Transfer Operator Research Articles

A novel trusted hardware-based scalable security framework for IoT edge devices

The Internet of Things (IoT) devices are pervasively deployed and embedded into our daily lives. Over several years, the massive assimilation of IoT devices has given rise to smart cities, smart factories, smart farms, etc. While IoTs can collect immense amounts of user and environmental information, the lack of adequate security measures is among the major concerns about information security and privacy. With the ever-increasing presence of IoTs, information flow between IoT devices in a single or multi-layered network is becoming increasingly vulnerable to attacks. Although several software-based solutions have been developed over the years that improve the security of resource-constrained IoT devices, there are limited efforts on hardware-oriented IoT security solutions. This paper proposes a Trusted HArdware-based Scalable Secure Architecture (THASSA) for IoT Edge systems. Leveraging standard cryptographic algorithms, THASSA provides a secure mechanism for data transfer and off-loads cryptography operations to trusted hardware. The modularized THASSA architecture allows devices to be added or removed without user intervention. Also, THASSA could be scaled to multiple subsystems using multiple trusted hardware to form IoT clusters with secure data path(s) for mission-critical applications. An experimental study has verified the correctness and effectiveness of THASSA.

CLT for $$\beta $$-Ensembles at High Temperature and for Integrable Systems: A Transfer Operator Approach

AbstractIn this paper, we prove a polynomial central limit theorem for several integrable models and for the$$\beta $$β-ensembles at high temperature with polynomial potential. Furthermore, we connect the mean values, the variances and the correlations of the moments of the Lax matrices of these integrable systems with the ones of the$$\beta $$β-ensembles. Moreover, we show that the local functions’ space-correlations decay exponentially fast for the considered integrable systems. For these models, we also established a Berry–Esseen-type bound.

An Integrated Framework for Dynamic Vehicle Routing Problems with Pick-up and Delivery Time Windows and Shared Fleet Capacity Planning

This paper proposes a novel route optimization framework to solve the problem of instant pick-up and delivery for e-grocery orders. The proposed framework extends the traditional time-windowed package delivery problem. We demonstrate the effectiveness of our approach for this integrated problem using actual delivery data from HepsiJet, a leading e-commerce logistics provider in Turkey. We first employ several machine learning algorithms and simulations to investigate the capacity of the courier. Subsequently, a dynamic route planning workflow is executed with a highly specialized and novel routing algorithm. Our proposed heuristic approach considers combined fleet operations for delivering regular packages originating from a central depot and dynamic e-grocery orders picked up at local supermarkets and delivered to the customers. The heuristic algorithm constitutes k-opt and node transfer operation variations customized for this integrated problem. We report the performance of our approach in problem instances from the literature and instances from HepsiJet’s daily operations, which we also publicly share as new route optimization problem instances. Our results suggest that, despite the more complex nature of the integrated problem, our proposed algorithm and solution framework produce more efficient and cost-effective solutions that offer additional business opportunities for companies such as HepsiJet. The computational analyses reveal that implementing our proposed approach yields significant efficiency gains and cost reductions for the company, with a distance reduction of over 30%, underscoring our approach’s effectiveness in achieving substantial cost savings and enhanced efficiency through integrating two distinct delivery operations.

Liquid mass gauging during propellant transfer in microgravity

Advancing the precision of low-gravity liquid propellant mass gauging is a roadmap challenge for NASA and a significant obstacle to expanding human presence in space. We report flight test data for an implementation of a low-gravity liquid propellant mass gauging technology that is both non-invasive and propellant agnostic. The TRIO payload experiment flew twice on the Blue Origin New Shepard suborbital rocket and validated computational models of liquid distribution in microgravity at three different fill levels. The Propellant Refueling and On-orbit Transfer Operations (PROTO) payload experiment also flew twice on New Shepard and acquired mass gauging data before, during, and after a tank drain and fill that simulated in-space propellant transfers. Propellant volume estimates were derived at 1 Hz using the Modal Propellant Gauging (MPG) system. Analytical, semi-empirical, and finite element (FE) model results for predicted mode frequencies are compared to flight data for mode frequencies across a range of fill levels during the simulated propellant transfer. Flight (0-g), ground (1-g) and FEM mode frequencies for both 0- and 1-g are well-predicted by the semi-empirical models for frequency dependence on tank fill level.

Casimir Energy through Transfer Operators for Sine-Gordon Backgrounds

Abstract The quantum vacuum interaction energy between a pair of semitransparent two-dimensional plates represented by Dirac delta potentials and its first derivative, embedded in the topological background of a sine-Gordon kink, is studied through an extension of the TGTG-formula (developped by O. Kenneth and I. Klich in the scattering approach). Quantum vacuum oscillations around the sine-Gordon kink solutions are interpreted as a quantum scalar field theory in the spacetime of a domain wall. Moreover, the relation between the phase shift and the density of states (the well-known Dashen–Hasslacher–Neveu or DHN formula) is also exploited to characterize the quantum vacuum energy.

Asymptotically ɑ hemicontractive mappings in Hilbert spaces and a new algorithm for solving associated split common fixed point problem

We introduce a novel class of asymptotically $\alpha-$hemicontractive mappings and demonstrate its relationship with the existing related families of mappings. We establish certain interesting properties of the fixed point set of the new class of mappings. Furthermore, we propose and investigate a new iterative algorithm for solving split common fixed point problem for the new class of mappings. In particular, weak and strong convergence theorems for solving split common fixed point problem for our new class of mappings in Hilbert spaces are proved. Moreover, using our method, we require no prior knowledge of norm of the transfer operator. The results presented in the paper extend and improve the results of Censor and Segal [Censor, Y.; Segal, A. The split common fixed point problem for directed operators. {\it J. Convex Anal.} {\bf 16 } (2009), no. 2, 587–600.], Moudafi [Moudafi, A. The split common fixed-point problem for demicontractive mappings. {\it Inverse Problems} {\bf 26} (2010), no. 5:055007.; Moudafi, A. A note on the split common fixed-point problem for quasi-nonexpansive operators. {\it Nonlinear Anal.} {\bf 74} (2011), no. 12, 4083–4087.], Chima and Osilike [Chima, E. E.; Osilike, M. O. Split common fixed point problem for class of asymptotically hemicontractive mappings. {\it J. Nigerian Math. Soc.} {\bf 38} (2019), no. 3, 363--390.], Fan \textit{et al} [Fan, Q.; Peng, J.; He, H. Weak and strong convergence theorems for the split common fixed point problem with demicontractive operators. {\it Optimization} {\bf 70} (2021), no. 5-6, 1409--1423.] and host of other related results in literature.

Entropic transfer operators

We propose a new concept for the regularization and discretization of transfer and Koopman operators in dynamical systems. Our approach is based on the entropically regularized optimal transport between two probability measures. In particular, we use optimal transport plans in order to construct a finite-dimensional approximation of some transfer or Koopman operator which can be analyzed computationally. We prove that the spectrum of the discretized operator converges to the one of the regularized original operator, give a detailed analysis of the relation between the discretized and the original peripheral spectrum for a rotation map on the n-torus and provide code for three numerical experiments, including one based on the raw trajectory data of a small biomolecule from which its dominant conformations are recovered.

Thermodynamic formalism on the Skorokhod space: the continuous-time Ruelle operator, entropy, pressure, entropy production and expansiveness

Thermodynamic formalism on the Skorokhod space: the continuous-time Ruelle operator, entropy, pressure, entropy production and expansiveness

Data-Driven Stochastic Optimal Control With Safety Constraints Using Linear Transfer Operators

We provide a data-driven framework for optimal control of a continuous-time control-affine stochastic dynamical system. The proposed framework relies on the linear operator theory involving Perron-Frobenius (P-F) and Koopman operators. Our first result involving the P-F operator provides a convex formulation to the optimal control problem in the dual space of densities. This convex formulation of the stochastic optimal control problem leads to an infinite-dimensional convex program. The finite-dimensional approximation of the convex program is obtained using a data-driven approximation of the linear operators. We provide rigorous error bounds and convergence rate for the data-driven approximation of the linear operators and comment on the convergence rate of the optimal control w.r.t. data size. Our second results demonstrate using the Koopman operator, dual to the P-F operator, for the stochastic optimal control design. We show that the Hamilton Jacobi Bellman (HJB) equation can be expressed using the Koopman operator. We provide an iterative procedure along the lines of a popular policy iteration algorithm based on the data-driven approximation of the Koopman operator for solving the HJB equation. The two formulations, namely the convex formulation involving the P-F operator and the Koopman-based formulation using the HJB equation, can be viewed as dual to each other where the duality follows due to the dual nature of the P-F and Koopman operators. Finally, we present examples to demonstrate the efficacy of the developed framework and verify the convergence rates for the operator and optimal control numerically.

Augmented Lagrangian Acceleration of Global-in-Time Pressure Schur Complement Solvers for Incompressible Oseen Equations

This work is focused on an accelerated global-in-time solution strategy for the Oseen equations, which highly exploits the augmented Lagrangian methodology to improve the convergence behavior of the Schur complement iteration. The main idea of the solution strategy is to block the individual linear systems of equations at each time step into a single all-at-once saddle point problem. By elimination of all velocity unknowns, the resulting implicitly defined equation can then be solved using a global-in-time pressure Schur complement (PSC) iteration. To accelerate the convergence behavior of this iterative scheme, the augmented Lagrangian approach is exploited by modifying the momentum equation for all time steps in a strongly consistent manner. While the introduced discrete grad-div stabilization does not modify the solution of the discretized Oseen equations, the quality of customized PSC preconditioners drastically improves and, hence, guarantees a rapid convergence. This strategy comes at the cost that the involved auxiliary problem for the velocity field becomes ill conditioned so that standard iterative solution strategies are no longer efficient. Therefore, a highly specialized multigrid solver based on modified intergrid transfer operators and an additive block preconditioner is extended to solution of the all-at-once problem. The potential of the proposed overall solution strategy is discussed in several numerical studies as they occur in commonly used linearization techniques for the incompressible Navier–Stokes equations.

Evaluation of Individual Variation of d-Amino Acids in Human Plasma by a Two-Dimensional LC-MS/MS System and Application to the Early Diagnosis of Chronic Kidney Disease.

For the discovery of sensitive biomarkers of kidney function focusing on chiral amino acids, a multiple heart-cutting two-dimensional (2D) liquid chromatography-mass spectrometry (LC-MS)/MS system has been designed/developed. As the target analytes, alanine (Ala), aspartic acid, glutamic acid (Glu), leucine (Leu), lysine, methionine, phenylalanine (Phe), proline (Pro), serine (Ser), and valine were selected considering the presence of their d-forms in mammals. The 2D LC-MS/MS system consisted of the nonenantioselective reversed-phase separation of the target amino acids, the separations of the d- and l-enantiomers, and detection using MS/MS. Using the method, the plasma chiral amino acids, precolumn derivatized with 4-fluoro-7-nitro-2,1,3-benzoxadiazole, were isolated from other intrinsic substances, then determined without losing sensitivity by the fully automated whole-peak volume transfer operation from first to second dimension. In all of the tested plasma samples obtained from five healthy individuals and 15 patients with chronic kidney disease (CKD), the target chiral amino acids were determined without interference. In healthy individuals, the levels of all the tested d-amino acids were regulated in the low ranges. In contrast, the % d values of Glu, Leu, and Phe significantly increased with the progress of kidney dysfunction, besides the previously reported values of d-Ala, Pro, and Ser. Concerning Phe, the significant increase of the % d values (p < 0.05) was reported for the first time even in the mild CKD group compared to those of the healthy group; d-Phe might be a more sensitive marker than the previously reported d-forms. These results demonstrated the potential of these d-forms as the sensitive biomarkers of kidney function for the early diagnosis of CKD.

A multi‐objective transportation model for COVID‐19 patients: lesson learned from France

AbstractThe current COronaVIrus Disease 2019 (COVID‐19) pandemic has revealed many challenges to the world. The pandemic obliged public authorities to impose lockdowns and stop several activities. Limited hospital capacity was considered one of the main reasons behind lockdown decisions. To partially face hospital congestion, the healthcare authorities suggested transferring patients to hospitals in regions with available beds to relieve overloaded hospitals. Such transfer operations required exceptional modes of transportation such as trains and airplanes. This paper aims to demonstrate that efficient health logistics might help face the pandemic health effects and save lives. In this paper, we propose a multi‐objective mathematical program to schedule the transfer of patients using trains and airplanes. The proposed sustainable logistics model was tested using French real‐life data for the period March–April 2020 using CPLEX software. We also illustrate the health benefits of our solution.

Controlled transport of fluid particles by microrotors in a Stokes flow using linear transfer operators

The manipulation of a collection of fluid particles in a low Reynolds number environment has several important applications. As we demonstrate in this paper, this manipulation problem is related to the scientific question of how fluid flow structures direct Lagrangian transport. We investigate this problem of directing the transport by manipulating the flow, specifically in the Stokes flow context, by controlling the strengths of two rotors fixed in space. We demonstrate a novel dynamical systems approach for this problem and apply this method to several scenarios of Stokes flow in unbounded and bounded domains. Furthermore, we show that the time-varying flow field produced by the optimal control can be understood in terms of dynamical structures such as coherent sets that define Lagrangian transport. We model the time evolution of the fluid particle density using finite-dimensional approximations of the Liouville operators for the microrotor flow fields. Using these operators, the particle transport problem is framed as an optimal control problem, which we solve numerically. This framework is then applied to the problem of transporting a blob of fluid particles in domains with different boundary conditions: free space, near to a plane wall, in a circular confinement, and the transport of two distributions of particles to a common target. These examples demonstrate the effectiveness of the proposed framework and also shed light on the effects of boundaries on the ability to achieve a desired fluid transport using a rotor-driven flow.

Transfer operators on graphs: spectral clustering and beyond

Graphs and networks play an important role in modeling and analyzing complex interconnected systems such as transportation networks, integrated circuits, power grids, citation graphs, and biological and artificial neural networks. Graph clustering algorithms can be used to detect groups of strongly connected vertices and to derive coarse-grained models. We define transfer operators such as the Koopman operator and the Perron–Frobenius operator on graphs, study their spectral properties, introduce Galerkin projections of these operators, and illustrate how reduced representations can be estimated from data. In particular, we show that spectral clustering of undirected graphs can be interpreted in terms of eigenfunctions of the Koopman operator and propose novel clustering algorithms for directed graphs based on generalized transfer operators. We demonstrate the efficacy of the resulting algorithms on several benchmark problems and provide different interpretations of clusters.

File Packer-Un packer System

The File Packer/ Un packer Application is a software designed to streamline the process of compressing and decompressing files and folders. In the digital age, the need for efficient data storage and transfer is paramount. This Application aims to address this need by providing a versatile and user-friendly tool for packing multiple files and directories into a single compressed archive, as well as extracting them when required. The application features a robust user interface that allows users to select files and folders for packing and specify compression settings. It supports various compression algorithms, such as ZIP, GZIP, and RAR, offering flexibility to accommodate different user preferences and requirements. Additionally, the application provides options for password protection and encryption to enhance data security [1]. In a world where data management and security are of paramount importance, Our File Packer/Unpacker Application aims to simplify and enhance the process of file compression and decompression. This Application offers a versatile and secure solution for individuals and organizations seeking to optimize their data storage and transfer operations. Key Word: File Management, Lempel-Ziv-Welch (LZW), Data security, Data storage, Achive Files

Entanglement and confinement in lattice gauge theory tensor networks

We develop a transfer operator approach for the calculation of Rényi entanglement entropies in arbitrary (i.e. Abelian and non-Abelian) pure lattice gauge theory projected entangled pair states in 2+1 dimensions. It is explicitly shown how the long-range behavior of these quantities gives rise to an entanglement area law in both the thermodynamic limit and in the continuum. We numerically demonstrate the applicability of our method to the ℤ2 lattice gauge theory and relate some entanglement properties to the confinement-deconfinement transition therein. We provide evidence that Rényi entanglement entropies in certain cases do not provide a complete probe of (de)confinement properties compared to Wilson loop expectation values as other genuine (nonlocal) observables.

Joint optimal operation of the South-to-North Water Diversion Project considering the evenness of water deficit

Abstract. Inter-basin water transfer projects are the main measure to address the water deficit crisis caused by uneven distribution of water resources. The current water transfer operation mainly tends to be present in areas with small water transfer costs and is prone to encounter the problem of spatial and temporal imbalances in water allocation. To address these issues, this paper defines a water deficit evenness index (WDEI), aimed at minimizing regional differences in water scarcity and sharing the pressure of water scarcity as a social demand objective. This index is incorporated into a joint optimization model for the Jiangsu section of the South-to-North Water Diversion Project (J-SNWDP), which comprises both the ecological objective of the total water deficit (TWD) and the economic objective of the pumping water (PW). Further, the Nondominated Sorting Genetic Algorithm III (NSGA-III) and multi-attribute decision-making were applied to solve the model and obtain an optimal operation strategy. The results showed the following: (1) the WDEI defined in this paper can mitigate the synchronized water scarcity in certain water users. In typical normal years (wet year and dry year), the WDEI shows a reduction of 94.2 % (81.8 %, 76.7 %) compared to the historical operation strategy. (2) The optimized operation strategy can significantly reduce TWD and PW by 82.06% (37.69 %, 52.36 %) and 45.13 % (3.25 %, 21.51 %) compared with the historical values, respectively, which can improve the water supply satisfaction and reduce the project cost. At the same time, the lake storage capacity of the optimal operation strategy performs well, and the water transfer efficiency of the river is significantly improved. (3) In this paper, targeted optimal operation strategies and potential ways to secure the project tasks are proposed for different natural flow. Overall, it is of great significance to study the water supply equity in the J-SNWDP to alleviate the concentrated water deficit in Jiangsu Province and other similar regions.

Dual symplectic classical circuits: An exactly solvable model of many-body chaos

We propose a general exact method of calculating dynamical correlation functions in dual symplectic brick-wall circuits in one dimension. These are deterministic classical many-body dynamical systems which can be interpreted in terms of symplectic dynamics in two orthogonal (time and space) directions. In close analogy with quantum dual-unitary circuits, we prove that two-point dynamical correlation functions are non-vanishing only along the edges of the light cones. The dynamical correlations are exactly computable in terms of a one-site Markov transfer operator, which is generally of infinite dimensionality. We test our theory in a specific family of dual-symplectic circuits, describing the dynamics of a classical Floquet spin chain. Remarkably, expressing these models in the form of a composition of rotations leads to a transfer operator with a block diagonal form in the basis of spherical harmonics. This allows us to obtain analytical predictions for simple local observables. We demonstrate the validity of our theory by comparison with Monte Carlo simulations, displaying excellent agreement with the latter for a choice of observables.

Exponential rate of decay of correlations of equilibrium states associated with non-uniformly expanding circle maps

In the context of expanding maps of the circle with an indifferent fixed point, understanding the joint behavior of dynamics and pairs of moduli of continuity (ω,Ω) may be a useful element for the development of equilibrium theory. Here we identify a particular feature of modulus Ω (precisely limx→0+supdΩ(dx)/Ω(d)=0 ) as a sufficient condition for the system to exhibit exponential decay of correlations with respect to the unique equilibrium state associated with a potential having ω as modulus of continuity. This result is derived from obtaining the spectral gap property for the transfer operator acting on the space of observables with Ω as modulus of continuity, a property that, as is well known, also ensures the Central Limit Theorem. Examples of application of our results include the Manneville–Pomeau family.

Transfer operation ride though control strategy of the aircraft power supply system with lithium battery energy storage

The aircraft power supply system turns towards multi-source, and transfer operation will likely happen during flight missions and fault conditions. The transfer may lead to voltage interruptions and current surges, adversely affecting power quality. This paper proposes incorporating a lithium battery energy storage system (ESS) into the aircraft high-voltage direct current (HVDC) power system. The ESS employs a voltage control model with a lower voltage reference base, facilitating a smooth transfer operation during power interruptions. This approach reduces voltage fluctuations in the power supply system, enhances power quality, and enables seamless power transfer during the transfer operation.