Randomized trace estimation is a popular technique to approximate the trace of an implicitly-defined matrix $A$ by averaging the quadratic form $x’Ax$ across several samples of a random vector $x$. This paper focuses on the application of randomized trace estimators on asynchronous computing environments where the quadratic form $x’Ax$ is computed partially by observing only a random row subset of $A$ for each sample of the random vector $x$. Our asynchronous framework treats the number of rows, as well as the row subset observed for each sample, as random variables, and our theoretical analysis establishes the variance of the randomized estimator for Rademacher and Gaussian samples. We also present error analysis and sampling complexity bounds for the proposed asynchronous randomized trace estimator. Our numerical experiments illustrate that the asynchronous variant can be competitive even when a small number of rows is updated per each sample.

We are living amidst a pandemic caused by a ravaging coronavirus and an accompanying pandemic of misinformation that has strained our economy and socio-political institutions. A key scientific goal is to examine mechanisms that lead to the widespread propagation of contagions, e.g., misinformation and pathogens, and identify risk factors that can trigger widespread outbreaks. A common phenomenon underlying the spread of disease and misinformation epidemics is the evolution of the contagion as it propagates, leading to the emergence of different strains, e.g., through genetic mutations in pathogens and alterations in the information content. Recent studies have revealed that models that do not account for heterogeneity in transmission risks associated with different strains of the circulating contagion can lead to inaccurate predictions. However, existing results on multi-strain spreading assume that the network has a vanishingly small clustering coefficient, whereas, clustering is widely known to be a fundamental property of real-world social networks. In this work, we investigate spreading processes that entail evolutionary adaptations on random graphs with tunable clustering and arbitrary degree distributions. We derive a mathematical framework that predicts the epidemic threshold and the probability of emergence as functions of the characteristics of the spreading object, the evolutionary pathways of the pathogen/misinformation, and the structure of the underlying network as given by the joint degree distribution of single-edges and triangles. To the best of our knowledge, our work is the first to jointly characterize the impact of clustering and evolution on the emergence of epidemic outbreaks. We supplement our theoretical finding with numerical simulations and case studies, shedding light on how clustering can offer pathways for mutation, thereby altering the course of the epidemic.

Stochastic computing has a long history as an alternative method of performing arithmetic on a computer. While it can be considered an unbiased estimator of real numbers, it has a variance and MSE on the order of$\displaystyle \Omega(\frac{1}{N})$. On the other hand, deterministic variants of stochastic computing remove the stochastic aspect, but cannot approximate arbitrary real numbers with arbitrary precision and are biased estimators. However, they have an asymptotically superior MSE on the order of$O(\frac{1}{N^{2}})$. Recent results in deep learning with stochastic rounding suggest that the bias in the rounding can degrade performance. We proposed an alternative framework, called dither computing, that combines aspects of stochastic computing and its deterministic variants and that can perform computing with similar efficiency, is unbiased, and with a variance and MSE also on the optimal order of$\displaystyle \Theta(\frac{1}{N^{2}})$. We also show that it can be beneficial in stochastic rounding applications as well. We provide implementation details and give experimental results to comparatively show the benefits of the proposed scheme.

We present an application of machine learning to automated robust optimization of electronic circuit design that combines artificial neural networks and global optimization. A neural network regressor is constructed to predict circuit operation metrics such as power, offset, delay, phase margin based on input parameters such as device size, temperature, supply voltage and current, and process corner. This regressor is then used to build an objective function for global optimization to find the optimal set of controllable parameters that optimize the objective function subject to input constraints such as device size range and output constraints such as power consumption or delay. Experimental results from tuning state-of-the-art high performance PLL circuits show that this framework is promising and can in much less time find optimized circuits that outperform circuit designs that were manually tuned by a skilled circuit designer.

In this paper, we consider decentralized stochastic non-convex optimization over a class of weakly connected digraphs. First, we quantify the convergence behaviors of the weight matrices of this type of digraphs. By leveraging the perturbed push sum protocol and gradient tracking techniques, we propose a decentralized stochastic algorithm that is able to converge to the first-order stationary points of non-convex problems with provable convergence rates. Our digraph structure considered in this work generalizes the existing settings such that the proposed algorithm can be applied to more practical decentralized learning scenarios. Numerical results showcase the strengths of our theory and superiority of the proposed algorithm in decentralized training problems compared with the existing counterparts.

We study 2 approaches, called TableNet and Prod-SumNet respectively, to simplify the implementation of neural networks. First we look at using Look Up Tables (LUT) to remove the multiplication operations and obviate the need of a multiplier. We compare the different tradeoffs of this approach in terms of accuracy versus LUT size and the number of operations and show that similar performance can be obtained with a comparable memory footprint as a full precision linear classifier, but without the use of any multipliers. Secondly we reduce the number of trainable model parameters by decomposing linear operators in neural networks as a product of sums of simpler linear operators which generalizes recently proposed deep learning architectures such as CNN, KFC, Dilated CNN, etc. We show that good accuracy on MNIST and Fashion MNIST can be obtained using a relatively small number of trainable parameters. In addition, since implementation of the convolutional layer is resource-heavy, we also consider an implementation in the transform domain that obviates the need for convolutional layers. We illustrate the tradeoff of varying the number of trainable variables and the corresponding error rate. As an example, by using this decomposition on a reference CNN architecture for MNIST with over 3 · 106trainable parameters, we are able to obtain an accuracy of 98.44% using only 3554 trainable parameters. Furthermore, the generality of the framework allows it to be be suitable for general problems unlike CNN which performs best in the image processing or other shift-invariant domains.

We consider a new family of stochastic operators for reinforcement learning with the goal of alleviating negative effects and becoming more robust to approximation or estimation errors. Various theoretical results are established, which include showing that our family of operators preserve optimality and increase the action gap in a stochastic sense. Our empirical results illustrate the strong benefits of our robust stochastic operators, significantly outperforming the classical Bellman operator and recently proposed operators.

For a network of dynamical systems coupled via an undirected weighted tree, we consider the problem of which system to apply control, in the case when only a single system receives control. We abstract this problem into a study of eigenvalues of a perturbed Laplacian matrix. We show that this eigenvalue problem has a complete solution for arbitrarily large control by showing that the best and the worst places to apply control have well-known characterization in graph theory, thus linking the computational eigenvalue problem with graph-theoretical concepts. Some partial results are proved in the case when the control effort is bounded. In particular, we show that a local maximum in localizing the best place for control is also a global maximum. We conjecture in the bounded control case that the best place to apply control must also necessarily be a characteristic vertex and present evidence from numerical experiments to support this conjecture.

This paper proposes lower bounds for the coupling strengths of oscillators in directed networks to guarantee global synchronization. The novel idea of graph comparison from spectral graph theory is employed so that the topological features of a given network can be fully utilized to simplify computations. For large networks that can be decomposed into a set of smaller strongly connected components, the comparison can be carried out at the local level as well.

Multi-bit screening is an extension of binary screening, in which every pixel in continuous-tone image can be rendered to one among multiple absorptance levels. Many multi-bit screen algorithms face the problem of contouring artifacts due to sudden changes in the majority absorptance level between gray levels. In this paper, we have extended the direct binary search to the multi-bit case where at every pixel the algorithm chooses the best drop absorptance level to create a visually pleasing halftone pattern without any user defined guidance. This is repeated throughout the entire range of gray levels to create a high quality multi-bit screen.

The optimal power flow problem is concerned with finding a proper operating point for a power network while attempting to minimize a cost function and satisfy network constraints. We analyze the optimal power flow problem subject to contingency constraints and investigate the relationship between the cost of the optimal power flow problem and network topology. We find that when the network topology is that of a small world graph or a scale-free graph, the optimal power flow problem is robust in terms of satisfying contingency constraints.

We illustrate how employing Graphics Processing Units (GPU) can speed-up intensive image processing operations. In particular, we demonstrate the use of the NVIDIA CUDA architecture to implement a color digital binary halftoning algorithm based on Direct Binary Search (DBS). Halftoning a color image is more computationally expensive than the single color case as there is a need to minimize dot interaction between different color planes as well. We propose processing all color planes in parallel. In addition we employ processing several non-overlapping neighborhoods in parallel, by utilizing the GPU's parallel architecture, to further improve the computational efficiency. This parallel approach allows us to use a large neighborhood and filter size, to achieve the highest halftone quality, while having minimal impact on performance.

Positioning disk-shaped sensors to optimize certain coverage parameters is a fundamental problem in ad hoc sensor networks. The hexagon lattice arrangement is known to be optimally efficient in the plane, even though 20.9% of the area is unnecessarily covered twice, however, the arrangement is very rigid—any movement of a sensor from its designated grid position (due to, e.g., placement error or obstacle avoidance) leaves some region uncovered, as would the failure of any one sensor. In this article, we consider how to arrange sensors in order to guarantee multiple coverage, that is, k -coverage for some value k > 1. A naive approach is to superimpose multiple hexagon lattices, but for robustness reasons, we may wish to space sensors evenly apart. We present two arrangement methods for k -coverage: (1) optimizing a Riesz energy function in order to evenly distribute nodes, and (2) simply shrinking the hexagon lattice and making it denser. The first method often approximates the second, and so we focus on the latter. We show that a density increase tantamount to k copies of the lattice can yield k ′-coverage, for k ′ > k (e.g., k = 11, k ′ = 12 and k = 21, k ′ = 24), by exploiting the double-coverage regions. Our examples' savings provably converge in the limit to the ≈ 20.9% maximum. We also provide analogous results for the square lattice and its ≈ 57% inefficiency (e.g., k = 3, k ′ = 4 and k =5, k ′ = 7) and show that for multi-coverage for some values of k ′, the square lattice can actually be more efficient than the hexagon lattice. We also explore other benefits of shrinking the lattice: Doing so allows all sensors to move about their intended positions independently while nonetheless guaranteeing full coverage and can also allow us to tolerate probabilistic sensor failure when providing 1-coverage or k -coverage. We conclude by construing the shrinking factor as a budget to be divided among these three benefits.

Programmable Graphics Processing Unit (GPU) has emerged as a powerful parallel processing architecture for various applications requiring a large amount of CPU cycles. In this paper, we study the feasibility for using this architecture for image halftoning, in particular implementing computationally intensive neighborhood halftoning algorithms such as error diffusion and Direct Binary Search (DBS). We show that it is possible to deliver very high performance even for high speed printers.

The naming game is a dynamical system that is used to model and study language formation, in particular to determine how words are formed that are used by all members of a community to denote the same object or concept. We propose a model of the naming game that allows for theoretical investigation under various behavior for agent interaction. In particular, we give conditions on the network such that consensus is reached where at most p synonyms are used to describe a single object. In addition, we give lower bounds on the convergence rate to consensus. Furthermore, we study various agent interaction behaviors and their effect on the time needed to reach consensus. We show that even though a democratic strategy is in general the best strategy for reaching consensus, a stubborn or a gullible strategy can allow for faster word formation than a democratic strategy for certain connection topologies among the agents.

Cellular Neural Networks is a multiprocessor computing architecture where the processors are only directly connected to nearby processors. This results in a trade off between the number of connections between processors and the number of steps needed to perform global computation. We consider such a locally connected computing architecture and present some preliminary analysis on this trade off and study this architecture's applicability to the specific problem of matrix multiplication including linear transforms applications such as 1-D and 2-D DCT and DWT. We illustrate that in general there is a trade-off between the following 3 parameters: the number of iterations needed to perform the global computation, the amount of memory in each processor and the connectedness of the graph. This latter parameter is expressed as the relative diameter of the computer architecture graph with respect to the problem graph.

Video transmission in multiparty video conferencing is challenging due to the demanding bandwidth usage and stringent latency requirement. In this paper, we systematically analyze the problem of collaborative stream routing using one-hop forwarding assistance in a bandwidth constraint environment. We model the problem as a multi-source degree-constrained multicast tree construction problem, and investigate heuristic algorithms to construct bandwidth-feasible shared multicast trees. The contribution of this work is primarily two-fold: (1) we study the solution space of finding a feasible bandwidth configuration for stream routing in a peer-to-peer (P2P) setting, and propose two heuristic algorithms that can quickly produce a bandwidth-feasible solution, making them suitable for large-scale conference sessions, (2) we conduct an empirical study using a realistic dataset and show the effectiveness of our heuristic algorithms. Various QoS metrics are taken into account to evaluate the performance of our algorithms. Finally, we discuss open issues for further exploration. The feasibility study presented in this paper will shed light on the design and implementation of practical P2P multiparty video conferencing applications.

We study several classes of related scheduling problems including the carpool problem, its generalization to arbitrary inputs and the chairman assignment problem. We derive both lower and upper bounds for online algorithms solving these problems. We show that the greedy algorithm is optimal among online algorithms for the chairman assignment problem and the generalized carpool problem. We also consider geometric versions of these problems and show how the bounds adapt to these cases.

We consider a network of dynamical systems whose trajectories we wish to control by applying stimuli to a subset of systems. We study the minimum number of systems to control and which systems to control and provide sufficient conditions and necessary conditions for successful control. These conditions are given in terms of graph theoretical properties of the underlying network. For instance, we show that for the cycle graph, the best way to achieve control is by applying control to systems that are approximately equally spaced apart.

Motivated by the problem of limited bandwidth in peer-to-peer (P2P) multi-party video conferencing systems, in this paper we propose a non-intrusive adaptive multi-media routing algorithm that effectively calculates stream routing to achieve a maximum number of receiving streams. The technique is non-intrusive in that it makes use of current streaming status to infer link bottlenecks rather than sending active probing packets, which would seriously interfere with the latency-sensitive video conferencing application and waste bandwidth. When link bottlenecks are detected, the method will adaptively calculate streaming routes, allowing bandwidth abundant peers to act as relays. To test the performance, we use real data from a world wide bandwidth distribution archive and investigate the algorithm convergence rate and distribution fairness through simulation. Results show that the technique works well to achieve effective multi-media routing for latency-sensitive video conferencing applications.

As an efficient distribution mechanism, Peer-to-Peer (P2P) technology has become a tremendously attractive solution to offload servers in large-scale video streaming applications. However, in providing on-demand asynchronous streaming services, P2P streaming design faces two major challenges: how to schedule efficient video sharing between peers with asynchronous playback progresses? how to provide incentives for peers to contribute their resources to achieve a high level of system-wide Quality-of-Experience (QoE)? In this paper, we present iPASS, a novel mesh-based P2P VoD system, to address these challenges. Specifically, iPASS adopts a dynamic buffering-progress-based peering strategy to achieve high peer bandwidth utilization with low system maintenance cost. To provide incentives for peer uploading, iPASS employs a differentiated prefetching design that enables peers with higher contribution prefetch content at higher speed. A distributed adaptive taxation algorithm is developed to balance the system-wide QoE and service differentiations among heterogeneous peers. To assess the performance of iPASS, we built a detailed packet-level P2P VoD simulator and conducted extensive simulations. It was demonstrated that iPASS can completely offload server when the average peer upload bandwidth is more than 1.2 times the streaming rate. Furthermore, we showed that the distributed incentive algorithm motivates peers to contribute and collaboratively achieve a high level of system wide QoE.

Positioning disk-shaped sensors to optimize certain coverage parameters is a fundamental problem in ad-hoc sensor networks. The hexagon grid lattice is known to be optimally efficient, but the 20.9% of the area covered by two sensors may be considered a waste. Furthermore, any movement of a sensor from its designated grid position or sensor failure, due to placement error or obstacle avoidance, leaves some region uncovered, as would the failure of any one sensor. We explore how shrinking the grid can help to remedy these shortcomings. First, shrinking to obtain a denser hexagonal lattice allows all sensors to move about their intended positions independently while nonetheless guaranteeing full coverage. Second, sufficiently increasing the lattice density will naturally yield k-coverage for k > 1. Moreover, we show that a density increase tantamount to fc copies of the lattice can yield k' -coverage, for kj> k (e.g. k = 11, kj= 12), through the exploitation of the double-coverage regions. Our examples' savings provably converge in the limit to the ap 20.9% maximum. We also provide analogous results for the square lattice and its ap 57% inefficiency, including k = 3, kj= 4, k = 5,kj= 7, indicating that for multi-coverage, the square lattice can actually be more efficient than the hexagon lattice. All these efficiency gains can be used to provide 1-coverage or fc-coverage even in the face of probabilistic sensor failure. We conclude by construing the shrinking factor as a budget to be divided among these three benefits.

As an efficient distribution mechanism, peer-to-peer technology has become a tremendously attractive solution to offload servers in large scale video streaming applications. However, in providing on-demand asynchronous streaming services, P2P streaming design faces two major challenges: how to schedule efficient video sharing between peers with asynchronous playback progresses? how to provide incentives for peers to contribute their resources to achieve a high level of system-wide quality-of-experience (QoE)? In this paper, we present iPASS, a novel mesh-based P2P VoD system, to address these challenges. Specifically, iPASS adopts a dynamic buffering-progress-based peering strategy to achieve high peer bandwidth utilization with low system maintenance cost. To provide incentives for peer uploading, iPASS employs a differentiated pre-fetching design that enables peers with higher contribution pre-fetch content at higher speed. Through packet-level simulations, it was demonstrated that iPASS can effectively offload server and the proposed distributed incentive algorithm motivates peers to contribute and collectively achieve a high level of of QoE.

In this paper we study the video streaming bandwidth of peer-to-peer streaming networks where the underlying topology is a complex network. We focus on the maximal streaming rate and how it depends on the type of network. We consider networks such as small world networks, scale free networks, locally connected networks and random networks. The experimental results indicate that a more connected graph does not necessarily imply a higher streaming rate, whereas properties such as the existence of a Hamiltonian path from the source do.

We consider a sensor network placement problem where the sensing range of a sensor depends on its location in order to model the effect of terrain features. We study how sensors should be placed in order to maximize the coverage and illustrate how digital halftoning algorithms from the field of image processing can be useful in this respect. In particular, we reduce the sensor placement problem to a corresponding image halftoning problem and then apply two well known halftoning algorithms to the problem: dither mask halftoning and direct binary search. We illustrate our approach with experimental results and show that this approach is also applicable to the problem of preferential coverage.

Compared with the traditional client/server streaming model, peer-assisted video streaming has been shown to provide better scalability with lower infrastructure cost. In this paper, we describe how peer-assisted video streaming can be implemented through real-time service oriented architecture. Our architecture, dubbed PACTS, is composed of 5 distinct service components: directory service, content service, peer download service, peer upload service and rate composition service. PACTS is designed to meet the specific QoS requirements of different users, entered through a simple Web interface. It also provides a distributed implementation of the content and peer directory services for effectively handling flash crowd situations, when a large number of users join during a very short period of time. We discuss the functionalities of the main PACTS services and specify the workflow of how these services work together to deliver real-time streaming services leveraging the benefits of peer to peer technology. By organizing elements of traditional video streaming and peer to peer computing into loosely-coupled composable middleware services and distributing them among participating entities, PACTS enables high-quality low- cost video streaming at a large scale and in real time.

This paper concerns pinning control in complex networks of dynamical systems, where an external forcing signal is applied to the network in order to align the state of all the systems to the forcing signal. By considering the control signal as the state of a virtual dynamical system, this problem can be studied in a synchronization framework. Prior studies have determined that a single controller can pin an entire network under certain conditions. This paper aims to further this study by looking at sufficient and necessary conditions for the possible locations where pinning control can be applied. We also study how the ease of control is influenced by the topology and in particular the algebraic connectivity of the network. In particular, we show that for systems with locally connected coupling it is harder to achieve pinning control than for systems with random or fully connected coupling.We also show that when pinning control is applied to a single system and the underlying topology of the network is a vertex-balanced graph, then the amount of control needed to effect pinning control grows at least as fast as the number of vertices. Furthermore, in order to achieve pinning control in systems coupled via locally connected graphs, as the number of systems grows, both the pinning control and the coupling among all systems need to increase.

We present an algorithm for sensor placement with redundancy where each point in a 2-dimensional space is covered by at least k sensors under the constraint that all the sensors are located away from each other. We reduce the problem to distributing points evenly on the surface of a torus manifold and solve it computationally by minimizing the Riesz energy. We also study the case where the coverings are incrementally constructed. We illustrate our approach with numerical results and compare it to similar approaches in dispersed dither mask halftoning.

An ad-hoc sensor network is composed of sensing devices which can measure or detect features of their environment, communicate with one other and possibly with other devices that perform data fusion. One of the problems motivated by ad-hoc sensor networks is to position sensors in order to maximize coverage, or equivalently to minimize the number of sensors required to cover a given area.

The quantities of coefficient of ergodicity and algebraic connectivity have been used to estimate the convergence rates of discrete-time and continuous-time network consensus algorithms respectively. Both of these two quantities are defined with respect to network topologies without the symmetry assumption, and they are applicable to the case when network topologies change with time. We present results identifying deterministic network topologies that optimize these quantities. We will also propose heuristics that can accelerate convergence in random networks by redirecting a small portion of the links assuming that the network topology is controllable.

Recently there is a great interest in studying consensus and flocking problems by analyzing dynamics of linear interacting systems coupled via a complex network. Two approaches have emerged to study this problem. In one approach the system is analyzed via the theory of inhomogeneous Markov chains and consensus is related to weak ergodicity of Markov chains. More recently, consensus problems are studied with communication delays between the coupled systems and the approach used is based on paracontracting and pseudocontracting operators. The purpose of this paper is to illustrate the connections between these two approaches and show that under certain conditions they are in fact equivalent.

In this paper, we present a novel content-based image authentication framework which embeds the authentication information into the host image using a lossless data hiding approach. In this framework the features of a target image are first extracted and signed using the digital signature algorithm (DSA). The authentication information is generated from the signature and the features are then inserted into the target image using a lossless data hiding algorithm. In this way, the unperturbed version of the original image can be obtained after the embedded data are extracted. An important advantage of our approach is that it can tolerate JPEG compression to a certain extent while rejecting common tampering to the image. The experimental results show that our framework works well with JPEG quality factors greater than or equal to 80 which are acceptable for most authentication applications.

The twisted-nematic mode liquid-crystal display (LCD) display used in most laptop computers has the property that the luminance and color changes dramatically as the viewing angle changes. The present paper utilizes this property to embed several images into the LCD display that are viewable depending on the viewing angle. Applications include improving the viewing angle characteristics of LCD displays.

Recently, a number of authentication schemes have been proposed for multimedia data. The main requirement for such authentication systems is that minor modifications which do not alter the content of the data preserve the authenticity of the data, whereas modifications which do modify the content render the data not authentic. These schemes can be classified into two classes depending on the underlying model of image authentication. We look at some of the advantages and disadvantages of these schemes and their relationship with limitations of the underlying model of image authentication. In particular, we study feature-based algorithms and hash-based algorithms. The main disadvantage of feature-based algorithms is that similar images generate similar features, and therefore it is possible for a forger to generate dissimilar images with the same features. On the other hand, the class of hash-based algorithms utilizes a cryptographic digital signature scheme and inherits the security of digital signatures to thwart forgery attacks. The main disadvantage of hash-based algorithms is that the image needs to be modified in order to be made authenticatable. We propose a multimedia authentication scheme which combines some of the best features of these two classes of algorithms. The proposed scheme utilizes cryptographic digital signature schemes and the data does not need to be modified in order to be made authenticatable. We show how results in sphere packings and coverings can be useful in the design. Several applications including the authentication of images on CD-ROM and handwritten documents are discussed.

Automating the transistor and wire-sizing process is an important step toward being able to rapidly design high-performance, custom circuits. This paper presents a circuit optimization tool that automates the tuning task by means of state-of-the-art nonlinear optimization. It makes use of a fast circuit simulator and a general-purpose nonlinear optimization package. It includes minimax and power optimization, simultaneous transistor and wire tuning, general choices of objective functions and constraints, and recovery from nonworking circuits. In addition, the tool makes use of designer-friendly interfaces that automate the specification of the optimization task, the running of the optimizer, and the back-annotation of the results of optimization onto the circuit schematic. Particularly for large circuits, gradient computation is usually the bottleneck in the optimization procedure. In addition to traditional adjoint and direct methods, we use a technique called the adjoint Lagrangian method, which computes all the gradients necessary for one iteration of optimization in a single adjoint analysis. This paper describes the algorithms and the environment in which they are used and presents extensive circuit optimization results. A circuit with 6900 transistors, 4128 tunable transistors, and 60 independent parameters was optimized in about 108 min of CPU time on an IBM RISC/System 6000, model 590.

The circuit tuning problem is best approached by means of gradient-based nonlinear optimization algorithms. For large circuits, gradient computation can be the bottleneck in the optimization procedure. Traditionally, when the number of measurements is large relative to the number of tunable parameters, the direct method is used to repeatedly solve the associated sensitivity circuit to obtain all the necessary gradients. Likewise, when the parameters outnumber the measurements, the adjoint method is employed to solve the adjoint circuit repeatedly for each measurement to compute the sensitivities. In this paper we propose the adjoint Lagrangian method, which computes all the gradients necessary for augmented-Lagrangian-based optimization in a single adjoint analysis. After the nominal simulation of the circuit has been carried out, the gradients of the merit function are expressed as the gradients of a weighted sum of circuit measurements. The weights are dependent on the nominal solution and on optimizer quantities such as Lagrange multipliers. By suitably choosing the excitations of the adjoint circuit, the gradients of the merit function are computed via a single adjoint analysis, irrespective of the number of measurements and the number of parameters of the optimization. This procedure requires close integration between the nonlinear optimization software and the circuit simulation program.

Cellular neural/nonlinear networks (CNN) are considered for efficient implementation of the most computationally intensive steps of dynamic image coding. Several analogic CNN algorithms are presented for the generation of binary image masks and image decomposition. Measurement results for the first CNN universal chips executing an analogic algorithm for a reconstruction operator are also presented. Based on measured execution times, the viability of the CNN implementation of efficient but computationally expensive compression algorithms such as dynamic image coding is assessed.