecessary computed tomography

Extensive Systemic Sarcoidosis with Testicular Involvement Mimicking Metastatic Testicular Cancer

Sarcoidosis is an idiopathic, multisystem disease that rarely involves the genitourinary tract. Here we present an unusual case of testicular sarcoidosis with extensive lymphadenopathy that mimicked a metastatic testicular tumor. A 27-year-old male presented with a palpable right testicular mass accompanied by multiple palpable inguinal lymph nodes. The scrotal ultrasound showed a hypoechoic lesion at the inferior portion of the right testis. Extensive enlarged lymph nodes were noted in multiple areas on the abdominal computed tomography. Preoperative testicular tumor markers were within the normal range. Exploration of the right testis with a frozen section analysis of the right testicular mass and of a palpable right inguinal lymph node showed granulomatous inflammation. The testis was salvaged and the final pathological diagnosis was sarcoidosis. Treatment with high-dose corticosteroids resulted in complete resolution of the intratesticular mass and a significant decrease in the extent of the lymphadenopathy