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Let $U/K$ be a smooth affine curve over a number field and let $L$ be an irreducible rank 3 $\overline{\mathbb Q}_{\ell}$-local system on $U$ with trivial determinant and infinite geometric monodromy around a cusp. Suppose further that $L$ extends to an integral model such that the Frobenius traces are contained in a fixed totally real number field. Then, after potentially shrinking $U$, there exists an abelian scheme $f\colon B_U\rightarrow U$ such that $L$ is a summand of $R^2f_*\overline{\mathbb Q}_{\ell}(1)$. The key ingredients are: (1) the totally real assumption implies $L$ admits a square root $M$; (2) the trace field of $M$ is sufficiently bounded, allowing us to use recent work of Krishnamoorthy-Yang-Zuo to construct an abelian scheme over $U_{\bar K}$ geometrically realizing $L$; and (3) Deligne's weight-monodromy theorem and the Rapoport-Zink spectral sequence, which allow us to pin down the arithmetizations using the total degeneration., Comment: 3 pages, comments welcome!

Diffusion of native defects such as vacancies and their interactions with impurities are fundamental in semiconductor crystal growth, device processing, and long-term aging of equilibration and transient diffusion of vacancies are rarely investigated. We used aluminum-gallium oxide/gallium oxide superlattices (SLs) to detect and analyze transient diffusion of cation vacancies during annealing in O2 at 1000-1100 C. Using a novel finite difference scheme for the diffusion equation with time- and space-varying diffusion constant, we extract diffusion constants for Al, Fe, and cation vacancies under the given conditions, including the vacancy concentration dependence for Al. indicate that vacancies present in the substrate transiently diffuse through the SLs, interacting with Sn as it also diffuses. In the case of SLs grown on Sn-doped beta-gallium oxide substrates, gradients observed in the extent of Al diffusion indicate that vacancies present in the substrate transiently diffuse through the SLs, interacting with Sn as it also diffuses. In the case of SLs grown on (010) Fe-doped substrates, the Al diffusion is uniform through the SLs, indicating a depth-uniform concentration of vacancies. We find no evidence in either case for the introduction of gallium vacancies from the free surface at rates sufficient to affect Al diffusion down to ppm concentrations, which has important bearing on the validity of typically-made assumptions of vacancy equilibration. Additionally, we show that unintentional impurities in Sn-doped gallium oxide such as Fe, Ni, Mn, Cu, and Li also diffuse towards the surface and accumulate. Many of these likely have fast interstitial diffusion modes capable of destabilizing devices over time, thus highlighting the importance of controlling unintentional impurities in beta-gallium oxide wafers., Comment: 11 pages, 4 figures, references a supplimental which will be submitted seperately

Let $F$ (over $\mathbb{Q}$) be a totally real number field of narrow class number $1$. We generalize a result of Kohnen on the determination of half integral weight modular forms by their Fourier coefficients supported on squarefree (algebraic) integers. We also give a soft proof that infinitely many Fourier coefficients supported on squarefree integers are non-vanishing., Comment: Comments and suggestions welcome

We study the problem of comparing a pair of geometric networks that may not be similarly defined, i.e., when they do not have one-to-one correspondences between their nodes and edges. Our motivating application is to compare power distribution networks of a region. Due to the lack of openly available power network datasets, researchers synthesize realistic networks resembling their actual counterparts. But the synthetic digital twins may vary significantly from one another and from actual networks due to varying underlying assumptions and approaches. Hence the user wants to evaluate the quality of networks in terms of their structural similarity to actual power networks. But the lack of correspondence between the networks renders most standard approaches, e.g., subgraph isomorphism and edit distance, unsuitable. We propose an approach based on the multiscale flat norm, a notion of distance between objects defined in the field of geometric measure theory, to compute the distance between a pair of planar geometric networks. Using a triangulation of the domain containing the input networks, the flat norm distance between two networks at a given scale can be computed by solving a linear program. In addition, this computation automatically identifies the 2D regions (patches) that capture where the two networks are different. We demonstrate through 2D examples that the flat norm distance can capture the variations of inputs more accurately than the commonly used Hausdorff distance. As a notion of stability, we also derive upper bounds on the flat norm distance between a simple 1D curve and its perturbed version as a function of the radius of perturbation for a restricted class of perturbations. We demonstrate our approach on a set of actual power networks from a county in the USA., Comment: A shorter version (with subset of results) appeared in ICCS 2023

Given a bipartite graph $G(V= (A \cup B),E)$ with $n$ vertices and $m$ edges and a function $b \colon V \to \mathbb{Z}_+$, a $b$-matching is a subset of edges such that every vertex $v \in V$ is incident to at most $b(v)$ edges in the subset. When we are also given edge weights, the Max Weight $b$-Matching problem is to find a $b$-matching of maximum weight, which is a fundamental combinatorial optimization problem with many applications. Extending on the recent work of Zheng and Henzinger (IPCO, 2023) on standard bipartite matching problems, we develop a simple auction algorithm to approximately solve Max Weight $b$-Matching. Specifically, we present a multiplicative auction algorithm that gives a $(1 - \varepsilon)$-approximation in $O(m \varepsilon^{-1} \log \varepsilon^{-1} \log \beta)$ worst case time, where $\beta$ the maximum $b$-value. Although this is a $\log \beta$ factor greater than the current best approximation algorithm by Huang and Pettie (Algorithmica, 2022), it is considerably simpler to present, analyze, and implement., Comment: 14 pages; Accepted as a refereed paper in the 2024 INFORMS Optimization Society conference

This paper introduces a model-free real-time optimization (RTO) framework based on unconstrained Bayesian optimization with embedded constraint control. The main contribution lies in demonstrating how this approach simplifies the black-box optimization problem while ensuring "always-feasible" setpoints, addressing a critical challenge in real-time optimization with unknown cost and constraints. Noting that controlling the constraint does not require detailed process models, the key idea of this paper is to control the constraints to "some" setpoint using simple feedback controllers. Bayesian optimization then computes the optimum setpoint for the constraint controllers. By searching over the setpoints for the constraint controllers, as opposed to searching directly over the RTO degrees of freedom, this paper achieves an inherently safe and practical model-free RTO scheme. In particular, this paper shows that the proposed approach can achieve zero cumulative constraint violation without relying on assumptions about the Gaussian process model used in Bayesian optimization. The effectiveness of the proposed approach is demonstrated on a benchmark Williams-Otto reactor example., Comment: IFAC ADCHEM 2024

In this paper, we demonstrate the communication capabilities of light-fidelity (LiFi) systems based on highbrightness and high-bandwidth integrated laser-based sources in a surface mount device (SMD) packaging platform. The laserbased source is able to deliver 450 lumens of white light illumination and the resultant light brightness is over 1000 cd mm2. It is demonstrated that a wavelength division multiplexing (WDM) LiFi system with ten parallel channels is able to deliver over 100 Gbps data rate with the assistance of Volterra filter-based nonlinear equalisers. In addition, an aggregated transmission data rate of 4.8 Gbps has been achieved over a link distance of 500 m with the same type of SMD light source. This work demonstrates the scalability of LiFi systems that employ laserbased light sources, particularly in their capacity to enable highspeed short range, as well as long-range data transmission.

Application of nonlinear model predictive control (NMPC) to problems with hybrid dynamical systems, disjoint constraints, or discrete controls often results in mixed-integer formulations with both continuous and discrete decision variables. However, solving mixed-integer nonlinear programming problems (MINLP) in real-time is challenging, which can be a limiting factor in many applications. To address the computational complexity of solving mixed integer nonlinear model predictive control problem in real-time, this paper proposes an approximate mixed integer NMPC formulation based on value function approximation. Leveraging Bellman's principle of optimality, the key idea here is to divide the prediction horizon into two parts, where the optimal value function of the latter part of the prediction horizon is approximated offline using expert demonstrations. Doing so allows us to solve the MINMPC problem with a considerably shorter prediction horizon online, thereby reducing the online computation cost. The paper uses an inverted pendulum example with discrete controls to illustrate this approach.

The application of supervised learning techniques in combination with model predictive control (MPC) has recently generated significant interest, particularly in the area of approximate explicit MPC, where function approximators like deep neural networks are used to learn the MPC policy via optimal state-action pairs generated offline. While the aim of approximate explicit MPC is to closely replicate the MPC policy, substituting online optimization with a trained neural network, the performance guarantees that come with solving the online optimization problem are typically lost. This paper considers an alternative strategy, where supervised learning is used to learn the optimal value function offline instead of learning the optimal policy. This can then be used as the cost-to-go function in a myopic MPC with a very short prediction horizon, such that the online computation burden reduces significantly without affecting the controller performance. This approach differs from existing work on value function approximations in the sense that it learns the cost-to-go function by using offline-collected state-value pairs, rather than closed-loop performance data. The cost of generating the state-value pairs used for training is addressed using a sensitivity-based data augmentation scheme., Comment: IFAC NMPC 2024

With increasingly more powerful compute capabilities and resources in today's devices, traditionally compute-intensive automatic speech recognition (ASR) has been moving from the cloud to devices to better protect user privacy. However, it is still challenging to implement on-device ASR on resource-constrained devices, such as smartphones, smart wearables, and other smart home automation devices. In this paper, we propose a series of model architecture adaptions, neural network graph transformations, and numerical optimizations to fit an advanced Conformer based end-to-end streaming ASR system on resource-constrained devices without accuracy degradation. We achieve over 5.26 times faster than realtime (0.19 RTF) speech recognition on smart wearables while minimizing energy consumption and achieving state-of-the-art accuracy. The proposed methods are widely applicable to other transformer-based server-free AI applications. In addition, we provide a complete theory on optimal pre-normalizers that numerically stabilize layer normalization in any Lp-norm using any floating point precision.

This work reports high carrier mobilities and growth rates, simultaneously in low unintentionally-doped UID (10$^{15}$ cm$^{-3}$) MOCVD-grown thick $\beta$-Ga$_2$O$_3$ epitaxial drift layers, with thicknesses reaching up to 6.3 $\mu$m, using triethylgallium (TEGa) as a precursor. Record high room temperature Hall mobilities of 187-190 cm$^2$/Vs were measured for background carrier density values of 2.4 - 3.5$\times$10$^{15}$ cm$^{-3}$ grown at a rate of 2.2 $\mu$m/hr. A controlled background carrier density scaling from 3.3$\times$10$^{16}$ cm$^{-3}$ to 2.4$\times$10$^{15}$ cm$^{-3}$ is demonstrated, without the use of intentional dopant gases such as silane, by controlling the growth rate and O$_2$/TEGa ratio. Films show smooth surface morphologies of 0.8-3.8 nm RMS roughness for film thicknesses of 1.24 - 6.3$\mu$m. Vertical Ni Schottky barrier diodes (SBDs) fabricated on UID MOCVD material were compared with those fabricated on hydride vapor phase epitaxy (HVPE) material, revealing superior material and device characteristics. MOCVD SBDs on a 6.3 $\mu$m thick epitaxial layer show a uniform charge vs. depth profile of $\sim$2.4$\times$10$^{15}$ cm$^{-3}$, an estimated $\mu$$_{drift}$ of 132 cm$^2$/Vs, a breakdown voltage (V$_{BR}$) close to 1.2 kV and a surface parallel plane field of 2.05MV/cm without any electric field management - setting record-high parameters for any MOCVD-grown $\beta$-Ga$_2$O$_3$ vertical diode to date., Comment: 14 pages, 14 figures, 1 table

The investigation of the ideal class group $Cl_K$ of an algebraic number field $K$ is one of the key subjects of inquiry in algebraic number theory since it encodes a lot of arithmetic information about K. There is a considerable amount of research on many topics linked to quadratic field class groups notably intriguing aspect is the divisibility of the class numbers. This article discusses a few recent results on the divisibility of class numbers and the Izuka conjecture. We also discuss the quantitative aspect of the Izuka conjecture., Comment: Comments are welcome.11 pages

For a positive integer $n$, let $B_{\ell_1,\dots,\ell_r}(n)$ denote the number of $(\ell_1,\ell_2,\cdots,\ell_r)$-regular multipartitions of $n$. If $\ell_1=\ell_2=\cdots=\ell_r=\ell$, then we denote $B_{\ell_1,\dots,\ell_r}(n)$ as $B_\ell^{(r)}(n)$. In this paper, we prove several infinite families of congruences satisfied by $B_\ell^{(r)}(n)$ for different values of $\ell$ and $r$.

We design and implement two single-pass semi-streaming algorithms for the maximum weight $k$-disjoint matching ($k$-DM) problem. Given an integer $k$, the $k$-DM problem is to find $k$ pairwise edge-disjoint matchings such that the sum of the weights of the matchings is maximized. For $k \geq 2$, this problem is NP-hard. Our first algorithm is based on the primal-dual framework of a linear programming relaxation of the problem and is $\frac{1}{3+\varepsilon}$-approximate. We also develop an approximation preserving reduction from $k$-DM to the maximum weight $b$-matching problem. Leveraging this reduction and an existing semi-streaming $b$-matching algorithm, we design a $(\frac{1}{2+\varepsilon})(1 - \frac{1}{k+1})$-approximate semi-streaming algorithm for $k$-DM. For any constant $\varepsilon > 0$, both of these algorithms require $O(nk \log_{1+\varepsilon}^2 n)$ bits of space. To the best of our knowledge, this is the first study of semi-streaming algorithms for the $k$-DM problem. We compare our two algorithms to state-of-the-art offline algorithms on 95 real-world and synthetic test problems, including thirteen graphs generated from data center network traces. On these instances, our streaming algorithms used significantly less memory (ranging from 6$\times$ to 512$\times$ less) and were faster in runtime than the offline algorithms. Our solutions were often within 5% of the best weights from the offline algorithms. We highlight that the existing offline algorithms run out of 1 TB memory for most of the large instances ($>1$ billion edges), whereas our streaming algorithms can solve these problems using only 100 GB memory for $k=8$., Comment: 24 pages, To appear in ESA 2024

This paper presents a Bayesian optimization framework for the automatic tuning of shared controllers which are defined as a Model Predictive Control (MPC) problem. The proposed framework includes the design of performance metrics as well as the representation of user inputs for simulation-based optimization. The framework is applied to the optimization of a shared controller for an Image Guided Therapy robot. VR-based user experiments confirm the increase in performance of the automatically tuned MPC shared controller with respect to a hand-tuned baseline version as well as its generalization ability.

We consider the following question of bounded simultaneous messages (BSM) protocols: Can computationally unbounded Alice and Bob evaluate a function $f(x,y)$ of their inputs by sending polynomial-size messages to a computationally bounded Carol? The special case where $f$ is the mod-2 inner-product function and Carol is bounded to AC$^0$ has been studied in previous works. The general question can be broadly motivated by applications in which distributed computation is more costly than local computation, including secure two-party computation. In this work, we initiate a more systematic study of the BSM model, with different functions $f$ and computational bounds on Carol. In particular, we give evidence against the existence of BSM protocols with polynomial-size Carol for naturally distributed variants of NP-complete languages., Comment: This version has a modified variant of the succinct subset sum candidate from the original version of this paper

Given an elliptic curve $E/\mathbb{Q}$ of conductor $N$, there exists a surjective morphism $\phi_E: X_0(N) \to E$ defined over $\mathbb{Q}$. In this article, we discuss the growth of $\mathrm{deg}(\phi_E)$ and shed some light on Watkins's conjecture, which predicts $2^{\mathrm{rank}(E(\mathbb{Q}))} \mid \mathrm{deg}(\phi_E)$. Moreover, for any elliptic curve over $\mathbb{F}_q(T)$, we have an analogous modular parametrization relating to the Drinfeld modular curves. In this case, we also discuss growth and the divisibility properties., Comment: 23 pages, incorporating the anonymous referee's suggestions

Let $X/\mathbb{C}$ be a smooth variety with simple normal crossings compactification $\bar{X}$, and let $L$ be an irreducible $\overline{\mathbb{Q}}_{\ell}$-local system on $X$ with torsion determinant. Suppose $L$ is cohomologically rigid. The pair $(X, L)$ may be spread out to a finitely generated base, and therefore reduced modulo $p$ for almost all $p$; the Frobenius traces of this mod $p$ reduction lie in a number field $F_p$, by a theorem of Deligne. We investigate to what extent the fields $F_p$ are bounded, meaning that they are contained in a fixed number field, independent of $p$. We prove a host of results around this question. For instance: assuming $L$ has totally degenerate unipotent monodromy around some component of $Z$, then we prove that $L$ admits a spreading out such that the $F_p$'s are bounded; without any local monodromy assumptions, we show that the $F_p$'s are bounded as soon as they are bounded at one point of $X$. We also speculate on the relation between the boundedness of the $F_p$'s, and the local system $L$ being strongly of geometric origin, a notion due to Langer-Simpson., Comment: v2--substantially expanded to include stronger results in the case of bad reduction, as well as several more results. Comments welcome!