Recent research on Doeblin coefficients has shed light on their usefulness as a multi-way generalization of the Dobrushin contraction coefficient for TV distance, in a separate vein from their classic role in the theory of Markov chain ergodicity. However, strong conditions, such as being bounded away from 0, are typically necessary for Doeblin coefficients to establish the existence of information contraction. Building on recently formulated concepts of nonlinear information contraction, we aim to propose a finer-grained Doeblin-based characterization of multi-way contraction behavior which yields non-vacuous contraction guarantees even for channels whose Doeblin coefficient is 0. To this end, we introduce the notion of aDoeblin curve—a nonlinear function which quantifies the contraction behavior of a Markov kernel on collections of input distributions at specific levels of divergence and power. Through the course of our analysis, we develop a new variational characterization of Doeblin coefficients, present several properties of Doeblin curves, define several versions of power-constrained Doeblin curves, and derive upper and lower bounds using our aforementioned variational characterization. We then utilize these results in diverse areas, including generalization bounds for noisy iterative optimization, error bounds for reliable computation with noisy circuits, and differential privacy guarantees for online iterative algorithms. In particular, we extend results in these areas to broader domains or group settings, leveraging Doeblin curves to reveal finer-grained contraction phenomena than Doeblin coefficients.

Although standards of living are increasing rapidly worldwide, a considerable segment of the global population continues to live in poverty. Local governments and decision makers urgently need actionable fine-scale poverty maps to know the locations of the low income population for operational resource distribution. However, most existing studies focus on coarse-resolution poverty maps (e.g., county level) and offer limited information to help deliver the resources to the right locations. Moreover, coarse-resolution maps generated by machine learning models are often trained on higher-level economic statistics that have greater availability. However, such labels at the fine-scale remain very scarce, and existing maps are commonly based on household-level visits that are highly expensive and time-consuming, making them only available in a limited number of cities. We develop a cost-effective approach to tackle the challenge. First, we design a multi-view training data construction approach using data from both street views and very-high-resolution satellite images. Next, we integrate different types of foundation models including the general-purpose vision transformer ViT and the segmentation-focused SegFormer for training and map generation in new cities. Via the use of pretrained large models, the goal is to enhance the generalizability with a smaller amount of samples. To validate the approach, we carried out a case study in Ghana with the cities of Accra, Kumasi, and Tamale. The results showed the effectiveness of the cost-effective approach in capturing low-income areas with unique characteristics, and the foundation models also demonstrated enhanced ability in generalization with smaller training data sizes.

Designing effective positional encodings for graphs is key to building powerful graph transformers and enhancing message-passing graph neural networks. Although widespread, using Laplacian eigenvectors as positional encodings faces two fundamental challenges: (1) *Non-uniqueness*: there are many different eigendecompositions of the same Laplacian, and (2) *Instability*: small perturbations to the Laplacian could result in completely different eigenspaces, leading to unpredictable changes in positional encoding. Despite many attempts to address non-uniqueness, most methods overlook stability, leading to poor generalization on unseen graph structures. We identify the cause of instability to be the use of "hard partition'' of eigenspaces. Hence, we introduce Stable and Expressive Positional Encodings (SPE), an architecture for processing eigenvectors that uses eigenvalues to ``softly partition'' eigenspaces. SPE is the first architecture that is (1) provably stable, and (2) universally expressive for basis invariant functions whilst respecting all symmetries of eigenvectors. Besides guaranteed stability, we prove that SPE is at least as expressive as existing methods, and highly capable of counting graph structures. Finally, we evaluate the effectiveness of our method on molecular property prediction, and out-of-distribution generalization tasks, finding improved generalization compared to existing positional encoding methods. Our code is available at https://github.com/Graph-COM/SPE.

Permutation networks and multiple-access channels (MACs) are objects of interest in modern information theory which find application in modeling biological storage mechanisms and wireless communication systems. In this paper, we present two variations of the recently introduced permutation adder multiple-access channel (PAMAC), and characterize their respective permutation capacity regions as an initial step towards establishing such results for general MACs. Firstly, we define the left-permutation adder MAC by interchanging the order of the adder and random permutation blocks in the original PAMAC, causing each sender's codeword to be shuffled by a different random permutation. We show that multiset coding with Bernoulli samples is a viable achievability scheme under this structural modification by extending a root stability argument from the binary PAMAC literature to general p-ary alphabets. Separately from the above, we define the permutation group-adder MAC by replacing the integer addition block in the original PAMAC with a modular addition block over$\mathbb{Z}_{p}$. Our achievability proof in this setting crucially demonstrates that time sharing strategies based on mixed-radix coding naturally generalize to an array of permutation network models beyond the original PAMAC. Lastly, using Fano's inequality and manipulations of directed graphical models, we obtain converse bounds matching our achievability results, ultimately illustrating that subtle modifications to a permutation network model may bring about significant qualitative changes in its capacity region.

Doeblin coefficients are fundamental tools in the analysis of Markov chains for establishing ergodicity and exponential convergence rates. However, strong conditions, such as Doeblin coefficients being bounded away from 0, are typically required to yield useful convergence or information contraction guarantees. Our work aims to illuminate the contraction behavior of Markov kernels under more relaxed conditions, such as the case where Doeblin coefficients are 0. To do this, we introduce the notion of a Doeblin curve—a nonlinear function that quantifies the contraction behavior of a Markov kernel on a collection of input distributions. We develop new variational characterizations of Doeblin coefficients and use them to derive useful bounds on the Doeblin curve. In the course of this analysis, we present several properties of Doeblin curves and define power-constrained Doeblin curves. Furthermore, our analysis motivates a generalized definition of differential privacy in the group setting. We discuss this motivation and several properties of this definition to lay the groundwork for its application in future.

Point-to-point permutation channels are useful models of communication networks and biological storage mechanisms and have received theoretical attention in recent years. Propelled by relevant advances in this area, we analyze thepermutation adder multiple-access channel(PAMAC) in this work. In the PAMAC network model,dsenders communicate with a single receiver by transmittingp-ary codewords through an adder multiple-access channel whose output is subsequently shuffled by a random permutation block. We define a suitable notion ofpermutation capacity regionCpermfor this model, and establish thatCpermis the simplex consisting of all rated-tuples that sum tod(p- 1)/2 or less. We achieve this sum-rate by encoding messages as i.i.d. samples from categorical distributions with carefully chosen parameters, and we derive an inner bound onCpermby extending the concept of time sharing to the permutation channel setting. Our proof notably illuminates various connections between mixed-radix numerical systems and coding schemes for multiple-access channels. Furthermore, we derive an alternative inner bound onCpermfor the binary PAMAC by analyzing the root stability of the probability generating function of the adder’s output distribution. Using eigenvalue perturbation results, we obtain error bounds on the spectrum of the probability generating function’s companion matrix, providing quantitative estimates of decoding performance. Finally, we obtain a converse bound onCpermmatching our achievability result.

Propelled by recent advances in the study of point-to-point permutation channels, which stem from communication networks and biological communications applications, we analyze the permutation binary adder multiple-access channel (PAMAC) in this work. The PAMAC network model consists of d senders communicating with a single receiver through a standard binary adder multiple-access channel followed by a random permutation block that shuffles the output codeword of the multiple-access channel. We formally define an appropriate notion of permutation sum-capacity Cpsumfor this model, and then establish that ${{\text{C}}_{{\text{psum }}}} = \frac{d}{2}$. To derive an achievability bound we construct d randomized encoders where input codewords are i.i.d. samples from Bernoulli distributions with carefully chosen parameters. These parameters can be perceived as roots of the probability generating function of the distribution over the output alphabet after the PAMAC's addition operation. Our achievability proof crucially uses eigenvalue perturbation results to provide quantitative estimates on the stability of the roots, which allows us to analyze decoding performance. This argument also yields an inner bound on the permutation capacity region of the PAMAC model. Finally, we also obtain a converse bound on Cpsummatching our achievability result.

Monitoring of colonial waterbird nesting islands is essential to tracking waterbird population trends, which are used for evaluating ecosystem health and informing conservation management decisions. Recently, unmanned aerial vehicles, or drones, have emerged as a viable technology to precisely monitor waterbird colonies. However, manually counting waterbirds from hundreds, or potentially thousands, of aerial images is both difficult and time-consuming. In this work, we present a deep learning pipeline that can be used to precisely detect, count, and monitor waterbirds using aerial imagery collected by a commercial drone. By utilizing convolutional neural network-based object detectors, we show that we can detect 16 classes of waterbird species that are commonly found in colonial nesting islands along the Texas coast. Our experiments using Faster R-CNN and RetinaNet object detectors give mean interpolated average precision scores of 67.9% and 63.1% respectively.

Diverse links (i.e., wireless links, satellite links and ADSL links) are being widely deployed in current Internet, unlike wired links, these heterogeneous links are causing significant performance degradation of TCP. Recently one sender-side enhancement of TCP, called Veno TCP, is proposed to mainly eliminate TCP's suffering in wireless environments. Real network measurements and live Internet results validated Veno's throughput improvement and its harmonious co-existence with legacy TCP connections. In this paper, we revisit Veno TCP and evaluate its performance in more practical way. Specifically, we measure Veno from four metrics - compatibility, flexibility, robustness and deployablity. Our extensive arguments not only prove Veno's advantages, but also illuminate some basic philosophies behind Veno, which could provide helpful guidelines for future protocol design.