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1. Fractional order memcapacitive neuromorphic elements reproduce and predict neuronal function

   https://doi.org/10.1038/s41598-024-55784-1  

   Vazquez-Guerrero, Patricia; Tuladhar, Rohisha; Psychalinos, Costas; Elwakil, Ahmed; Chacron, Maurice J; Santamaria, Fidel (December 2024, Scientific Reports)

   There is an increasing need to implement neuromorphic systems that are both energetically and computationally efficient. There is also great interest in using electric elements with memory, memelements, that can implement complex neuronal functions intrinsically. A feature not widely incorporated in neuromorphic systems is history-dependent action potential time adaptation which is widely seen in real cells. Previous theoretical work shows that power-law history dependent spike time adaptation, seen in several brain areas and species, can be modeled with fractional order differential equations. Here, we show that fractional order spiking neurons can be implemented using super-capacitors. The super-capacitors have fractional order derivative and memcapacitive properties. We implemented two circuits, a leaky integrate and fire and a Hodgkin–Huxley. Both circuits show power-law spiking time adaptation and optimal coding properties. The spiking dynamics reproduced previously published computer simulations. However, the fractional order Hodgkin–Huxley circuit showed novel dynamics consistent with criticality. We compared the responses of this circuit to recordings from neurons in the weakly-electric fish that have previously been shown to perform fractional order differentiation of their sensory input. The criticality seen in the circuit was confirmed in spontaneous recordings in the live fish. Furthermore, the circuit also predicted long-lasting stimulation that was also corroborated experimentally. Our work shows that fractional order memcapacitors provide intrinsic memory dependence that could allow implementation of computationally efficient neuromorphic devices. Memcapacitors are static elements that consume less energy than the most widely studied memristors, thus allowing the realization of energetically efficient neuromorphic devices. 

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2. PbZrO3-based thin film capacitors with high energy storage efficiency

   https://doi.org/10.1063/5.0237948  

   Son, Yeongwoo; Udovenko, Stanislav; Gaur, Anand_P S; Cui, Jun; Tan, Xiaoli; Trolier-McKinstry, Susan (November 2024, Applied Physics Letters)

   Antiferroelectric (Pb0.87Sr0.05Ba0.05La0.02)(Zr0.52Sn0.40Ti0.08)O3 thin film capacitors were fabricated for dielectric energy storage. Thin films with excellent crystal quality (FWHM 0.021°) were prepared on (100) SrRuO3/SrTiO3 substrates by pulsed laser deposition. The out-of-plane lattice constant of the thin film was 4.110 ± 0.001 Å. An average maximum recoverable energy storage density, 88 ± 17 J cm−3 with an efficiency of 85% ± 6% at 1 kHz and 80 ± 15 J cm−3 with an efficiency of 91% ± 4% at 10 kHz, was achieved at room temperature. The capacitor was fatigue resistant up to 106 cycles at an applied electric field of 2 MV cm−1. These properties are linked to a low level of hysteresis and slow polarization saturation. PbZrO3-derived oxide thin film capacitors are promising for high efficiency and low loss dielectric energy storage applications. 

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3. Liouville partial-differential-equation methods for computing 2D complex multivalued eikonals in attenuating media

   https://doi.org/10.1190/GEO2021-0113.1  

   Leung, Shingyu; Hu, Jiangtao; Qian, Jianliang (March 2022, GEOPHYSICS)

   We have developed a Liouville partial-differential-equation (PDE)-based method for computing complex-valued eikonals in real phase space in the multivalued sense in attenuating media with frequency-independent qualify factors, where the new method computes the real and imaginary parts of the complex-valued eikonal in two steps by solving Liouville equations in real phase space. Because the earth is composed of attenuating materials, seismic waves usually attenuate so that seismic data processing calls for properly treating the resulting energy losses and phase distortions of wave propagation. In the regime of high-frequency asymptotics, the complex-valued eikonal is one essential ingredient for describing wave propagation in attenuating media because this unique quantity summarizes two wave properties into one function: Its real part describes the wave kinematics and its imaginary part captures the effects of phase dispersion and amplitude attenuation. Because some popular ordinary-differential-equation (ODE)-based ray-tracing methods for computing complex-valued eikonals in real space distribute the eikonal function irregularly in real space, we are motivated to develop PDE-based Eulerian methods for computing such complex-valued eikonals in real space on regular meshes. Therefore, we solved novel paraxial Liouville PDEs in real phase space so that we can compute the real and imaginary parts of the complex-valued eikonal in the multivalued sense on regular meshes. We call the resulting method the Liouville PDE method for complex-valued multivalued eikonals in attenuating media; moreover, this new method provides a unified framework for Eulerianizing several popular approximate real-space ray-tracing methods for complex-valued eikonals, such as viscoacoustic ray tracing, real viscoelastic ray tracing, and real elastic ray tracing. In addition, we also provide Liouville PDE formulations for computing multivalued ray amplitudes in a weakly viscoacoustic medium. Numerical examples, including a synthetic gas-cloud model, demonstrate that our methods yield highly accurate complex-valued eikonals in the multivalued sense. 

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4. DG‐GL: Differential geometry‐based geometric learning of molecular datasets

   https://doi.org/10.1002/cnm.3179  

   Nguyen, Duc Duy; Wei, Guo‐Wei (February 2019, International Journal for Numerical Methods in Biomedical Engineering)

   Abstract Motivation:Despite its great success in various physical modeling, differential geometry (DG) has rarely been devised as a versatile tool for analyzing large, diverse, and complex molecular and biomolecular datasets because of the limited understanding of its potential power in dimensionality reduction and its ability to encode essential chemical and biological information in differentiable manifolds. Results:We put forward a differential geometry‐based geometric learning (DG‐GL) hypothesis that the intrinsic physics of three‐dimensional (3D) molecular structures lies on a family of low‐dimensional manifolds embedded in a high‐dimensional data space. We encode crucial chemical, physical, and biological information into 2D element interactive manifolds, extracted from a high‐dimensional structural data space via a multiscale discrete‐to‐continuum mapping using differentiable density estimators. Differential geometry apparatuses are utilized to construct element interactive curvatures in analytical forms for certain analytically differentiable density estimators. These low‐dimensional differential geometry representations are paired with a robust machine learning algorithm to showcase their descriptive and predictive powers for large, diverse, and complex molecular and biomolecular datasets. Extensive numerical experiments are carried out to demonstrate that the proposed DG‐GL strategy outperforms other advanced methods in the predictions of drug discovery‐related protein‐ligand binding affinity, drug toxicity, and molecular solvation free energy. Availability and implementation:http://weilab.math.msu.edu/DG‐GL/ Contact:wei@math.msu.edu 

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5. Measurements of variable capacitance using single port radio frequency reflectometry

   https://doi.org/10.1063/5.0146064  

   Celis-Cordova, Rene; Gose, Jacob J.; Brown, Abigail F.; Behn, AnnahMarie G.; Huebner, Matthew; Williams, Ethan M.; Xiang, Yang; Chisum, Jonathan D.; Orlov, Alexei O.; Snider, Gregory L. (August 2023, Review of Scientific Instruments)

   A radio frequency (RF) reflectometry technique is presented to measure device capacitances using a probe station. This technique is used to characterize micro-electromechanical system (MEMS) variable capacitor devices that can be connected to create pull-up and pull-down networks used in digital gates for reversible computing. Adiabatic reversible computing is a promising approach to energy-efficient computing that can dramatically reduce heat dissipation by switching circuits at speeds below their RC time constants, introducing a trade-off between energy and speed. The variable capacitors in this study will be measured using single port RF reflectometry achieved with a custom-made RF probe. The RF probe consists of a micromanipulator with an on-board matching network and is calibrated by measuring a capacitive bank that shows a clearly visible frequency shift with the increase in capacitance. The RF probe worked well when measuring static capacitors with no parasitic resistance; however, the frequency shift is masked when measuring the MEMS variable capacitors due to their high in-series parasitic resistance (around 80 kΩ). Therefore, RF reflectometry has the potential to measure MEMS variable capacitors in the range of 0–30 fF when not masked by a high in-series parasitic resistance, creating a fast and versatile method for characterizing variable capacitors that can be used in energy-efficient computing. 

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