 NSFPAR ID:
 10230646
 Date Published:
 Journal Name:
 Sensors
 Volume:
 21
 Issue:
 4
 ISSN:
 14248220
 Page Range / eLocation ID:
 1341
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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Continuum robots suffer large deflections due to internal and external forces. Accurate modeling of their passive compliance is necessary for accurate environmental interaction, especially in scenarios where direct force sensing is not practical. This paper focuses on deriving analytic formulations for the compliance of continuum robots that can be modeled as Kirchhoff rods. Compared to prior works, the approach presented herein is not subject to the constantcurvature assumptions to derive the configuration space compliance, and we do not rely on computationallyexpensive finite difference approximations to obtain the task space compliance. Using modal approximations over curvature space and Lie group integration, we obtain closedform expressions for the task and configuration space compliance matrices of continuum robots, thereby bridging the gap between constantcurvature analytic formulations of configuration space compliance and variable curvature task space compliance. We first present an analytic expression for the compliance of aingle Kirchhoff rod.We then extend this formulation for computing both the task space and configuration space compliance of a tendonactuated continuum robot. We then use our formulation to study the tradeoffs between computation cost and modeling accuracy as well as the loss in accuracy from neglecting the Jacobian derivative term in the compliance model. Finally, we experimentally validate the model on a tendonactuated continuum segment, demonstrating the model’s ability to predict passive deflections with error below 11.5% percent of total arc length.more » « less

Timefrequency (TF) filtering of analog signals has played a crucial role in the development of radiofrequency communications and is currently being recognized as an essential capability for communications, both classical and quantum, in the optical frequency domain. How best to design optical timefrequency (TF) filters to pass a targeted temporal mode (TM), and to reject background (noise) photons in the TF detection window? The solution for ‘coherent’ TF filtering is known—the quantum pulse gate—whereas the conventional, more common method is implemented by a sequence of incoherent spectral filtering and temporal gating operations. To compare these two methods, we derive a general formalism for twostage incoherent timefrequency filtering, finding expressions for signal pulse transmission efficiency, and for the ability to discriminate TMs, which allows the blocking of unwanted background light. We derive the tradeoff between efficiency and TM discrimination ability, and find a remarkably concise relation between these two quantities and the timebandwidth product of the combined filters. We apply the formalism to two examples—rectangular filters or Gaussian filters—both of which have known orthogonalfunction decompositions. The formalism can be applied to any state of light occupying the input temporal mode, e.g., ‘classical’ coherentstate signals or pulsed singlephoton states of light. In contrast to the radiofrequency domain, where coherent detection is standard and one can use coherent matched filtering to reject noise, in the optical domain direct detection is optimal in a number of scenarios where the signal flux is extremely small. Our analysis shows how the insertion loss and SNR change when one uses incoherent optical filters to reject background noise, followed by direct detection, e.g. photon counting. We point out implications in classical and quantum optical communications. As an example, we study quantum key distribution, wherein strong rejection of background noise is necessary to maintain a high quality of entanglement, while high signal transmission is needed to ensure a useful key generation rate.

Abstract A recently proposed SLOPE estimator [6] has been shown to adaptively achieve the minimax $\ell _2$ estimation rate under highdimensional sparse linear regression models [25]. Such minimax optimality holds in the regime where the sparsity level $k$, sample size $n$ and dimension $p$ satisfy $k/p\rightarrow 0, k\log p/n\rightarrow 0$. In this paper, we characterize the estimation error of SLOPE under the complementary regime where both $k$ and $n$ scale linearly with $p$, and provide new insights into the performance of SLOPE estimators. We first derive a concentration inequality for the finite sample mean square error (MSE) of SLOPE. The quantity that MSE concentrates around takes a complicated and implicit form. With delicate analysis of the quantity, we prove that among all SLOPE estimators, LASSO is optimal for estimating $k$sparse parameter vectors that do not have tied nonzero components in the low noise scenario. On the other hand, in the large noise scenario, the family of SLOPE estimators are suboptimal compared with bridge regression such as the Ridge estimator.more » « less

MCMC chains for the GWB analyses performed in the paper "The NANOGrav 15 yr Data Set: Search for Signals from New Physics".
The data is provided in pickle format. Each file contains a NumPy array with the MCMC chain (with burnin already removed), and a dictionary with the model parameters' names as keys and their priors as values. You can load them as
with open ('path/to/file.pkl', 'rb') as pick: temp = pickle.load(pick) params = temp[0] chain = temp[1]
The naming convention for the files is the following:
 igw: inflationary Gravitational Waves (GWs)
 sigw: scalarinduced GWs
 sigw_box: assumes a boxlike feature in the primordial power spectrum.
 sigw_delta: assumes a deltalike feature in the primordial power spectrum.
 sigw_gauss: assumes a Gaussian peak feature in the primordial power spectrum.
 pt: cosmological phase transitions
 pt_bubble: assumes that the dominant contribution to the GW productions comes from bubble collisions.
 pt_sound: assumes that the dominant contribution to the GW productions comes from sound waves.
 stable: stable cosmic strings
 stablec: stable strings emitting GWs only in the form of GW bursts from cusps on closed loops.
 stablek: stable strings emitting GWs only in the form of GW bursts from kinks on closed loops.
 stablem: stable strings emitting monochromatic GW at the fundamental frequency.
 stablen: stable strings described by numerical simulations including GWs from cusps and kinks.
 meta: metastable cosmic strings
 metal: metastable strings with GW emission from loops only.
 metals metastable strings with GW emission from loops and segments.
 super: cosmic superstrings.
 dw: domain walls
 dwsm: domain walls decaying into Standard Model particles.
 dwdr: domain walls decaying into dark radiation.
For each model, we provide four files. One for the run where the newphysics signal is assumed to be the only GWB source. One for the run where the newphysics signal is superimposed to the signal from Supermassive Black Hole Binaries (SMBHB), for these files "_bhb" will be appended to the model name. Then, for both these scenarios, in the "compare" folder we provide the files for the hypermodel runs that were used to derive the Bayes' factors.
In addition to chains for the stochastic models, we also provide data for the two deterministic models considered in the paper (ULDM and DM substructures). For the ULDM model, the naming convention of the files is the following (all the ULDM signals are superimposed to the SMBHB signal, see the discussion in the paper for more details)
 uldm_e: ULDM Earth signal.
 uldm_p: ULDM pulsar signal
 uldm_p_cor: correlated limit
 uldm_p_unc: uncorrelated limit
 uldm_c: ULDM combined Earth + pulsar signal direct coupling
 uldm_c_cor: correlated limit
 uldm_c_unc: uncorrelated limit
 uldm_vecB: vector ULDM coupled to the baryon number
 uldm_vecB_cor: correlated limit
 uldm_vecB_unc: uncorrelated limit
 uldm_vecBL: vector ULDM coupled to BL
 uldm_vecBL_cor: correlated limit
 uldm_vecBL_unc: uncorrelated limit
 uldm_c_grav: ULDM combined Earth + pulsar signal for gravitationalonly coupling
 uldm_c_grav_cor: correlated limit
 uldm_c_cor_grav_low: low mass region
 uldm_c_cor_grav_mon: monopole region
 uldm_c_cor_grav_low: high mass region
 uldm_c_unc: uncorrelated limit
 uldm_c_unc_grav_low: low mass region
 uldm_c_unc_grav_mon: monopole region
 uldm_c_unc_grav_low: high mass region
 uldm_c_grav_cor: correlated limit
For the substructure (static) model, we provide the chain for the marginalized distribution (as for the ULDM signal, the substructure signal is always superimposed to the SMBHB signal)

We consider the highdimensional linear regression model and assume that a fraction of the responses are contaminated by an adversary with complete knowledge of the data and the underlying distribution. We are interested in the situation when the dense additive noise can be heavytailed but the predictors have subGaussian distribution. We establish minimax lower bounds that depend on the the fraction of the contaminated data and the tails of the additive noise. Moreover, we design a modification of the square root Slope estimator with several desirable features: (a) it is provably robust to adversarial contamination, with the performance guarantees that take the form of subGaussian deviation inequalities and match the lower error bounds up to logfactors; (b) it is fully adaptive with respect to the unknown sparsity level and the variance of the noise, and (c) it is computationally tractable as a solution of a convex optimization problem. To analyze the performance of the proposed estimator, we prove several properties of matrices with subGaussian rows that could be of independent interest.more » « less