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This paper is devoted to the estimation of the Lipschitz constant of general neural network architectures using semidefinite programming. For this purpose, we interpret neural networks as time-varying dynamical systems, where the $k$-th layer corresponds to the dynamics at time $k$. A key novelty with respect to prior work is that we use this interpretation to exploit the series interconnection structure of feedforward neural networks with a dynamic programming recursion. Nonlinearities, such as activation functions and nonlinear pooling layers, are handled with integral quadratic constraints. If the neural network contains signal processing layers (convolutional or state space model layers), we realize them as 1-D/2-D/N-D systems and exploit this structure as well. We distinguish ourselves from related work on Lipschitz constant estimation by more extensive structure exploitation (scalability) and a generalization to a large class of common neural network architectures. To show the versatility and computational advantages of our method, we apply it to different neural network architectures trained on MNIST and CIFAR-10.

We present a simple and effective way to account for non-convex costs and constraints~in~state feedback synthesis, and an interpretation for the variables in which state feedback synthesis is typically convex. We achieve this by deriving the controller design using moment matrices of state and input. It turns out that this approach allows the consideration of non-convex constraints by relaxing them as expectation constraints, and that the variables in which state feedback synthesis is typically convexified can be identified with blocks of these moment matrices., Comment: Preprent to be submitted to IEEE Conference on Decision and Control

From the perspective of control theory, convolutional layers (of neural networks) are 2-D (or N-D) linear time-invariant dynamical systems. The usual representation of convolutional layers by the convolution kernel corresponds to the representation of a dynamical system by its impulse response. However, many analysis tools from control theory, e.g., involving linear matrix inequalities, require a state space representation. For this reason, we explicitly provide a state space representation of the Roesser type for 2-D convolutional layers with $c_\mathrm{in}r_1 + c_\mathrm{out}r_2$ states, where $c_\mathrm{in}$/$c_\mathrm{out}$ is the number of input/output channels of the layer and $r_1$/$r_2$ characterizes the width/length of the convolution kernel. This representation is shown to be minimal for $c_\mathrm{in} = c_\mathrm{out}$. We further construct state space representations for dilated, strided, and N-D convolutions.

Diverse demonstration datasets have powered significant advances in robot learning, but the dexterity and scale of such data can be limited by the hardware cost, the hardware robustness, and the ease of teleoperation. We introduce ALOHA 2, an enhanced version of ALOHA that has greater performance, ergonomics, and robustness compared to the original design. To accelerate research in large-scale bimanual manipulation, we open source all hardware designs of ALOHA 2 with a detailed tutorial, together with a MuJoCo model of ALOHA 2 with system identification. See the project website at aloha-2.github.io., Comment: Project website: aloha-2.github.io

With the increasing adoption of decentralized information systems based on a variety of permissionless blockchain networks, the choice of consensus mechanism is at the core of many controversial discussions. Ethereum's recent transition from (PoW) to proof-of-stake (PoS)-based consensus has further fueled the debate on which mechanism is more favorable. While the aspects of energy consumption and degree of (de-)centralization are often emphasized in the public discourse, seminal research has also shed light on the formal security aspects of both approaches individually. However, related work has not yet comprehensively structured the knowledge about the security properties of PoW and PoS. Rather, it has focused on in-depth analyses of specific protocols or high-level comparative reviews covering a broad range of consensus mechanisms. To fill this gap and unravel the commonalities and discrepancies between the formal security properties of PoW- and PoS-based consensus, we conduct a systematic literature review over 26 research articles. Our findings indicate that PoW-based consensus with the longest chain rule provides the strongest formal security guarantees. Nonetheless, PoS can achieve similar guarantees when addressing its more pronounced tradeoff between safety and liveness through hybrid approaches., Comment: To appear in the Decentralized Applications with Blockchain, DLT, and Crypto-Currencies track at ACM/SIGAPP SAC 2024

In this work, we develop a method based on robust control techniques to synthesize robust time-varying state-feedback policies for finite, infinite, and receding horizon control problems subject to convex quadratic state and input constraints. To ensure constraint satisfaction of our policy, we employ (initial state)-to-peak gain techniques. Based on this idea, we formulate linear matrix inequality conditions, which are simultaneously convex in the parameters of an affine control policy, a Lyapunov function along the trajectory and multiplier variables for the uncertainties in a time-varying linear fractional transformation model. In our experiments this approach is less conservative than standard tube-based robust model predictive control methods., Comment: Extended version of a contribution to be submitted to the European Control Conference 2024

In this paper, we revisit structure exploiting SDP solvers dedicated to the solution of Kalman-Yakubovic-Popov semi-definite programs (KYP-SDPs). These SDPs inherit their name from the KYP Lemma and they play a crucial role in e.g. robustness analysis, robust state feedback synthesis, and robust estimator synthesis for uncertain dynamical systems. Off-the-shelve SDP solvers require $O(n^6)$ arithmetic operations per Newton step to solve this class of problems, where $n$ is the state dimension of the dynamical system under consideration. Specialized solvers reduce this complexity to $O(n^3)$. However, existing specialized solvers do not include semi-definite constraints on the Lyapunov matrix, which is necessary for controller synthesis. In this paper, we show how to include such constraints in structure exploiting KYP-SDP solvers., Comment: Submitted to Conference on Decision and Control, copyright owned by ieee

This paper introduces a novel representation of convolutional Neural Networks (CNNs) in terms of 2-D dynamical systems. To this end, the usual description of convolutional layers with convolution kernels, i.e., the impulse responses of linear filters, is realized in state space as a linear time-invariant 2-D system. The overall convolutional Neural Network composed of convolutional layers and nonlinear activation functions is then viewed as a 2-D version of a Lur'e system, i.e., a linear dynamical system interconnected with static nonlinear components. One benefit of this 2-D Lur'e system perspective on CNNs is that we can use robust control theory much more efficiently for Lipschitz constant estimation than previously possible.

New particle formation (NPF) in the tropical free troposphere (FT) is a globally important source of cloud condensation nuclei, affecting cloud properties and climate. Oxidized organic molecules (OOMs) produced from biogenic volatile organic compounds are believed to contribute to aerosol formation in the tropical FT, but without direct chemical observations. We performed in-situ molecular-level OOMs measurements at the Bolivian station Chacaltaya at 5240 meters above sea level, on the western edge of Amazonia. For the first time, we demonstrate the presence of OOMs, mainly with 4-5 carbon atoms, simultaneously in both gas and particulate phases in tropical FT air from Amazonia. These observations, combined with air mass history analyses, indicate that the observed OOMs are linked to isoprene emitted from the rainforests hundreds of kilometers away. Based on particle-phase measurements, we find that these compounds can contribute to the growth of newly formed particles, and are potentially crucial for new particle formation in the tropical free troposphere on a continental scale. Our study will thus improve the understanding of aerosol formation process in the tropics.

In this work, we propose a dissipativity-based method for Lipschitz constant estimation of 1D convolutional neural networks (CNNs). In particular, we analyze the dissipativity properties of convolutional, pooling, and fully connected layers making use of incremental quadratic constraints for nonlinear activation functions and pooling operations. The Lipschitz constant of the concatenation of these mappings is then estimated by solving a semidefinite program which we derive from dissipativity theory. To make our method as efficient as possible, we exploit the structure of convolutional layers by realizing these finite impulse response filters as causal dynamical systems in state space and carrying out the dissipativity analysis for the state space realizations. The examples we provide show that our Lipschitz bounds are advantageous in terms of accuracy and scalability.

Outstanding optoelectronic properties and a facile synthesis render halide perovskite nanocrystals (NCs) a promising material for nanostructure-based devices. However, the commercialization is hindered mainly by the lack of NC stability under ambient conditions and inefficient charge carrier injection. Here, we investigate solutions to both problems, employing methylammonium lead bromide (MAPbBr_3) NCs encapsulated in diblock copolymer core-shell micelles of tunable size. We confirm that the shell does not prohibit energy transfer, as FRET efficiencies between these NCs and 2D CsPbBr_3 nanoplatelets (NPLs) reach 73.6%. This value strongly correlates to the micelle size, with thicker shells displaying significantly reduced FRET efficiencies. Those high efficiencies come with a price, as the thinnest shells protect the encapsulated NCs less from environmentally induced degradation. Finding the sweet spot between efficiency and protection could lead to the realization of tailored energy funnels with enhanced carrier densities for high-power perovskite NC-based optoelectronic applications.

In the present work, a simple algorithm for stabilizing an unknown linear time-invariant system is proposed, assuming only that this system is stabilizable. The suggested algorithm is based on first performing a partial identification of the system and then stabilizing the controllable subsystem. It should be emphasized that our approach does not depend on any prior model knowledge and requires only a minimal number of samples.

Granular materials, such as sand or grain, exhibit many structural and dynamic characteristics similar to those observed in molecular systems, despite temperature playing no role in their properties. This has led to an effort to develop a statistical mechanics for granular materials that has focused on establishing an equivalent to the microcanonical ensemble and a temperature-like thermodynamic variable. Here, we expand on these ideas by introducing a granular potential into the Edwards ensemble, as an analogue to the chemical potential, and explore its properties using a simple model of a granular system. A simple kinetic Monte Carlo simulation of the model shows the effect of mass transport leading to equilibrium and how this is connected to the redistribution of volume in the system. An exact analytical treatment of the model shows that the compactivity and the ratio of the granular potential to the compactivity determine the equilibrium between two open systems that are able to exchange volume and particles, and that mass moves from high to low values of this ratio. Analysis of the granular potential shows that adding a particle to the system increases the entropy at high compactivity, but decreases the entropy at low compactivity. Finally, we demonstrate the use of a small system thermodynamics method for the measurement of granular potential differences., Comment: 11 Pages, 7 Figures. Extended Introduction and Discussion. New section on Measuring granular potential

Many experiments in particle physics, in particular in the field of neutrino searches, rely on organic liquid scintillators as target and detection material. The size of these detectors was continously growing in the last decades, up to the kiloton scale. In several cases these detectors are located at sites with enhanced safety requirements as underground laboratories or in the vicinity of nuclear reactors. Therefore, there is strong demand in liquids which are safe with respect to aspects as fire protection, human health or environmental pollution. In particular, properties as the flash point, the vapor pressure or the toxicity need to be significantly improved as compared to classical solvents such as xylene or pseudocumene. We present and compare the performance and optical properties of scintillators based on high flash point solvents. In particular polysiloxane based scintillators are characterized by outstanding properties in terms of safety., Comment: 13 pages, 4 figures

Differential Dynamic Programming is an optimal control technique often used for trajectory generation. Many variations of this algorithm have been developed in the literature, including algorithms for stochastic dynamics or state and input constraints. In this contribution, we develop a robust version of Differential Dynamic Programming that uses generalized plants and multiplier relaxations for uncertainties. To this end, we study a version of the Bellman principle and use convex relaxations to account for uncertainties in the dynamic program. The resulting algorithm can be seen as a robust trajectory generation tool for nonlinear systems., Comment: submitted to IEEE Conference on Decision and Control, 2022