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Nonlinear dynamic simulations of mechanical resonators have been facilitated by the advent of computational techniques that generate nonlinear reduced order models (ROMs) using the finite element (FE) method. However, designing devices with specific nonlinear characteristics remains inefficient since it requires manual adjustment of the design parameters and can result in suboptimal designs. Here, we integrate an FE-based nonlinear ROM technique with a derivative-free optimization algorithm to enable the design of nonlinear mechanical resonators. The resulting methodology is used to optimize the support design of high-stress nanomechanical Si3N4 string resonators, in the presence of conflicting objectives such as simultaneous enhancement of Q-factor and nonlinear Duffing constant. To that end, we generate Pareto frontiers that highlight the trade-offs between optimization objectives and validate the results both numerically and experimentally. To further demonstrate the capability of multi-objective optimization for practical design challenges, we simultaneously optimize the design of nanoresonators for three key figure-of-merits in resonant sensing: power consumption, sensitivity and response time. The presented methodology can facilitate and accelerate designing (nano)mechanical resonators with optimized performance for a wide variety of applications.

Deformation detection is vital for enabling accurate assessment and prediction of structural changes in materials, ensuring timely and effective interventions to maintain safety and integrity. Automating deformation detection through computer vision is crucial for efficient monitoring, but it faces significant challenges in creating a comprehensive dataset of both deformed and non-deformed objects, which can be difficult to obtain in many scenarios. In this paper, we introduce a novel framework for generating controlled synthetic data that simulates deformed objects. This approach allows for the realistic modeling of object deformations under various conditions. Our framework integrates an intelligent adapter network that facilitates sim-to-real domain adaptation, enhancing classification results without requiring real data from deformed objects. We conduct experiments on domain adaptation and classification tasks and demonstrate that our framework improves sim-to-real classification results compared to simulation baseline., Comment: 7 pages, 5 figures, submitted to SMC

Recently, frame multipliers, pair frames, and controlled frames have been investigated to improve the numerical efficiency of iterative algorithms for inverting the frame operator and other applications of frames. In this paper, the concept of biframe is introduced for a Hilbert space. A biframe is a pair of sequences in a Hilbert space that applies to an inequality similar to frame inequality. Also, it can be regarded as a generalization of controlled frames and a special kind of pair frames. The basic properties of biframes are investigated based on the biframe operator. Then, biframes are classified based on the type of their constituent sequences. In particular, biframes for which one of the constituent sequences is an orthonormal basis $\{e_k\}_{k=1}^\infty$ are studied. Then, a new class of Riesz bases denoted by $[\{e_k\}]$, is introduced and is called b-Riesz bases. An interesting result is also proved, showing that the set of all b-Riesz bases is a proper subset of the set of all Riesz bases. More precisely, b-Riesz bases induce an equivalence relation on $[\{e_k\}]$., Comment: 29 PAGES

Synchronization plays a crucial role in the dynamics of living organisms, from fireflies flashing in unison to pacemaker cells that jointly generate heartbeats. Uncovering the mechanism behind these phenomena requires an understanding of individual biological oscillators and the coupling forces between them. Here, we develop a single-cell assay that studies rhythmic behavior in the motility of individual E.coli cells that can be mutually synchronized. Circular microcavities are used to isolate E.coli cells that swim along the cavity wall, resulting in self-sustained oscillations. Upon connecting these cavities by microchannels the bacterial motions can be coupled, yielding nonlinear dynamic synchronization patterns with phase slips. We demonstrate that the coordinated movement observed in coupled E. coli oscillators follows mathematical rules of synchronization which we use to quantify the coupling strength. These findings advance our understanding of motility in confinement, and lay the foundation for engineering desired dynamics in microbial active matter.

Deep learning models are often evaluated in scenarios where the data distribution is different from those used in the training and validation phases. The discrepancy presents a challenge for accurately predicting the performance of models once deployed on the target distribution. Domain adaptation and generalization are widely recognized as effective strategies for addressing such shifts, thereby ensuring reliable performance. The recent promising results in applying vision transformers in computer vision tasks, coupled with advancements in self-attention mechanisms, have demonstrated their significant potential for robustness and generalization in handling distribution shifts. Motivated by the increased interest from the research community, our paper investigates the deployment of vision transformers in domain adaptation and domain generalization scenarios. For domain adaptation methods, we categorize research into feature-level, instance-level, model-level adaptations, and hybrid approaches, along with other categorizations with respect to diverse strategies for enhancing domain adaptation. Similarly, for domain generalization, we categorize research into multi-domain learning, meta-learning, regularization techniques, and data augmentation strategies. We further classify diverse strategies in research, underscoring the various approaches researchers have taken to address distribution shifts by integrating vision transformers. The inclusion of comprehensive tables summarizing these categories is a distinct feature of our work, offering valuable insights for researchers. These findings highlight the versatility of vision transformers in managing distribution shifts, crucial for real-world applications, especially in critical safety and decision-making scenarios., Comment: 28 pages, 5 figures, Preprint submitted to Elsevier

Resonators based on two-dimensional (2D) materials have exceptional properties for application as nanomechanical sensors, which allows them to operate at high frequencies with high sensitivity. However, their performance as nanomechanical sensors is currently limited by their low quality ($Q$)-factor. Here, we make use of micro-electromechanical systems (MEMS) to apply pure in-plane mechanical strain, enhancing both their resonance frequency and Q-factor. In contrast to earlier work, the 2D material resonators are fabricated on the MEMS actuators without any wet processing steps, using a dry-transfer method. A platinum clamp, that is deposited by electron beam-induced deposition, is shown to be effective in fixing the 2D membrane to the MEMS and preventing slippage. By in-plane straining the membranes in a purely mechanical fashion, we increase the tensile energy, thereby diluting dissipation. This way, we show how dissipation dilution can increase the $Q$-factor of 2D material resonators by 91\%. The presented MEMS actuated dissipation dilution method does not only pave the way towards higher $Q$-factors in resonators based on 2D materials, but also provides a route toward studies of the intrinsic loss mechanisms of 2D materials in the monolayer limit., Comment: 20 pages, 15 figures

Carbon nanotubes are devices of choice for investigating the interplay between electronic transport and nanomechanical motion. In this work, we report the co-existence of thermal vibrations and large-amplitude self-sustained oscillations in a carbon nanotube that originates from electron tunneling and thermal effects. The measured transitions between the two states are described by a Poisson process, revealing that the interstate switching is induced by noise. We observe the coexistence of the stable low-amplitude thermal state and the stable large-amplitude state (limit cycle) over a finite parameter range, which points to an isola bifurcation. We propose a minimalistic model based on nonlinear friction to account for the isola. Our work provides evidence for a new type of bifurcation leading to self-sustained oscillations that largely differs from the classical Hopf bifurcation, since these large-amplitude oscillations are a hidden state that can be unveiled via stochastic switching. We envision that this new dynamical regime and the means to reveal it will be of interest for various mesoscopic vibrational systems.

Background and objective: Uncertainty quantification is a pivotal field that contributes to realizing reliable and robust systems. It becomes instrumental in fortifying safe decisions by providing complementary information, particularly within high-risk applications. existing studies have explored various methods that often operate under specific assumptions or necessitate substantial modifications to the network architecture to effectively account for uncertainties. The objective of this paper is to study Conformal Prediction, an emerging distribution-free uncertainty quantification technique, and provide a comprehensive understanding of the advantages and limitations inherent in various methods within the medical imaging field. Methods: In this study, we developed Conformal Prediction, Monte Carlo Dropout, and Evidential Deep Learning approaches to assess uncertainty quantification in deep neural networks. The effectiveness of these methods is evaluated using three public medical imaging datasets focused on detecting pigmented skin lesions and blood cell types. Results: The experimental results demonstrate a significant enhancement in uncertainty quantification with the utilization of the Conformal Prediction method, surpassing the performance of the other two methods. Furthermore, the results present insights into the effectiveness of each uncertainty method in handling Out-of-Distribution samples from domain-shifted datasets. Our code is available at: Conclusions: Our conclusion highlights a robust and consistent performance of conformal prediction across diverse testing conditions. This positions it as the preferred choice for decision-making in safety-critical applications.

Suspended drums made of 2D materials hold potential for sensing applications. However, the industrialization of these applications is hindered by significant device-to-device variations presumably caused by non-uniform stress distributions induced by the fabrication process. Here we introduce a new methodology to determine the stress distribution from their mechanical resonance frequencies and corresponding mode shapes as measured by a laser Doppler vibrometer (LDV). To avoid limitations posed by the optical resolution of the LDV, we leverage a unique manufacturing process to create ultra-large graphene drums with diameters of up to 1000 um. We solve the inverse problem of a F\"oppl--von K\'arm\'an plate model by an iterative procedure to obtain the stress distribution within the drums from the experimental data. Our results show that the generally used uniform pre-tension assumption overestimates the pre-stress value, exceeding the averaged stress obtained by more than 47%. Moreover, it is is found that the reconstructed stress distributions are bi-axial, which likely originates from the transfer process. The introduced metholodogy allows one to estimate the tension distribution in drum resonators from their mechanical response and thereby paves the way for linking the used fabrication processes to the resulting device performance.

The paper presents a method for using fractional concepts in a neural network to modify the activation and loss functions. The methodology allows the neural network to define and optimize its activation functions by determining the fractional derivative order of the training process as an additional hyperparameter. This will enable neurons in the network to adjust their activation functions to match input data better and reduce output errors, potentially improving the network's overall performance., Comment: 12 pages, 6 figures, submitted to Neurocomputing journal

Nanomechanical resonances of two-dimensional (2D) materials are sensitive probes for condensed-matter physics, offering new insights into magnetic and electronic phase transitions. Despite extensive research, the influence of the spin dynamics near a second-order phase transition on the nonlinear dynamics of 2D membranes has remained largely unexplored. Here, we investigate nonlinear magneto-mechanical coupling to antiferromagnetic order in suspended FePS$_3$-based heterostructure membranes. By monitoring the motion of these membranes as a function of temperature, we observe characteristic features in both nonlinear stiffness and damping close to the N\'{e}el temperature $T_{\rm{N}}$. We account for these experimental observations with an analytical magnetostriction model in which these nonlinearities emerge from a coupling between mechanical and magnetic oscillations, demonstrating that magneto-elasticity can lead to nonlinear damping. Our findings thus provide insights into the thermodynamics and magneto-mechanical energy dissipation mechanisms in nanomechanical resonators due to the material's phase change and magnetic order relaxation.

Two-dimensional (2D) layered metal dichalcogenides constitute a promising class of materials for photodetector applications due to their excellent optoelectronic properties. The most common photodetectors, which work on the principle of photoconductive or photovoltaic effects, however, require either the application of external voltage biases or built-in electric fields, which makes it challenging to simultaneously achieve high responsivities across broadband wavelength excitation - especially beyond the material's nominal band gap - while producing low dark currents. In this work, we report the discovery of an intricate phonon-photon-electron coupling - which we term the acoustophotoelectric effect - in SnS$_2$ that facilitates efficient photodetection through the application of 100-MHz-order propagating surface acoustic waves (SAWs). This effect not only reduces the band gap of SnS$_2$, but also provides the requisite momentum for indirect band gap transition of the photoexcited charge carriers, to enable broadband photodetection beyond the visible light range, whilst maintaining pA-order dark currents - remarkably without the need for any external voltage bias. More specifically, we show in the infrared excitation range that it is possible to achieve up to eight orders of magnitude improvement in the material's photoresponsivity compared to that previously reported for SnS$_2$-based photodetectors, in addition to exhibiting superior performance compared to most other 2D materials reported to date for photodetection.

Mechanical nonlinearities dominate the motion of nanoresonators already at relatively small oscillation amplitudes. Although single and coupled two-degrees-of-freedom models have been used to account for experimentally observed nonlinear effects, it is shown that these models quickly deviate from experimental findings when multiple modes influence the nonlinear response. Here, we present a nonlinear reduced-order modelling methodology based on FEM simulations for capturing the global nonlinear dynamics of nanomechanical resonators. Our physics-based approach obtains the quadratic and cubic nonlinearities of resonators over a wide frequency range that spans 70 MHz. To qualitatively validate our approach, we perform experiments on a graphene nanodrum driven opto-thermally and show that the model can replicate diverse ranges of nonlinear phenomena, including multi-stability, parametric resonance, and different internal resonances without considering any empirical nonlinear fitting parameters. By providing a direct link between microscopic geometry, material parameters, and nonlinear dynamic response, we clarify the physical significance of nonlinear parameters that are obtained from fitting the dynamics of nanomechanical systems, and provide a route for designing devices with desired nonlinear behaviour.

Let $G$ be a locally compact abelian (LCA) group. We denote by $G_{op}$, the intersection of all open pure subgroups of $G$, which we call the $OP$ subgroup of $G$. In this paper, we prove that the $OP$ subgroup of a torsion-free LCA group $G$ is a non-zero pure subgroup of $G$.

The resonance frequency of ultra-thin layered two-dimensional (2D) materials changes nonlinearly with the tension induced by the pressure from the surrounding gas. Although the dynamics of pressurized 2D material membranes have been extensively explored, recent experimental observations show significant deviations from analytical predictions. Here, we present a multi-mode continuum approach to capture the nonlinear pressure-frequency response of pre-tensioned membranes undergoing large deflections. We validate the model using experiments conducted on polysilicon drums excited opto-thermally and subjected to pressure changes in the surrounding medium. We demonstrate that considering the effect of pressure on the membrane tension is not sufficient for determining the resonance frequencies. In fact, it is essential to also account for the change in the membrane's shape in the pressurized configuration, the mid-plane stretching, and the contributions of higher modes to the mode shapes. Finally, we show how the presented high-frequency mechanical characterization method can be used to determine Young's modulus of ultra-thin membranes.

Mechanical resonators that possess coupled modes with harmonic frequency relations have recently sparked interest due to their suitability for controllable energy transfer and non-Hermitian dynamics. Here, we show coupling between high Q-factor ($>\!\!10^4$) resonances with a nearly 1:1 frequency relation in spatially-symmetric microresonators. We develop and demonstrate a method to analyze their dynamical behavior based on the simultaneous and resonant detection of both spectral peaks, and validate this with experimental results. The frequency difference between the peaks modulates their ringdown, and creates a beat pattern in the linear decay. This method applies both to the externally driven and the Brownian motion (thermal) regime, and allows characterization of both linear and nonlinear parameters. The mechanism behind this method renders it broadly applicable to both optical and electrical readout, as well as to different mechanical systems. This will aid studies using near-degenerate mechanical modes, for e.g., optomechanical energy transfer, synchronization and gyroscopic sensors.

In this paper, we present a comprehensive study on the utility of deep convolutional neural networks with two state-of-the-art pooling layers which are placed after convolutional layers and fine-tuned in an end-to-end manner for visual place recognition task in challenging conditions, including seasonal and illumination variations. We compared extensively the performance of deep learned global features with three different loss functions, e.g. triplet, contrastive and ArcFace, for learning the parameters of the architectures in terms of fraction of the correct matches during deployment. To verify effectiveness of our results, we utilized two real world datasets in place recognition, both indoor and outdoor. Our investigation demonstrates that fine tuning architectures with ArcFace loss in an end-to-end manner outperforms other two losses by approximately 1~4% in outdoor and 1~2% in indoor datasets, given certain thresholds, for the visual place recognition tasks.

In this paper, we study some properties of $*-$open and $*-$closed subsets of a space. The collection of all $*-$open subsets of a space $X$ form a topology on $X$ which is denoted by $^{*}O(X)$. We investigate the relations between topological properties of $X$ with the topology $^{*}O(X)$ and $X$. Also, we introduce the concept of a $*-$continuous map.

Let $\ell$ be the category of all locally compact abelian (LCA) groups. Let $G\in\ell$ and $H\subseteq G$. The first Ulm subgroup of $G$ is denoted by $G^{(1)}$ and the closure of $H$ by $\overline{H}$. A proper short exact sequence $0\to A\stackrel{\phi}{\to} B\stackrel{\psi}{\to} C\to 0$ in $\ell$ is said to be a $TFU$ extension if $0\to \overline{A^{(1)}}\stackrel{\overline{\phi}}{\to} \overline{B^{(1)}}\stackrel{\overline{\psi}}{\to} \overline{C^{(1)}}\to 0$ is a proper short exact sequence where $\overline{\phi}=\phi\mid_{\overline{A^{(1)}}}$ and $\overline{\psi}=\psi\mid_{\overline{B^{(1)}}}$. We introduce some results on $TFU$ extensions. Also, we establish conditions under which the $TFU$ extensions split.

A locally compact abelian group $G$ is called a generalized $\unicode{x00A3}$-cotosion group if $G$ contains an open $\unicode{x00A3}$-cotosion subgroup $H$ such that $G/H$ is a cotorsion group. In this paper, we determine the generalized $\unicode{x00A3}$-cotorsion LCA groups.

The aim of this paper is to introduce and give preliminary investigation of T-locally compact spaces. Locally compact and T-locally compact are independent of each other. Every Hausdorff, locally compact space is T-locally compact. T-locally compact is a topological property. T-locally compact is not preserved by the product topology.

Levitation offers extreme isolation of mechanical systems from their environment, while enabling unconstrained high-precision translation and rotation of objects. Diamagnetic levitation is one of the most attractive levitation schemes, because it allows stable levitation at room temperature without the need for a continuous power supply. However, dissipation by eddy currents in conventional diamagnetic materials significantly limits the application potential of diamagnetically levitating systems. Here, we present a route towards high $Q$ macroscopic levitating resonators by substantially reducing eddy current damping using graphite particle based diamagnetic composites. We demonstrate resonators that feature quality factors $Q$ above 450,000 and vibration lifetimes beyond one hour, while levitating above permanent magnets in high vacuum at room temperature. The composite resonators have a $Q$ that is more than 400 times higher than that of diamagnetic graphite plates. By tuning the composite particle size and density, we investigate the dissipation reduction mechanism and enhance the $Q$ of the levitating resonators. Since their estimated acceleration noise is as low as some of the best superconducting levitating accelerometers at cryogenic temperatures, the high $Q$ and large mass of the presented composite resonators positions them as one of the most promising technologies for next generation ultra-sensitive room temperature accelerometers.