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Giant planets exhibit diverse orbital properties, hinting at their distinct formation and dynamic histories. In this paper, using $\textit{Gaia}$ DR3, we investigate if and how the orbital properties of Jupiters are linked to their host star properties, particularly their metallicity and age. We obtain metallicities for main sequence stars of spectral type F, G, and K, hosting hot, warm, and cold Jupiters with varying eccentricities. We compute the velocity dispersion of host stars of these three groups using kinematic information from $\textit{Gaia}$ DR3 and obtain average ages using velocity dispersion-age relation. We find that host stars of hot Jupiters are relatively metal-rich ([Fe/H]=$0.18 \pm 0.13$) and young ( median age $3.97 \pm 0.51$ Gyr) compared to the host stars of cold Jupiters in nearly circular orbits, which are relatively metal-poor ($0.03 \pm 0.18$) and older (median age $6.07 \pm 0.79$ Gyr). Host stars of cold Jupiters in high eccentric orbits, on the other hand, show metallicities similar to that of the hosts of hot Jupiters, but are older, on average (median age $6.25 \pm 0.92$ Gyr). The similarity in metallicity between hosts of hot Jupiters and hosts of cold Jupiters in high eccentric orbits supports high eccentricity migration as the potential origin of hot Jupiters, with the latter serving as the progenitors. However, the average age difference between them suggests that the older hot Jupiters may have been engulfed by the star in a timescale of $\sim 6$ Gyr. This allows us to estimate the value of stellar tidal quality factor $Q'_\ast\sim10^{6\pm1}$.

This work aims to utilize the increased sensitivity and resolution of the JWST to quantify the HDO/H$_{2}$O ratio in ices toward young stellar objects (YSOs) and to determine if the HDO/H$_{2}$O ratios measured in the gas phase toward massive YSOs (MYSOs) are representative of the ratios in their ice envelopes. Two protostars observed in the Investigating Protostellar Accretion (IPA) program using JWST NIRSpec were analyzed: HOPS 370, an intermediate-mass YSO (IMYSO), and IRAS 20126+4104, a MYSO. The HDO ice toward these sources was detected above the 3$\sigma$ level and quantified via its 4.1 $\mu$m band. The contributions from the CH$_{3}$OH combination modes to the observed optical depth in this spectral region were constrained via the CH$_{3}$OH 3.53 $\mu$m band to ensure that the integrated optical depth of the HDO feature was not overestimated. H$_{2}$O ice was quantified via its 3 $\mu$m band. From these fits, ice HDO/H$_{2}$O abundance ratios of 4.6$\pm$1.8$\times$10$^{-3}$ and 2.6$\pm$1.2$\times$10$^{-3}$ are obtained for HOPS 370 and IRAS 20126+4104, respectively. The simultaneous detections of both crystalline HDO and crystalline H$_{2}$O corroborate the assignment of the observed feature at 4.1 $\mu$m to HDO ice. The ice HDO/H$_{2}$O ratios are similar to the highest reported gas HDO/H$_{2}$O ratios measured toward MYSOs as well as the hot inner regions of isolated low-mass protostars, suggesting that at least some of the gas HDO/H$_{2}$O ratios measured toward massive hot cores are representative of the HDO/H$_{2}$O ratios in ices. The need for an H$_{2}$O-rich CH$_{3}$OH component in the CH$_{3}$OH ice analysis supports recent experimental and observational results that indicate that some CH$_{3}$OH ice may form prior to the CO freeze-out stage in H$_{2}$O-rich ice layers., Comment: Accepted for publication in A&A. 23 pages, 17 figures, 10 tables

Using the MIRI/MRS spectrometer on JWST, we have detected pure rotational, suprathermal OH emissions from the vicinity of the intermediate-mass protostar HOPS 370 (OMC2/FIR3). These emissions are observed from shocked knots in a jet/outflow, and originate in states of rotational quantum number as high as 46 that possess excitation energies as large as $E_U/k = 4.65 \times 10^4$ K. The relative strengths of the observed OH lines provide a powerful diagnostic of the ultraviolet radiation field in a heavily-extinguished region ($A_V \sim 10 - 20$) where direct UV observations are impossible. To high precision, the OH line strengths are consistent with a picture in which the suprathermal OH states are populated following the photodissociation of water in its $\tilde B - X$ band by ultraviolet radiation produced by fast ($\sim 80\,\rm km\,s^{-1}$) shocks along the jet. The observed dominance of emission from symmetric ($A^\prime$) OH states over that from antisymmetric ($A^{\prime\prime}$) states provides a distinctive signature of this particular population mechanism. Moreover, the variation of intensity with rotational quantum number suggests specifically that Ly$\alpha$ radiation is responsible for the photodissociation of water, an alternative model with photodissociation by a 10$^4$ K blackbody being disfavored at a high level of significance. Using measurements of the Br$\alpha$ flux to estimate the Ly$\alpha$ production rate, we find that $\sim 4\%$ of the Ly$\alpha$ photons are absorbed by water. Combined with direct measurements of water emissions in the $\nu_2 = 1 -0$ band, the OH observations promise to provide key constraints on future models for the diffusion of Ly$\alpha$ photons in the vicinity of a shock front., Comment: 30 pages, 7 figures. Accepted for publication in ApJ Letters

Internet platforms depend on accurately determining the geographical locations of online users to deliver targeted services (e.g., advertising). The advent of decentralized platforms (blockchains) emphasizes the importance of geographically distributed nodes, making the validation of locations more crucial. In these decentralized settings, mutually non-trusting participants need to {\em prove} their locations to each other. The incentives for claiming desired location include decentralization properties (validators of a blockchain), explicit rewards for improving coverage (physical infrastructure blockchains) and regulatory compliance -- and entice participants towards prevaricating their true location malicious via VPNs, tampering with internet delays, or compromising other parties (challengers) to misrepresent their location. Traditional delay-based geolocation methods focus on reducing the noise in measurements and are very vulnerable to wilful divergences from prescribed protocol. In this paper we use Internet delay measurements to securely prove the location of IP addresses while being immune to a large fraction of Byzantine actions. Our core methods are to endow Internet telemetry tools (e.g., ping) with cryptographic primitives (signatures and hash functions) together with Byzantine resistant data inferences subject to Euclidean geometric constraints. We introduce two new networking protocols, robust against Byzantine actions: Proof of Internet Geometry (PoIG) converts delay measurements into precise distance estimates across the Internet; Proof of Location (PoLoc) enables accurate and efficient multilateration of a specific IP address. The key algorithmic innovations are in conducting ``Byzantine fortified trigonometry" (BFT) inferences of data, endowing low rank matrix completion methods with Byzantine resistance.

In this work, we present the results from a study using the Giant Meterwave Radio Telescope (GMRT) to search for radio {emission} from planets around three evolved stars namely $\alpha$~Tau, $\beta$~UMi, and $\beta$~Gem. Both $\alpha$~Tau and $\beta$~UMi host massive $\sim$ 6 $M_J$ mass planets at about $\sim$1.4 au from the central star, while $\beta$~Gem is host to a 2.9 $M_J$ mass planet at 1.7 au from the host star. We observe $\alpha$~Tau and $\beta$~ UMi at two u(upgraded)GMRT bands; band~3 (250-500~MHz) and band~4 (550-900~MHz). We also analyzed the archival observations from $\beta$ Gem at 150~MHz from GMRT. We did not detect any radio signals from these systems. At 400~MHz, the 3$\sigma$ upper limit is 87 $\mu$Jy/beam for $\alpha$~Tau~{b} and 77.4 $\mu$Jy/beam for $\beta$~UMi~{b}. From our observations at 650~MHz, we place a 3$\sigma$ upper limit of 28.2 $\mu$Jy/beam for $\alpha$~Tau~b and 33.6 $\mu$Jy/beam for $\beta$~UMi~b. For $\beta$ Gem b, at 150~MHz, we place an upper limit of 2.5 mJy. At 400~MHz and 650~MHz, our observations are the deepest radio images for any exoplanetary system., Comment: 9 pages, 6 figures, accepted at MNRAS

Layer 1 (L1) blockchains such as Ethereum are secured under an "honest supermajority of stake" assumption for a large pool of validators who verify each and every transaction on it. This high security comes at a scalability cost which not only effects the throughput of the blockchain but also results in high gas fees for executing transactions on chain. The most successful solution for this problem is provided by optimistic rollups, Layer 2 (L2) blockchains that execute transactions outside L1 but post the transaction data on L1. The security for such L2 chains is argued, informally, under the assumption that a set of nodes will check the transaction data posted on L1 and raise an alarm (a fraud proof) if faulty transactions are detected. However, all current deployments lack a proper incentive mechanism for ensuring that these nodes will do their job ``diligently'', and simply rely on a cursory incentive alignment argument for security. We solve this problem by introducing an incentivized watchtower network designed to serve as the first line of defense for rollups. Our main contribution is a ``Proof of Diligence'' protocol that requires watchtowers to continuously provide a proof that they have verified L2 assertions and get rewarded for the same. Proof of Diligence protocol includes a carefully-designed incentive mechanism that is provably secure when watchtowers are rational actors, under a mild rational independence assumption. Our proposed system is now live on Ethereum testnet. We deployed a watchtower network and implemented Proof of Diligence for multiple optimistic rollups. We extract execution as well as inclusion proofs for transactions as a part of the bounty. Each watchtower has minimal additional computational overhead beyond access to standard L1 and L2 RPC nodes.

The structure and composition of simple ices can be modified during stellar evolution by protostellar heating. Key to understanding the involved processes are thermal and chemical tracers that can diagnose the history and environment of the ice. The 15.2 $\mu$m bending mode of $^{12}$CO$_2$ has proven to be a valuable tracer of ice heating events but suffers from grain shape and size effects. A viable alternative tracer is the weaker $^{13}$CO$_2$ isotopologue band at 4.39 $\mu$m which has now become accessible at high S/N with the $\textit{James Webb}$ Space Telescope (JWST). We present JWST NIRSpec observations of $^{13}$CO$_2$ ice in five deeply embedded Class 0 sources spanning a wide range in luminosities (0.2 - 10$^4$ L$_{\odot}$ ) taken as part of the Investigating Protostellar Accretion Across the Mass Spectrum (IPA) program. The band profiles vary significantly, with the most luminous sources showing a distinct narrow peak at 4.38 $\mu$m. We first apply a phenomenological approach and show that a minimum of 3-4 Gaussian profiles are needed to fit the $^{13}$CO$_2$ absorption feature. We then combine these findings with laboratory data and show that a 15.2 $\mu$m $^{12}$CO$_2$ band inspired five-component decomposition can be applied for the isotopologue band where each component is representative of CO$_2$ ice in a specific molecular environment. The final solution consists of cold mixtures of CO$_2$ with CH$_3$OH, H$_2$O and CO as well as segregated heated pure CO$_2$ ice. Our results are in agreement with previous studies of the $^{12}$CO$_2$ ice band, further confirming that $^{13}$CO$_{2}$ is a useful alternative tracer of protostellar heating events. We also propose an alternative solution consisting only of heated CO$_2$:CH$_3$OH and CO$_2$:H$_2$O ices and warm pure CO$_2$ ice for decomposing the ice profiles of the two most luminous sources in our sample.

We investigate the bright CO fundamental emission in the central regions of five Class 0 protostars using the JWST's Near-Infrared Spectrograph (NIRSpec) and provide clues to what processes excite the gas. CO line emission images are extracted for a forest of $\sim$150 ro-vibrational transitions from two vibrational bands, $v=1-0$ and $v=2-1$. However, ${}^{13}$CO is not detected, and thus we can only statistically constrain the ${}^{12}$CO optical depth. Using noise measurements to determine upper limits to the ${}^{13}$CO emission, the flux ratio of ${}^{12}$CO/${}^{13}$CO indicates that the ${}^{12}$CO emission itself is not optically thick for ro-vibrational transitions with upper state rotational quantum number $J_u \geq 15$. We construct population diagrams to estimate the rotational temperature and number of molecules from extinction-corrected CO line fluxes assuming CO emission is optically thin. Two different temperature components are required for $v=1$ ($\sim600-1000$ K and $\sim1500-3500$ K), while one hotter component is required for $v=2$ ($\sim2000-6000$ K). The vibrational temperature is $\sim 900$ K among our sources and shows no trend with luminosity. Using vibrational temperatures and the inferred total amount of CO molecules for our sources, the total warm gas mass correlates strongly with luminosity ranging from $\sim$0.1 $\rm M_{Earth}$ for the low-mass protostars to $\sim$1 M$_{\rm sun}$ for the high-mass protostars. Interpreting the distribution of gas column densities and temperatures depends on radiative and chemical processes affecting CO. The presence of a $v=2$ population may indicate CO gas radiatively excited. Selective UV photodissociation of CO isotopologues around our high-mass sources may explain their depletion of ${}^{13}$CO., Comment: 30 pages, 6 figures, 5 tables, submitted to ApJ

With the third data release of the Gaia mission $Gaia$ DR3 with its precise photometry and astrometry, it is now possible to study the behaviour of stars at a scale never seen before. In this paper, we developed new criteria to identify T-Tauri stars (TTS) candidates using UV and optical CMDs by combining the GALEX and Gaia surveys. We found 19 TTS candidates and 5 of them are newly identified TTS in the Taurus Molecular Cloud (TMC), not catalogued before as TMC members. For some of the TTS candidates, we also obtained optical spectra from several Indian telescopes. We also present the analysis of the distance and proper motion of young stars in the Taurus using data from $Gaia$ DR3. We found that the stars in Taurus show a bimodal distribution with distance, having peaks at $130.17_{-1.24}^{1.31}$ pc and $156.25_{-5.00}^{1.86}$ pc. The reason for this bimodality, we think, is due to the fact that different clouds in the TMC region are at different distances. We further show that the two populations have similar ages and proper motion distribution. Using the $Gaia$ DR3 colour-magnitude diagram, we show that the age of Taurus is consistent with 1 Myr., Comment: 13 pages, 10 figures

Investigating Protostellar Accretion (IPA) is a JWST Cycle~1 GO program that uses NIRSpec IFU and MIRI MRS to obtain 2.9--28~$\mu$m spectral cubes of young, deeply embedded protostars with luminosities of 0.2 to 10,000~L$_{\odot}$ and central masses of 0.15 to 12~M$_{\odot}$. In this Letter, we report the discovery of a highly collimated atomic jet from the Class~0 protostar IRAS~16253$-$2429, the lowest luminosity source ($L_\mathrm{bol}$ = 0.2 $L_\odot$) in the IPA program. The collimated jet is detected in multiple [Fe~II] lines, [Ne~II], [Ni~II], and H~I lines, but not in molecular emission. The atomic jet has a velocity of about 169~$\pm$~15~km\,s$^{-1}$, after correcting for inclination. The width of the jet increases with distance from the central protostar from 23 to~60 au, corresponding to an opening angle of 2.6~$\pm$~0.5\arcdeg. By comparing the measured flux ratios of various fine structure lines to those predicted by simple shock models, we derive a shock {speed} of 54~km\,s$^{-1}$ and a preshock density of 2.0$\times10^{3}$~cm$^{-3}$ at the base of the jet. {From these quantities and using a suite of jet models and extinction laws we compute a mass loss rate between $0.4 -1.1\times10^{-10}~M_{\odot}$~yr~$^{-1}$.} The low mass loss rate is consistent with simultaneous measurements of low mass accretion rate ($2.4~\pm~0.8~\times~10^{-9}~M_{\odot}$~yr$^{-1}$) for IRAS~16253$-$2429 from JWST observations (Watson et al. in prep), indicating that the protostar is in a quiescent accretion phase. Our results demonstrate that very low-mass protostars can drive highly collimated, atomic jets, even during the quiescent phase., Comment: Accepted to ApJL. Comments and feedback welcome

Investigating Protostellar Accretion is a Cycle 1 JWST program using the NIRSpec+MIRI integral field units to obtain 2.9--28 $\mu$m spectral cubes of five young protostars with luminosities of 0.2-10,000 L$_{\odot}$ in their primary accretion phase. This paper introduces the NIRSpec 2.9--5.3 $\mu$m data of the inner 840-9000 au with spatial resolutions from 28-300 au. The spectra show rising continuum emission; deep ice absorption; emission from H$_{2}$, H~I, and [Fe~II]; and the CO fundamental series in emission and absorption. Maps of the continuum emission show scattered light cavities for all five protostars. In the cavities, collimated jets are detected in [Fe~II] for the four $< 320$~L$_{\odot}$ protostars, two of which are additionally traced in Br-$\alpha$. Knots of [Fe~II] emission are detected toward the most luminous protostar, and knots of [FeII] emission with dynamical times of $< 30$~yrs are found in the jets of the others. While only one jet is traced in H$_2$, knots of H$_2$ and CO are detected in the jets of four protostars. H$_2$ is seen extending through the cavities, showing that they are filled by warm molecular gas. Bright H$_2$ emission is seen along the walls of a single cavity, while in three cavities narrow shells of H$_2$ emission are found, one of which has an [Fe~II] knot at its apex. These data show cavities containing collimated jets traced in atomic/ionic gas surrounded by warm molecular gas in a wide-angle wind and/or gas accelerated by bow shocks in the jets., Comment: 26 pages, 12 figures

Optical spectroscopy offers the most direct view of the stellar properties and the accretion indicators. Standard accretion tracers, such as $H\beta$, $H\alpha$, and, Ca II triplet lines, and most photospheric features, fall in the optical wavelengths. However, these tracers are not readily observable from deeply embedded protostars because of the large line of sight extinction (Av $\sim$ 50-100 mag) toward them. In some cases, however, it is possible to observe protostars at optical wavelengths if the outflow cavity is aligned along the line-of-sight that allows observations of the photosphere, or the envelope is very tenuous and thin such that the extinction is low. In such cases, we can not only detect these protostars at optical wavelengths but also follow up spectroscopically. We have used the HOPS catalog (Furlan et al. 2016) of protostars in Orion to search for optical counterparts for protostars in the Gaia DR3 survey. Out of the 330 protostars in the HOPS sample, an optical counterpart within 2" is detected for 62 of the protostars. For 17 out of 62 optically detected protostars, we obtained optical spectra { (between 5500 to 8900 $\AA$) using the Aries-Devasthal Faint Object Spectrograph \& Camera (ADFOSC) on the 3.6-m Devasthal Optical Telescope (DOT) and Hanle Faint Object Spectrograph Camera (HFOSC) on 2-m Himalayan Chandra Telescope (HCT)}. We detect strong photospheric features, such as the TiO bands in the spectra {(of 4 protostars)}, hinting that photospheres can form early on in the star formation process. We further determined the spectral types of protostars, which show photospheres similar to a late M-type. Mass accretion rates derived for the protostars are similar to those found for T-Tauri stars, in the range of 10$^{-7}$ to 10$^{-8}$ $M_\odot$/yr., Comment: 9 pages, 5 figures accepted in Journal of Astrophysics and Astronomy as part of the "Star formation studies in the context of NIR instruments on 3.6m DOT" special issue

Large AI models (e.g., Dall-E, GPT4) have electrified the scientific, technological and societal landscape through their superhuman capabilities. These services are offered largely in a traditional web2.0 format (e.g., OpenAI's GPT4 service). As more large AI models proliferate (personalizing and specializing to a variety of domains), there is a tremendous need to have a neutral trust-free platform that allows the hosting of AI models, clients receiving AI services efficiently, yet in a trust-free, incentive compatible, Byzantine behavior resistant manner. In this paper we propose SAKSHI, a trust-free decentralized platform specifically suited for AI services. The key design principles of SAKSHI are the separation of the data path (where AI query and service is managed) and the control path (where routers and compute and storage hosts are managed) from the transaction path (where the metering and billing of services are managed over a blockchain). This separation is enabled by a "proof of inference" layer which provides cryptographic resistance against a variety of misbehaviors, including poor AI service, nonpayment for service, copying of AI models. This is joint work between multiple universities (Princeton University, University of Illinois at Urbana-Champaign, Tsinghua University, HKUST) and two startup companies (Witness Chain and Eigen Layer)., Comment: 23 pages, 9 figures

Exomoons have so far eluded ongoing searches. Several studies have exploited transit and transit timing variations and high-resolution spectroscopy to identify potential exomoon candidates. One method of detecting and confirming these exomoons is to search for signals of planet-moon interactions. In this work, we present the first radio observations of the exomoon candidate system WASP 69b. Based on the detection of alkali metals in the transmission spectra of WASP-69b, it was deduced that the system might be hosting an exomoon. WASP 69b is also one of the exoplanet systems that will be observed as part of JWST cycle-1 GTO. This makes the system an excellent target to observe and follow up. We observed the system for 32 hrs at 150 MHz and 218 MHz using the upgraded Giant Metrewave Radio Telescope (uGMRT). Though we do not detect radio emission from the systems, we place strong $3\sigma$ upper limits of 3.3 mJy at 150 MHz and 0.9 mJy at 218 MHz. We then use these upper limits to estimate the maximum mass loss from the exomoon candidate., Comment: Accepted in MNRAS, 8 pages, 4 Figures

We consider the problem of continually releasing an estimate of the population mean of a stream of samples that is user-level differentially private (DP). At each time instant, a user contributes a sample, and the users can arrive in arbitrary order. Until now these requirements of continual release and user-level privacy were considered in isolation. But, in practice, both these requirements come together as the users often contribute data repeatedly and multiple queries are made. We provide an algorithm that outputs a mean estimate at every time instant $t$ such that the overall release is user-level $\varepsilon$-DP and has the following error guarantee: Denoting by $M_t$ the maximum number of samples contributed by a user, as long as $\tilde{\Omega}(1/\varepsilon)$ users have $M_t/2$ samples each, the error at time $t$ is $\tilde{O}(1/\sqrt{t}+\sqrt{M}_t/t\varepsilon)$. This is a universal error guarantee which is valid for all arrival patterns of the users. Furthermore, it (almost) matches the existing lower bounds for the single-release setting at all time instants when users have contributed equal number of samples.

Recent years have seen the emergence of decentralized wireless networks consisting of nodes hosted by many individuals and small enterprises, reawakening the decades-old dream of open networking. These networks have been deployed in an organic, distributed manner and are driven by new economic models resting on tokenized incentives. A critical requirement for the incentives to scale is the ability to prove network performance in a decentralized trustfree manner, i.e., a Byzantine fault tolerant network telemetry system. In this paper, we present a Proof of Backhaul (PoB) protocol which measures the bandwidth of the (broadband) backhaul link of a wireless access point, termed prover, in a decentralized and trustfree manner. In particular, our proposed protocol is the first one to satisfy the following two properties: (1) Trustfree. Bandwidth measurement is secure against Byzantine attacks by collaborations of challenge servers and the prover. (2) Open. The barrier-to-entry for being a challenge server is low; there is no requirement of having a low latency and high throughput path to the measured link. At a high-level, our protocol aggregates the challenge traffic from multiple challenge servers and uses cryptographic primitives to ensure that a subset of challengers or, even challengers and provers, cannot maliciously modify results in their favor. A formal security model allows us to establish guarantees of accurate bandwidth measurement as a function of the fraction of malicious actors. Our evaluation shows that our PoB protocol can verify backhaul bandwidth of up to 1000 Mbps with less than 8% error using measurements lasting only 100 ms. The measurement accuracy is not affected in the presence of corrupted challengers. Importantly, the basic verification protocol lends itself to a minor modification that can measure available bandwidth even in the presence of cross-traffic.

We study high-dimensional sparse estimation under three natural constraints: communication constraints, local privacy constraints, and linear measurements (compressive sensing). Without sparsity assumptions, it has been established that interactivity cannot improve the minimax rates of estimation under these information constraints. The question of whether interactivity helps with natural inference tasks has been a topic of active research. We settle this question in the affirmative for the prototypical problems of high-dimensional sparse mean estimation and compressive sensing, by demonstrating a gap between interactive and noninteractive protocols. We further establish that the gap increases when we have more structured sparsity: for block sparsity this gap can be as large as polynomial in the dimensionality. Thus, the more structured the sparsity is, the greater is the advantage of interaction. Proving the lower bounds requires a careful breaking of a sum of correlated random variables into independent components using Baranyai's theorem on decomposition of hypergraphs, which might be of independent interest.

We consider over-the-air convex optimization on a $d-$dimensional space where coded gradients are sent over an additive Gaussian noise channel with variance $\sigma^2$. The codewords satisfy an average power constraint $P$, resulting in the signal-to-noise ratio (SNR) of $P/\sigma^2$. We derive bounds for the convergence rates for over-the-air optimization. Our first result is a lower bound for the convergence rate showing that any code must slowdown the convergence rate by a factor of roughly $\sqrt{d/\log(1+\mathtt{SNR})}$. Next, we consider a popular class of schemes called $analog$ $coding$, where a linear function of the gradient is sent. We show that a simple scaled transmission analog coding scheme results in a slowdown in convergence rate by a factor of $\sqrt{d(1+1/\mathtt{SNR})}$. This matches the previous lower bound up to constant factors for low SNR, making the scaled transmission scheme optimal at low SNR. However, we show that this slowdown is necessary for any analog coding scheme. In particular, a slowdown in convergence by a factor of $\sqrt{d}$ for analog coding remains even when SNR tends to infinity. Remarkably, we present a simple quantize-and-modulate scheme that uses $Amplitude$ $Shift$ $Keying$ and almost attains the optimal convergence rate at all SNRs., Comment: Few typos fixed and one reference added. An abridged version of this paper will appear in the proceedings of IEEE Global Communications Conference (GLOBECOM), Spain, 2021

We consider density estimation for Besov spaces when each sample is quantized to only a limited number of bits. We provide a noninteractive adaptive estimator that exploits the sparsity of wavelet bases, along with a simulate-and-infer technique from parametric estimation under communication constraints. We show that our estimator is nearly rate-optimal by deriving minimax lower bounds that hold even when interactive protocols are allowed. Interestingly, while our wavelet-based estimator is almost rate-optimal for Sobolev spaces as well, it is unclear whether the standard Fourier basis, which arise naturally for those spaces, can be used to achieve the same performance.

In the problem of multiple support recovery, we are given access to linear measurements of multiple sparse samples in $\mathbb{R}^{d}$. These samples can be partitioned into $\ell$ groups, with samples having the same support belonging to the same group. For a given budget of $m$ measurements per sample, the goal is to recover the $\ell$ underlying supports, in the absence of the knowledge of group labels. We study this problem with a focus on the measurement-constrained regime where $m$ is smaller than the support size $k$ of each sample. We design a two-step procedure that estimates the union of the underlying supports first, and then uses a spectral algorithm to estimate the individual supports. Our proposed estimator can recover the supports with $m

We revisit first-order optimization under local information constraints such as local privacy, gradient quantization, and computational constraints limiting access to a few coordinates of the gradient. In this setting, the optimization algorithm is not allowed to directly access the complete output of the gradient oracle, but only gets limited information about it subject to the local information constraints. We study the role of adaptivity in processing the gradient output to obtain this limited information from it.We consider optimization for both convex and strongly convex functions and obtain tight or nearly tight lower bounds for the convergence rate, when adaptive gradient processing is allowed. Prior work was restricted to convex functions and allowed only nonadaptive processing of gradients. For both of these function classes and for the three information constraints mentioned above, our lower bound implies that adaptive processing of gradients cannot outperform nonadaptive processing in most regimes of interest. We complement these results by exhibiting a natural optimization problem under information constraints for which adaptive processing of gradient strictly outperforms nonadaptive processing.

We study the problem of recovering the common $k$-sized support of a set of $n$ samples of dimension $d$, using $m$ noisy linear measurements per sample. Most prior work has focused on the case when $m$ exceeds $k$, in which case $n$ of the order $(k/m)\log(d/k)$ is both necessary and sufficient. Thus, in this regime, only the total number of measurements across the samples matter, and there is not much benefit in getting more than $k$ measurements per sample. In the measurement-constrained regime where we have access to fewer than $k$ measurements per sample, we show an upper bound of $O((k^{2}/m^{2})\log d)$ on the sample complexity for successful support recovery when $m\ge 2\log d$. Along with the lower bound from our previous work, this shows a phase transition for the sample complexity of this problem around $k/m=1$. In fact, our proposed algorithm is sample-optimal in both the regimes. It follows that, in the $m\ll k$ regime, multiple measurements from the same sample are more valuable than measurements from different samples.

We study goodness-of-fit and independence testing of discrete distributions in a setting where samples are distributed across multiple users. The users wish to preserve the privacy of their data while enabling a central server to perform the tests. Under the notion of local differential privacy, we propose simple, sample-optimal, and communication-efficient protocols for these two questions in the noninteractive setting, where in addition users may or may not share a common random seed. In particular, we show that the availability of shared (public) randomness greatly reduces the sample complexity. Underlying our public-coin protocols are privacy-preserving mappings which, when applied to the samples, minimally contract the distance between their respective probability distributions., Comment: To appear in the Special Issue on Privacy and Security of Information Systems of the IEEE Journal on Selected Areas in Information Theory (JSAIT), 2021. Journal version of the AISTATS'19 paper "Test without Trust: Optimal Locally Private Distribution Testing" (arXiv:1808.02174), which it extends and supersedes

Communication efficient distributed mean estimation is an important primitive that arises in many distributed learning and optimization scenarios such as federated learning. Without any probabilistic assumptions on the underlying data, we study the problem of distributed mean estimation where the server has access to side information. We propose \emph{Wyner-Ziv estimators}, which are communication and computationally efficient and near-optimal when an upper bound for the distance between the side information and the data is known. As a corollary, we also show that our algorithms provide efficient schemes for the classic Wyner-Ziv problem in information theory. In a different direction, when there is no knowledge assumed about the distance between side information and the data, we present an alternative Wyner-Ziv estimator that uses correlated sampling. This latter setting offers {\em universal recovery guarantees}, and perhaps will be of interest in practice when the number of users is large and keeping track of the distances between the data and the side information may not be possible. With this mean estimator at our disposal, we revisit basic problems in decentralized optimization and compression where our Wyner-Ziv estimator yields algorithms with almost optimal performance. First, we consider the problem of communication constrained distributed optimization and provide an algorithm which attains the optimal convergence rate by exploiting the fact that the gradient estimates are close to each other. Specifically, the gradient compression scheme in our algorithm first uses half of the parties to form side information and then uses our Wyner-Ziv estimator to compress the remaining half of the gradient estimates.

We consider distributed parameter estimation using interactive protocols subject to local information constraints such as bandwidth limitations, local differential privacy, and restricted measurements. We provide a unified framework enabling us to derive a variety of (tight) minimax lower bounds for different parametric families of distributions, both continuous and discrete, under any $\ell_p$ loss. Our lower bound framework is versatile and yields "plug-and-play" bounds that are widely applicable to a large range of estimation problems, and, for the prototypical case of the Gaussian family, circumvents limitations of previous techniques. In particular, our approach recovers bounds obtained using data processing inequalities and Cram\'er--Rao bounds, two other alternative approaches for proving lower bounds in our setting of interest. Further, for the families considered, we complement our lower bounds with matching upper bounds., Comment: Streamline some statements; add the low-privacy corollary (high value of the privacy parameter) for Corollary 1, along with the implications for the applications considered; add the upper bound for the low-privacy regimes for Bernoulli (Theorem 3) and Gaussian (Theorem 4); slightly improve Lemma 5 by relaxing the independence assumption

Recent cyber-attacks on power grids highlight the necessity to protect the critical functionalities of a control center vital for the safe operation of a grid. Even in a distributed framework one central control center acts as a coordinator in majority of the control center architectures. Such a control center can become a prime target for cyber as well as physical attacks, and, hence, a single point failure can lead to complete loss of visibility of the power grid. If the control center which runs the critical functions in a distributed computing environment can be randomly chosen between the available control centers in a secure framework, the ability of the attacker in causing a single point failure can be reduced to a great extent. To achieve this, a novel distributed hierarchy based framework to secure critical functions is proposed in this paper. The proposed framework ensures that the data aggregation and the critical functions are carried out at a random location, and incorporates security features such as attestation and trust management to detect compromised agents. A theoretical result is proved on the evolution and convergence of the trust values in the proposed trust management protocol. It is also shown that the system is nominally robust so long as the number of compromised nodes is strictly less than one-half of the nodes minus 1. For demonstration, a Kalman filter-based state estimation using phasor measurements is used as the critical function to be secured. The proposed framework's implementation feasibility is tested on a physical hardware cluster of Parallella boards. The framework is also validated using simulations on the IEEE 118 bus system.

We study the role of interactivity in distributed statistical inference under information constraints, e.g., communication constraints and local differential privacy. We focus on the tasks of goodness-of-fit testing and estimation of discrete distributions. From prior work, these tasks are well understood under noninteractive protocols. Extending these approaches directly for interactive protocols is difficult due to correlations that can build due to interactivity; in fact, gaps can be found in prior claims of tight bounds of distribution estimation using interactive protocols. We propose a new approach to handle this correlation and establish a unified method to establish lower bounds for both tasks. As an application, we obtain optimal bounds for both estimation and testing under local differential privacy and communication constraints. We also provide an example of a natural testing problem where interactivity helps., Comment: Modifying the proof and statement of Proposition 24 to address an issue in the variance analysis

Two parties observe independent copies of a $d$-dimensional vector and a scalar. They seek to test if their data is correlated or not, namely they seek to test if the norm $\|\rho\|_2$ of the correlation vector $\rho$ between their observations exceeds $\tau$ or is it $0$. To that end, they communicate interactively and declare the output of the test. We show that roughly order $d/\tau^2$ bits of communication are sufficient and necessary for resolving the distributed correlation testing problem above. Furthermore, we establish a lower bound of roughly $d^2/\tau^2$ bits for communication needed for distributed correlation estimation, rendering the estimate-and-test approach suboptimal in communication required for distributed correlation testing. For the one-dimensional case with one-way communication, our bounds are tight even in the constant and provide a precise dependence of communication complexity on the probabilities of error of two types., Comment: 30 pages, 1 figure

The number of confirmed cases of COVID-19 is often used as a proxy for the actual number of ground truth COVID-19 infected cases in both public discourse and policy making. However, the number of confirmed cases depends on the testing policy, and it is important to understand how the number of positive cases obtained using different testing policies reveals the unknown ground truth. We develop an agent-based simulation framework in Python that can simulate various testing policies as well as interventions such as lockdown based on them. The interaction between the agents can take into account various communities and mobility patterns. A distinguishing feature of our framework is the presence of another `flu'-like illness with symptoms similar to COVID-19, that allows us to model the noise in selecting the pool of patients to be tested. We instantiate our model for the city of Bengaluru in India, using census data to distribute agents geographically, and traffic flow mobility data to model long-distance interactions and mixing. We use the simulation framework to compare the performance of three testing policies: Random Symptomatic Testing (RST), Contact Tracing (CT), and a new Location Based Testing policy (LBT). We observe that if a sufficient fraction of symptomatic patients come out for testing, then RST can capture the ground truth quite closely even with very few daily tests. However, CT consistently captures more positive cases. Interestingly, our new LBT, which is operationally less intensive than CT, gives performance that is comparable with CT. In another direction, we compare the efficacy of these three testing policies in enabling lockdown, and observe that CT flattens the ground truth curve maximally, followed closely by LBT, and significantly better than RST.

Samples from a high-dimensional AR[1] process are observed by a sender which can communicate only finitely many bits per unit time to a receiver. The receiver seeks to form an estimate of the process value at every time instant in real-time. We consider a time-slotted communication model in a slow-sampling regime where multiple communication slots occur between two sampling instants. We propose a successive update scheme which uses communication between sampling instants to refine estimates of the latest sample and study the following question: Is it better to collect communication of multiple slots to send better refined estimates, making the receiver wait more for every refinement, or to be fast but loose and send new information in every communication opportunity? We show that the fast but loose successive update scheme with ideal spherical codes is universally optimal asymptotically for a large dimension. However, most practical quantization codes for fixed dimensions do not meet the ideal performance required for this optimality, and they typically will have a bias in the form of a fixed additive error. Interestingly, our analysis shows that the fast but loose scheme is not an optimal choice in the presence of such errors, and a judiciously chosen frequency of updates outperforms it.

We consider stochastic optimization over $\ell_p$ spaces using access to a first-order oracle. We ask: {What is the minimum precision required for oracle outputs to retain the unrestricted convergence rates?} We characterize this precision for every $p\geq 1$ by deriving information theoretic lower bounds and by providing quantizers that (almost) achieve these lower bounds. Our quantizers are new and easy to implement. In particular, our results are exact for $p=2$ and $p=\infty$, showing the minimum precision needed in these settings are $\Theta(d)$ and $\Theta(\log d)$, respectively. The latter result is surprising since recovering the gradient vector will require $\Omega(d)$ bits.

Data samples from $\mathbb{R}^{d}$ with a common support of size $k$ are accessed through $m$ random linear projections (measurements) per sample. It is well-known that roughly $k$ measurements from a single sample are sufficient to recover the support. In the multiple sample setting, do $k$ overall measurements still suffice when only $m$ measurements per sample are allowed, with $m

We present Rotated Adaptive Tetra-iterated Quantizer (RATQ), a fixed-length quantizer for gradients in first order stochastic optimization. RATQ is easy to implement and involves only a Hadamard transform computation and adaptive uniform quantization with appropriately chosen dynamic ranges. For noisy gradients with almost surely bounded Euclidean norms, we establish an information theoretic lower bound for optimization accuracy using finite precision gradients and show that RATQ almost attains this lower bound. For mean square bounded noisy gradients, we use a gain-shape quantizer which separately quantizes the Euclidean norm and uses RATQ to quantize the normalized unit norm vector. We establish lower bounds for performance of any optimization procedure and shape quantizer, when used with a uniform gain quantizer. Finally, we propose an adaptive quantizer for gain which when used with RATQ for shape quantizer outperforms uniform gain quantization and is, in fact, close to optimal. As a by-product, we show that our fixed-length quantizer RATQ has almost the same performance as the optimal variable-length quantizers for distributed mean estimation. Also, we obtain an efficient quantizer for Gaussian vectors which attains a rate very close to the Gaussian rate-distortion function and is, in fact, universal for subgaussian input vectors.

We study goodness-of-fit of discrete distributions in the distributed setting, where samples are divided between multiple users who can only release a limited amount of information about their samples due to various information constraints. Recently, a subset of the authors showed that having access to a common random seed (i.e., shared randomness) leads to a significant reduction in the sample complexity of this problem. In this work, we provide a complete understanding of the interplay between the amount of shared randomness available, the stringency of information constraints, and the sample complexity of the testing problem by characterizing a tight trade-off between these three parameters. We provide a general distributed goodness-of-fit protocol that as a function of the amount of shared randomness interpolates smoothly between the private- and public-coin sample complexities. We complement our upper bound with a general framework to prove lower bounds on the sample complexity of this testing problems under limited shared randomness. Finally, we instantiate our bounds for the two archetypal information constraints of communication and local privacy, and show that our sample complexity bounds are optimal as a function of all the parameters of the problem, including the amount of shared randomness. A key component of our upper bounds is a new primitive of domain compression, a tool that allows us to map distributions to a much smaller domain size while preserving their pairwise distances, using a limited amount of randomness.

A central server needs to perform statistical inference based on samples that are distributed over multiple users who can each send a message of limited length to the center. We study problems of distribution learning and identity testing in this distributed inference setting and examine the role of shared randomness as a resource. We propose a general-purpose simulate-and-infer strategy that uses only private-coin communication protocols and is sample-optimal for distribution learning. This general strategy turns out to be sample-optimal even for distribution testing among private-coin protocols. Interestingly, we propose a public-coin protocol that outperforms simulate-and-infer for distribution testing and is, in fact, sample-optimal. Underlying our public-coin protocol is a random hash that when applied to the samples minimally contracts the chi-squared distance of their distribution to the uniform distribution., Comment: To appear in IEEE Transactions on Information Theory. An abridged version of this work appeared in the 2019 International Conference on Machine Learning (ICML)