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Neural networks are known to be susceptible to adversarial samples: small variations of natural examples crafted to deliberately mislead the models. While they can be easily generated using gradient-based techniques in digital and physical scenarios, they often differ greatly from the actual data distribution of natural images, resulting in a trade-off between strength and stealthiness. In this paper, we propose a novel framework dubbed Diffusion-Based Projected Gradient Descent (Diff-PGD) for generating realistic adversarial samples. By exploiting a gradient guided by a diffusion model, Diff-PGD ensures that adversarial samples remain close to the original data distribution while maintaining their effectiveness. Moreover, our framework can be easily customized for specific tasks such as digital attacks, physical-world attacks, and style-based attacks. Compared with existing methods for generating natural-style adversarial samples, our framework enables the separation of optimizing adversarial loss from other surrogate losses (e.g., content/smoothness/style loss), making it more stable and controllable. Finally, we demonstrate that the samples generated using Diff-PGD have better transferability and anti-purification power than traditional gradient-based methods. Code will be released in https://github.com/xavihart/Diff-PGD, Comment: code repo: https://github.com/xavihart/Diff-PGD

We present DiffCollage, a compositional diffusion model that can generate large content by leveraging diffusion models trained on generating pieces of the large content. Our approach is based on a factor graph representation where each factor node represents a portion of the content and a variable node represents their overlap. This representation allows us to aggregate intermediate outputs from diffusion models defined on individual nodes to generate content of arbitrary size and shape in parallel without resorting to an autoregressive generation procedure. We apply DiffCollage to various tasks, including infinite image generation, panorama image generation, and long-duration text-guided motion generation. Extensive experimental results with a comparison to strong autoregressive baselines verify the effectiveness of our approach., Comment: CVPR 2023 project page https://research.nvidia.com/labs/dir/diffcollage

In this work we approach the dual optimal reach-safe control problem using sparse approximations of Koopman operator. Matrix approximation of Koopman operator needs to solve a least-squares (LS) problem in the lifted function space, which is computationally intractable for fine discretizations and high dimensions. The state transitional physical meaning of the Koopman operator leads to a sparse LS problem in this space. Leveraging this sparsity, we propose an efficient method to solve the sparse LS problem where we reduce the problem dimension dramatically by formulating the problem using only the non-zero elements in the approximation matrix with known sparsity pattern. The obtained matrix approximation of the operators is then used in a dual optimal reach-safe problem formulation where a linear program with sparse linear constraints naturally appears. We validate our proposed method on various dynamical systems and show that the computation time for operator approximation is greatly reduced with high precision in the solutions.

A paradigm put forth by E. Schr\"odinger in 1931/32, known as Schr\"odinger bridges, represents a formalism to pose and solve control and estimation problems seeking a perturbation from an initial control schedule (in the case of control), or from a prior probability law (in the case of estimation), sufficient to reconcile data in the form of marginal distributions and minimal in the sense of relative entropy to the prior. In the same spirit, we consider traffic-flow and apply a Schr\"odinger-type dictum, to perturb minimally with respect to a suitable relative entropy functional a prior schedule/law so as to reconcile the traffic flow with scarce aggregate distributions on families of indistinguishable individuals. Specifically, we consider the problem to regulate/estimate multi-commodity network flow rates based only on empirical distributions of commodities being transported (e.g., types of vehicles through a network, in motion) at two given times. Thus, building on Schr\"odinger's large deviation rationale, we develop a method to identify {\em the most likely flow rates (traffic flow)}, given prior information and aggregate observations. Our method further extends the Schr\"odinger bridge formalism to the multi-commodity setting, allowing commodities to exit or enter the flow field as well (e.g., vehicles to enter and stop and park) at any time. The behavior of entering or exiting the flow field, by commodities or vehicles, is modeled by a Markov chains with killing and creation states. Our method is illustrated with a numerical experiment., Comment: 12 pages, 5 figures

This paper is concerned with data-driven optimal control of nonlinear systems. We present a convex formulation to the optimal control problem (OCP) with a discounted cost function. We consider OCP with both positive and negative discount factor. The convex approach relies on lifting nonlinear system dynamics in the space of densities using the linear Perron-Frobenius (P-F) operator. This lifting leads to an infinite-dimensional convex optimization formulation of the optimal control problem. The data-driven approximation of the optimization problem relies on the approximation of the Koopman operator using the polynomial basis function. We write the approximate finite-dimensional optimization problem as a polynomial optimization which is then solved efficiently using a sum-of-squares-based optimization framework. Simulation results are presented to demonstrate the efficacy of the developed data-driven optimal control framework.

Graph convolutional networks (GCNs) and its variants are designed for unsigned graphs containing only positive links. Many existing GCNs have been derived from the spectral domain analysis of signals lying over (unsigned) graphs and in each convolution layer they perform low-pass filtering of the input features followed by a learnable linear transformation. Their extension to signed graphs with positive as well as negative links imposes multiple issues including computational irregularities and ambiguous frequency interpretation, making the design of computationally efficient low pass filters challenging. In this paper, we address these issues via spectral analysis of signed graphs and propose two different signed graph neural networks, one keeps only low-frequency information and one also retains high-frequency information. We further introduce magnetic signed Laplacian and use its eigendecomposition for spectral analysis of directed signed graphs. We test our methods for node classification and link sign prediction tasks on signed graphs and achieve state-of-the-art performances.

We study the proximal sampler of Lee, Shen, and Tian (2021) and obtain new convergence guarantees under weaker assumptions than strong log-concavity: namely, our results hold for (1) weakly log-concave targets, and (2) targets satisfying isoperimetric assumptions which allow for non-log-concavity. We demonstrate our results by obtaining new state-of-the-art sampling guarantees for several classes of target distributions. We also strengthen the connection between the proximal sampler and the proximal method in optimization by interpreting the proximal sampler as an entropically regularized Wasserstein proximal method, and the proximal point method as the limit of the proximal sampler with vanishing noise., Comment: 34 pages

We consider the problem of navigation with safety constraints. The safety constraints are probabilistic, where a given set is assigned a degree of safety, a number between zero and one, with zero being safe and one being unsafe. The deterministic unsafe set will arise as a particular case of the proposed probabilistic description of safety. We provide a convex formulation to the navigation problem with probabilistic safety constraints. The convex formulation is made possible by lifting the navigation problem in the dual space of density using linear transfer operator theory methods involving Perron-Frobenius and Koopman operators. The convex formulation leads to an infinite-dimensional feasibility problem for probabilistic safety verification and control design. The finite-dimensional approximation of the optimization problem relies on the data-driven approximation of the linear transfer operator.

The past few years have witnessed the great success of Diffusion models~(DMs) in generating high-fidelity samples in generative modeling tasks. A major limitation of the DM is its notoriously slow sampling procedure which normally requires hundreds to thousands of time discretization steps of the learned diffusion process to reach the desired accuracy. Our goal is to develop a fast sampling method for DMs with a much less number of steps while retaining high sample quality. To this end, we systematically analyze the sampling procedure in DMs and identify key factors that affect the sample quality, among which the method of discretization is most crucial. By carefully examining the learned diffusion process, we propose Diffusion Exponential Integrator Sampler~(DEIS). It is based on the Exponential Integrator designed for discretizing ordinary differential equations (ODEs) and leverages a semilinear structure of the learned diffusion process to reduce the discretization error. The proposed method can be applied to any DMs and can generate high-fidelity samples in as few as 10 steps. In our experiments, it takes about 3 minutes on one A6000 GPU to generate $50k$ images from CIFAR10. Moreover, by directly using pre-trained DMs, we achieve the state-of-art sampling performance when the number of score function evaluation~(NFE) is limited, e.g., 4.17 FID with 10 NFEs, 3.37 FID, and 9.74 IS with only 15 NFEs on CIFAR10. Code is available at https://github.com/qsh-zh/deis, Comment: iclr camera ready,https://github.com/qsh-zh/deis

We consider the problem of optimal navigation control design for navigation on off-road terrain. We use traversability measure to characterize the degree of difficulty of navigation on the off-road terrain. The traversability measure captures the property of terrain essential for navigation, such as elevation map, terrain roughness, slope, and terrain texture. The terrain with the presence or absence of obstacles becomes a particular case of the proposed traversability measure. We provide a convex formulation to the off-road navigation problem by lifting the problem to the density space using the linear Perron-Frobenius (P-F) operator. The convex formulation leads to an infinite-dimensional optimal navigation problem for control synthesis. The finite-dimensional approximation of the infinite-dimensional convex problem is constructed using data. We use a computational framework involving the Koopman operator and the duality between the Koopman and P-F operator for the data-driven approximation. This makes our proposed approach data-driven and can be applied in cases where an explicit system model is unavailable. Finally, we demonstrate the application of the developed framework for the navigation of vehicle dynamics with Dubin's car model.

Website fingerprinting attack (WFA) aims to deanonymize the website a user is visiting through anonymous networks channels (e.g., Tor). Despite of remarkable progress in the past years, most existing methods make implicitly a couple of artificial assumptions that (1) only a single website (i.e., single-tab) is visited each time, and (2) website fingerprinting data are pre-trimmed into a single trace per website manually. In reality, a user often open multiple tabs for multiple websites spontaneously. Indeed, this multi-tab WFA (MT-WFA) setting has been studied in a few recent works, but all of them still fail to fully respect the real-world situations. In particular, the overlapping challenge between website fingerprinting has never been investigated in depth. In this work, we redefine the problem of MT-WFA as detecting multiple monitored traces, given a natural untrimmed traffic data including monitored traces, unmonitored traces, and potentially unconstrained overlapping between them. This eliminates the above assumptions, going beyond the conventional single website fingerprint classification perspective taken by all previous WFA methods. To tackle this realistic MT-WFA problem, we formulate a novel Website Fingerprint Detection (WFD) model capable of detecting accurately the start and end points of all the monitored traces and classifying them jointly, given long, untrimmed raw traffic data. WFD is end-to-end, with the trace localization and website classification integrated in a single unified pipeline. To enable quantitative evaluation in our MT-WFA setting, we introduce new performance metrics. Extensive experiments on several newly constructed benchmarks show that our WFD outperforms the state-of-the-art alternative methods in both accuracy and efficiency by a large margin, even with a very small training set. Code is available at https://github.com/WFDetector/WFDetection, Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible

In the present paper, we study the power output and efficiency of overdamped stochastic thermodynamic engines that are in contact with a heat bath having a temperature that varies periodically with time. This is in contrast to most of the existing literature that considers the Carnot paradigm of alternating contact with heat baths having different fixed temperatures, hot and cold. Specifically, we consider a periodic and bounded but otherwise arbitrary temperature profile and derive explicit bounds on the power and efficiency achievable by a suitable controlling potential that couples the thermodynamic engine to the external world. Standing assumptions in our analysis are bounds on the norm of the gradient of effective potentials -- in the absence of any such constraint, the physically questionable conclusion of arbitrarily large power can be drawn., Comment: 14 pages

Additional file 1: Figure S1. Influence of difference in the sepsis definitions on the results of the meta-analysis.

We consider inference problems for a class of continuous state collective hidden Markov models, where the data is recorded in aggregate (collective) form generated by a large population of individuals following the same dynamics. We propose an aggregate inference algorithm called collective Gaussian forward-backward algorithm, extending recently proposed Sinkhorn belief propagation algorithm to models characterized by Gaussian densities. Our algorithm enjoys convergence guarantee. In addition, it reduces to the standard Kalman filter when the observations are generated by a single individual. The efficacy of the proposed algorithm is demonstrated through multiple experiments.

BACKGROUNDInfiltrating ductal carcinoma (IDCA) is the most common form of invasive breast cancer. Immunohistochemistry (IHC) is widely used to analyze estrogen receptor 1 (ER), progesterone receptor (PR), and human epidermal growth factor receptor 2 (HER2) that can help classify the tumor to guide the medical treatment. IHC examinations require experienced pathologists to provide interpretations that are subjective, thereby lowering the reproducibility of IHC-based diagnosis. In this study, we developed a 4-plex droplet digital PCR (ddPCR) for the simultaneous and quantitative analyses of estrogen receptor 1 (ESR1), progesterone receptor (PGR), erb-b2 receptor tyrosine kinase 2 (ERBB2), and pumilio RNA binding family member 1 (PUM1) expression levels in formalin-fixed paraffin-embedded (FFPE) samples.METHODSWe evaluated the sensitivity, reproducibility, and linear dynamic range of 4-plex ddPCR. We applied this method to analyze 95 FFPE samples from patients with breast IDCA and assessed the agreement rates between ddPCR and IHC to evaluate its potential in classifying breast cancer subtypes.RESULTSThe limits of quantification (LOQ) were 25, 50, 50, and 50 copies per reaction for ERBB2, ESR1, PGR, and PUM1, respectively. The dynamic ranges of ESR1, PGR, and PUM1 extended over 50–1600 copies per reaction and those of ERBB2 from 25 to 1600 copies per reaction. The concordance correlation coefficients between 4-plex ddPCR and IHC were 96.8%, 91.5%, and 85.1% for ERBB2, ESR1, and PGR, respectively. Receiver operating characteristic curve area under the curve values of 0.991, 0.977, and 0.920 were generated for ERBB2, ESR1, and PGR, respectively.CONCLUSIONSEvaluation of breast cancer biomarker status by 4-plex ddPCR was highly concordant with IHC in this study.

At present, S-lay method is widely used as an important deep-sea submarine pipe laying method. As the key equipment that has been in complex marine environment all the year round, the stinger is subjected to extremely complex environmental loads and working loads, which have great influence on its safety. Therefore, the real-time dynamic monitoring for the stinger to get the health information, to ensure the structural safety has been obvious engineering value. In this paper, a structural health monitoring system of the stinger is suggested. The scheme and the monitoring equipment of the monitoring system have been established and the sea tests were carried out during actual operations. Through the analysis of monitoring data, the structural response characteristics in operation state and navigation state were determined, and the fatigue characteristics of the stinger structure were obtained. By comparing with the conventional fatigue analysis method, it was found that some different between the fatigue characteristics based on the measured data and the theoretical analysis.

We present a new particle filtering algorithm for nonlinear systems in the discrete-time setting. Our algorithm is based on the Stein variational gradient descent (SVGD) framework, which is a general approach to sample from a target distribution. We merge the standard two-step paradigm in particle filtering into one step so that SVGD can be used. A distinguishing feature of the proposed algorithm is that, unlike most particle filtering methods, all the particles at any time step are equally weighted and thus no update on the weights is needed. We further extended our algorithm to allow for updating previous particles within a sliding window. This strategy may improve the reliability of the algorithm with respect to unexpected disturbance in the dynamics or outlier-measurements. The efficacy of the proposed algorithms is illustrated through several numerical examples in comparison with a standard particle filtering method., Comment: 6 pages

We consider the covariance steering problem for nonlinear control-affine systems. Our objective is to find an optimal control strategy to steer the state of a system from an initial distribution to a target one whose mean and covariance are given. Due to the nonlinearity, the existing techniques for linear covariance steering problems are not directly applicable. By leveraging the celebrated Girsanov theorem, we formulate the problem into an optimization over the space path distributions. We then adopt a generalized proximal gradient algorithm to solve this optimization, where each update requires solving a linear covariance steering problem. Our algorithm is guaranteed to converge to a local optimal solution with a sublinear rate. In addition, each iteration of the algorithm can be achieved in closed form, and thus the computational complexity of it is insensitive to the resolution of time-discretization. In the examples, our method achieves 1000 times speedup over an existing algorithm., Comment: 8 pages

In this work, we develop a new framework for dynamic network flow problems based on optimal transport theory. We show that the dynamic multi-commodity minimum-cost network flow problem can be formulated as a multi-marginal optimal transport problem, where the cost function and the constraints on the marginals are associated with a graph structure. By exploiting these structures and building on recent advances in optimal transport theory, we develop an efficient method for such entropy-regularized optimal transport problems. In particular, the graph structure is utilized to efficiently compute the projections needed in the corresponding Sinkhorn iterations, and we arrive at a scheme that is both highly computationally efficient and easy to implement. To illustrate the performance of our algorithm, we compare it with a state-of-the-art Linear programming (LP) solver. We achieve good approximations to the solution at least one order of magnitude faster than the LP solver. Finally, we showcase the methodology on a traffic routing problem with a large number of commodities., Comment: 29 pages, 10 figures

In this work, we examine sampling problems with non-smooth potentials. We propose a novel Markov chain Monte Carlo algorithm for sampling from non-smooth potentials. We provide a non-asymptotical analysis of our algorithm and establish a polynomial-time complexity $\tilde {\cal O}(d\varepsilon^{-1})$ to obtain $\varepsilon$ total variation distance to the target density, better than most existing results under the same assumptions. Our method is based on the proximal bundle method and an alternating sampling framework. This framework requires the so-called restricted Gaussian oracle, which can be viewed as a sampling counterpart of the proximal mapping in convex optimization. One key contribution of this work is a fast algorithm that realizes the restricted Gaussian oracle for any convex non-smooth potential with bounded Lipschitz constant., Comment: 20 pages

The optimal transport problem has recently developed into a powerful framework for various applications in estimation and control. Many of the recent advances in the theory and application of optimal transport are based on regularizing the problem with an entropy term, which connects it to the Schr��dinger bridge problem and thus to stochastic optimal control. Moreover, the entropy regularization makes the otherwise computationally demanding optimal transport problem feasible even for large scale settings. This has lead to an accelerated development of optimal transport based methods in a broad range of fields. Many of these applications have a underlying graph structure, for instance information fusion and tracking problems can be described by trees. In this work we consider multi-marginal optimal transport problems with a cost function that decouples according to a tree structure. The entropy regularized multi-marginal optimal transport problem can be viewed as a generalization of the Schr��dinger bridge problem with the same tree-structure, and by utilizing these connections we extend the computational methods for the classical optimal transport problem in order to solve structured multi-marginal optimal transport problems in an efficient manner. In particular, the algorithm requires only matrix-vector multiplications of relatively small dimensions. We show that the multi-marginal regularization introduces less diffusion, compared to the commonly used pairwise regularization, and is therefore more suitable for many applications. Numerical examples illustrate this, and we finally apply the proposed framework for tracking of an ensemble of indistinguishable agents., 27 pages, 16 figures

Wasserstein Barycenter is a principled approach to represent the weighted mean of a given set of probability distributions, utilizing the geometry induced by optimal transport. In this work, we present a novel scalable algorithm to approximate the Wasserstein Barycenters aiming at high-dimensional applications in machine learning. Our proposed algorithm is based on the Kantorovich dual formulation of the Wasserstein-2 distance as well as a recent neural network architecture, input convex neural network, that is known to parametrize convex functions. The distinguishing features of our method are: i) it only requires samples from the marginal distributions; ii) unlike the existing approaches, it represents the Barycenter with a generative model and can thus generate infinite samples from the barycenter without querying the marginal distributions; iii) it works similar to Generative Adversarial Model in one marginal case. We demonstrate the efficacy of our algorithm by comparing it with the state-of-art methods in multiple experiments., Comment: 21 pages

Despite the empirical success of the actor-critic algorithm, its theoretical understanding lags behind. In a broader context, actor-critic can be viewed as an online alternating update algorithm for bilevel optimization, whose convergence is known to be fragile. To understand the instability of actor-critic, we focus on its application to linear quadratic regulators, a simple yet fundamental setting of reinforcement learning. We establish a nonasymptotic convergence analysis of actor-critic in this setting. In particular, we prove that actor-critic finds a globally optimal pair of actor (policy) and critic (action-value function) at a linear rate of convergence. Our analysis may serve as a preliminary step towards a complete theoretical understanding of bilevel optimization with nonconvex subproblems, which is NP-hard in the worst case and is often solved using heuristics., Comment: 41 pages

We study the global convergence of generative adversarial imitation learning for linear quadratic regulators, which is posed as minimax optimization. To address the challenges arising from non-convex-concave geometry, we analyze the alternating gradient algorithm and establish its Q-linear rate of convergence to a unique saddle point, which simultaneously recovers the globally optimal policy and reward function. We hope our results may serve as a small step towards understanding and taming the instability in imitation learning as well as in more general non-convex-concave alternating minimax optimization that arises from reinforcement learning and generative adversarial learning.

Cortex Lycii, the root barks of Lycium barbarum and L. chinense, known as “di gu pi” in traditional Chinese herbal drugs, is an important ingredient of formulations used for treating a variety of diseases. During the last 3 decades, more than 70 chemical entities have been separated and purified from either the aqueous or aqueous ethyl alcohol extracts of Cortex Lycii. In this study, high-performance liquid chromatography together with quadrupole-time-of-flight mass spectrometry (MS) was employed to explore new analog structures from aqueous ethyl alcohol extracts (50%, v/v), which led us to discover 4 new phenolic amides and a new cyclic peptide. The structure-based manual screening method, on the basis of the analysis of the fragmentation pathway of the previously known compounds, was used to make a preliminary analysis of the negative total ion chromatography and negative extract ion spectra. Three ions at m/ z 472.1, 314.1, and 445.2 were assigned to phenolic amides, and by further analysis of their MS/MS data, the structure of 1, corresponding to one of them ( m/ z 314.1), was illustrated as an analog of the known compound KN1. A parent ion at m/ z 856.1 was assigned to a cyclic peptide analog (2) in the manual analysis procedure. Furthermore, the MS/MS data were profiled on the Global Natural Product Social Molecular Networking (GNPS, https://gnps.ucsd.edu/ProteoSAFe/static/gnps-splash.jsp ) workflow to weave a visualization molecular network. Three more new analog ions ( m/ z 604.3 [3], 597.3 [4], and 611.3 [5]) were found in the aggregation of KN5 and KN7, and their structures were all determined by comparisons with known compounds. This manual and networking automatic screening method may provide a sensitive and efficient procedure to facilitate the mining of novel trace components.

Straightforward, rapid and high-throughput pretreatment for single nucleotide polymorphisms (SNP) genotyping is critically needed in clinical practice. However, all existing SNP genotyping methods require DNA purification step, which is labor-intensive and time-consuming. We develop a protocol for SNP genotyping by combining whole blood lysis (WBL) with qPCR and justify the practicality of our method in blood samples from 140 donors, including 40 samples from healthy donors, and 100 samples from donors with either low white blood cell counts, high level of serum uric acid or triglyceride. When compared with Sanger sequencing, the gold standard for SNP genotyping, our method exhibits a 100% consistency in the aspect of sensitivity and specificity. In addition, our method can obtain amplifiable DNA within 25 mins (which is the fastest to the best of our knowledge) from 48 samples. The blood samples, even with low white blood cell counts, high level of serum uric acid or triglyceride could not affect the sensitivity and specificity of our method. Our study demonstrates that the combination of WBL and qPCR genotyping can serve as a high-throughput and robust approach for routine clinical SNP genotyping.

We consider network routing under random link failures with a desired final distribution. We provide a mathematical formulation of a relaxed transport problem where the final distribution only needs to be close to the desired one. The problem is a maximum entropy problem for path distributions with an extra terminal cost. We show that the unique solution may be obtained solving a generalized Schroedinger system. An iterative algorithm to compute the solution is provided. It contracts the Hilbert metric with contraction ratio less than 1/2 leading to extremely fast convergence., Comment: 16 pages, 1 figure

In this article, samples of phenolic foam reinforced with graphene oxide were prepared. Gel time of resole was tested to choose the appropriate foaming agent. Friability and Mechanical properties of the composite were tested. Dynamic mechanical analysis (DMA) was employed to study the mechanical properties in varied temperatures. The results show that gel time is increased 68.2% by using of 0.5% graphene oxide; n-hexane is more fitting as blowing agent for graphene oxide reinforced phenolic foam; Impact toughness increase along with the graphene oxide content. It is not obvious when the amount is lower than 0.3% and there is a sudden enhancement when the amount reaches 0.5%. There is a 26.7% reduction in mass loss by reinforcing with 0.5% graphene oxide. Ester bonds between graphene oxide and phenolic foam matrix may be considered as “nails,” while graphene oxide may be considered as a “net.” The “net” mantle up the matrix tightly with those “nails” and stops separating of particles whose size is smaller than the “net.” POLYM. COMPOS., 35:581–586, 2014. © 2013 Society of Plastics Engineers

In this paper, thermomechanical analysis (TMA) and dynamic mechanical analysis were employed to study the properties of phenolic foam reinforced with glass fiber mat. Unreinforced phenolic foam was taken as the control sample. Mechanical tests and scanning electron microscopy were performed to confirm the results of TMA. The results show that glass fiber mat reinforcement improves the mechanical performance of phenolic foam, and nucleating agents improve it further. Phenolic foam reinforced with glass fiber mat has a smaller thermal expansion coefficient compared with unreinforced foam. The storage modulus of the reinforced phenolic foam is also higher than that in unreinforced foam, whereas the loss modulus of the former is lower than that of the latter. The glass transition temperature of the phenolic foam matrix remains unchanged during the reinforcement.

In this article, samples of phenolic resin reinforced with graphene oxide were prepared. Mechanical properties of the composite were tested. Dynamic mechanical analysis, Fourier transform infrared spectroscopy, Differential scanning calorimetry, and thermogravimetric analysis were employed to study the mechanical properties in varied temperatures to infer the influence of graphene oxide on thermal performance of phenolic resin. The results show that the addition of graphene oxide resulted in a significant improvement in the elastic modulus of phenolic resin; Young's modulus, and tensile strength increase along with the graphene oxide content. Esterification reaction happened between alcohol OH groups on resole and carbonyl (sbond]COOH) groups on graphene oxide. Addition of graphene oxide improved residue rate of phenolic resin by 5.8%, whereas the temperature distribution of phenolic pyrolysis stay unchanged. The glass transition temperature of phenolic resin has been improved by 30°C. POLYM. COMPOS. 34:1245–1249, 2013. © 2013 Society of Plastics Engineers

Since the early nineties, it has been observed that the Schroedinger bridge problem can be formulated as a stochastic control problem with atypical boundary constraints. This in turn has a fluid dynamic counterpart where the flow of probability densities represents an entropic interpolation between the given initial and final marginals. In the zero noise limit, such entropic interpolation converges in a suitable sense to the displacement interpolation of optimal mass transport (OMT). We consider two absolutely continuous curves in Wasserstein space ${\cal W}_2$ and study the evolution of the relative entropy on ${\cal W}_2\times {\cal W}_2$ on a finite time interval. Thus, this study differs from previous work in OMT theory concerning relative entropy from a fixed (often equilibrium) distribution (density). We derive a gradient flow on Wasserstein product space. We find the remarkable property that fluxes in the two components are opposite. Plugging in the "steepest descent" into the evolution of the relative entropy we get what appears to be a new formula: The two flows approach each other at a faster rate than that of two solutions of the same Fokker-Planck. We then study the evolution of relative entropy in the case of uncontrolled-controlled diffusions. In two special cases of the Schroedinger bridge problem, we show that such relative entropy may be monotonically decreasing or monotonically increasing., Comment: 7 pages, submitted to MTNS2016

We consider the problem to steer a linear dynamical system with full state observation from an initial gaussian distribution in state-space to a final one with minimum energy control. The system is stochastically driven through the control channels; an example for such a system is that of an inertial particle experiencing random "white noise" forcing. We show that a target probability distribution can always be achieved in finite time. The optimal control is given in state-feedback form and is computed explicitely by solving a pair of differential Lyapunov equations that are coupled through their boundary values. This result, given its attractive algorithmic nature, appears to have several potential applications such as to active control of nanomechanical systems and molecular cooling. The problem to steer a diffusion process between end-point marginals has a long history (Schr\"odinger bridges) and therefore, the present case of steering a linear stochastic system constitutes a Schr\"odinger bridge for possibly degenerate diffusions. Our results, however, provide the first implementable form of the optimal control for a general Gauss-Markov process. Illustrative examples of the optimal evolution and control for inertial particles and a stochastic oscillator are provided. A final result establishes directly the property of Schr\"{o}dinger bridges as the most likely random evolution between given marginals to the present context of linear stochastic systems., Comment: 11 pages, 7 figures

New technology is reported here for the synthesis of an effective weak acid–cation exchanger for ion chromatography. Monodisperse macroporous poly(ethylvinylbenzene-co-divinylbezene) (PEVB–DVB) beads of 5 μm diameter were prepared by a two-step swelling and polymerization method. Then carboxyl groups were introduced by polymerization of maleic anhydride with unreacted vinyl groups on the resin beads, followed by hydrolysis of the maleic anhydride groups. A column packed with the carboxylate beads was used to separate alkali and alkaline earth metal ions in a single isocratic run. Separations were found to be better than those with similar resin particles that are simply coated with maleic acid. The columns containing the new particles were 100% compatible with solvents commonly used for HPLC. Additionally, the prepared column was stable and could be used for a long time in a wide range of pH. The column gave good resolution, low detection limits and good repeatability for the separation of common cations. Satisfactory results were also obtained for separations of organic amines and of common cations in rainwater.

In this work, we develop a new framework for dynamic network flow pro-blems based on optimal transport theory. We show that the dynamic multicommodity minimum-cost network flow problem can be formulated as a multimarginal optimal transport problem, where the cost function and the constraints on the marginals are asso-ciated with a graph structure. By exploiting these structures and building on recent advances in optimal transport theory, we develop an efficient method for such entropy -regularized optimal transport problems. In particular, the graph structure is utilized to efficiently compute the projections needed in the corresponding Sinkhorn iterations, and we arrive at a scheme that is both highly computationally efficient and easy to implement. To illustrate the performance of our algorithm, we compare it with a state-of-the-art linear programming (LP) solver. We achieve good approximations to the solution at least one order of magnitude faster than the LP solver. Finally, we showcase the methodology on a traffic routing problem with a large number of commodities.