Stochastic Step Research Articles

Diffusion policy: Visuomotor policy learning via action diffusion

This paper introduces Diffusion Policy, a new way of generating robot behavior by representing a robot’s visuomotor policy as a conditional denoising diffusion process. We benchmark Diffusion Policy across 15 different tasks from 4 different robot manipulation benchmarks and find that it consistently outperforms existing state-of-the-art robot learning methods with an average improvement of 46.9%. Diffusion Policy learns the gradient of the action-distribution score function and iteratively optimizes with respect to this gradient field during inference via a series of stochastic Langevin dynamics steps. We find that the diffusion formulation yields powerful advantages when used for robot policies, including gracefully handling multimodal action distributions, being suitable for high-dimensional action spaces, and exhibiting impressive training stability. To fully unlock the potential of diffusion models for visuomotor policy learning on physical robots, this paper presents a set of key technical contributions including the incorporation of receding horizon control, visual conditioning, and the time-series diffusion transformer. We hope this work will help motivate a new generation of policy learning techniques that are able to leverage the powerful generative modeling capabilities of diffusion models. Code, data, and training details are available (diffusion-policy.cs.columbia.edu).

Structural Estimation of Markov Decision Processes in High-Dimensional State Space with Finite-Time Guarantees

Researchers have introduced a new algorithm to estimate structural models of dynamic decisions by human agents, addressing the challenge of high computational complexity. Traditionally, this task involves a nested structure: an inner problem identifying an optimal policy and an outer problem maximizing a measure of fit. Previous methods have struggled with large discrete state spaces or high-dimensional continuous state spaces, often sacrificing reward estimation accuracy. The new approach combines policy improvement with a stochastic gradient step for likelihood maximization, ensuring accurate reward estimation without compromising computational efficiency. This single-loop algorithm, designed to handle high-dimensional state spaces, converges to a stationary solution with finite-time guarantees. When the reward is linearly parameterized, it approximates the maximum likelihood estimator sublinearly, offering a robust solution for complex decision modeling tasks.

A stochastic algorithm for the ParaTuck decomposition

This paper introduces a novel stochastic algorithm for the ParaTuck Decomposition (PTD), addressing the challenge of local minima encountered in the traditional alternating least squares (ALS) approach. The proposed method integrates stochastic steps into the ALS framework to avoid the common swamp problems, where numerical difficulties prevent accurate decompositions. Our simulations indicate good convergence properties for PTD, suggesting a potential increase in the efficiency and reliability of this tensor decomposition across various applications.

AdaSAM: Boosting sharpness-aware minimization with adaptive learning rate and momentum for training deep neural networks

Sharpness aware minimization (SAM) optimizer has been extensively explored as it can generalize better for training deep neural networks via introducing extra perturbation steps to flatten the landscape of deep learning models. Integrating SAM with adaptive learning rate and momentum acceleration, dubbed AdaSAM, has already been explored empirically to train large-scale deep neural networks without theoretical guarantee due to the triple difficulties in analyzing the coupled perturbation step, adaptive learning rate and momentum step. In this paper, we try to analyze the convergence rate of AdaSAM in the stochastic non-convex setting. We theoretically show that AdaSAM admits a O(1/bT) convergence rate, which achieves linear speedup property with respect to mini-batch size b. Specifically, to decouple the stochastic gradient steps with the adaptive learning rate and perturbed gradient, we introduce the delayed second-order momentum term to decompose them to make them independent while taking an expectation during the analysis. Then we bound them by showing the adaptive learning rate has a limited range, which makes our analysis feasible. To the best of our knowledge, we are the first to provide the non-trivial convergence rate of SAM with an adaptive learning rate and momentum acceleration. At last, we conduct several experiments on several NLP tasks and the synthetic task, which show that AdaSAM could achieve superior performance compared with SGD, AMSGrad, and SAM optimizers.

Finite-time convergence rates of distributed local stochastic approximation

We consider a distributed learning framework, where there are a group of agents communicating with a centralized coordinator. The goal of the agents is to find the root of an operator composed of the local operators at the agents. Such a framework models many practical problems in different areas, including those in federated learning and reinforcement learning. For solving this problem, we study the popular distributed stochastic approximation. Over a series of time epoch, each agent runs a number of local stochastic approximation steps based on its own data, whose results are then aggregated at the centralized coordinator.Existing theoretical guarantees for the finite-time performance of local stochastic approximation are studied under the common assumption that the local data at each agent is sampled i.i.d. Such an assumption may not hold in many applications, where the data are temporally dependent, for example, they are sampled from some dynamical systems. In this paper, we study the setting where the data are generated from Markov random processes, which are often used to model the systems in stochastic control and reinforcement learning. Our main contribution is to characterize the finite-time performance of the local stochastic approximation under this setting. We provide explicit formulas for the rates of this method for both constant and time-varying step sizes when the local operators are strongly monotone. Our results show that these rates are within a logarithmic factor of the comparable bounds under independent data. We also provide a number of numerical simulations to illustrate our theoretical results by applying local SA in solving problems in robust identification and reinforcement learning over multi-agent systems.

Rapid and Automated Ab Initio Metabolite Collisional Cross Section Prediction from SMILES Input.

We implemented an ab initio CCS prediction workflow which incrementally refines generated structures using molecular mechanics, a deep learning potential, conformational clustering, and quantum mechanics (QM). Automating intermediate steps for a high performance computing (HPC) environment allows users to input the SMILES structure of small organic molecules and obtain a Boltzmann averaged collisional cross section (CCS) value as output. The CCS of a molecular species is a metric measured by ion mobility spectrometry (IMS) which can improve annotation of untargeted metabolomics experiments. We report only a minor drop in accuracy when we expedite the CCS calculation by replacing the QM geometry refinement step with a single-point energy calculation. Even though the workflow involves stochastic steps (i.e., conformation generation and clustering), the final CCS value was highly reproducible for multiple iterations on L-carnosine. Finally, we illustrate that the gas phase ensembles modeled for the workflow are intermediate files which can be used for the prediction of other properties such as aqueous phase nuclear magnetic resonance chemical shift prediction. The software is available at the following link: https://github.com/DasSusanta/snakemake_ccs.

The role of local steps in local SGD

We consider the distributed stochastic optimization problem where n agents want to minimize a global function given by the sum of agents' local functions and focus on the heterogeneous setting when agents' local functions are defined over non-i.i.d. datasets. We study the Local SGD method, where agents perform a number of local stochastic gradient steps and occasionally communicate with a central node to improve their local optimization tasks. We analyze the effect of local steps on the convergence rate and the communication complexity of Local SGD. In particular, instead of assuming a fixed number of local steps across all communication rounds, we allow the number of local steps during the jth communication round, , to be different and arbitrary numbers. Our main contribution is to characterize the convergence rate of Local SGD as a function of under various settings of strongly convex, convex, and nonconvex local functions, where R is the total number of communication rounds. Based on this characterization, we provide sufficient conditions on the sequence such that Local SGD can achieve linear speedup with respect to the number of workers. Furthermore, we propose a new communication strategy with increasing local steps that is superior to constant local steps for strongly convex local functions. On the other hand, for convex and nonconvex local functions, we argue that fixed local steps are the best communication strategy for Local SGD and recover state-of-the-art convergence rate results. Finally, we justify our theoretical results through extensive numerical experiments.

Simulations suggest robust microtubule attachment of kinesin and dynein in antagonistic pairs

Intracellular transport is propelled by kinesin and cytoplasmic dynein motors that carry membrane-bound vesicles and organelles bidirectionally along microtubule tracks. Much is known about these motors at the molecular scale, but many questions remain regarding how kinesin and dynein cooperate and compete during bidirectional cargo transport at the cellular level. The goal of the present study was to use a stochastic stepping model constructed by using published load-dependent properties of kinesin-1 and dynein-dynactin-BicD2 (DDB) to identify specific motor properties that determine the speed, directionality, and transport dynamics of a cargo carried by one kinesin and one dynein motor. Model performance was evaluated by comparing simulations to recently published experiments of kinesin-DDB pairs connected by complementary oligonucleotide linkers. Plotting the instantaneous velocity distributions from kinesin-DDB experiments revealed a single peak centered around zero velocity. In contrast, velocity distributions from simulations displayed a central peak around 100 nm/s, along with two side peaks corresponding to the unloaded kinesin and DDB velocities. We hypothesized that frequent motor detachment events and relatively slow motor reattachment rates resulted in periods in which only one motor is attached. To investigate this hypothesis, we varied specific model parameters and compared the resulting instantaneous velocity distributions, and we confirmed this systematic investigation using a machine-learning approach that minimized the residual sum of squares between the experimental and simulation velocity distributions. The experimental data were best recapitulated by a model in which the kinesin and dynein stall forces are matched, the motor detachment rates are independent of load, and the kinesin-1 reattachment rate is 50 s−1. These results provide new insights into motor dynamics during bidirectional transport and put forth hypotheses that can be tested by future experiments.

Network revenue management with online inverse batch gradient descent method

We consider a general class of price‐based network revenue management problems that a firm aims to maximize revenue from multiple products produced with multiple types of resources endowed with limited inventory over a finite selling season. A salient feature of our problem is that the firm does not know the underlying demand function that maps prices to demand rate, which must be learned from sales data. It is well known that for almost all classes of demand functions, such as linear, exponential, multinomial logit, and nested logit models, the revenue rate function is not concave in the products' prices but is concave in products' market shares (or price‐controlled demand rates). This creates challenges in adopting any stochastic gradient descent based methods in the price space. We propose a novel nonparametric learning algorithm termed the online inverse batch gradient descent (IGD) algorithm. This algorithm proceeds in batches. In each batch, the firm implements each product's perturbed prices and then uses the sales information to estimate the market shares. Leveraging these estimates, the firm carries out a stochastic gradient descent step in the market share space that takes into account the relative inventory scarcity for the entire horizon and then inversely maps the updated market shares back to the price space to obtain the prices for the next batch. Moreover, we also propose an inventory‐adjusted algorithm (IGD‐I) that the feasible market share set is dynamically adjusted to capture the real‐time relative inventory scarcity for the remaining season. For the large‐scale systems wherein all resources' inventories and the length of the horizon are proportionally scaled by a parameter k, we establish a dimension‐independent regret bound of [Formula: see text]. This result is independent of the number of products and resources and works for a continuum action‐set prices and the demand functions that are only once differentiable. Our theoretical result guarantees the efficacy of both algorithms in the high‐dimensional systems where the number of products or resources is large and the prices are continuous. Our algorithms also numerically outperform the existing algorithms in the literature.

Mini-batch stochastic subgradient for functional constrained optimization

In this paper, we consider finite sum composite optimization problems with many functional constraints. The objective function is expressed as a finite sum of two terms, one of which admits easy computation of (sub)gradients while the other is amenable to proximal evaluations. We assume a generalized bounded gradient condition on the objective which allows us to simultaneously tackle both smooth and nonsmooth problems. We also consider the cases of both with and without a quadratic functional growth property. Further, we assume that each constraint set is given as the level set of a convex but not necessarily a differentiable function. We reformulate the constrained finite sum problem into a stochastic optimization problem for which the stochastic subgradient projection method from Necoara and Singh [Stochastic subgradient projection methods for composite optimization with functional constraints; 2022 Journal of Machine Learning Research, 23, 1–35] specializes in a collection of mini-batch variants, with different mini-batch sizes for the objective function and functional constraints, respectively. More specifically, at each iteration, our algorithm takes a mini-batch stochastic proximal subgradient step aimed at minimizing the objective function and then a subsequent mini-batch subgradient projection step minimizing the feasibility violation. By specializing in different mini-batching strategies, we derive exact expressions for the stepsizes as a function of the mini-batch size and in some cases we also derive insightful stepsize-switching rules which describe when one should switch from a constant to a decreasing stepsize regime. We also prove sublinear convergence rates for the mini-batch subgradient projection algorithm which depend explicitly on the mini-batch sizes and on the properties of the objective function. Numerical results also show a better performance of our mini-batch scheme over its single-batch counterpart.

Kinesin-1, -2 and -3 use family-specific mechanochemical strategies to effectively compete with dynein during bidirectional transport.

Bidirectional cargo transport in neurons requires competing activity of motors from the kinesin-1, -2 and -3 superfamilies against cytoplasmic dynein-1. Previous studies demonstrated that when kinesin-1 attached to dynein-dynactin-BicD2 (DDB) complex, the tethered motors move slowly with a slight plus-end bias, suggesting kinesin-1 overpowers DDB but DDB generates a substantial hindering load. Compared to kinesin-1, motors from the kinesin-2 and -3 families display a higher sensitivity to load in single-molecule assays and are thus predicted to be overpowered by dynein complexes in cargo transport. To test this prediction, we used a DNA scaffold to pair DDB with members of the kinesin-1, -2 and -3 families to recreate bidirectional transport in vitro, and tracked the motor pairs using two-channel TIRF microscopy. Unexpectedly, we find that when both kinesin and dynein are engaged and stepping on the microtubule, kinesin-1, -2, and -3 motors are able to effectively withstand hindering loads generated by DDB. Stochastic stepping simulations reveal that kinesin-2 and -3 motors compensate for their faster detachment rates under load with faster reattachment kinetics. The similar performance between the three kinesin transport families highlights how motor kinetics play critical roles in balancing forces between kinesin and dynein, and emphasizes the importance of motor regulation by cargo adaptors, regulatory proteins, and the microtubule track for tuning the speed and directionality of cargo transport in cells.

PARS-Push: Personalized, Asynchronous and Robust Decentralized Optimization

We study the multi-step Model-Agnostic Meta-Learning (MAML) framework where a group of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> agents seeks to find a common point that enables “few-shot” learning (personalization) via local stochastic gradient steps on their local functions. We formulate the personalized optimization problem under the MAML framework and propose PARS-Push, a decentralized asynchronous algorithm robust to message failures, communication delays, and directed message sharing. We characterize the convergence rate of PARS-Push under arbitrary multi-step personalization for smooth strongly convex, and smooth non-convex functions. Moreover, we provide numerical experiments showing its performance under heterogeneous data setups.

Training Variational Quantum Circuits with CoVaR: Covariance Root Finding with Classical Shadows

Exploiting near-term quantum computers and achieving practical value is a considerable and exciting challenge. Most prominent candidates as variational algorithms typically aim to find the ground state of a Hamiltonian by minimising a single classical (energy) surface which is sampled from by a quantum computer. Here we introduce a method we call CoVaR, an alternative means to exploit the power of variational circuits: We find eigenstates by finding joint roots of a polynomially growing number of properties of the quantum state as covariance functions between the Hamiltonian and an operator pool of our choice. The most remarkable feature of our CoVaR approach is that it allows us to fully exploit the extremely powerful classical shadow techniques, i.e., we simultaneously estimate a very large number $>10^4-10^7$ of covariances. We randomly select covariances and estimate analytical derivatives at each iteration applying a stochastic Levenberg-Marquardt step via a large but tractable linear system of equations that we solve with a classical computer. We prove that the cost in quantum resources per iteration is comparable to a standard gradient estimation, however, we observe in numerical simulations a very significant improvement by many orders of magnitude in convergence speed. CoVaR is directly analogous to stochastic gradient-based optimisations of paramount importance to classical machine learning while we also offload significant but tractable work onto the classical processor.

Kinesin-1, -2, and -3 motors use family-specific mechanochemical strategies to effectively compete with dynein during bidirectional transport.

Bidirectional cargo transport in neurons requires competing activity of motors from the kinesin-1, -2, and -3 superfamilies against cytoplasmic dynein-1. Previous studies demonstrated that when kinesin-1 attached to dynein-dynactin-BicD2 (DDB) complex, the tethered motors move slowly with a slight plus-end bias, suggesting kinesin-1 overpowers DDB but DDB generates a substantial hindering load. Compared to kinesin-1, motors from the kinesin-2 and -3 families display a higher sensitivity to load in single-molecule assays and are thus predicted to be overpowered by dynein complexes in cargo transport. To test this prediction, we used a DNA scaffold to pair DDB with members of the kinesin-1, -2, and -3 families to recreate bidirectional transport in vitro, and tracked the motor pairs using two-channel TIRF microscopy. Unexpectedly, we find that when both kinesin and dynein are engaged and stepping on the microtubule, kinesin-1, -2, and -3 motors are able to effectively withstand hindering loads generated by DDB. Stochastic stepping simulations reveal that kinesin-2 and -3 motors compensate for their faster detachment rates under load with faster reattachment kinetics. The similar performance between the three kinesin transport families highlights how motor kinetics play critical roles in balancing forces between kinesin and dynein, and emphasizes the importance of motor regulation by cargo adaptors, regulatory proteins, and the microtubule track for tuning the speed and directionality of cargo transport in cells.

Non-stationary response determination of nonlinear systems subjected to combined deterministic and evolutionary stochastic excitations

A semi-analytical method is proposed for determining the response of a lightly damped single-degree-of-freedom nonlinear system subjected to combined deterministic and non-stationary stochastic excitations. This is attained by combining the stochastic averaging and statistical linearization methodologies. Specifically, first, the system response is decomposed into two components, namely the deterministic and the stochastic parts. This leads to a set of coupled differential sub-equations governing, respectively, the deterministic and the stochastic component of the response. Next, aiming at solving the set of differential sub-equations, an additional expression is derived by applying the statistical linearization methodology, followed by the application of a stochastic averaging step to the stochastic sub-equations. Therefore, an equivalent time-varying linear system is defined for the original nonlinear system. The stochastic averaging method is then applied to the linearized system for reducing its order, and thus, its complexity from a solution perspective. In this regard, an additional equation is derived, which connects the deterministic and stochastic components of the response. The latter and the deterministic differential sub-equations are solved simultaneously for determining the system response. A single-degree-of-freedom nonlinear system exhibiting quadratic and cubic nonlinear stiffness is considered for assessing the reliability of the proposed technique. The obtained results are compared with pertinent Monte-Carlo simulation estimates.

Extensions of the deep Galerkin method

We extend the Deep Galerkin Method (DGM) introduced in Sirignano and Spiliopoulos(2018)[25] to solve a number of partial differential equations (PDEs) that arise in the context of optimal stochastic control and mean field games. First, we consider PDEs where the function is constrained to be positive and integrate to unity, as is the case with Fokker–Planck equations. Our approach involves reparameterizing the solution as the exponential of a neural network appropriately normalized to ensure both requirements are satisfied. This then gives rise to nonlinear a partial integro-differential equation (PIDE) where the integral appearing in the equation is handled by a novel application of importance sampling. Secondly, we tackle a number of Hamilton–Jacobi–Bellman (HJB) equations that appear in stochastic optimal control problems. The key contribution is that these equations are approached in their unsimplified primal form which includes an optimization problem as part of the equation. We extend the DGM algorithm to solve for the value function and the optimal control simultaneously by characterizing both as deep neural networks. Training the networks is performed by taking alternating stochastic gradient descent steps for the two functions, a technique inspired by the policy improvement algorithms (PIA).

Multiple molecular events underlie stochastic switching between 2 heritable cell states in fungi.

Eukaryotic transcriptional networks are often large and contain several levels of feedback regulation. Many of these networks have the ability to generate and maintain several distinct transcriptional states across multiple cell divisions and to switch between them. In certain instances, switching between cell states is stochastic, occurring in a small subset of cells of an isogenic population in a seemingly homogenous environment. Given the scarcity and unpredictability of switching in these cases, investigating the determining molecular events is challenging. White-opaque switching in the fungal species Candida albicans is an example of stably inherited cell states that are determined by a complex transcriptional network and can serve as an experimentally accessible model system to study characteristics important for stochastic cell fate switching in eukaryotes. In standard lab media, genetically identical cells maintain their cellular identity (either "white" or "opaque") through thousands of cell divisions, and switching between the states is rare and stochastic. By isolating populations of white or opaque cells, previous studies have elucidated the many differences between the 2 stable cell states and identified a set of transcriptional regulators needed for cell type switching and maintenance of the 2 cell types. Yet, little is known about the molecular events that determine the rare, stochastic switching events that occur in single cells. We use microfluidics combined with fluorescent reporters to directly observe rare switching events between the white and opaque states. We investigate the stochastic nature of switching by beginning with white cells and monitoring the activation of Wor1, a master regulator and marker for the opaque state, in single cells and throughout cell pedigrees. Our results indicate that switching requires 2 stochastic steps; first an event occurs that predisposes a lineage of cells to switch. In the second step, some, but not all, of those predisposed cells rapidly express high levels of Wor1 and commit to the opaque state. To further understand the rapid rise in Wor1, we used a synthetic inducible system in Saccharomyces cerevisiae into which a controllable C. albicans Wor1 and a reporter for its transcriptional control region have been introduced. We document that Wor1 positive autoregulation is highly cooperative (Hill coefficient > 3), leading to rapid activation and producing an "all or none" rather than a graded response. Taken together, our results suggest that reaching a threshold level of a master regulator is sufficient to drive cell type switching in single cells and that an earlier molecular event increases the probability of reaching that threshold in certain small lineages of cells. Quantitative molecular analysis of the white-opaque circuit can serve as a model for the general understanding of complex circuits.

Gas Diffusion Layers: Experimental and Modeling Approach for Morphological and Transport Properties

ConspectusElectrochemical technologies are key to decarbonizing the energy sector. Electrification of the energy sector is underway with battery technologies dominating the light-duty electric vehicles market. It is more challenging to decarbonize historically difficult to decarbonize sectors, such as heavy-duty transportation, planes, ships, and the chemical manufacturing industry (ammonia, cement, steel). Green hydrogen produced via electrolysis will be used as a fuel and a feedstock in some of these processes. At the heart of the hydrogen economy are polymer electrolyte fuel cells (PEFCs), devices that convert hydrogen into electricity. Gas diffusion layers (GDLs) have an integral role in PEFCs, as they are porous carbon layers that transport reactants and products and also remove heat and conduct electricity. To improve the PEFCs’ performance and reduce degradation of materials, an understanding of coupled morphological properties and transport phenomena in the GDLs is needed. In this Account, we emphasize the integration of experimental and modeling approaches to achieve complete understanding of materials and transport properties of the GDLs. Our approach builds in complexity from simpler ex situ experiments to in situ and last to 3-D integrated modeling predictions. GDL morphology is complex, as its fabrication includes several stochastic steps (immersion of GDL in various baths to achieve the desired surface wettability) and only 3-D techniques, such as X-ray computed tomography can capture morphology correctly. Porosity, pore-size distribution, tortuosity, and formation factor are the most important morphological properties of the GDLs. For PEFC applications, water is generated in the catalyst layers and is transported through the GDLs. Therefore, GDL wettability directly impacts water permeability through the GDLs. Using in situ water injection experiments, we directly observe which pores water fill at what liquid pressure. This result provides information about the GDL’s affinity to intake water. GDLs are typically of mixed wettabilities, and internal wettability until recently has been unknown. Having images of water inside the GDL enabled us to track the triple-phase boundary at the fiber–water–air interface to obtain local contact angles in the locations where water was present. The percentage of contact angles that were hydrophilic correlated well to the percentage of surface oxides on the GDL surface using X-ray photoelectron spectroscopy (XPS). We envision many other groups using the method of XPS to determine internal surface wettability of the GDLs, as it is relatively fast. Heat transport and evaporation/condensation of water in the GDL is studied using in situ X-ray CT experiments. These provide direct insight into pore-scale water transport under thermal gradients. Three-dimensional geometries of GDLs are exported for transport simulations using the lattice Boltzmann method (LBM). Similarly, we advocate for building the LBM simulations, from water injection studies first to validate the model only to operando PEFC models later. LBM coupling with a continuum model enables a computational saving, allowing us to map local temperature, reactant, and product distributions in the GDLs.

Random-walk model of the sodium-glucose transporter SGLT2 with stochastic steps and inhibition

Random-walk models are frequently used to model distinct natural phenomena such as diffusion processes, stock-market fluctuations, and biological systems. Here, we present a random-walk model to describe the dynamics of glucose uptake by the sodium-glucose transporter of type 2, SGLT2. Our starting point is the canonical alternating-access model, which suggests the existence of six states for the transport cycle. We propose the inclusion of two new states to this canonical model. The first state is added to implement the recent discovery that the Na+ ion can exit before the sugar is released into the proximal tubule epithelial cells. The resulting model is a seven-state mechanism with stochastic steps. Then we determined the transition probabilities between these seven states and used them to write a set of master equations to describe the time evolution of the system. We showed that our model converges to the expected equilibrium configuration and that the binding of Na+ and glucose to SGLT2 in the inward-facing conformation must be necessarily unordered. After that, we added another state to implement inhibition in the model. Our results reproduce the experimental dependence of glucose uptake on the inhibitor concentration and they reveal that the inhibitors act by decreasing the number of available SGLT2s, which increases the chances of glucose escaping reabsorption.

Unusual domain growth during local switching in triglycine sulfate crystals

Formation and growth of isolated lenticular domains created by local switching using a biased tip of the scanning probe microscope in nominally pure triglycine sulfate single crystals have been studied experimentally. The obtained unusual change in the domain shape during growth has been considered in terms of a kinetic approach and attributed to simultaneous stochastic step generation for domain widening and deterministic nucleation (step generation at the domain vertices) for domain elongation. The main parameters of the domain wall motion have been extracted by fitting of the field dependence of the domain length and width. The obtained results provide a useful insight into the features of the domain structure kinetics in the uniaxial ferroelectrics and can be used for development of the domain engineering methods.