Differential Version Research Articles

A strong Differentiable Absorption of Hilbert 𝑪∗-Modules with Connections, and Lifts of Unbounded Operators

The Kasparov absorption (or stabilization) theorem states that any countably generated Hilbert 𝐶∗-module is isomorphic to a direct summand in the standard module of square summable sequences in the base 𝐶∗-algebra. This result be generalized byJens Kaad [Jka10] by incorporating a densely defined derivation on the base 𝐶∗-algebra. It following the perfect densely method of Jens Kaad[Jka10] leads to a differentiable version of the Kasparov absorption theorem. The extra compatibility assumptions needed are minimal: It will only be required that there exists a sequence of generators with mutual inner products in the domain of the derivation. The differentiable absorption theorem is then applied to construct densely defined connections (or correspondences) on Hilbert 𝐶∗-modules. These connections can in turn be used to define selfadjoint and regular ”lifts” of unbounded operators which act on an auxiliary Hilbert 𝐶∗- module.

THE METHOD OF QUANTITATIVE DETERMINATION OF THE AMOUNT OF FLAVONOIDS IN THE FLOWERS OF GIANT CEPHALARIA

Giant cephalaria (Cephalaria gigantea (LEDEB.) BOBROV) is a powerful perennial whose height reaches two meters. This plant is found in Southern Europe, Western and Central Asia, as well as in North and South Africa. It is cultivated in the Botanical garden of Samara University. The extracts of giant cephalaria have been used in traditional medicine for many years due to their antimicrobial, antifungal, cytotoxic, antioxidant, antidiabetic and antipyretic activities, which may be due to various biologically active compounds. It is known that the leaves contain triterpenoids, phenolic carboxylic acids and their derivatives, flavonoids, and the flowers contain flavonoid compounds: luteolin, quercetin, cynaroside, quercimeritrin and gigantoside A. The article describes the development of a technique for quantifying of the amount of flavonoids in the flowers of giant cephalaria. Spectrophotometric analysis of water-alcohol extracts from giant cephalaria flowers allowed us to establish that the main contribution to the absorption curve of their UV-spectra in the presence of AlCl3 is made by flavonols having a free OH group at the C-3 position, and in the differential version, the maximum absorption of the tested solution is close to that of the standard sample of quercetin (428±2 nm). Optimal conditions for the extraction of flavonoids in giant cephalaria flowers were determined: extractant 70% ethyl alcohol; the ratio "raw material-extractant" – 1 : 50; extraction time – extraction in a boiling water bath for 60 minutes, the degree of grinding of raw materials – 2 mm, analytical wavelength – 426 nm. It was determined that the content of the total flavonoids calculated on quercetin in the flowers of giant cephalaria varies from 1.58±0.05% to 2.63±0.05%. The error of a single determination with a 95% confidence probability is ±1.75%. The obtained results were used in the development of the FS project for a new type of medicinal plant raw materials "Cephalaria giant flowers" for introduction into the State Pharmacopoeia of the Russian Federation.

WGDPool: A broad scope extraction for weighted graph data

Graph pooling is a commonly used operation in graph neural networks to reduce the size of graph representation. To extract key information, pooling and representation need to be coupled. We propose a graph pooling method for weighted graphs called WGDPool (Weighted Graph Dual Pooling). Unlike traditional graph representation learning methods, the weight information of edges is also fed into convolutional graph neural networks (ConvGNN) to obtain graph representations. Dual branch convolutional graph neural networks is designed to learn the nodes’ and edges’ embeddings independently, and they are fused into a comprehensive representation of graph data. Pooling, as a tool of feature extraction and scale reduction of graph representation, adopts a differentiable version of k-means clustering and a multi-item parameterized loss function. Cut loss, orthogonality loss, clustering loss, and reconstruction loss are simultaneously considered. By parameterization, WGDPool is competent for diverse graph tasks. WGDPool outperformed other graph pooling methods in such common supervised and unsupervised tasks as biological or chemical classification, bibliography clustering and integrated circuit partition, demonstrating the effectiveness of our proposed pooling method.

Differentiable phylogenetics via hyperbolic embeddings with Dodonaphy.

Navigating the high dimensional space of discrete trees for phylogenetics presents a challenging problem for tree optimization. To address this, hyperbolic embeddings of trees offer a promising approach to encoding trees efficiently in continuous spaces. However, they require a differentiable tree decoder to optimize the phylogenetic likelihood. We present soft-NJ, a differentiable version of neighbour joining that enables gradient-based optimization over the space of trees. We illustrate the potential for differentiable optimization over tree space for maximum likelihood inference. We then perform variational Bayesian phylogenetics by optimizing embedding distributions in hyperbolic space. We compare the performance of this approximation technique on eight benchmark datasets to state-of-the-art methods. Results indicate that, while this technique is not immune from local optima, it opens a plethora of powerful and parametrically efficient approach to phylogenetics via tree embeddings. Dodonaphy is freely available on the web at https://www.github.com/mattapow/dodonaphy. It includes an implementation of soft-NJ.

Interplay between wall slip and shear banding in a thixotropic yield stress fluid.

We study the local dynamics of a thixotropic yield stress fluid that shows a pronounced non-monotonic flow curve. This mechanically unstable behavior is generally not observable from standard rheometry tests, resulting in a stress plateau that stems from the coexistence of a flowing band with an unyielded region below a critical shear rate c. Combining ultrasound velocimetry with standard rheometry, we discover an original shear-banding scenario in the decreasing branch of the flow curve of model paraffin gels, in which the velocity profile of the flowing band is set by the applied shear rate  instead of c. As a consequence, the material slips at the walls with a velocity that shows a non-trivial dependence on the applied shear rate. To capture our observations, we propose a differential version of the so-called lever rule, describing the extent of the flowing band and the evolution of wall slip with shear rate. This phenomenological model holds down to very low shear rates, at which the dimension of the flowing band becomes comparable to the size of the individual wax particles that constitute the gel microstructure, leading to cooperative effects. Our approach provides a framework where constraints imposed in the classical shear-banding scenario can be relaxed, with wall slip acting as an additional degree of freedom.

DETERMINISTIC AND STOCHASTIC ANALYSIS OF A SIZE-DEPENDENT PHYTOPLANKTON–ZOOPLANKTON MODEL WITH ADDITIVE ALLEE EFFECT

In this paper, a deterministic size-dependent phytoplankton–zooplankton (PZ) model with additive Allee effect as well as its stochastic differential equation version is formulated to explore the growth dynamic of phytoplankton. A stability and Hopf bifurcation analysis is performed towards deterministic PZ model, and stochastic dynamic analysis is carried out on the stochastic PZ model, including the stochastic extinction, persistence in mean and the unique ergodic stationary distribution, which in turn provides a theoretical basis for numerical simulation analysis. Numerical simulations reveal that the synergistic effect of plankton body size and Allee effect can have a complex impact on the growth of phytoplankton in the deterministic and stochastic environments. One of the most interesting findings suggests that the reduced phytoplankton cell size can trigger bistable phenomenon, while the increased phytoplankton cell size or the weakened Allee effect has the ability to destroy such bistable phenomenon.

Physics-to-Geometry Transformation to Construct Identities between Reynolds Stresses

Modeling has become firmly established as a methodology to close the Reynolds-averaged Navier–Stokes (RANS) equations, owing to theoretical and empirical efforts towards a complete formulation of the Reynolds stress tensor and, recently, breakthroughs in data-processing technology. However, mathematical exactness is not generally ensured by modeling, which is an intrinsic reason why the reliability of RANS closure models is not supposed to be consistent for all kinds of turbulent flow. Rather than straightforwardly overcoming this inherent limitation, most of the studies to date were reasonably directed towards broadening the range of turbulent flows, where reliable prediction accuracy can be obtained via modeling. In this paper, we present three identities between components of the Reynolds stress tensor, constructed via spatial mapping on the basis of the differential version of the Gauss–Bonnet formula. Further, we present a constraint condition that gives a set of equations as numerous as the parameters within a RANS model.

Dynamical Analysis of a Local Lengley-Epstein System Coupled with Fractional Delayed Differential Equations

We consider a system of fractional delayed differential equations. The ordinary differential version of the system without delay is introduced in the Lengyel-Epstein reaction-diffusion system. We evaluate the system with and without delay and explore the stability of the unique positive equilibrium. We also prove the existence of Hopf bifurcation for both cases. Furthermore, the impacts of Caputo fractional order parameter and time delay parameter on the dynamics of the system are investigated with numerical simulations. It is also concluded that for different values of time delay parameter, the decreament of the Caputo fractional order parameter has opposite effects on the system in terms of stability.

A differentiable, physics-informed ecosystem modeling and learning framework for large-scale inverse problems: demonstration with photosynthesis simulations

Abstract. Photosynthesis plays an important role in carbon, nitrogen, and water cycles. Ecosystem models for photosynthesis are characterized by many parameters that are obtained from limited in situ measurements and applied to the same plant types. Previous site-by-site calibration approaches could not leverage big data and faced issues like overfitting or parameter non-uniqueness. Here we developed an end-to-end programmatically differentiable (meaning gradients of outputs to variables used in the model can be obtained efficiently and accurately) version of the photosynthesis process representation within the Functionally Assembled Terrestrial Ecosystem Simulator (FATES) model. As a genre of physics-informed machine learning (ML), differentiable models couple physics-based formulations to neural networks (NNs) that learn parameterizations (and potentially processes) from observations, here photosynthesis rates. We first demonstrated that the framework was able to correctly recover multiple assumed parameter values concurrently using synthetic training data. Then, using a real-world dataset consisting of many different plant functional types (PFTs), we learned parameters that performed substantially better and greatly reduced biases compared to literature values. Further, the framework allowed us to gain insights at a large scale. Our results showed that the carboxylation rate at 25 ∘C (Vc,max25) was more impactful than a factor representing water limitation, although tuning both was helpful in addressing biases with the default values. This framework could potentially enable substantial improvement in our capability to learn parameters and reduce biases for ecosystem modeling at large scales.

Development of an anatomical breast phantom from polyvinyl chloride plastisol with lesions of various shape, elasticity and echogenicity for teaching ultrasound examination.

The WHO reported an increasing trend in the number of new cases of breast cancer, making it the most prevalent cancer in the world. This fact necessitates the availability of highly qualified ultrasonographers, which can be achieved by the widespread implementation of training phantoms. The goal of the present work is to develop and test an inexpensive, accessible, and reproducible technology for creating an anatomical breast phantom for practicing ultrasound diagnostic skills in grayscale and elastography imaging, as well as ultrasound-guided biopsy sampling. We used FDM 3D printer and PLA plastic for printing an anatomical breast mold. We made a phantom using a mixture of polyvinyl chloride plastisol, graphite powder, and metallic glitter to simulate soft tissues and lesions. Various degrees of elasticity were imparted using plastisols of stiffness ranging from 3 to 17 on the Shore scale. The lesions were shaped by hand. The materials and methods used are easily accessible and reproducible. Using the proposed technology, we have developed and tested a basic, differential, and elastographic versions of the breast phantom. The three versions of the phantom are anatomical and intended for use in medical education: the basic version is for practicing primary hand-eye coordination skills; the differential one is for practicing the differential diagnosis skills; the elastographic version helps developing the skills needed for assessing the stiffness of tissues. The proposed technology allows the creation of breast phantoms for practicing hand-eye coordination and develop the critical skills for navigation and assessment of the shape, margins, and size of the lesion, as well as performing an ultrasound-guided biopsy. It is cost-effective, reproducible, and easily implementable, and could be instrumental in generating ultrasonographers with crucial skills for accurate diagnosis of breast cancer, especially in low-resource settings.

QUANTITATIVE DETERMINATION OF THE SUM OF FLAVONOIDS OF THE ABOVEGROUND PART OF SCUTELLARIA COMOSA

As a result of pharmacological studies, it was revealed that the sum of flavonoids from the aboveground part of the plant Scutellaria comosa (Lamiaceae family) has adaptogenic and antihypoxic effects. For the introduction into medical practice of a drug based on the sum of flavonoids, studies have been conducted on the standardization of raw materials – the aboveground part of the crested helmet. The analysis of plant raw materials by TLC and HPLC methods showed that the dominant flavonoid of the aboveground part of the crested skullcap is isoscutellarein 7-O-β-D-glucopyranoside.
 A differential spectrophotometric technique has been developed for the quantitative determination of the sum of flavonoids of the aboveground part of the crested helmet in terms of isoscutellarein 7-O-β-D-glucopyranoside. The optimal parameters for the extraction of vegetable raw materials are: extraction with 70% ethyl alcohol in a boiling water bath for 60 minutes in the ratio "raw material – extractant" – 1 : 100, the degree of grinding of raw materials – 2 mm. It was found that with the differential version of spectrophotometric analysis, the flavonoids – AlCl3 system reaches equilibrium after 40 minutes. The maximum of the differential absorption spectrum of the alcohol extraction of Scutellaria comosa is observed at 346 nm and can be used to analyze this group of compounds.
 The content of the sum of flavonoids in the aboveground part of the crested helmet varies from 9.72% to 10.27%. In order to establish the optimal harvesting time of plant raw materials, the content of the sum of flavonoids was determined by the vegetation periods of the plant in terms of isoscutellarein 7-O-β-D-glucopyranoside and it was determined that the maximum accumulation of the sum of flavonoids is observed during the flowering period (10.13% of the weight of air-dry raw materials).

Single-Ended and Differentially Operated Microwave Microfluidic Sensors for Biomedical Applications.

This research is focused on the design of highly sensitive microfluidic sensors for the applications in liquid dielectric characterizations including biomedical samples. Considering the narrow-band operation of microfluidic sensors based on microwave resonators, in this study, microfluidic sensors based on the variation of transmission phase in microwave transmission lines (TLs) are proposed. It is shown that among different microwave TLs, slot-lines are an appropriate type of TL for sensing applications because a major portion of the electromagnetic (EM) field passes above the line, where a microfluidic channel can be easily devised. The proposed concept is presented and the functionality of the proposed sensor is validated through full-wave EM simulations. Moreover, the effects of the dimensions of the microfluidic channel and the thickness of the substrate on the sensitivity of the sensor are studied. Furthermore, taking the advantages of differential circuits and systems into account, a differential version of the microfluidic sensor is also presented. It is shown that the sensitivity of the sensor can be adjusted according to the application. Specifically speaking, the sensitivity of the proposed microfluidic sensor is almost linearly proportional to the length of the channel, i.e., the sensitivity can be doubled by doubling the channel length. In this research, it is shown that using slot-line TLs highly sensitive microfluidic sensors can be designed for the applications in liquid dielectric characterizations, especially for biomedical samples where small variations of permittivity have to be detected.

Direction of Arrival Estimation of Sound Sources Using Icosahedral CNNs

In this paper, we present a new model for Direction of Arrival (DOA) estimation of sound sources based on an Icosahedral Convolutional Neural Network (CNN) applied over SRP-PHAT power maps computed from the signals received by a microphone array. This icosahedral CNN is equivariant to the 60 rotational symmetries of the icosahedron, which represent a good approximation of the continuous space of spherical rotations, and can be implemented using standard 2D convolutional layers, having a lower computational cost than most of the spherical CNNs. In addition, instead of using fully connected layers after the icosahedral convolutions, we propose a new soft-argmax function that can be seen as a differentiable version of the argmax function and allows us to solve the DOA estimation as a regression problem interpreting the output of the convolutional layers as a probability distribution. We prove that using models that fit the equivariances of the problem allows us to outperform other state-of-the-art models with a lower computational cost and more robustness, obtaining root mean square localization errors lower than 10{\deg} even in scenarios with a reverberation time $T_{60}$ of 1.5 s.

End-to-end learning of multiple sequence alignments with differentiable Smith-Waterman.

Multiple sequence alignments (MSAs) of homologous sequences contain information on structural and functional constraints and their evolutionary histories. Despite their importance for many downstream tasks, such as structure prediction, MSA generation is often treated as a separate pre-processing step, without any guidance from the application it will be used for. Here, we implement a smooth and differentiable version of the Smith-Waterman pairwise alignment algorithm that enables jointly learning an MSA and a downstream machine learning system in an end-to-end fashion. To demonstrate its utility, we introduce SMURF (Smooth Markov Unaligned Random Field), a new method that jointly learns an alignment and the parameters of a Markov Random Field for unsupervised contact prediction. We find that SMURF learns MSAs that mildly improve contact prediction on a diverse set of protein and RNA families. As a proof of concept, we demonstrate that by connecting our differentiable alignment module to AlphaFold2 and maximizing predicted confidence, we can learn MSAs that improve structure predictions over the initial MSAs. Interestingly, the alignments that improve AlphaFold predictions are self-inconsistent and can be viewed as adversarial. This work highlights the potential of differentiable dynamic programming to improve neural network pipelines that rely on an alignment and the potential dangers of optimizing predictions of protein sequences with methods that are not fully understood. Our code and examples are available at: https://github.com/spetti/SMURF. Supplementary data are available at Bioinformatics online.

Displacement Sensors Based on the Phase of the Reflection Coefficient of a Split Ring Resonator-Loaded Transmission Line

In this article, novel displacement sensors using a microstrip loaded with a pair of split ring resonators (SRRs) are proposed. It is shown that the phase of the reflection coefficient from the loading SRRs can be used for displacement sensing. The article also proposes a differential version of the sensor that benefits from a higher sensitivity and reference zero, which is useful for alignment purposes. It is further shown that the concept of interferometry can be used to convert the output variable of the sensor from changes in the phase to variations in the amplitude of the reflected wave, which can be easily measured. To this end, the proposed single-ended or differential sensors are used along with a branch-line coupler. The proposed sensing mechanism is validated through electromagnetic (EM) simulation of the structures. The concept is further validated through the fabrication and measurement of a prototype.

Joint optimization of linear and nonlinear models for sequential regression

We investigate nonlinear regression and introduce a novel approach based on the joint optimization of linear and nonlinear models. In order to capture both the nonlinear and linear characteristics in sequential data, we model the underlying data as a combination of linear and nonlinear models, where we optimize the models jointly to minimize the final regression error. As the nonlinear model, we employ a differentiable version of the boosted decision trees. As the linear model, we use the well-known SARIMAX model. Our approach is generic so that any differentiable nonlinear or linear model can be readily employed provided that they are differentiable. By this joint optimization, we alleviate the well-known underfitting and overfitting problems in modeling sequential data. Through our experiments on synthetic and real-life data, we demonstrate significant improvements over individual components as well as the combination/mixture methods in the literature.

Capillary constant and surface tension of hydrogen and helium solutions in n-butane (R600)

The results of measuring the capillary constant of n-butane + hydrogen and n-butane + helium solutions are presented. The measurements were carried out by a differential version of the capillary rise method in the temperature range of 138–408 K at pressures from the saturation vapor pressure of a pure solvent to 4 MPa. The uncertainty of the calculated values is uc(a2)=0.019 mm2 (n-butane + helium solution) and uc(a2)=0.015 mm2, uc(γ)=0.034 mN/m (n-butane + hydrogen solution).The surface tension of the n-butane + hydrogen solution was determined. Equations are proposed that describe the concentration and pressure dependences of the capillary constant and surface tension. A qualitatively different effect of small additions of hydrogen and helium on the surface tension of n-butane has been established.

SEMG-Based Minimally Supervised Regression Using Soft-DTW Neural Networks for Robot Hand Grasping Control

One of the major challenges in robotics consists in developing successful control strategies for robotic grasping devices. In this scenario, one of the most interesting approaches regards the exploitation of surface electromyography(sEMG). In this work, we propose a novel sEMG-based <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">minimally supervised</i> regression approach capable of performing nonlinear fitting without the necessity for point-by-point training data labelling. The proposed method exploits a differentiable version of the Dynamic Time Warping (DTW) similarity – referred to as soft-DTW divergence – as loss function for a flexible neural network architecture. This is a different paradigm with respect to state-of-the-art approaches in which sEMG-based control of robot hands is mainly realized using supervised or unsupervised machine learning based regression. An experimental session was carried out involving 10 healthy subjects in an offline experiment for systematic and statistical evaluations, and an online experiment for the evaluation of the control of a robot hand. The reported results demonstrate that the proposed soft-DTW neural network can be trained by means of a labelling that does not require to be temporally aligned with the sEMG training dataset, while reporting performances comparable with a standard mean square error(MSE)-based neural network. Also, the subjects were able to successfully control a robot hand for grasping motions and tasks with error levels comparable to state-of-the-art regression approaches.

Intricate relations among particle collision, relative motion and clustering in turbulent clouds: computational observation and theory

Abstract. Considering turbulent clouds containing small inertial particles, we investigate the effect of particle collision, in particular collision–coagulation, on particle clustering and particle relative motion. We perform direct numerical simulation (DNS) of coagulating particles in isotropic turbulent flow in the regime of small Stokes number (St=0.001–0.54) and find that, due to collision–coagulation, the radial distribution functions (RDFs) fall off dramatically at scales r∼d (where d is the particle diameter) to small but finite values, while the mean radial component of the particle relative velocity (MRV) increases sharply in magnitude. Based on a previously proposed Fokker–Planck (drift-diffusion) framework, we derive a theoretical account of the relationship among particle collision–coagulation rate, RDF and MRV. The theory includes contributions from turbulent fluctuations absent in earlier mean-field theories. We show numerically that the theory accurately accounts for the DNS results (i.e., given an accurate RDF, the theory could produce an accurate MRV). Separately, we also propose a phenomenological model that could directly predict MRV and find that it is accurate when calibrated using fourth moments of the fluid velocities. We use the model to derive a general solution of RDF. We uncover a paradox: the past empirical success of the differential version of the theory is theoretically unjustified. We see a further shape-preserving reduction of the RDF (and MRV) when the gravitational settling parameter (Sg) is of order O(1). Our results demonstrate strong coupling between RDF and MRV and imply that earlier isolated studies on either RDF or MRV have limited relevance for predicting particle collision rate.

Indirect adaptive control of nonlinearly parameterized nonlinear dissipative systems

AbstractIn this note we address the problem of indirect adaptive (regulation or tracking) control of nonlinear, input affine dissipative systems. It is assumed that the supply rate, the storage and the internal dissipation functions may be expressed as nonlinearly parameterized regression equations where the mappings (depending on the unknown parameters) satisfy a monotonicity condition—this encompasses a large class of physical systems, including passive systems. We propose to estimate the system parameters using the “power‐balance” equation, which is the differential version of the classical dissipation inequality, with a new estimator that ensures global, exponential, parameter convergence under the very weak assumption of interval excitation of the power‐balance equation regressor. To design the indirect adaptive controller we make the standard assumption of existence of an asymptotically stabilizing controller that depends—possibly nonlinearly—on the unknown plant parameters, and apply a certainty‐equivalent control law. The benefits of the proposed approach, with respect to other existing solutions, are illustrated with examples.