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This paper presents Sparse Gradient Descent as a solution for variable selection in convex piecewise linear regression where the model is given as $\mathrm{max}\langle a_j^\star, x \rangle + b_j^\star$ for $j = 1,\dots,k$ where $x \in \mathbb R^d$ is the covariate vector. Here, $\{a_j^\star\}_{j=1}^k$ and $\{b_j^\star\}_{j=1}^k$ denote the ground-truth weight vectors and intercepts. A non-asymptotic local convergence analysis is provided for Sp-GD under sub-Gaussian noise when the covariate distribution satisfies sub-Gaussianity and anti-concentration property. When the model order and parameters are fixed, Sp-GD provides an $\epsilon$-accurate estimate given $\mathcal{O}(\max(\epsilon^{-2}\sigma_z^2,1)s\log(d/s))$ observations where $\sigma_z^2$ denotes the noise variance. This also implies the exact parameter recovery by Sp-GD from $\mathcal{O}(s\log(d/s))$ noise-free observations. Since optimizing the squared loss for sparse max-affine is non-convex, an initialization scheme is proposed to provide a suitable initial estimate within the basin of attraction for Sp-GD, i.e. sufficiently accurate to invoke the convergence guarantees. The initialization scheme uses sparse principal component analysis to estimate the subspace spanned by $\{ a_j^\star\}_{j=1}^k$ then applies an $r$-covering search to estimate the model parameters. A non-asymptotic analysis is presented for this initialization scheme when the covariates and noise samples follow Gaussian distributions. When the model order and parameters are fixed, this initialization scheme provides an $\epsilon$-accurate estimate given $\mathcal{O}(\epsilon^{-2}\max(\sigma_z^4,\sigma_z^2,1)s^2\log^4(d))$ observations. Numerical Monte Carlo results corroborate theoretical findings for Sp-GD and the initialization scheme.

Rotating magnets have recently emerged as an efficient method for producing ultra-low frequency signals for through-earth and through-seawater communications. Magneto-mechanical resonator (MMR) arrays, which are magnetized torsional rotors with a restoring torque, are a promising implementation of this idea that use resonance to enhance the magnetic signal generation. The fundamental challenge for MMR design is to have a suspension system for the rotors capable of resisting large transverse magnetic forces while allowing for a large angle of motion at low dissipation and hence high efficiency. Here, we study flexure-based pivot bearings as compliant support elements for MMR rotors which address this challenge and demonstrate their efficient low damping operation. A crossed-flexure configuration enables large angular rotation around a central axis, large transverse stiffness, and compact assembly of closely spaced rotor arrays via geometric flexure interlocking. We characterize the eigen frequency performance and structural damping of MMR supported by these proposed pivot bearings. We develop analytical and numerical models to study their static and dynamic behaviors, including their coupled dynamic modes. We demonstrate that their damping coefficient is up to 80 times lower than corresponding ball bearing MMR. This study is broadly applicable to various systems that leverage arrays of coupled torsional oscillators such as magneto-mechanical transmitters, metamaterials, and energy harvesters., Comment: 26 pages, 12 figures

We investigate spin-rectification phenomena in canted antiferromagnets, closely connected to the family of altermagnetic materials. Our results show that excitation efficiency is significantly enhanced by the Dzyaloshinskii-Moriya interaction. Antiferromagnetic dynamics can be detected through spin-Hall magnetoresistance and bolometric effects, with an efficiency reaching up to mV/W. The rectified voltage shape is influenced by both the symmetry of the exciting torques, detection mechanisms (continuous spin-pumping and spin-Hall magnetoresistance), and the antiferromagnetic crystalline axis. Under high pumping power, we observe a saturation effect related to Suhl-like spin-wave instabilities and a nonlinear redshift of the antiferromagnetic resonance. These findings open new avenues for studying nonlinear dynamics in antiferromagnetic and altermagnetic spintronic devices.

Several works have recently investigated the parameterized complexity of data completion problems, motivated by their applications in machine learning, and clustering in particular. Interestingly, these problems can be equivalently formulated as classical graph problems on induced subgraphs of powers of partially-defined hypercubes. In this paper, we follow up on this recent direction by investigating the Independent Set problem on this graph class, which has been studied in the data science setting under the name Diversity. We obtain a comprehensive picture of the problem's parameterized complexity and establish its fixed-parameter tractability w.r.t. the solution size plus the power of the hypercube. Given that several such FO-definable problems have been shown to be fixed-parameter tractable on the considered graph class, one may ask whether fixed-parameter tractability could be extended to capture all FO-definable problems. We answer this question in the negative by showing that FO model checking on induced subgraphs of hypercubes is as difficult as FO model checking on general graphs., Comment: A preliminary version of this article appeared in the proceedings of IPEC 2023. arXiv admin note: substantial text overlap with arXiv:1911.01465

We study the parameterized complexity of a generalization of the coordinated motion planning problem on graphs, where the goal is to route a specified subset of a given set of $k$ robots to their destinations with the aim of minimizing the total energy (i.e., the total length traveled). We develop novel techniques to push beyond previously-established results that were restricted to solid grids. We design a fixed-parameter additive approximation algorithm for this problem parameterized by $k$ alone. This result, which is of independent interest, allows us to prove the following two results pertaining to well-studied coordinated motion planning problems: (1) A fixed-parameter algorithm, parameterized by $k$, for routing a single robot to its destination while avoiding the other robots, which is related to the famous Rush-Hour Puzzle; and (2) a fixed-parameter algorithm, parameterized by $k$ plus the treewidth of the input graph, for the standard \textsc{Coordinated Motion Planning} (CMP) problem in which we need to route all the $k$ robots to their destinations. The latter of these results implies, among others, the fixed-parameter tractability of CMP parameterized by $k$ on graphs of bounded outerplanarity, which include bounded-height subgrids. We complement the above results with a lower bound which rules out the fixed-parameter tractability for CMP when parameterized by the total energy. This contrasts the recently-obtained tractability of the problem on solid grids under the same parameterization. As our final result, we strengthen the aforementioned fixed-parameter tractability to hold not only on solid grids but all graphs of bounded local treewidth -- a class including, among others, all graphs of bounded genus.

We study computationally-hard fundamental motion planning problems where the goal is to translate $k$ axis-aligned rectangular robots from their initial positions to their final positions without collision, and with the minimum number of translation moves. Our aim is to understand the interplay between the number of robots and the geometric complexity of the input instance measured by the input size, which is the number of bits needed to encode the coordinates of the rectangles' vertices. We focus on axis-aligned translations, and more generally, translations restricted to a given set of directions, and we study the two settings where the robots move in the free plane, and where they are confined to a bounding box. We obtain fixed-parameter tractable (FPT) algorithms parameterized by $k$ for all the settings under consideration. In the case where the robots move serially (i.e., one in each time step) and axis-aligned, we prove a structural result stating that every problem instance admits an optimal solution in which the moves are along a grid, whose size is a function of $k$, that can be defined based on the input instance. This structural result implies that the problem is fixed-parameter tractable parameterized by $k$. We also consider the case in which the robots move in parallel (i.e., multiple robots can move during the same time step), and which falls under the category of Coordinated Motion Planning problems. Finally, we show that, when the robots move in the free plane, the FPT results for the serial motion case carry over to the case where the translations are restricted to any given set of directions.

We study two variants of the fundamental problem of finding a cluster in incomplete data. In the problems under consideration, we are given a multiset of incomplete $d$-dimensional vectors over the binary domain and integers $k$ and $r$, and the goal is to complete the missing vector entries so that the multiset of complete vectors either contains (i) a cluster of $k$ vectors of radius at most $r$, or (ii) a cluster of $k$ vectors of diameter at most $r$. We give tight characterizations of the parameterized complexity of the problems under consideration with respect to the parameters $k$, $r$, and a third parameter that captures the missing vector entries., Comment: Short version appeared at ESA 2022. arXiv admin note: substantial text overlap with arXiv:1911.01465

In Coordinated Motion Planning (CMP), we are given a rectangular-grid on which $k$ robots occupy $k$ distinct starting gridpoints and need to reach $k$ distinct destination gridpoints. In each time step, any robot may move to a neighboring gridpoint or stay in its current gridpoint, provided that it does not collide with other robots. The goal is to compute a schedule for moving the $k$ robots to their destinations which minimizes a certain objective target - prominently the number of time steps in the schedule, i.e., the makespan, or the total length traveled by the robots. We refer to the problem arising from minimizing the former objective target as CMP-M and the latter as CMP-L. Both CMP-M and CMP-L are fundamental problems that were posed as the computational geometry challenge of SoCG 2021, and CMP also embodies the famous $(n^2-1)$-puzzle as a special case. In this paper, we settle the parameterized complexity of CMP-M and CMP-L with respect to their two most fundamental parameters: the number of robots, and the objective target. We develop a new approach to establish the fixed-parameter tractability of both problems under the former parameterization that relies on novel structural insights into optimal solutions to the problem. When parameterized by the objective target, we show that CMP-L remains fixed-parameter tractable while CMP-M becomes para-NP-hard. The latter result is noteworthy, not only because it improves the previously-known boundaries of intractability for the problem, but also because the underlying reduction allows us to establish - as a simpler case - the NP-hardness of the classical Vertex Disjoint and Edge Disjoint Paths problems with constant path-lengths on grids., Comment: Short version appeared in SoCG 2023

Hypersphere classification is a classical and foundational method that can provide easy-to-process explanations for the classification of real-valued and binary data. However, obtaining an (ideally concise) explanation via hypersphere classification is much more difficult when dealing with binary data than real-valued data. In this paper, we perform the first complexity-theoretic study of the hypersphere classification problem for binary data. We use the fine-grained parameterized complexity paradigm to analyze the impact of structural properties that may be present in the input data as well as potential conciseness constraints. Our results include stronger lower bounds and new fixed-parameter algorithms for hypersphere classification of binary data, which can find an exact and concise explanation when one exists., Comment: Short version appeared at ICML 2023

We present streaming algorithms for the graph $k$-matching problem in both the insert-only and dynamic models. Our algorithms, with space complexity matching the best upper bounds, have optimal or near-optimal update time, significantly improving on previous results. More specifically, for the insert-only streaming model, we present a one-pass algorithm with optimal space complexity $O(k^2)$ and optimal update time $O(1)$, that with high probability computes a maximum weighted $k$-matching of a given weighted graph. The update time of our algorithm significantly improves the previous upper bound of $O(\log k)$, which was derived only for $k$-matching on unweighted graphs. For the dynamic streaming model, we present a one-pass algorithm that with high probability computes a maximum weighted $k$-matching in $O(Wk^2 \cdot \mbox{polylog}(n)$ space and with $O(\mbox{polylog}(n))$ update time, where $W$ is the number of distinct edge weights. Again the update time of our algorithm improves the previous upper bound of $O(k^2 \cdot \mbox{polylog}(n))$. This algorithm, when applied to unweighted graphs, gives a streaming algorithm on the dynamic model whose space and update time complexities are both near-optimal. Our results also imply a streaming approximation algorithm for maximum weighted $k$-matching whose space complexity matches the best known upper bound with a significantly improved update time.

Foam characterization is essential in many applications of foams, such as cleaning, food processing, cosmetics, and oil production, due to these applications diversified requirements. The standard characterization method, the foam column test, cannot provide sufficient information for in-depth studies. Hence, there have been many studies that incorporated different characterization methods into the standard test. It should be enlightening and feasible to measure the foam viscosity, which is both of practical and fundamental interest, during the foam column test, but it has never been done before. Here, we demonstrate a method to characterize aqueous foams and their aging behaviors with simultaneous measurement of foam viscosity and foam height. Using a vibration viscometer, we integrate foam column experiments with in-situ foam viscosity measurements. We studied the correlation among the foam structure, foam height, and foam viscosity during the foam decay process. We found a drastic decrease in foam viscosity in the early foam decay while the foam height remained unchanged, which is explained by coarsening. This method is much more sensitive and time-efficient than conventional foam-height-based methods by comparing the half-life. This method successfully characterizes the stability of foams made of various combinations of surfactants and gases.

Automatic Speech Recognition systems have been shown to be vulnerable to adversarial attacks that manipulate the command executed on the device. Recent research has focused on exploring methods to create such attacks, however, some issues relating to Over-The-Air (OTA) attacks have not been properly addressed. In our work, we examine the needed properties of robust attacks compatible with the OTA model, and we design a method of generating attacks with arbitrary such desired properties, namely the invariance to synchronization, and the robustness to filtering: this allows a Denial-of-Service (DoS) attack against ASR systems. We achieve these characteristics by constructing attacks in a modified frequency domain through an inverse Fourier transform. We evaluate our method on standard keyword classification tasks and analyze it in OTA, and we analyze the properties of the cross-domain attacks to explain the efficiency of the approach., Comment: 10 pages, 11 Figures

Legged locomotion is a highly promising but under-researched subfield within the field of soft robotics. The compliant limbs of soft-limbed robots offer numerous benefits, including the ability to regulate impacts, tolerate falls, and navigate through tight spaces. These robots have the potential to be used for various applications, such as search and rescue, inspection, surveillance, and more. The state-of-the-art still faces many challenges, including limited degrees of freedom, a lack of diversity in gait trajectories, insufficient limb dexterity, and limited payload capabilities. To address these challenges, we develop a modular soft-limbed robot that can mimic the locomotion of pinnipeds. By using a modular design approach, we aim to create a robot that has improved degrees of freedom, gait trajectory diversity, limb dexterity, and payload capabilities. We derive a complete floating-base kinematic model of the proposed robot and use it to generate and experimentally validate a variety of locomotion gaits. Results show that the proposed robot is capable of replicating these gaits effectively. We compare the locomotion trajectories under different gait parameters against our modeling results to demonstrate the validity of our proposed gait models., Comment: This paper has been accepted to 2023 IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM)

Soft robotics holds tremendous potential for various applications, especially in unstructured environments such as search and rescue operations. However, the lack of autonomy and teleoperability, limited capabilities, absence of gait diversity and real-time control, and onboard sensors to sense the surroundings are some of the common issues with soft-limbed robots. To overcome these limitations, we propose a spatially symmetric, topologically-stable, soft-limbed tetrahedral robot that can perform multiple locomotion gaits. We introduce a kinematic model, derive locomotion trajectories for different gaits, and design a teleoperation mechanism to enable real-time human-robot collaboration. We use the kinematic model to map teleoperation inputs and ensure smooth transitions between gaits. Additionally, we leverage the passive compliance and natural stability of the robot for toppling and obstacle navigation. Through experimental tests, we demonstrate the robot's ability to tackle various locomotion challenges, adapt to different situations, and navigate obstructed environments via teleoperation.

Magnonic nano-devices exploit magnons -- quanta of spin waves -- to transmit and process information within a single integrated platform that has the potential to outperform traditional semiconductor-based electronics for low power applications. The main missing cornerstone of this information nanotechnology is an efficient scheme for the direct amplification of propagating spin waves. The recent discovery of spin-orbit torque provided an elegant mechanism for propagation losses compensation. While partial compensation of the spin-wave damping has allowed for spin-wave signal modulation, true amplification - the exponential increase in the spin-wave intensity during propagation - has so far remained elusive. Here we evidence the operating conditions to achieve unambiguous amplification using clocked nanoseconds-long spin-orbit torque pulses in sub-micrometer wide magnonic waveguides, where the effective magnetization has been engineered to be close to zero to suppress the detrimental magnon-magnon scattering. As a result, we achieve an exponential increase in the intensity of propagating spin waves up to 500 % at a propagation distance of several micrometers. These results pave the way towards the implementation of energy efficient, cascadable magnonic architectures for wave-based information processing and complex on-chip computation., Comment: This preprint has not undergone peer review or any post-submission improvements or corrections. The Version of Record of this article is published in Nature Communications, and is available online at https://doi.org/10.1038/s41467-024-45783-1

Soft robotic snakes made of compliant materials can continuously deform their bodies and, therefore, mimic the biological snakes' flexible and agile locomotion gaits better than their rigid-bodied counterparts. Without wheel support, to date, soft robotic snakes are limited to emulating planar locomotion gaits, which are derived via kinematic modeling and tested on robotic prototypes. Given that the snake locomotion results from the reaction forces due to the distributed contact between their skin and the ground, it is essential to investigate the locomotion gaits through efficient dynamic models capable of accommodating distributed contact forces. We present a complete spatial dynamic model that utilizes a floating-base kinematic model with distributed contact dynamics for a pneumatically powered soft robotic snake. We numerically evaluate the feasibility of the planar and spatial rolling gaits utilizing the proposed model and experimentally validate the corresponding locomotion gait trajectories on a soft robotic snake prototype. We qualitatively and quantitatively compare the numerical and experimental results which confirm the validity of the proposed dynamic model., Comment: This paper has been accepted to 2023 IEEE International Conference on Control, Automation and Robotics (ICCAR)

Soft robotic snakes (SRSs) have a unique combination of continuous and compliant properties that allow them to imitate the complex movements of biological snakes. Despite the previous attempts to develop SRSs, many have been limited to planar movements or use wheels to achieve locomotion, which restricts their ability to imitate the full range of biological snake movements. We propose a new design for the SRSs that is wheelless and powered by pneumatics, relying solely on spatial bending to achieve its movements. We derive a kinematic model of the proposed SRS and utilize it to achieve two snake locomotion trajectories, namely sidewinding and helical rolling. These movements are experimentally evaluated under different gait parameters on our SRS prototype. The results demonstrate that the SRS can successfully mimic the proposed spatial locomotion trajectories. This is a significant improvement over the previous designs, which were either limited to planar movements or relied on wheels for locomotion. The ability of the SRS to effectively mimic the complex movements of biological snakes opens up new possibilities for its use in various applications., Comment: This paper has been accepted to 2023 IEEE-RAS International Conference on Soft Robotics (RoboSoft)

Thin garnet films are becoming central for magnon-spintronics and spin-orbitronics devices as they show versatile magnetic properties together with low magnetic losses. These fields would benefit from materials in which heat does not affect the magnetization dynamics, an effect known as the non-linear thermal frequency shift. In this study, low damping Bi substituted Iron garnet (Bi:YIG) ultra-thin films have been grown using Pulsed Laser Deposition. Through a fine tuning of the growth parameters, the precise control of the perpendicular magnetic anisotropy allows to achieve a full compensation of the dipolar magnetic anisotropy. Strikingly, once the growth conditions are optimized, varying the growth temperature from 405 {\deg}C to 475 {\deg}C as the only tuning parameter induces the easy-axis to go from out-of-plane to in-plane. For films that are close to the dipolar compensation, Ferromagnetic Resonance measurements yield an effective magnetization $\mu _{0}M_{eff} (T)$ that has almost no temperature dependence over a large temperature range (260 K to 400 K) resulting in an anisotropy temperature exponent of 2. These findings put Bi:YIG system among the very few materials in which the temperature dependence of the magnetic anisotropy varies at the same rate than the saturation magnetization. This interesting behavior is ascribed phenomenologically to the sizable orbital moment of $Bi^{3+}$., Comment: 15 pages 4 figures and supplemental Material

On-chip phononic circuits tailor the transmission of elastic waves, which can couple to electronic and photonic systems, enabling new signal manipulation capabilities. Phononic circuits rely on waveguides that transmit elastic waves within desired frequency passbands, typically designed based on the Bloch modes of the waveguide constitutive cell, assuming linearity and periodicity. MEMS waveguides composed of coupled drumhead (membrane) resonators offer tunable MHz operation frequencies for applications in nonlinear optomechanics, topological insulators, phononic cavities, and acoustic switching. Here, we construct a reduced-order model (ROM) to demonstrate the switching of signal transmission in drumhead-resonator waveguides due to thermoelastic buckling. The ROM shows that buckling amplifies existing structural disorders, breaking the periodicity required for waveguide transmission through the first passband. This periodicity breaking manifests in the localization of the first-passband modes, like classical Anderson localization caused by disorders. The proposed ROM is essential to study the investigated phenomena since Bloch mode analysis fails for weakly-disordered (< 5%) finite waveguides due to the disorder amplification caused by the thermoelastic buckling. The illustrated transmission control should be useful for logical acoustic operations, like switching, and can be extended to 2D circuits in the future., Comment: 32 pages, 10 figures

We address the problem of mitigating damage to a power grid following a storm by managing a vehicle that has to be routed while simultaneously performing two tasks: learning about damage from the grid (which requires direct observation) and repairing damage that it observes. The learning process is assisted by calls from customers notifying the utility that they have lost power (``lights-out calls''). However, when a tree falls and damages a line, it triggers the first upstream circuit breaker, which results in power outages for everyone on the grid below the circuit breaker. We present a dynamic routing model that captures observable state variables such as the location of the truck and the state of the grid on segments the truck has visited, and beliefs about outages on segments that have not been visited. Trucks are routed over a physical transportation network, but the pattern of outages is governed by the structure of the power grid. We introduce a form of Monte Carlo tree search based on information relaxation that we call {\it optimistic MCTS} which improves its application to problems with larger action spaces. We show that the method significantly outperforms standard escalation heuristics used in industry.}, Comment: 44 pages, 7 figures. arXiv admin note: substantial text overlap with arXiv:1605.05711

Spin-waves in antiferromagnets hold the prospects for the development of faster, less power-hungry electronics, as well as promising physics based on spin-superfluids and coherent magnon-condensates. For both these perspectives, addressing electrically coherent antiferromagnetic spin-waves is of importance, a prerequisite that has so far been elusive, because unlike ferromagnets,antiferromagnets couple weakly to radiofrequency fields. Here, we demonstrate the detection of ultra-fast non-reciprocal spin-waves in the dipolar-exchange regime of a canted antiferromagnet using both inductive and spintronic transducers. Using time-of-flight spin-wave spectroscopy on hematite ({\alpha}-Fe2O3), we find that the magnon wave packets can propagate as fast as 20 km/s for reciprocal bulk spin-wave modes and up to 6 km/s for surface-spin waves propagating parallel to the antiferromagnetic Neel vector. We finally achieve efficient electrical detection of non-reciprocal spin-wave transport using non-local inverse spin-Hall effects. The electrical detection of coherent non-reciprocal antiferromagnetic spin waves paves the way for the development of antiferromagnetic and altermagnet-based magnonic devices.

Nonlinear micro-electro-mechanical systems (MEMS) resonators open new opportunities in sensing and signal manipulation compared to their linear counterparts by enabling frequency tuning and increased bandwidth. Here, we design, fabricate and study drumhead resonators exhibiting strongly nonlinear dynamics and develop a reduced order model (ROM) to capture their response accurately. The resonators undergo electrostatically-mediated thermoelastic buckling which tunes their natural frequency from 4.7 to 11.3 MHz, a factor of 2.4x tunability. Moreover, the imposed buckling switches the nonlinearity of the resonators between purely stiffening, purely softening, and even softening-to-stiffening. Accessing these exotic dynamics requires precise control of the temperature and the DC electrostatic forces near the resonator's critical-buckling point. To explain the observed tunability, we develop a one-dimensional physics-based ROM that predicts the linear and nonlinear response of the fundamental bending mode of these drumhead resonators. The ROM captures the dynamic effects of the internal stresses resulting from three sources: The residual stresses from the fabrication process, the mismatch in thermal expansion between the constituent layers, and lastly, the applied electrostatic forces. The ROM replicates the observed tunability of linear (within 5.5% error) and nonlinear responses even near the states of critical buckling. These remarkable nonlinear and large tunability of the natural frequency are valuable features for on-chip acoustic devices in broad applications such as signal manipulation, filtering, and MEMS waveguides.