Indian Institute of Science Bangalore
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Renormalization Group Summation at High Orders and Implications to the Determination of Some Standard Model Parameters
No full textIn perturbation theory, predictions from theories like Quantum Chromodynamics (QCD)
are obtained by evaluating Feynman diagrams to high orders. Such calculations for re sults for various processes are already available in the literature, and their theoretical
predictions depend on various parameters. With the availability of a large amount of
data from experiments, it is possible to extract these parameters by comparing theoretical
predictions with data. However, due to the finite order terms available from theory, any
parameter determination depends on the perturbative scheme used and the choice of the
renormalization scale. Once a renormalization scheme is fixed, the variation of the renor malization scale in a certain range can lead to large uncertainties, and optimizing pertur bative series with respect to such free parameters is necessary. We have achieved such op timization using the renormalization group summed perturbation theory (RGSPT), and the resulting perturbative series is significantly less sensitive to the renormalization scale
dependence. It is a renormalization group (RG) improved version of the fixed order per turbation theory (FOPT), where the running RG-logarithms are summed to all orders
using the RG equation. Once these running logarithms are summed, various operations
such as analytic continuation, contour integrals, and Borel-Laplace transform are found
to have enhanced convergence and scale variation improvement compared to a FOPT
analysis. These operations are important in the precision determination of pQCD param eters using methods such as QCD sum rules
Flavivirus RNA replication: Probe development, structural dynamics, and role of zinc ions.
No full textFlaviviruses share a typical genome architecture where the highly conserved UTRs flank a central coding region. They also share a common genome replication strategy called genome cyclization where the UTRs interact to form a long-range, dynamic, 3D RNA interactome. Recent studies focused on the involvement of the capsid coding region in modulating these UTR interactions. Along similar lines, we have investigated the effect of CCR on the UTRs interactions in Dengue using ensemble FRET with cyanine dye-labeled Dengue UTRs. As a part of this study, we have developed a novel, generic chemoenzymatic, bead-based method for base-specific modification of RNA called “T7 RNA polymerase extension-based RNA modification (TERM)”. Here, we describe TERM development, demonstrate the synthesis of single, site-specific cyanine dye-labeled Dengue UTRs and discuss the UTR interaction studies performed using the TERM-synthesized cyanine dye-labeled UTRs. Our results bridge the knowledge gap in understanding the role of the capsid coding region in Flavivirus UTRs
Capacity Computation and Coding for Input-Constrained Channels
No full textThe setting of the transmission of information over noisy, binary-input, memoryless channels is today well-understood, owing to the work of several information theorists, beginning with Claude Shannon. It is known that it is impossible to transmit information reliably over such channels at rates larger than the fundamental limit that is the capacity of the channel. Moreover, progress made in the last three decades has led to the construction of explicit, practically-implementable coding schemes that achieve rates arbitrarily close to the capacities of such channels. Now, suppose that the inputs of the memoryless channel are required to obey an additional constraint, which stems from physical limitations of the medium over which transmission or storage occurs. What then can be said about the fundamental limits of information transmission over such input-constrained channels, with and without decoder feedback? Is it possible to design good constrained coding schemes of high rate over these channels? If the channel introduces errors adversarially, instead of randomly, how much information can then be sent through, reliably? This dissertation explores answers to such questions.
We first derive computable lower bounds on the capacities of runlength limited (RLL) input-constrained memoryless channels, such as the binary symmetric and binary erasure channels (BSC and BEC, respectively), by considering random Markov input distributions that respect the constraint. These bounds unify well-known approaches in the literature, and extend them to the so-called input-driven finite-state channels (FSCs). For the special case of the BEC with a no-consecutive-ones input constraint, we discuss an iterative stochastic approximation algorithm that numerically computes achievable rates that are very close to known upper bounds on the capacity of the channel. We also derive improved analytical lower bounds, for this specific channel.
Next, we consider the special case of the -runlength limited (RLL) constraint, which mandates that any pair of successive s be separated by at least s. We design explicit coding schemes, derived from Reed-Muller (RM) codes, for transmission over binary-input memoryless symmetric (BMS) channels, whose inputs respect the constraint. In particular, we provide constructions using constrained subcodes of RM codes, analytically compute their rates, and derive converse upper bounds on the rates of the largest constrained subcodes of RM codes. We also provide a Fourier-theoretic perspective on the problem of counting arbitrarily-constrained codewords in general linear codes, which can help estimate the rates achievable by using linear codes over input-constrained BMS channels. We illustrate the utility of our method using the somewhat surprising observation that for different constraints of interest, the Fourier transforms of the indicator functions of the constraints are efficiently computable.
We then shift our attention to the setting of the -RLL input-constrained BEC in the presence of noiseless feedback from the decoder. We demonstrate a simple, labelling-based, zero-error feedback coding scheme, which we prove to be feedback capacity-achieving, and, as a by-product, obtain an explicit characterization of the feedback capacity. The feedback capacity thus computed is an upper bound on the non-feedback capacity of such a channel. Numerical comparisons made with upper bounds on the non-feedback capacity then reveal that that feedback increases the capacity of such a channel, at least for select values of .
Finally, we consider the setting of an input-constrained adversarial channel, where there is an upper bound on the number of bit-flip errors that the channel can introduce, and we seek to design codes that can be recovered with zero error. We present numerical upper bounds on the sizes of the largest such codes, via a version of Delsarte’s linear program. We observe that for different constraints of interest, our upper bounds beat the “generalized sphere packing bounds” that are the state-of-the-art.Prime Minister's Research Fellowship, Qualcomm Innovation Fellowship Indi
Strain engineering of 2D NEMS for resonant sensing
No full text2D material-based nanoelectromechanical systems have emerged as excellent tools for force measurement with extreme sensitivity levels. Most sensing methods with 2D nanoelectromechanical (2D NEMS) systems utilize frequency tuning of the resonant mode in response to external stimuli. However, the interaction of the harsh external stimulus with the delicate 2D NEMS limited these devices’ utility only in the research labs. We propose a fabrication and packaging method for 2D NEMS devices to extend their application outside the research labs. Under the proposed scheme, the 2D NEMS is coupled to the external stimulus through substrate strain. The substrate acts as a protective barrier between the NEMS and the environment. At the same time, the substrate also influences the strain on the 2D NEMS. The external stimulus changes the strain on the substrate and hence on the 2D NEMS device. The strain change on 2D NEMS changes the frequency of vibration modes. 2D materials such as graphene have a high Young’s modulus. High Young’s modulus allows the strain to frequency transductions with high accuracy and sensitivity. We report the most straightforward application of this scheme for pressure sensing with a responsivity of 20Hz/Pa.
Using the proposed scheme, we also demonstrate the ability to utilize duffing nonlinear response of the graphene resonator for pressure sensing. The resonant response of the 2D nanoresonators becomes nonlinear, even at very small excitation voltages. The nonlinear response of the 2D nanoresonators shows sharp amplitude jumps at the bifurcation points and hysteresis. We utilize the sharp amplitude jumps to realize the bifurcation amplifier for pressure sensing. While the hysteresis in the frequency response is used to demonstrate basic logic operations such as OR, AND, and XOR with pressure pulse as input and vibration amplitude as output.
The external stimulus can also have a dynamic variation that can excite the substrate’s vibration modes. In this case, the frequency tuning of the 2D NEMS is also dynamic as it follows the strain on the substrate. Utilizing this principle, we report the ability of the 2D NEMS to track the dynamic stimulus with a frequency component as high as 40kHz. Characterizing time-varying stimuli is crucial for accelerometers, acoustic sensors, and vibrometers. We demonstrate the use of highly responsive 2D nanoresonators for such dynamic sensing.
Since the proposed 2D NEMS package allows external stimulus to couple to the 2D NEMS efficiently, the 2D NEMS is also susceptible to various environmental noise sources. We use the Allan Deviation of the frequency fluctuations to study the performance of these devices against noise. The measurements reveal that the primary cause of the frequency fluctuations of the 2D NEMS is the temperature of the surrounding air. These measurements provide crucial insights into designing a sensor with the required sensitivity, bandwidth and noise isolation. The barrier-substrate design can be changed according to specific applications to achieve the intended transduction. This concept can be extended easily for sensing inertial forces, biological stimuli, and temperature
Electron Microscopy Investigations of Surface-modulated Nanomaterials for Electrocatalytic Applications
No full textWith advancement and increasing usage of technologies, the demand for energy is also growing. However, the limited and ever-depleting stock of natural gas and fossil fuels has necessitated for better solutions in energy generation, conversion, and storage. To address the upcoming energy crisis, research on alternative energy conversion and storage applications has become an active field of interest. One of the most explored fields among them is electrocatalytic energy conversion reactions involving nanomaterials, which are interesting owing to their high activity originating from increased surface to volume ratio compared to the bulk counterpart.
In recent literature, electrocatalysis has been employed for a variety of reactions like alcohol oxidation and water splitting. The activity of any catalyst depends on the surface /sub-surface atomic configuration, their electronic structure, and adsorption/ desorption energy of intermediates. Changing the composition of surface and sub-surface leads to change the adsorption and desorption energy of the intermediates on surface. The activity of any catalyst is tuned by surface modifications as and whenever required and their surface modifications lead to improvement in the corresponding property. Noble metal catalysts are well known in literature and were explored for different types of electrocatalysis.
In this thesis, nanomaterial-based catalysts based on ultrathin Au nanowires as a template, are explored and their activities were investigated after their surface modifications. Extensive electron microscopic investigations were carried out using scanning transmission electron microscopy as a tool to understand the surface and sub-surface structure and composition at atomic scale. In some scenarios, high-angle annular dark field (HAADF)-STEM imaging can be limited by close atomic numbers of the constituent elements. There, other complementary techniques like XPS have been used to understand the composition. The synthesized templated catalysts have been tested for various reactions like electrocatalytic alcohol oxidations and water splitting reactions
Investigating spin transport across magnetic insulators and their interfaces
No full textSpin transport across magnetic insulator/heavy metal (MI/HM) interfaces has been a topic of interest
in spintronics. The spin Seebeck effect (SSE) and spin Hall magnetoresistance (SMR) are two
phenomena that have garnered much attention. The SSE studies magnon spin current induced by
thermal effects, while SMR investigates the change in HM resistivity due to spin transfer torque at the
MI/HM interface. This thesis investigates the use of electrical insulating magnetic materials for spin
information transmission at room temperature, with a focus on understanding spin transport
phenomena across magnetic insulators and their interfaces. The first part of the thesis presents the
work on detecting spin-Hall magnetoresistance (SMR) on a crystalline b-plate of Ho0.5Dy0.5FeO3
(HDFO)/Pt hybrid. The SMR measurements were conducted at various temperatures, ranging from 11
to 300 K. The first set of experiments focused on measuring the angular dependence of SMR at room
temperature under fields above and below the critical field, revealing anomalies in the signal. These
anomalies were then explained through the simulation of the SMR signal using a simple Hamiltonian
model. Further analysis of SMR measurements was conducted under a constant field above the critical
field at different temperatures, and the results were discussed. The second part of the thesis describes
research on the measurement of SMR and SSE on a polycrystalline Sr3Co2Fe24O41 (SCFO)/Pt
heterostructure, a room-temperature magneto-electric multiferroic material. The amplitude of SMR
data obtained from two measurement sets shows a non-monotonic behaviour with a sign reversal from
negative to positive as the external magnetic field is varied. The observed SMR data in SCFO is
analysed using a simple Hamiltonian model. Additionally, longitudinal SSE measurements are
performed, which resemble the dc magnetization results at 300 K. In the last part, spin transport (SMR
and SSE) was investigated on trilayer devices consisting of MgO/Ni0.8Zn0.2Fe2O4 (NZFO)/NiO/Pt
heterostructures with varying NiO thicknesses. SMR (1ω) measurements were conducted at various
temperatures, followed by current-induced heating to detect 2ω signal. The lock-in detection
technique was used to measure 2ω signals by varying magnetic field, current, and temperature that
shows non-sinusoidal SSE signal. This non-sinusoidal SSE signal was attributed to unidirectional
anisotropy (UDA), caused by ferrimagnetic/antiferromagnetic exchange coupling, using a simple
Hamiltonian model. Overall, this thesis contributes to the advancement of spintronic research by
exploring the potential of electrical insulating magnetic materials as carriers of spin information and
developing a simple Hamiltonian model for analysing spin-related phenomena in these materials
Tropical Teleconnections to the Indian Summer Monsoon in Observations and in a Coupled Model
No full textAn accurate seasonal prediction of Indian summer monsoon rainfall (ISMR) holds immense importance for the socio-economic well-being of South-Asian countries, as it directly impacts agricultural output and overall economies. The interannual variability of ISMR is strongly associated with climatic events occurring in various ocean basins, particularly the eastern and central Pacific oceans. However, despite this association, accurately predicting ISMR with a lead time of one season remains a challenging task. While there exist several theories on ISMR teleconnections, they differ significantly in their approaches. Hence, gaining insights into the role of global climatic patterns through a unified physical mechanism is crucial to improve ISMR prediction. Therefore, in this study, we investigate the physical processes that connect major climatic events with the Indian summer monsoon through a single physical mechanism by utilizing both observations and climate model simulations. By employing moisture budget theory, we highlight the crucial role of surface pressure modulation in controlling the ISMR variability, which is difficult to simulate accurately using numerical prediction models.
In the first part, we proposed a unified teleconnection framework that links tropical teleconnections to ISMR through the net moisture convergence driven by surface pressure () gradients surrounding the Indian region. The positive and negative phases of major tropical climate patterns modulate these pressure gradients asymmetrically in the zonal and/or meridional directions leading to asymmetric changes in moisture convergence and ISM rainfall. Stronger El Nino droughts than La Nina floods are due to greater decreased eastward moisture flux over the Arabian Sea during El Nino than the corresponding increase during La Nina driven by proportionate meridional gradients. While the equatorial Atlantic Ocean’s sea surface temperature in boreal summer and El Nino Southern Oscillation (ENSO) in the preceding winter changes ISMR significantly, moisture convergence anomalies driven by the Indian Ocean Dipole were insignificant. Moreover, while ISMR extremes during ENSO are due to asymmetric changes in zonal and meridional gradients in , non-ENSO ISMR extremes arise due to the zonal gradient in zonally symmetric anomalies.
In the second part, we employ the previously proposed theory to examine the underlying physical processes that contribute to the occurrence of ISMR seasonal droughts in both observation and Climate Forecast System version 2 (CFSv2) model. In observations, a reduction in incoming zonal moisture flux over the Arabian Sea ( ) is essential for droughts to occur. In addition, an increase
in outgoing flux over the Bay of Bengal () results in a severe drought. On the contrary, droughts in CFSv2 primarily occur due to an enhancement in , seldom accompanied by a decrease in . This hypersensitivity of the CFSv2 ISMR to is further explained using the Matsuno-Gill response to moist convection. During El Nino droughts, precipitation decreases over the equatorial western
Pacific and eastern Indian Oceans. The resulting anomalous diabatic cooling increases local surface pressure (), intensifying meridional gradient, and thus, . The reduction in , however, is associated with a cooling of the central north Pacific Ocean in tandem with El Nino. During non-El Nino droughts, frequent occurrences of cold sea surface temperatures over the western north
Pacific Ocean are noticed. This cooling decreases over east Asia, increasing . To summarize, droughts in CFSv2 are controlled by the pan-Pacific climate but weakly decreasing . But in observations, a strong decrease in and a moderate increase in together lead to droughts.
Numerous previous studies have consistently highlighted that most climate models tend to overestimate the relationship between ENSO and ISMR. However, in the final part of this thesis, we argue that this strong relationship is not an inherent characteristic of the CFSv2 model but rather stems from the methodology employed to calculate the ensemble mean. The dominance of the ENSO-ISMR relationship in the ensemble mean results from a higher occurrence of ensemble members having the same sign of an anomaly. However, for non-ENSO forcing, the limited number of ensemble members with coherent anomalies leads to a diminished impact and inadequate ISMR response in the ensemble mean. This study highlights the limitations of relying solely on the ensemble mean for analyzing model characteristics and making forecasts. By exclusively focusing on the ensemble mean, there is a risk of making incorrect assessments of the model’s teleconnection patterns.
This thesis presents a comprehensive physical theory that connects tropical teleconnections and the Indian summer monsoon through the net moisture convergence driven by gradients around the Indian region. We have demonstrated the utility of this theory in analyzing the characteristics of climate models, which serves as a yardstick for enhancing the performance of dynamic models used for seasonal prediction
Design and Analysis of Random Access Protocols for Massive Machine-Type Communications
No full textMassive machine-type communications (mMTC) is a 5G and beyond use case, where the network is expected to serve millions of devices per square kilometre. Typical mMTC devices include smart energy meters, pressure sensors, temperature indicators, smart factory equipment, etc. These devices sporadically transmit short packets, i.e., they transmit a short burst of data once in a while and then largely remain inactive. In order to serve mMTC scenarios, we need to use grant-free random access (GFRA) protocols since they have the advantage of a low control and signalling overhead as well as non-orthogonal use of the channel. GFRA for mMTC is a relatively new research topic and has received immense interest in the recent past. In this thesis, we analyze several practical aspects of irregular repetition slotted aloha (IRSA), which is a GFRA protocol for mMTC.
IRSA is a distributed GFRA protocol where users transmit multiple replicas of their packets in randomly selected resource blocks within a frame to a base station (BS). The BS recovers the packets using successive interference cancellation (SIC). Existing studies have analyzed IRSA with idealized assumptions, i.e., neglecting fading, path-loss, channel estimation errors, pilot contamination, multi-cell interference, etc. These non-idealities can greatly reduce the performance of the system and must be accounted for in the design and analysis of any mMTC system.
In this thesis, we first analyze channel estimation in IRSA, exploiting the sparsity structure of IRSA transmissions, when non-orthogonal pilots are employed across users to facilitate channel estimation at the BS. Allowing for the use of non-orthogonal pilots is important, as the length of orthogonal pilots scales linearly with the total number of devices, leading to prohibitive overhead as the number of devices increases. Next, we present a novel analysis of the throughput of IRSA under practical channel estimation errors, and with the use of multiple antennas at the BS. Finally, we theoretically characterize the asymptotic throughput of IRSA using a density evolution based analysis. Simulation results underline the importance of accounting for channel estimation errors in analyzing IRSA, which can even lead to 70% loss in performance in severely interference-limited regimes. We also provide novel insights on the effect of parameters such as pilot length, SNR, number of antennas at the BS, etc, on the system throughput.
Next, we develop a novel Bayesian user activity detection (UAD) algorithm for IRSA, which exploits both the sparsity in user activity as well as the underlying structure of IRSA transmissions. We then derive the Cramer-Rao bound (CRB) on the mean squared error in channel estimation. We empirically show that the channel estimates obtained as a by-product of the proposed UAD algorithm achieves the CRB. Then, we analyze the signal to interference plus noise ratio achieved by the users, accounting for UAD, channel estimation errors, and pilot contamination. Finally, we illustrate the impact of these non-idealities on the throughput of IRSA via Monte Carlo simulations. For example, in a system with 1500 users and 10% of the users being active per frame, a pilot length of as low as 20 symbols is sufficient for accurate user activity detection. In contrast, using classical compressed sensing approaches for UAD would require a pilot length of about 346 symbols. Our results reveal crucial insights into dependence of UAD errors and throughput on parameters such as the length of the pilot sequence, the number of antennas at the BS, the number of users, and the SNR.
Then, we develop an enhanced version of IRSA that can be operated at the peak performance even at high system loads. IRSA can be used to serve a large number of users in mMTC while achieving a near-zero packet loss rate (PLR). However, in overloaded mMTC scenarios, the system is interference-limited, and the PLR is close to one. We develop a variant of IRSA in the interference limited-regime, namely Censored-IRSA (C-IRSA), in which users with poor channel states self-censor, i.e., they refrain from transmitting their packets. This censoring depends on a censor threshold that can be varied depending on the number of users in the system. Firstly, we empirically and theoretically analyze the performance of C-IRSA. Next, we derive the optimal choice of the censor threshold via a semi-analytic approach and a PLR-optimal algorithmic approach. This choice of the threshold maximizes the throughput while achieving zero PLR among uncensored users. Through extensive numerical simulations, we show that C-IRSA operates at full system throughput at high system loads compared to vanilla IRSA which has near-zero throughput.
After this, we analyze IRSA in the multi-cell (MC) and cell-free (CF) setups, accounting for pilot contamination, channel estimation errors, and multi-user interference. Via extensive simulations, we illustrate that, in practical settings, MC IRSA can have a drastic loss of throughput, up to 70%, compared to SC IRSA. Further, MC IRSA requires a significantly higher training length, in order to support the same user density and achieve the same throughput: for example, MC IRSA may need about 4−5x compared to SC IRSA. We provide insights into the effect of system parameters such as number of antennas, pilot length, and SNR on the throughput of MC IRSA and CF IRSA. With the proposed CF architectures, we show that we can achieve more than 14x improvement in the throughput of CF IRSA compared to a massive MIMO SC setup. We also study the densification trends in MC IRSA, where we observe an inverse behaviour in the throughput compared to CF IRSA.
Finally, we optimize the repetition distributions in IRSA with the throughput and the energy efficiency objectives. Via extensive numerical simulations, we study the effect of various system parameters such as the maximum repetition factor, the average repetition factor, the number of antennas, and the pilot length, on the repetition distributions, the inflection load, and the peak energy efficiency. Compared to the best existing distributions, we show that our optimized distributions can achieve up to 58% increase in the inflection load and up to 49% increase in the peak energy efficiency.
Overall, this thesis analyzes and designs the IRSA protocol under several practical non-idealities. The developed algorithms vastly outperform state-of-the-art and can efficiently serve mMTC applications
Structure and dynamics of quantum supercooled liquids:Insights from molecular dynamics simulations
No full textSupercooled liquids are formed when a liquid is cooled below the melting temperature, avoiding crystallization. The system gets trapped in one of the many metastable states in the free energy surface. In supercooled state, the dynamics of the system shows marked differences compared to the normal liquid state. Upon decreasing the temperature further, molecular motion becomes so slow that it cannot be identified in experimentally accessible timescales, with no significant changes in the liquid structure. The dynamic slow-down in supercooled liquids arises from the collective behavior or “caging” of particles by their neighbors.
The thesis begins with a discussion of cage dynamics in a classical 2D model liquid. The cage time diverges as a power-law, which is much slower than the exponential divergence of the structural relaxation time. The cage sizes are correlated with the cage dynamics: small changes in the cage sizes in the deeply supercooled regime show large changes in the dynamics.
Quantum effects may lead to counterintuitive behavior in the properties of liquids in the supercooled regime. The effects of quantum fluctuations on the dynamical and structural properties of supercooled liquids are studied in a simple atomistic model system, using molecular dynamics simulations. The quantum effects are accounted for using the quantum-classical ring polymer isomorphism. The interplay of the classical confining potential and the quantum tunneling brings in interesting effects. The effects of quantumness on the cages are analyzed.
Dynamic heterogeneity is a hallmark of supercooled liquids. The qualitative changes in the dynamic heterogeneity due to quantum effects are studied by analyzing the tagged particle dynamics. In contrast to the classical case, quantum liquids show large dynamic heterogeneities at short timescales.
Finally, the manifestations of quantum effects in supercooled water are studied. Molecular systems have additional degrees of freedom as compared to the atomistic system, which can give rise to more complex dynamics. The inclusion of quantum nature affects the structure and dynamics of water in the low-temperature regime. The dynamics is discussed in terms of the neighbor shells of a molecule, which shows some interesting features that arise due to inter-shell migration of molecules
On the Optimality of Generative Adversarial Networks — A Variational Perspective
No full textGenerative adversarial networks (GANs) are a popular learning framework to model the underlying distribution of images. GANs comprise a min-max game between the generator and the discriminator. While the generator transforms noise into realistic images, the discriminator learns to distinguish between the reals and the fakes. GANs are trained to either minimize a divergence function or an integral probability metrics (IPMs). In this thesis, we focus on understanding the optimality of GAN discriminator, generator, and its inputs, viewed from the perspective of Variational Calculus. Considering both divergence- and IPM-minimizing GANs, with and without gradient-based regularizers, we analyze the optimality of the GAN discriminator. We show that the optimal discriminator solves the Poisson partial differential equation, and derive solutions involving Fourier-series and radial basis function expansions. We show that providing the generator with data coming from a closely related input datasets accelerates and stabilizes training even in scenarios where there is no visual similarity between the source and target datasets. To identify closely related datasets, we propose the “signed Inception distance” (SID) as a novel GAN measure. Through the variational formulation, we demonstrate that the the optimal generator in GANs is linked to score-based Langevin diffusion and gradient flows. Leveraging these insights, we explore training GANs with flow-based and score-based costs, and diffusion models that perform discriminator-based updates