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Visual anomaly detection targets to detect images that notably differ from normal pattern, and it has found extensive application in identifying defective parts within the manufacturing industry. These anomaly detection paradigms predominantly focus on training detection models using only clean, unlabeled normal samples, assuming an absence of contamination; a condition often unmet in real-world scenarios. The performance of these methods significantly depends on the quality of the data and usually decreases when exposed to noise. We introduce a systematic adaptive method that employs deviation learning to compute anomaly scores end-to-end while addressing data contamination by assigning relative importance to the weights of individual instances. In this approach, the anomaly scores for normal instances are designed to approximate scalar scores obtained from the known prior distribution. Meanwhile, anomaly scores for anomaly examples are adjusted to exhibit statistically significant deviations from these reference scores. Our approach incorporates a constrained optimization problem within the deviation learning framework to update instance weights, resolving this problem for each mini-batch. Comprehensive experiments on the MVTec and VisA benchmark datasets indicate that our proposed method surpasses competing techniques and exhibits both stability and robustness in the presence of data contamination., Comment: Accepted to IEEE/CVF Winter Conference on Applications of Computer Vision (WACV 2025)

Zero-shot domain adaptation for dialogue state tracking (DST) remains a challenging problem in task-oriented dialogue (TOD) systems, where models must generalize to target domains unseen at training time. Current large language model approaches for zero-shot domain adaptation rely on prompting to introduce knowledge pertaining to the target domains. However, their efficacy strongly depends on prompt engineering, as well as the zero-shot ability of the underlying language model. In this work, we devise a novel data augmentation approach, Schema Augmentation, that improves the zero-shot domain adaptation of language models through fine-tuning. Schema Augmentation is a simple but effective technique that enhances generalization by introducing variations of slot names within the schema provided in the prompt. Experiments on MultiWOZ and SpokenWOZ showed that the proposed approach resulted in a substantial improvement over the baseline, in some experiments achieving over a twofold accuracy gain over unseen domains while maintaining equal or superior performance over all domains.

Interface-type resistive switching (RS) devices with lower operation current and more reliable switching repeatability exhibits great potential in the applications for data storage devices and ultra-low-energy computing. However, the working mechanism of such interface-type RS devices are much less studied compared to that of the filament-type devices, which hinders the design and application of the novel interface-type devices. In this work, we fabricate a metal/TiOx/TiN/Si (001) thin film memristor by using a one-step pulsed laser deposition. In situ transmission electron microscopy (TEM) imaging and current-voltage (I-V) characteristic demonstrate that the device is switched between high resistive state (HRS) and low resistive state (LRS) in a bipolar fashion with sweeping the applied positive and negative voltages. In situ scanning transmission electron microscopy (STEM) experiments with electron energy loss spectroscopy (EELS) reveal that the charged defects (such as oxygen vacancies) can migrate along the intrinsic grain boundaries of TiOx insulating phase under electric field without forming obvious conductive filaments, resulting in the modulation of Schottky barriers at the metal/semiconductor interfaces. The fundamental insights gained from this study presents a novel perspective on RS processes and opens up new technological opportunities for fabricating ultra-low-energy nitride-based memristive devices.

The time evolution of moderately dense gas evolving in vacuum described by the Boltzmann-Enskog equation is studied. The associated stochastic process, the Boltzmann-Enskog process, was constructed by Albeverio, R\"udiger and Sundar (2017) and further studied by Friesen, R\"udiger and Sundar (2019, 2022). The process is given by the solution of a McKean-Vlasov equation driven by a Poisson random measure, the compensator depending on the distribution of the solution. The existence of a marginal probability density function at each time for the measure-valued solution is established here by using a functional-analytic criterion in Besov spaces Debussche and Romito (2014), and Fournier (2015). In addition to existence, the density is shown to reside in a Besov space. The support of the velocity marginal distribution is shown to be the whole of $\mathbb{R}^3$., Comment: 36 pages

With the rise of AI-generated content spewed at scale from large language models (LLMs), genuine concerns about the spread of fake news have intensified. The perceived ability of LLMs to produce convincing fake news at scale poses new challenges for both human and automated fake news detection systems. To address this gap, this work presents the findings from a university-level competition which aimed to explore how LLMs can be used by humans to create fake news, and to assess the ability of human annotators and AI models to detect it. A total of 110 participants used LLMs to create 252 unique fake news stories, and 84 annotators participated in the detection tasks. Our findings indicate that LLMs are ~68% more effective at detecting real news than humans. However, for fake news detection, the performance of LLMs and humans remains comparable (~60% accuracy). Additionally, we examine the impact of visual elements (e.g., pictures) in news on the accuracy of detecting fake news stories. Finally, we also examine various strategies used by fake news creators to enhance the credibility of their AI-generated content. This work highlights the increasing complexity of detecting AI-generated fake news, particularly in collaborative human-AI settings.

Potential-driven steady-state flow in networks is an abstract problem which manifests in various engineering applications, such as transport of natural gas, water, electric power through infrastructure networks or flow through fractured rocks modeled as discrete fracture networks. The relevance of steady-state network flow to control systems and optimization, as well as the question of the existence of a solution for a particular class of flows, has been established in a prior article (IEEE Control Systems Letters (2024), doi:10.1109/LCSYS.2024.3394317). Building on that foundation, this article concerns itself with computation of such a solution for a large network since the problem while simple when restricted to a single edge of a network, ceases to be so for a large network. The resultant system of nonlinear equations depends on the network topology and in general there is no numerical algorithm that offers guaranteed convergence to the solution (assuming a solution exists). Some methods offer guarantees in cases where the network topology satisfies certain assumptions, but these methods fail for larger networks. On the other hand, the Newton-Raphson algorithm offers a convergence guarantee if the starting point lies close to the (unknown) solution. It would be advantageous to compute the solution of the large nonlinear system through the solution of smaller nonlinear sub-systems wherein the solution algorithms (Newton-Raphson or otherwise) are more likely to succeed. This article proposes and describes such a procedure, an hierarchical network partitioning algorithm that enables the solution of large nonlinear systems corresponding to potential-driven steady-state network flow equations.

The analysis of non-local regularisations of scalar conservation laws is an active research program. Applications of such equations are found in the modelling of physical phenomena such as traffic flow. In this paper, we propose a novel inviscid, non-local regularisation in non-divergence form. The salient feature of our approach is that we can obtain sharp a priori estimates on the total variation and supremum norm, and justify the singular limit for Lipschitz initial data up to the time of catastrophe. For generic conservation laws, this result is sharp, since we can demonstrate non-convergence when the initial data features simple discontinuities. Conservation laws with linear flux derivative, such as the Burgers equation, behave better in the presence of discontinuities. Hence, we devote special attention to the limiting behaviour of non-local solutions with respect to the Burgers equation for a simple class of discontinuous initial data., Comment: 21 pages

The widespread adoption of large language models (LLMs) and generative AI (GenAI) tools across diverse applications has amplified the importance of addressing societal biases inherent within these technologies. While the NLP community has extensively studied LLM bias, research investigating how non-expert users perceive and interact with biases from these systems remains limited. As these technologies become increasingly prevalent, understanding this question is crucial to inform model developers in their efforts to mitigate bias. To address this gap, this work presents the findings from a university-level competition, which challenged participants to design prompts for eliciting biased outputs from GenAI tools. We quantitatively and qualitatively analyze the competition submissions and identify a diverse set of biases in GenAI and strategies employed by participants to induce bias in GenAI. Our finding provides unique insights into how non-expert users perceive and interact with biases from GenAI tools.

The shallow water equations are numerically solved to simulate free surface flows. The convective flux terms in the shallow water equations need to be discretized using a Riemann solver to capture shocks and discontinuity for certain flow situations such as hydraulic jump, dam-break wave propagation or bore wave propagation, levee-breaching flows, etc. The approximate Riemann solver can capture shocks and is popular for studying open-channel flow dynamics with traditional mesh-based numerical methods. Though meshless methods can work on highly irregular geometry without involving the complex mesh generation procedure, the shock-capturing capability has not been implemented, especially for solving open-channel flows. Therefore, we have proposed a numerical method, namely, a shock-capturing meshless geometric conservation weighted least square (GC-WLS) method for solving the shallow water equations. The HLL (Harten-Lax-Van Leer) Riemann solver is implemented within the framework of the proposed meshless method. The spatial derivatives in the shallow water equations and the reconstruction of conservative variables for high-order accuracy are computed using the GC-WLS method. The proposed meshless method is tested for various numerically challenging open-channel flow problems, including analytical, laboratory experiments, and a large-scale physical model study on dam-break event.

Constrained optimization problems arise in various engineering system operations such as inventory management and electric power grids. However, the requirement to repeatedly solve such optimization problems with uncertain parameters poses a significant computational challenge. This work introduces a learning scheme using Bayesian Neural Networks (BNNs) to solve constrained optimization problems under limited labeled data and restricted model training times. We propose a semi-supervised BNN for this practical but complex regime, wherein training commences in a sandwiched fashion, alternating between a supervised learning step (using labeled data) for minimizing cost, and an unsupervised learning step (using unlabeled data) for enforcing constraint feasibility. Both supervised and unsupervised steps use a Bayesian approach, where Stochastic Variational Inference is employed for approximate Bayesian inference. We show that the proposed semi-supervised learning method outperforms conventional BNN and deep neural network (DNN) architectures on important non-convex constrained optimization problems from energy network operations, achieving up to a tenfold reduction in expected maximum equality gap and halving the optimality and inequality (feasibility) gaps, without requiring any correction or projection step. By leveraging the BNN's ability to provide posterior samples at minimal computational cost, we demonstrate that a Selection via Posterior (SvP) scheme can further reduce equality gaps by more than 10%. We also provide tight and practically meaningful probabilistic confidence bounds that can be constructed using a low number of labeled testing data and readily adapted to other applications.

Scene Change Detection is a challenging task in computer vision and robotics that aims to identify differences between two images of the same scene captured at different times. Traditional change detection methods rely on training models that take these image pairs as input and estimate the changes, which requires large amounts of annotated data, a costly and time-consuming process. To overcome this, we propose ZeroSCD, a zero-shot scene change detection framework that eliminates the need for training. ZeroSCD leverages pre-existing models for place recognition and semantic segmentation, utilizing their features and outputs to perform change detection. In this framework, features extracted from the place recognition model are used to estimate correspondences and detect changes between the two images. These are then combined with segmentation results from the semantic segmentation model to precisely delineate the boundaries of the detected changes. Extensive experiments on benchmark datasets demonstrate that ZeroSCD outperforms several state-of-the-art methods in change detection accuracy, despite not being trained on any of the benchmark datasets, proving its effectiveness and adaptability across different scenarios.

Coded caching in a wireless device-to-device (D2D) network was first studied by Ji \textit{et al.} in [4] (referred to as the JCM scheme). In a D2D network, a central server first places the data in the user cache memories and all the user's demands are served by inter-user coded multicast transmissions. Low subpacketization level D2D coded caching schemes are desirable for practical implementations. Wang \textit{et al.} in [7] proposed an array called D2D placement delivery array (DPDA) which characterizes the placement phase and the delivery phase in a D2D network. A lower bound on the transmission load of a DPDA is derived and only the JCM scheme achieves this lower bound, but requires a subpacketization level that grows exponentially with the number of users. Low subpacketization level D2D schemes can be obtained by constructing appropriate DPDAs. In this paper, we propose two new classes of DPDA constructions that give low subpacketization level D2D schemes using cross resolvable designs. The first class of constructed DPDA achieves the known lower bound on the transmission load of DPDA while requiring a subpacketization level lesser than that of the JCM scheme. We propose another lower bound on the transmission load of a DPDA and show that the second class of constructed DPDA achieves this lower bound., Comment: 9 pages, 3 tables and 7 figures

We study the largest eigenvalue of a Gaussian random symmetric matrix $X_n$, with zero-mean, unit variance entries satisfying the condition $\sup_{(i, j) \ne (i', j')}|\mathbb{E}[X_{ij} X_{i'j'}]| = O(n^{-(1 + \varepsilon)})$, where $\varepsilon > 0$. It follows from Catalano et al. (2024) that the empirical spectral distribution of $n^{-1/2} X_n$ converges weakly almost surely to the standard semi-circle law. Using a F\"{u}redi-Koml\'{o}s-type high moment analysis, we show that the largest eigenvalue $\lambda_1(n^{-1/2} X_n)$ of $n^{-1/2} X_n$ converges almost surely to $2$. This result is essentially optimal in the sense that one cannot take $\varepsilon = 0$ and still obtain an almost sure limit of $2$. We also derive Gaussian fluctuation results for the largest eigenvalue in the case where the entries have a common non-zero mean. Let $Y_n = X_n + \frac{\lambda}{\sqrt{n}}\mathbf{1} \mathbf{1}^\top$. When $\varepsilon \ge 1$ and $\lambda \gg n^{1/4}$, we show that \[ n^{1/2}\bigg(\lambda_1(n^{-1/2} Y_n) - \lambda - \frac{1}{\lambda}\bigg) \xrightarrow{d} \sqrt{2} Z, \] where $Z$ is a standard Gaussian. On the other hand, when $0 < \varepsilon < 1$, we have $\mathrm{Var}(\frac{1}{n}\sum_{i, j}X_{ij}) = O(n^{1 - \varepsilon})$. Assuming that $\mathrm{Var}(\frac{1}{n}\sum_{i, j} X_{ij}) = \sigma^2 n^{1 - \varepsilon} (1 + o(1))$, if $\lambda \gg n^{\varepsilon/4}$, then we have \[ n^{\varepsilon/2}\bigg(\lambda_1(n^{-1/2} Y_n) - \lambda - \frac{1}{\lambda}\bigg) \xrightarrow{d} \sigma Z. \] While the ranges of $\lambda$ in these fluctuation results are certainly not optimal, a striking aspect is that different scalings are required in the two regimes $0 < \varepsilon < 1$ and $\varepsilon \ge 1$., Comment: 23 pages, 2 figures

We study adjacency and Laplacian matrices of Erd\H{o}s-R\'{e}nyi $r$-uniform hypergraphs on $n$ vertices with hyperedge inclusion probability $p$, in the setting where $r$ can vary with $n$ such that $r / n \to c \in [0, 1)$. Adjacency matrices of hypergraphs are contractions of adjacency tensors and their entries exhibit long range correlations. We show that under the Erd\H{o}s-R\'{e}nyi model, the expected empirical spectral distribution of an appropriately normalised hypergraph adjacency matrix converges weakly to the semi-circle law with variance $(1 - c)^2$ as long as $\frac{d_{\avg}}{r^7} \to \infty$, where $d_{\avg} = \binom{n-1}{r-1} p$. In contrast with the Erd\H{o}s-R\'{e}nyi random graph ($r = 2$), two eigenvalues stick out of the bulk of the spectrum. When $r$ is fixed and $d_{\avg} \gg n^{r - 2} \log^4 n$, we uncover an interesting Baik-Ben Arous-P\'{e}ch\'{e} (BBP) phase transition at the value $r = 3$. For $r \in \{2, 3\}$, an appropriately scaled largest (resp. smallest) eigenvalue converges in probability to $2$ (resp. $-2$), the right (resp. left) end point of the support of the standard semi-circle law, and when $r \ge 4$, it converges to $\sqrt{r - 2} + \frac{1}{\sqrt{r - 2}}$ (resp. $-\sqrt{r - 2} - \frac{1}{\sqrt{r - 2}}$). Further, in a Gaussian version of the model we show that an appropriately scaled largest (resp. smallest) eigenvalue converges in distribution to $\frac{c}{2} \zeta + \big[\frac{c^2}{4}\zeta^2 + c(1 - c)\big]^{1/2}$ (resp. $\frac{c}{2} \zeta - \big[\frac{c^2}{4}\zeta^2 + c(1 - c)\big]^{1/2}$), where $\zeta$ is a standard Gaussian. We also establish analogous results for the bulk and edge eigenvalues of the associated Laplacian matrices.

Determinantal Point Processes (DPPs), which originate from quantum and statistical physics, are known for modelling diversity. Recent research [Ghosh and Rigollet (2020)] has demonstrated that certain matrix-valued $U$-statistics (that are truncated versions of the usual sample covariance matrix) can effectively estimate parameters in the context of Gaussian DPPs and enhance dimension reduction techniques, outperforming standard methods like PCA in clustering applications. This paper explores the spectral properties of these matrix-valued $U$-statistics in the null setting of an isotropic design. These matrices may be represented as $X L X^\top$, where $X$ is a data matrix and $L$ is the Laplacian matrix of a random geometric graph associated to $X$. The main mathematically interesting twist here is that the matrix $L$ is dependent on $X$. We give complete descriptions of the bulk spectra of these matrix-valued $U$-statistics in terms of the Stieltjes transforms of their empirical spectral measures. The results and the techniques are in fact able to address a broader class of kernelised random matrices, connecting their limiting spectra to generalised Mar\v{c}enko-Pastur laws and free probability., Comment: 26 pages, 2 figures

The impact of discrete clutter and co-channel interference on the performance of automotive radar networks has been studied using stochastic geometry, in particular, by leveraging two-dimensional Poisson point processes (PPPs). However, such characterization does not take into account the impact of street geometry and the fact that the location of the automotive radars are restricted to the streets as their domain rather than the entire Euclidean plane. In addition, the structure of the streets may change drastically as a vehicle moves out of a city center towards the outskirts. Consequently, not only the radar performance change but also the radar parameters and protocols must be adapted for optimum performance. In this paper, we propose and characterize line and Cox process-based street and point models to analyze large-scale automotive radar networks. We consider the classical Poisson line process (PLP) and the newly introduced Binomial line process (BLP) model to emulate the streets and the corresponding PPP-based Cox process to emulate the vehicular nodes. In particular, the BLP model effectively considers the spatial variation of street geometry across different parts of the city. We derive the effective interference set experienced by an automotive radar, the statistics of distance to interferers, and characterize the detection probability of the ego radar as a function of street and vehicle density. Finally, leveraging the real-world data on urban streets and vehicle density across different cities of the world, we present how the radar performance varies in different parts of the city as well as across different times of the day. Thus, our study equips network operators and automotive manufacturers with essential system design insights to plan and optimize automotive radar networks., Comment: Submitted to IEEE TWC

We consider a variant of the coded caching problem where users connect to two types of caches, called private caches and access caches. The problem setting consists of a server having a library of files and a set of access caches. Every user, equipped with a private cache, connects to $L$ neighboring access caches in a cyclic wrap-around fashion. The server populates the private and access caches with file contents in either coded or uncoded format. For this setting, we derive a lower bound on the optimal worst-case transmission rate using cut-set arguments. This lower bound applies to both coded and uncoded placements. We then provide an achievable scheme with uncoded placement and show that our scheme specializes to the well-known Maddah-Ali-Niesen scheme for the dedicated cache network in the absence of access caches. Finally, we show that the proposed scheme achieves optimality in large memory regimes and provide numerical plots comparing the rate of the proposed scheme with the derived lower bound, demonstrating the optimality of our scheme., Comment: 15 pages, 5 figures and one table. Some overlap of introductory and background materials with our earlier submission arXiv:2407.00677v1 dated 30 June 2024

Quantum approximate optimization is one of the promising candidates for useful quantum computation, particularly in the context of finding approximate solutions to Quadratic Unconstrained Binary Optimization (QUBO) problems. However, the existing quantum processing units (QPUs) are relatively small, and canonical mappings of QUBO via the Ising model require one qubit per variable, rendering direct large-scale optimization infeasible. In classical optimization, a general strategy for addressing many large-scale problems is via multilevel/multigrid methods, where the large target problem is iteratively coarsened, and the global solution is constructed from multiple small-scale optimization runs. In this work, we experimentally test how existing QPUs perform as a sub-solver within such a multilevel strategy. We combine and extend (via additional classical processing) the recent Noise-Directed Adaptive Remapping (NDAR) and Quantum Relax $\&$ Round (QRR) algorithms. We first demonstrate the effectiveness of our heuristic extensions on Rigetti's transmon device Ankaa-2. We find approximate solutions to $10$ instances of fully connected $82$-qubit Sherrington-Kirkpatrick graphs with random integer-valued coefficients obtaining normalized approximation ratios (ARs) in the range $\sim 0.98-1.0$, and the same class with real-valued coefficients (ARs $\sim 0.94-1.0$). Then, we implement the extended NDAR and QRR algorithms as subsolvers in the multilevel algorithm for $6$ large-scale graphs with at most $\sim 27,000$ variables. The QPU (with classical post-processing steps) is used to find approximate solutions to dozens of problems, at most $82$-qubit, which are iteratively used to construct the global solution. We observe that quantum optimization results are competitive regarding the quality of solutions compared to classical heuristics used as subsolvers within the multilevel approach., Comment: 7+3 pages; 6+0 figures; 2+0 tables; comments and suggestions are welcome!

The relation between magnetic field strength B and gas density n in the interstellar medium is of fundamental importance to many areas of astrophysics, from protostellar disks to galaxy evolution. We present and compare Bayesian analyses of the B - n relation for a comprehensive observational data set, as well as a large body of numerical MHD simulations. We extend the original Zeeman relation of Crutcher et al. (2010) with a large body of magnetic data that includes 700 observations with the Davis-Chandrasekhar-Fermi method. By using a new multiparameter Bayesian analysis we present a new, more general, time-averaged observational relation: B \propto n^{0.27 \pm 0.017} for n \leq n_0 and B \propto n^{0.54 \pm 0.18} for n \geq n_0, with n_0 = 924^(+145-144) cm^-3. We perform a separate analysis on 19 numerical magnetohydrodynamics simulations that cover a wide range of scales, resolutions, initial conditions, and completed with a variety of codes: arepo, flash, pencil, and ramses. The power law exponents derived from the simulations depend on several physical factors including: dynamo effects, time scales, turbulence, and the initial seed field strength. In particular, early-time simulations where the density, velocity and magnetic fields are unevolved do not match the observational scalings. The simulations that trace the observed density range best, the evolved dwarf galaxy and Milky Way like galaxy simulations, settle into a near consistent exponent of = 0.5 in the dense gas, with variability in the diffuse gas exponent., Comment: 23 figures, 28 pages, submitted to MNRAS, Comments welcome

We present a novel algorithm that fuses the existing convex-programming based approach with heuristic information to find optimality guarantees and near-optimal paths for the Shortest Path Problem in the Graph of Convex Sets (SPP-GCS). Our method, inspired by $A^*$, initiates a best-first-like procedure from a designated subset of vertices and iteratively expands it until further growth is neither possible nor beneficial. Traditionally, obtaining solutions with bounds for an optimization problem involves solving a relaxation, modifying the relaxed solution to a feasible one, and then comparing the two solutions to establish bounds. However, for SPP-GCS, we demonstrate that reversing this process can be more advantageous, especially with Euclidean travel costs. In other words, we initially employ $A^*$ to find a feasible solution for SPP-GCS, then solve a convex relaxation restricted to the vertices explored by $A^*$ to obtain a relaxed solution, and finally, compare the solutions to derive bounds. We present numerical results to highlight the advantages of our algorithm over the existing approach in terms of the sizes of the convex programs solved and computation time.

Quantum optimization solvers typically rely on one-variable-to-one-qubit mapping. However, the low qubit count on current quantum computers is a major obstacle in competing against classical methods. Here, we develop a qubit-efficient algorithm that overcomes this limitation by mapping a candidate bit string solution to an entangled wave function of fewer qubits. We propose a variational quantum circuit generalizing the quantum approximate optimization ansatz (QAOA). Extremizing the ansatz for Sherrington-Kirkpatrick spin glass problems, we show valuable properties such as the concentration of ansatz parameters and derive performance guarantees. This approach could benefit near-term intermediate-scale and future fault-tolerant small-scale quantum devices., Comment: 4 pages, 4 figures + 8 pages of supplementary material

Event cameras capture the world at high time resolution and with minimal bandwidth requirements. However, event streams, which only encode changes in brightness, do not contain sufficient scene information to support a wide variety of downstream tasks. In this work, we design generalized event cameras that inherently preserve scene intensity in a bandwidth-efficient manner. We generalize event cameras in terms of when an event is generated and what information is transmitted. To implement our designs, we turn to single-photon sensors that provide digital access to individual photon detections; this modality gives us the flexibility to realize a rich space of generalized event cameras. Our single-photon event cameras are capable of high-speed, high-fidelity imaging at low readout rates. Consequently, these event cameras can support plug-and-play downstream inference, without capturing new event datasets or designing specialized event-vision models. As a practical implication, our designs, which involve lightweight and near-sensor-compatible computations, provide a way to use single-photon sensors without exorbitant bandwidth costs., Comment: CVPR 2024

Submillimeter and millimeter wavelengths provide a unique view of the Universe, from the gas and dust that fills and surrounds galaxies to the chromosphere of our own Sun. Current single-dish facilities have presented a tantalising view of the brightest (sub-)mm sources, and interferometers have provided the exquisite resolution necessary to analyse the details in small fields, but there are still many open questions that cannot be answered with current facilities. In this report we summarise the science that is guiding the design of the Atacama Large Aperture Submillimeter Telescope (AtLAST). We demonstrate how tranformational advances in topics including star formation in high redshift galaxies, the diffuse circumgalactic medium, Galactic ecology, cometary compositions and solar flares motivate the need for a 50m, single-dish telescope with a 1-2 degree field of view and a new generation of highly multiplexed continuum and spectral cameras. AtLAST will have the resolution to drastically lower the confusion limit compared to current single-dish facilities, whilst also being able to rapidly map large areas of the sky and detect extended, diffuse structures. Its high sensitivity and large field of view will open up the field of submillimeter transient science by increasing the probability of serendipitous detections. Finally, the science cases listed here motivate the need for a highly flexible operations model capable of short observations of individual targets, large surveys, monitoring programmes, target of opportunity observations and coordinated observations with other observatories. AtLAST aims to be a sustainable, upgradeable, multipurpose facility that will deliver orders of magnitude increases in sensitivity and mapping speeds over current and planned submillimeter observatories., Comment: 47 pages, 12 figures. For further details on AtLAST see https://atlast.uio.no

We consider a variant of the coded caching problem where users connect to two types of caches, called private and access caches. The problem setting consists of a server with a library of files and a set of access caches. Each user, equipped with a private cache, connects to a distinct $r-$subset of the access caches. The server populates both types of caches with files in uncoded format. For this setting, we provide an achievable scheme and derive a lower bound on the number of transmissions for this scheme. We also present a lower and upper bound for the optimal worst-case rate under uncoded placement for this setting using the rates of the Maddah-Ali--Niesen scheme for dedicated and combinatorial multi-access coded caching settings, respectively. Further, we derive a lower bound on the optimal worst-case rate for any general placement policy using cut-set arguments. We also provide numerical plots comparing the rate of the proposed achievability scheme with the above bounds, from which it can be observed that the proposed scheme approaches the lower bound when the amount of memory accessed by a user is large. Finally, we discuss the optimality w.r.t worst-case rate when the system has four access caches., Comment: 13 pages and 6 figures

We consider a wireless distributed computing system based on the MapReduce framework, which consists of three phases: \textit{Map}, \textit{Shuffle}, and \textit{Reduce}. The system consists of a set of distributed nodes assigned to compute arbitrary output functions depending on a file library. The computation of the output functions is decomposed into Map and Reduce functions, and the Shuffle phase, which involves the data exchange, links the two. In our model, the Shuffle phase communication happens over a full-duplex wireless interference channel. For this setting, a coded wireless MapReduce distributed computing scheme exists in the literature, achieving optimal performance under one-shot linear schemes. However, the scheme requires the number of input files to be very large, growing exponentially with the number of nodes. We present schemes that require the number of files to be in the order of the number of nodes and achieve the same performance as the existing scheme. The schemes are obtained by designing a structure called wireless MapReduce array that succinctly represents all three phases in a single array. The wireless MapReduce arrays can also be obtained from the extended placement delivery arrays known for multi-antenna coded caching schemes., Comment: Communicated to 2024 IEEE Information Theory Workshop (ITW'24), Shenzhen, China

Multi-group multicast (MGM) is an increasingly important form of multi-user wireless communications with several potential applications, such as video streaming, federated learning, safety-critical vehicular communications, etc. Rate-Splitting Multiple Access (RSMA) is a powerful interference management technique that can, in principle, achieve higher data rates and greater fairness for all types of multi-user wireless communications, including MGM. This paper presents the first-ever experimental evaluation of RSMA-based MGM, as well as the first-ever three-way comparison of RSMA-based, Space Divison Multiple Access (SDMA)-based and Non-Orthogonal Multiple Access (NOMA)-based MGM. Using a measurement setup involving a two-antenna transmitter and two groups of two single-antenna users per group, we consider the problem of realizing throughput (max-min) fairness across groups for each of three multiple access schemes, over nine experimental cases in a line-of-sight environment capturing varying levels of pathloss difference and channel correlation across the groups. Over these cases, we observe that RSMA-based MGM achieves fairness at a higher throughput for each group than SDMA- and NOMA-based MGM. These findings validate RSMA-based MGM's promised gains from the theoretical literature., Comment: Accepted for publication in IEEE Transactions on Broadcasting

Existing ML benchmarks lack the depth and diversity of annotations needed for evaluating models on business process management (BPM) tasks. BPM is the practice of documenting, measuring, improving, and automating enterprise workflows. However, research has focused almost exclusively on one task - full end-to-end automation using agents based on multimodal foundation models (FMs) like GPT-4. This focus on automation ignores the reality of how most BPM tools are applied today - simply documenting the relevant workflow takes 60% of the time of the typical process optimization project. To address this gap we present WONDERBREAD, the first benchmark for evaluating multimodal FMs on BPM tasks beyond automation. Our contributions are: (1) a dataset containing 2928 documented workflow demonstrations; (2) 6 novel BPM tasks sourced from real-world applications ranging from workflow documentation to knowledge transfer to process improvement; and (3) an automated evaluation harness. Our benchmark shows that while state-of-the-art FMs can automatically generate documentation (e.g. recalling 88% of the steps taken in a video demonstration of a workflow), they struggle to re-apply that knowledge towards finer-grained validation of workflow completion (F1 < 0.3). We hope WONDERBREAD encourages the development of more "human-centered" AI tooling for enterprise applications and furthers the exploration of multimodal FMs for the broader universe of BPM tasks. We publish our dataset and experiments here: https://github.com/HazyResearch/wonderbread

An emerging area of research in situated and multimodal interactive conversations (SIMMC) includes interactions in scientific papers. Since scientific papers are primarily composed of text, equations, figures, and tables, SIMMC methods must be developed specifically for each component to support the depth of inquiry and interactions required by research scientists. This work introduces Conversational Papers (cPAPERS), a dataset of conversational question-answer pairs from reviews of academic papers grounded in these paper components and their associated references from scientific documents available on arXiv. We present a data collection strategy to collect these question-answer pairs from OpenReview and associate them with contextual information from LaTeX source files. Additionally, we present a series of baseline approaches utilizing Large Language Models (LLMs) in both zero-shot and fine-tuned configurations to address the cPAPERS dataset., Comment: 14 pages, 1 figure

We study transfer learning for estimation in latent variable network models. In our setting, the conditional edge probability matrices given the latent variables are represented by $P$ for the source and $Q$ for the target. We wish to estimate $Q$ given two kinds of data: (1) edge data from a subgraph induced by an $o(1)$ fraction of the nodes of $Q$, and (2) edge data from all of $P$. If the source $P$ has no relation to the target $Q$, the estimation error must be $\Omega(1)$. However, we show that if the latent variables are shared, then vanishing error is possible. We give an efficient algorithm that utilizes the ordering of a suitably defined graph distance. Our algorithm achieves $o(1)$ error and does not assume a parametric form on the source or target networks. Next, for the specific case of Stochastic Block Models we prove a minimax lower bound and show that a simple algorithm achieves this rate. Finally, we empirically demonstrate our algorithm's use on real-world and simulated graph transfer problems.

We propose the use of phonon$\unicode{x2013}$mediated interactions as an entanglement resource to engineer Einstein$\unicode{x2013}$Podolsky$\unicode{x2013}$Rosen (EPR) correlations and to perform teleportation of collective spin states in two$\unicode{x2013}$dimensional ion crystals. We emulate continuous variable quantum teleportation protocols between subsystems corresponding to different nuclear spin degrees of freedom. In each of them, a quantum state is encoded in an electronic spin degree of freedom that couples to the vibrational modes of the crystal. We show that high fidelity teleportation of spin-coherent states and their phase-displaced variant, entangled spin-squeezed states, and Dicke states, is possible for realistic experimental conditions in arrays from a few tens to a few hundred ions., Comment: 9 pages, 7 figure

Coded caching scheme originally proposed by Maddah-Ali and Niesen (MN) considered a broadcast network consisting of a single server connected to a set of users each having a cache memory. Motivated by practical scenarios, Karamchandani \textit{et al.} in [16] proposed a coded caching scheme for a two-layer hierarchical network consisting of a single server connected to multiple mirror sites and each mirror site connected to a distinct set of users, in which both mirror sites and users having cache memories. Low subpacketization level coded caching schemes are desirable for practical implementations. Placement delivery array (PDA) was proposed as a tool to design coded caching schemes with reduced subpacketization level by Yan \textit{et al.} in [4]. Schemes with reduced subpacketization levels are studied extensively in the literature for single-layer networks. Kong \textit{et al.} in [17] proposed a structure called hierarchical placement delivery arrays (HPDA), which characterizes a hierarchical coded caching system and also proposed a class of HPDAs that gives low subpacketization level schemes by using two PDAs. Low subpacketization level hierarchical schemes using combinatorial $t$-designs is proposed in [20]. Apart from that there is no other existing work that discusses the subpacketization problem in a hierarchical network. This paper proposes a class of HPDA construction that gives low subpacketization level hierarchical coded caching schemes, by first constructing a new class of PDAs. Compared with the existing schemes, in cases where the system parameters and subpacketization level are the same, the proposed hierarchical scheme has a better coding delay. Further, the new class of PDAs constructed either subsumes several known PDA constructions or achieves better transmission load for the same system parameters., Comment: Added Section IV - (performance analysis of proposed HPDA construction). The term 'coding delay' is formally defined (page no. 5). 14 pages, 10 figures and 9 tables

Spectral energy distribution (SED) fitting is one of most commonly used techniques to study the dust properties in Active Galactic Nuclei (AGN). Works implementing this technique commonly use radiative transfer models that assume a variety of dust properties. Despite the key role of this aspect, limited effort has been put forward to explore the chemical composition, the role of different optical properties, and the grain size distribution of dust, all of which can have a substantial impact on the theoretical radiative transfer calculations. In this work, we explore the role of the dust chemical composition in the AGN dusty torus through SED fitting to \emph{Spitzer}/IRS spectra of a sample of 49 nearby AGN with silicate features in emission. We implement a mineralogy model including the popular astronomical silicates and a set of oxides and amorphous silicates with different grain sizes. We find that best fits use principally porous alumina, periclase, and olivine. In terms of mass fractions, $\sim99\%$ of the dust is composed of dust grains of size $\rm{0.1 \mu m}$, with a $<1\%$ contribution from $\rm{3 \mu m}$ grains. Moreover, the astronomical silicates have a very low occurrence in the best fits, suggesting that they are not the most suited dust species to reproduce the silicate features in our sample., Comment: 16 pages, 13 figures, Accepted by MNRAS

We consider a coded caching network consisting of a server with a library of $N$ files connected to $K$ users, where each user is equipped with a dedicated cache of size $M_p$ units. In addition to that, the network consists of $\Lambda\leq K$ helper caches, each with a size $M_h$ units. Each helper cache can serve an arbitrary number of users; however, each user can access only a single helper cache. Also, we assume that the server knows the user-to-helper cache association, defined as the sets of users connected to each helper cache, during the cache placement phase. We propose a solution for the aforementioned coded caching problem by introducing a combinatorial structure called a Shared and Private Placement Delivery Array (SP-PDA). These SP-PDAs describe the helper cache placement, private cache placement, and the server transmissions in a single array. Further, we propose a novel construction of SP-PDAs using two Placement Delivery Arrays (PDAs). Interestingly, we observe that the permutations of the columns of the two chosen PDAs result in SP-PDAs with different performances. Moreover, we characterize the conditions for selecting the best column permutations of the chosen PDAs. Furthermore, the coded caching schemes resulting from SP-PDAs subsume two existing coded caching schemes as special cases. Additionally, SP-PDAs enable the construction of coded caching schemes with much smaller subpacketization numbers -subpacketization number is defined as the number of subfiles to which a file is divided- compared to the existing schemes, without paying much in terms of rate (the size of the transmission in the delivery phase)., Comment: A shorter version is accepted for presentation in ISIT 2024. 11 pages, 4 figures

This work introduces a multi-antenna coded caching problem in a two-dimensional multi-access network, where a server with $L$ transmit antennas and $N$ files communicates to $K_1K_2$ users, each with a single receive antenna, through a wireless broadcast link. The network consists of $K_1K_2$ cache nodes and $K_1K_2$ users. The cache nodes, each with capacity $M$, are placed on a rectangular grid with $K_1$ rows and $K_2$ columns, and the users are placed regularly on the square grid such that a user can access $r^2$ neighbouring caches in a cyclic wrap-around fashion. For a given cache memory $M$, the goal of the coded caching problem is to serve the user demands with a minimum delivery time. We propose a solution for the aforementioned coded caching problem by designing two arrays: a caching array and a delivery array. Further, we present two classes of caching and delivery arrays and obtain corresponding multi-access coded caching schemes. The first scheme achieves a normalized delivery time (NDT) $\frac{K_1K_2(1-r^2\frac{M}{N})}{L+K_1K_2\frac{M}{N}}$. The second scheme achieves an NDT $\frac{K_1K_2(1-r^2\frac{M}{N})}{L+K_1K_2r^2\frac{M}{N}}$ when $M/N=1/K_1K_2$ and $L=K_1K_2-r^2$, which is optimal under uncoded placement and one-shot delivery., Comment: A shorter version is accepted for presentation in ISIT 2024. 8 pages, 4 figures

We examine the modeling, simulation, and optimization of district heating systems, which are widely used for thermal transport using steam or hot water as a carrier. We propose a generalizable framework to specify network models and scenario parameters, and develop an optimization method for evaluating system states including pressures, fluid flow rates, and temperatures throughout the network. The network modeling includes pipes, thermal plants, pumps, and passive or controllable loads as system components. We propose basic models for thermodynamic fluid transport and enforce the balance of physical quantities in steady-state flow over co-located outgoing and return networks. We formulate an optimization problem with steam and hot water as the outgoing and return carriers, as in legacy 20th century systems. The physical laws and engineering limitations are specified for each component type, and the thermal network flow optimization (TNFO) problem is formulated and solved for a realistic test network under several scenarios.

Achieving high-quality solutions faster than classical solvers on computationally hard problems is a challenge for quantum optimization to deliver utility. Using a superconducting quantum computer, we experimentally investigate the performance of a hybrid quantum-classical algorithm inspired by semidefinite programming approaches for solving the maximum cut problem on 3-regular graphs up to several thousand variables. We leverage the structure of the input problems to address sizes beyond what current quantum machines can naively handle. We attain an average performance of 99% over a random ensemble of thousands of problem instances. We benchmark the quantum solver against similarly high-performing classical heuristics, including the Gurobi optimizer, simulated annealing, and the Burer-Monteiro algorithm. A runtime analysis shows that the quantum solver on large-scale problems is competitive against Gurobi but short of others. We explore multiple leads to close the gap and discuss prospects for a practical quantum speedup., Comment: 8 pages, 3 figures (+ 32 pages, 23 figures)

Function-correcting codes were introduced in the work "Function-Correcting Codes" (FCC) by Lenz et al. 2023, which provides a graphical representation for the problem of constructing function-correcting codes. We use this function dependent graph to get a lower bound on the redundancy required for function correction. By considering the function to be a bijection, such an approach leads to a lower bound on the redundancy required for classical systematic error correcting codes (ECCs) of small distances. We propose a range of parameters for which the bound is tight. For single error correcting codes, we show that this bound is at least as good as a bound proposed by Zinoviev, Litsyn, and Laihonen in 1998. Thus, this framework helps to study systematic classical error correcting codes. Further, we study the structure of this function dependent graph for linear functions, which leads to bounds on the redundancy of linear-function correcting codes. We show that the Plotkin-like bound for Function-Correcting Codes that was proposed by Lenz et.al 2023 is simplified for linear functions. Also, we propose a version of the sphere packing bound for linear-function correcting codes. We identify a class of linear functions for which an upper bound proposed by Lenz et al., is tight and also identify a class of functions for which coset-wise coding is equivalent to a lower dimensional classical error correction problem., Comment: Three figures and three examples have been included. 30 pages and 3 figures

This paper introduces Interactive Tables (iTBLS), a dataset of interactive conversations situated in tables from scientific articles. This dataset is designed to facilitate human-AI collaborative problem-solving through AI-powered multi-task tabular capabilities. In contrast to prior work that models interactions as factoid QA or procedure synthesis, iTBLS broadens the scope of interactions to include mathematical reasoning, natural language manipulation, and expansion of existing tables from natural language conversation by delineating interactions into one of three tasks: interpretation, modification, or generation. Additionally, the paper presents a suite of baseline approaches to iTBLS, utilizing zero-shot prompting and parameter-efficient fine-tuning for different computing situations. We also introduce a novel multi-step approach and show how it can be leveraged in conjunction with parameter-efficient fine-tuning to achieve the state-of-the-art on iTBLS; outperforming standard parameter-efficient fine-tuning by up to 15% on interpretation, 18% on modification, and 38% on generation., Comment: 14 pages, 4 figures

We carry out deep near-ultraviolet (NUV) and far-ultraviolet (FUV) imaging of an interacting galaxy system, comprised of a Seyfert type 1 galaxy NGC 7469 and its companion IC 5283. Our aim is to resolve and map the star-forming regions in the outer arms and look for signs of interaction between the two galaxies. We used AstroSat Ultra Violet Imaging Telescope (UVIT) to obtain NUV and FUV images of NGC 7469 in a range of filters. We have carried out photometry of star-forming regions in the two galaxies and found their spatial distributions. We also obtained the distributions of star formation rates (SFR) in NGC 7469 and IC 5283 using the estimates obtained from the FUV and NUV bands. We also carried out Kolmogorov-Smirnov tests to look for differences in the SFRs in the two galaxies. We derived the spectral energy distribution (SED), leading to the determination of physical parameters, including the overall SFR, stellar mass ($\text{M}_{*}$), dust mass ($\text{M}_\text{Dust}$), and specific star formation rates (sSFRs) in both the galaxies. Our NUV and FUV images show the presence of an outer spiral arm that is better resolved. We have identified 33 new star-forming regions out of 51 total identified in the UVIT composite image. Enhanced star formation activity is observed to coincide with the interaction, and KS tests show that there are no significant differences in the SFR distributions of NGC 7469 and IC 5283, indicating that the interaction between the galaxies has not influenced their star formation processes differently. The SED plots and the photometric results demonstrate that most of the star formation activity is confined inside the central starburst (SB) ring., Comment: 13 pages, 7 figures, 6 tables. Paper accepted for publication in the Astronomy & Astrophysics (A&A)

Narrowband radar micro-Doppler signatures are heavily used to identify and classify human activities. When the radar is operated in through-wall environments, the complex electromagnetic propagation phenomenology introduces considerable distortions in the micro-Doppler signatures through attenuation and multipath. The problem is particularly severe in inhomogeneous wall scenarios involving multiple wall layers, air gaps, or metal reinforcements. Through-wall radar data collection using simulations and measurements involves significant time and effort. In this paper, we propose an alternative method of synthesizing through-wall radar micro-Doppler signatures from their free space counterparts using the generative adversarial network (GAN). We train the GAN using radar micro-Doppler signatures generated from electromagnetic simulations. We generate the radar data for different human motions, along different orientations, and under diverse through-wall conditions. The synthetic radar micro-Dopplers generated from the neural networks are then evaluated for their realism using a denoising autoencoder, which shows an excellent realism score.

Non-orthogonal unicast multicast (NOUM) is a variant of multi-antenna multi-user communications where the users desire a shared message (multicast) in addition to their respective unique messages (unicast). The multicast rate is capped in many emerging NOUM applications, such as live-event broadcasting, location-based services and vehicular communications. Given this constraint, we experimentally show that when the user channels are highly correlated, Rate-Splitting Multiple Access (RSMA)-based NOUM can meet the multicast rate while supporting a larger unicast sum rate than multi-user linear precoding (MULP)-based NOUM and orthogonal unicast multicast., Comment: Accepted by 2024 IEEE 25th International Workshop on Signal Processing Advances in Wireless Communications

The Multiple Traveling Salesman Problem (MTSP) with a single depot is a generalization of the well-known Traveling Salesman Problem (TSP) that involves an additional parameter, namely, the number of salesmen. In the MTSP, several salesmen at the depot need to visit a set of interconnected targets, such that each target is visited precisely once by at most one salesman while minimizing the total length of their tours. An equally important variant of the MTSP, the min-max MTSP, aims to distribute the workload (length of the individual tours) among salesmen by requiring the longest tour of all the salesmen to be as short as possible, i.e., minimizing the maximum tour length among all salesmen. The min-max MTSP appears in real-life applications to ensure a good balance of workloads for the salesmen. It is known in the literature that the min-max MTSP is notoriously difficult to solve to optimality due to the poor lower bounds its linear relaxations provide. In this paper, we formulate two novel parametric variants of the MTSP called the "fair-MTSP". One variant is formulated as a Mixed-Integer Second Order Cone Program (MISOCP), and the other as a Mixed Integer Linear Program (MILP). Both focus on enforcing the workloads for the salesmen to be equitable, i.e., the distribution of tour lengths for the salesmen to be fair while minimizing the total cost of their tours. We present algorithms to solve the two variants of the fair-MTSP to global optimality and computational results on benchmark and real-world test instances that make a case for fair-MTSP as a viable alternative to the min-max MTSP., Comment: 10 pages

In the original coded caching model introduced by Maddah-Ali and Niesen in 2014, the server starts broadcasting only after it receives demands from all the users. So, all the users must be active during the delivery phase. In this work, we consider a coded caching model called hotplug coded caching in which some of the users are offline during the delivery phase. This model was first introduced by Ma and Tuninetti (``On Coded Caching Systems with Offline Users," 2022 IEEE International Symposium on Information Theory). The concept of Hotplug Placement Delivery Arrays (HpPDAs) for the hotplug coded caching systems was introduced in (``Improved Hotplug Caching Schemes Using PDAs and $t$-Designs," \emph{arXiv:2311.02856}, 2024), in which the authors have constructed HpPDAs from $t$-designs. This work provides a new hotplug coded caching scheme from the existing HpPDAs. The performance comparison of the proposed scheme with the existing schemes is presented. When applied for HpPDAs from $t$-designs, our scheme outperforms the baseline scheme by Ma and Tuninetti, and the Improved $t$-scheme by Rajput and Rajan in some memory regimes., Comment: 8 pages, 4 figures and 1 table. arXiv admin note: text overlap with arXiv:2311.02856

This article presents a deep reinforcement learning-based approach to tackle a persistent surveillance mission requiring a single unmanned aerial vehicle initially stationed at a depot with fuel or time-of-flight constraints to repeatedly visit a set of targets with equal priority. Owing to the vehicle's fuel or time-of-flight constraints, the vehicle must be regularly refueled, or its battery must be recharged at the depot. The objective of the problem is to determine an optimal sequence of visits to the targets that minimizes the maximum time elapsed between successive visits to any target while ensuring that the vehicle never runs out of fuel or charge. We present a deep reinforcement learning algorithm to solve this problem and present the results of numerical experiments that corroborate the effectiveness of this approach in comparison with common-sense greedy heuristics., Comment: 6 pages

In Pliable Private Information Retrieval (PPIR) with a single server, messages are partitioned into $\Gamma$ non-overlapping classes. The user wants to retrieve a message from its desired class without revealing the identity of the desired class to the server. In S. A. Obead, H. Y. Lin and E. Rosnes, Single-Server Pliable Private Information Retrieval With Side Information, arXiv:2305.06857, authors consider the problem of PPIR with Side Information (PPIR-SI), where the user now has side information. The user wants to retrieve any new message (not included in the side information) from its desired class without revealing the identity of the desired class and its side information. A scheme for the PPIR-SI is given by Obead et al. for the case when the users side information is unidentified, and this case is referred to as PPIR with Unidentifiable SI (PPIR-USI). In this paper, we study the problem of PPIR for the single server case when the side information is partially identifiable, and we term this case as PPIR with Identifiable Side Information (PPIR-ISI). The user is well aware of the identity of the side information belonging to $\eta$ number of classes, where $1\leq \eta \leq \Gamma$. In this problem, The user wants to retrieve a message from its desired class without revealing the identity of the desired class to the server. We give a scheme for PPIR-ISI, and we prove that having identifiable side information is advantageous by comparing the rate of the proposed scheme to the rate of the PPIR-USI scheme given by Obead et al. for some cases. Further, we extend the problem of PPIR-ISI for multi-user case, where users can collaborately generate the query sets, and we give a scheme for this problem., Comment: 11 pages and 3 figures Additional references included

Draco dwarf Spheroidal galaxy (dSph) is one of the nearest and the most dark matter dominated satellites of the Milky Way. We obtained multi-epoch near-infrared (NIR, $JHK_s$) observations of the central region of Draco dSph covering a sky area of $\sim 21'\times21'$ using the WIRCam instrument at the 3.6-m Canada-France-Hawaii Telescope. Homogeneous $JHK_s$ time-series photometry for 212 RR Lyrae (173 fundamental-mode, 24 first-overtone, and 15 mixed-mode variables) and 5 Anomalous Cepheids in Draco dSph is presented and used to derive their period-luminosity relations at NIR wavelengths for the first-time. The small scatter of $\sim 0.05$~mag in these empirical relations for RR Lyrae stars is consistent with those in globular clusters and suggests a very small metallicity spread, up to $\sim0.2$~dex, among these centrally located variables. Based on empirically calibrated NIR period-luminosity-metallicity relations for RR Lyrae in globular clusters, we determined a distance modulus to Draco dSph of $\mu_\textrm{RRL} = 19.557 \pm 0.026$ mag. The calibrated $K_s$-band period-luminosity relations for Anomalous Cepheids in the Draco dSph and the Large Magellanic Cloud exhibit statistically consistent slopes but systematically different zero-points, hinting at possible metallicity dependence of $\sim-0.3$ mag~dex$^{-1}$. Finally, the apparent magnitudes of the tip of the red giant branch in $I$ and $J$ bands also agree well with their absolute calibrations with the adopted RR Lyrae distance to Draco. Our recommended $\sim1.5\%$ precise RR Lyrae distance, $D_\textrm{Draco} = 81.55 \pm 0.98 \textrm{(statistical)} \pm 1.17 \textrm{(systematic)}$~kpc, is the most accurate and precise distance to Draco dSph galaxy., Comment: Accepted for publication in The Astronomical Journal