Given the rise in the number of cases and their recurrences, Urinary Tract Infections (UTI) are one of the major burdens on public healthcare worldwide. Rapid, inexpensive and selective detection of Uropathogenic E. coli (UPEC), a major contributor to UTIs, is the need of the hour for effective treatment, given the rise of antibiotic-resistant bacteria due to improper diagnosis. Here we present a rapid, real-time, selective and label-free detection of UPEC using an integrated sensing platform based on Crossed Surface Relief Gratings (CSRGs) as nanoplasmonic sensors. Detection is achieved due to the unique Surface Plasmon Resonance (SPR)-based light energy exchange attributed to the CSRGs, allowing real-time sensing in a very narrow bandwidth of the incident light to pass where the SPR energy conversion occurs. The sensing ability of the platform is experimentally demonstrated by the detection of bulk Refractive Index (RI) changes, with a bulk sensitivity of 382.2 nm/RIU and a resolution in the order of 10-6 RIU. We demonstrate selective capture and detection of clinical concentration of UPEC, as opposed to other gram-negative bacteria, in real-time, a first for CSRGs. This work is particularly important for effective treatment of UTIs, allowing point-of-care diagnosis for economically disadvantaged regions around the world.

In this paper, we define the cohomology of a modified $\lambda$-differential left-symmetric algebra with coefficients in a suitable representation. We also introduce the notion of modified $\lambda$-differential left-symmetric 2-algebra. We classify linear deformations and abelian extensions of modified $\lambda$-differential left-symmetric algebras using the second cohomology group and classify skeletal modified $\lambda$-differential left-symmetric 2-algebra using the third cohomology group as our propose cohomology applications. Moreover, we prove that strict modified $\lambda$-differential left-symmetric 2-algebras are equivalent to crossed modules of modified $\lambda$-differential left-symmetric algebras.