Nonlinear Transition Research Articles

Revisiting Approximate Linear Programming: Constraint-Violation Learning with Applications to Inventory Control and Energy Storage

Approximate linear programs (ALPs) are well-known models for computing value function approximations (VFAs) of intractable Markov decision processes (MDPs). VFAs from ALPs have desirable theoretical properties, define an operating policy, and provide a lower bound on the optimal policy cost. However, solving ALPs near-optimally remains challenging, for example, when approximating MDPs with nonlinear cost functions and transition dynamics or when rich basis functions are required to obtain a good VFA. We address this tension between theory and solvability by proposing a convex saddle-point reformulation of an ALP that includes as primal and dual variables, respectively, a vector of basis function weights and a constraint violation density function over the state-action space. To solve this reformulation, we develop a proximal stochastic mirror descent (PSMD) method that learns regions of high ALP constraint violation via its dual update. We establish that PSMD returns a near-optimal ALP solution and a lower bound on the optimal policy cost in a finite number of iterations with high probability. We numerically compare PSMD with several benchmarks on inventory control and energy storage applications. We find that the PSMD lower bound is tighter than a perfect information bound. In contrast, the constraint-sampling approach to solve ALPs may not provide a lower bound, and applying row generation to tackle ALPs is not computationally viable. PSMD policies outperform problem-specific heuristics and are comparable or better than the policies obtained using constraint sampling. Overall, our ALP reformulation and solution approach broadens the applicability of approximate linear programming.This paper was accepted by Yinyu Ye, optimization.

Formula omitted] performance for delayed singular nonlinear Markovian jump systems with unknown transition rates via adaptive control method

We work on the investigation of the H∞ performance for uncertain stochastic singular Markovian jump systems with both nonlinear external disturbance and general unknown transition rates (TRs) in this paper. There exist uncertainties in both parameters and TRs. Every transition rate could be totally unavailable or only its estimated value is available. With a generalized H∞ disturbance attenuation level γ, some robust controllers are designed such that the delayed singular Markovian jump system is stochastically admissible. The novel controllers designed in this paper consist of an adaptive controller and a linear controller. Moreover, some sufficient linear matrices inequalities (LMIs) conditions are provided according to Lyapunov stability theory and Itoˆ’s differential formula. Finally, an example is presented to demonstrate our main results.

Transiciones y configuraciones laborales de egresados universitarios: ruptura del significado lineal

Analizamos los recorridos de 46 egresados universitarios de la carrera en Ciencias de la Educación de una universidad pública hacia el mundo del trabajo con base en dos conceptos: transiciones laborales y configuraciones. Proponemos 13 indicadores laborales con base en los cuales configuramos cuatro tipos de transiciones laborales que permiten discutir tres supuestos: linealidad del paso de la universidad al trabajo; mejores condiciones de trabajo que corresponderían a este nivel educativo, y la adecuación entre formación y ocupación. Los resultados muestran transiciones lineales al trabajo, pero en la mayoría observamos una tendencia hacia transiciones no lineales, caracterizadas por su diversidad y precariedad.

Consistent sorting but contrasting transition zones in plant communities along bioclimatic gradients

Correlations between plant species occurrences and climate are used as evidence of ecological sorting and climate sensitivity. However, because observed patterns may be spatially and historically contingent, interpretations of compositional responses to spatial differences in climate should ideally consider past climatic fluctuations, edaphic factors, nonlinear turnover rates and transition zones (ecotones) in environmental and geographic space. We tested whether drivers of plant community compositional turnover and transition zones are consistent, rather than spatially contingent, across spatially isolated and biologically contrasting (independent) ecosystems. We used four broad-scale transects in Australia, which are spatially isolated and climatically and ecologically diverse: NATT (Northern Territory); BATS (New South Wales); SWATT (Western Australia) and TREND (South Australia). We used Generalised Dissimilarity Modelling to ascertain the relative contributions of space (geographic distance) and environmental variables to compositional turnover. We mapped transition zones using modelled nonlinear responses. Purely spatial contributions were estimated using variance partitioning. Models explained 26–52% of deviance in compositional dissimilarity. Mean annual rainfall and geographic distance were the most important explanatory variables, although topographic relief outranked rainfall for the topographically complex BATS transect. Purely spatial structure accounted for only 7–12% of explained deviance, pointing to the shared prevalence of species sorting along spatially structured rainfall gradients. Zones of rapid compositional turnover across bioclimatic gradients were evident across the contrasting ecosystems. These transitions zones tended to occur at the arid extremes of rainfall gradients and as plains transitioned into complex topography. Responses to other variables were inconsistent among transects. Transition zones were spatially contingent, influenced by local topography, and generally occurred within different subintervals (value ranges) along gradients. The somewhat idiosyncratic compositional responses suggest that assessment of broadscale compositional drivers including climate change should incorporate regional variation. However, the consistently strong species sorting along rainfall gradients demonstrates a common key response to moisture limitation.

Joint instability and abrupt nonlinear transitions in a differentially rotating plasma

Global magnetohydrodynamic (MHD) instabilities are investigated in a computationally tractable two-dimensional model of the solar tachocline. The model’s differential rotation yields stability in the absence of a magnetic field, but if a magnetic field is present, a joint instability is observed. We analyse the nonlinear development of the instability via fully nonlinear direct numerical simulation, the generalized quasi-linear approximation (GQL) and direct statistical simulation (DSS) based upon low-order expansion in equal-time cumulants. As the magnetic diffusivity is decreased, the nonlinear development of the instability becomes more complicated until eventually a set of parameters is identified that produces a previously unidentified long-term cycle in which energy is transformed from kinetic energy to magnetic energy and back. We find that the periodic transitions, which mimic some aspects of solar variability – for example, the quasiperiodic seasonal exchange of energy between toroidal field and waves or eddies – are unable to be reproduced when eddy-scattering processes are excluded from the model.

Testing for cointegration in nonlinear asymmetric smooth transition error correction models

The present paper proposes an alternative procedure to test for cointegration in asymmetric exponential smooth transition autoregressive (AESTAR) model. The proposed new F-statistics test the null hypothesis of no cointegration against the alternative hypothesis of cointegration with asymmetric ESTAR adjustment. We derive the nonstandard limit distributions analytically via Monte Carlo simulations. We also study the finite sample properties and the power of proposed tests with Monte Carlo simulations and find that the empirical sizes of two tests are quite close to the nominal one and the proposed tests do not lead to over-rejections of the null hypothesis of no cointegration.

Nonlinear symmetry breaking of Aharonov-Bohm cages

We study the influence of mean field cubic nonlinearity on Aharonov-Bohm caging in a diamond lattice with synthetic magnetic flux. For sufficiently weak nonlinearities the Aharonov-Bohm caging persists as periodic nonlinear breathing dynamics. Above a critical nonlinearity, symmetry breaking induces a sharp transition in the dynamics and enables stronger wavepacket spreading. This transition is distinct from other flatband networks, where continuous spreading is induced by effective nonlinear hopping or resonances with delocalized modes, and is in contrast to the quantum limit, where two-particle hopping enables arbitrarily large spreading. This nonlinear symmetry breaking transition is readily observable in femtosecond laser-written waveguide arrays.

Prevention of network destruction of partially hydrolyzed polyacrylamide (HPAM): Effects of salt, temperature, and fumed silica nanoparticles

Polymer flooding is one of the most effective enhanced oil recovery (EOR) methods. High temperature and a high salt content in oil reservoirs significantly decrease the performance of polymer flooding. In this work, the viscoelastic properties of a partially hydrolyzed polyacrylamide (HPAM) solution with and without salt (NaCl) and at two different temperatures (35 °C and 70 °C) were evaluated using rheological approaches. Two fumed silica nanoparticles (NPs) featuring different surface chemistries were used, and their ability to prevent destruction of the polymer network structure against salt addition and temperature increase was investigated. Linear rheological tests (frequency sweep, creep, and creep recovery) and nonlinear rheological tests (large amplitude oscillatory shear) were employed to evaluate the network structure of these systems. The results showed that either adding salt or increasing the temperature destroyed the mechanical integrity of the HPAM 3-dimensional elastic network. However, the introduction of both types of NPs at a sufficient concentration maintained the network structure of HPAM solutions in the small deformation region. In the large deformation region, it was shown that the extent of intra-cycle shear-thickening behavior in the HPAM solution (T = 35 °C and without any salt) decreased by incorporating salt or by increasing the temperature. Moreover, upon incorporating either of the NPs to the HPAM solution, the nonlinear viscoelastic behavior dramatically changed, and the critical strain (linear to nonlinear transition) decreased to a much lower strain amplitude. The outcomes of this study will help petroleum scientists to design more efficient EOR methods.

Waves and Sediment Transport Due to Granular Landslides Impacting Reservoirs

AbstractGranular landslides impacting reservoirs may generate large waves and cause active sediment transport, and an increased understanding of these processes is important for public safety and effective reservoir management. This study investigates the waves and sediment transport caused by landslides impacting reservoirs using a two‐dimensional coupled double‐layer‐averaged shallow water hydro‐sediment‐morphodynamic model. In contrast to existing models, which cannot fully account for sediment transport, the model makes a physical step forward. The model is benchmarked against laboratory experiments of landslide‐generated waves in both two and three dimensions. Based on extended numerical cases, the capability of the model is further demonstrated by comparisons with empirical relationships of waves in 2‐D. In addition, sediment transport is resolved in terms of the sediment concentration and bed deformation. The results show that the wave types and amplitudes in 2‐D are dictated by the sediment transport speed, which also governs the landslide‐to‐wave momentum transfer and the landslide efficiency, which is defined as the ratio of the horizontal runout distance to the vertical fall height. With increasing sediment transport speed, landslide‐generated waves in 2‐D vary gradually from smaller nonlinear oscillatory waves to larger waves with solitary‐like wave characteristics, including nonlinear transition waves, solitary waves, and dissipative transient bores. In contrast to the momentum transfer ratio, the landslide efficiency increases with the sediment transport speed and decreases with the reservoir water depth and the lateral spreading in 3‐D cases.

Forecasting the exchange rate using nonlinear Taylor rule based models

This research utilises a non-linear Smooth Transition Regression (STR) approach to modelling and forecasting the exchange rate, based on the Taylor rule model of exchange rate determination. The separate literatures on exchange rate models and the Taylor rule have already shown that the non-linear specification can outperform the equivalent linear one. In addition the Taylor rule based exchange rate model used here has been augmented with a wealth effect to reflect the increasing importance of the asset markets in monetary policy. Using STR models, the results offer evidence of non-linearity in the variables used and that the interest rate differential is the most appropriate transition variable. We conduct the conventional out-of-sample forecasting performance test, which indicates that the non-linear models outperform their linear equivalents as well as the non-linear UIP model and random walk.

Kernel cross-view collaborative representation based classification for person re-identification

Person re-identification aims at the maintenance of a global identity as a person moves among non-overlapping surveillance cameras. It is a hard task due to different illumination conditions, viewpoints and the small number of annotated individuals from each pair of cameras (small-sample-size problem). Common subspace learning methods have been proposed to handle the camera transition problems. However, after learning the low-dimensional representation, these methods usually compute distances using a simple cosine or Mahalanobis distance. Therefore, an still open question is how to better match probe and gallery images in the learned common subspace considering reduced number of training samples and the nonlinear behavior of the data. Collaborative Representation based Classification (CRC) has been employed successfully to address the small-sample-size problem in computer vision. However, the original CRC formulation is not well-suited for person re-identification since it does not consider that probe and gallery samples are from different cameras. Furthermore, it is a linear model, while appearance changes caused by different camera conditions indicate a strong nonlinear transition between cameras. To overcome such limitations, we propose the Kernel Cross-View Collaborative Representation based Classification (Kernel X-CRC), method that represents probe and gallery images by balancing representativeness and similarity nonlinearly. According to experimental results, we achieve state-of-the-art for rank-1 matching rates in three person re-identification datasets (CUHK03, PRID450S and GRID) and the second best results on VIPeR and CUHK01 datasets. Furthermore, we present outperforming results on Market-1501 dataset demonstrating that the Kernel X-CRC is suitable to a large-scale and multiple cameras scenario.

Mean-reversion and structural change in European food prices

Mean-reversion in unprocessed food prices and beef prices towards the long-run trend is examined for twenty-two European countries, using linear and nonlinear unit root tests. As the argument goes, food prices might display short-term deviations from their long-run values due to disturbances such as changes in climate or speculation; yet, once the impact of these short-lived shocks fade away, the prices convert to the long-run equilibrium level determined by fundamentals. The nonlinear smooth transition framework suggest that the speed of this adjustment might depend on the size and sign of the deviation of prices from their long-run values. The results carry important policy implications regarding the benefits of short-term demand management policies along with structural policies.

Genomic transitions during host race and species formation.

Darwin recognized species as discontinuous, yet considered them to be formed by an incremental process of natural selection. Recent theoretical work on 'genome-wide congealing' is bridging this gap between the gradualism of divergent selection and rapid genome-wide divergence, particularly during ecological speciation-with-gene-flow. Host races and species of phytophagous insects, displaying a spectrum of divergence and gene flow among member taxa, provide model systems for testing predicted non-linear transitions from 'genic' divergence at a few uncoupled loci to 'genomic' divergence with genome-wide coupling of selected loci and strong reproductive isolation. Integrating across natural history, genomics, and evolutionary theory, emerging research suggests a tipping point from 'genic' to 'genomic' divergence between host races and species, during both sympatric speciation and secondary contact.

Nonlinear Dicke Quantum Phase Transition and Its Quantum Witness in a Cavity-Bose–Einstein-Condensate System**Supported by the National Natural Science Foundation of China under Grant Nos 11775075 and 1143401.

We investigate nonlinear Dicke quantum phase transition (QPT) induced by inter-atomic nonlinear interaction and its quantum witness in a cavity-Bose–Einstein-condensate (BEC) system. It is shown that inter-atomic nonlinear interaction in a cavity BEC system can induce first-order Dicke QPT. It is found that this nonlinear Dicke QPT can happen in an arbitrary coupling regime of the cavity and atoms. It is demonstrated that the quantum speed limit time can witness the Dicke QPT through its sudden change at the critical point of the QPT.

Higher Order Algorithm for Solving Lambert’s Problem

This work presents a high-order perturbation expansion method for solving Lambert’s problem. The necessary condition for the problem is defined by a fourth-order Taylor expansion of the terminal error vector. The Taylor expansion partial derivative models are generated by Computational Differentiation (CD) tools. A novel derivative enhanced numerical integration algorithm is presented for computing nonlinear state transition tensors, where only the equation of motion is coded. A high-order successive approximation algorithm is presented for inverting the problems nonlinear necessary condition. Closed-form expressions are obtained for the first, second,third, and fourth order perturbation expansion coefficients. Numerical results are presented that compare the convergence rate and accuracy of first-through fourth-order expansions. The initial p-iteration starting guess is used as the Lambert’s algorithm initial condition. Numerical experiments demonstrate that accelerated convergence is achieved for the second-, third-, and fourth-order expansions, when compared to a classical first-order Newton method.

Forecasting the Exchange Rate Using Non-Linear Taylor Rule Based Models

This research utilises a non-linear Smooth Transition Regression (STR) approach to modelling and forecasting the exchange rate, based on the Taylor rule model of exchange rate determination. The separate literatures on exchange rate models and the Taylor rule have already shown that the non-linear specification can outperform the equivalent linear one. In addition the Taylor rule based exchange rate model used here has been augmented with a wealth effect to reflect the increasing importance of the asset markets in monetary policy. Using STR models, the results offer evidence of non-linearity in the variables used and that the interest rate differential is the most appropriate transition variable. We conduct the conventional out-of-sample forecasting performance test, which indicates that the non-linear models outperform their linear equivalents as well as the non-linear UIP model and random walk.

Nonlinear transition from convective to absolute Raman instability with trapped electrons and inflationary growth of reflectivity

We propose a nonlinear mechanism for transition from convective to absolute in stimulated Raman backscattering instability due to the effect of trapped particles in the plasma wave. Convective instability saturates at the low level, yet it is sufficient to trap electrons near the plasma phase velocity. The trapped electrons tend to flatten the distribution function. With spatial averaging over the trapped region, we find that the flattened distribution function reduces the damping rate due to bounce resonance of the plasma wave and then decreases the threshold for absolute instability. So the transition from a weak, convective instability to a strong, absolute instability can occur, leading to exponential growth everywhere and inflation of reflectivity of several orders of magnitude as observed in the experiment, once the threshold is exceeded.

Climbing the Ladder: Socioeconomic Mobility in Malaysia

This study investigates the existence and extent of intergenerational mobility in Malaysia in terms of educational attainment, occupational skills level, and income level. It compares the status of working adults born between the years 1945 and 1960 and their adult children born between 1975 and 1985, using non-linear transition matrix techniques. On average, the majority of adult children have better educational attainment and occupational skills level compared with their parents. Income mobility, in absolute and relative terms, is highest among children born to parents in the lowest income quintile. The results of a logistic regression model show that education, assets ownership, gender, and location matter for upward mobility. Moving forward, there will be difficulties for the children from poor families to move up the socioeconomic ladder because of changes in policies. An inclusive development approach is vital in enhancing socioeconomic mobility to promote social cohesion, economic growth, and greater equity for the next generation.

Structural transition of vortices to nonlinear regimes in a dusty plasma

The structural transition of a steady state dust flow from linear to nonlinear regimes is analyzed using a two-dimensional hydrodynamic model for the dust fluid confined in an axisymmetric toroidal system along with an unbounded streaming plasma. Numerical solutions of the employed hydrodynamical model not only confirms the analytical structure of the driven dust vortex flow in the linear limit as reported in the previous analysis but also shows how the dust vortices are strongly affected by the nonlinear convective transport of the flow at the higher Reynolds number (Re) regime. Effects of various system parameters including external driving field and the Reynolds number are investigated within the linear to nonlinear transition regime 0.001 ≤ Re < 50. In agreement with relevant experimental observations, the steady flow structure which is symmetric around the center in the linear regime begins to turn asymmetric in the nonlinear regime. The structure of the steady dust flow is found to be influenced mainly by the dissipation scales due to kinematic viscosity, ion drag, and neutral collision in the nonlinear regime, whereas, in the linear regime, it is mainly controlled by the external driving field and the confining boundaries.

Loss of biodiversity alters ecosystem function in freshwater streams: potential evidence from benthic macroinvertebrates

AbstractParticular attention has been paid on the evidence that ecosystem function can be impacted by changes of biodiversity. However, how the loss of biodiversity alters the ecosystem function in aquatic ecosystems remains unclear. Here, the effects of benthic macroinvertebrate community structure on ecosystem function and the possibility of which being shifted by ecological threshold along the habitat condition gradient were examined by quantifying community structure and ecosystem function in streams of Lake Dianchi basin. The results demonstrated that the relative abundance of Oligochaete was significantly linear correlated with ecosystem multifunctions, especially N and P cycling functions, as well as the dominant taxon% and Gather‐Collectors% closely affected P cycling function and multifunctions, respectively, while no remarkable nonlinearities were observed. Besides, there was a distinct shift from sensitive taxa‐dominated healthy state to tolerant taxa‐dominated degraded state with an increase in habitat pressure. The nonlinear transition of benthic macroinvertebrate community structure in combination with altered ecosystem function clearly indicated the present of extinction threshold in the process of stream habitat degradation. The findings contribute to the growing evidence for fully understanding the implications of biodiversity loss in ecosystem function.