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We investigate an urban network characterized by blockages, where unmanned aerial vehicles (UAVs) offer ad-hoc coverage to mobile users with distinct service rate requirements. The UAV-BSs are modeled using a two-dimensional (2-D) marked-poisson point process (MPPP), where the marks represent the altitude of each UAV-base station (UAV-BS). Initially, we model the network blockages and analyze the association probabilities of line-of-sight (LoS) and non-line-of-sight (NLoS) UAV-BSs using stochastic geometry. Subsequently, we derive the bth moment of the conditional success probability (CSP) and employ a meta distribution (MD)-based analytical framework of signal-to-interference noise ratio (SINR) taking into account the blockage distribution in the network. Furthermore, we proposea cache-based handover management strategy that dynamically selects the cell search time and delays the received signal strength (RSS)-based base station (BS) associations. This strategy aims to minimize unnecessary handovers (HOs) experienced by users by leveraging caching capabilities at user equipment (UE). We evaluate the HO rate and average throughput experienced by users ensuring their service rate requirements are met. We demonstrate that LoS associations decrease as the network density increases due to the substantial increase of NLoS UAV-BSs in the network. Additionally, we show that the presence of blockages does not necessarily have a negative impact on network reliability

The impact of discrete clutter and co-channel interference on the performance of automotive radar networks has been studied using stochastic geometry, in particular, by leveraging two-dimensional Poisson point processes (PPPs). However, such characterization does not take into account the impact of street geometry and the fact that the location of the automotive radars are restricted to the streets as their domain rather than the entire Euclidean plane. In addition, the structure of the streets may change drastically as a vehicle moves out of a city center towards the outskirts. Consequently, not only the radar performance change but also the radar parameters and protocols must be adapted for optimum performance. In this paper, we propose and characterize line and Cox process-based street and point models to analyze large-scale automotive radar networks. We consider the classical Poisson line process (PLP) and the newly introduced Binomial line process (BLP) model to emulate the streets and the corresponding PPP-based Cox process to emulate the vehicular nodes. In particular, the BLP model effectively considers the spatial variation of street geometry across different parts of the city. We derive the effective interference set experienced by an automotive radar, the statistics of distance to interferers, and characterize the detection probability of the ego radar as a function of street and vehicle density. Finally, leveraging the real-world data on urban streets and vehicle density across different cities of the world, we present how the radar performance varies in different parts of the city as well as across different times of the day. Thus, our study equips network operators and automotive manufacturers with essential system design insights to plan and optimize automotive radar networks., Comment: Submitted to IEEE TWC

Sharpe Ratio (SR) is a critical parameter in characterizing financial time series as it jointly considers the reward and the volatility of any stock/portfolio through its variance. Deriving online algorithms for optimizing the SR is particularly challenging since even offline policies experience constant regret with respect to the best expert Even-Dar et al (2006). Thus, instead of optimizing the usual definition of SR, we optimize regularized square SR (RSSR). We consider two settings for the RSSR, Regret Minimization (RM) and Best Arm Identification (BAI). In this regard, we propose a novel multi-armed bandit (MAB) algorithm for RM called UCB-RSSR for RSSR maximization. We derive a path-dependent concentration bound for the estimate of the RSSR. Based on that, we derive the regret guarantees of UCB-RSSR and show that it evolves as O(log n) for the two-armed bandit case played for a horizon n. We also consider a fixed budget setting for well-known BAI algorithms, i.e., sequential halving and successive rejects, and propose SHVV, SHSR, and SuRSR algorithms. We derive the upper bound for the error probability of all proposed BAI algorithms. We demonstrate that UCB-RSSR outperforms the only other known SR optimizing bandit algorithm, U-UCB Cassel et al (2023). We also establish its efficacy with respect to other benchmarks derived from the GRA-UCB and MVTS algorithms. We further demonstrate the performance of proposed BAI algorithms for multiple different setups. Our research highlights that our proposed algorithms will find extensive applications in risk-aware portfolio management problems. Consequently, our research highlights that our proposed algorithms will find extensive applications in risk-aware portfolio management problems., Comment: Submitted to ACML Journal Track 2024

Message passing on hypergraphs has been a standard framework for learning higher-order correlations between hypernodes. Recently-proposed hypergraph neural networks (HGNNs) can be categorized into spatial and spectral methods based on their design choices. In this work, we analyze the impact of change in hypergraph topology on the suboptimal performance of HGNNs and propose DPHGNN, a novel dual-perspective HGNN that introduces equivariant operator learning to capture lower-order semantics by inducing topology-aware spatial and spectral inductive biases. DPHGNN employs a unified framework to dynamically fuse lower-order explicit feature representations from the underlying graph into the super-imposed hypergraph structure. We benchmark DPHGNN over eight benchmark hypergraph datasets for the semi-supervised hypernode classification task and obtain superior performance compared to seven state-of-the-art baselines. We also provide a theoretical framework and a synthetic hypergraph isomorphism test to express the power of spatial HGNNs and quantify the expressivity of DPHGNN beyond the Generalized Weisfeiler Leman (1-GWL) test. Finally, DPHGNN was deployed by our partner e-commerce company for the Return-to-Origin (RTO) prediction task, which shows ~7% higher macro F1-Score than the best baseline., Comment: Accepted in SIGKDD'24 -- Research Track

Given a natural number $n \geq 1$, the odometer semigroup $O_n$, also known as the adding machine or the Baumslag-Solitar monoid with two generators, is a well-known object in group theory. This paper examines the odometer semigroup in relation to representations of bounded linear operators. We focus on noncommutative operators and prove that contractive representations of $O_n$ always admit to nicer representations of $O_n$. We give a complete description of representations of $O_n$ on the Fock space and relate it to the odometer lifting and subrepresentations of $O_n$. Along the way, we also classify Nica covariant representations of $O_n$., Comment: 29 pages. Revised

Prior works have analyzed the performance of millimeter wave automotive radars in the presence of diverse clutter and interference scenarios using stochastic geometry tools instead of more time-consuming measurement studies or system-level simulations. In these works, the distributions of radars or discrete clutter scatterers were modeled as Poisson point processes in the Euclidean space. However, since most automotive radars are likely to be mounted on vehicles and road infrastructure, road geometries are an important factor that must be considered. Instead of considering each road geometry as an individual case for study, in this work, we model each case as a specific instance of an underlying Poisson line process and further model the distribution of vehicles on the road as a Poisson point process - forming a Poisson line Cox process. Then, through the use of stochastic geometry tools, we estimate the average number of interfering radars for specific road and vehicular densities and the effect of radar parameters such as noise and beamwidth on the radar detection metrics. The numerical results are validated with Monte Carlo simulations., Comment: Submitted to IEEE Radar Conference 2024 (RadarConf24)

The Boreal Summer Intraseasonal Oscillation (BSISO) is a pronounced mode of tropical variability. Here, we identify two types of BSISO events, one which propagates northward over South Asia (SA) from the equatorial Indian Ocean (EIO), and the other which doesn't. Contrasting their behaviour shows that northward propagation occurs in multiple stages after convection is initiated over the EIO. First, convection moves into the southern Arabian Sea (AS) due to moistening of the free troposphere via horizontal BSISO anomalous winds acting on the background moisture distribution, and forms a northwest-southeast (NW-SE) oriented convection band. Subsequently, in the presence of an easterly vertical shear of monsoon winds and meridional gradient of anomalous vertical velocity, a NW-SE oriented tilting term is generated that results in a tilted gyre north of the existing convective anomaly and south-easterly BSISO winds over the South Asian landmass. In the second stage, these winds tap the ambient north-westward moisture gradient and help move convection further north over land. Moreover, background winds advect anomalous moisture to initiate convection over the Bay of Bengal. For non-propagating events, though a Rossby gyre results as a response to nascent EIO convection, it is smaller, thus BSISO advection of moisture is weaker and does not initiate convection over the southern AS. In turn, the meridional gradient of anomalous vertical velocity is weak, and the background vertical shear does not generate sufficient tilting over the northern AS. Thus, the convective wind response stalls, and large-scale convection does not propagate north of 15N. Thus, free-tropospheric moisture advection and vortex tilting due to the background vertical shear work together for robust northward propagation of the BSISO., Comment: 36 pages, 14 figures. Submitted to JGR:Atmospheres

We study the initial beam acquisition problem in millimeter wave (mm-wave) networks from the perspective of best arm identification in multi-armed bandits (MABs). For the stationary environment, we propose a novel algorithm called concurrent beam exploration, CBE, in which multiple beams are grouped based on the beam indices and are simultaneously activated to detect the presence of the user. The best beam is then identified using a Hamming decoding strategy. For the case of orthogonal and highly directional thin beams, we characterize the performance of CBE in terms of the probability of missed detection and false alarm in a beam group (BG). Leveraging this, we derive the probability of beam selection error and prove that CBE outperforms the state-of-the-art strategies in this metric. Then, for the abruptly changing environments, e.g., in the case of moving blockages, we characterize the performance of the classical sequential halving (SH) algorithm. In particular, we derive the conditions on the distribution of the change for which the beam selection error is exponentially bounded. In case the change is restricted to a subset of the beams, we devise a strategy called K-sequential halving and exhaustive search, K-SHES, that leads to an improved bound for the beam selection error as compared to SH. This policy is particularly useful when a near-optimal beam becomes optimal during the beam-selection procedure due to abruptly changing channel conditions. Finally, we demonstrate the efficacy of the proposed scheme by employing it in a tandem beam refinement and data transmission scheme.

Diet is central to the epidemic of lifestyle disorders. Accurate and effortless diet logging is one of the significant bottlenecks for effective diet management and calorie restriction. Dish detection from food platters is a challenging problem due to a visually complex food layout. We present an end-to-end computational framework for diet management, from data compilation, annotation, and state-of-the-art model identification to its mobile app implementation. As a case study, we implement the framework in the context of Indian food platters known for their complex presentation that poses a challenge for the automated detection of dishes. Starting with the 61 most popular Indian dishes, we identify the state-of-the-art model through a comparative analysis of deep-learning-based object detection architectures. Rooted in a meticulous compilation of 68,005 platter images with 134,814 manual dish annotations, we first compare ten architectures for multi-label classification to identify ResNet152 (mAP=84.51%) as the best model. YOLOv8x (mAP=87.70%) emerged as the best model architecture for dish detection among the eight deep-learning models implemented after a thorough performance evaluation. By comparing with the state-of-the-art model for the IndianFood10 dataset, we demonstrate the superior object detection performance of YOLOv8x for this subset and establish Resnet152 as the best architecture for multi-label classification. The models thus trained on richly annotated data can be extended to include dishes from across global cuisines. The proposed framework is demonstrated through a proof-of-concept mobile application with diverse applications for diet logging, food recommendation systems, nutritional interventions, and mitigation of lifestyle disorders., Comment: 11 pages, 5 figures, 5 tables. Submitted to the 8th International Conference on Computer Vision & Image Processing (CVIP-2023)

Wireless communications aided by reconfigurable intelligent surfaces (RISs) is a promising way to improve the coverage for cellular users. The controlled reflection of signals from RISs is especially useful in mm-wave/THz networks when the direct link between a cellular user and its serving base station (BS) is weak or unavailable due to blockages. However, the joint blockage of the user-RIS and the user-BS links may significantly degrade the performance of RIS-aided transmissions. This paper aims to study the impact of joint blockages on downlink performance. When RIS locations are coupled with BS locations, using tools from stochastic geometry, we obtain an optimal placement of RISs to either minimize the joint blockage probability of the user-RIS and the user-BS links or maximize the downlink coverage probability. The results show that installing RISs near the cell edge of BSs usually provides optimal coverage. Moreover, deploying RISs on street intersections improves the coverage probability. For users associated with BSs that are deployed sufficiently close to intersections, the intersection-mounted RISs offer a better coverage performance as compared to BS-coupled RISs.

Let $\mathcal{H}$ be a complex Hilbert space and let $\big\{A_{n}\big\}_{n\geq 1}$ be a sequence of bounded linear operators on $\mathcal{H}$. Then a bounded operator $B$ on a Hilbert space $\mathcal{K} \supseteq \mathcal{H}$ is said to be a dilation of this sequence if \begin{equation*} A_{n} = P_{\mathcal{H}}B^{n}|_{\mathcal{H}} \; \text{for all}\; n\geq 1, \end{equation*} where $P_{\mathcal{H}}$ is the projection of $\mathcal{K}$ onto $\mathcal{H}.$ The question of existence of dilation is a generalization of the classical moment problem. We recall necessary and sufficient conditions for the existence of self-adjoint, isometric and unitary dilations and present block operator representations for these dilations. For instance, for self-adjoint dilations one gets block tridiagonal representations similar to the classical moment problem. Given a positive invertible operator $A$, an operator $T$ is said to be in the $\mathcal{C}_{A}$-class if the sequence $\{A^{-\frac{1}{2}}T^nA^{-\frac{1}{2}}:n\geq 1\}$ admits a unitary dilation. We identify a tractable collection of $\mathcal{C}_A$-class operators for which isometric and unitary dilations can be written down explicitly in block operator form. This includes the well-known $\rho$-dilations for positive scalars. Here the special cases $\rho =1$ and $\rho =2$ correspond to Sch\"{a}ffer representation for contractions and Ando representation for operators with numerical radius not more than one respectively., Comment: 27 pages

Rate of a reaction is enhanced by increase in temperature, partial pressure or the concentration of reactants, and/or via use of a catalyst or an enzyme. Whereas the former increases the probability of collision rate between different molecules, the latter provides an alternate reaction path that diminishes the activation energy barrier for reaction, both effects increase the reaction rate. The deformability of the substrate on which a reaction occurs is not known to affect this rate. In contrast, by carrying out reduction of Gold and Silver salt on soft, crosslinked layers of poly(dimethylsiloxane) (PDMS), we show here that surface tension driven deformation of the solid too can increase the reaction rate. The PDMS contains SiH groups as organosilanes which reduces the salt thereby producing the corresponding metallic nano-particles. When an aqueous solution of the salt is dispensed as a sessile drop on a sufficiently soft PDMS layer, nano-particles get generated at ~3 times the rate over which when the salt solution is dispensed as a pool on the same surface. Unlike the pool, the drop has a three-phase contact line, where it pulls up the solid forming a ridge. By balancing the resultant surface stresses at the vicinity of this ridge, we have estimated the excess surface free energy associated with it. We show that this excess energy can diminish the activation energy barrier and increase the reaction rate to the extent that would have been achieved by increasing the reaction temperature by over 30o C., Comment: 27 pages, 4 figures

The current analysis of wireless networks whose transceivers are confined to streets is largely based on Poissonian models, such as Poisson line processes and Poisson line Cox processes. We demonstrate important scenarios where a model with a finite and deterministic number of streets, termed binomial line process, is more accurate. We characterize the statistical properties of the BLP and the corresponding binomial line Cox process and apply them to analyze the performance of a network whose access points are deployed along the streets of a city. Such a deployment scenario will be typical for 5G and future wireless networks. In order to obtain a fine-grained insight into the network performance, we derive the meta distribution of the signal-to-interference and noise ratio. Accordingly, we investigate the mean local delay in transmission and the density of successful transmission. These metrics, respectively, characterize the latency and coverage performance of the network and are key performance indicators of next-generation wireless systems., Comment: Submitted to IEEE Transactions on Wireless Communications