Smooth Function Research Articles

Dynamics of convolutional recurrent neural networks near their critical point

We examine the dynamical properties of a single-layer convolutional recurrent network with a smooth sigmoidal activation function, for small values of the inputs and when the convolution kernel is unitary, so all eigenvalues lie exactly at the unit circle. Such networks have a variety of hallmark properties: the outputs depend on the inputs via compressive nonlinearities such as cubic roots and both the and the depend sensitively on the inputs as power laws, both diverging as the input →0. The basic dynamical mechanism is that inputs to the network generate ongoing activity, which in turn controls how additional inputs or signals propagate spatially or attenuate in time. We present analytical solutions for the steady states when the network is forced with a single oscillation and when a background value creates a steady state of “ongoing activity” and derive the relationships shaping the value of the temporal decay and spatial propagation length as a function of this background value. Published by the American Physical Society 2024

SMARTboost Learning for Tabular Data

We introduce SMARTboost (boosting of symmetric smooth additive regression trees), an extension of gradient boosting machines with improved accuracy when the underlying function is smooth or the sample small or noisy. In extensive simulations, we find that the combination of smooth symmetric trees and of carefully designed priors gives SMARTboost a large edge (in comparison with XGBoost and BART) on data generated by the most common parametric models in econometrics, and on a variety of other smooth functions. XGBoost outperforms SMARTboost only when the sample is large, and the underlying function is highly discontinuous. SMARTboost’s performance is illustrated in two applications to global equity returns and realized volatility prediction.

The sliding mode controller with composite reaching law for upper limb rehabilitation robot

Purpose Assisted training using upper limb rehabilitation robots is beneficial for flaccid paralysis patients in recovering their functional abilities. In the assisted training mode, the patient’s motor ability is limited by factors such as limb muscle tension, and it is prone for the rehabilitation robot to deviate from the prescribed training trajectory. A sliding mode control method based on a fixed time observer is proposed to address the problem of delayed trajectory tracking response of upper limb rehabilitation robots caused by external disturbances such as patient limbs. Design/methodology/approach First, aiming at the problem of estimating and compensating for external disturbances in the upper limb rehabilitation robot system, a fixed time observer was designed based on the robot’s dynamic model. Second, the composite sliding mode reaching law combining the smooth function and the power-exponential function is proposed to shorten the convergence time of system states in the startup phase, thereby reducing chattering in the control process and realizing the real-time tracking of the training trajectory by the control system. Findings The proposed method provides a solution for the trajectory tracking speed of upper limb rehabilitation robot controllers. In the circular trajectory tracking control, compared to the sliding-mode control method combined with the variable-exponential composite reaching law based on the fixed-time observer, the method in this paper reduces the time for the system state to reach the sliding surface by 0.89 s and improves the response speed by 0.66%. Originality/value The composite sliding mode approach law based on smooth function and power exponent function can reduce the time it takes for the system state to reach and remain on the sliding surface and improve the trajectory tracking speed of upper limb rehabilitation robots. This controller improves the accuracy of trajectory control and ensures the robustness of auxiliary rehabilitation training.

On Convergence of Toeplitz Quantization of the Sphere

In this paper, we give an explicit expression of the Toeplitz quantization of a C∞ smooth function on the sphere and show that the sequence of spectra of Toeplitz quantization of the function determines its decreasing rearrangement. We also use Toeplitz quantization to prove a version of Szegö’s Theorem.

Semiclassical instanton theory for reaction rates at any temperature: How a rigorous real-time derivation solves the crossover temperature problem.

Instanton theory relates the rate constant for tunneling through a barrier to the periodic classical trajectory on the upturned potential energy surface, whose period is τ = ℏ/(kBT). Unfortunately, the standard theory is only applicable below the "crossover temperature," where the periodic orbit first appears. This paper presents a rigorous semiclassical (ℏ → 0) theory for the rate that is valid at any temperature. The theory is derived by combining Bleistein's method for generating uniform asymptotic expansions with a real-time modification of Richardson's flux-correlation function derivation of instanton theory. The resulting theory smoothly connects the instanton result at low temperature to the parabolic correction to Eyring transition state theory at high-temperature. Although the derivation involves real time, the final theory only involves imaginary-time (thermal) properties, consistent with the standard version of instanton theory. Therefore, it is no more difficult to compute than the standard theory. The theory is illustrated with application to model systems, where it is shown to give excellent numerical results. Finally, the first-principles approach taken here results in a number of advantages over previous attempts to extend the imaginary free-energy formulation of instanton theory. In addition to producing a theory that is a smooth (continuously differentiable) function of temperature, the derivation also naturally incorporates hyperasymptotic (i.e., multi-orbit) terms and provides a framework for further extensions of the theory.

Abstract 4134475: Effects of E-cigarette Vaping on Endothelial Function in Diet-Induced Obese Mice

Introduction: Although electronic cigarettes (e-cigs) have been known to increase the risk of vascular complications, little is known about whether e-cig represents an independent risk factor for the development and worsening of obesity and its associated vascular diseases. We hypothesize that a high-fat diet (HFD) enhances e-cig-induced vascular complications. Methods: Male and female eight-week-old C57Bl/6J mice were fed normal chow (NC) or HFD for 15 weeks before being exposed to e-cigs (PG/VG only [PGVG] or PG/VG + 24 mg/ml nicotine [Nic]) or fresh air (FA) for 12 weeks (n=6-8). At the end of the experiments, glucose level and thoracic aortic responses to phenylephrine (PE), acetylcholine (ACh), and sodium nitroprusside (SNP) were assessed via the glucose tolerance test (GTT) and wire myography, respectively. Total RNA from male aortas was extracted and RNA-seq was utilized to identify the transcriptomic changes in our diet-induced obesity mouse model subjected to e-cig vapors (n=4). Results: Compared to NC with FA, HFD alone caused glucose intolerance as shown by the GTT, which was improved only by exposure to nicotine-containing e-cigs (HFD+Nic). Similar improvement in glucose intolerance were found in the NC group with e-cigs (PGVG or Nic). In addition, both NC and HFD-fed male mice exhibited endothelial dysfunction characterized by a decrease in the ACh-dependent (endothelium) relaxation of PE-induced contractions. Importantly, nicotine-containing e-cig exposure (Nic) dramatically reduced the sensitivity of the aorta in the HFD group (HFD+Nic) to both ACh and SNP, while it only affected the sensitivity and maximum relaxation to ACh in the male NC group (NC+Nic). There were no significant differences in the vasoreactivity of female mice exposed to e-cig or HFD. Finally, RNA-seq results suggested that e-cig-treated male mice had altered expression of genes related to endothelial and smooth muscle function and metabolism, particularly fatty acid metabolism, which was also significant with the addition of HFD. Conclusion: Collectively, our results suggest that acute e-cig exposure results in significant vascular dysfunction in male mice, which is worsened in HFD mice. The identification of genes dysregulated in mice exposed to e-cigs provides novel insights into vascular biology and could have a significant impact on our understanding of vascular complications associated with e-cig usage and provide insights into its contributions to obesity and diabetes.

A Squared Smoothing Newton Method for Semidefinite Programming

This paper proposes a squared smoothing Newton method via the Huber smoothing function for solving semidefinite programming problems (SDPs). We first study the fundamental properties of the matrix-valued mapping defined upon the Huber function. Using these results and existing ones in the literature, we then conduct rigorous convergence analysis and establish convergence properties for the proposed algorithm. In particular, we show that the proposed method is well-defined and admits global convergence. Moreover, under suitable regularity conditions, that is, the primal and dual constraint nondegenerate conditions, the proposed method is shown to have a super-linear convergence rate. To evaluate the practical performance of the algorithm, we conduct extensive numerical experiments for solving various classes of SDPs. Comparison with the state-of-the-art SDP solvers demonstrates that our method is also efficient for computing accurate solutions of SDPs. Funding: The research of D. Sun was supported in part by the Hong Kong Research Grants Council under Grant 15307523, and the research of K.-C. Toh was supported by the Ministry of Education, Singapore, under its Academic Research Fund Tier 3 grant call [MOE-2019-T3-1-010].

THEORETICAL BASES OF INVESTMENT ACTIVITY OF TRANSPORT AND LOGISTICS ENTERPRISES

The article discusses the theoretical foundations of investment activity of transport and logistics enterprises, which are key participants in the world economy and play an important role in ensuring the efficiency of supply chains. Investments in this area make it possible to modernize infrastructure, introduce the latest technologies and increase productivity, which in turn affects the growth of markets and economic systems. The article focuses on different definitions of the term "investment" presented by such economists as I. Fisher and J. S. Fisher. M. Keynes, emphasizing the importance of strategic development of enterprises in the context of investment activity. The role of investment in ensuring the smooth functioning of supply chains, including infrastructure development, procurement of new transport, automation and digitalization of management processes, is also considered. The key directions of investment in transport and logistics enterprises are described, including the modernization of the transport fleet, the introduction of information technologies, infrastructure improvement and staff training. It is emphasized that the efficient operation of transport is an important factor for the formation of the country's gross domestic product, the development of international relations and the creation of a favorable economic climate. The article also discusses the problems associated with investment activity in Ukraine in the context of hostilities, as well as the need to develop an effective investment policy that will help attract investment and introduce innovations. Statistical data on the structure of capital investments in the transport sector are provided, which indicates the priority directions of investment activity. Finally, the article emphasizes the importance of introducing innovations and modern information technologies to optimize costs, increase efficiency and competitiveness of transport and logistics enterprises. The authors emphasize the need to create new mechanisms for investment and innovative development that will allow the transport sector to adapt to the challenges of our time and achieve strategic goals in the face of competitive competition.

Group Forward–Backward Orthogonal Matching Pursuit for General Convex Smooth Functions

This paper introduces the Group Forward–Backward Orthogonal Matching Pursuit (Group-FoBa-OMP) algorithm, a novel approach for sparse feature selection. The core innovations of this algorithm include (1) an integrated backward elimination process to correct earlier misidentified groups; (2) a versatile convex smooth model that generalizes previous research; (3) the strategic use of gradient information to expedite the group selection phase; and (4) a theoretical validation of its performance in terms of support set recovery, variable estimation accuracy, and objective function optimization. These advancements are supported by experimental evidence from both synthetic and real-world data, demonstrating the algorithm’s effectiveness.

Observer-based resilient cooperative output regulation for nonlinear multiagent systems with time-varying parameters and DoS attacks

This paper aims to address the cooperative output regulation (COR) problem of nonlinear multiagent systems (MASs) with time-varying parameters under denial-of-service (DoS) attacks. First, to address the challenges of unavailable leader signals and non-differentiability issue caused by the DoS attacks, a class of first-order low-pass filters is employed to develop a novel distributed resilient observer, which accurately estimate the exosystem state with the existence of high-order derivatives. Then, by viewing the output of observer as the reference signal, a distributed resilient controller is designed for each follower to address the reference-tracking problem. By introducing a smooth function with positive integrable time-varying function, novel adaptive laws are developed and incorporated with the controller design to effectively compensate for the unknown time-varying parameters. By utilising Lyapunov stability theory, the asymptotic convergence of output regulation error can be ensured. Finally, simulation results are conducted to verify the validity of the designed method.

Accelerated-gradient-based generalized Levenberg–Marquardt method with oracle complexity bound and local quadratic convergence

AbstractMinimizing the sum of a convex function and a composite function appears in various fields. The generalized Levenberg–Marquardt (LM) method, also known as the prox-linear method, has been developed for such optimization problems. The method iteratively solves strongly convex subproblems with a damping term. This study proposes a new generalized LM method for solving the problem with a smooth composite function. The method enjoys three theoretical guarantees: iteration complexity bound, oracle complexity bound, and local convergence under a Hölderian growth condition. The local convergence results include local quadratic convergence under the quadratic growth condition; this is the first to extend the classical result for least-squares problems to a general smooth composite function. In addition, this is the first LM method with both an oracle complexity bound and local quadratic convergence under standard assumptions. These results are achieved by carefully controlling the damping parameter and solving the subproblems by the accelerated proximal gradient method equipped with a particular termination condition. Experimental results show that the proposed method performs well in practice for several instances, including classification with a neural network and nonnegative matrix factorization.

Diagnosis, prevention and management of delirium: spot it, stop it, treat it

SUMMARY Delirium frequently occurs among hospital in-patients, with significant attributable healthcare costs. It is associated with long-term adverse outcomes, including an eightfold increased risk of subsequent dementia. The purpose of this article is to inform clinicians of the best practices for spotting, stopping and treating delirium and provide guidance on common challenging clinical dilemmas. For spotting delirium, suggested screening tools are the 4 ‘A's Test (in general medical settings) and the Confusion Assessment Method for the Intensive Care Unit (CAM-ICU). Prevention is best achieved with multicomponent interventions and targeted strategies focusing on: (a) avoiding iatrogenic causes; (b) brain optimisation by ensuring smooth bodily functioning; (c) maintaining social interactions and normality. Non-pharmacological approaches are the first line for treatment; they largely mirror prevention strategies, but the focus of empirical evidence is on prevention. Although sufficient evidence is lacking for most pharmacological approaches, an antipsychotic at low doses for short durations may be of utility for highly distressing or high-risk situations, particularly in hyperactive delirium, but only as a last resort.

Unwrapping the Intricate Interplay Between Energy Dependency and Macroeconomic Volatility in OECD Countries

While research has explored the connection between oil prices and macroeconomic performance, there is limited understanding of the interaction between overseas energy imports dependency and macroeconomic fluctuations. This work addresses the foregoing study using the augmented mean group (AMG) econometrics technique on panel data of 29 OECD net energy‐importing countries from 2001 to 2021. The long‐run finding unearthed that energy dependency intensifies macroeconomic instability, confirming that relying on overseas energy imports will hamper the smooth functioning of domestic economic machinery in the form of energy supply interruption. Besides energy dependency, this study uses government consumption spending, regulatory quality, and globalisation as control variables in macroeconomic instability function. The long‐run outcomes further depict that government consumption spending and globalisation aggravate macroeconomic instability while regulatory quality reduces it. These findings are further checked by applying the pooled mean group‐autoregressive distributed lag (PMG‐ARDL) method. In conclusion, this study provides policy implications to prioritise domestically produced energy use and diversify energy sources by increasing the share of clean energy in the total energy mix.

Early vascular aging in chronic kidney disease: focus on microvascular maintenance, senescence signature and potential therapeutics

Chronic kidney disease (CKD) is a strong risk factor for cardiovascular mortality and morbidity. We hypothesized that a senescent phenotype instigated by uremic toxins could account for early vascular aging (EVA) and vascular dysfunctions of microvasculature in end stage kidney disease (ESKD) patients which ultimately lead to increased cardiovascular complication. To test this hypothesis, we utilized both in vivo, and ex vivo approaches to study endothelial and smooth muscle function and structure, and characterized markers related to EVA in 82 ESKD patients (eGFR <15 ml/min) and 70 non-CKD controls. In vivo measurement revealed no major difference in endothelial function between ESKD and control group, aside from higher stiffness detected in the microcirculation of ESKD participants. In contrast, ex vivo measurements revealed a notable change in the contribution of endothelium-derived factors and increased stiffness in ESKD patients vs. controls. In support, we demonstrated that ex vivo exposure of arteries to uremic toxins such as Trimethylamine N-oxide, Phenylacetyl glutamine, or extracellular vesicles from CKD patients impaired endothelial function via diminishing the contribution of endothelium-derived relaxing factors such as nitric oxide and endothelium derived hyperpolarizing factor. Uremic arteries displayed elevated expression of senescence markers (p21CIP1, p16INK4a, and SA-β-gal), calcification marker (RUNX2), and reduced expression of Ki67, sirtuin1, Nrf2, and MHY11 markers, indicating the accumulation of senescent cells and EVA phenotype. Correspondingly, treating uremic vessel rings ex vivo with senolytic agents (Dasatinib + Quercetin) effectively reduced the senescence-associated secretory phenotype and changed the origin of extracellular vesicles. Notably, sex differences exist for certain abnormalities suggesting the importance of biological sex in the pathogenesis of vascular complications. In conclusion, the uremic microvasculature is characterized by a “senescence signature”, which may contribute to EVA and cardiovascular complications in ESKD patients and could be alleviated by treatment with senolytic agents.

Virtual Roaming of Cultural Heritage Based on Image Processing

ABSTRACTWith the digital protection and development of cultural heritage as a focus, an analysis of the trends in cultural heritage digitization reveals the importance of digital technology in this field, as demonstrated by the application of virtual reality (VR) to the protection and development of the Lingjiatan site. The implementation of the Lingjiatan roaming system involves sequential steps, including image acquisition, image splicing, and roaming system production. A user test was conducted to evaluate the usability and user experience of the system. The results show that the system operates normally, with smooth interactive functions that allow users to tour the Lingjiatan site virtually. Users can learn about Lingjiatan's culture from this virtual environment. This study further explores the system's potential for site preservation and development, and its role in the integration of cultural heritage and tourism.

Robust frequency-domain acoustic waveform inversion using a measurement of smooth radical function derived from compressive sensing

Robust frequency-domain acoustic waveform inversion using a measurement of smooth radical function derived from compressive sensing

Shaped pattern synthesis for hybrid analog–digital arrays via manifold optimization-enabled block coordinate descent

Hybrid analog–digital (HAD) architecture is a promising means to realize large-scale arrays owing to the judicious trade-off between system performance and hardware complexity. This paper investigates the beampattern shaping of HAD arrays through minimizing the beampattern matching error between desired and actual patterns. Due to the nonconvex constraints on analog and digital weights and the nonconvex nonsmooth objective function, the resultant codesign is NP-hard. To address this issue, we create an efficient algorithm by leveraging block coordinate descent (BCD) and Riemannian manifold optimization. We first equivalently represent the objective function as a smooth bi-quadratic function by introducing a uni-modulus auxiliary variable. Subsequently, we alternatingly optimize the scaling factor, digital weights, analog weights and auxiliary variable under the BCD framework, where the simultaneous update of analog weights and auxiliary variable is recast as uni-modular constrained quadratic programming which is efficiently solved by Riemannian Newton method, and the digital weights have a global optimal solution via Lagrangian multiplier method. We also derive an explicit convergence condition of this algorithm. Numerical results demonstrate that the proposed algorithm has superior performance and faster convergence speed than alternative algorithms, and produces nearly the same mainlobe gain as fully digital arrays with significantly fewer radio-frequency chains.

Determination of trace analytes in nuclear grade Calcium Metal Samples by Axially Viewed Inductively Coupled Plasma – Atomic Emission Spectrometric technique

An Inductively Coupled Plasma – Atomic Emission Spectrometric (ICP-AES) method has been developed for the direct determination of 19 analytes namely, Al, B, Be, Cd, Co, Cr, Cu, Fe, Li, Mg, Mo, Mn, Ni, Pb, Pd, Si, Ta, V and W at trace concentration levels in calcium matrix. In nuclear industry, quality control and assurance of nuclear fuels and associated materials for trace metallic impurity contents form an integral part of the system for the smooth functioning of the reactor for the stipulated time span. In this context, it was required to determine trace analytes in nuclear grade Calcium which is used as a reducing agent for the production of U, Th, Pu, etc. in nuclear industry. Using axial ICP-AES, initially calibration curve for Ca with 396.847nm analytical line was obtained. Systematic studies were carried out to identify various analytical wavelengths of the analyte elements which are almost free from Ca, being the main matrix and calibration curves were obtained. For all analytes and Ca, detection limits and sensitivity values were calculated. To validate the method, three synthetic samples with analyte contents in the range of 0.1 - 5 g/mL and Ca at 1 mg/mL were analyzed, the % recovery being in the range of 80-120% with precision better than 5% RSD. The method was found to be useful for the direct determination of the elements of interest in calcium matrix and was applied for the analysis of two nuclear grade real life calcium metal samples.

On delivering polar solvation free energy of proteins from energy minimized structures using a regularized super-Gaussian Poisson-Boltzmann model.

The biomolecules interact with their partners in an aqueous media; thus, their solvation energy is an important thermodynamics quantity. In previous works (J. Chem. Theory Comput. 14(2): 1020-1032), we demonstrated that the Poisson-Boltzmann (PB) approach reproduces solvation energy calculated via thermodynamic integration (TI) protocol if the structures of proteins are kept rigid. However, proteins are not rigid bodies and computing their solvation energy must account for their flexibility. Typically, in the framework of PB calculations, this is done by collecting snapshots from molecular dynamics (MD) simulations, computing their solvation energies, and averaging to obtain the ensemble-averaged solvation energy, which is computationally demanding. To reduce the computational cost, we have proposed Gaussian/super-Gaussian-based methods for the dielectric function that use the atomic packing to deliver smooth dielectric function for the entire computational space, the protein and water phase, which allows the ensemble-averaged solvation energy to be computed from a single structure. One of the technical difficulties associated with the smooth dielectric function presentation with respect to polar solvation energy is the absence of a dielectric border between the protein and water where induced charges should be positioned. This motivated the present work, where we report a super-Gaussian regularized Poisson-Boltzmann method and use it for computing the polar solvation energy from single energy minimized structures and assess its ability to reproduce the ensemble-averaged polar solvation on a dataset of 74 high-resolution monomeric proteins.

Branched-chain α-ketoacids aerobically activate HIF1α signalling in vascular cells.

Hypoxia-inducible factor 1α (HIF1α) is a master regulator of biological processes in hypoxia. Yet, the mechanisms and biological consequences of aerobic HIF1α activation by intrinsic factors, particularly in normal (primary) cells, remain elusive. Here we show that HIF1α signalling is activated in several human primary vascular cells in normoxia and in vascular smooth muscle cells of normal human lungs. Mechanistically, aerobic HIF1α activation is mediated by paracrine secretion of three branched-chain α-ketoacids (BCKAs), which suppress PHD2 activity via direct inhibition and via LDHA-mediated generation of L-2-hydroxyglutarate. BCKA-mediated HIF1α signalling activation stimulated glycolytic activity and governed a phenotypic switch of pulmonary artery smooth muscle cells, which correlated with BCKA metabolic dysregulation and pathophenotypic changes in pulmonary arterial hypertension patients and male rat models. We thus identify BCKAs as previously unrecognized signalling metabolites that aerobically activate HIF1α and that the BCKA-HIF1α pathway modulates vascular smooth muscle cell function, an effect that may be relevant to pulmonary vascular pathobiology.