Input-output Operator Research Articles

Asynchronous links that re-order samples: An L2 gain embedding

An embedding of the uncertain time-varying delay associated with a class of asynchronous sampled-data links is devised in terms of the L 2 gain of a related input-output operator. For links in the class considered, each output zero-order-hold update event occurs after an uncertain time-varying delay from a corresponding aperiodic input sampling event. The encapsulation of the effective link delay is parametrized by upper and lower bounds on the uncertain interval between sample events and the variable delay for the corresponding update events. The possibility of sample re-ordering at the output can arise when the update delay is allowed to vary freely within the specified bounds, which is accommodated in the analysis. The gain bound based embedding is relevant within the context of input-output based robustness analysis of asynchronous sampled-data networks via small-gain arguments and integral quadratic constraints more generally.

Identification of a space- and time-dependent source in a variable coefficient advection-diffusion equation from Dirichlet and Neumann boundary measured outputs

Abstract This paper considers the inverse problem of identifying an unknown space- and time-dependent source function F ⁢ ( x , t ) F(x,t) in the variable coefficient advection-diffusion equation u t = ( D ⁢ ( x ) ⁢ u x ) x - ( V ⁢ ( x ) ⁢ u ) x + F ⁢ ( x , t ) u_{t}=(D(x)u_{x})_{x}-(V(x)u)_{x}+F(x,t) from the Dirichlet ν ⁢ ( t ) := u ⁢ ( ℓ , t ) \nu(t):=u(\ell,t) and Neumann f ⁢ ( t ) := - D ⁢ ( 0 ) ⁢ u x ⁢ ( 0 , t ) f(t):=-D(0)u_{x}(0,t) , t ∈ ( 0 , T ] t\in(0,T] , boundary measured outputs. This problem was motivated by several important real-world applications in the field of contaminant hydrogeology, and the novel analysis presented here is highly relevant to problems of practical interest. The input-output operators corresponding to the Dirichlet and Neumann measured boundary data are introduced. The inverse problem is then formulated as a system of operator equations consisting of these operators and the measured outputs. The compactness and Lipschitz continuity of the input-output operators are proved in the relevant classes of admissible source functions ℱ and F r \mathcal{F}_{r} . These results together with the derived trace estimates allow us to show the existence of a quasi-solution of the inverse source problem as a minimum of the Tikhonov functional, under minimal regularity assumptions with respect to the source function and other inputs. An explicit gradient formula for the Fréchet gradient of the Tikhonov functional is also derived by means of an appropriate adjoint problem.

Automatic design of mechanical metamaterial actuators

Mechanical metamaterial actuators achieve pre-determined input–output operations exploiting architectural features encoded within a single 3D printed element, thus removing the need for assembling different structural components. Despite the rapid progress in the field, there is still a need for efficient strategies to optimize metamaterial design for a variety of functions. We present a computational method for the automatic design of mechanical metamaterial actuators that combines a reinforced Monte Carlo method with discrete element simulations. 3D printing of selected mechanical metamaterial actuators shows that the machine-generated structures can reach high efficiency, exceeding human-designed structures. We also show that it is possible to design efficient actuators by training a deep neural network which is then able to predict the efficiency from the image of a structure and to identify its functional regions. The elementary actuators devised here can be combined to produce metamaterial machines of arbitrary complexity for countless engineering applications.

An offline framework for high-dimensional ensemble Kalman filters to reduce the time to solution

Abstract. The high computational resources and the time-consuming IO (input/output) are major issues in offline ensemble-based high-dimensional data assimilation systems. Bearing these in mind, this study proposes a sophisticated dynamically running job scheme as well as an innovative parallel IO algorithm to reduce the time to solution of an offline framework for high-dimensional ensemble Kalman filters. The dynamically running job scheme runs as many tasks as possible within a single job to reduce the queuing time and minimize the overhead of starting and/or ending a job. The parallel IO algorithm reads or writes non-overlapping segments of multiple files with an identical structure to reduce the IO times by minimizing the IO competitions and maximizing the overlapping of the MPI (Message Passing Interface) communications with the IO operations. Results based on sensitive experiments show that the proposed parallel IO algorithm can significantly reduce the IO times and have a very good scalability, too. Based on these two advanced techniques, the offline and online modes of ensemble Kalman filters are built based on PDAF (Parallel Data Assimilation Framework) to comprehensively assess their efficiencies. It can be seen from the comparisons between the offline and online modes that the IO time only accounts for a small fraction of the total time with the proposed parallel IO algorithm. The queuing time might be less than the running time in a low-loaded supercomputer such as in an operational context, but the offline mode can be nearly as fast as, if not faster than, the online mode in terms of time to solution. However, the queuing time is dominant and several times larger than the running time in a high-loaded supercomputer. Thus, the offline mode is substantially faster than the online mode in terms of time to solution, especially for large-scale assimilation problems. From this point of view, results suggest that an offline ensemble Kalman filter with an efficient implementation and a high-performance parallel file system should be preferred over its online counterpart for intermittent data assimilation in many situations.

Admissibility criteria for nonuniform dichotomic behavior of nonautonomous systems on the whole line

We give new criteria for nonuniform dichotomy of nonautonomous systems on the whole line in terms of admissibility relative to an integral equation. In our approach the input space I(R,X) is an intersection of spaces that can be successively minimized and the output space C(R,X) can be one of some well-known spaces of continuous functions. Using computational arguments, we show that the admissibility of (C(R,X),I(R,X)) leads to a nonuniform exponential dichotomy. We expose a complete analysis of the connections between admissibility and nonuniform dichotomy on the whole line and we also discuss several interesting consequences. Moreover, we obtain the explicit expression of the growth rates for dichotomy in terms of the initial exponential growth and the norm of the input-output operator. Finally, we present a direct application of the main result in the case of evolution families which admit uniform exponential growth.

Extending Shared-Memory Computations to Multiple Distributed Nodes

With the emergence of accelerators like GPUs, MICs and FPGAs, the availability of domain specific libraries (like MKL) and the ease of parallelization associated with CUDA and OpenMP based shared-memory programming, node-based parallelization has recently become a popular choice among developers in the field of scientific computing. This is evident from the large volume of recently published work in various domains of scientific computing, where shared-memory programming and accelerators have been used to accelerate applications. Although these approaches are suitable for small problem-sizes, there are issues that need to be addressed for them to be applicable to larger input domains. Firstly, the primary focus of these works has been to accelerate the core kernel; acceleration of input/output operations is seldom considered. Many operations in scientific computing operate on large matrices - both sparse and dense - that are read from and written to external files. These input-output operations present themselves as bottlenecks and significantly effect the overall application time. Secondly, node-based parallelization limits a developer from distributing the computation beyond a single node without him having to learn an additional programming paradigm like MPI. Thirdly, the problem size that can be effectively handled by a node is limited by the memory of the node and accelerator. In this paper, an Asynchronous Multi-node Execution (AMNE) approach is presented that uses a unique combination of the shared-file system and pseudo-replication to extend node-based algorithms to a distributed multiple node implementation with minimal changes to the original node-based code. We demonstrate this approach by applying it to GEMM, a popular kernel in dense linear algebra and show that the presented methodology significantly advances the state of art in the field of parallelization and scientific computing.

UEB parallel: Distributed snow accumulation and melt modeling using parallel computing

The Utah Energy Balance (UEB) model supports gridded simulation of snow processes over a watershed. To enhance computational efficiency, we developed two parallel versions of the model, one using the Message Passing Interface (MPI) and the other using NVIDIA's CUDA code on Graphics Processing Unit (GPU). Evaluation of the speed-up and efficiency of the MPI version shows that the effect of input/output (IO) operations on the parallel model performance increases as the number of processor cores increases. As a result, although the computation kernel scales well with the number of cores, the efficiency of the parallel code as a whole degrades. The performance improves when the number of IO operations is reduced by reading/writing larger data arrays. The CUDA GPU implementation was done without major refactoring of the original UEB code, and tests demonstrated that satisfactory performance could be obtained without a major re-work of the existing UEB code.

On [formula omitted]-gain control of 2-D positive Roesser systems with directional delays: Necessary and sufficient conditions

In this paper, the problem of ℓ1-gain control is addressed for two-dimensional (2-D) positive Roesser systems with directional delays. A complete solution to the design problem is presented for the first time. Specifically, by exploiting a new approach based on 2-D Z-transform, an exact value of ℓ1-induced norm of the input–output operator is obtained. This analytical result is utilized to derive necessary and sufficient conditions under which a 2-D positive system with delays is asymptotically stable with a prescribed ℓ1-gain performance. Then, by utilizing a vertex optimization approach, necessary and sufficient conditions are established for the existence of a state-feedback controller (SFC) that makes the closed-loop system positive and stable subject to ℓ1-induced performance. The proposed synthesis conditions are formulated in terms of linear programming (LP), which can be effectively solved by various convex algorithms to minimize the ℓ1-performance index.

QCs characterization of robust stability with simultaneous uncertainties in plant and controller

Within the frame work of nest algebra, the robust stability of feedback interconnections of time-varying discrete-time systems with combined uncertainties in the plant and controller is derived via quadratic constraint (QC) approach, where the plant and controller are taken from two path connected uncertainty sets with respect to the topology induced by the gap metric. Some sufficient conditions for the existence of complementary QCs for the components of stable uncertain feedback systems are derived. The path-connectedness is established for some uncertainty sets with particular properties. The fundamental robust stability result represents a generalization of the input–output operator robust stability theorem of uncertainties appearing in the plant alone, to include the case of simultaneous uncertainties appearing in the controller.

Identification of a temporal load in a cantilever beam from measured boundary bending moment

This paper provides a theoretical foundation and numerical method for an inverse source problem of identifying a temporal load in a cantilever beam, with Neumann measured boundary output (i.e. bending moment) , governed by the Euler–Bernoulli equation , , subject to the initial u(x, 0) = ut(x, 0) = 0, , and the boundary conditions u(0, t) = ux(0, t) = 0, , . The spatial load is assumed to be known. The inverse problem is reformulated as an operator equation , , by introducing the input–output operator . Our approach is based on detailed analysis of this operator by developing the regular weak solution theory for the direct problem. We show how to choose the temporal load and the Neumann measured output in order to guarantee solvability of the inverse problem. We introduce a weaker solution to the adjoint problem corresponding to the inverse problem and prove Fréchet differentiability of the Tikhonov functional . An explicit gradient formula for the Tikhonov functional is derived by making use of the unique weaker solution of the adjoint problem. Furthermore, under additional regularity and consistency conditions, the Lipschitz continuity of the Fréchet gradient is proved. This property allows use of the conjugate gradient algorithm (CGA) which is the main computational tool in solving inverse problems. A numerical method based on the finite-element discretization and the CGA is developed for the solution of the inverse source problem. Numerical examples with random noisy measured output are presented to illustrate the validity and effectiveness of the proposed approach.

Sustainability Assessment of a Qingyuan Mushroom Culture System Based on Emergy

The Qingyuan mushroom culture system (QMCS) in Zhejiang Province has been recognized as the source of the world’s first artificial cultivation of mushrooms with a history of more than 800 years. The system embodies the farming wisdom of the local people who have adapted themselves to and utilized nature and has integrated the traditional bark hacking method with multiple modern patterns for mushroom cultivation based on artificial microbial strains. We have investigated the input–output operation of farmers and assessed and analyzed emergy indicators in a bid to reflect and compare their economic and ecological benefits, as well as their sustainable development by analyzing the three typical mushroom cultivation patterns. The cost-benefit analysis of the three patterns shows that the sawdust medium-cultivated method (SMCM) is characterized by dominance in both net income without labor cost and labor productivity; while the evaluation based on emergy indicators has proven that each has its own advantages and disadvantages in terms of ecological and economic benefits and sustainable development. Among them, the bark hacking method (BHM) features the highest utilization rates of local and renewable resources, the smallest damage to the environment, the lowest production efficiency, and the highest exchange efficiency, but the sawdust medium-cultivated method is just the opposite, and the log-cultivated method (LCM) is the most favorable one for sustainable development. As its agricultural heritage, the QMCS’ core of dynamic protection and adaptive management lies in enhancing the sustainable development of its agricultural production methods. It is recommended that the three patterns be improved by targeting their respective shortcomings and at the same time, integrate their advantages to explore a new sustainable development pattern for mushroom cultivation.

On the finite-time boundedness of linear systems

This paper deals with the finite-time boundedness (FTB) of linear time-varying (LTV) systems; in this context, the novel contribution of our work goes in several directions. The first result is a sufficient condition for FTB when the plant input is generated by an exo-system; it is worth noting that constant, norm bounded signals, which most part of the previous literature has considered so far, belong to such class of inputs. To this regard, it is possible to compare our result with the existing literature, which shows that our approach yields less conservative conditions. The second result provided in the paper, is a sufficient condition for FTB when the input belongs to L2, the class of square integrable signals, which have never been considered so far. In both cases, the proposed results require the solution of a feasibility problem constrained by differential linear matrix inequalities (DLMIs). A third contribution of the paper proves that, from the system-theoretic point of view, the obtained FTB conditions can be interpreted in terms of the norm of a suitable input–output operator. As a consequence of this fact, we are able to find alternative and equivalent conditions for FTB, both for the exogenous and the L2 cases, which are based on the solution of differential Lyapunov equations (DLEs), which are much more efficient from the computational point of view. The DLMI-based condition, however, is fundamental to solve the design problem, which is also investigated in the paper. Some examples show that the proposed technique is less conservative with respect to the previous literature, when exogenous inputs are considered, and its effectiveness when L2 signals are considered. Moreover, one example is devoted to show that the analysis approach, based on the solution of DLE, is much more efficient from the computational point of view with respect to the one based on DLMIs; finally the last example investigates the application of the state feedback control technique.

Linear Compartmental Models: Input-Output Equations and Operations That Preserve Identifiability

This work focuses on the question of how identifiability of a mathematical model, that is, whether parameters can be recovered from data, is related to identifiability of its submodels. We look specifically at linear compartmental models and investigate when identifiability is preserved after adding or removing model components. In particular, we examine whether identifiability is preserved when an input, an output, an edge, or a leak is added or deleted. Our approach, via differential algebra, is to analyze specific input-output equations of a model and the Jacobian of the associated coefficient map. We clarify a prior determinantal formula for these equations, and then use it to prove that, under some hypotheses, a model's input-output equations can be understood in terms of certain submodels we call “output-reachable.” Our proofs use algebraic and combinatorial techniques.

Complete stabilizability and stability radius of time-varying Sturm-Liouville systems

There are many physical systems which can be modeled by a time-varying Sturm-Liouville system i.e. a system is inducted by the negative of a time-varying Sturm-Liouville operator. The system is a time-varying Riesz-spectral system. The goals of this paper are to analyze exact controllability, stabilizability, and stability radius of the time-varying Riesz-spectral systems. The steps of analysis of methods of the paper are to define a time-varying Sturm-Liouville system, to construct sufficient and necessary conditions for exact controllability and stabilizability, and to find stability radius. The analysis uses a strongly continuous quasi-semigroup approach. The results show that sufficient and necessary conditions for exact controllability, exact null controllability, and stabilizability can be constructed. Moreover, in the time-varying Sturm-Liouville systems, the exact null controllability implies the complete stabilizability. This is parallel with infinite dimensional of time-invariant systems. Also, the lower bound for the stability radius of the time-varying Sturm-Liouville systems is a reciprocal of the norm of the input-output operator. An example is provided to confirm the results.

Iteration of database relations for queries of special form

In this paper, the material for compiling a plan of performing “join-selection-projection” queries to relational databases is systematized. This is necessary for counting the number of iterations in the query execution algorithms. The presented topic is relevant for a considerable period of time. However, every time there are new requirements for queries, new methods of data presentation, etc. This leads to the necessity of resolving old problems. Many papers were devoted to various aspects of the optimization of queries to relational databases. Thus, it is possible to define two main directions. They are logical optimization of the queries and physical optimization of the queries execution. The basis of logical optimization is heuristics about the order of relational operations. However, more effective solution to the optimization problem is minimization of input-output operation quantity during the query execution. The approach to the development of the query execution plan on the basis of estimators for input-output operations for conventional and specialized methods of data storage is offered in this paper. The expediency of transformations, use of indexes etc. are determined by estimators.

Development of Predictive Model based Control Scheme for a Molten Carbonate Fuel Cell (MCFC) Process

To improve availability and performance of fuel cells, the operating temperature of a molten carbonate fuel cells (MCFC) stack should be strictly maintained within a specified operation range and an efficient control technique should be employed to meet this objective. While most of modern control strategies are based on process models, many existing models for a MCFC process are not ready to be applied in synthesis and operation of control systems. In this study, auto-regressive moving average (ARMA) model, least square support vector machine (LSSVM) model and artificial neural network (ANN) model for the MCFC system are developed based on input-output operating data. Among these models, the ARMA model showed the best tracking performance. A model predictive control (MPC) method for the operation of a MCFC process is developed based on the proposed ARMA model. For the purpose of comparison, a MPC scheme based on the linearized rigorous model for a MCFC process is developed. Results of numerical simulations show that MPC based on the ARMA model exhibits better control performance than that based on the linearized rigorous model.

On geometric conditions for reduction of the Moreau sweeping process to the Prandtl-Ishlinskii operator

The sweeping process was proposed by J. J. Moreau as a general mathematical formalism for quasistatic processes in elastoplastic bodies. This formalism deals with connected Prandtl's elastic-ideal plastic springs, which can form a system with an arbitrarily complex topology. The model describes the complex relationship between stresses and elongations of the springs as a multi-dimensional differential inclusion (variational inequality). On the other hand, the Prandtl-Ishlinskii model assumes a very simple connection of springs. This model results in an input-output operator, which has many good mathematical properties and admits an explicit solution for an arbitrary input. It turns out that the sweeping processes can be reducible to the Prandtl-Ishlinskii operator even if the topology of the system of springs is complex. In this work, we analyze the conditions for such reducibility.

Model-based control of a molten carbonate fuel cell (MCFC) process

To improve availability and performance of fuel cells, the operating temperature of molten carbonate fuel cells (MCFC) stack should be strictly maintained within a specified operation range, and an efficient control technique should be employed to meet this objective. While most modern control strategies are based on process models, many existing models of MCFC are not ready to be applied in synthesis and operation of control systems. In this study, we developed an auto-regressive moving average (ARMA) model and machine learning methods of least squares support vector machine (LS-SVM), artificial neural network (ANN) and partial least squares (PLS) for the MCFC system based on input-output operating data. The ARMA model showed the best tracking performance. A model predictive control method for the operation of MCFC system was developed based on the proposed ARMA model. The control performance of the proposed MPC methods was compared with that of conventional controllers using numerical simulations performed on various process models including an MCFC process. Numerical results show that ARMA model based control provides improved control performance compared to other control methods.

An inverse problem for the KdV equation with Neumann boundary measured data

Abstract In this paper, we consider an inverse coefficient problem for the linearized Korteweg–de Vries (KdV) equation u t + u x ⁢ x ⁢ x + ( c ⁢ ( x ) ⁢ u ) x = 0 {u_{t}+u_{xxx}+(c(x)u)_{x}=0} , with homogeneous boundary conditions u ⁢ ( 0 , t ) = u ⁢ ( 1 , t ) = u x ⁢ ( 1 , t ) = 0 {u(0,t)=u(1,t)=u_{x}(1,t)=0} , when the Neumann data g ⁢ ( t ) := u x ⁢ ( 0 , t ) {g(t):=u_{x}(0,t)} , t ∈ ( 0 , T ) {t\in(0,T)} , is given as an available measured output at the boundary x = 0 {x=0} . The inverse problem is formulated as a minimum problem for the regularized Tikhonov functional 𝒥 α ⁢ ( c ) = 1 2 ⁢ ∥ u x ⁢ ( 0 , ⋅ ; c ) - g ∥ L 2 ⁢ ( 0 , T ) 2 + α 2 ⁢ ∥ c ′ ∥ L 2 ⁢ ( 0 , 1 ) 2 {\mathcal{J}_{\alpha}(c)=\frac{1}{2}\|u_{x}(0,\cdot\,;c)-g\|^{2}_{L^{2}(0,T)}+% \frac{\alpha}{2}\|c^{\prime}\|^{2}_{L^{2}(0,1)}} with Sobolev norm. Based on a priori estimates for the weak and regular weak solutions of the direct and adjoint problems, it is proved that the input-output operator is compact, which shows the ill-posedness of the inverse problem. Then Fréchet differentiability of the Tikhonov functional and Lipschitz continuity of the Fréchet gradient are proved. It is shown that the last result allows us to use an important advantage of gradient methods when the functional is from the class C 1 , 1 ⁢ ( ℳ ) {C^{1,1}(\mathcal{M})} . In the final part, an existence of a solution of the minimum problem for the regularized Tikhonov functional 𝒥 α ⁢ ( c ) {\mathcal{J}_{\alpha}(c)} is proved.

Platform Storage Performance With 3D XPoint Technology

With a combination of high performance and nonvolatility, the arrival of 3D XPoint memory promises to fundamentally change the memory-storage hierarchy at the hardware, system software, and application levels. This memory will be deployed first as a block addressable storage device, known as the Intel Optane SSD, and even in this familiar form it will drive basic system change. Access times consistently as fast, or faster, than the rest of the system will blur the line between storage and memory. The low latencies from these solid-state drives (SSDs) allow rethinking even basic storage methodologies to be more memory-like. For example, the manner in which storage performance is measured shifts from input–output operations (IOs) at a given queue depth to response time for a given load, like memory is typically measured. System changes to match the low latency of these SSDs are already advanced, and in many cases they enable the application to utilize the SSD’s performance. In other cases, additional work is required, particularly on policies set originally with slow storage in mind. On top of these already-capable systems are real applications. System-level tests show that applications such as key–value stores and real-time analytics can benefit immediately. These application benefits include significantly faster runtime (up to $3\times $ ) and access to larger data sets than supported in DRAM. Newly viable mechanisms for expanding application memory footprint include native application support or native operating system paging, a significant change in the use of SSDs. The next step in this convergence is 3D XPoint memory accessed through processor load/store operations. Significant operating system support is already in place. The implications of consistently low latency storage and fast persistent memory on computing are great, with applications and systems taking advantage of this new technology as storage as the first to benefit.