Abstract

The rapid proliferation of energy-constrained electronic systems, including IoT nodes, biomedical
implants, and portable devices, has intensified the demand for ultra-low-power and area-efficient analog
circuit design. This thesis presents the design and analysis of advanced ultra-low-power analog building
blocks with a focus on current and voltage references, as well as high-speed comparators, optimized for
energy and area efficiency under wide process, voltage, and temperature variations.
A series of resistorless current and voltage reference architectures are explored, leveraging subthreshold operation and the complementary temperature characteristics of CTAT and PTAT voltages to
achieve robust temperature compensation. A sub-1V current reference generating 593 pA is demonstrated, achieving a temperature coefficient of 378 ppm/◦C over a range of −40◦C to 100◦C, with a line
sensitivity of 0.198%/V across a supply range of 0.8 V to 2.5 V. The design consumes only 3.3 nW at
27◦C and occupies 0.074 mm2
, while maintaining ±0.75% (3σ/µ) process variation, enabling trim-free
operation. Further, an integrated ultra-low-voltage reference operating at 0.5 V generates 90.7 pA and
288 mV current and voltage references, respectively, achieving temperature coefficients of 15.2 ppm/◦C
and 36.8 ppm/◦C. The circuit operates across a wide supply range of 0.5 V to 2.6 V with line sensitivities
of 0.028%/V and 0.154%/V, consuming only 275.26 pW and occupying 0.087 mm2
through the use of
gate leakage-based techniques.
To address line sensitivity and enable operation over extreme temperature ranges, a compact voltage
reference architecture employing only four transistors and a dual-loop regulation scheme is proposed.
The design achieves a reference voltage of 451.6 mV while consuming 37.6 pW, with an ultra-low
line sensitivity of 0.009%/V. It operates over a wide temperature range of −30◦C to 160◦C with a
temperature coefficient of 70.2 ppm/◦C, enabled by threshold voltage modulation and leakage control
techniques.
In addition to reference generation, a 0.3 V bulk-driven rail-to-rail comparator with dynamic transient
enhancement is introduced to overcome the speed limitations of subthreshold operation. The proposed
design achieves a 10× improvement in rise time, with a transient response of 7.56 ns and a bandwidth of
1.07 MHz while consuming only 28 nW of power, demonstrating portability across 65 nm and 180 nm
CMOS technologies.
While the previously presented resistorless architectures demonstrate excellent simulated performance in terms of ultra-low power and compactness, their reliance on device-level characteristics makes
them inherently more susceptible to process variations, potentially impacting yield and long-term reliability. To address these limitations, area-efficient resistance-based current references are investigated
and validated through silicon tape-out measurements. A fabricated design in 0.18 µm CMOS delivers
a 10 nA reference current while consuming 40 nW, achieving a temperature coefficient of 136 ppm/◦C
over −40◦C to 100◦C and a line sensitivity of 1.1%/V across a 1.4 V to 1.9 V supply range, with a compact area of 0.03 mm2
. Furthermore, a low-cost single-point auto-calibration technique is proposed,
enabling compensation of temperature and process variations. The calibrated 1 µA current reference
achieves ±2% accuracy with a temperature coefficient below 150 ppm/◦C over −40◦C to 100◦C, offering performance comparable to conventional trimming methods while significantly reducing calibration
complexity, time, and cost.
Additionally, this thesis presents a fully integrated ultra-low-power and area-efficient RC oscillator based on a resistance amplification technique for compact on-chip timing generation. Implemented
in a 0.18 µm CMOS process, the oscillator synthesizes a large effective resistance using amplified
polysilicon resistor characteristics, significantly reducing silicon area while maintaining frequency stability. Continuous-time offset mitigation techniques are employed to suppress low-frequency noise and
amplifier-induced offsets. The proposed oscillator generates a stable 5 kHz clock from a 1.4 V supply
with ultra-low power consumption, achieving a temperature coefficient of 100 ppm/◦C over −40◦C to
100◦C and a line sensitivity of 1%/V across a 1.4 V to 2 V supply range using single-point calibration.
Overall, the proposed architectures demonstrate significant improvements in power consumption,
area efficiency, temperature stability, and robustness, making them well-suited for next-generation ultralow-power analog and mixed-signal systems.

Abstract

Software architecture is shaped by the design decisions made throughout a system's lifecycle. These
decisions influence the structure and quality of the system, and when the reasoning behind them is not
preserved, future maintenance becomes more difficult and error-prone. An effective way of capturing
this reasoning and the decision in a structured manner has been the use of architectural decision records.
However, keeping these records up to date requires sustained manual effort, which often leads to incomplete or missing entries as project timelines tighten. Beyond individual decisions, assessing whether
an architecture as a whole meets its quality goals requires organising dedicated review sessions with
multiple stakeholders, a process that is difficult to fit into the pace of most development cycles.
Generative AI has shown practical value in supporting software engineering tasks such as code generation and requirements analysis. Because architecture knowledge management relies heavily on writing
and interpreting text, these models are a reasonable fit for this area. However, current uses of LLMs in
software architecture tend to rely on basic prompting strategies, which often fall short when tasks require project-specific context or consistent, structured reasoning. As a result, the manual effort involved
in managing architecture design decisions has remained largely unaddressed.
This thesis investigates how LLMs and agentic workflows can be applied to reduce the manual effort
across the architecture design decision lifecycle. It proposes a structured approach to help developers
draft complete architectural decision records from brief inputs. To support the ongoing quality of these
records, the work examines automated assessment techniques using different language model configurations. These ideas are then extended to whole-architecture evaluation through a multi-agent framework
designed to simulate established review processes.
The work is grounded in a dataset of open-source architectural decision records and published architecture case studies. The results show that combining model fine-tuning with historical examples
supports the generation of concise records that align reasonably well with human writing patterns. The
automated assessment configurations offer a practical way to flag unclear or incomplete records without requiring continuous human review. The multi-agent evaluation framework shows some ability to
identify structural risks and tradeoffs, and can reduce the initial effort required for scenario-based architecture reviews.
Overall, the thesis suggests that combining domain-adapted language models with structured agentic
workflows can provide a useful foundation for managing architecture design decisions. By lowering
the effort involved in recording and evaluating decisions, these approaches support more consistent
documentation practices and easier long-term system maintenance.

Abstract

The identification of Drug-Target Interactions (DTIs) is a critical step in the drug discovery process,
involving the assessment of binding affinities between small-molecule drug candidates and biological
target proteins. Over the past decade, graph neural network (GNN) based approaches have substantially
improved the accuracy of binding affinity prediction by representing drug molecules as molecular graphs
and learning chemically informative embeddings through message-passing operations. Despite these
advances, a fundamental gap persists in the literature: existing GNN-based DTI models predict whether
a drug candidate is likely to bind to a target, but do not identify which subgraph of the drug molecule
is structurally responsible for that interaction. From a drug discovery perspective, this subgraph, known
as the pharmacophore, is the essential structural and chemical feature that mediates binding, and its
identification is indispensable for lead optimisation, scaffold design, and the rationalisation of structureactivity relationships. There is an opportunity to address this gap by exploiting the knowledge encoded
in a trained GNN model to identify potential pharmacophores from drug candidates.
To address this problem, in this thesis we propose ExplainableDeepGNN, a two-phase GNN-based
framework in which the Monte Carlo Tree Search (MCTS) algorithm is employed to extract potential pharmacophores from drug candidates by leveraging a trained GNN model. In the first phase, we
employ a GNN-based model named GraphNetDTI to compute the binding affinity score for a given
drug-target pair, and potential drug candidates are identified based on this score. In the second phase,
by employing the MCTS algorithm, the trained GraphNetDTI model is leveraged to extract potential
subgraphs representing pharmacophores from the identified drug candidates.
The framework is evaluated on three benchmark datasets: Davis, Kiba, and Allergy. The experimental results show that GraphNetDTI achieves high predictive accuracy on all three datasets. Furthermore,
ExplainableDeepGNN successfully extracts pharmacophores of relatively small size from the identified
drug candidates, with the predicted binding affinities of the extracted subgraphs being very similar to
those of the corresponding drug candidates.
The proposed approach helps explore the potential pharmacophore of a given drug candidate, which
enhances the explainability of drug-target interaction prediction and provides deeper insights into crucial
molecular interactions.

Abstract

Imagine an embodied agent navigating a complex, unstructured environment. To operate effectively,
whether it is retrieving a specific object or building a comprehensive map of a building, the robot must
reliably recognize and associate the same physical entities across different points in time and space.
Historically, this capability relied on matching sparse, isolated pixels. However, the paradigm of visual
correspondence is shifting toward segment matching: establishing connections between semantically
and geometrically coherent regions. By reasoning over entire objects or structural surfaces rather
than individual points, robots can achieve a higher-level, interpretable, and fundamentally more robust
understanding of their surroundings.
Despite its vast potential, segment matching breaks down under wide-baseline conditions. When an
agent revisits a scene from an opposing viewpoint and experiences extreme perspective distortion, scale
variation, and camera rotations up to 180◦
, the 2D appearance of objects changes drastically. Current
state-of-the-art vision foundation models and video propagators, trained primarily on 2D priors, struggle
severely in these scenarios. Their routine failure modes include perceptual instance aliasing (confusing
identical but distinct objects) and topological collapse (failing to recognize the exact same object from a
new angle), ultimately leading to fragmented maps and navigational failures.
To resolve this blindspot, this thesis introduces SegMASt3R (Geometry Grounded Segment Matching), a novel architecture that repurposes the strong spatial inductive biases of a 3D Foundation Model
(3DFM) for robust, wide-baseline segment association. The proposed pipeline leverages a frozen MASt3R
backbone to extract dense, 3D-aware patch features. A newly designed segment-feature head then aggregates these dense representations into compact, instance-discriminative descriptors. To gracefully handle
the reality of occlusions and restricted fields-of-view, the assignment process is formulated through a
differentiable optimal transport layer. By employing a Sinkhorn solver equipped with a learnable dustbin
parameter, the network learns to explicitly reject unmatchable segments while enforcing strict geometric
consistency for valid pairs.
Extensive empirical evaluations demonstrate that SegMASt3R achieves state-of-the-art accuracy
in wide-baseline segment association. It outperforms existing 2D foundational baselines and dense
local feature matchers by up to 30% on the AUPRC metric across challenging indoor benchmarks,
including ScanNet++ and Replica. Furthermore, the learned geometry-grounded representations exhibit
strong zero-shot generalization to unconstrained outdoor environments, such as the MapFree dataset.
Finally, this thesis validates the practical utility of SegMASt3R in downstream robotic perception
pipelines, demonstrating significantly reduced identity fragmentation in 3D instance mapping and
enhanced localization success in object-relative topological navigation.

Abstract

This study explores the classic hide-and-seek game as a model for real-world scenarios such
as intruder capture in closed spaces and area surveillance. Unlike previous work that focused
on static environments, this research investigates pursuit-evasion dynamics in the presence of
moving obstacles. Traditionally, mobile entities in robotics are treated primarily as collision
hazards. However, this thesis formalizes them as dynamic occlusions--mobile shields that
cast dynamic shadows, which adversarial agents (hiders) can actively exploit to systematically
contaminate previously cleared zones and stay hidden in the environment.
To neutralize this threat, we propose and rigorously evaluate a progression of novel multiagent search strategies for autonomous seeker agents. We first establish an uncoordinated Baseline model to quantify the inefficiency of random traversal, followed by a Greedy Set-Cover
strategy that optimizes initial deployment position of seekers by formulating the environment
as a discrete Art Gallery problem1
. To achieve continuous spatial clearance, we introduce a systematic Sweep Strategy, a novel geometric traversal algorithm explicitly designed to actively
encircle and neutralize the dynamic shadows cast by moving obstacles.
To overcome the topological rigidity and agent "clumping" inherent in strict geometric formations, we further develop the Multi-Sweep Strategy. This advanced algorithmic approach
models search as a continuous topological frontier expansion. It utilizes linear sum assignment (the Hungarian algorithm) to dynamically optimize seeker target allocation based on
shortest-path routing, ensuring maximum spatial distribution. Furthermore, to resolve the issue of unbounded pursuit when encountering moving obstacles, we introduce a mathematical
"Frontier Sealing" mechanism, guaranteeing the neutralization of dynamic shadows without
forcing seekers into infinite chase sequences.
Extensive empirical evaluations within a custom simulation environment validate these approaches. The results demonstrate the superior scalability, resource efficiency, and mathematically robust Time-to-Capture (TTC) of the proposed sweep strategies across complex, highly
dynamic architectural topologies.

Abstract

Time series forecasting has been transformed in recent years by the appearance of large pretrained
foundation models such as Moirai, Chronos, TimeGPT, and Lag-LLaMA. A single such model can be
applied zero-shot to a new series without any per-dataset training, which makes forecasting an inference
operation rather than a training operation and allows one model artefact to serve many heterogeneous use
cases. These models expose a small number of user-controlled parameters at inference time, in particular
the context length and the patch size, whose choice strongly affects forecasting accuracy. The optimal
choice differs across series, so any single global configuration is a compromise. The standard remedy
of per-series hyperparameter optimization is accurate but expensive, since every new series requires its
own iterative search and every search trial requires a full forward pass of a large model. This cost scales
poorly when the same model is deployed across many heterogeneous series.
In this thesis we propose Tune-as-Inference, a framework that converts configuration selection from a
per-series optimization problem into a cross-series prediction problem. The framework operates in two
phases. An offline phase profiles a set of training series under every candidate configuration, extracts
inexpensive statistical meta-features for each series, and trains a lightweight rank-based meta-learner
that maps meta-features to predicted configuration ranks. An online phase, applied to any unseen
series, computes the same meta-features, scores all configurations using the meta-learner, and selects the
configuration with the lowest predicted rank. No iterative search is performed at deployment, and the
deployment cost is dominated by a single foundation model evaluation per series. In our implementation,
we use TSFresh for meta-feature extraction and LightGBM for the rank-based meta-learner.
We evaluate the framework on two real-world benchmarks, Uber TLC and Electricity (NIPS), using the Moirai 1.1-R-small foundation model. Tune-as-Inference improves over the strongest static
configuration on both datasets and reaches mean absolute error within three to five percent of 20-trial
Bayesian optimization, while reducing per-series configuration cost by approximately twenty times. A
complementary study with PatchTST suggests that the framework also applies to per-dataset supervised
transformers, with no change to the meta-learning components. Alongside the research contribution,
we developed Time Series Council, an open-source Python library for time series analysis and anomaly
detection built in collaboration with Salesforce, which is documented in the thesis as a practical artefact
that emerged from the same broader research direction

Abstract

Non-Structural Elements (NSEs), such as building contents, appendages, services
and utilities of buildings are not considered usually as part of lateral force resisting system
and are not included commonly in the earthquake analysis of structures. But, experiences
from the past earthquakes demonstrate that the presence of some NSEs alter the load paths
of the Structural Elements (SEs), thereby jeopardizing earthquake safety and functionality
of the buildings. These failures are unacceptable in important buildings like hospitals;
such structures need to be designed to remain occupiable after earthquakes. Alongside,
those buildings that are equipped with expensive acceleration-sensitive NSEs, such as
medical instruments, need to remain operational after an earthquake. Further, most
analytical studies utilize the Floor Response Spectrum approach (with NSEs not considered)
or the Decoupled Model Approach (with NSEs modelled separately), to estimate acceleration
demands on NSEs. This approach neglects the dynamic interaction between SE-NSE,
consequently estimating unrealistic seismic demands on NSEs. Further, the acceleration
demands on NSEs are influenced by the characteristics of ground motions, higher mode
participation, structural irregularities, etc. Thus, there is a need to fine-tune the design
parameters of NSEs using the Coupled Model Approach (with SEs-NSEs modelled together)
and consider other influencing parameters.
In this thesis, firstly, the seismic responses of critical 5-storey and 10-storey RC
wall-frame buildings are assessed using nonlinear static and nonlinear response history
analyses under near-fault and far-fault ground motions. Secondly, the earthquake
responses are investigated of acceleration-sensitive, floor-mounted elastic NSEs with
fundamental periods (TNSE) ranging from 0.1s to 1.0s (in increments of 0.1s) and weights
ranging from 10 kN to 50 kN (in increments of 10 kN), mounted on all floors of these
buildings employing coupled modelling. Results suggest that higher-mode effects are
prominent in 10-storey buildings than in 5-storey buildings. The extent of building
nonlinearity is maximum under near-fault ground motions in high seismic zones
compared to far-fault ground motions and low seismic zones. Floor Amplification Factor
(FAF) and Component Amplification Factor (CAF) are the design parameters influencing
the seismic behaviour of NSEs in estimating the design horizontal lateral force. 5-storey
and 10-storey buildings have maximum FAFs of 2.5 and 2.0, respectively. In 5-storey
buildings, maximum CAF is 5.0 when TSE < 0.5s and TNSE ≥ 0.5s, due to amplification
between TNSE and elongated fundamental period of the building, resulting from structural
nonlinearity. In 10-storey buildings, maximum CAF is 4.0 when TSE < 1.4s and 0.3s ≤ TNSE
≤ 0.7s, due to influence of higher modes. Based on these findings, analytical expressions
for FAF and CAF spectra are proposed. The proposed expressions aim to complement
current code recommendations, specifically tailored to the characteristics of 5-storey and
10-storey critical RC wall-frame buildings. The efficacy of the proposed expressions is
demonstrated by comparing them with current code provisions and results from previous
studies; the proposed FAF and CAF are found to provide realistic estimation of the
earthquake demands on NSEs.

Abstract

Large Language Models have grown to be remarkably capable at tasks which require a sophisticated use of language, yet what they have actually learnt about language is poorly understood.
The models have billions of parameters and are trained on vast corpora, making their internal
representations difficult to inspect directly. This opacity is a practical concern for general deployment of these models. We already possess rich, formally precise theories of linguistic structure.
Whether language models, trained without explicit linguistic supervision, converge on anything
resembling those theories is a question that bears on both linguistics and interpretability: it tests
whether the theories capture structure latent in language, and it gives interpretability research
a principled target to search for. In this thesis, we pursue this question through the Paninian
grammatical tradition, a dependency based syntactico-semantic framework centred on participant roles (karakas ¯ ) and morphological case markers (vibhakti). The framework is particularly
interesting due to its categories encoding the syntax-semantics interface rather than surface
syntax alone, and is better suited than mainstream frameworks like Universal Dependencies for
the morphologically rich, free word order languages of the Indian subcontinent. We present
two complementary studies, moving from representation to mechanism. In the first, we probe
three multilingual transformers across seven Indian languages annotated under the Paninian
scheme, and find that karaka-labelled dependency relations and vibhakti features are linearly ¯
decodable from frozen representations. The layer profile follows a consistent hierarchy: lexical
features emerge earliest, morphological features plateau broadly, and syntactic structure peaks
latest, suggesting that the models implicitly recapitulate the informational order of the Paninian
analytical framework. In the second study, we move from correlation to causation. Using causal
tracing and activation patching on Gemma-2-2B, we reverse-engineer the circuit implementing
the sampradana/ap ¯ ad¯ ana (recipient/source) k ¯ araka distinction, isolating a compact mechanism ¯
in which a prepositional gate token, functioning as a vibhakti marker, steers late-layer attention
to retrieve the correct entity. The circuit aligns with the Paninian view that surface morphological cues mechanistically drive semantic role selection. Together, these findings suggest that
formally specified linguistic theories can productively guide interpretability research: from establishing that a grammatical distinction is encoded in a model's representations to identifying
the mechanism by which it is computed.

Abstract

Modern Optical character recognition (OCR) systems increasingly rely on deep visual sequence
models, yet they are often evaluated mainly through final recognition accuracy. This leaves an important
question underexplored: how do such models learn, stabilize, and exhibit persistent errors over the
course of training? This question is especially relevant for Indic scripts, where visual text recognition is
shaped by complex orthographic structures such as aksharas, modifiers, conjunct-like forms, and dense
character compositions.
This thesis studies the learning behavior of two representative OCR models, CRNN and PARSeq,
using a five-language corpus covering Hindi, Bengali, Tamil, Telugu, and English. The main chapters
present representative analyses, and the same qualitative trends were observed in the remaining languages. The experiments are conducted on cropped printed word images, allowing the analysis to focus
on recognition behavior at the word level. Rather than comparing models only by final CER and WER,
the thesis examines their behavior across four complementary dimensions: training data scale, sequence
length, subword structure, and optimization geometry.
The results show that learning behavior varies meaningfully across model family, data regime, sequence length, and script structure. Under the tested settings, CRNN is more sensitive to reductions in
training data, while PARSeq remains comparatively more stable. Short words are learned faster than
long words, showing that sequence length remains an important source of recognition difficulty. Frequent and structurally simpler subword patterns stabilize earlier than rarer and more compositionally
involved patterns. Loss landscape visualizations further suggest that training moves from sharper and
more irregular regions toward smoother and more stable basins, with fuller data settings reaching such
regions more readily.
Together, these findings show that final recognition scores alone do not fully characterize OCR model
behavior. The analysis can support more informed model selection, especially when data availability,
script complexity, and word length vary across recognition settings. The findings may also inform
dataset design by indicating where additional examples are likely to be useful. By focusing on learning
trajectories, this thesis offers a structured way to evaluate OCR models beyond final accuracy, with
attention to how their behavior changes with data availability, word length, script structure, and training
stability.

Abstract

Random graph theory studies how global structure emerges from simple local rules. The classical
Erd˝os-R´enyi model is the most prominent example: every pair of vertices is connected independently
with the same probability. This model has a remarkably complete theory and displays sharp transitions
for the appearance of components, cycles, a giant component, and connectivity. Nevertheless, many
mathematical and physical networks are not well represented by a completely homogeneous model. In
systems with an underlying geometry, edges are often constrained by spatial locality. Particles interact
mainly with nearby particles, lattice Hamiltonians are often local or quasi-local, communication links
may be restricted by distance, and random walks on such networks inherit the geometry of the ambient
space.
This thesis introduces a new model in which randomness and geometry coexist: the periodic
band random graph. The vertices are placed on the discrete cycle Zn, two vertices are eligible to be
connected only when their cyclic distance is at most a bandwidth parameter m, and each eligible edge
is then retained independently with probability p
The first main result of the thesis is a sharp connectivity threshold for this model. Since each
vertex has exactly 2m admissible neighbours in the deterministic host graph, the probability that a
fixed vertex is isolated is (1 − p)
2m. This suggests that isolated vertices disappear when
pconn(n) ∼
log n
2m
.
We prove that this is the correct sharp threshold: below this scale, isolated vertices persist with high
probability, while above this scale the graph is connected with high probability.
The proof above the threshold is not a purely mean-field argument. In the Erd˝os-R´enyi graph, the
number of possible edges between a set and its complement depends only on the size of the set. In
the band random graph, it also depends on the shape and location of the set along the cycle. Long
intervals have much smaller boundaries than scattered sets of the same size. To overcome this, we
use a geometric block-decomposition argument: large connected pieces are built inside consecutive
intervals, neighbouring pieces are joined across their interfaces, and all small leftover sets are shown to
attach to the resulting connected chain.
We also analyze the graph just below the connectivity threshold. When
p =
log n − c
2m
, c > 0,
the graph is disconnected, but the disconnectedness is caused only by isolated vertices. More precisely,
the number Niso of isolated vertices converges in distribution to a Poisson random variable with mean
e
c
, and with high probability there is a unique giant component C1 satisfying
|C1| = n − Niso.
Thus every non-isolated vertex lies in the giant component. Moreover, unlike in the homogeneous Erd˝os-R´enyi model, this giant component has an explicit geometric structure: it contains an ordered
chain of large connected pieces inside consecutive m-blocks of the cycle, joined across neighbouring
interfaces.
The thesis also studies the random walk on the band random graph. The underlying cycle geometry
creates bottlenecks which persist even after the graph becomes connected. These bottlenecks are
reflected in the spectral gap of the lazy random walk. We show that, in the regime considered here,
the lazy spectral gap has order
γlazy(G) = Θ
m2
n2

and consequently obtain the corresponding mixing-time estimate. Finally, using electrical-network
methods, effective resistance, and explicit flow constructions, we prove that the maximal hitting time
of the simple random walk has order
Hmax(PG) = Θ
max
n
2
m2
, n .
The first term reflects diffusive motion around the cycle with step range m, while the second term
is the natural order of the time needed to hit a specified vertex when the stationary distribution is
close to uniform.
Overall, the thesis shows that the periodic band random graph is a useful model for studying
how independent randomness interacts with deterministic geometry. On the graph-theoretic side,
the model retains part of the Erd˝os-R´enyi connectivity picture: isolated vertices still determine the
sharp connectivity threshold. On the random-walk side, however, the behaviour is controlled by the
one-dimensional band structure, which produces the spectral-gap and hitting-time scales described
above.
The model also suggests a broader spectral direction. If AH denotes the adjacency matrix of the
deterministic host graph C
m
n
, then the adjacency matrix of the sampled graph can be written as
AG = pAH +
p
2mp(1 − p) W,
where W is a centered random band matrix supported on the same band. Thus AG is the sum of a
full-rank deterministic band operator and a random band fluctuation. While this thesis focuses mainly
on connectivity and random walks, the bulk and edge spectra of AG remain largely open and are a
natural direction for future work, connec