General Operator Research Articles

Purification of noisy measurements and faithful distillation of entanglement

Abstract We consider entanglement distillation with noisy operations in which quantum measurements that constitute a general quantum operation are particularly noisy. We present a protocol for purifying noisy measurements and show that imperfect local operations can distill entanglement. The protocol works for arbitrary noisy measurements in general and is cost-effective and resource-efficient with single additional qubits to resolve the distillation of entanglement. The purification protocol is feasible with currently available quantum technologies and readily applied to entanglement applications.

Uncertainty and worst-case expectation analysis for multiphysics QPR simulations

Abstract Quadrupole resonators (QPRs) serve to characterize superconducting samples. Like any cavity, during operation, they will deviate from the design geometry for various reasons. Those deviations can be static, stemming from manufacturing variations reflected in the manufacturing tolerances, or dynamic, such as electromagnetic radiation pressure (Lorentz detuning) or microphonics. As a result, a QPR's measurement accuracy and general operation can be severely limited. In particular, during operation, it became evident that the third operating mode of typical QPRs is mainly affected. In this work, by solving the underlying multiphysics problem with random input parameters, we predict the predominant sources of significant measurement bias in surface resistance. On the one hand, we employ the stochastic collocation method compound with the polynomial chaos expansion (PC-SCM) to quantify uncertainties in the physical model governed by a coupled electro-stress-heat (E-S-H) problem. On the other hand, we explore the perturbation analysis to calculate the mean-worst-scenario bound of the merit functions due to the first-order truncation of the Taylor expansion around mean parameter values. The developed method allows us to study the effect of a small nonlinear deformation on the performance of the QPR. Finally, we discuss the simulation results and their implication for the operational conditions of the QPRs.

SpaGAN: A spatially-aware generative adversarial network for building generalization in image maps

Building generalization is an essential task in generating multi-scale topographic maps. The progress of deep learning offers a new paradigm to overcome the coordination challenges faced by conventional building generalization algorithms. Some studies have confirmed the feasibility of several original semantic segmentation networks, such as U-Net and its variants and the conditional generative adversarial network (cGAN), for building generalization in image maps. However, they suffer from critical deformation effects, especially for large and geometrically complex buildings. Since learning building generalization essentially means modeling the subtle transformation of building footprints across scales, we argue that the spatial awareness of a neural network, for instance, regarding building size and shape, is crucial to effective learning. Thus, we propose a spatially-aware generative adversarial network, SpaGAN. It takes a representative cGAN, pix2pix, as the backbone, and modifies two modules: In the U-Net-based generator, an atrous spatial pyramid pooling (ASPP) module replaces the conventional convolutional module to extract multi-scale features of buildings of varying sizes and shapes; in the PatchGAN-based discriminator, a signed distance map (SDM) module is used to capture the fine-grained shape difference for discrimination. The proposed network was comprehensively evaluated with a synthetic and a real-world dataset. The results demonstrate that SpaGAN outperforms existing baseline models (U-Net, ResU-Net, pix2pix) for building generalization, particularly in the real-world dataset. The new model can achieve more reasonable aggregation, simplification, and squaring generalization operators.

Experimental analysis on the prototype of decentralised air handling unit with ball-packed regenerator

Decentralised, wall mounted ventilation is one of alternative to typical – cross flow or “heat wheel” recovery air handling units (AHU) system when it is not possible to install it. It solves problems such as the need for more space, power consumption of fans, and investment costs. This experimental study aims to analyse the performance of the unique constructed decentralised air handling unit (DAHU) prototype that has a special balls-packed regenerative heat exchanger. The development of the DAHU also aimed to simplify the operation and production of the unit to make it more affordable and easier to manufacture. As the DAHU is constructed from individually sized components, the pressure losses of the diffuser, the regenerator, the screens to hold the balls, the filter and the fan were measured and the actual DAHU airflow was determined. The general operation of the DAHU was tested in a climatic chamber to determine the appropriate cycle times for this type of device, as well as the heat recovery efficiency at different outdoor air temperatures. Five different DAHU operating cycles were analysed. It was found that the duration of supply air must be longer than the duration of extract air to achieve higher efficiency. Therefore, DAHU's subsequent heat exchanger studies were performed for four airflows. The highest DAHU heat recovery efficiency was achieved (above 70%) with a supply and extract duration of 150 s. It has been found that the efficiency of this DAHU increases with decreasing outdoor air temperature because of the storage properties of the balls. The analysis showed that this type of DAHU could be suitable for use in cooler and colder climates.

Towards safer general aviation operations using a vision-based decision support system for weather threat avoidance

The commercial aviation sector has achieved significant advancements in safety owing to robust Air Traffic Management technologies and rigorous regulatory measures. In contrast, General Aviation (GA) operations present unique safety challenges that demand focused attention. This study proposes an innovative decision support system tailored for GA pilots to augment their situational awareness. Our approach leverages on-board camera data in conjunction with semantic weather descriptors to construct an uncertainty-aware neural network model. The model provides predictions with quantified uncertainties while handling multiple labels and categories across diverse weather conditions. To validate the effectiveness of our framework, extensive experiments were conducted utilizing a flight simulator as a data collection platform. The results demonstrate that our model showcased significant improvements over the multiple baselines. We also found that a cost-sensitive learning approach can provide more conservative predictions while yielding performance improvements. Ultimately, our decision support framework aims to complement existing weather data sources, such as Next Generation Weather Radar (NEXRAD) data and Meteorological Aerodrome Reports (METAR) from airports, without imposing the burden of mounting expensive and bulky on-board weather radar systems.

Significant Study of Fuzzy Fractional Inequalities with Generalized Operators and Applications

There are many techniques for the extension and generalization of fractional theories, one of which improves fractional operators by means of their kernels. This paper is devoted to the most general concept of interval-valued functions, studying fractional integral operators for interval-valued functions, along with the multi-variate extension of the Bessel–Maitland function, which acts as kernel. We discuss the behavior of Hermite–Hadamard Fejér (HHF)-type inequalities by using the convex fuzzy interval-valued function (C-FIVF) with generalized fuzzy fractional operators. Also, we obtain some refinements of Hermite–Hadamard(H-H)-type inequalities via convex fuzzy interval-valued functions (C-FIVFs). Our results extend and generalize existing findings from the literature.

On the Problem of the Uniqueness of Fixed Points and Solutions for Quadratic Fractional-Integral Equations on Banach Algebras

In this paper, we study the problem of the uniqueness of fixed points for operators defined on subspaces of the space of continuous functions C[a,b] equipped with norms stronger than the supremum norm. We are particularly interested in Hölder spaces since they are natural ranges of integral operators of fractional order. Our goal is to preserve the expected regularity of the fixed points (solutions of the equations) when investigating their uniqueness, without assuming a contraction condition on the space under study. We claim some symmetry between the case of the obtained results and the case of the classical Banach fixed-point theorem in such spaces, even for operators which are not necessarily contractions in the sense of the norm of these subspaces. This result is of particular interest for the study of quadratic integral equations, and as an application example we prove the uniqueness theorem for such a kind equations with general fractional order integral operators, which are not necessarily contractions, in a suitably constructed generalized Hölder space.

Unambiguous discrimination of general quantum operations.

The discrimination of quantum operations has long been an intriguing challenge, with theoretical research notably advancing our understanding of the quantum features in discriminating quantum objects. This challenge is closely related to the discrimination of quantum states, and proof-of-principle demonstrations of the latter have already been realized using optical photons. However, the experimental demonstration of discriminating general quantum operations, including both unitary and nonunitary operations, has remained elusive. In general quantum systems, especially those with high dimensions, the preparation of arbitrary quantum states and the implementation of arbitrary quantum operations and generalized measurements are nontrivial tasks. Here, we experimentally demonstrate the optimal unambiguous discrimination of up to six displacement operators and the unambiguous discrimination of nonunitary quantum operations. Our results demonstrate powerful tools for experimental research in quantum information processing and are expected to stimulate a wide range of valuable applications in the field of quantum sensing.

Examining failures in rubber-cord couplings within ER2 series electric trains

The article provides statistics on failures of rubber-cord couplings of electric trains of the ER2 and ER2T series and of the diesel trains over the past 7 years. According to statistics, over the past 7 years, 107 rubber-cord couplings have failed. Of these, the largest number of cases of failure of rubber-cord couplings occurred on rolling stock of the ER2 series. Examining failed rubber-cord couplings, it was revealed that the cause of its failure was a rupture of the side surface. Replacing a rubber-cord coupling is a labour-intensive and costly process. Accordingly, the question arises: what causes the problem and what measures should be proposed to reduce the failures. For these purposes, the work presents a number of experiments in order to identify possible causes of failure of the rubber-cord coupling. The article presents studies of the heating temperature of rubber-cord couplings in operation on motor cars, as well as a number of studies of failed rubber-cord couplings removed from motor cars. During the research, such parameters as the date of the last repair and the date of failure of the rubber-cord coupling were taken into account. The number of days the motor car was in general operation was taken into account until the failure of the rubber-cord coupling, as well as the mileage of the motor car after the repair. Measurements were carried out of the geometric parameters of the rubber-cord coupling: outer and inner diameter, thickness of the side of the rubber-cord coupling. The torque of the rubber-cord coupling acting at speeds from 5 to 40 km/h, the forces acting in operation on the rubber-cord coupling were calculated, and torsional and shear stresses were also studied and determined. Research was carried out to determine the hardness of the rubber-cord coupling in the temperature range from –20 °C to 0 °C and from 0 °C to +22 °C, as well as from +22 °C to +60 °C. These parameters were taken since a rubber-cord coupling operates under the mentioned conditions. In conclusion, possible reasons for the failure of rubber-cord couplings are given, and recommendations for reduction of their frequency are proposed.

EGS SO09 - Documentation Of Mortality While Consenting For Major Emergency Operation In General Surgery : Are We Informing Patients Or Just Impressing NELA? A Three-Cycle Clinical Audit

Abstract Background Approximately 30,000 to 50,000 emergency laparotomies are performed annually in the United Kingdom (UK), with an in-hospital mortality rate of 9.2%. The UK National Confidential Enquiry into Patient Outcome and Death (NCEPOD) report from 2011 recommends that the risk of mortality should be explicitly discussed with patients and clearly documented on consent forms and in medical records. The purpose of our audit was to assess the frequency of documenting the risk of mortality in consent forms and to evaluate the reporting of corresponding discussions in the medical records of patients undergoing major emergency general surgical operations. Method Patients were identified from our National Emergency Laparotomy Audit (NELA) database, and data was collected retrospectively from our online medical records. We included procedures from NELA performed on patients aged 16 and older who had the capacity to give consent. The first audit cycle took place from April to June 2021, the second from March to May 2022, and the third from March to May 2023. The results of the first cycle revealed gaps in documentation, leading to the implementation of periodic reminders for surgeons during meetings and the use of posters to reinforce best practices. Results The 1st cycle included 40 cases, with 93% documented mortality in NELA, 40% in consent forms, and 35% documented discussion about mortality in medical notes. The 2nd cycle reviewed 38 cases, showing 92% documented mortality in NELA, 71% in the consent forms, and 42% of documented discussion about mortality in the medical notes. The 3rd cycle assessed 32 cases, with 90% documented mortality in NELA, 92% in consent forms, and 51% in the medical notes. The improvement in documentation of the risk of death in the consent forms was statistically significant across all three cycles (p < 0.0001). Conclusion The three audit cycles demonstrated that implementing periodic reminders and posters for surgeons significantly improved the documentation of mortality risk. Documentation rates in consent forms increased from 40% in the first cycle to 92% by the third cycle, and in medical notes from 35% to 51%. These interventions effectively enhanced compliance with best practices. However, continuous effort is essential to maintain this improved practice. Regular monitoring, ongoing education, and reinforcement strategies should be employed to ensure that the documentation standards remain high and continue to improve patient care and safety.

Analysis of Bioheat Transfer with Thermoelastic Effect

The development of thermal therapy always requires more reasonable temperature distribution predictions. Controlling the amount of heating is a common practice within general thermal therapy operations. This paper used a modified three-phase lag (TPL) bioheat transfer equation to describe the behavior of heat conduction in tissue with thermoelastic effect. To explore the effect of thermal load, the tissue was subjected to a constant surface temperature and a pulsed surface heat flux, respectively. The modified TPL bioheat transfer equation involves mixed derivative terms and higher-order time derivatives of temperature. In analyzing such problems, there are mathematical difficulties. Therefore, the hybrid numerical scheme based on the Laplace transform and an improved discrete method was proposed to solve the present problem. The influence of thermoelastic parameters on the behavior of heat transfer in tissue has been investigated. The results depict the effect of thermal load on thermal response within heat transfer medium is obvious. The thermoelastic effect excites the thermal response oscillation, which is intensified for the reduction of material constant characteristic [Formula: see text] and phase lag [Formula: see text], in the heat conduction medium.

Inverted oscillator: quantum discrete spectrum

Abstract We use the invariant operator method to investigate the quantum characteristics of the inverted oscillator. We introduce a unitary transformation that maps a time-dependent general Hermitian linear invariant operator to a time-independent one, which describes a harmonic oscillator with a unit mass and a constant frequency. Our investigation includes three distinguished cases: negative frequency, zero frequency, and positive frequency. Our most interesting result concerns the last case. For the case of negative frequency, we propose a new inner product by the introduction of the new metric operator η. Coherent state for this case will be constructed.

Stability of complement value problems for p-Lévy operators

We set up a general framework tailor-made to solve complement value problems governed by symmetric nonlinear nonlocal integro-differential p-Lévy operators. A prototypical example of integro-differential p-Lévy operators is the well-known fractional p-Laplace operator. Our main focus is on nonlinear integro-differential equations in the presence of Dirichlet, Neumann and Robin conditions and we show well-posedness results. Several results are new even for the fractional p-Laplace operator but we develop the approach for general translation-invariant nonlocal operators. We also bridge the gap from nonlocal to local, by showing that solutions to the local Dirichlet and Neumann boundary value problems associated with p-Laplacian are strong limits of the nonlocal ones.

A unified framework for the analysis of accuracy and stability of a class of approximate Gaussian filters for the Navier–Stokes equations

Abstract Bayesian state estimation of a dynamical system utilising a stream of noisy measurements is important in many geophysical and engineering applications. In these cases, nonlinearities, high (or infinite) dimensionality of the state space, and sparse observations pose key challenges for deriving efficient and accurate data assimilation (DA) techniques. A number of DA algorithms used commonly in practice, such as the Ensemble Kalman Filter (EnKF) or Ensemble Square Root Kalman Filter (EnSRKF), suffer from serious drawbacks such as catastrophic filter divergence and filter instability. The analysis of stability and accuracy of these DA schemes has thus far focused either on finite-dimensional dynamics, or on complete observations in case of infinite-dimensional dissipative systems. We develop a unified framework for the analysis of several well-known and empirically efficient DA techniques derived from various Gaussian approximations of the Bayesian filtering schemes for geophysical-type dissipative dynamics with quadratic nonlinearities. We establish rigorous results on (time-asymptotic) accuracy and stability of these algorithms with general covariance and observation operators. The accuracy and stability results for EnKF and EnSRKF for dissipative PDEs are, to the best of our knowledge, completely new in this general setting. It turns out that a hitherto unexploited cancellation property involving the ensemble covariance and observation operators and the concept of covariance localization in conjunction with covariance inflation play a pivotal role in the accuracy and stability for EnKF and EnSRKF. Our approach also elucidates the links, via determining functionals, between the approximate-Bayesian and control-theoretic approaches to DA. We consider the ‘model’ dynamics governed by the two-dimensional incompressible Navier–Stokes equations (NSEs) and observations given by noisy measurements of averaged volume elements or spectral/modal observations of the velocity field. In this setup, several continuous-time DA techniques, namely the so-called 3DVar, EnKF and EnSRKF reduce to a stochastically forced NSEs. For the first time, we derive conditions for accuracy and stability of EnKF and EnSRKF. The derived bounds are given for the limit supremum of the expected value of the L 2 norm and of the H 1 Sobolev norm of the difference between the approximating solution and the actual solution as the time tends to infinity. Moreover, our analysis reveals an interplay between the resolution of the observations (roughly, the ‘richness’ of the observation space) associated with the observation operator underlying the DA algorithms and covariance inflation and localization which are employed in practice for improved filter performance.

Quantum Cournot model based on general entanglement operator

The properties of the Cournot model based on the most general entanglement operator containing quadratic expressions which is symmetric with respect to the exchange of players are considered. The degree of entanglement of games dependent on one and two squeezing parameters and their payoff values in Nash equilibrium are compared. The analysis showed that the relationship between the degree of entanglement of the initial state of the game and the payoff values in Nash equilibrium is ambiguous. The phase values included in the entanglement operator have a strong influence on the final outcome of the game. In a quantum duopoly based on the initial state of a game that depends on one squeezing parameter, the maximum possible payoff in Nash equilibrium cannot be reached when the value of the phase parameter is greater than zero, in contrast with a game that depends on two parameters.

Kernels of Context-Free Languages

While the closure of a language family [Formula: see text] under certain language operations is the least family of languages which contains all members of [Formula: see text] and is closed under all of the operations, a kernel of [Formula: see text] is a maximal family of languages which is a sub-family of [Formula: see text] and is closed under all of the operations. Here we investigate properties of kernels of general language families and operations defined thereon as well as kernels of (deterministic) (linear) context-free languages with a focus on Boolean operations. While the closures of language families are unique, this uniqueness is not obvious for kernels. We consider properties of language families and of operations that yield unique and non-unique, i.e. a set, of kernels. For the latter case, the question whether the union of all kernels coincides with the language family, or whether there are languages that do not belong to any kernel is addressed. Additionally, languages that are mandatory for each (Boolean) kernel and languages that are optional for (Boolean) kernels are studied. That is, we consider the intersection of all Boolean kernels as well as their union. The expressive capacities of these families are addressed leading to a hierarchical structure. Further closure properties are considered. Furthermore, we study descriptional complexity aspects of these families, where languages are represented by context-free grammars with proofs attached. It turns out that the size trade-offs between all families in question and deterministic context-free languages are non-recursive. That is, one can choose an arbitrarily large recursive function [Formula: see text], but the gain in economy of description eventually exceeds [Formula: see text] when changing from the latter system to the former.

Higher-order fractional equations and related time-changed pseudo-processes

We study Cauchy problems of fractional differential equations in both space and time variables by expressing the solution in terms of “stochastic composition” of the solutions to two simpler problems. These Cauchy sub-problems respectively concern the space and the time differential operator involved in the main equation. We provide some probabilistic and pseudo-probabilistic applications, where the solution can be interpreted as the pseudo-transition density of a time-changed pseudo-process. To extend our results to higher order time-fractional problems, we introduce stable pseudo-subordinators as well as their pseudo-inverses. Finally, we present our results in the case of more general differential operators and we interpret the results by means of a linear combination of pseudo-subordinators and their inverse processes.

Comprehensive Survey of Image Steganography Systems based on FPGA Implementation

Steganography is the art of concealed communication. The basic idea of steganography is to hide secret data inside a cover media in an undetectable manner. Cover media and Secret data can be any popular digital media such as image, video, audio, or text. Various types of image steganography methods have been proposed according to the cover image domain, i.e. spatial domain and transform domain. The spatial domain methods are easy and simple while the transform domain methods are more complex. However, the transform domain methods are more robust against image processing operations. Besides, they are more secure and less detectable in an unsecured channel. The recent steganography methods are based on sophisticated algorithms that include several computational time-consuming tasks, and hence they are unable to embed and extract the hidden data in real-time. Therefore, the trend is to implement the steganography methods in the hardware to speed up their processing time and so improves the efficacy of steganography techniques. FPGA is used in various fields in the modern era due to lower development cost, flexibility, and reconfigurability. Most of the published steganography techniques carried out on FPGA are based on the spatial domain. In this paper, it has comprehensively studied and reviewed various existing implementations of image steganography on FPGAs. This includes studying their general operations, requirements, and performance evaluations. This review would assist researchers in finding the research gaps in FPGA implementation of steganography methods for real-time applications.

A Comparative Evaluation Of Efficacy Between Besdata, Ambu Ascope, And Macintosh Laryngoscope For Intubation In Adult General Surgical Patients

Background: In the context of general surgical operations, patient safety and procedure success are directly tied to the effectiveness of endotracheal intubation equipment. The comparative effectiveness of these devices in actual clinical situations is essential, notwithstanding the many technical breakthroughs that have been made. Objective: The purpose of this research was to compare the performance of three different intubation devices— the Besdata, the Ambu aScope, and the Macintosh Laryngoscope—in adult patients undergoing general surgical procedures. Methods: Between 2019 and 2022, researchers from Jawaharlal Nehru Medical College of AMU in Aligarh's Department of Anaesthesiology and Critical Care gathered data. Ninety patients were recruited, ranging in age from 20 to 70 years and in weight from 40 to 70 kg. After getting participants' consent, they were split into three groups at random. The Ambu aScope was used to intubate patients in Group A, the Besdata was used in Group B, and the Macintosh laryngoscope was used in Group M. Age, gender, height, and weight were recorded, as well as the participant's Mallampati status. Results: There was universal success with intubation using all three devices. Average intubation times were found to be quickest using the Ambu aScope, then the Besdata, and finally the Macintosh Laryngoscope. The incidence of postoperative sore throat was lowest in patients intubated using the Macintosh Laryngoscope and greatest in those intubated with the Besdata. Ambu aScope had the best percentage of success on the first attempt. There were no statistically significant variations between patients in terms of demographic information or Mallampati grade. Conclusion: While each of the three tools was useful, it also had its own set of advantages and disadvantages. It is important to consider the patient's anatomy, the clinician's level of expertise, and the clinical setting before settling on an intubation device.

Management Of Inguinal Hernias In Adults In Mulongo: A Local Anesthesia Approach

Introduction: Inguinal hernia, passage through the transversalis fascia of a peritoneal diverticulum, is a common condition often requiring surgical intervention. It represents one of the most frequent reasons for consultation in surgery, with a worldwide incidence estimated at 4.6% of the population. Objective: Describe the epidemiological, clinical aspects and therapeutic modalities of sublocal hernia repair of inguinal hernias in adults in the territory of Mulongo. Materials and Methods: This descriptive cross-sectional and prospective study was conducted during a campaign of free general surgery operations in Mulongo, Haut-Lomami, DRC, between June 1, 2021 and December 31, 2021. Local anesthesia with xylocaine was used. The parameters evaluated were frequency, age, sex, anatomoclinical type, type of anesthesia and postoperative evolution. Results :A total of 162 patients were included. The mean age was 41.5 years (range: 18-70). There were 90.7% men, the sex ratio was 9.8. The hernia was simple in 95.6% of cases and located on the right in 50% of cases. In 4.4% of cases the hernia was operated on urgently (strangulated and engorged and painful). Postoperative pain was the most common postoperative complication found in 54.9% of cases. Conclusion: The management of inguinal hernias in adults in Mulongo is often carried out under local anesthesia, due to the high prevalence of this pathology in the professional context of patients. Inguinal hernia thus remains a significant problem in this region, justifying adapted approaches such as local anesthesia