Random Interactions Research Articles

Excitons in a disordered medium: A numerical study in InGaN quantum wells

Excitons in InGaN quantum wells are investigated numerically, considering random alloy disorder and Coulomb interaction on equal footing in the Schr\"odinger equation. Their statistical properties are systemically explored as a function of the quantum well thickness and composition, revealing a complex competition between disorder-induced carrier localization, Coulomb attraction, and field-induced wave function separation. This results in a class of semiconductor quasiparticle with hybrid properties in between hydrogenoid excitons and disorder-localized free particles. Exciton screening by free carriers is investigated and shows distinct behavior from the screening of bulk excitons. Finally, a highly accurate approximate solution of the excitonic Schr\"odinger equation, with reduced numerical complexity, is introduced.

Opinion Shaping in Social Networks Using Reinforcement Learning

In this article, we consider a variant of the classical DeGroot model of opinion propagation with random interactions, in which a prescribed subset of agents is amenable to a control parameter. There are also some stubborn agents and some agents that are neither stubborn nor amenable to control. We map the problem to a shortest path problem, where the control parameter is coupled across controlled nodes because of a common resource constraint. Hence, the problem is not amenable to a pure dynamic programming approach, and the classical reinforcement learning schemes for the latter cannot be applied here for maximizing average influence in the long run. We view it instead as a parametric optimization problem and not a control problem and use a nonclassical policy gradient scheme. We analyze its performance theoretically and through numerical experiments. We also consider a situation when only certain interactions between agents are observed.

Random field ϕ3 model and Parisi-Sourlas supersymmetry

We use the RG framework set up in [1] to explore the ϕ3 theory with a random field interaction. According to the Parisi-Sourlas conjecture this theory admits a fixed point with emergent supersymmetry which is related to the pure Lee-Yang CFT in two less dimensions. We study the model using replica trick and Cardy variables in d = 8 − ϵ where the RG flow is perturbative. Allowed perturbations are singlets under the Sn symmetry that permutes the n replicas. These are decomposed into operators with different scaling dimensions: the lowest dimensional part, ‘leader’, controls the RG flow in the IR; the other operators, ‘followers’, can be neglected. The leaders are classified into: susy-writable, susy-null and non-susy-writable according to their mixing properties. We construct low lying leaders and compute the anomalous dimensions of a number of them. We argue that there is no operator that can destabilize the SUSY RG flow in d ≤ 8. This agrees with the well known numerical result for critical exponents of Branched Polymers (which are in the same universality class as the random field ϕ3 model) that match the ones of the pure Lee-Yang fixed point according to dimensional reduction in all 2 ≤ d ≤ 8. Hence this is a second strong check of the RG framework that was previously shown to correctly predict loss of dimensional reduction in random field Ising model.

Thermodynamic stability and critical points in multicomponent mixtures with structured interactions.

Theoretical work has shed light on the phase behavior of idealized mixtures of many components with random interactions. However, typical mixtures interact through particular physical features, leading to a structured, nonrandom interaction matrix of lower rank. Here, we develop a theoretical framework for such mixtures and derive mean-field conditions for thermodynamic stability and critical behavior. Irrespective of the number of components and features, this framework allows for a generally lower-dimensional representation in the space of features and proposes a principled way to coarse-grain multicomponent mixtures as binary mixtures. Moreover, it suggests a way to systematically characterize different series of critical points and their codimensions in mean-field. Since every pairwise interaction matrix can be expressed in terms of features, our work is applicable to a broad class of mean-field models.

Substantive model compatible multilevel multiple imputation: A joint modeling approach.

Substantive model compatible multiple imputation (SMC-MI) is a relatively novel imputation method that is particularly useful when the analyst's model includes interactions, non-linearities, and/or partially observed random slope variables. Here we thoroughly investigate a SMC-MI strategy based on joint modeling of the covariates of the analysis model. We provide code to apply the proposed strategy and we perform an extensive simulation work to test it in various circumstances. We explore the impact on the results of various factors, including whether the missing data are at the individual or cluster level, whether there are non-linearities and whether the imputation model is correctly specified. Finally, we apply the imputation methods to the motivating example data. SMC-JM appears to be superior to standard JM imputation, particularly in presence of large variation in random slopes, non-linearities, and interactions. Results seem to be robust to slight mis-specification of the imputation model for the covariates. When imputing level 2 data, enough clusters have to be observed in order to obtain unbiased estimates of the level 2 parameters. SMC-JM is preferable to standard JM imputation in presence of complexities in the analysis model of interest, such as non-linearities or random slopes.

Stick-Slip Vibration Suppression in Drill String Using Observer-Based LQG Controller.

Hydrocarbon exploration and production activities are guaranteed through various operations including the drilling process, which is realized by using rotary drilling systems. The process involves crushing the rock by rotating the drill bit along a drill string to create a borehole. However, during this operation, violent vibrations can occur at the level of the drill string due to its random interaction with the rocks. According to their axes of occurrence, there are three types of vibrations: axial, lateral, and torsional, where the relentless status of the torsional vibrations is terminologically known as the stick-slip phenomenon. Such a phenomenon can lead to increased fatigue of the drill string and cause its abortive fracture, in addition to reducing the efficiency of the drilling process and consequently making the exploration and production operations relatively expensive. Thus, the main objective of this paper is to eliminate the severe stick-slip vibrations that appear along the drill string of the rotary drilling system according to the LQG observer-based controller approach. The rock–bit interaction term is highly nonlinear, and the bit rotational velocity is unmeasurable; an observer was first designed to estimate the unknown inputs of the model, and then the controller was implemented in the drill string model with 10 degrees of freedom. The estimation process was essentially based on surface measurements, namely, the current and rotational velocity of the top drive. Thereafter, the performance of the proposed observer-based LQG controller was tested for different simulation scenarios in a SimScape/Matlab environment, for which the controller demonstrated good robustness in suppressing the severe stick-slip vibrations. Furthermore, the simulation and experimental results were compared to other controllers designed for the same model; the proposed observer-based LQG controller showed better performance, and it was less sensitive to structured disturbances than H∞. Thence, it is highly recommended to use the proposed approach in smart rotary drilling systems.

Instabilities of complex fluids with partially structured and partially random interactions

We develop a theory for thermodynamic instabilities of complex fluids composed of many interacting chemical species organised in families. This model includes partially structured and partially random interactions and can be solved exactly using tools from random matrix theory. The model exhibits three kinds of fluid instabilities: one in which the species form a condensate with a local density that depends on their family (family condensation); one in which species demix in two phases depending on their family (family demixing); and one in which species demix in a random manner irrespective of their family (random demixing). We determine the critical spinodal density of the three types of instabilities and find that the critical spinodal density is finite for both family condensation and family demixing, while for random demixing the critical spinodal density grows as the square root of the number of species. We use the developed framework to describe phase-separation instability of the cytoplasm induced by a change in pH.

Spatio‐temporal co‐occurrence of Anastrepha species in papaya orchards in the state of Espírito Santo, Brazil

AbstractThe variation in co‐occurrence between pests may influence spatio‐temporal persistence strategies of species, with implications for pest management. The co‐occurrence of Anastrepha species (Diptera: Tephritidae) in papaya orchards was investigated in areas at different distances from a native forest reserve in Espírito Santo, Brazil, to investigate positive, negative, or random interactions, understood as potential coexistence, interspecific competition, or neutral interactions, respectively. Data were obtained from a papaya‐growing area divided into three sub‐areas – a buffer zone bordering the forest, neighbourhood 1, and neighbourhood 2 – and the co‐occurrence results were compared with the entire area. The buffer zone along the protected native Atlantic Forest (semideciduous seasonal forest vegetation) was created to filter negative environmental impacts. Neighbourhood 1 was closer to the forest than neighbourhood 2. Based on a long‐term dataset from 1998 to 2010, co‐occurrence of fruit flies was investigated by comparing two periods: from 1998 to 2003, when a special pest management system was implemented, termed the systems approach, and from 2004 to 2010, showing the impact of this system on fruit fly diversity. The strength of interaction between species was also evaluated for significant co‐occurrences. The patterns of co‐occurrence and interaction of Anastrepha species were influenced by area and time. In all scenarios, only positive and random associations were observed, with Anastrepha fraterculus (Wiedemann) and Anastrepha obliqua (Macquart) showing the most positive associations. Co‐occurrence was greater in areas farther from the reserve. However, the strength of the interaction between the areas showed little variation. We concluded that the distance from the reserve and the pest management (systems approach) influenced co‐occurrence, as species co‐occurred much more frequently when collected far from the native forest. The impact during the period of the systems approach (1998–2003) provided fewer positive associations, but with stronger interactions over time. These results confirm that identifying pest co‐occurrence distribution patterns in crops and the respective neighbourhoods can be helpful in improving strategies for pest management associated with a systems approach.

Individual-based model highlights the importance of trade-offs for virus-host population dynamics and long-term co-existence.

Viruses play diverse and important roles in ecosystems. In recent years, trade-offs between host and virus traits have gained increasing attention in viral ecology and evolution. However, microbial organism traits, and viral population parameters in particular, are challenging to monitor. Mathematical and individual-based models are useful tools for predicting virus-host dynamics. We have developed an individual-based evolutionary model to study ecological interactions and evolution between bacteria and viruses, with emphasis on the impacts of trade-offs between competitive and defensive host traits on bacteria-phage population dynamics and trait diversification. Host dynamics are validated with lab results for different initial virus to host ratios (VHR). We show that trade-off based, as opposed to random bacteria-virus interactions, result in biologically plausible evolutionary outcomes, thus highlighting the importance of trade-offs in shaping biodiversity. The effects of nutrient concentration and other environmental and organismal parameters on the virus-host dynamics are also investigated. Despite its simplicity, our model serves as a powerful tool to study bacteria-phage interactions and mechanisms for evolutionary diversification under various environmental conditions.

Estimation in tensor Ising models

AbstractThe $p$-tensor Ising model is a one-parameter discrete exponential family for modeling dependent binary data, where the sufficient statistic is a multi-linear form of degree $p \geqslant 2$. This is a natural generalization of the matrix Ising model that provides a convenient mathematical framework for capturing, not just pairwise, but higher-order dependencies in complex relational data. In this paper, we consider the problem of estimating the natural parameter of the $p$-tensor Ising model given a single sample from the distribution on $N$ nodes. Our estimate is based on the maximum pseudolikelihood (MPL) method, which provides a computationally efficient algorithm for estimating the parameter that avoids computing the intractable partition function. We derive general conditions under which the MPL estimate is $\sqrt N$-consistent, that is, it converges to the true parameter at rate $1/\sqrt N$. Our conditions are robust enough to handle a variety of commonly used tensor Ising models, including spin glass models with random interactions and models where the rate of estimation undergoes a phase transition. In particular, this includes results on $\sqrt N$-consistency of the MPL estimate in the well-known $p$-spin Sherrington–Kirkpatrick model, spin systems on general $p$-uniform hypergraphs and Ising models on the hypergraph stochastic block model (HSBM). In fact, for the HSBM we pin down the exact location of the phase transition threshold, which is determined by the positivity of a certain mean-field variational problem, such that above this threshold the MPL estimate is $\sqrt N$-consistent, whereas below the threshold no estimator is consistent. Finally, we derive the precise fluctuations of the MPL estimate in the special case of the $p$-tensor Curie–Weiss model, which is the Ising model on the complete $p$-uniform hypergraph. An interesting consequence of our results is that the MPL estimate in the Curie–Weiss model saturates the Cramer–Rao lower bound at all points above the estimation threshold, that is, the MPL estimate incurs no loss in asymptotic statistical efficiency in the estimability regime, even though it is obtained by minimizing only an approximation of the true likelihood function for computational tractability.

Human-Induced Response and Reliability Analysis of Stochastic Dynamic System

This paper proposed a method analyzing crowd-induced stochastic vibration response by the dynamic reliability method. The efficiency of the probability density evolution method (PDEM) is improved by embedding the Kullback-Leibler (K-L) relative sensitivity analysis in response analysis of stochastic dynamic system. Then the complicated point selection technique of high dimension uncertain variables is avoided. The proposed method is illustrated by the response analysis of random crowd-structure interaction system where the load parameter randomness is considered. The acceleration induced by the crossing of crowd is predicted with the proposed method. Results obtained highlight the computation improvement in PDEM probabilistic response analysis in high dimension dynamic system. And the method could be used as an efficient way to predict and evaluate vibration serviceability of structures with human-induced vibration.

OReO/ENGOT Ov-38 trial: Impact of maintenance olaparib rechallenge according to ovarian cancer patient prognosis—An exploratory joint analysis of the BRCA and non-BRCA cohorts.

5558 Background: In the Phase IIIb OReO/ENGOT Ov-38 trial (NCT03106987), maintenance olaparib (O) rechallenge significantly improved progression-free survival (PFS) vs placebo in patients (pts) with platinum-sensitive relapsed ovarian cancer (PSROC) regardless of their BRCA status (Pujade-Lauraine, ESMO 2021). The impact of prognostic factors on this PFS benefit were unknown. Methods: Pts had PSROC, one prior line of PARP inhibitor (PARPi) maintenance and were in response to platinum-based chemotherapy (Cx). Pts were enrolled into two cohorts – BRCA mutated (BRCAm) and non-BRCAm – and randomized to receive maintenance O (300 mg bid) or placebo. Primary endpoint was PFS. Post-hoc individual patient data meta-analysis was used to combine both cohorts using fixed and random effect models, interaction, and stratified tests in the Cox model. Stepwise Cox multivariate model for PFS and logistic regression models were used for late relapse, defined as disease progression occurring >24 weeks after randomization. Randomization stratification criteria and cohort effect were included in all models. Results: This study included 220 pts from the BRCAm (n=112) and non-BRCAm (n=108) cohorts recruited between October 3, 2017 and February 10, 2021. No heterogeneity was detected between cohorts: Cochran’s Q test P=0.53 (fixed and random); interaction test P=0.63. The O effect was consistent, and no significant interactions were observed between subgroups. In the multivariate PFS analyses, the main independent factors for prognosis were CA-125 level, visceral disease (liver, lung, pleura, brain), and treatment arm. These factors were independent predictive factors for late relapse among the 181 evaluable pts with the opportunity of at least 6 months of follow-up (Table). Conclusions: In the OReO/ENGOT Ov-38 trial, CA-125 level and presence of visceral disease at baseline were the best predictors of patient outcome. Maintenance olaparib rechallenge was effective overall regardless of prognostic subgroup. Clinical trial information: NCT03106987. [Table: see text]

Convergence analysis of the discrete consensus-based optimization algorithm with random batch interactions and heterogeneous noises

We present stochastic consensus and convergence of the discrete consensus-based optimization (CBO) algorithm with random batch interactions and heterogeneous external noises. Despite the wide applications and successful performance in many practical simulations, the convergence of the discrete CBO algorithm was not rigorously investigated in such a generality. In this work, we introduce a generalized discrete CBO algorithm with a weighted representative point and random batch interactions, and show that the proposed discrete CBO algorithm exhibits stochastic consensus and convergence toward the common equilibrium state exponentially fast under suitable assumptions on system parameters. For this, we recast the given CBO algorithm with random batch interactions as a discrete consensus model with a random switching network topology, and then we use the mixing property of interactions over sufficiently long time interval to derive stochastic consensus and convergence estimates in mean square and almost sure senses. Our proposed analysis significantly improves earlier works on the convergence analysis of CBO models with full batch interactions and homogeneous external noises.

Injury Severity Analysis for Large Truck-Involved Crashes: Accounting for Heterogeneity

This study explores the crash injury severity of large truck-involved crashes, where the truck driver was identified as the at-fault driver. The paper focuses on vehicle-in-motion crashes that occurred on Florida’s state highways between 2007 and 2016. A random parameter ordered logit (RPOL) model was developed to identify random parameters and interaction effects. Results indicated that not using restraint systems, running a red light, wrong-way driving, failing to yield the right of way, tire or brake defects, and dark conditions had positive associations with higher levels of crash injury severity. The random variables—straight alignment, paved shoulders, and unpaved shoulders—showed significant random effects among the observations. For straight alignment, running red lights, following too closely, vision obstruction caused by fixed objects, and vision obstruction caused by fog were the sources of heterogeneity. Unpaved shoulders, running red lights, wrong-way driving, and the presence of parked or stopped vehicles were found as interaction effects. Results showed that accounting for heterogeneity and interaction effects significantly improved the goodness of fit of the model. This study provides more comprehensive knowledge of the influencing factors of large truck crashes by considering the role of heterogeneity and its potential sources in crash injury severity.

Disorder- driven gradual transition of the continuous symmetry- breaking phase transition

We study the influence of random anisotropy type quenched disorder on the phase behavior of the system, which exhibits in undistorted case the 2nd order continuous symmetry breaking phase transition. Invoking the central limit theorem we express the free energy of the system in terms of the order parameter η and the characteristic length ξ of the gauge field ϕ. The latter exhibits the Goldstone fluctuation mode and is consequently extremely susceptible to the imposed disorder. In case of negligible distribution width ΔT of the local transition temperatures the disorder converts the 2nd order transition into a discontinuous one for W<WC, where Wrepresents the disorder strength. Above the critical disorder strength WC the transition becomes gradual. However for the finite width ΔT the transition becomes gradual for any W>0. We demonstrate that for large enough values of ΔT the system behavior is dominated by the distribution of temperatures, while the details of the random field interaction term play a secondary role. The influence of distribution of local (quasi) phase transitions is in most theoretical approaches dealing with randomly perturbed systems neglected from the outset.

Random anisotropy magnet at finite temperature

We present finite-temperature Monte Carlo studies of a 2D random-anisotropy (RA) magnet on lattices containing one million spins. The correlated spin-glass state predicted by analytical theories is reproduced in simulations, as are the field-cooled and zero-field-cooled magnetization curves observed in experiments. The orientations of lattice spins begin to freeze when the temperature is lowered. The freezing transition is due to the energy barriers generated by the RA rather than due to random interactions in conventional spin-glasses. We describe freezing by introducing the time-dependent spin-glass order parameter q and the spin-melting time τ M defined via q = τ M/t above freezing, where t is the time of the experiment represented by the number of Monte Carlo steps.

Pairing instabilities of the Yukawa-SYK models with controlled fermion incoherence

The interplay of non-Fermi liquid and superconductivity born out of strong dynamical interactions is at the heart of the physics of unconventional superconductivity. As a solvable platform of the strongly correlated superconductors, we study the pairing instabilities of the Yukawa-Sachdev-Ye-Kitaev (Yukawa-SYK) model, which describes spin-1/2 fermions coupled to bosons by the random, all-to-all, spin-independent and dependent Yukawa interactions. In contrast to the previously studied models, the random Yukawa couplings are sampled from a collection of Gaussian ensembles whose variances follow a continuous distribution rather than being fixed to a constant. By tuning the analytic behaviour of the distribution, we could control the fermion incoherence to systematically examine various normal states ranging from the Fermi liquid to non-Fermi liquids that are different from the conformal solution of the SYK model with a constant variance. Using the linearised Eliashberg theory, we show that the onset of the unconventional spin-triplet pairing is preferred with the spin-dependent interactions while all pairing channels show instabilities with the spin-independent interactions. Although the interactions shorten the lifetime of the fermions in the non-Fermi liquid, the same interactions also dress the bosons to strengthen the tendency to pair the incoherent fermions. As a consequence, the onset temperature T_cTc of the pairing is enhanced in the non-Fermi liquid compared to the case of the Fermi liquid.

Utilization of high entropy in rare earth-based magnetocaloric metallic glasses

In this study, the magnetic behavior and magnetocaloric effect (MCE) of Dy18Er18Y18Ni26Al20 and Dy13.5Er13.5Y13.5Gd13.5Ni26Al20 high-entropy bulk metallic glasses (BMGs) were systematically investigated, as well as Dy27Er27Ni26Al20 and Dy54Ni26Al20 medium-entropy BMGs. Distinct spin glass-like behavior below the Curie temperature and large MCE at cryogenic temperature were observed in all BMGs. Competitive magnetic entropy change values of 10.6 and 10.2 J kg−1K−1 were obtained for the Dy27Er27Ni26Al20 and Dy18Er18Y18Ni26Al20 BMGs, respectively, under a magnetic field change of 5 T. Accordingly, the effect of configuration entropy on the magnetic response and MCE was discussed. It was found that the magnetic phase transition temperature, magnetic hysteresis and refrigeration capacity can be altered by utilization of configuration entropy, which can be ascribed to the change in random magnetic anisotropy and magnetic interactions. However, no distinct difference in the magnetic entropy change was observed from the ternary Dy54Ni26Al20 to senary Dy13.5Er13.5Y13.5Gd13.5Ni26Al20 BMGs with increasing configuration entropy. The results reveal that the typical cocktail effect of high-entropy alloys is not applicable to magnetic entropy changes in these BMGs. Nevertheless, all BMGs in this study show good glass-forming ability and MCE which make them promising refrigerant candidates at cryogenic temperatures.

Anderson localization in the Anderson–Hubbard model with site-dependent interactions

We consider Anderson localization in the half-filled Anderson–Hubbard model in the presence of either random on-site interactions or spatially alternating interactions in the lattice. By using dynamical mean field theory with the equation of motion method as an impurity solver, we calculate the arithmetically and geometrically averaged local density of states and derive the equations determining the critical value for the phase transition between metallic, Anderson and Mott insulating phases. The nonmagnetic ground state phase diagrams are constructed numerically. We figure out that the presence of Coulomb disorder drives the system toward the Anderson localized phase that can occur even in the absence of Anderson structural disorder. For the spatially alternating interactions, we find that the metallic region is reduced and the Anderson insulator one is enlarged with increasing interaction modulation. Our obtained results are relevant to current research in ultracold atoms in disordered optical lattices where metal–insulator transition can be observed experimentally by using ultracold atom techniques.

Characterizing the dynamics and uncertainty of queues at signalized intersections with left-turn bay

In most signalized intersections, in order to solve the problem of insufficient road space, left-turn bays are commonly set up at intersections with a shared through and left-turn lane. However, this design tends to result in the potential queue overflow and blockage problems, which further make the discharge process of either left-turn vehicles or through vehicles at the intersections to be interrupted unexpectedly during their respective green phase. As a result, the queueing processes of vehicles present high nonlinearity and uncertainty during a signal cycle. In this paper, a stochastic queueing model is proposed to characterize the dynamics and uncertainty of queues at signalized intersections with a left-turn bay. The proposed model takes full account of the random interaction between the through movement and the left-turn movement under the influence of overflow and blockage of queues. We obtain some average performance indicators as well as the signal-state-dependent dynamic performance measure of queues and its variance at any given time point within a signal cycle. The proposed analytical model is validated against the VISSIM simulation model under different scenarios; the results show a good degree of agreement. In addition, in order to systematically determine the queue dynamics and uncertainty, we also conduct a series of numerical simulations to quantitatively capture the queue characteristics of vehicles at signalized intersections with left-turn bay by considering possible factors.