Nonmonotonic Function Research Articles

Long-duration Gamma-Ray Burst Progenitors and Magnetar Formation

Millisecond magnetars produced in the center of dying massive stars are one prominent model to power gamma-ray bursts (GRBs). However, their detailed nature remains a mystery. To explore the effects of the initial mass, rotation rate, wind mass loss, and metallicity on the GRB progenitors and the newborn magnetar properties, we evolve 227 of 10–30 M ⊙ single star models from the pre-main sequence to core collapse by using the stellar evolution code MESA. The presupernova properties, the compactness parameter, and the magnetar characteristics of models with different initial parameters are presented. The compactness parameter remains a nonmonotonic function of the initial mass and initial rotation rate when the effects of varying metallicity and the “Dutch” wind scale factor are taken into account. We find that the initial rotation rate and mass play the dominant roles in whether a star can evolve into a GRB progenitor. The minimum rotation rate necessary to generate a magnetar gradually reduces as the initial mass increases. The greater the initial metallicity and “Dutch” wind scale factor, the larger the minimum rotation rate required to produce a magnetar. In other words, massive stars with low metallicity are more likely to harbor magnetars. Furthermore, we present the estimated period, magnetic field strength, and masses of magnetars in all cases. The typical rotational energy of these millisecond magnetars is sufficient to power long-duration GRBs.

Inference and optimal censoring scheme for a competing-risks model with type-II progressive censoring

ABSTRACT For statistical inference of competing risks under type-II progressive censoring, lifetimes are modeled by an inverted exponential Rayleigh distribution, which allows the use of a non-monotonic hazard function. Maximum-likelihood estimators for all parameters exist and are unique. The Newton-Raphson algorithm and maximum stochastic expectation each provide estimates. Confidence intervals result from the Fisher matrix and the asymptotic normality of maximum-likelihood estimators. For small samples, the Bootstrap estimators of the parameters do not need to be asymptotically normal. In addition, the Monte Carlo method with the Metropolis-Hastings algorithm and importance sampling allow for Bayesian estimation, with the associated highest posterior-density intervals. The Bayesian method takes account of prior information, contrary to the frequentist method. The Bootstrap method improves the precision of the estimation, especially in the case of small sample sizes. The estimated range obtained by Bootstrap is between 20% and 60% smaller than that obtained by maximum likelihood. Frequentist and Bayesian estimations using the inverted exponentiated Rayleigh distribution under type-II progressive censoring allow for fitting empirical mouse mortality data and obtaining parameter estimates of this distribution. A quantile-dependent criterion and a quantile-independent criterion are used to determine the optimal censoring and to design the experiment.

Stress Strength Reliability in Multicomponent Model for Rayleigh-Exponential (Log Logistic) Distribution

In this article, the Rayleigh-Exponential {Log Logistic} distribution has been proposed using T-X{Y} framework based on quantile function. Some reliability measures has been obtained. The proposed model is flexible as it exhibits monotone and non-monotone failure rate functions, which are quiet common in survival analysis. Also stress strength reliability for single and multicomponent system has been derived. The bias, mean square error and average confidence interval of R based on Maximum likelihood method has been obtained and its performance is studied through MonteCarlo simulation technique. Further the usefulness of proposed model is demonstrated by comparing the results with the some already known distribution.

Magnetocaloric effect and magnetic phase diagram of EuRhAl4Si2

We report magnetocaloric effect (MCE) landscape and rich magnetic phase diagram of the quaternary compound EuRhAl4Si2 for magnetic field applied along the long axis (H || [001]) of the tetragonal unit cell. The MCE turns out to be a non-monotonic function of magnetic fields and temperatures containing regions of normal as well as inverse MCE. Our high-resolution magnetization data reveal the appearance of first order minor magnetization jumps with emergent phase separation below 5.5 K, within the magnetization plateau state. The magnetic phase diagram of EuRhAl4Si2 provides a fertile ground for statistical models.

Uncovering enzymatic structural adaptations from energy dissipation

Abstract While genetic mutations, natural selection and environmental pressures are well-known drivers of enzyme evolution, we show that their structural adaptations are significantly influenced by energy dissipation. Enzymes use chemical energy to do work, which results in a loss of free energy due to the irreversible nature of the process. By assuming that the catalytic process occurs along a potential barrier, we describe the kinetics of the conversion of enzyme-substrate complexes to enzyme-product complexes and calculate the energy dissipation. We show that the behaviour of the dissipated energy is a non-monotonic function of the energy of the intermediate state. This finding supports our main result that enzyme configurations evolve to minimise energy dissipation and simultaneously improve kinetic and thermodynamic efficiencies. Our study provides a novel insight into the complex process of enzyme evolution and highlights the crucial role of energy dissipation in shaping structural adaptations.

Differentially Private Learning with Per-Sample Adaptive Clipping

Privacy in AI remains a topic that draws attention from researchers and the general public in recent years. As one way to implement privacy-preserving AI, differentially private learning is a framework that enables AI models to use differential privacy (DP). To achieve DP in the learning process, existing algorithms typically limit the magnitude of gradients with a constant clipping, which requires carefully tuned due to its significant impact on model performance. As a solution to this issue, latest works NSGD and Auto-S innovatively propose to use normalization instead of clipping to avoid hyperparameter tuning. However, normalization-based approaches like NSGD and Auto-S rely on a monotonic weight function, which imposes excessive weight on small gradient samples and introduces extra deviation to the update. In this paper, we propose a Differentially Private Per-Sample Adaptive Clipping (DP-PSAC) algorithm based on a non-monotonic adaptive weight function, which guarantees privacy without the typical hyperparameter tuning process of using a constant clipping while significantly reducing the deviation between the update and true batch-averaged gradient. We provide a rigorous theoretical convergence analysis and show that with convergence rate at the same order, the proposed algorithm achieves a lower non-vanishing bound, which is maintained over training iterations, compared with NSGD/Auto-S. In addition, through extensive experimental evaluation, we show that DP-PSAC outperforms or matches the state-of-the-art methods on multiple main-stream vision and language tasks.

A circulant inertia three Hopfield neuron system: dynamics, offset boosting, multistability and simple microcontroller- based practical implementation

This work investigates the dynamics and implementation of a circulant inertia three Hopefield neuron model with each neuron activated by a non-monotonic Crespi function. Owing its source to the work previously done by Song and co-authors [Song et al (2019) Mathematical Biosciences and Engineering 16. 6406–6426], we propose a network made up of three neurons connected cyclically. We demonstrate that the model is capable of the coexistence of two, three, four, six, seven, eight and ten attractors basing on different initial states. The system is dissipative and presents fifteen unstable equilibrium points for a given rank of parameters. Accordingly, we demonstrate the Hopf bifurcation in the model when the bifurcation parameter is the first synaptic weight. Moreover, using bifurcation diagrams, Maximum Lyapunov Exponent diagram, phase portraits, two parameters Lyapunov diagrams, double-sided Poincaré section and basin of attraction, intriguing phenomena have been revealed such as hysteresis, coexistence of parallel branches of bifurcation, antimonotonicity and transient chaos to name a few. A number of coexisting attractors have been developed by the new network which can be used to build sophisticated cryptosystem or to explain the possible tasks of a brain in normal or abnormal cases. To verify the feasibility of the model, a microcontroller-based implementation has been used to demonstrate the period-doubling route to chaos obtained numerically.

Unifying performance specifications in tracking control of MIMO nonlinear systems with actuation faults

Guaranteeing prescribed performance is critical to maintaining system efficiency and reliability. The state-of-the-art approaches achieve different performance specifications with different control structures and settings. In this paper, we propose a novel control methodology to uniformly address the prescribed performance problem for uncertain multiple-input multiple-output (MIMO) nonlinear systems in the presence of actuator faults. By constructing a non-monotonic function transformation and an asymmetric barrier function, we recast the underlying problem into one that only needs for simple selection of certain design parameters. With such a treatment, different performance behaviors can be achieved under a single (unified) control framework without the requirement for alternating the control structure, making the design more user-friendly and implementation less demanding. Furthermore, by embedding the available information on the state-dependent diagonal matrix into the filtered-error-like design procedure, the obstacle of ensuring the controllability of the closed-loop system, caused by the actuator faults and performance behaviors, is circumvented. Both theoretical analysis and numerical simulation demonstrate the effectiveness and benefits of the proposed method.

Theory of chromatin organization maintained by active loop extrusion

The active loop extrusion hypothesis proposes that chromatin threads through the cohesin protein complex into progressively larger loops until reaching specific boundary elements. We build upon this hypothesis and develop an analytical theory for active loop extrusion which predicts that loop formation probability is a nonmonotonic function of loop length and describes chromatin contact probabilities. We validate our model with Monte Carlo and hybrid Molecular Dynamics-Monte Carlo simulations and demonstrate that our theory recapitulates experimental chromatin conformation capture data. Our results support active loop extrusion as a mechanism for chromatin organization and provide an analytical description of chromatin organization that may be used to specifically modify chromatin contact probabilities.

Corona Phase Molecular Recognition of the Interleukin-6 (IL-6) Family of Cytokines Using nIR Fluorescent Single-Walled Carbon Nanotubes

The Interleukin-6 (IL-6) family of cytokines regulates inflammation and plays important roles in numerous biochemical pathways. Typically, cytokine levels are measured using enzyme-linked immunosorbent assay (ELISA) or western blot. However, these techniques usually require substantial processing time, cost, machinery, and specialist training. Understanding the fundamental molecular recognition mechanism of cytokines with synthetic substrates is key to developing new biomedical technologies such as assays, sensors, and therapeutics that overcome the above limitations. Herein, we use the corona phase molecular recognition (CoPhMoRe) approach to engineer new carbon nanotube constructs and study their binding to the inflammatory cytokines: IL-6, interleukin-11 (IL-11), ciliary neurotrophic factor (CNTF), and leukemia inhibitory factor (LIF). Library screening identified two polymer-based CoPhMoRe constructs consisting of single-walled carbon nanotubes complexed with p(AA68-rand-BA16-rand-CD16) polymer (MK2) or p(SS80-rand-BS20) polymer (P14) corona phases. The resulting dissociation constants (KD) were 8.38 ng/mL and 16.7 μg/mL, respectively, compared to that of the natural IL-6 receptor at ∼0.32 ng/mL. In addition, the MK2 constructs showed a nonmonotonic response function upon binding with IL-6. Comparative binding experiments suggest that both constructs appear to recognize the axially aligned α-helical structures present in the Interleukin-6 family. The findings from this study elucidate how nanoparticle interfaces, such as those produced by CoPhMoRe, can be designed to lock onto specific protein features. We find that the α-helical structure of the IL-6 family of cytokines can enable facile molecular recognition, opening the door to new types of label-free, low-cost sensing technologies.

Numerical simulations of the wake and deformations of a flexible rotor blade in a turbulent flow

We present, for the first time, the mean deflection evolution of a flexible rotor blade using a coupled model based on Navier–Stokes equations, for the fluid flow, and linear elasticity equations for the blade deformation. Three turbulence models are tested to reach Reynolds numbers as high as 8 104. The absolute tip speed ratios are in the range [0,25]. The numerical results are validated by comparisons with available tip displacements from experiments. For the parameter ranges, above mentioned, the elastic behavior of the flexible rotor is characterized, and the vorticity field is compared with results obtained for a rigid rotor. The effects of the pitch, the tip speed ratio (or frequency), and its sign on the blade deformation are reported. Typically, the blade deforms in the downstream direction, and it is shown that this deformation is a non-monotonic function of the rotation frequency and the pitch angle. Furthermore, it is found that, for particular values of the frequency and pitch angle, the blade is subject to deformations in the upstream direction. It is shown also that the flexible rotor could develop a vortex ring state, but not the rigid one, under the same conditions. It is found that there is a supercritical frequency associated with the apparition of this vortex ring state and this frequency occurs for negative pitches only, for the considered blade. The vorticity field revealed, as well, that the tip vortex changes sign with that of the blade deflection. Finally, we present the effect of the pitch and frequency on the twist angle of the blade and characterize its evolution along the span.

An adaptive endogenous network model for dynamic interbank lending market with central bank

In this paper, an adaptive endogenous model is introduced to explain the formation and evolution mechanism of interbank lending market with central bank. We investigate the evolution of structure of interbank lending market and the impact of structure of bank assets, bank adaptive behaviors, liquidity and dispersion on the resilience of interbank lending market, respectively. Simulation results demonstrate that the structure of the initial interbank lending market has scale-free and small-world features, which keeps in the evolution of the network. Moreover, we find risk gathering requires relatively long time but the outbreak is concentrated and percentage of defaults is a nonmonotonic function of percentage of initial liquid assets. Furthermore, we discover that moderate liquidity hoarding helps to reduce risk contagion effect in the initial stage of contagion while excessive hoarding of liquidity increases the fragility of the network.

Rejection prices and an auctioneer with non-monotonic utility

This paper considers an auctioneer who has a non-monotonic utility function with a unique maximizer. The auctioneer is able to reject all bids over some amount by using rejection prices. We show that the optimal rejection price for such an auctioneer is lower than and equal to that maximizer in first-price and second-price sealed-bid auctions, respectively. Further, in each auction we characterize a necessary and sufficient condition that by using the optimal rejection price not only the auctioneer but also bidders can be better off, compared to a standard auction. Finally, we find that the auctioneer strictly prefers a first-price sealed-bid auction if he is risk-averse when his revenue is lower than the maximizer or if the distribution of revenues which are lower than the maximizer in a standard first-price sealed-bid auction is first-order stochastic dominant over the one in a standard second-price sealed-bid auction.

On maximizing monotone or non-monotone k-submodular functions with the intersection of knapsack and matroid constraints

On maximizing monotone or non-monotone k-submodular functions with the intersection of knapsack and matroid constraints

Understanding stable/unstable miscible A+B→C reaction front and mixing in porous medium

The transport phenomena of A + B → C type reactive miscible front undergoing radial displacement in a porous medium are numerically investigated. For a stable displacement when the viscosity of fluids A, B, and C is same, the dependence of various reaction characteristics on the Damköhler number (Da) is analyzed. The total reaction rate is found to be a non-monotonic function of time depending upon Da, while the total amount of product follows the temporal scaling ∝ t f ( D a ). The viscosity contrast in the system renders unstable flow and results in a hydrodynamic instability called viscous fingering. The effect of hydrodynamics on the reaction product formation is discussed. An insight into the reaction characteristics due to interaction of chemical reaction and instability is obtained for various log-mobility ratios R b and R c. It is observed that the onset of instability, as well as the mixing of the fluids, depends on whether the reaction generates a high or less viscous product or equivalently, the sign of | R b − R c |, keeping Rb fixed. Furthermore, the relation between the first moment of averaged reaction rate for stable and unstable displacement is influenced by the sign of | R b − R c | and Da. The coupling of convection and diffusion on the chemo-hydrodynamic instability is presented, and the existence of the frozen fingers in this reactive fluid system is reported. Our numerical results allow us to understand how instability and chemical reaction interplay to affect the reaction characteristics and the mixing of fluids.

Group fairness in non-monotone submodular maximization

Maximizing a submodular function has a wide range of applications in machine learning and data mining. One such application is data summarization whose goal is to select a small set of representative and diverse data items from a large dataset. However, data items might have sensitive attributes such as race or gender, in this setting, it is important to design fairness-aware algorithms to mitigate potential algorithmic bias that may cause over- or under- representation of particular groups. Motivated by that, we propose and study the classic non-monotone submodular maximization problem subject to novel group fairness constraints. Our goal is to select a set of items that maximizes a non-monotone submodular function, while ensuring that the number of selected items from each group is proportionate to its size, to the extent specified by the decision maker. We develop the first constant-factor approximation algorithms for this problem. We also extend the basic model to incorporate an additional global size constraint on the total number of selected items.

Profit maximization in social networks and non-monotone DR-submodular maximization

In this paper, we study the non-monotone DR-submodular function maximization over integer lattice. Functions over integer lattice have been defined submodular property that is similar to submodularity of set functions. DR-submodular is a further extended submodular concept for functions over the integer lattice, which captures the diminishing return property. Such functions find many applications in machine learning, social networks, wireless networks, etc. The techniques for submodular set function maximization can be applied to DR-submodular function maximization, e.g., the double greedy algorithm has a 1/2-approximation ratio, whose running time is O(nB), where n is the size of the ground set, B is the integer bound of a coordinate. In our study, we design a 1/2-approximate binary search double greedy algorithm, and we prove that its time complexity is O(nlog⁡B), which significantly improves the running time. Specifically, we consider its application to the profit maximization problem in social networks with a bipartite model, the goal of this problem is to maximize the net profit gained from a product promoting activity, which is the difference of the influence gain and the promoting cost. We prove that the objective function is DR-submodular over integer lattice. We apply binary search double greedy algorithm to this problem and verify the effectiveness.

A Novel Image Classification Method Based on Residual Network, Inception, and Proposed Activation Function

In deeper layers, ResNet heavily depends on skip connections and Relu. Although skip connections have demonstrated their usefulness in networks, a major issue arises when the dimensions between layers are not consistent. In such cases, it is necessary to use techniques such as zero-padding or projection to match the dimensions between layers. These adjustments increase the complexity of the network architecture, resulting in an increase in parameter number and a rise in computational costs. Another problem is the vanishing gradient caused by utilizing Relu. In our model, after making appropriate adjustments to the inception blocks, we replace the deeper layers of ResNet with modified inception blocks and Relu with our non-monotonic activation function (NMAF). To reduce parameter number, we use symmetric factorization and 1×1 convolutions. Utilizing these two techniques contributed to reducing the parameter number by around 6 M parameters, which has helped reduce the run time by 30 s/epoch. Unlike Relu, NMAF addresses the deactivation problem of the non-positive number by activating the negative values and outputting small negative numbers instead of zero in Relu, which helped in enhancing the convergence speed and increasing the accuracy by 5%, 15%, and 5% for the non-noisy datasets, and 5%, 6%, 21% for non-noisy datasets.

Wave interference at the contralateral ear helps explain non-monotonic envelope interaural time differences as a function of azimuth.

Interaural time differences (ITDs), an important acoustic cue for perceptual sound-source localization, are conventionally modeled as monotonic functions of azimuth. However, recent literature and publicly available databases from binaural manikins demonstrated ITDs conveyed by the envelopes (ENV-ITDs) of high-frequency (≥2 kHz) signals that were non-monotonic functions of azimuth. This study demonstrates using a simple, time-dependent geometric model of an elliptic head that the back-traveling (longer) sound path around the head, delayed and added to the conventionally treated front-traveling path, can account for non-monotonic ENV-ITDs. These findings have implications for spatial-hearing models in acoustic and electric (cochlear-implant) hearing.

Gauging response time distributions to examine the effect of facial expression inversion.

We used images of facial expressions (FEs) of emotion in a speeded Same/Different task to examine (i) distributional characteristics of response times (RTs) in relation to inter-stimulus similarity and (ii) the impact of inversion on FE processing. Stimuli were seven emotion prototypes, posed by one male and one female, and eight intermediate morphs. Image pairs (N = 225) were presented for 500 ms, upright or inverted, in a block design, each 100 times. For both upright and inverted FEs, RTs were a non-monotonic function: median values were longest for stimulus pairs of intermediate similarity, decreasing for both more-dissimilar and more-similar pairs. RTs of "Same" and "Different" judgments followed ex-Gaussian distributions. The non-monotonicity is interpreted within a dual-process decision model framework as reflecting the infrequency of identical pairs, shifting the balance between the Same and Different processes. The effect of stimulus inversion was gauged by comparing RT-based multidimensional scaling solutions for the two presentation modes. Solutions for upright and inverted FEs showed little difference, with both displaying some evidence of categorical perception. The same features appeared in hierarchical clustering solutions. This outcome replicates and reinforces the solutions derived from accuracy of "Different" responses reported in our earlier companion paper. We attribute this lack of inversion effect to the brief exposure time, allowing low-level visual processing to dominate Same/Different decisions while elevating early featural analysis, which is insensitive to face orientation but enables initial positive/negative valence categorization of FEs.