Mixing of 3-Term Progressions in Quasirandom Groups

In this note, we show the mixing of three-term progressions $(x, xg, xg^2)$ in every finite quasirandom groups, fully answering a question of Gowers. More precisely, we show that for any $D$-quasirandom group $G$ and any three sets $A_1, A_2, A_3 \subset G$, we have $$\left|\Pr_{x,y\sim G}\left[ x \in A_1, xy \in A_2, xy^2 \in A_3\right] - \prod_{i=1}^3 \Pr_{x\sim G}\left[x \in A_i\right] \right| \leq \left(\frac{2}{\sqrt{D}}\right)^{\frac{1}{4}}.$$ Prior to this, Tao answered this question when the underlying quasirandom group is $\mathrm{SL}_{d}(\mathbb{F}_q)$. Subsequently, Peluse extended the result to all nonabelian finite $\textit{simple}$ groups. In this work, we show that a slight modification of Peluse's argument is sufficient to fully resolve Gower's quasirandom conjecture for 3-term progressions. Surprisingly, unlike the proofs of Tao and Peluse, our proof is elementary and only uses basic facts from nonabelian Fourier analysis

Sex Role Segregation and Mixing among Men Who Have Sex with Men: Implications for Biomedical HIV Prevention Interventions

Objective: Men who have sex with men (MSM) practice role segregation – insertive or receptive only sex positions instead of a versatile role - in several international settings where candidate biomedical HIV prevention interventions (e.g., circumcision, anal microbicide) will be tested. The effects of these position-specific interventions on HIV incidence are modeled.Materials and Methods: We developed a deterministic compartmental model to predict HIV incidence among Indian MSM using data from 2003–2010. The model’s sex mixing matrix was derived from network data of Indian MSM (n = 4604). Our model captures changing distribution of sex roles over time. We modeled microbicide and circumcision efficacy on trials with heterosexuals.Results: Increasing numbers of versatile MSM resulted in little change in HIV incidence over 20 years. Anal microbicides and circumcision would decrease the HIV prevalence at 10 years from 15.6% to 12.9% and 12.7% respectively. Anal microbicides would provide similar protection to circumcision at the population level despite lower modeled efficacy (54% and 60% risk reduction, respectively). Combination of the interventions were additive: in 5 years, the reduction in HIV prevalence of the combination (−3.2%) is almost the sum of their individual reductions in HIV prevalence (−1.8% and −1.7%).Conclusions: MSM sex role segregation and mixing, unlike changes in the sex role distribution, may be important for evaluating HIV prevention interventions in international settings. Synergies between some position-specific prevention interventions such as circumcision and anal microbicides warrant further study.</p

Learning Long-Term Spatial-Temporal Graphs for Active Speaker Detection

Active speaker detection (ASD) in videos with multiple speakers is a challenging task as it requires learning effective audiovisual features and spatial-temporal correlations over long temporal windows. In this paper, we present SPELL, a novel spatial-temporal graph learning framework that can solve complex tasks such as ASD. To this end, each person in a video frame is first encoded in a unique node for that frame. Nodes corresponding to a single person across frames are connected to encode their temporal dynamics. Nodes within a frame are also connected to encode inter-person relationships. Thus, SPELL reduces ASD to a node classification task. Importantly, SPELL is able to reason over long temporal contexts for all nodes without relying on computationally expensive fully connected graph neural networks. Through extensive experiments on the AVA-ActiveSpeaker dataset, we demonstrate that learning graph-based representations can significantly improve the active speaker detection performance owing to its explicit spatial and temporal structure. SPELL outperforms all previous state-of-the-art approaches while requiring significantly lower memory and computational resources. Our code is publicly available at https://github.com/SRA2/SPELLComment: ECCV 2022 camera ready (Supplementary videos: on ECVA soon). This paper supersedes arXiv:2112.0147

Variations in the SDN Loop of Class A Beta-Lactamases: A Study of the Molecular Mechanism of BlaC (Mycobacterium tuberculosis) to Alter the Stability and Catalytic Activity Towards Antibiotic Resistance of MBIs

The emergence of multidrug-resistant (MDR) and extensively drug-resistant (XDR) tuberculosis calls for an immediate search for novel treatment strategies. Recently, BlaC, the principal beta-lactamase of Mycobacterium tuberculosis, was recognized as a potential therapeutic target. BlaC belongs to Ambler class A, which is generally susceptible to the beta-lactamase inhibitors currently used in clinics: tazobactam, sulbactam, and clavulanate. Alterations at Ser130 in conserved SDN loop confer resistance to mechanism-based inhibitors (MBIs) commonly observed in various clinical isolates. The absence of clinical evidence of S130G conversion in M. tuberculosis draws our attention to build laboratory mutants of S130G and S130A of BlaC. The study involving steady state, inhibition kinetics, and fluorescence microscopy shows the emergence of resistance against MBIs to the mutants expressing S130G and S130A. To understand the molecular reasoning behind the unavailability of such mutation in real life, we have used circular dichroism (CD) spectroscopy, differential scanning calorimetry (DSC), molecular dynamics (MD) simulation, and stability-based enzyme activity to compare the stability and dynamic behaviors of native and S130G/A mutant form of BlaC. A significant decrease in melting temperature (BlaC T M 60°C, S130A T M 50°C, and S130G T M 45°C), kinetic instability at higher temperature, and comparative dynamic instability correlate the fact that resistance to beta-lactam/beta-lactamase inhibitor combinations will likely not arise from the structural alteration of BlaC, therefore establishing confidence that this therapeutic modality can be potentially applied as a part of a successful treatment regimen against M. tuberculosis

A Study of Pseudorandomness and its Applications to Coding Theory

Pseudo-randomness is an indispensable tool in theoretical computer science. In this dissertation, we aim to study several questions related to pseudo-randomness and its applications in designing codes.First, we give an alternate proof of Ta-Shma's breakthrough result on near-optimal binary error correcting code construction. While Ta-Shma’s original analysis was entirely linear algebraic, our approach is more combinatorial in nature. In our second work, we show the mixing of three term arithmetic progressions in quasi-random groups and fully resolve a question by Gowers. Our proof is elementary and builds upon a work by Peluse. Finally, we propose a generalization of locally testable codes that are resilient against adversarial channels in a certain information theoretic sense. We call these codes 'locally testable, non-malleable' and give a construction of such objects. Our construction heavily uses properties of certain pseudo-random objects called sampler graphs and tools from low degree testing literature. This allows us to establish a connection between cryptographic non-malleability and polynomial codes