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Let $P$ be a (possibly empty) subset of primes, and let $H = \{h_1, \ldots, h_d\}$ be a subset of $\{0,1,2,\ldots\}$. We consider the limit \[ \lim_{x\to\infty}\frac{1}{x} \sum_{n\leqslant x} \lambda_P(n+h_1)\ldots\lambda_P(n+h_d) \] where $\lambda_P$ denotes the completely multiplicative function taking the value $-1$ at primes $p$ in $P$ and $1$ at every other prime. When $P$ is a small set, we evaluate the limit exactly, in particular showing that it exists. For arbitrary non-empty $P$, we show that limit (assuming that it exists) does not equal $\{\pm 1\}$, extending a result of Matom\"aki and Radziwi\l\l. We also determine the corresponding ``spectrum''., Comment: 14 Pages, Comments and suggestions welcome

The exponential growth in the size and complexity of Large Language Models (LLMs) has introduced unprecedented challenges in their deployment and operational management. Traditional MLOps approaches often fail to efficiently handle the scale, resource requirements, and dynamic nature of these models. This research presents a novel framework that leverages Deep Neural Networks (DNNs) to optimize MLOps pipelines specifically for LLMs. Our approach introduces an intelligent system that automates deployment decisions, resource allocation, and pipeline optimization while maintaining optimal performance and cost efficiency. Through extensive experimentation across multiple cloud environments and deployment scenarios, we demonstrate significant improvements: 40% enhancement in resource utilization, 35% reduction in deployment latency, and 30% decrease in operational costs compared to traditional MLOps approaches. The framework's ability to adapt to varying workloads and automatically optimize deployment strategies represents a significant advancement in automated MLOps management for large-scale language models. Our framework introduces several novel components including a multi-stream neural architecture for processing heterogeneous operational metrics, an adaptive resource allocation system that continuously learns from deployment patterns, and a sophisticated deployment orchestration mechanism that automatically selects optimal strategies based on model characteristics and environmental conditions. The system demonstrates robust performance across various deployment scenarios, including multi-cloud environments, high-throughput production systems, and cost-sensitive deployments. Through rigorous evaluation using production workloads from multiple organizations, we validate our approach's effectiveness in reducing operational complexity while improving system reliability and cost efficiency., Comment: 22 pages, 15 figures, submitting to a AI Journal

Given a pair of time series, we study how the periodicity of one influences the periodicity of the other. There are several known methods to measure the similarity between a pair of time series, such as cross-correlation, coherence, cross-recurrence, and dynamic time warping. But we have yet to find any measures with theoretical stability results. Persistence homology has been utilized to construct a scoring function with theoretical guarantees of stability that quantifies the periodicity of a single univariate time series f1, denoted score(f1). Building on this concept, we propose a conditional periodicity score that quantifies the periodicity of one univariate time series f1 given another f2, denoted score(f1|f2), and derive theoretical stability results for the same. With the use of dimension reduction in mind, we prove a new stability result for score(f1|f2) under principal component analysis (PCA) when we use the projections of the time series embeddings onto their respective first K principal components. We show that the change in our score is bounded by a function of the eigenvalues corresponding to the remaining (unused) N-K principal components and hence is small when the first K principal components capture most of the variation in the time series embeddings. Finally we derive a lower bound on the minimum embedding dimension to use in our pipeline which guarantees that any two such embeddings give scores that are within a given epsilon of each other. We present a procedure for computing conditional periodicity scores and implement it on several pairs of synthetic signals. We experimentally compare our similarity measure to the most-similar statistical measure of cross-recurrence, and show the increased accuracy and stability of our score when predicting and measuring whether or not the periodicities of two time series are similar., Comment: 24 pages, 9 figures

Optical wireless communication (OWC) is a promising technology anticipated to play a key role in the next-generation network of networks. To this end, this paper details the potential of OWC, as a complementary technology to traditional radio frequency communications, in enhancing networking capabilities beyond conventional terrestrial networks. Several usage scenarios and the current state of development are presented. Furthermore, a summary of existing challenges and opportunities are provided. Emerging technologies aimed at further enhancing future OWC capabilities are introduced. Additionally, value-added OWC-based technologies that leverage the unique properties of light are discussed, including applications such as positioning and gesture recognition. The paper concludes with the reflection that OWC provides unique functionalities that can play a crucial role in building convergent and resilient future network of networks., Comment: This work has been submitted to the IEEE for possible publication. 15pp, 16 figures, and one table

J.-P. Serre, in his paper [1], established a sufficient condition on $n$ for the $n$-th coefficient of the series $\eta^{26}$ to vanish. However, the question that whether this is a necessary condition remained unanswered. In this paper, using the theory of Hecke eigenforms explored by Serre, we prove some partial cases for the converse part., Comment: arXiv admin note: text overlap with arXiv:2006.15511 by other authors

We establish the existence of a positive proportion of \( d \in \mathbb{N} \) such that the class numbers of \( \mathbb{Q}(\sqrt{d}), \mathbb{Q}(\sqrt{d+1}), \dots, \mathbb{Q}(\sqrt{d+n}) \) are not divisible by \( 3^k \), where \( n = 3^{k+1} - 5 \) and \( k \in \mathbb{N} \). This provides an indivisibility analog of Iizuka's conjecture. Similarly, for \( d < 0 \) and the same \( n \), a positive proportion of \( d \) ensures that the class numbers of \( \mathbb{Q}(\sqrt{d}), \mathbb{Q}(\sqrt{d+1}), \dots, \mathbb{Q}(\sqrt{d+n}) \) are not divisible by \( 3^{k+1} \). Denoting the square-free natural numbers by \( (d_n) \), we prove the existence of a positive density set of \( i\in\mathbb{N} \) such that the class numbers of \( \mathbb{Q}(\sqrt{d_i}), \mathbb{Q}(\sqrt{d_{i+1}}), \dots, \mathbb{Q}(\sqrt{d_{i+n}}) \) are not divisible by \( 3^k \). Moreover, we study the indivisibility of class numbers by $3$ for imaginary biquadratic fields.

This paper details a significant milestone towards maturing a buoyant aerial robotic platform, or aerobot, for flight in the Venus clouds. We describe two flights of our subscale altitude-controlled aerobot, fabricated from the materials necessary to survive Venus conditions. During these flights over the Nevada Black Rock desert, the prototype flew at the identical atmospheric densities as 54 to 55 km cloud layer altitudes on Venus. We further describe a first-principle aerobot dynamics model which we validate against the Nevada flight data and subsequently employ to predict the performance of future aerobots on Venus. The aerobot discussed in this paper is under JPL development for an in-situ mission flying multiple circumnavigations of Venus, sampling the chemical and physical properties of the planet's atmosphere and also remotely sensing surface properties., Comment: Preprint submitted to AIAA Journal of Aircraft

This paper considers the problem of steady-state real-time optimization (RTO) of interconnected systems with a common constraint that couples several units, for example, a shared resource. Such problems are often studied under the context of distributed optimization, where decisions are made locally in each subsystem, and are coordinated to optimize the overall performance. Here, we use distributed feedback-optimizing control framework, where the local systems and the coordinator problems are converted into feedback control problems. This is a powerful scheme that allows us to design feedback control loops, and estimate parameters locally, as well as provide local fast response, allowing different closed-loop time constants for each local subsystem. This paper provides a comparative study of different distributed feedback optimizing control architectures using two case studies. The first case study considers the problem of demand response in a residential energy hub powered by a common renewable energy source, and compares the different feedback optimizing control approaches using simulations. The second case study experimentally validates and compares the different approaches using a lab-scale experimental rig that emulates a subsea oil production network, where the common resource is the gas lift that must be optimally allocated among the wells. %The pros and cons of the different approaches are discussed., Comment: Accepted to IEEE Transactions on Control Systems Technology

The Artificial intelligence in critical sectors-healthcare, finance, and public safety-has made system integrity paramount for maintaining societal trust. Current verification methods for AI systems lack comprehensive lifecycle assurance, creating significant vulnerabilities in deployment of both powerful and trustworthy AI. This research introduces Meta-Sealing, a cryptographic framework that fundamentally changes integrity verification in AI systems throughout their operational lifetime. Meta-Sealing surpasses traditional integrity protocols through its implementation of cryptographic seal chains, establishing verifiable, immutable records for all system decisions and transformations. The framework combines advanced cryptography with distributed verification, delivering tamper-evident guarantees that achieve both mathematical rigor and computational efficiency. Our implementation addresses urgent regulatory requirements for AI system transparency and auditability. The framework integrates with current AI governance standards, specifically the EU's AI Act and FDA's healthcare AI guidelines, enabling organizations to maintain operational efficiency while meeting compliance requirements. Testing on financial institution data demonstrated Meta-Sealing's capability to reduce audit timeframes by 62% while enhancing stakeholder confidence by 47%. Results can establish a new benchmark for integrity assurance in enterprise AI deployments. This research presents Meta-Sealing not merely as a technical solution, but as a foundational framework ensuring AI system integrity aligns with human values and regulatory requirements. As AI continues to influence critical decisions, provides the necessary bridge between technological advancement and verifiable trust. Meta-Sealing serves as a guardian of trust, ensuring that the AI systems we depend on are as reliable and transparent as they are powerful., Comment: 24 pages, 3 figures and 10 Code blocks, to be presented in the conference

As AI systems increasingly integrate into critical societal sectors, the demand for robust privacy-preserving methods has escalated. This paper introduces Data Obfuscation through Latent Space Projection (LSP), a novel technique aimed at enhancing AI governance and ensuring Responsible AI compliance. LSP uses machine learning to project sensitive data into a latent space, effectively obfuscating it while preserving essential features for model training and inference. Unlike traditional privacy methods like differential privacy or homomorphic encryption, LSP transforms data into an abstract, lower-dimensional form, achieving a delicate balance between data utility and privacy. Leveraging autoencoders and adversarial training, LSP separates sensitive from non-sensitive information, allowing for precise control over privacy-utility trade-offs. We validate LSP's effectiveness through experiments on benchmark datasets and two real-world case studies: healthcare cancer diagnosis and financial fraud analysis. Our results show LSP achieves high performance (98.7% accuracy in image classification) while providing strong privacy (97.3% protection against sensitive attribute inference), outperforming traditional anonymization and privacy-preserving methods. The paper also examines LSP's alignment with global AI governance frameworks, such as GDPR, CCPA, and HIPAA, highlighting its contribution to fairness, transparency, and accountability. By embedding privacy within the machine learning pipeline, LSP offers a promising approach to developing AI systems that respect privacy while delivering valuable insights. We conclude by discussing future research directions, including theoretical privacy guarantees, integration with federated learning, and enhancing latent space interpretability, positioning LSP as a critical tool for ethical AI advancement., Comment: 19 pages, 6 figures, submitted to Conference ICADCML2025

This work reports the fabrication and characterization of a NiOx/\b{eta}-Ga2O3 heterojunction diode (HJD) that uses a metallic nickel (Ni) target to deposit NiOx layers via reactive RF magnetron sputtering and lift-off processing with >3 kV breakdown voltage, record-low reverse current leakage under high reverse bias, and high junction electric fields (>3.34 MV/cm). The heterojunction diodes are fabricated via bilayer NiOx sputtering followed by self-aligned mesa-etching for field-termination on both large (1-mm2) and small area (100-{\mu}m diameter) devices. The HJD exhibits a ~135 A/cm2 forward current density at 5 V with a rectifying ratio of ~1010. The minimum differential specific on-resistance is measured to be 17.26 m{\Omega} cm2. The breakdown voltage on 100-{\mu}m diameter pads was measured to be greater than 3 kV with a noise floor-level reverse leakage current density (10-8~10-6 A/cm2) until 3 kV, accomplishing a parallel-plane junction electric field to be at least 3.34 MV/cm at 3 kV with a power figure of merit (PFOM) >0.52 GW/cm2. Temperature-dependent forward current density-voltage (J-V) measurements are performed from room temperature (25 C) to 200 C which showed a temperature coefficient of resistance ({\alpha}) equaling 1.56, higher than that of \b{eta}-Ga2O3 Schottky barrier diodes (SBDs), indicating potential conductivity degradation within NiOx at elevated temperatures., Comment: 6 pages, 5 figures, APL Journal

Aerosol effects on climate, weather, and air quality depend on characteristics of individual particles, which are tremendously diverse and change in time. Particle-resolved models are the only models able to capture this diversity in particle physiochemical properties, and these models are computationally expensive. As a strategy for accelerating particle-resolved microphysics models, we introduce Graph-based Learning of Aerosol Dynamics (GLAD) and use this model to train a surrogate of the particle-resolved model PartMC-MOSAIC. GLAD implements a Graph Network-based Simulator (GNS), a machine learning framework that has been used to simulate particle-based fluid dynamics models. In GLAD, each particle is represented as a node in a graph, and the evolution of the particle population over time is simulated through learned message passing. We demonstrate our GNS approach on a simple aerosol system that includes condensation of sulfuric acid onto particles composed of sulfate, black carbon, organic carbon, and water. A graph with particles as nodes is constructed, and a graph neural network (GNN) is then trained using the model output from PartMC-MOSAIC. The trained GNN can then be used for simulating and predicting aerosol dynamics over time. Results demonstrate the framework's ability to accurately learn chemical dynamics and generalize across different scenarios, achieving efficient training and prediction times. We evaluate the performance across three scenarios, highlighting the framework's robustness and adaptability in modeling aerosol microphysics and chemistry.

Designing algorithms for space bounded models with restoration requirements on the space used by the algorithm is an important challenge posed about the catalytic computation model introduced by Buhrman et al. (2014). Motivated by the scenarios where we do not need to restore unless is useful, we define $ACL(A)$ to be the class of languages that can be accepted by almost-catalytic Turing machines with respect to $A$ (which we call the catalytic set), that uses at most $c\log n$ work space and $n^c$ catalytic space. We show that if there are almost-catalytic algorithms for a problem with catalytic set as $A \subseteq \Sigma^*$ and its complement respectively, then the problem can be solved by a ZPP algorithm. Using this, we derive that to design catalytic algorithms, it suffices to design almost-catalytic algorithms where the catalytic set is the set of strings of odd weight ($PARITY$). Towards this, we consider two complexity measures of the set $A$ which are maximized for $PARITY$ - random projection complexity (${\cal R}(A)$) and the subcube partition complexity (${\cal P}(A)$). By making use of error-correcting codes, we show that for all $k \ge 1$, there is a language $A_k \subseteq \Sigma^*$ such that $DSPACE(n^k) \subseteq ACL(A_k)$ where for every $m \ge 1$, $\mathcal{R}(A_k \cap \{0,1\}^m) \ge \frac{m}{4}$ and $\mathcal{P}(A_k \cap \{0,1\}^m)=2^{m/4}$. This contrasts the catalytic machine model where it is unclear if it can accept all languages in $DSPACE(\log^{1+\epsilon} n)$ for any $\epsilon > 0$. Improving the partition complexity of the catalytic set $A$ further, we show that for all $k \ge 1$, there is a $A_k \subseteq \{0,1\}^*$ such that $\mathsf{DSPACE}(\log^k n) \subseteq ACL(A_k)$ where for every $m \ge 1$, $\mathcal{R}(A_k \cap \{0,1\}^m) \ge \frac{m}{4}$ and $\mathcal{P}(A_k \cap \{0,1\}^m)=2^{m/4+\Omega(\log m)}$., Comment: 22 pages, A new lower bound on the subcube partition complexity of Hamming balls (Proposition 2.6 and Lemma 2.7), improving the bound and fixing an error in the previous version

In this article, we investigate the in-situ growth of Al$_2$O$_3$ on $\beta$-Ga$_2$O$_3$ using metal-organic chemical vapor deposition (MOCVD) at a high temperature of 800{\deg}C. The Al$_2$O$_3$ is grown within the same reactor as the $\beta$-Ga$_2$O$_3$, employing trimethylaluminum (TMAl) and O$_2$ as precursors without breaking the vacuum. We characterize the shallow and deep-level traps through stressed capacitance-voltage (C-V) and photo-assisted C-V methods. The high-temperature deposited dielectric demonstrates an impressive breakdown field of approximately 10 MV/cm. Furthermore, we evaluate the reliability and lifetime of the dielectrics using time-dependent dielectric breakdown (TDDB) measurements. By modifying the dielectric deposition process to include a high-temperature (800{\deg}C) thin interfacial layer and a low-temperature (600{\deg}C) bulk layer, we report a 10-year lifetime under a stress field of 3.5 MV/cm along a breakdown field of 7.8 MV/cm.

Watkins's conjecture suggests that for an elliptic curve $E/\mathbb{Q}$, the rank of the group $E(\mathbb{Q})$ of rational points is bounded above by $\nu_2 (m_E)$, where $m_E$ is the modular degree associated with $E$. It is known that Watkins's conjecture holds on average. This article investigates the conjecture over certain thin families of elliptic curves. For example, for prime $\ell$, we quantify the elliptic curves featuring a rational $\ell$-torsion that satisfies Watkins's conjecture. Additionally, the study extends to a broader context, investigating the inequality $\mathrm{rank}(E(\mathbb{Q}))+M\leq \nu_2(m_E)$ for any positive integer $M$., Comment: 26 pages; comments, and feedback are welcome

We report on metalorganic chemical vapor deposition (MOCVD) growth of controllably Si-doped 4.5 $\mu$m thick $\beta$-Ga$_2$O$_3$ films with electron concentrations in the 10$^{15}$ cm$^{-3}$ range and record-high room temperature Hall electron mobilities of up to 200 cm$^2$/V.s, reaching the predicted theoretical maximum room temperature mobility value for $\beta$-Ga$_2$O$_3$. Growth of the homoepitaxial films was performed on Fe-doped (010) $\beta$-Ga$_2$O$_3$ substrates at a growth rate of 1.9 $\mu$m/hr using TEGa as the Gallium precursor. To probe the background electron concentration, an unintentionally doped film was grown with a Hall concentration of 3.43 x 10$^{15}$ cm$^{-3}$ and Hall mobility of 196 cm$^2$/V.s. Growth of intentionally Si-Doped films was accomplished by fixing all growth conditions and varying only the silane flow, with controllable Hall electron concentrations ranging from 4.38 x 10$^{15}$ cm$^{-3}$ to 8.30 x 10$^{15}$ cm$^{-3}$ and exceptional Hall mobilities ranging from 194 - 200 cm$^2$/V.s demonstrated. C-V measurements showed a flat charge profile with the N$_D^+$ - N$_A^-$ values correlating well with the Hall-measured electron concentration in the films. SIMS measurements showed the silicon atomic concentration matched the Hall electron concentration with Carbon and Hydrogen below detection limit in the films. The Hall, C-V, and SIMS data indicate the growth of high-quality 4.5 $\mu$m thick $\beta$-Ga$_2$O$_3$ films and controllable doping into the mid 10$^{15}$ cm$^{-3}$ range. These results demonstrate MOCVD growth of electronics grade record-high mobility, low carrier density, and thick $\beta$-Ga$_2$O$_3$ drift layers for next generation vertical $\beta$-Ga$_2$O$_3$ power devices., Comment: 16 Pages, 10 Figures, 2 Tables

Sample Return Capsules (SRCs) entering Earth's atmosphere at hypervelocity from interplanetary space are a valuable resource for studying meteor phenomena. The 24 September 2023 arrival of the OSIRIS-REx (Origins, Spectral Interpretation, Resource Identification, and Security-Regolith Explorer) SRC provided an unprecedented chance for geophysical observations of a well-characterized source with known parameters, including timing and trajectory. A collaborative effort involving researchers from 16 institutions executed a carefully planned geophysical observational campaign at strategically chosen locations, deploying over 400 ground-based sensors encompassing infrasound, seismic, distributed acoustic sensing (DAS), and GPS technologies. Additionally, balloons equipped with infrasound sensors were launched to capture signals at higher altitudes. This campaign (the largest of its kind so far) yielded a wealth of invaluable data anticipated to fuel scientific inquiry for years to come. The success of the observational campaign is evidenced by the near-universal detection of signals across instruments, both proximal and distal. This paper presents a comprehensive overview of the collective scientific effort, field deployment, and preliminary findings. The early findings have the potential to inform future space missions and terrestrial campaigns, contributing to our understanding of meteoroid interactions with planetary atmospheres. Furthermore, the dataset collected during this campaign will improve entry and propagation models as well as augment the study of atmospheric dynamics and shock phenomena generated by meteoroids and similar sources., Comment: 87 pages, 14 figures

Magneto-optical properties of materials are utilized in numerous applications both in scientific research and industries. The novel properties of these materials can be further investigated by performing metrology in the infrared wavelength range, thereby enriching their potential applications. However, current infrared metrology techniques can be challenging and resource-intensive due to the unavailability of suitable components. To address these challenges, we propose and demonstrate a set of measurements based on nonlinear interferometry, which allows us investigating magneto-optical properties of materials at infrared wavelength range by performing optical detection at the visible range. For a proof-of-principle study, we measure the Verdet constant of a bismuth-iron-garnet, over a spectral bandwidth of 600 nm in the near-IR range., Comment: 10 pages, 12 fugures

In this paper, a hydrogen-based energy storage system (ESS) is proposed for DC microgrids, which can potentially be integrated with battery ESS to meet the needs of future grids with high renewable penetration. Hydrogen-based ESS can provide a stable energy supply for a long time but has a slower response than battery ESSs. However, a combination of battery and hydrogen storage provides stable energy for an extended period of time and can easily handle the sudden demands and surpluses of the microgrid. One of the main challenges in this system is the integration of power electronics with fuel cell technology to convert renewable energy into electricity seamlessly. This paper proposes a system that uses an isolated DC-DC converter to activate clean hydrogen production using an electrolyzer and then pressurize the hydrogen to store in a tank. The pressured hydrogen becomes an essential input to the fuel cell, which regulates and transforms it into electricity. The electricity produced is then transferred to the grid using a DC-DC boost converter. A Simulink model of the hybrid system with a 1 kV DC bus voltage is used to demonstrate the hydrogen production and fuel cell behavior based on the demand and surplus power of the loads. The proposed system simulates aspects of the power conversion, electrolyzer, storage tank, and fuel cell needed for the proposed hybrid ESS. Due to its economic feasibility, the polymer electrolyte membrane (PEM) is the primary technology considered for the electrolyzer and fuel cell., Comment: A 5-pages Digest paper summarizes in detail the work done

This paper investigates the radio resource management (RRM) design for multiuser rate-splitting multiple access (RSMA), accounting for various characteristics of practical wireless systems, such as the use of discrete rates, the inability to serve all users, and the imperfect successive interference cancellation (SIC). Specifically, failure to consider these characteristics in RRM design may lead to inefficient use of radio resources. Therefore, we formulate the RRM of RSMA as optimization problems to maximize respectively the weighted sum rate (WSR) and weighted energy efficiency (WEE), and jointly optimize the beamforming, user admission, discrete/continuous rates, accounting for imperfect SIC, which result in nonconvex mixed-integer nonlinear programs that are challenging to solve. Despite the difficulty of the optimization problems, we develop algorithms that can find high-quality solutions. We show via simulations that carefully accounting for the aforementioned characteristics, can lead to significant gains. Precisely, by considering that transmission rates are discrete, the transmit power can be utilized more intelligently, allocating just enough power to guarantee a given discrete rate. Additionally, we reveal that user admission plays a crucial role in RSMA, enabling additional gains compared to random admission by facilitating the servicing of selected users with mutually beneficial channel characteristics. Furthermore, provisioning for possibly imperfect SIC makes RSMA more robust and reliable.

Electronic health records (EHR) even though a boon for healthcare practitioners, are growing convoluted and longer every day. Sifting around these lengthy EHRs is taxing and becomes a cumbersome part of physician-patient interaction. Several approaches have been proposed to help alleviate this prevalent issue either via summarization or sectioning, however, only a few approaches have truly been helpful in the past. With the rise of automated methods, machine learning (ML) has shown promise in solving the task of identifying relevant sections in EHR. However, most ML methods rely on labeled data which is difficult to get in healthcare. Large language models (LLMs) on the other hand, have performed impressive feats in natural language processing (NLP), that too in a zero-shot manner, i.e. without any labeled data. To that end, we propose using LLMs to identify relevant section headers. We find that GPT-4 can effectively solve the task on both zero and few-shot settings as well as segment dramatically better than state-of-the-art methods. Additionally, we also annotate a much harder real world dataset and find that GPT-4 struggles to perform well, alluding to further research and harder benchmarks., Comment: To appear in NAACL 2024 at the 6th Clinical Natural Language Processing Workshop