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This expository article makes a connection between Euler's homogeneous function theorem and a Lagrange integral for a simplified version of the Clairaut Equation. After describing both solutions in detail, we prove a new result, that the Lagrange solution is strictly more general than Euler's solution. This is shown using a few examples which substitute Euler's homogeneous function with a more general surface. The first rather complicated example is based directly on Goursat's definition of a general integral, while the subsequent simpler examples are based on a suitably expanded notion of the general integral. These new examples, and the expanded notion of the general integral may be of interest. We aim to present these classical PDE concepts to readers with a basic knowledge of multivariable calculus., Comment: 14 pages, 7 figures

We give the first deterministic algorithm that makes sub-quadratic queries to find the global min-cut of a simple graph in the cut query model. Given an $n$-vertex graph $G$, our algorithm makes $\widetilde{O}(n^{5/3})$ queries to compute the global min-cut in $G$. As a key ingredient, we also show an algorithm for finding $s$-$t$ max-flows of size $\widetilde{O}(n)$ in $\widetilde{O}(n^{5/3})$ queries. We also show efficient cut-query implementations of versions of expander decomposition and isolating cuts, which may be of independent interest., Comment: 27 pages

We revisit knowledge-aware text-based visual question answering, also known as Text-KVQA, in the light of modern advancements in large multimodal models (LMMs), and make the following contributions: (i) We propose VisTEL - a principled approach to perform visual text entity linking. The proposed VisTEL module harnesses a state-of-the-art visual text recognition engine and the power of a large multimodal model to jointly reason using textual and visual context obtained using surrounding cues in the image to link the visual text entity to the correct knowledge base entity. (ii) We present KaLMA - a knowledge-aware large multimodal assistant that augments an LMM with knowledge associated with visual text entity in the image to arrive at an accurate answer. Further, we provide a comprehensive experimental analysis and comparison of our approach with traditional visual question answering, pre-large multimodal models, and large multimodal models, as well as prior top-performing approaches. Averaging over three splits of Text-KVQA, our proposed approach surpasses the previous best approach by a substantial 23.3% on an absolute scale and establishes a new state of the art. We make our implementation publicly available., Comment: Accepted to EMNLP (Main) 2024

Given a fixed arity $k \geq 2$, Min-$k$-CSP on complete instances involves a set of $n$ variables $V$ and one nontrivial constraint for every $k$-subset of variables (so there are $\binom{n}{k}$ constraints). The goal is to find an assignment that minimizes unsatisfied constraints. Unlike Max-$k$-CSP that admits a PTAS on dense or expanding instances, the approximability of Min-$k$-CSP is less understood. For some CSPs like Min-$k$-SAT, there's an approximation-preserving reduction from general to dense instances, making complete instances unique for potential new techniques. This paper initiates a study of Min-$k$-CSPs on complete instances. We present an $O(1)$-approximation algorithm for Min-2-SAT on complete instances, the minimization version of Max-2-SAT. Since $O(1)$-approximation on dense or expanding instances refutes the Unique Games Conjecture, it shows a strict separation between complete and dense/expanding instances. Then we study the decision versions of CSPs, aiming to satisfy all constraints; which is necessary for any nontrivial approximation. Our second main result is a quasi-polynomial time algorithm for every Boolean $k$-CSP on complete instances, including $k$-SAT. We provide additional algorithmic and hardness results for CSPs with larger alphabets, characterizing (arity, alphabet size) pairs that admit a quasi-polynomial time algorithm on complete instances., Comment: Appearing in ACM-SIAM Symposium on Discrete Algorithms (SODA25)

The Mixture-of-Experts (MoE) architecture enables a significant increase in the total number of model parameters with minimal computational overhead. However, it is not clear what performance tradeoffs, if any, exist between MoEs and standard dense transformers. In this paper, we show that as we increase the number of experts (while fixing the number of active parameters), the memorization performance consistently increases while the reasoning capabilities saturate. We begin by analyzing the theoretical limitations of MoEs at reasoning. We prove that there exist graph problems that cannot be solved by any number of experts of a certain width; however, the same task can be easily solved by a dense model with a slightly larger width. On the other hand, we find that on memory-intensive tasks, MoEs can effectively leverage a small number of active parameters with a large number of experts to memorize the data. We empirically validate these findings on synthetic graph problems and memory-intensive closed book retrieval tasks. Lastly, we pre-train a series of MoEs and dense transformers and evaluate them on commonly used benchmarks in math and natural language. We find that increasing the number of experts helps solve knowledge-intensive tasks, but fails to yield the same benefits for reasoning tasks.

Recent advancements in Text-to-Speech (TTS) technology have led to natural-sounding speech for English, primarily due to the availability of large-scale, high-quality web data. However, many other languages lack access to such resources, relying instead on limited studio-quality data. This scarcity results in synthesized speech that often suffers from intelligibility issues, particularly with low-frequency character bigrams. In this paper, we propose three solutions to address this challenge. First, we leverage high-quality data from linguistically or geographically related languages to improve TTS for the target language. Second, we utilize low-quality Automatic Speech Recognition (ASR) data recorded in non-studio environments, which is refined using denoising and speech enhancement models. Third, we apply knowledge distillation from large-scale models using synthetic data to generate more robust outputs. Our experiments with Hindi demonstrate significant reductions in intelligibility issues, as validated by human evaluators. We propose this methodology as a viable alternative for languages with limited access to high-quality data, enabling them to collectively benefit from shared resources., Comment: 11 pages, 1 figure, 3 tables

Automatic Speech Recognition (ASR) systems have been examined and shown to exhibit biases toward particular groups of individuals, influenced by factors such as demographic traits, accents, and speech styles. Noise can disproportionately impact speakers with certain accents, dialects, or speaking styles, leading to biased error rates. In this work, we introduce a novel framework DENOASR, which is a selective denoising technique to reduce the disparity in the word error rates between the two gender groups, male and female. We find that a combination of two popular speech denoising techniques, viz. DEMUCS and LE, can be effectively used to mitigate ASR disparity without compromising their overall performance. Experiments using two state-of-the-art open-source ASRs - OpenAI WHISPER and NVIDIA NEMO - on multiple benchmark datasets, including TIE, VOX-POPULI, TEDLIUM, and FLEURS, show that there is a promising reduction in the average word error rate gap across the two gender groups. For a given dataset, the denoising is selectively applied on speech samples having speech intelligibility below a certain threshold, estimated using a small validation sample, thus ameliorating the need for large-scale human-written ground-truth transcripts. Our findings suggest that selective denoising can be an elegant approach to mitigate biases in present-day ASR systems., Comment: Paper accepted at IEEE ICKG 2024

Recent studies have shown that capillary waves generated by bursting of an oil drop at the water-air interface produces a daughter droplet inside the bath while part of it floats above it. Successive bursting events produce next generations of daughter droplets, gradually diminishing in size until the entire volume of oil rests atop the water-air interface. In this work, we demonstrate two different ways to modulate this process by modifying the constitution of the drop. Firstly, we introduce hydrophilic clay particles inside the parent oil drop and show that it arrests the cascade of daughter droplet generation preventing it from floating over the water-air interface. Secondly, we show that bursting behavior can be modified by a compound water-oil-air interface made of a film of oil with finite thickness and design a regime map which displays each of these outcomes. We underpin both of these demonstrations by theoretical arguments providing criteria to predict outcomes resulting therein. Lastly, all our scenarios have a direct relation to control of oil-water separation and stability of emulsified solutions in a wide variety of applications which include drug delivery, enhanced oil recovery, oil spills and food processing where a dispersed oil phase tries to separate from a continuous phase.

Open-vocabulary audio language models (ALMs), like Contrastive Language Audio Pretraining (CLAP), represent a promising new paradigm for audio-text retrieval using natural language queries. In this paper, for the first time, we perform controlled experiments on various benchmarks to show that existing ALMs struggle to generalize to linguistic variations in textual queries. To address this issue, we propose RobustCLAP, a novel and compute-efficient technique to learn audio-language representations agnostic to linguistic variations. Specifically, we reformulate the contrastive loss used in CLAP architectures by introducing a multi-view contrastive learning objective, where paraphrases are treated as different views of the same audio scene and use this for training. Our proposed approach improves the text-to-audio retrieval performance of CLAP by 0.8%-13% across benchmarks and enhances robustness to linguistic variation., Comment: 15 pages

This paper investigates the massive gauge field within spacetime context from a $\mathbb{Z}_2$ quotient of the constant curvature black hole. We investigate how the matter field's back reaction affects the spacetime geometry, considering perturbations in the metric up to the first order. The stress-energy tensor's expectation value can be precisely calculated by evaluating its pull-back onto the covering space. By appropriately selecting boundary conditions for the massive vector field along a non-contractible cycle of the quotient manifold, achieving a negative average energy along a null geodesic becomes feasible, enabling a traversable wormhole., Comment: 19 pages, 4 figures

With the increasing adoption of large language models (LLMs) in education, concerns about inherent biases in these models have gained prominence. We evaluate LLMs for bias in the personalized educational setting, specifically focusing on the models' roles as "teachers". We reveal significant biases in how models generate and select educational content tailored to different demographic groups, including race, ethnicity, sex, gender, disability status, income, and national origin. We introduce and apply two bias score metrics--Mean Absolute Bias (MAB) and Maximum Difference Bias (MDB)--to analyze 9 open and closed state-of-the-art LLMs. Our experiments, which utilize over 17,000 educational explanations across multiple difficulty levels and topics, uncover that models perpetuate both typical and inverted harmful stereotypes., Comment: 46 Pages, 55 Figures, dataset release pending publication

As the use of web browsers continues to grow, the potential for cybercrime and web-related criminal activities also increases. Digital forensic investigators must understand how different browsers function and the critical areas to consider during web forensic analysis. Web forensics, a subfield of digital forensics, involves collecting and analyzing browser artifacts, such as browser history, search keywords, and downloads, which serve as potential evidence. While existing research has provided valuable insights, many studies focus on individual browsing modes or limited forensic scenarios, leaving gaps in understanding the full scope of data retention and recovery across different modes and browsers. This paper addresses these gaps by defining four browsing scenarios and critically analyzing browser artifacts across normal, private, and portable modes using various forensic tools. We define four browsing scenarios to perform a comprehensive evaluation of popular browsers -- Google Chrome, Mozilla Firefox, Brave, Tor, and Microsoft Edge -- by monitoring changes in key data storage areas such as cache files, cookies, browsing history, and local storage across different browsing modes. Overall, this paper contributes to a deeper understanding of browser forensic analysis and identifies key areas for enhancing privacy protection and forensic methodologies., Comment: 34 pages

Electroencephalography (EEG)--based turn intention prediction for lower limb movement is important to build an efficient brain-computer interface (BCI) system. This study investigates the feasibility of intention detection of left-turn, right-turn, and straight walk by utilizing EEG signals obtained before the event occurrence. Synchronous data was collected using 31-channel EEG and IMU-based motion capture systems for nine healthy participants while performing left-turn, right-turn, and straight walk movements. EEG data was preprocessed with steps including Artifact Subspace Reconstruction (ASR), re-referencing, and Independent Component Analysis (ICA) to remove data noise. Feature extraction from the preprocessed EEG data involved computing various statistical measures (mean, median, standard deviation, skew, and kurtosis), and Hjorth parameters (activity, mobility, and complexity). Further, the feature selection was performed using the Random forest algorithm for the dimensionality reduction. The feature set obtained was utilized for 3-class classification using XG boost, gradient boosting, and support vector machine (SVM) with RBF kernel classifiers in a five-fold cross-validation scheme. Using the proposed intention detection methodology, the SVM classifier using an EEG window of 1.5 s and 0 s time-lag has the best decoding performance with mean accuracy, precision, and recall of 81.23%, 85.35%, and 83.92%, respectively, across the nine participants. The decoding analysis shows the feasibility of turn intention prediction for lower limb movement using the EEG signal before the event onset., Comment: *Equal contributions by the authors

Design skills are increasingly recognized as a core competency for software professionals. Unfortunately, these skills are difficult to teach because design requires freedom and open-ended thinking, but new designers require a structured process to keep them from being overwhelmed by possibilities. We scaffolded this by creating worksheets for every Design Thinking step, and embedding them in a PowerPoint deck on which students can collaborate. We present our experience teaching a team design project course to 200 first-year-university students, taking them from user interviews to functional prototypes. To challenge and support every student in a class where high school programming experience ranged from zero hours to three computer science courses, we gave teams the option of developing single-user or multi-user (distributed) web applications, using two Event-Driven Programming frameworks. We identified common failure modes from previous years, and developed the scaffolded approach and problem definition to avoid them. The techniques developed include using a "game matrix" for structured brainstorming and developing projects that require students to empathize with users very different from themselves. We present quantitative and qualitative evidence from surveys and focus groups that show how these strategies impacted learning, and the extent to which students' awareness of the strategies led to the development of metacognitive abilities.

How can instructors facilitate spreading out the work in a software engineering or computer science capstone course across time and among team members? Currently teams often compromise the quality of their learning experience by frantically working before each deliverable. Some team members further compromise their own learning, and that of their colleagues, by not contributing their fair share to the team effort. To mitigate these problems, we propose using a GitHub template that contains all the initial infrastructure a team needs, including the folder structure, text-based template documents and template issues. In addition, we propose each team begins the year by identifying specific quantifiable individual productivity metrics for monitoring, such as the count of meetings attended, issues closed and number of commits. Initial data suggests that these steps may have an impact. In 2022/23 we observed 24% of commits happening on the due dates. After partially introducing the above ideas in 2023/24, this number improved to 18%. To measure the fairness we introduce a fairness measure based on the disparity between number of commits between all pairs of teammates. Going forward we propose an experiment where commit data and interview data is compared between teams that use the proposed interventions and those that do not.

Deep state-space models (Deep SSMs) have shown capabilities for in-context learning on autoregressive tasks, similar to transformers. However, the architectural requirements and mechanisms enabling this in recurrent networks remain unclear. This study demonstrates that state-space model architectures can perform gradient-based learning and use it for in-context learning. We prove that a single structured state-space model layer, augmented with local self-attention, can reproduce the outputs of an implicit linear model with least squares loss after one step of gradient descent. Our key insight is that the diagonal linear recurrent layer can act as a gradient accumulator, which can be `applied' to the parameters of the implicit regression model. We validate our construction by training randomly initialized augmented SSMs on simple linear regression tasks. The empirically optimized parameters match the theoretical ones, obtained analytically from the implicit model construction. Extensions to multi-step linear and non-linear regression yield consistent results. The constructed SSM encompasses features of modern deep state-space models, with the potential for scalable training and effectiveness even in general tasks. The theoretical construction elucidates the role of local self-attention and multiplicative interactions in recurrent architectures as the key ingredients for enabling the expressive power typical of foundation models., Comment: 16 pages, 5 figures

Magnetic Resonance Imaging (MRI) is the gold standard for measuring fat and iron content non-invasively in the body via measures known as Proton Density Fat Fraction (PDFF) and $R_2^*$, respectively. However, conventional PDFF and $R_2^*$ quantification methods operate on MR images voxel-wise and require at least three measurements to estimate three quantities: water, fat, and $R_2^*$. Alternatively, the two-point Dixon MRI protocol is widely used and fast because it acquires only two measurements; however, these cannot be used to estimate three quantities voxel-wise. Leveraging the fact that neighboring voxels have similar values, we propose using a generative machine learning approach to learn PDFF and $R_2^*$ from Dixon MRI. We use paired Dixon-IDEAL data from UK Biobank in the liver and a Pix2Pix conditional GAN to demonstrate the first large-scale $R_2^*$ imputation from two-point Dixon MRIs. Using our proposed approach, we synthesize PDFF and $R_2^*$ maps that show significantly greater correlation with ground-truth than conventional voxel-wise baselines.

In recent years, there has been increasing interest in using formal methods-based techniques to safely achieve temporal tasks, such as timed sequence of goals, or patrolling objectives. Such tasks are often expressed in real-time logics such as Signal Temporal Logic (STL), whereby, the logical specification is encoded into an optimization problem. Such approaches usually involve optimizing over the quantitative semantics, or robustness degree, of the logic over bounded horizons: the semantics can be encoded as mixed-integer linear constraints or into smooth approximations of the robustness degree. A major limitation of this approach is that it faces scalability challenges with respect to temporal complexity: for example, encoding long-term tasks requires storing the entire history of the system. In this paper, we present a quantitative generalization of such tasks in the form of symbolic automata objectives. Specifically, we show that symbolic automata can be expressed as matrix operators that lend themselves to automatic differentiation, allowing for the use of off-the-shelf gradient-based optimizers. We show how this helps solve the need to store arbitrarily long system trajectories, while efficiently leveraging the task structure encoded in the automaton., Comment: The paper has been accepted to IROS 2024

We introduce a novel Einstein-Rosen BTZ wormhole metric as a solution to the Einstein field equations with a negative cosmological constant and explore in detail its various phenomenological aspects. We show that the wormhole metric is characterized by a horizon at the throat, resembling a black hole horizon. This implies that our wormhole metric describes a one-way traversable wormhole at the throat, with Hawking radiation observed by an observer located at some distance from the wormhole. It is also found the same Hawking temperature using the BTZ-like coordinates and Kruskal-like coordinates. This temperature is invariant not only on the type of coordinates but also the nature of the spin of quantum fields. Importantly, we find that at the wormhole throat, the spacetime is not a pure vacuum solution, but rather contains an exotic string matter source with negative tension, which may stabilize the wormhole geometry. To this end, we found that the size of the wormhole throat is proportional to the number of quantum bits suggesting a possible implications on ER=EPR. Further we studied the particle dynamics and, finally, we tested the ANEC with a test scalar and vector fields. For the double null-component computed in BTZ coordinates, we found an apparent divergence at the wormhole throat, which is then shown to be regularized by means of Kruskal-like coordinates. The ANEC for such a scalar/vector field is violated at the wormhole throat., Comment: Accepted in EPJC

Image-based Joint-Embedding Predictive Architecture (IJEPA) offers an attractive alternative to Masked Autoencoder (MAE) for representation learning using the Masked Image Modeling framework. IJEPA drives representations to capture useful semantic information by predicting in latent rather than input space. However, IJEPA relies on carefully designed context and target windows to avoid representational collapse. The encoder modules in IJEPA cannot adaptively modulate the type of predicted and/or target features based on the feasibility of the masked prediction task as they are not given sufficient information of both context and targets. Based on the intuition that in natural images, information has a strong spatial bias with spatially local regions being highly predictive of one another compared to distant ones. We condition the target encoder and context encoder modules in IJEPA with positions of context and target windows respectively. Our "conditional" encoders show performance gains on several image classification benchmark datasets, improved robustness to context window size and sample-efficiency during pretraining., Comment: NeurIPS 2024 Workshop on Self-Supervised Learning - Theory and Practice. Comments welcome!

The high cost of obtaining accurate annotations for image segmentation and localization makes the use of one and few shot algorithms attractive. Several state-of-the-art methods for few-shot segmentation have emerged, including text-based prompting for the task but suffer from sub-optimal performance for medical images. Leveraging sub-pixel level features of existing Vision Transformer (ViT) based foundation models for identifying similar region of interest (RoI) based on a single template image have been shown to be very effective for one shot segmentation and localization in medical images across modalities. However, such methods rely on assumption that template image and test image are well matched and simple correlation is sufficient to obtain correspondences. In practice, however such an approach can fail to generalize in clinical data due to patient pose changes, inter-protocol variations even within a single modality or extend to 3D data using single template image. Moreover, for multi-label tasks, the RoI identification has to be performed sequentially. In this work, we propose foundation model (FM) based adapters for single label, multi-label localization and segmentation to address these concerns. We demonstrate the efficacy of the proposed method for multiple segmentation and localization tasks for both 2D and 3D data as we well as clinical data with different poses and evaluate against the state of the art few shot segmentation methods.

Lubricated contacts in soft materials are important in various engineering systems and natural settings. Three major lubrication regimes are boundary (BL), mixed (ML), and elasto-hydrodynamic (EHL) lubrication, where the contact region is dry, partially wetted, or fully wetted, respectively. The transition between these regimes is insufficiently understood, especially for soft contacts, which impedes desired control of lubricated sliding friction. Here, we report on the role of solid wettability and adhesion on these transitions. Wettability of glycerol on polydimethylsiloxane (PDMS) surface, and adhesion between a glass indenter and PDMS, were varied by exposure of the PDMS to an ultraviolet light-ozone (UV-Ozone) cleaner. By combining friction tests and visualization, we demonstrate that the transition from ML to BL regime is dominated by the wettability of the lubricant; increasing wettability of glycerol makes removal of liquid from the contact region more difficult. Transition from EHL to ML is related to a series of events with increasing normal load, which are thinning of the lubricant layer, sudden jump to contact between the glass indenter and solid substrate across a gap of tens to a few hundreds of nanometers, and attendant elastic instabilities such as wrinkling and stick-slip. These results provide a deeper understanding of transitions in lubricated frictional behavior of soft materials which govern the maximum and minimum friction achievable.

We investigate the physical properties and redshift evolution of simulated galaxies residing in protoclusters at cosmic noon, to understand the influence of the environment on galaxy formation. This work is to build clear expectations for the ongoing ODIN survey, devoted to mapping large-scale structures at z=2.4, 3.1, and 4.5 using Ly$\alpha$-emitting galaxies (LAEs) as tracers. From the IllustrisTNG simulations, we define subregions centered on the most massive clusters ranked by total stellar mass at z=0 and study the properties of galaxies within, including LAEs. To model the LAE population, we take a semi-analytical approach that assigns Ly$\alpha$ luminosity and equivalent width based on the UV luminosities to galaxies in a probabilistic manner. We investigate stellar mass, star formation rate, major mergers, and specific star formation rate of the population of star-forming galaxies and LAEs in the field and protocluster environment and trace their evolution. We find that the overall shape of the UV luminosity function (LF) in simulated protocluster environments is characterized by a shallower faint-end slope and an excess on the bright end, signaling different formation histories for galaxies therein. The difference is milder for the Ly$\alpha$ LF. While protocluster galaxies follow the same SFR-$M_{\odot}$ scaling relation as average field galaxies, a larger fraction appears to have experienced major mergers in the last 200 Myr and as a result shows enhanced star formation at a ~60% level, leading to a flatter distribution in both SFR and $M_{\odot}$ relative to galaxies in the average field. We find that protocluster galaxies, including LAEs, begin to quench much earlier (z~0.8-1.6) than field galaxies (z~0.5-0.9); our result is in agreement with recent observational results and highlights the importance of large-scale environment on the overall formation history of galaxies., Comment: 18 pages, 13 figures, to be submitted to Astronomy & Astrophysics, the abstract was reduced to meet character requirements; edits include: updating coauthor list and affiliations, updating citations in Sec 2.1

We present ZeroComp, an effective zero-shot 3D object compositing approach that does not require paired composite-scene images during training. Our method leverages ControlNet to condition from intrinsic images and combines it with a Stable Diffusion model to utilize its scene priors, together operating as an effective rendering engine. During training, ZeroComp uses intrinsic images based on geometry, albedo, and masked shading, all without the need for paired images of scenes with and without composite objects. Once trained, it seamlessly integrates virtual 3D objects into scenes, adjusting shading to create realistic composites. We developed a high-quality evaluation dataset and demonstrate that ZeroComp outperforms methods using explicit lighting estimations and generative techniques in quantitative and human perception benchmarks. Additionally, ZeroComp extends to real and outdoor image compositing, even when trained solely on synthetic indoor data, showcasing its effectiveness in image compositing.

We conduct an analysis of a stochastic hydrodynamic pilot-wave theory, which is a Langevin equation with a memory kernel that describes the dynamics of a walking droplet (or "walker") subjected to a repulsive singular potential and random perturbations through additive Gaussian noise. Under suitable assumptions on the singularities, we show that the walker dynamics is exponentially attracted toward the unique invariant probability measure. The proof relies on a combination of the Lyapunov technique and an asymptotic coupling specifically tailored to our setting. We also present examples of invariant measures, as obtained from numerical simulations of the walker in two-dimensional Coulomb potentials. Our results extend previous work on the ergodicity of stochastic pilot-wave dynamics established for smooth confining potentials.

Spin precession is a textbook example of dynamics of a quantum system that exactly mimics its classical counterpart. Here we challenge this view by certifying the quantumness of exotic states of a nuclear spin through its uniform precession. The key to this result is measuring the positivity, instead of the expectation value, of the $x$-projection of the precessing spin, and using a spin > 1/2 qudit, that is not restricted to semi-classical spin coherent states. The experiment is performed on a single spin-7/2 $^{123}$Sb nucleus, implanted in a silicon nanoelectronic device, amenable to high-fidelity preparation, control, and projective single-shot readout. Using Schr\"odinger cat states and other bespoke states of the nucleus, we violate the classical bound by 19 standard deviations, proving that no classical probability distribution can explain the statistic of this spin precession, and highlighting our ability to prepare quantum resource states with high fidelity in a single atomic-scale qudit., Comment: Main text: 11 pages, 5 figures. Supplementary information: 13 pages, 11 figures

In this paper, we study the problem of Participatory Budgeting (PB) with approval ballots, inspired by Multi-Winner Voting schemes. We present generalized preference aggregation methods for participatory budgeting, especially for finding seemingly fair budget allocations. To achieve this, we generalize such preference aggregation methods from the well-known methods, namely the Sequential Chamberlin Courant rule and the Sequential Monroe Rule in the realm of social choice theory. Further, we provide an experimental evaluation of the preference aggregation methods using an impartial culture method of preference generation and study the extent to which such polynomial time algorithms satisfy one of the most popular notions of fairness called proportional representation., Comment: 8 pages, 3 figures