Local Operators Research Articles

The Advection Boundary Law in absence of mean flow: Passivity, nonreciprocity and enhanced noise transmission attenuation

Sound attenuation along a waveguide is intensively studied for applications ranging from heating and air-conditioning ventilation systems, to aircraft turbofan engines. In particular, the new generation of Ultra-High-By-Pass-Ratio turbofan requires higher attenuation at low frequencies, in less space for liner treatment. This demands to go beyond the classical acoustic liner concepts and overcome their limitations. In this paper, we discuss an unconventional boundary operator, called Advection Boundary Law, which can be artificially synthesized by electroactive means, such as Electroacoustic Resonators. This boundary condition entails nonreciprocal propagation, meanwhile enhancing noise transmission attenuation with respect to purely locally-reacting boundaries, along one sense of propagation. Because of its artificial nature though, its acoustical passivity limits are yet to be defined. A thorough numerical study is provided to assess the performances of the Advection Boundary Law, in absence of mean flow. An experimental test-bench validates the numerical outcomes in terms of passivity limits, non-reciprocal propagation and enhanced isolation with respect to local impedance operators. Guidelines are outlined to properly implement the Advection Boundary Law for optimal noise transmission attenuation. Moreover, the tools and criteria provided here can also be employed for the design and characterization of other innovative liners.

Rényi mutual information in quantum field theory, tensor networks, and gravity

We explore a large class of correlation measures called the α − z Rényi mutual informations (RMIs). Unlike the commonly used notion of RMI involving linear combinations of Rényi entropies, the α − z RMIs are positive semi-definite and monotonically decreasing under local quantum operations, making them sensible measures of total (quantum and classical) correlations. This follows from their descendance from Rényi relative entropies. In addition to upper bounding connected correlation functions between subsystems, we prove the much stronger statement that for certain values of α and z, the α − z RMIs also lower bound certain connected correlation functions. We develop an easily implementable replica trick which enables us to compute the α − z RMIs in a variety of many-body systems including conformal field theories, free fermions, random tensor networks, and holography.

Fusion and Positivity in Chiral Conformal Field Theory

In this article we show that the conformal nets corresponding to WZW models are rational, resolving a long-standing open problem. Specifically, we show that the Jones-Wassermann subfactors associated with these models have finite index. This result was first conjectured in the early 90s but had previously only been proven in special cases, beginning with Wassermann’s landmark results in type A. The proof relies on a new framework for the systematic comparison of tensor products (a.k.a. ‘fusion’) of conformal net representations with the corresponding tensor product of vertex operator algebra modules. This framework is based on the geometric technique of ‘bounded localized vertex operators,’ which realizes algebras of observables via insertion operators localized in partially thin Riemann surfaces. We obtain a general method for showing that Jones-Wassermann subfactors have finite index, and apply it to additional families of important examples beyond WZW models. We also consider applications to a class of positivity phenomena for VOAs, and use this to outline a program for identifying unitary tensor product theories of VOAs and conformal nets even for badly-behaved models.

Towards Sustainable Local Development: Comparative Analysis of Periodic Plans in Nepalese Municipalities

The Local Government Operation Act of 2017 mandates that rural municipalities and municipalities in Nepal develop periodic, annual, and strategic medium- and long-term plans for local-level development. Guided by directives from the National Planning Commission, these plans outline visions, goals, and strategies across social, economic, and physical domains, crucial for sustainable development amidst political stability. These plans integrate governance, environmental considerations, and social inclusion by emphasizing alignment with sustainable development goals and national policies. As primary governance agents, local governments are tasked with formulating these plans to enhance prosperity and socio-economic development within constitutional frameworks. This study examines the objectives, formulation processes, and comparative analysis of periodic plans across Jiri Municipality, Mahankal Rural Municipality, Gauri Shankar Rural Municipality, and Mahalaxmi Municipality in Nepal. It compares their long-term visions, SWOT analyses, sector-wise budgetary allocations, strengths, weaknesses, opportunities, and threats. The findings highlight distinct priorities and challenges each municipality faces, offering insights into tailored strategies for balanced and sustainable development.

Feature ensemble network for medical image segmentation with multi‐scale atrous transformer

AbstractRecent years have witnessed notable advancements in medical image segmentation through deep convolutional neural networks. However, a notable limitation lies in the local operation of convolution, which hinders the ability to fully exploit global semantic information. To overcome the challenges prevalent in medical image segmentation, the feature ensemble network with multi‐scale atrous transformer is proposed. At the core of the approach lies the multi‐scale contextual integration module, which is based on the multi‐scale atrous transformer and facilitates contextual integration of multi‐level features. To extract discriminative fine‐grained features of the target region, a hybrid attention mechanism that synergistically combines spatial and channel attention, thereby sharpening the model's focus on crucial target information within high‐level features, is incorporated. Additionally, the channel‐aware feature reconstruction module is introduced as an innovative component engineered to tackle feature similarity issues across different categories. This module performs feature reconstruction based on channel perception, effectively widening the feature gap between categories and enhancing the segmentation capability. It is worth mentioning that our approach surpasses the state‐of‐the‐art method using three benchmark datasets in medical image segmentation.

A multi-objective PSO for DC microgrids: Efficient battery management to minimize energy losses and operating costs

This article addresses the challenge of battery energy management in a Direct Current (DC) Microgrid (MG) with distributed photovoltaic generators working at their highest power point. This study adopted a multi-objective approach whose main goals is to reduce energy losses and operating costs. To mathematically model this problem, we used Multi-Objective Mixed-Integer Nonlinear Programming (MOMINLP) that incorporated two conflicting objective functions that minimize — at the same time — the energy losses and operating costs of DC MGs. To solve this problem, we followed a master–slave approach. Two multi-objective algorithms were used in the master stage: the Multi-Objective Particle Swarm Optimizer (MOPSO) and the Multi-Objective Lion Ant Optimizer (MOALO). The slave stage applied an hourly load flow analysis employing the method of Successive Approximations (SAs). To validate our methodology, the 33-bus test feeder was adapted by incorporating specific data on generated power and electricity demand from a specific region in Colombia. These data (obtained from the local network operator) are projections of electricity demand for an average day in the region under analysis. The methodology was implemented in the MATLAB environment, and each algorithm was run 100 times to assess standard deviations, maximum reductions, average reductions, and processing times. The two algorithms were compared to identify which one exhibited the best performance when they solved the problem examined here. The results proved that the MOPSO was the most effective approach in terms of minimizing operating costs and significantly reducing energy losses compared to the benchmark scenario.

Entropy transfer efficiency-effectiveness method for heat exchangers, part 1: Local entropy generation number and operation performance limits

Here, to resolve the open problem of the second-law efficiency evaluation for heat exchangers, an efficiency-effectiveness method is developed from pure convection theory, where the entropy transfer efficiency defined as the outlet temperature ratio of cold and hot fluids exchanging entropy and local entropy generation number can measure the global and local irreversibilities of heat transfer. The efficiency and effectiveness are related by the inlet temperature ratio τ and capacity rate ratio φ, and their maxima subject to the local entropy generation number are determined for different flow arrangements. When τ = φ2, the effectiveness maxima are 0.5/(1 + φ) and 1/(1 + φ) while the highest efficiencies are φ and unity for parallelflow and counterflow arrangements, respectively. The optimum operating points of counterflow exchangers, at which the equal outlet temperature τT1∞ (T1∞ represents the hot inlet temperature) of two fluids with a critical capacity rate ratio τ induces uniform irreversibility, the effectiveness limit of 1/(1+τ), and the efficiency limit of unity, are obtained. A linear temperature difference method is also developed based on the redefined convective and overall heat transfer coefficients, invariably yielding an effectiveness equal to the number of heat transfer units. This method has potentials to be extended to wet heat exchangers with phase-change flows.

Quantum Information Spreading in Generalized Dual-Unitary Circuits.

We study the spreading of quantum information in a recently introduced family of brickwork quantum circuits that generalizes the dual-unitary class. These circuits are unitary in time, while their spatial dynamics is unitary only in a restricted subspace. First, we show that local operators spread at the speed of light as in dual-unitary circuits, i.e., the butterfly velocity takes the maximal value allowed by the geometry of the circuit. Then, we prove that the entanglement spreading can still be characterized exactly for a family of compatible initial states (in fact, for an extension of the compatible family of dual-unitary circuits) and that the asymptotic entanglement slope is again independent on the Rényi index. Remarkably, however, we find that the entanglement velocity is generically smaller than 1. We use these properties to find a closed-form expression for the entanglement-membrane line tension.

Quantum Nonlocality: Multicopy Resource Interconvertibility and Their Asymptotic Inequivalence.

Quantum nonlocality, pioneered in Bell's seminal work and subsequently verified through a series of experiments, has drawn substantial attention due to its practical applications in various protocols. Evaluating and comparing the extent of nonlocality within distinct quantum correlations holds significant practical relevance. Within the resource theoretic framework this can be achieved by assessing the interconversion rate among different nonlocal correlations under free local operations and shared randomness. In this study we, however, present instances of quantum nonlocal correlations that are incomparable in the strongest sense. Specifically, when starting with an arbitrary many copies of one nonlocal correlation, it becomes impossible to obtain even a single copy of the other correlation, and this incomparability holds in both directions. Such incomparable quantum correlations can be obtained even in the simplest Bell scenario, which involves two parties, each having two dichotomic measurements setups. Notably, there exist an uncountable number of such incomparable correlations. Our result challenges the notion of a "unique gold coin," often referred to as the "maximally resourceful state," within the framework of the resource theory of quantum nonlocality. To this end, we provide examples of isotropic quantum correlations that cannot be distilled up to the Tsirelson point, and thus partially answer a long-standing open question in nonlocality distillation.

Benchmarking techno-economic performance of greenhouses with different technology levels in a hot humid climate

Greenhouse agriculture is expected to play a critical role in sustainable crop production in the coming decades, opening new markets in climate zones that have been traditionally unproductive for agriculture. Extreme hot and humid conditions, prevalent in rapidly growing economies including the Arabian Peninsula, present unique design and operational challenges to effective greenhouse climate control. These challenges are often poorly understood by local operators and inadequately researched in the literature. This study addresses this knowledge gap by presenting, for the first time, a comprehensive set of benchmarks for water and energy usage, CO2 emissions (CO2e) contribution, and economic performance for low-, mid-, and high-tech greenhouse designs in such climates. Utilising a practical and adaptable model-based framework, the analysis reveals the high-tech design generated the best results for economic return, achieving a 4.9-year payback period with superior water efficiency compared to 5.8 years for low-tech and 7.0 years for mid-tech; however, the high-tech design used significantly more energy to operate its mechanical cooling system, corresponding with higher CO2e per unit area (8.3 and 4.0 times higher than the low- and mid-tech, respectively). These benchmarks provide new insights for greenhouse operators, researchers, and other stakeholders, facilitating the development of effective greenhouse design and operational strategies tailored to meet the challenges of hot and humid climates.

State diagrams to determine tree tensor network operators

This work is concerned with tree tensor network operators (TTNOs) for representing quantum Hamiltonians. We first establish a mathematical framework connecting tree topologies with state diagrams. Based on these, we devise an algorithm for constructing a TTNO given a Hamiltonian. The algorithm exploits the tensor product structure of the Hamiltonian to add paths to a state diagram, while combining local operators if possible. We test the capabilities of our algorithm on random Hamiltonians for a given tree structure. Additionally, we construct explicit TTNOs for nearest neighbour interactions on a tree topology. Furthermore, we derive a bound on the bond dimension of tensor operators representing arbitrary interactions on trees. Finally, we consider an open quantum system in the form of a Heisenberg spin chain coupled to bosonic bath sites as a concrete example. We find that tree structures allow for lower bond dimensions of the Hamiltonian tensor network representation compared to a matrix product operator structure. This reduction is large enough to reduce the number of total tensor elements required as soon as the number of baths per spin reaches 3.

An improved genetic algorithm for robot path planning

The conventional genetic algorithm (GA) for path planning exists several drawbacks, such as uncertainty in the direction of robot movement, circuitous routes, low convergence rates, and prolonged search time. To solve these problems, this study introduces an improved GA-based path-planning algorithm that adopts adaptive regulation of crossover and mutation probabilities. This algorithm uses a hybrid selection strategy that merges elite, tournament, and roulette wheel selection methods. An adaptive approach is implemented to control the speed of population evolution through crossover and mutation. Combining with a local search operation enhances the optimization capability of the algorithm. The proposed algorithm was compared with the traditional GA through simulations, demonstrating shorter path lengths and reduced search times.

Lieb-Robinson correlation function for the quantum transverse-field Ising model

The Lieb-Robinson correlation function is the norm of a commutator between local operators acting on separate subsystems at different times. This provides a useful state-independent measure for characterizing the specifically quantum interaction between spatially separated qubits. The finite propagation velocity for this correlator defines a “light cone” of quantum influence. We calculate the Lieb-Robinson correlation function for one-dimensional qubit arrays described by the transverse-field Ising model. Direct calculations of this correlation function have been limited by the exponential increase in the size of the state space with the number of qubits. We introduce a technique that avoids this barrier by transforming the calculation to a sum over Pauli walks which results in linear scaling with system size. We can then explore propagation in arrays of hundreds of qubits and observe the effects of the quantum phase transition in the system. We observe the emergence of two distinct velocities of propagation: a correlation front velocity, which is affected by the phase transition, and the Lieb-Robinson velocity which is not. The correlation front velocity is equal to the maximum group velocity of single quasiparticle excitations. The Lieb-Robinson velocity describes the extreme leading edge of correlations when the value of the correlation function itself is still very small. For the semi-infinite chain of qubits at the quantum critical point, we derive an analytical result for the correlation function. Published by the American Physical Society 2024

A multiplicity result for critical elliptic problems involving differences of local and nonlocal operators

We study some critical elliptic problems involving the difference of two nonlocal operators, or the difference of a local operator and a nonlocal operator. The main result is the existence of two nontrivial weak solutions, one with negative energy and the other with positive energy, for all sufficiently small values of a parameter. The proof is based on an abstract result recently obtained in \cite{MR4293883}.

Learning Topological Operations on Meshes with Application to Block Decomposition of Polygons

We present a learning based framework for mesh quality improvement on unstructured triangular and quadrilateral meshes. Our model learns to improve mesh quality according to a prescribed objective function purely via self-play reinforcement learning with no prior heuristics. The actions performed on the mesh are standard local and global element operations. The goal is to minimize the deviation of the node degrees from their ideal values, which in the case of interior vertices leads to a minimization of irregular nodes.

An unmanned aerial vehicle autonomous flight trajectory planning method and algorithm for the early detection of the ignition source during fire monitoring

ABSTRACT Timely identification of a fire’s origin in its initial stages is essential for minimizing human as well as material losses. Hence, formulating a methodology and algorithm for autonomously planning the flight path of an unmanned aerial vehicle (UAV) during fire monitoring to identify ignition sources early is a pressing objective. The proposed ignition detection method comprises three flight plans (FPs); Flight Plan A (FPA) involves surveying the monitored area with tacks, and assessing harmful substance concentrations in each pixel. Upon identifying a pixel surpassing the threshold concentration, Flight Plan B (FPB) directs the UAV control for targeted navigation, employing local planning based on calculating local differential operators within a nine-element mask. FPB enables the UAV to directly reach and pinpoint the fire source coordinates. Flight Plan C (FPC) outlines the UAV’s return journey to the departure point from any pixel within the monitoring zone. A multi-criteria algorithm for UAV flight path control has been devised, facilitating the determination of local target pixels and subsequent Local Flight Plan (LFP) construction. The guiding principle for constructing an LFP is the ‘at least three pixels on the tack’ rule, yielding a nine-element matrix with known harmful substance concentrations in the target pixel. It enables the identification of pixels within the LFP where obtaining this matrix is unattainable. Mathematical modelling of the UAV flight control algorithm, as per the proposed methodology, was executed using MATLAB® R2019b, demonstrating control stability and accelerated attainment of ignition source pixel coordinates. The achieved speed surpassed the set goal by 1.5 to 2 times, contingent on the ignition source’s location concerning the monitored territory’s flyby direction.

Protection of entanglement in two independently decohering qubits via local prior and post parity-time symmetry operations

Protection of entanglement of two qubits undergoing two independent amplitude damping channels using a local parity-time ( PT ) symmetric operation is exactly studied. First, the explicit expressions of concurrence quantifying the entanglement of two qubits with both local PT symmetric operation and two amplitude damping channels are obtained. Then, we give two schemes, i.e. prior and post PT symmetric operations, to show the performance of PT symmetric operation on entanglement dynamics of two qubits. By investigation, we find that the effect of prior PT symmetric operation schemes on the protection of entanglement of two qubits in the double channel case is superior to that of the single channel case. Conversely, the effect of post PT symmetric operation scheme on the protection of entanglement of two qubits in the single channel case is better than that in the double channel case. In other words, the local PT symmetric operation approach may have potential applications in combating amplitude damping decoherence.

Amplification of genuine tripartite nonlocality and entanglement in the Schwarzschild spacetime under decoherence

We investigate the amplification of the genuine tripartite nonlocality (GTN) and the genuine tripartite entanglement (GTE) of Dirac particles in the background of a Schwarzschild black hole by a local filtering operation under decoherence. It is shown that the physically accessible GTN will be completely destroyed by decoherence, and the local filtering operation can cause the physically accessible GTN to be generated in the system coupled with the environment, which has not been discovered before and is beneficial for quantum information processing. Furthermore, we also find that the physically accessible GTE approaches a stable value in the limit of infinite Hawking temperature for most cases, and the nonzero stable value of GTE can be increased by performing the local filtering operation, even in the presence of decoherence. In particular, if the decoherence parameter p is less than 1, the “sudden death” of GTE will take place when the decoherence strength is large enough. Finally, we have shown that physically inaccessible GTE can be enhanced with the operation of the local filter, whereas inaccessible GTN are not allowed to occur in the presence of decoherence.

On unitary time evolution out of equilibrium

We consider d-dimensional quantum systems which for positive times evolve with a time-independent Hamiltonian in a nonequilibrium state that we keep generic in order to account for arbitrary evolution at negative times. We show how the one-point functions of local operators depend on the coefficients of the expansion of the nonequilibrium state on the basis of energy eigenstates. We express in this way the asymptotic offset and show under which conditions oscillations around this value stay undamped at large times. We also show how, in the case of small quenches, the structure of the general results simplifies and reproduces that known perturbatively.

Asymmetric controlled remote implementation of operations in different dimensions

Quantum entanglement is essential for the realization of distributed computing and has been implemented in various types of two-level systems. However, high-dimensional quantum protocols are rarely investigated both theoretically and experimentally, despite the remarkable advantages that high-dimensional quantum systems exhibit over two-level systems for certain quantum information and computing tasks. Here, we propose asymmetric protocols that utilize different dimensional systems to prepare the stator and achieve remote state operations with the assistance of shared N-partite graph states. Our protocols demonstrate convincing control power and security, with all implementations achievable through local operations and classical communications. The experimental realization of high-dimensional quantum systems and operations is presented using current technology. Our work contributes towards achieving arbitrary high-dimensional quantum protocols and paves the way for implementing high-dimensional quantum communication and computation.