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Cryptocurrency lending pools are services that allow lenders to pool together assets in one cryptocurrency and loan it out to borrowers who provide collateral worth more (than the loan) in a separate cryptocurrency. Borrowers can repay their loans to reclaim their collateral unless their loan was liquidated, which happens when the value of the collateral dips significantly. Interest rates for these pools are currently set via supply and demand heuristics, which have several downsides, including inefficiency, inflexibility, and being vulnerable to manipulation. Here, we reduce lending pools to options, and then use ideas from options pricing to search for fair interest rates for lending pools. In a simplified model where the loans have a fixed duration and can only be repaid at the end of the term, we obtain analytical pricing results. We then consider a more realistic model, where loans can be repaid dynamically and without expiry. Our main theoretical contribution is to show that fair interest rates do not exist in this setting. We then show that impossibility results generalize even to models of lending pools which have no obvious reduction to options. To address these negative results, we introduce a model of lending pools with fixed fees, and model the ability of borrowers to top-up their loans to reduce the risk of liquidation. As a proof of concept, we use simulations to show how our model's predicted interest rates compare to interest rates in practice.

In this paper, we investigate the problem of "generation supervision" in large language models, and present a novel bicameral architecture to separate supervision signals from their core capability, helpfulness. Doppelg\"anger, a new module parallel to the underlying language model, supervises the generation of each token, and learns to concurrently predict the supervision score(s) of the sequences up to and including each token. In this work, we present the theoretical findings, and leave the report on experimental results to a forthcoming publication.

Modern artificial intelligence (AI) systems are powered by foundation models. This paper presents a new set of foundation models, called Llama 3. It is a herd of language models that natively support multilinguality, coding, reasoning, and tool usage. Our largest model is a dense Transformer with 405B parameters and a context window of up to 128K tokens. This paper presents an extensive empirical evaluation of Llama 3. We find that Llama 3 delivers comparable quality to leading language models such as GPT-4 on a plethora of tasks. We publicly release Llama 3, including pre-trained and post-trained versions of the 405B parameter language model and our Llama Guard 3 model for input and output safety. The paper also presents the results of experiments in which we integrate image, video, and speech capabilities into Llama 3 via a compositional approach. We observe this approach performs competitively with the state-of-the-art on image, video, and speech recognition tasks. The resulting models are not yet being broadly released as they are still under development.

We introduce a novel technique for enhancing the robustness of light-pulse atom interferometers against the pulse infidelities that typically limit their sensitivities. The technique uses quantum optimal control to favorably harness the multipath interference of the stray trajectories produced by imperfect atom-optics operations. We apply this method to a resonant atom interferometer and achieve thousand-fold phase amplification, representing a fifty-fold improvement over the performance observed without optimized control. Moreover, we find that spurious interference can arise from the interplay of spontaneous emission and many-pulse sequences and demonstrate optimization strategies to mitigate this effect. Given the ubiquity of spontaneous emission in quantum systems, these results may be valuable for improving the performance of a diverse array of quantum sensors. We anticipate our findings will significantly benefit the performance of matter-wave interferometers for a variety of applications, including dark matter, dark energy, and gravitational wave detection.

Large language models (LLMs) have demonstrated strong potential in performing automatic scoring for constructed response assessments. While constructed responses graded by humans are usually based on given grading rubrics, the methods by which LLMs assign scores remain largely unclear. It is also uncertain how closely AI's scoring process mirrors that of humans, or if it adheres to the same grading criteria. To address this gap, this paper uncovers the grading rubrics that LLMs used to score students' written responses to science tasks and their alignment with human scores. We also examine whether enhancing the alignments can improve scoring accuracy. Specifically, we prompt LLMs to generate analytic rubrics that they use to assign scores and study the alignment gap with human grading rubrics. Based on a series of experiments with various configurations of LLM settings, we reveal a notable alignment gap between human and LLM graders. While LLMs can adapt quickly to scoring tasks, they often resort to shortcuts, bypassing deeper logical reasoning expected in human grading. We found that incorporating high-quality analytical rubrics designed to reflect human grading logic can mitigate this gap and enhance LLMs' scoring accuracy. These results caution against the simplistic application of LLMs in science education and highlight the importance of aligning LLM outputs with human expectations to ensure efficient and accurate automatic scoring., Comment: Non-archival Presenting at EDM 2024 Workshop on Large Language Models

It is well-known that the cohomology of symmetric quandles generates robust cocycle invariants for unoriented classical and surface links. Expanding on the recently introduced module-theoretic generalized cohomology for symmetric quandles, we derive a four-term exact sequence that relates 1-cocycles, second cohomology, and a specific group of automorphisms associated with the extensions of symmetric quandles. This exact sequence shows that the obstruction to lifting and extending automorphisms is found in the second symmetric quandle cohomology. Additionally, some general aspects of dynamical cocycles and extensions are discussed., Comment: 18 pages

A novel method to reconstruct the energy of hadronic showers in the CMS High Granularity Calorimeter (HGCAL) is presented. The HGCAL is a sampling calorimeter with very fine transverse and longitudinal granularity. The active media are silicon sensors and scintillator tiles readout by SiPMs and the absorbers are a combination of lead and Cu/CuW in the electromagnetic section, and steel in the hadronic section. The shower reconstruction method is based on graph neural networks and it makes use of a dynamic reduction network architecture. It is shown that the algorithm is able to capture and mitigate the main effects that normally hinder the reconstruction of hadronic showers using classical reconstruction methods, by compensating for fluctuations in the multiplicity, energy, and spatial distributions of the shower's constituents. The performance of the algorithm is evaluated using test beam data collected in 2018 prototype of the CMS HGCAL accompanied by a section of the CALICE AHCAL prototype. The capability of the method to mitigate the impact of energy leakage from the calorimeter is also demonstrated., Comment: Prepared for submission to JINST

We study the importance of precise modelling of the photometric redshift error distributions on the estimation of parameters from cross correlation measurements and present a working example of the scattering matrix formalism to correct for the redshift bin mismatch of objects in tomographic cross correlation analysis. We measured the angular galaxy auto-power spectrum and cross-power spectrum in four tomographic bins with redshift intervals $z = [0.0,0.3,0.45,0.6,0.8]$ from the cross correlation of Planck Cosmic Microwave Background lensing potential and photometric galaxy catalogue from the Dark Energy Spectroscopic Instrument Legacy Imaging Survey Data Release 8. We estimated galaxy linear bias and amplitude of cross correlation using maximum likelihood estimation to put constraints on the $\sigma_{8}$ parameter. We show that the modified Lorentzian function used to fit the photometric redshift error distribution performs well only near the peaks of the distribution. We adopt a sum of Gaussians model to capture the broad tails of the error distribution. Our sum of Gaussians model yields $\sim 2-5\,\sigma$ smaller values of cross correlation amplitude compared to the $\Lambda$CDM expectations. We compute the $\sigma_{8}$ parameter after correcting for the redshift bin mismatch of objects following the scattering matrix approach. The $\sigma_{8}$ parameter becomes consistent with $\Lambda$CDM model in the last tomographic bin but shows $\sim 1-3\,\sigma$ tension in other redshift bins., Comment: 20 pages, 17 figures, 4 tables, published in Astronomy and Astrophysics

Recent advancements in LLMs have shown their significant potential in tasks like text summarization and generation. Yet, they often encounter difficulty while solving complex physics problems that require arithmetic calculation and a good understanding of concepts. Moreover, many physics problems include images that contain important details required to understand the problem's context. We propose an LMM-based chatbot to answer multimodal physics MCQs. For domain adaptation, we utilize the MM-PhyQA dataset comprising Indian high school-level multimodal physics problems. To improve the LMM's performance, we experiment with two techniques, RLHF (Reinforcement Learning from Human Feedback) and Image Captioning. In image captioning, we add a detailed explanation of the diagram in each image, minimizing hallucinations and image processing errors. We further explore the integration of Reinforcement Learning from Human Feedback (RLHF) methodology inspired by the ranking approach in RLHF to enhance the human-like problem-solving abilities of the models. The RLHF approach incorporates human feedback into the learning process of LLMs, improving the model's problem-solving skills, truthfulness, and reasoning capabilities, minimizing the hallucinations in the answers, and improving the quality instead of using vanilla-supervised fine-tuned models. We employ the LLaVA open-source model to answer multimodal physics MCQs and compare the performance with and without using RLHF.

While Large Language Models (LLMs) can achieve human-level performance in various tasks, they continue to face challenges when it comes to effectively tackling multi-step physics reasoning tasks. To identify the shortcomings of existing models and facilitate further research in this area, we curated a novel dataset, MM-PhyQA, which comprises well-constructed, high schoollevel multimodal physics problems. By evaluating the performance of contemporary LLMs that are publicly available, both with and without the incorporation of multimodal elements in these problems, we aim to shed light on their capabilities. For generating answers for questions consisting of multimodal input (in this case, images and text) we employed Zero-shot prediction using GPT-4 and utilized LLaVA (LLaVA and LLaVA-1.5), the latter of which were fine-tuned on our dataset. For evaluating the performance of LLMs consisting solely of textual input, we tested the performance of the base and fine-tuned versions of the Mistral-7B and LLaMA2-7b models. We also showcased the performance of the novel Multi-Image Chain-of-Thought (MI-CoT) Prompting technique, which when used to train LLaVA-1.5 13b yielded the best results when tested on our dataset, with superior scores in most metrics and the highest accuracy of 71.65% on the test set.

Empirical studies of the relationship between baryonic matter in galaxies and the gravitational potential of their host halos are important to constrain our theoretical framework for galaxy formation and evolution. One such relation, between the atomic hydrogen (HI) mass of central galaxies ($M_{\rm{HI,c}}$) and the total mass of their host halos ($M_{\rm{halo}}$), has attracted significant interest in the last few years. In this work, we use the extended GALEX Arecibo SDSS Survey to examine the scatter of the HI-halo mass relation for a representative sample of central galaxies. Our findings reveal a flat median relation at $\rm{log}_{10}$$(M_{\rm{HI,c}}/\rm{M}_{\odot}) \approx 9.40$, across $11.1 < \rm{log}_{10}$$(M_{\rm{halo}}/\rm{M_{\odot}}) < 14.1$. This flat relation stems from the statistical dominance of star-forming, disc galaxies at low $M_{\rm{halo}}$ in combination with the increasing prevalence of passive, high stellar-concentration systems at higher $M_{\rm{halo}}$. The scatter of this relation and the stellar specific angular momentum of centrals have a strong link (Spearman's rank correlation coefficient $\geq 0.5$). Comparisons with simulations suggest that the kinematic state of host halos may be primarily driving this scatter. Our findings highlight that the HI-halo mass parameter space is too complex to be completely represented by simple median or average relations and we show that tensions with previous works are most likely due to selection biases. We recommend that future observational studies, and their comparisons with theoretical models, bin central galaxies also by their secondary properties to enable a statistically robust understanding of the processes regulating the cold gas content within central galaxies of dark-matter halos., Comment: 11 pages, 6 figures (4 additional figures in appendix)

Reference resolution is an important problem, one that is essential to understand and successfully handle context of different kinds. This context includes both previous turns and context that pertains to non-conversational entities, such as entities on the user's screen or those running in the background. While LLMs have been shown to be extremely powerful for a variety of tasks, their use in reference resolution, particularly for non-conversational entities, remains underutilized. This paper demonstrates how LLMs can be used to create an extremely effective system to resolve references of various types, by showing how reference resolution can be converted into a language modeling problem, despite involving forms of entities like those on screen that are not traditionally conducive to being reduced to a text-only modality. We demonstrate large improvements over an existing system with similar functionality across different types of references, with our smallest model obtaining absolute gains of over 5% for on-screen references. We also benchmark against GPT-3.5 and GPT-4, with our smallest model achieving performance comparable to that of GPT-4, and our larger models substantially outperforming it., Comment: Accepted at SIGDIAL 2024 (Oral presentation)

In this paper, we investigate residual finiteness and subquandle separability of quandles. The existence of these finiteness properties implies the solvability of the word problem and the generalised word problem for quandles. We prove that the fundamental $n$-quandle of any link in the 3-sphere is residually finite for each $n \ge 2$. This supplements the recent result on residual finiteness of link quandles and the classification of links whose fundamental $n$-quandles are finite for some $n$. We also establish several general results on these finiteness properties and give many families of quandles admitting them., Comment: 16 pages, comments are welcomed

The paper presents a new approach of stability evaluation of the approximate Riemann solvers based on the direct Lyapunov method. The present methodology offers a detailed understanding of the origins of numerical shock instability in the approximate Riemann solvers. The pressure perturbation feeding the density and transverse momentum perturbations is identified as the cause of the numerical shock instabilities in the complete approximate Riemann solvers, while the magnitude of the numerical shock instabilities are found to be proportional to the magnitude of the pressure perturbations. A shock-stable HLLEM scheme is proposed based on the insights obtained from this analysis about the origins of numerical shock instability in the approximate Riemann solvers. A set of numerical test cases are solved to show that the proposed scheme is free from numerical shock instability problems of the original HLLEM scheme at high Mach numbers., Comment: arXiv admin note: text overlap with arXiv:2207.06830

We present a comprehensive analysis of the detailed chemical abundances for a sample of 11 metal-poor, very metal-poor and extremely metal-poor stars ([Fe/H] = -1.65 to [Fe/H] = -3.0) as part of the HESP-GOMPA (Galactic survey Of Metal Poor stArs) survey. The abundance determinations encompass a range of elements, including C, Na, Mg, Al, Si, Ca, Sc, Ti, Cr, Mn, Fe, Co, Ni, Cu, Zn, Sr, and Ba, with a subset of the brighter objects allowing for the measurement of additional key elements. Notably, the abundance analysis of a relatively bright highly r-process-enhanced (r-II) star (SDSS J0019+3141) exhibits a predominantly main r-process signature and variations in the lighter r-process elements. Moreover, successful measurements of thorium in this star facilitate stellar age determinations. We find a consistent odd-even nucleosynthesis pattern in these stars, aligning with expectations for their respective metallicity levels, thus implicating Type II supernovae as potential progenitors. From the interplay between the light and heavy r-process elements, we infer a diminishing relative production of light r-process elements with increasing Type II supernova contributions, challenging the notion that Type II supernovae are the primary source of these light r-process elements in the early Milky Way. A chemodynamical analysis based on Gaia astrometric data and our derived abundances indicates that all but one of our program stars are likely to be of accreted origin. Additionally, our examination of alpha-poor stars underscores the occurrence of an early accretion event from a satellite on a prograde orbit, similar to that of the Galactic disc., Comment: 22 pages, 12 figures, Accepted for publication in MNRAS

Chest X-ray is a commonly used tool during triage, diagnosis and management of respiratory diseases. In resource-constricted settings, optimizing this resource can lead to valuable cost savings for the health care system and the patients as well as to and improvement in consult time. We used prospectively-collected data from 137 patients referred for chest X-ray at the Christian Medical Center and Hospital (CMCH) in Purnia, Bihar, India. Each patient provided at least five coughs while awaiting radiography. Collected cough sounds were analyzed using acoustic AI methods. Cross-validation was done on temporal and spectral features on the cough sounds of each patient. Features were summarized using standard statistical approaches. Three models were developed, tested and compared in their capacity to predict an abnormal result in the chest X-ray. All three methods yielded models that could discriminate to some extent between normal and abnormal with the logistic regression performing best with an area under the receiver operating characteristic curves ranging from 0.7 to 0.78. Despite limitations and its relatively small sample size, this study shows that AI-enabled algorithms can use cough sounds to predict which individuals presenting for chest radiographic examination will have a normal or abnormal results. These results call for expanding this research given the potential optimization of limited health care resources in low- and middle-income countries.

A quandle equipped with a good involution is referred to as symmetric. It is known that the cohomology of symmetric quandles gives rise to strong cocycle invariants for classical and surface links, even when they are not necessarily oriented. In this paper, we introduce the category of symmetric quandle modules and prove that these modules completely determine the Beck modules in the category of symmetric quandles. Consequently, this establishes suitable coefficient objects for constructing appropriate (co)homology theories. We develop an extension theory of modules over symmetric quandles and propose a generalized (co)homology theory for symmetric quandles with coefficients in a homogeneous Beck module, which also recovers the symmetric quandle (co)homology developed by Kamada and Oshiro [Trans. Amer. Math. Soc. (2010)]. Our constructions also apply to symmetric racks. We conclude by establishing an explicit isomorphism between the second cohomology of a symmetric quandle and the first cohomology of its associated group., Comment: 30 pages

In this paper, we prove super-polynomial lower bounds for the model of \emph{sum of ordered set-multilinear algebraic branching programs}, each with a possibly different ordering ($\sum \mathsf{smABP}$). Specifically, we give an explicit $nd$-variate polynomial of degree $d$ such that any $\sum \mathsf{smABP}$ computing it must have size $n^{\omega(1)}$ for $d$ as low as $\omega(\log n)$. Notably, this constitutes the first such lower bound in the low degree regime. Moreover, for $d = \poly(n)$, we demonstrate an exponential lower bound. This result generalizes the seminal work of Nisan (STOC, 1991), which proved an exponential lower bound for a single ordered set-multilinear ABP. The significance of our lower bounds is underscored by the recent work of Bhargav, Dwivedi, and Saxena (to appear in TAMC, 2024), which showed that super-polynomial lower bounds against a sum of ordered set-multilinear branching programs -- for a polynomial of sufficiently low degree -- would imply super-polynomial lower bounds against general ABPs, thereby resolving Valiant's longstanding conjecture that the permanent polynomial can not be computed efficiently by ABPs. More precisely, their work shows that if one could obtain such lower bounds when the degree is bounded by $O(\log n/ \log \log n)$, then it would imply super-polynomial lower bounds against general ABPs. Our results strengthen the works of Arvind \& Raja (Chic. J. Theor. Comput. Sci., 2016) and Bhargav, Dwivedi \& Saxena (to appear in TAMC, 2024), as well as the works of Ramya \& Rao (Theor. Comput. Sci., 2020) and Ghoshal \& Rao (International Computer Science Symposium in Russia, 2021), each of which established lower bounds for related or restricted versions of this model. They also strongly answer a question from the former two, which asked to prove super-polynomial lower bounds for general $\sum \mathsf{smABP}$.

Upcoming surveys of the large-scale structure of our Universe will employ a large coverage area of about half of the sky and will significantly increase the observational depth. With these surveys, we will be able to cross-correlate CMB gravitational lensing and galaxy surveys divided into narrow redshift bins to map the evolution of the cosmological parameters with redshift. In this paper, we study the effect of the redshift bin mismatch of objects that is due to photometric redshift errors in tomographic cross-correlation measurements. We used the code FLASK to create Monte Carlo simulations of the Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST) and Planck CMB lensing convergence. We simulated log-normal fields and divided galaxies into nine redshift bins with the Gaussian and modified Lorentzian photometric redshift errors. To estimate the parameters, we used angular power spectra of CMB lensing and galaxy density contrast fields and the maximum likelihood estimation method. We show that even with simple Gaussian errors with a standard deviation of $\sigma(z)=0.02(1+z)$, the galaxy auto-power spectra in tomographic bins are offset by $2-15\%$. The estimated cross-power spectra between galaxy clustering and CMB lensing are also biased, with smaller deviations $<5\%$. As a result, the $\sigma_{8}$ parameter deviates between $0.2-1.2\,\sigma$ due to the redshift bin mismatch of the objects. We propose a computationally fast and robust method based on the scattering matrix approach of Zhang et al. (2010), to correct for the redshift bin mismatch of the objects. The estimates of the parameters in tomographic studies such as the linear galaxy bias, the cross-correlation amplitude, and $\sigma_{8}$ are biased due to the redshift bin mismatch of the objects. The biases in these parameters are alleviated with our scattering matrix approach., Comment: 25 pages, 26 figures, 4 tables, accepted for publication in A&A journal

A detailed study of stellar populations in Milky Way (MW) satellite galaxies remains an observational challenge due to their faintness and fewer spectroscopically confirmed member stars. We use unsupervised machine learning methods to identify new members for nine nearby MW satellite galaxies using Gaia data release-3 (Gaia DR3) astrometry and the Dark Energy Survey (DES) and the DECam Local Volume Exploration Survey (DELVE) photometry. Two density-based clustering algorithms, DBSCAN and HDBSCAN, have been used in the four-dimensional astrometric parameter space to identify member stars belonging to MW satellite galaxies. Our results indicate that we can recover more than 80% of the known spectroscopically confirmed members in most of the satellite galaxies and also reject 95-100% of spectroscopic non-members. We have also added many new members using this method. We compare our results with previous studies that also use photometric and astrometric data and discuss the suitability of density-based clustering methods for MW satellite galaxies

Autism Spectrum Disorder (ASD) involves diverse neurodevelopmental syndromes with significant deficits in communication, motor behaviours, emotional and social comprehension. Often, individuals with ASD exhibit comorbid conditions, one of the most prevalent being depression characterized by a persistent change in mood and diminished interest in previously enjoyable activities. Due to communicative challenges and lack of appropriate assessments in individuals with ASD, comorbid depression can often go undiagnosed during routine clinical examinations, which may aggravate their problems. The current literature on comorbid depression in adults with ASD is limited. Therefore, understanding the neural basis of the comorbid psychopathology of depression in ASD is crucial for identifying objective brain-based markers for its timely and effective management. Towards this end, using structural MRI and phenotypic data from the Autism Brain Imaging Data Exchange II (ABIDE II) repository, we specifically examined the pattern of relationship regional grey matter volume (rGMV) has with comorbid depression and autism severity within regions of a priori interest in adults with ASD (n = 44). The severity of comorbid depression correlated negatively with the rGMV of the right thalamus. Additionally, a significant interaction was evident between the severity of comorbid depression and core ASD symptoms towards explaining the rGMV in the left cerebellum crus II. The whole-brain regional rGMV differences between ASD and typically developed (TD, n = 39) adults remained inconclusive. The results further the understanding of the neurobiological underpinnings of comorbid depression in adults with ASD and are relevant in exploring structural neuroimaging-based biomarkers in the same cohort., Comment: 33 pages, 3 figures, 3 tables, journal submission

In this note, we give very simple constructions of unique neighbor expander graphs starting from spectral or combinatorial expander graphs of mild expansion. These constructions and their analysis are simple variants of the constructions of LDPC error-correcting codes from expanders, given by Sipser-Spielman [SS96] (and Tanner [Tan81]), and their analysis. We also show how to obtain expanders with many unique neighbors using similar ideas. There were many exciting results on this topic recently, starting with Asherov-Dinur [AD23] and Hsieh-McKenzie-Mohanty-Paredes [HMMP23], who gave a similar construction of unique neighbor expander graphs, but using more sophisticated ingredients (such as almost-Ramanujan graphs) and a more involved analysis. Subsequent beautiful works of Cohen-Roth-TaShma [CRT23] and Golowich [Gol23] gave even stronger objects (lossless expanders), but also using sophisticated ingredients. The main contribution of this work is that we get much more elementary constructions of unique neighbor expanders and with a simpler analysis., Comment: Updated introduction, corrected minor typos

BaNi$_2$As$_2$ is a structural analog of the pnictide superconductor BaFe$_2$As$_2$, which, like the iron-based superconductors, hosts a variety of ordered phases including charge density waves (CDWs), electronic nematicity, and superconductivity. Upon isovalent Sr substitution on the Ba site, the charge and nematic orders are suppressed, followed by a sixfold enhancement of the superconducting transition temperature ($T_c$). To understand the mechanisms responsible for enhancement of $T_c$, we present high-resolution angle-resolved photoemission spectroscopy (ARPES) measurements of the Ba$_{1-x}$Sr$_{x}$Ni$_2$As$_2$ series, which agree well with our density functional theory (DFT) calculations throughout the substitution range. Analysis of our ARPES-validated DFT results indicates a Lifshitz transition and reasonably nested electron and hole Fermi pockets near optimal substitution where $T_c$ is maximum. These nested pockets host Ni $d_{xz}$/$d_{yz}$ orbital compositions, which we associate with the enhancement of nematic fluctuations, revealing unexpected connections to the iron-pnictide superconductors. This gives credence to a scenario in which nematic fluctuations drive an enhanced $T_c$., Comment: 19 pages, 12 figures, 1 table

Everyone puts things off sometimes. How can we combat this tendency to procrastinate? A well-known technique used by instructors is to break up a large project into more manageable chunks. But how should this be done best? Here we study the process of chunking using the graph-theoretic model of present bias introduced by Kleinberg and Oren (2014). We first analyze how to optimally chunk single edges within a task graph, given a limited number of chunks. We show that for edges on the shortest path, the optimal chunking makes initial chunks easy and later chunks progressively harder. For edges not on the shortest path, optimal chunking is significantly more complex, but we provide an efficient algorithm that chunks the edge optimally. We then use our optimal edge-chunking algorithm to optimally chunk task graphs. We show that with a linear number of chunks on each edge, the biased agent's cost can be exponentially lowered, to within a constant factor of the true cheapest path. Finally, we extend our model to the case where a task designer must chunk a graph for multiple types of agents simultaneously. The problem grows significantly more complex with even two types of agents, but we provide optimal graph chunking algorithms for two types. Our work highlights the efficacy of chunking as a means to combat present bias., Comment: Published in Economics and Computation 2023

Video matting has broad applications, from adding interesting effects to casually captured movies to assisting video production professionals. Matting with associated effects such as shadows and reflections has also attracted increasing research activity, and methods like Omnimatte have been proposed to separate dynamic foreground objects of interest into their own layers. However, prior works represent video backgrounds as 2D image layers, limiting their capacity to express more complicated scenes, thus hindering application to real-world videos. In this paper, we propose a novel video matting method, OmnimatteRF, that combines dynamic 2D foreground layers and a 3D background model. The 2D layers preserve the details of the subjects, while the 3D background robustly reconstructs scenes in real-world videos. Extensive experiments demonstrate that our method reconstructs scenes with better quality on various videos., Comment: ICCV 2023. Project page: https://omnimatte-rf.github.io/