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In this paper, we study a slightly different definition of popularity in bipartite graphs $G=(U,W,E)$ with two-sided preferences, when ties are present in the preference lists. This is motivated by the observation that if an agent $u$ is indifferent between his original partner $w$ in matching $M$ and his new partner $w'\ne w$ in matching $N$, then he may probably still prefer to stay with his original partner, as change requires effort, so he votes for $M$ in this case, instead of being indifferent. We show that this alternative definition of popularity, which we call weak-popularity allows us to guarantee the existence of such a matching and also to find a weakly-popular matching in polynomial-time that has size at least $\frac{3}{4}$ the size of the maximum weakly popular matching. We also show that this matching is at least $\frac{4}{5}$ times the size of the maximum (weakly) stable matching, so may provide a more desirable solution than the current best (and tight under certain assumptions) $\frac{2}{3}$-approximation for such a stable matching. We also show that unfortunately, finding a maximum size weakly popular matching is NP-hard, even with one-sided ties and that assuming some complexity theoretic assumptions, the $\frac{3}{4}$-approximation bound is tight. Then, we study a more general model than weak-popularity, where for each edge, we can specify independently for both endpoints the size of improvement the endpoint needs to vote in favor of a new matching $N$. We show that even in this more general model, a so-called $\gamma$-popular matching always exists and that the same positive results still hold. Finally, we define an other, stronger variant of popularity, called super-popularity, where even a weak improvement is enough to vote in favor of a new matching. We show that for this case, even the existence problem is NP-hard.

In this work, we prove over 3000 previously ATP-unproved Mizar/MPTP problems by using several ATP and AI methods, raising the number of ATP-solved Mizar problems from 75\% to above 80\%. First, we start to experiment with the cvc5 SMT solver which uses several instantiation-based heuristics that differ from the superposition-based systems, that were previously applied to Mizar,and add many new solutions. Then we use automated strategy invention to develop cvc5 strategies that largely improve cvc5's performance on the hard problems. In particular, the best invented strategy solves over 14\% more problems than the best previously available cvc5 strategy. We also show that different clausification methods have a high impact on such instantiation-based methods, again producing many new solutions. In total, the methods solve 3021 (21.3\%) of the 14163 previously unsolved hard Mizar problems. This is a new milestone over the Mizar large-theory benchmark and a large strengthening of the hammer methods for Mizar.

This paper introduces a universal approach to seamlessly combine out-of-distribution (OOD) detection scores. These scores encompass a wide range of techniques that leverage the self-confidence of deep learning models and the anomalous behavior of features in the latent space. Not surprisingly, combining such a varied population using simple statistics proves inadequate. To overcome this challenge, we propose a quantile normalization to map these scores into p-values, effectively framing the problem into a multi-variate hypothesis test. Then, we combine these tests using established meta-analysis tools, resulting in a more effective detector with consolidated decision boundaries. Furthermore, we create a probabilistic interpretable criterion by mapping the final statistics into a distribution with known parameters. Through empirical investigation, we explore different types of shifts, each exerting varying degrees of impact on data. Our results demonstrate that our approach significantly improves overall robustness and performance across diverse OOD detection scenarios. Notably, our framework is easily extensible for future developments in detection scores and stands as the first to combine decision boundaries in this context. The code and artifacts associated with this work are publicly available\footnote{\url{//github.com/edadaltocg/detectors}}.

In this paper, we focus on addressing the constraints faced when applying LLMs to ASR. Recent works utilize prefixLM-type models, which directly apply speech as a prefix to LLMs for ASR. We have found that optimizing speech prefixes leads to better ASR performance and propose applying RNNT loss to perform speech prefix-tuning. This is a simple approach and does not increase the model complexity or alter the inference pipeline. We also propose language-based soft prompting to further improve with frozen LLMs. Empirical analysis on realtime testset from 10 Indic languages demonstrate that our proposed speech prefix-tuning yields improvements with both frozen and fine-tuned LLMs. Our recognition results on an average of 10 Indics show that the proposed prefix-tuning with RNNT loss results in a 12\% relative improvement in WER over the baseline with a fine-tuned LLM. Our proposed approches with the frozen LLM leads to a 31\% relative improvement over basic soft-prompting prefixLM.

In this work, we design and analyze an asymptotic preserving (AP), semi-implicit finite volume scheme for the scaled compressible isentropic Euler system with a singular pressure law known as the congestion pressure law. The congestion pressure law imposes a maximal density constraint of the form $0\leq \varrho <1$, and the scaling introduces a small parameter $\varepsilon$ in order to control the stiffness of the density constraint. As $\varepsilon\to 0$, the solutions of the compressible system converge to solutions of the so-called free-congested Euler equations that couples compressible and incompressible dynamics. We show that the proposed scheme is positivity preserving and energy stable. In addition, we also show that the numerical densities satisfy a discrete variant of the constraint. By means of extensive numerical case studies, we verify the efficacy of the scheme and show that the scheme is able to capture the two dynamics in the limiting regime, thereby proving the AP property.

This paper introduces a "proof of concept" for a new approach to assistive robotics, integrating edge computing with Natural Language Processing (NLP) and computer vision to enhance the interaction between humans and robotic systems. Our "proof of concept" demonstrates the feasibility of using large language models (LLMs) and vision systems in tandem for interpreting and executing complex commands conveyed through natural language. This integration aims to improve the intuitiveness and accessibility of assistive robotic systems, making them more adaptable to the nuanced needs of users with disabilities. By leveraging the capabilities of edge computing, our system has the potential to minimize latency and support offline capability, enhancing the autonomy and responsiveness of assistive robots. Experimental results from our implementation on a robotic arm show promising outcomes in terms of accurate intent interpretation and object manipulation based on verbal commands. This research lays the groundwork for future developments in assistive robotics, focusing on creating highly responsive, user-centric systems that can significantly improve the quality of life for individuals with disabilities.

In this position paper, we explore the potential of generative AI (GenAI) tools in supporting HIV prevention initiatives among LGBTQ+ adolescents. GenAI offers opportunities to bridge information gaps and enhance healthcare access, yet it also risks exacerbating existing inequities through biased AI outputs reflecting heteronormative and cisnormative values. We advocate for the importance of queer adolescent-centered interventions, contend with the promise of GenAI tools while addressing concerns of bias, and position participatory frameworks for empowering queer youth in the design and development of AI tools. Viewing LGBTQ+ adolescents as designers, we propose a community-engaged approach to enable a group of queer teens with sexual health education expertise to design their own GenAI health tools. Through this collaborative effort, we put forward participatory ways to develop processes minimizing the potential iatrogenic harms of biased AI models, while harnessing AI benefits for LGBTQ+ teens. In this workshop, we offer specialized community-engaged knowledge in designing equitable AI tools to improve LGBTQ+ well-being.

In this paper, we extend the Generalized Moving Least-Squares (GMLS) method in two different ways to solve the vector-valued PDEs on unknown smooth 2D manifolds without boundaries embedded in $\mathbb{R}^{3}$, identified with randomly sampled point cloud data. The two approaches are referred to as the intrinsic method and the extrinsic method. For the intrinsic method which relies on local approximations of metric tensors, we simplify the formula of Laplacians and covariant derivatives acting on vector fields at the base point by calculating them in a local Monge coordinate system. On the other hand, the extrinsic method formulates tangential derivatives on a submanifold as the projection of the directional derivative in the ambient Euclidean space onto the tangent space of the submanifold. One challenge of this method is that the discretization of vector Laplacians yields a matrix whose size relies on the ambient dimension. To overcome this issue, we reduce the dimension of vector Laplacian matrices by employing an appropriate projection. The complexity of both methods scales well with the dimension of manifolds rather than the ambient dimension. We also present supporting numerical examples, including eigenvalue problems, linear Poisson equations, and nonlinear Burgers' equations, to examine the numerical accuracy of proposed methods on various smooth manifolds.

This paper investigates the information theoretic limit of a reconfigurable intelligent surface (RIS) aided communication scenario in which the RIS and the transmitter either jointly or independently send information to the receiver. The RIS is an emerging technology that uses a large number of passive reflective elements with adjustable phases to intelligently reflect the transmit signal to the intended receiver. While most previous studies of the RIS focus on its ability to beamform and to boost the received signal-to-noise ratio (SNR), this paper shows that if the information data stream is also available at the RIS and can be modulated through the adjustable phases at the RIS, significant improvement in the {degree-of-freedom} (DoF) of the overall channel is possible. For example, for an RIS system in which the signals are reflected from a transmitter with $M$ antennas to a receiver with $K$ antennas through an RIS with $N$ reflective elements, assuming no direct path between the transmitter and the receiver, joint transmission of the transmitter and the RIS can achieve a DoF of $\min\left(M+\frac{N}{2}-\frac{1}{2},N,K\right)$ as compared to the DoF of $\min(M,K)$ for the conventional multiple-input multiple-output (MIMO) channel. This result is obtained by establishing a connection between the RIS system and the MIMO channel with phase noise and by using results for characterizing the information dimension under projection. The result is further extended to the case with a direct path between the transmitter and the receiver, and also to the multiple access scenario, in which the transmitter and the RIS send independent information. Finally, this paper proposes a symbol-level precoding approach for modulating data through the phases of the RIS, and provides numerical simulation results to verify the theoretical DoF results.

In this paper, we investigate the impact of reward schemes and committee sizes motivated by governance systems over blockchain communities. We introduce a model for elections with a binary outcome space where there is a ground truth (i.e., a "correct" outcome), and where stakeholders can only choose to delegate their voting power to a set of delegation representatives (DReps). Moreover, the effort (cost) invested by each DRep positively influences both (i) her ability to vote correctly and (ii) the total delegation that she attracts, thereby increasing her voting power. This model constitutes the natural counterpart of delegated proof-of-stake (PoS) protocols, where delegated stakes are used to elect the block builders. As a way to motivate the representatives to exert effort, a reward scheme can be used based on the delegation attracted by each DRep. We analyze both the game-theoretic aspects and the optimization counterpart of this model. Our primary focus is on selecting a committee that maximizes the probability of reaching the correct outcome, given a fixed monetary budget allocated for rewarding the delegates. Our findings provide insights into the design of effective reward mechanisms and optimal committee structures (i.e., how many DReps are enough) in these PoS-like governance systems.