Search

We study the quasi-uniformity properties of digital nets, a class of quasi-Monte Carlo point sets. Quasi-uniformity is a space-filling property used for instance in experimental designs and radial basis function approximation. However, it has not been investigated so far whether common low-discrepancy digital nets are quasi-uniform, with the exception of the two-dimensional Sobol' sequence, which has recently been shown not to be quasi-uniform. In this paper, with the goal of constructing quasi-uniform low-discrepancy digital nets, we introduce the notion of \emph{well-separated} point sets and provide an algebraic criterion to determine whether a given digital net is well-separated. Using this criterion, we present an example of a two-dimensional digital net which has low-discrepancy and is quasi-uniform. Additionally, we provide several counterexamples of low-discrepancy digital nets that are not quasi-uniform. The quasi-uniformity properties of quasi-Monte Carlo lattice point sets and sequences will be studied in a forthcoming paper.

Benchmarks are important tools for tracking the rapid advancements in large language model (LLM) capabilities. However, benchmarks are not keeping pace in difficulty: LLMs now achieve over 90\% accuracy on popular benchmarks like MMLU, limiting informed measurement of state-of-the-art LLM capabilities. In response, we introduce Humanity's Last Exam (HLE), a multi-modal benchmark at the frontier of human knowledge, designed to be the final closed-ended academic benchmark of its kind with broad subject coverage. HLE consists of 3,000 questions across dozens of subjects, including mathematics, humanities, and the natural sciences. HLE is developed globally by subject-matter experts and consists of multiple-choice and short-answer questions suitable for automated grading. Each question has a known solution that is unambiguous and easily verifiable, but cannot be quickly answered via internet retrieval. State-of-the-art LLMs demonstrate low accuracy and calibration on HLE, highlighting a significant gap between current LLM capabilities and the expert human frontier on closed-ended academic questions. To inform research and policymaking upon a clear understanding of model capabilities, we publicly release HLE at https://lastexam.ai., Comment: 25 pages, 6 figures

Waveform signal analysis is a complex and important task in medical care. For example, mechanical ventilators are critical life-support machines, but they can cause serious injury to patients if they are out of synchronization with the patients' own breathing reflex. This asynchrony is revealed by the waveforms showing flow and pressure histories. Likewise, electrocardiograms record the electrical activity of a patients' heart as a set of waveforms, and anomalous waveforms can reveal important disease states. In both cases, subtle variations in a complex waveform are important information for patient care; signals which may be missed or mis-interpreted by human caregivers. We report on the design of a novel Lock Generative Adversarial Network architecture for anomaly detection in raw or summarized medical waveform data. The proposed architecture uses alternating optimization of the generator and discriminator networks to solve the convergence dilemma. Furthermore, the fidelity of the generator networks' outputs to the actual distribution of anomalous data is improved via synthetic minority oversampling. We evaluate this new architecture on one ventilator asynchrony dataset, and two electrocardiogram datasets, finding that the performance was either equal or superior to the state-of-the art on all three., Comment: 24 pages, 11 figures

Emotion recognition and touch gesture decoding are crucial for advancing human-robot interaction (HRI), especially in social environments where emotional cues and tactile perception play important roles. However, many humanoid robots, such as Pepper, Nao, and Furhat, lack full-body tactile skin, limiting their ability to engage in touch-based emotional and gesture interactions. In addition, vision-based emotion recognition methods usually face strict GDPR compliance challenges due to the need to collect personal facial data. To address these limitations and avoid privacy issues, this paper studies the potential of using the sounds produced by touching during HRI to recognise tactile gestures and classify emotions along the arousal and valence dimensions. Using a dataset of tactile gestures and emotional interactions from 28 participants with the humanoid robot Pepper, we design an audio-only lightweight touch gesture and emotion recognition model with only 0.24M parameters, 0.94MB model size, and 0.7G FLOPs. Experimental results show that the proposed sound-based touch gesture and emotion recognition model effectively recognises the arousal and valence states of different emotions, as well as various tactile gestures, when the input audio length varies. The proposed model is low-latency and achieves similar results as well-known pretrained audio neural networks (PANNs), but with much smaller FLOPs, parameters, and model size., Comment: ICASSP 2025

3D shape analysis has been largely focused on traditional 3D representations of point clouds and meshes, but the discrete nature of these data makes the analysis susceptible to variations in input resolutions. Recent development of neural fields brings in level-set parameters from signed distance functions as a novel, continuous, and numerical representation of 3D shapes, where the shape surfaces are defined as zero-level-sets of those functions. This motivates us to extend shape analysis from the traditional 3D data to these novel parameter data. Since the level-set parameters are not Euclidean like point clouds, we establish correlations across different shapes by formulating them as a pseudo-normal distribution, and learn the distribution prior from the respective dataset. To further explore the level-set parameters with shape transformations, we propose to condition a subset of these parameters on rotations and translations, and generate them with a hypernetwork. This simplifies the pose-related shape analysis compared to using traditional data. We demonstrate the promise of the novel representations through applications in shape classification (arbitrary poses), retrieval, and 6D object pose estimation. Code and data in this research are provided at https://github.com/EnyaHermite/LevelSetParamData.

Risk measures, which typically evaluate the impact of extreme losses, are highly sensitive to misspecification in the tails. This paper studies a robust optimization approach to combat tail uncertainty by proposing a unifying framework to construct uncertainty sets for a broad class of risk measures, given a specified nominal model. Our framework is based on a parametrization of robust risk measures using two (or multiple) $\phi$-divergence functions, which enables us to provide uncertainty sets that are tailored to both the sensitivity of each risk measure to tail losses and the tail behavior of the nominal distribution. In addition, our formulation allows for a tractable computation of robust risk measures, and elicitation of $\phi$-divergences that describe a decision maker's risk and ambiguity preferences., Comment: 51 pages, 2 figures

In this short note we report on a coincidence of two mathematical quantities that, at first glance, have little to do with each other. On the one hand, there are the Lebesgue constants of the Walsh function system that play an important role in approximation theory, and on the other hand there is the star discrepancy of the van der Corput sequence that plays a prominent role in uniform distribution theory. Over the decades, these two quantities have been examined in great detail independently of each other and important results have been proven. Work in these areas has been carried out independently, but as we show here, they actually coincide. Interestingly, many theorems have been discovered in both areas independently, but some results have only been known in one area but not in the other.

Recommender systems have become integral to digital experiences, shaping user interactions and preferences across various platforms. Despite their widespread use, these systems often suffer from algorithmic biases that can lead to unfair and unsatisfactory user experiences. This study introduces an interactive tool designed to help users comprehend and explore the impacts of algorithmic harms in recommender systems. By leveraging visualizations, counterfactual explanations, and interactive modules, the tool allows users to investigate how biases such as miscalibration, stereotypes, and filter bubbles affect their recommendations. Informed by in-depth user interviews, this tool benefits both general users and researchers by increasing transparency and offering personalized impact assessments, ultimately fostering a better understanding of algorithmic biases and contributing to more equitable recommendation outcomes. This work provides valuable insights for future research and practical applications in mitigating bias and enhancing fairness in machine learning algorithms.

Correctness is one of the more important criteria of qualitative software. However, it is often taught in isolation and most students consider it only as an afterthought. They also do not receive sufficient feedback on code quality and tests unless specified in the assignment. To improve this, we developed a procedural guidance that guides students to an implementation with appropriate tests. Furthermore, we have developed a toolkit that students can use to independently get individual feedback on their solution and the adequateness of their tests. A key instrument is a test coverage analysis which allows for teachers to customize the feedback with constructive instructions specific to the current assignment to improve a student's test suite. In this paper, we outline the procedural guidance, explain the working of the feedback toolkit and present a method for using the toolkit in conjunction with the different steps of the procedural guidance.

Rate-matching of low-density parity-check (LDPC) codes enables a single code description to support a wide range of code lengths and rates. In 5G NR, rate matching is accomplished by extending (lifting) a base code to a desired target length and by puncturing (not transmitting) certain code bits. LDPC codes and rate matching are typically designed for the asymptotic performance limit with an ideal decoder. Practical LDPC decoders, however, carry out tens or fewer message-passing decoding iterations to achieve the target throughput and latency of modern wireless systems. We show that one can optimize LDPC code puncturing patterns for such few-iteration-constrained decoders using a method we call swapping of punctured and transmitted blocks (SPAT). Our simulation results show that SPAT yields from 0.20 dB up to 0.55 dB improved signal-to-noise ratio performance compared to the standard 5G NR LDPC code puncturing pattern for a wide range of code lengths and rates., Comment: Accepted at the Asilomar Conference on Signals, Systems, and Computers 2024

We propose a new methodology for the experimental measurement of the Onsager coefficients of porous media flows by application of the fluctuation-dissipation theorem. The experimental setup consists of a steady-state flow condition in which two incompressible fluids are simultaneously injected into a modified Hele-Shaw cell. The cell is transparent and allows direct visualization of the dynamics via regular optical imaging methods. The fluctuations in the phase saturations are obtained and, by computing the temporal correlations of their time derivatives, we gain access to the Onsager coefficients. This work gives experimental grounding to recent theoretical development on the applications of the fluctuation-dissipation theorems to porous media flows.

In this paper, we present some new (in-)tractability results related to the integration problem in subspaces of the Wiener algebra over the $d$-dimensional unit cube. We show that intractability holds for multivariate integration in the standard Wiener algebra in the deterministic setting, in contrast to polynomial tractability in an unweighted subspace of the Wiener algebra recently shown by Goda (2023). Moreover, we prove that multivariate integration in the subspace of the Wiener algebra introduced by Goda is strongly polynomially tractable if we switch to the randomized setting. We also identify subspaces in which multivariate integration in the deterministic setting are (strongly) polynomially tractable and we compare these results with the bound which can be obtained via Hoeffding's inequality., Comment: 16 pages

We study the integration problem over the $s$-dimensional unit cube on four types of Banach spaces of integrands. First we consider Haar wavelet spaces, consisting of functions whose Haar wavelet coefficients exhibit a certain decay behavior measured by a parameter $\alpha >0$. We study the worst case error of integration over the norm unit ball and provide upper error bounds for quasi-Monte Carlo (QMC) cubature rules based on arbitrary $(t,m,s)$-nets as well as matching lower error bounds for arbitrary cubature rules. These results show that using arbitrary $(t,m,s)$-nets as sample points yields the best possible rate of convergence. Afterwards we study spaces of integrands of fractional smoothness $\alpha \in (0,1)$ and state a sharp Koksma-Hlawka-type inequality. More precisely, we show that on those spaces the worst case error of integration is equal to the corresponding fractional discrepancy. Those spaces can be continuously embedded into tensor product Bessel potential spaces, also known as Sobolev spaces of dominated mixed smoothness, with the same set of parameters. The latter spaces can be embedded into suitable Besov spaces of dominating mixed smoothness $\alpha$, which in turn can be embedded into the Haar wavelet spaces with the same set of parameters. Therefore our upper error bounds on Haar wavelet spaces for QMC cubatures based on $(t,m,s)$-nets transfer (with possibly different constants) to the corresponding spaces of integrands of fractional smoothness and to Sobolev and Besov spaces of dominating mixed smoothness. Moreover, known lower error bounds for periodic Sobolev and Besov spaces of dominating mixed smoothness show that QMC integration based on arbitrary $(t,m,s)$-nets yields the best possible convergence rate on periodic as well as on non-periodic Sobolev and Besov spaces of dominating smoothness., Comment: 56 pages

Video generation using diffusion-based models is constrained by high computational costs due to the frame-wise iterative diffusion process. This work presents a Diffusion Reuse MOtion (Dr. Mo) network to accelerate latent video generation. Our key discovery is that coarse-grained noises in earlier denoising steps have demonstrated high motion consistency across consecutive video frames. Following this observation, Dr. Mo propagates those coarse-grained noises onto the next frame by incorporating carefully designed, lightweight inter-frame motions, eliminating massive computational redundancy in frame-wise diffusion models. The more sensitive and fine-grained noises are still acquired via later denoising steps, which can be essential to retain visual qualities. As such, deciding which intermediate steps should switch from motion-based propagations to denoising can be a crucial problem and a key tradeoff between efficiency and quality. Dr. Mo employs a meta-network named Denoising Step Selector (DSS) to dynamically determine desirable intermediate steps across video frames. Extensive evaluations on video generation and editing tasks have shown that Dr. Mo can substantially accelerate diffusion models in video tasks with improved visual qualities.

Audio Event Recognition (AER) traditionally focuses on detecting and identifying audio events. Most existing AER models tend to detect all potential events without considering their varying significance across different contexts. This makes the AER results detected by existing models often have a large discrepancy with human auditory perception. Although this is a critical and significant issue, it has not been extensively studied by the Detection and Classification of Sound Scenes and Events (DCASE) community because solving it is time-consuming and labour-intensive. To address this issue, this paper introduces the concept of semantic importance in AER, focusing on exploring the differences between human perception and model inference. This paper constructs a Multi-Annotated Foreground Audio Event Recognition (MAFAR) dataset, which comprises audio recordings labelled by 10 professional annotators. Through labelling frequency and variance, the MAFAR dataset facilitates the quantification of semantic importance and analysis of human perception. By comparing human annotations with the predictions of ensemble pre-trained models, this paper uncovers a significant gap between human perception and model inference in both semantic identification and existence detection of audio events. Experimental results reveal that human perception tends to ignore subtle or trivial events in the event semantic identification, while model inference is easily affected by events with noises. Meanwhile, in event existence detection, models are usually more sensitive than humans., Comment: Dataset homepage: https://github.com/Voltmeter00/MAFAR

Both freeze-in of very weakly coupled dark matter and freeze-out of initially thermalized dark matter from the primordial heat bath provide interesting possibilities for dark matter creation in the early universe. Both scenarios allow for a calculation of baryon-dark matter coupling constants as a function of dark matter mass due to the constraint that freeze-in or freeze-out produce the observed dark matter abundance. Here we compare the resulting coupling constants in the two scenarios if dark matter couples to baryons through an antisymmetric tensor portal. The freeze-in scenario predicts much smaller coupling in agreement with the nonthermalization postulate. We find that the couplings as a function of mass behave very differently in the two scenarios., Comment: 6 pages, 6 figures,version accepted for publication in Journal of Subatomic Particles and Cosmology

In this work, we explore a time-fractional diffusion equation of order $\alpha \in (0,1)$ with a stochastic diffusivity parameter. We focus on efficient estimation of the expected values (considered as an infinite dimensional integral on the parametric space corresponding to the random coefficients) of linear functionals acting on the solution of our model problem. To estimate the expected value computationally, the infinite expansions of the random parameter need to be truncated. Then we approximate the high-dimensional integral over the random field using a high-order quasi-Monte Carlo method. This follows by approximating the deterministic solution over the space-time domain via a second-order accurate time-stepping scheme in combination with a spatial discretization by Galerkin finite elements. Under reasonable regularity assumptions on the given data, we show some regularity properties of the continuous solution and investigate the errors from estimating the expected value. We report on numerical experiments that complement the theoretical results.

We derive new small deviations bounds for a class of Gaussian multiplicative chaos measures obtained from Gaussian fields with zero spatial average. The upper bound holds for a class of fields closely related to the $\star$-scale invariant Gaussian fields in arbitrary number of dimensions, and the lower bound holds for the Gaussian free field with zero spatial average on the torus. The upper bound is obtained by a modification of the method that was used in \cite{LRV}, and the lower bound is obtained by applying the Donsker--Varadhan variational formula. We also give the probabilistic path integral formulation of the massless Sinh--Gordon model on a torus of side length $R$, and study its partition function $R$ tends to infinity. We apply the small deviation bounds for Gaussian multiplicative chaos to obtain lower and upper bounds for the logarithm of the partition function, leading to the existence of a non-zero and finite subsequential infinite volume limit for the free energy., Comment: Preliminary version

Increase in data, size, or compute can lead to sudden learning of specific capabilities by a neural network -- a phenomenon often called "emergence''. Beyond scientific understanding, establishing the causal factors underlying such emergent capabilities is crucial to enable risk regulation frameworks for AI. In this work, we seek inspiration from study of emergent properties in other fields and propose a phenomenological definition for the concept in the context of neural networks. Our definition implicates the acquisition of general structures underlying the data-generating process as a cause of sudden performance growth for specific, narrower tasks. We empirically investigate this definition by proposing an experimental system grounded in a context-sensitive formal language and find that Transformers trained to perform tasks on top of strings from this language indeed exhibit emergent capabilities. Specifically, we show that once the language's underlying grammar and context-sensitivity inducing structures are learned by the model, performance on narrower tasks suddenly begins to improve. We then analogize our network's learning dynamics with the process of percolation on a bipartite graph, establishing a formal phase transition model that predicts the shift in the point of emergence observed in our experiments when changing the data structure. Overall, our experimental and theoretical frameworks yield a step towards better defining, characterizing, and predicting emergence in neural networks., Comment: Preprint

The rise of generative artificial intelligence (GenAI) is transforming the telecom industry. GenAI models, particularly large language models (LLMs), have emerged as powerful tools capable of driving innovation, improving efficiency, and delivering superior customer services in telecom. This paper provides an overview of GenAI for telecom from theory to practice. We review GenAI models and discuss their practical applications in telecom. Furthermore, we describe the key technology enablers and best practices for applying GenAI to telecom effectively. We highlight the importance of retrieval augmented generation (RAG) in connecting LLMs to telecom domain specific data sources to enhance the accuracy of the LLMs' responses. We present a real-world use case on RAG-based chatbot that can answer open radio access network (O-RAN) specific questions. The demonstration of the chatbot to the O-RAN Alliance has triggered immense interest in the industry. We have made the O-RAN RAG chatbot publicly accessible on GitHub., Comment: 7 pages, 6 figures, submitted for possible publication

Due to the divergence-instability, the accuracy of low-order conforming finite element methods (FEMs) for nearly incompressible elasticity equations deteriorates as the Lam\'e parameter $\lambda\to\infty$, or equivalently as the Poisson ratio $\nu\to1/2$. This effect is known as \itshape{locking} or \itshape{non-robustness}. For the piecewise linear case, the error in the ${\bf L}^2$-norm of the standard Galerkin conforming FEM is bounded by $C\lambda h^2$, resulting in poor accuracy for practical values of $h$ if $\lambda$ is sufficiently large. In this paper, we show that for 2D problems the locking phenomenon can be controlled by replacing $\lambda$ with $\lambda_h=\lambda/(1+\lambda h/L)$ in the stiffness matrix, where $L$ is the diameter of the body $\Omega$. We prove that with this modification, the error in the ${\bf L}^2$-norm is bounded by $Ch$ for a constant $C$ that does not depend on $\lambda$. Numerical experiments confirm this convergence behaviour and show that, for practical meshes, our method is more accurate than the standard method if the material is nearly incompressible. Our analysis also shows that the error in the ${\bf H}^1$-norm is bounded by $Ch^{1/2}$, but our numerical experiments suggest that this bound is not sharp.

In exploring the simulation of human rhythmic perception and synchronization capabilities, this study introduces a computational model inspired by the physical and biological processes underlying rhythm processing. Utilizing a reservoir computing framework that simulates the function of cerebellum, the model features a dual-neuron classification and incorporates parameters to modulate information transfer, reflecting biological neural network characteristics. Our findings demonstrate the model's ability to accurately perceive and adapt to rhythmic patterns within the human perceptible range, exhibiting behavior closely aligned with human rhythm interaction. By incorporating fine-tuning mechanisms and delay-feedback, the model enables continuous learning and precise rhythm prediction. The introduction of customized settings further enhances its capacity to stimulate diverse human rhythmic behaviors, underscoring the potential of this architecture in temporal cognitive task modeling and the study of rhythm synchronization and prediction in artificial and biological systems. Therefore, our model is capable of transparently modelling cognitive theories that elucidate the dynamic processes by which the brain generates rhythm-related behavior.

As Fifth generation (5G) cellular systems transition to softwarized, programmable, and intelligent networks, it becomes fundamental to enable public and private 5G deployments that are (i) primarily based on software components while (ii) maintaining or exceeding the performance of traditional monolithic systems and (iii) enabling programmability through bespoke configurations and optimized deployments. This requires hardware acceleration to scale the Physical (PHY) layer performance, programmable elements in the Radio Access Network (RAN) and intelligent controllers at the edge, careful planning of the Radio Frequency (RF) environment, as well as end-to-end integration and testing. In this paper, we describe how we developed the programmable X5G testbed, addressing these challenges through the deployment of the first 8-node network based on the integration of NVIDIA Aerial RAN CoLab (ARC), OpenAirInterface (OAI), and a near-real-time RAN Intelligent Controller (RIC). The Aerial Software Development Kit (SDK) provides the PHY layer, accelerated on Graphics Processing Unit (GPU), with the higher layers from the OAI open-source project interfaced with the PHY through the Small Cell Forum (SCF) Functional Application Platform Interface (FAPI). An E2 agent provides connectivity to the O-RAN Software Community (OSC) near-real-time RIC. We discuss software integration, the network infrastructure, and a digital twin framework for RF planning. We then profile the performance with up to 4 Commercial Off-the-Shelf (COTS) smartphones for each base station with iPerf and video streaming applications, measuring a cell rate higher than 500 Mbps in downlink and 45 Mbps in uplink., Comment: 15 pages, 15 figures, 3 tables. arXiv admin note: text overlap with arXiv:2310.17062

We investigate experimentally the quantum coherence of an electronic two-level system in a double quantum dot under continuous charge detection. The charge-state of the two-level system is monitored by a capacitively coupled single quantum dot detector that imposes a back-action effect to the system. The measured back-action is well described by an additional decoherence rate, approximately linearly proportional to the detector electron tunneling rate. We provide a model for the decoherence rate arising due to level detuning fluctuations induced by detector charge fluctuations. The theory predicts a factor of two lower decoherence rate than observed in the experiment, suggesting the need for a more elaborate theory accounting for additional sources of decoherence., Comment: 5 pages, 3 figures

The measurement problem of quantum mechanics concerns the question under which circumstances coherent wave evolution becomes disrupted to produce eigenstates of observables, instead of evolving superpositions of eigenstates. The problem needs to be addressed already within wave mechanics, before second quantization, because low-energy interactions can be dominated by particle-preserving potential interactions. We discuss a scattering array of harmonic oscillators which can detect particles penetrating the array through interaction with a short-range potential. Evolution of the wave function of scattered particles, combined with Heisenberg's assertion that quantum jumps persist in wave mechanics, indicates that the wave function will collapse around single oscillator sites if the scattering is inelastic, while it will not collapse around single sites for elastic scattering. The Born rule for position observation is then equivalent to the statement that the wave function for inelastic scattering amounts to an epistemic superposition of possible scattering states, in the sense that it describes a sum of probability amplitudes for inelastic scattering off different scattering centers, whereas at most one inelastic scattering event can happen at any moment in time. Within this epistemic interpretation of the wave function, the actual underlying inelastic scattering event corresponds to a quantum jump, whereas the continuously evolving wave function only describes the continuous evolution of probability amplitudes for scattering off different sites. Quantum jumps then yield definite position observations as defined by the spatial resolution of the oscillator array., Comment: 5 pages

We live in a rich and varied acoustic world, which is experienced by individuals or communities as a soundscape. Computational auditory scene analysis, disentangling acoustic scenes by detecting and classifying events, focuses on objective attributes of sounds, such as their category and temporal characteristics, ignoring their effects on people, such as the emotions they evoke within a context. To fill this gap, we propose the soundscape captioning task, which enables automated soundscape analysis, thus avoiding labour-intensive subjective ratings and surveys in conventional methods. With soundscape captioning, context-aware descriptions are generated for soundscape by capturing the acoustic scene, event information, and the corresponding human affective qualities (AQs). To this end, we propose an automatic soundscape captioner (SoundSCaper) system composed of an acoustic model, i.e. SoundAQnet, and a large language model (LLM). SoundAQnet simultaneously models multi-scale information about acoustic scenes, events, and perceived AQs, while the LLM describes the soundscape with captions by parsing the information captured with SoundAQnet. The soundscape caption's quality is assessed by a jury of 16 audio/soundscape experts. The average score (out of 5) of SoundSCaper-generated captions is lower than the score of captions generated by two soundscape experts by 0.21 and 0.25, respectively, on the evaluation set and the model-unknown mixed external dataset with varying lengths and acoustic properties, but the differences are not statistically significant. Overall, the proposed SoundSCaper shows promising performance, with captions generated being comparable to those annotated by soundscape experts. The code of models, LLM scripts, human assessment data and instructions, and expert evaluation statistics are all publicly available., Comment: Code: https://github.com/Yuanbo2020/SoundSCaper

We present a superconducting cavity-coupled double quantum dot (DQD) photodiode that achieves a maximum photon-to-electron conversion efficiency of 25% in the microwave domain. With a higher-quality-factor cavity and improved device design to prevent photon leakages through unwanted pathways, our device measures microwave signals down to 100 aW power level and achieves sensitivity to probe microwave signals with one photon at a time in the cavity. We analyze the photodiode operation using Jaynes-Cummings input-output theory, identifying the key improvements of stronger cavity-DQD coupling needed to achieve near-unity photodetection efficiency. The results presented in this work represent a crucial advancement toward near unity microwave photodetection efficiency with single cavity-photon sensitivity for studies of photon statistics in the microwave range and applications related to quantum information processing., Comment: 8 pages, 4 figures

We propose reconstruction advantage measures to audit label privatization mechanisms. A reconstruction advantage measure quantifies the increase in an attacker's ability to infer the true label of an unlabeled example when provided with a private version of the labels in a dataset (e.g., aggregate of labels from different users or noisy labels output by randomized response), compared to an attacker that only observes the feature vectors, but may have prior knowledge of the correlation between features and labels. We consider two such auditing measures: one additive, and one multiplicative. These incorporate previous approaches taken in the literature on empirical auditing and differential privacy. The measures allow us to place a variety of proposed privatization schemes -- some differentially private, some not -- on the same footing. We analyze these measures theoretically under a distributional model which encapsulates reasonable adversarial settings. We also quantify their behavior empirically on real and simulated prediction tasks. Across a range of experimental settings, we find that differentially private schemes dominate or match the privacy-utility tradeoff of more heuristic approaches.

Let $\alpha$ be a Steinhaus or a Rademacher random multiplicative function. For a wide class of multiplicative functions $f$ we show that the sum $\sum_{n \le x}\alpha(n) f(n)$, normalised to have mean square $1$, has a non-Gaussian limiting distribution. More precisely, we establish a generalised central limit theorem with random variance determined by the total mass of a random measure associated with $\alpha f$. Our result applies to $d_z$, the $z$-th divisor function, as long as $z$ is strictly between $0$ and $\tfrac{1}{\sqrt{2}}$. Other examples of admissible $f$-s include any multiplicative indicator function with the property that $f(p)=1$ holds for a set of primes of density strictly between $0$ and $\tfrac{1}{2}$., Comment: 42 pages, 2 figures. Typos fixed, abstract and discussion of previous works updated. Codes for simulation experiment available on authors' personal page; comments are still welcome

Let $\alpha \colon \mathbb{N} \to S^1$ be the Steinhaus multiplicative function: a completely multiplicative function such that $(\alpha(p))_{p\text{ prime}}$ are i.i.d.~random variables uniformly distributed on $S^1$. Helson conjectured that $\mathbb{E}|\sum_{n\le x}\alpha(n)|=o(\sqrt{x})$ as $x \to \infty$, and this was solved in strong form by Harper. We give a short proof of the conjecture using a result of Saksman and Webb on a random model for the zeta function., Comment: 7 pages. Typos fixed and discussion of previous works added; comments are welcome