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In this paper, we study the inverse source problem for the biharmonic wave equation. Mathematically, we characterize the radiating sources and non-radiating sources at a fixed wavenumber. We show that a general source can be decomposed into a radiating source and a non-radiating source. The radiating source can be uniquely determined by Dirichlet boundary measurements at a fixed wavenumber. Moreover, we derive a Lipschitz stability estimate for determining the radiating source. On the other hand, the non-radiating source does not produce any scattered fields outside the support of the source function. Numerically, we propose a novel source reconstruction method based on Fourier series expansion by multi-wavenumber boundary measurements. Numerical experiments are presented to verify the accuracy and efficiency of the proposed method.

Transformer-based large-scale language models (LLMs) are able to generate highly realistic text. They are duly able to express, and at least implicitly represent, a wide range of sentiments and color, from the obvious, such as valence and arousal to the subtle, such as determination and admiration. We provide a first exploration of these representations and how they can be used for understanding the inner sentimental workings of single sentences. We train predictors of the quantiles of the distributions of final sentiments of sentences from the hidden representations of an LLM applied to prefixes of increasing lengths. After showing that predictors of distributions of valence, determination, admiration, anxiety and annoyance are well calibrated, we provide examples of using these predictors for analyzing sentences, illustrating, for instance, how even ordinary conjunctions (e.g., "but") can dramatically alter the emotional trajectory of an utterance. We then show how to exploit the distributional predictions to generate sentences with sentiments in the tails of distributions. We discuss the implications of our results for the inner workings of thoughts, for instance for psychiatric dysfunction.

Large Language Models work quite well with general-purpose data and many tasks in Natural Language Processing. However, they show several limitations when used for a task such as domain-specific abstractive text summarization. This paper identifies three of those limitations as research problems in the context of abstractive text summarization: 1) Quadratic complexity of transformer-based models with respect to the input text length; 2) Model Hallucination, which is a model's ability to generate factually incorrect text; and 3) Domain Shift, which happens when the distribution of the model's training and test corpus is not the same. Along with a discussion of the open research questions, this paper also provides an assessment of existing state-of-the-art techniques relevant to domain-specific text summarization to address the research gaps.

Bike sharing systems have been widely deployed around the world in recent years. A core problem in such systems is to reposition the bikes so that the distribution of bike supply is reshaped to better match the dynamic bike demand. When the bike-sharing company or platform is able to predict the revenue of each reposition task based on historic data, an additional constraint is to cap the payment for each task below its predicted revenue. In this paper, we propose an incentive mechanism called {\em TruPreTar} to incentivize users to park bicycles at locations desired by the platform toward rebalancing supply and demand. TruPreTar possesses four important economic and computational properties such as truthfulness and budget feasibility. Furthermore, we prove that even when the payment budget is tight, the total revenue still exceeds or equals the budget. Otherwise, TruPreTar achieves 2-approximation as compared to the optimal (revenue-maximizing) solution, which is close to the lower bound of at least $\sqrt{2}$ that we also prove. Using an industrial dataset obtained from a large bike-sharing company, our experiments show that TruPreTar is effective in rebalancing bike supply and demand and, as a result, generates high revenue that outperforms several benchmark mechanisms.

Multi-objective recommender systems (MORS) provide suggestions to users according to multiple (and possibly conflicting) goals. When a system optimizes its results at the individual-user level, it tailors them on a user's propensity towards the different objectives. Hence, the capability to understand users' fine-grained needs towards each goal is crucial. In this paper, we present the results of a user study in which we monitored the way users interacted with recommended items, as well as their self-proclaimed propensities towards relevance, novelty and diversity objectives. The study was divided into several sessions, where users evaluated recommendation lists originating from a relevance-only single-objective baseline as well as MORS. We show that despite MORS-based recommendations attracted less selections, its presence in the early sessions is crucial for users' satisfaction in the later stages. Surprisingly, the self-proclaimed willingness of users to interact with novel and diverse items is not always reflected in the recommendations they accept. Post-study questionnaires provide insights on how to deal with this matter, suggesting that MORS-based results should be accompanied by elements that allow users to understand the recommendations, so as to facilitate their acceptance.

In this paper, we propose a Dimension-Reduced Second-Order Method (DRSOM) for convex and nonconvex (unconstrained) optimization. Under a trust-region-like framework, our method preserves the convergence of the second-order method while using only curvature information in a few directions. Consequently, the computational overhead of our method remains comparable to the first-order such as the gradient descent method. Theoretically, we show that the method has a local quadratic convergence and a global convergence rate of $O(\epsilon^{-3/2})$ to satisfy the first-order and second-order conditions if the subspace satisfies a commonly adopted approximated Hessian assumption. We further show that this assumption can be removed if we perform a corrector step using a Krylov-like method periodically at the end stage of the algorithm. The applicability and performance of DRSOM are exhibited by various computational experiments, including $L_2 - L_p$ minimization, CUTEst problems, and sensor network localization.

While evolutionary computation is well suited for automatic discovery in engineering, it can also be used to gain insight into how humans and organizations could perform more effectively. Using a real-world problem of innovation search in organizations as the motivating example, this article first formalizes human creative problem solving as competitive multi-agent search (CMAS). CMAS is different from existing single-agent and team search problems in that the agents interact through knowledge of other agents' searches and through the dynamic changes in the search landscape that result from these searches. The main hypothesis is that evolutionary computation can be used to discover effective strategies for CMAS; this hypothesis is verified in a series of experiments on the NK model, i.e.\ partially correlated and tunably rugged fitness landscapes. Different specialized strategies are evolved for each different competitive environment, and also general strategies that perform well across environments. These strategies are more effective and more complex than hand-designed strategies and a strategy based on traditional tree search. Using a novel spherical visualization of such landscapes, insight is gained about how successful strategies work, e.g.\ by tracking positive changes in the landscape. The article thus provides a possible framework for studying various human creative activities as competitive multi-agent search in the future.

Starlink constellations are currently the largest LEO WAN and have seen considerable interest from the research community. In this paper, we use high-frequency and high-fidelity measurements to uncover evidence of hierarchical traffic controllers in Starlink -- a global controller which allocates satellites to terminals and an on-satellite controller that schedules transmission of user flows. We then devise a novel approach for identifying how satellites are allocated to user terminals. Using data gathered with this approach, we measure the characteristics of the global controller and identify the factors that influence the allocation of satellites to terminals. Finally, we use this data to build a model which approximates Starlink's global scheduler. Our model is able to predict the characteristics of the satellite allocated to a terminal at a specific location and time with reasonably high accuracy and at a rate significantly higher than baseline.

The unprecedented growth in DNN model complexity, size, and amount of training data has led to a commensurate increase in demand for computing and a search for minimal encoding. Recent research advocates Hybrid Block Floating Point (HBFP) to minimize silicon provisioning in accelerators by converting the majority of arithmetic operations in training to 8-bit fixed point. In this paper, we perform a full-scale exploration of the HBFP design space using mathematical tools to study the interplay among various parameters and identify opportunities for even smaller encodings across layers and epochs. Based on our findings, we propose Accuracy Boosters, an epoch-driven mixed-mantissa HBFP technique that uses 6-bit mantissas only in the last epoch and first/last layers, and 4-bit mantissas for $99.7\%$ of all other arithmetic operations in training. Using analytic models, we show Accuracy Boosters enable increasing arithmetic density for an HBFP training accelerator by up to $21.3\times$ compared to FP32 and up to $4.4\times$ compared to another SOTA format Bfloat16, while preserving or outperforming FP32 accuracy.

Audio source separation is often achieved by estimating the magnitude spectrogram of each source, and then applying a phase recovery (or spectrogram inversion) algorithm to retrieve time-domain signals. Typically, spectrogram inversion is treated as an optimization problem involving one or several terms in order to promote estimates that comply with a consistency property, a mixing constraint, and/or a target magnitude objective. Nonetheless, it is still unclear which set of constraints and problem formulation is the most appropriate in practice. In this paper, we design a general framework for deriving spectrogram inversion algorithm, which is based on formulating optimization problems by combining these objectives either as soft penalties or hard constraints. We solve these by means of algorithms that perform alternating projections on the subsets corresponding to each objective/constraint. Our framework encompasses existing techniques from the literature as well as novel algorithms. We investigate the potential of these approaches for a speech enhancement task. In particular, one of our novel algorithms outperforms other approaches in a realistic setting where the magnitudes are estimated beforehand using a neural network.