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Quantized function algebras at q=0: Type An case
No full textWe define the notion of quantized function algebras at q=0 or crystallization of the q deformations of the type An compact Lie groups at the C∗-algebra level. The C∗-algebra An(0) is defined as a universal C∗-algebra given by a finite set of generators and relations. We obtain these relations by looking at the irreducible representations of the quantized function algebras for q\u3e0 and taking limit as q→0+ after rescaling the generating elements appropriately. We then prove that in the n=2 case the irreducible representations A2(0) are precisely the q→0+ limits of the irreducible representations of the C∗-algebras A2(q)
QUANTILE PROCESSES AND THEIR APPLICATIONS IN FINITE POPULATIONS
No full textThe weak convergence of the quantile processes, which are constructed based on different estimators of the finite population quantiles, is shown under various well-known sampling designs based on a superpopulation model. The results related to the weak convergence of these quantile processes are applied to find asymptotic distributions of the smooth L-estimators and the estimators of smooth functions of finite population quantiles. Based on these asymptotic distributions, confidence intervals are constructed for several finite population parameters like the median, the α-trimmed means, the interquartile range and the quantile based measure of skewness. Comparisons of various estimators are carried out based on their asymptotic distributions. We show that the use of the auxiliary information in the construction of the estimators sometimes has an adverse effect on the performances of the smooth Lestimators and the estimators of smooth functions of finite population quantiles under several sampling designs. Further, the performance of each of the above-mentioned estimators sometimes becomes worse under sampling designs, which use the auxiliary information, than their performances under simple random sampling without replacement (SRSWOR)
Quantum Nonlocality: Multicopy Resource Interconvertibility and Their Asymptotic Inequivalence
No full textQuantum nonlocality, pioneered in Bell\u27s seminal work and subsequently verified through a series of experiments, has drawn substantial attention due to its practical applications in various protocols. Evaluating and comparing the extent of nonlocality within distinct quantum correlations holds significant practical relevance. Within the resource theoretic framework this can be achieved by assessing the interconversion rate among different nonlocal correlations under free local operations and shared randomness. In this study we, however, present instances of quantum nonlocal correlations that are incomparable in the strongest sense. Specifically, when starting with an arbitrary many copies of one nonlocal correlation, it becomes impossible to obtain even a single copy of the other correlation, and this incomparability holds in both directions. Such incomparable quantum correlations can be obtained even in the simplest Bell scenario, which involves two parties, each having two dichotomic measurements setups. Notably, there exist an uncountable number of such incomparable correlations. Our result challenges the notion of a unique gold coin, often referred to as the maximally resourceful state, within the framework of the resource theory of quantum nonlocality. To this end, we provide examples of isotropic quantum correlations that cannot be distilled up to the Tsirelson point, and thus partially answer a long-standing open question in nonlocality distillation
On Resource Efficient and Obstacle Aware Link Selection in D2D Communications
No full textDevice-to-device (D2D) communication has been envisioned as the solution to the bandwidth scarcity problem in the era of exponentially growing smart handheld devices. In D2D communications, two or more user equipment (UEs) are allowed to directly communicate with each other with limited or no involvement of the base station (BS). Since the number of available frequency channels is limited, one must judiciously allocate the channel resources among the demanding UEs. In cases where the direct communication link between two UEs offers poor signal quality, an idle UE may be judiciously selected to establish a relay-aided indirect communication link. To cope with the high bandwidth demands of modern applications, D2D communication using millimeter-wave (mmWave) signals has been proposed due to its improved spectral efficiency, higher data rates, and lower delays. The major challenge of using mmWave signals is that they suffer from high penetration and propagation losses and thus require short-distance obstacle-free line-of-sight (LOS) communication. The two problems, namely channel allocation and relay selection, have inherent interdependencies and thus must be jointly dealt with. To this end, in our first work of this thesis, we have tried to address the joint relay selection and channel assignment problem (JRSCAP) for D2D communications, and devised a near-optimal algorithm with polynomial time complexity. Both user mobility and the presence of static as well as dynamic obstacles can severely affect an mmWave communication link. Next, in this thesis, we have investigated the JRSCAP for mobile UEs in the presence of obstacles. After proving the hardness of this joint problem, we provide a greedy solution along with its approximation bound. For an energy-efficient green communication network, one must jointly allocate the frequency channel to requesting users as well as control their transmit power. As mentioned, the presence of obstacles can break an mmWave communication link, which may require a retransmission and contribute to wasteful energy consumption. While static obstacles are easier to avoid, dynamic obstacles pose the main hurdle, as they move independently outside the purview of the BS. Here, we have proposed a reinforcement learning (RL) framework for the joint power and channel allocation problem (JPCAP) for maximizing energy efficiency in the presence of dynamic obstacles. Information about dynamic obstacles can also be learned from link failures. To obtain a complete knowledge about the whole service area, sometimes we may be required to nonoptimally allocate resources so that all requesting links get an equal chance of activation. Although such non-optimal allocations are undesirable, they help in acquiring information about all the links uniformly. This brings us to the infamous exploration–exploitation dilemma. To this end, we have proposed a systematic way of inducing non-optimality in JPCAP. Given the hardness of this problem, we have devised a greedy solution and shown its effectiveness. In many modern applications, such as video streaming, the same data packets may need to be delivered to a group of users. Multicasting these packets has a clear advantage over repeated unicasts. Due to the dynamic nature of wireless communication links, establishing a stable multicast communication route is a challenging task, especially in the presence of dynamic obstacles. We address the multicast link selection problem (MLSP) as our final work in this thesis and present an optimal algorithm for stable link selection in the presence of dynamic obstacles. For all of our work in this thesis, we have performed extensive simulations and shown that our proposed solutions outperform existing state-of-the-art approaches
Obstacle Detection and Infrastructure Deployment for Efficient Millimeter-wave Communications
No full textThere has been growing interest in millimeter-wave (mmWave) communication due to the promising high speeds and immense amounts of unused bandwidth available. However, mmWaves suffer from unusually high attenuation, through free space, and especially through obstacles, which necessitates an obstacle free line-of-sight (LOS) transmission path. This thesis deals with establishment of such LOS paths, through obstacle detection and deployment of network infrastructure. The usual approach to avoid static obstacles on transmission paths is to use satellite imagery to detect the presence of static obstacles, an approach which apart from raising proprietary concerns, is not able to capture smaller obstacles. We propose a simple learning based approach to detect the presence of static as well as dynamic obstacles, without having apriori access to any data regarding their location from satellite imagery. We then use this knowledge to efficiently select an appropriate transmission path for a user equipment (UE), lowering the chance of allocating an obstacle prone link. Dynamic obstacles are usually tracked by dedicated tracking hardware like RGB-D cameras, which usually have small ranges, and hence lead to prohibitively increased deployment costs to achieve complete camera coverage of the deployment area. We propose an altogether different approach to track dynamic obstacles in an mmWave network, solely based on short-term historical link failure information, without resorting to any dedicated tracking hardware. Using the obtained trajectories, we perform proactive handoffs for at-risk links. We compare our approach with an RGB-D camera-based approach and show that our approach provides better handoff performances when the camera coverage is low to moderate, which is often the case in real deployment scenarios. Stability of allocated transmission paths is an important problem in the domain of mmWave communication. The quality of an allocated transmission path depends not only upon the present time, but also upon the maintenance of the said path in the near future; the fragile nature of mmWaves necessitates this. Thus, allocating the base station (BS) which provides the highest received signal strength (RSS) at the current time instant is not always the best idea, considering UE mobility, and presence of obstacles. We propose a simple geometric approach to allocate stable transmission paths which are less likely to be broken in the near future. One way to deal with obstacle free strict LOS requirements of mmWaves is to densely deploy small range mmWave BSs, to overcome outage due to obstacles. Low cost reflectors have also been proposed to augment the transmission environment, and reflect mmWaves in the desired direction, thereby bypassing the obstacles. We argue that considering the placement of mmWave BSs and reflectors independently may lead to suboptimal coverage. We consider an urban deployment scenario, and attempt to maximally cover it by jointly placing the mmWave BSs and reflectors. Given the hardness of the joint problem, we first develop a set cover based greedy solution, and also provide a linear programming (LP) relaxation based solution. With extensive simulations, we show that with a fixed number of available mmWave BSs and reflectors to be placed, both our proposed solutions achieve a larger coverage compared to an existing approach where BSs and reflectors were placed sequentially. Unmanned Aerial Vehicles (UAVs) are a potential platform for deployingmmWave BSs. One challenge that has to be addressed is the limited power onboard a UAV, which is used to hover and move the device, and of course, to transmit data. We deal with the deployment of UAVs with an aim to minimise their displacement in subsequent time instances. We take into consideration UE mobility, and propose LazyUAV, a set cover based geometric approach to minimise UAV displacement, while maintaining maximal coverage
Commutant Lifting, Interpolation and Toeplitz Operators In Several Variables
No full textAbstract not availabl
Distributed k-Circle Formation by Mobile Robots
No full textThe k-circle formation problem asks a group of robots to form disjoint circles. Each circle is restricted to being centered at one of the pre- xed points given in the plane, and each circle should have exactly k distinct robot positions. In this thesis, we investigate the solvability of the k-circle formation by a swarm of mobile robots in a deterministic manner. The robots are autonomous, and they execute Look-Compute-Move (LCM) cycle under a fair asynchronous scheduler. They are anonymous, i.e., they do not have any unique idenit er, and homogeneous, i.e., they execute the same deterministic algorithm. The robots are assumed to be oblivious and silent or may have limited persistent memory. We begin by investigating the k-circle formation problem in a setting where the robots have global agreement on the y-axis. In this setting, all the initial con gurations and values of k for which the k-circle formation problem is deterministically unsolvable are characterized. For the remaining con gurations and values of k, a deterministic distributed algorithm is proposed that solves the k-circle formation problem within nite time. It is shown that if the k-circle formation problem is deterministically solvable, then the k-EPF problem (a generalized version of the embedded pattern formation problem) can also be solved deterministically. We proceed by dropping the assumption of global y-axis agreement, where we assume that the robots do not have any agreement on the orientations and directions of any of the axes of a global coordinate system. In this setting, we provide a deterministic solution for the k-circle formation problem by characterizing all the deterministically unsolvable con gurations. If the robots are opaque, when three robots are collinear, then the terminal robots cannot see one another. In this setup, we consider two cases, namely, complete knowledge of xed points and zero knowledge of xed points. When the robots have complete knowledge of xed points, a distributed algorithm is proposed that solves k-circle formation problem for oblivious and silent robots in a deterministic manner. For robots with zero knowledge of xed points, a deterministic distributed solution is presented by assuming that the robots have one bit of persistent memory. In the real world, a robot cannot be dimensionless. We study the k-circle formation problem for unit disk robots. We propose a deterministic distributed solution under the assumption of global y-axis agreement. We conclude this thesis by discussing some future research directions related to the k-circle formation problem
Enhanced Security Approaches for Data Protection: Managing Consent, Data Breach, and Asset Inheritance
No full textThe journey of the Indian data protection framework started in 2018 with the introduction of the initial draft as “Personal Data Protection Bill (PDPB-2018)”. Subsequently, a revised draft PDPB-2019 was introduced. This went through revisions as PDPB 2021 and Digital Personal Data Protection Bill (DPDPB-2022). Finally, it was passed as “Digital Personal Data Protection Act” (DPDPA, 2023). The framework emphasized on protected data processing while the user’s privacy is honored. In this thesis, we look at the technical aspects in DPDPA and suggest ways to address the different clauses of the bill. We have analyzed four components: a) user’s consent that states the nature and scope of consent-based data processing, b) right to access/right to nominate to assure the right to nominate someone as a nominee, c) data breach to enable appropriate technical measures to prevent and analyze data breach. d) storage/logging to preserve and evaluate various logs that strengthen security posture and incident response. Enhanced approaches have been explored under each obligation for stronger data management and processing aligning with the framework. In analyzing user’s consent, we have described that encoding of requisite security and privacy properties will ascertain stronger consent processing. We formalize these properties as Proofs of Consent (PoC) and categorized them into three layers. The acquisition of a higher layer will minimize adversarial risks and ascertain greater transparency. Next, we have proposed a model Shielded Consent Manager (SCM) using blockchain and other cryptographic primitives for retrieval of consent to grant permissions to access android resources. Further, following the right to nominee obligations, we have proposed a model Digital Asset Inheritance Protocol (DAIP) using CertificateLess Encryption (CLE) and Identity Based System (IBS) to convey the user’s online persona efficiently to the descendent after his death. DAIP allows the nominee to successfully retrieve the asset after the user’s demise, even if a nominee is uninformed regarding the asset. Then, we have proposed the system model of a Data Breach Incident Assessor (DBIA) aiming for breach assessment. It helps in the validation of a threat actor’s claim, understanding the root cause of a breach, analyze the scope of the compromise, and provide analysis according to the regulation. Finally, an End System URL Analyzer (ESUL) to analyze the URL based logs in end system is presented. The simulation and result analysis is done for each of the above approaches. We show that enhanced security approaches can help to realize the obligations in DPDPA, thus ensuring robust data management and processing
2024 United States Elections: Air Pollution, Neurodegeneration, Neuropsychiatric, and Neurodevelopmental Disorders. Who Cares?
No full textAir pollution exposures ought to be of significant interest for the United States (US) public as health issues will play a role in the 2024 elections. Citizens are not aware of the harmful brain impact of exposures to ubiquitous anthropogenic combustion emissions and friction-derived nanoparticles, industrial nanoplastics, the growing risk of wildfires, and the smoke plumes of soot. Ample consideration of pediatric and early adulthood hallmarks of Alzheimer\u27s disease, Parkinson\u27s disease, frontotemporal lobar degeneration, and amyotrophic lateral sclerosis and associations with neuropsychiatric and neurodevelopmental disorders in the process of setting, reviewing, and implementing standards for particulate matter (PM)2.5, ultrafine PM, and industrial nanoparticles must be of interest to US citizens
A MINIMAL COMPLETION THEOREM AND ALMOST EVERYWHERE EQUIVALENCE FOR COMPLETELY POSITIVE MAPS
No full textA problem of completing a linear map on C∗-algebras to a completely positive map is analyzed. It is shown that whenever such a completion is feasible there exists a unique minimal completion. This theorem is used to show that under some very general conditions a completely positive map almost everywhere equivalent to a quasi-pure map is actually equal to that map