Arbitrary Assignment Research Articles

On arbitrary matrix coefficient assignment for the characteristic matrix polynomial of block matrix linear control systems

For block matrix linear control systems, we study the property of arbitrary matrix coefficient assignability for the characteristic matrix polynomial. This property is a generalization of the property of eigenvalue spectrum assignability or arbitrary coefficient assignability for the characteristic polynomial from system with scalar $(s=1)$ block matrices to systems with block matrices of higher dimensions $(s>1)$. Compared to the scalar case $(s=1)$, new features appear in the block cases of higher dimensions $(s>1)$ that are absent in the scalar case. New properties of arbitrary (upper triangular, lower triangular, diagonal) matrix coefficient assignability for the characteristic matrix polynomial are introduced. In the scalar case, all the described properties are equivalent to each other, but in block matrix cases of higher dimensions this is not the case. Implications between these properties are established.

Design and comprehensive analysis of improved Proportional-Integral-Retarded protocol for second-order multi-agent systems

BackgroundThe attractive characteristics of an innovative delay-based controller called Proportional-Integral-Retarded (PIR) controller are reported in many fields. However, a detailed investigation of the merits of the PIR controller for multi-agent systems (MASs) is still missing. MethodsTo bridge this gap, we propose an improved PIR protocol for a general class of second-order MASs. This protocol, using multiple intentional delays and heterogeneous gains as tunable parameters, realizes the optimal spectrum assignment of each subsystem in a completely independent way without affecting the stability of other subsystems. We then present a systematic and flexible parameter tuning strategy for the PIR protocol such that the desired exponential decay rate of the consensus system can be achieved. Specifically, this strategy achieves an arbitrary dominant root assignment in the domain of non-negative real numbers and enables enhanced control flexibility by adjusting an additionally introduced free variable in the analytical parameter formulae. To unveil the superiority of our proposed PIR protocol, we develop a comprehensive comparison of the PIR protocol with the Proportional-Integral-Derivative (PID) scheme and the Proportional-Retarded (PR) protocol. Significant findingsThe numerical simulations show that our PIR protocol outperforms the PID scheme regarding the noise attenuation property. Besides, this protocol can attain faster consensus, stronger robustness against parameter uncertainties, and superior disturbance resistance than the PR protocol. Our paper provides a valuable reference for the design of an effective and implementable multi-agent consensus protocol.

Arbitrary coefficient assignment to the characteristic function of the scalar type for linear systems with state delays by linear static delayed output feedback

We consider a control system defined by a system of linear differential equations in real or complex space with multiple lumped and distributed delays in the state variable. For this system, we study the problem of arbitrary coefficient assignment for the characteristic function of the scalar type by linear static delayed output feedback with lumped and distributed delays. We obtain necessary and sufficient conditions for solvability of the arbitrary coefficient assignment problem by the static delayed output feedback controller when the system coefficients have a special form. Corollaries on arbitrary finite spectrum assignment and on stabilization of the system are obtained. We prove that the obtained results generalize the corresponding theorem proved earlier for a control system defined by a linear delay-differential equation of nth order. Examples are presented illustrating the results obtained.

Finite Spectrum Assignment Problem and Stabilization of Bilinear Systems With Both Lumped and Distributed Delay

We consider a bilinear control system defined by a linear time-invariant system of differential equations with both lumped and distributed delay in the state variable. We study the arbitrary finite spectrum assignment problem. One needs to construct a control vector such that the characteristic function of the closed-loop system becomes a polynomial with arbitrary preassigned coefficients. We obtain conditions on coefficients of the system under which the criterion was found for solvability of this finite spectrum assignment problem. This criterion is expressed in terms of rank conditions for matrices of the special form. Corollaries on stabilization of bilinear systems with delay are obtained.

Development and testing of a new flexible, easily and widely applicable chemical water quality index (CWQI)

Water quality indices (WQIs) are numeric parameters that summarize the overall quality status of freshwaters compared to quality standards by aggregating multiple physicochemical data into a single value. Among the available WQIs in the literature, several criticalities were recognized including: (a) mathematical complexity of the computation, (b) lack of inclusivity, (c) arbitrary weight assignment method, and (d) site-specificity of most of the indexes. The proposed index, the Chemical Water Quality Index (CWQI), aims to overcome these flaws and provides a computation based on simple mathematic equations that are easily manageable on spreadsheet software. The computation is divided into two steps: (i) parametrization of the variables and (ii) index determination. The parametrization consists of assigning a score (s) from ∼1 to 10 to each chemical variable based on (i) measured concentrations and (ii) quality targets (e.g., the limits provided by the European legislation for drinking waters). In the second step, a weight (w), directly proportional to the score (s), is assigned to each parameter, allowing to overcome any bias related to subjective assignments from the user. The resulting CWQI ranges from ∼1 (very good quality) to 10 (extremely poor quality). The reliability and accuracy of the CWQI were assessed by (i) applying the computation to 1,810 waters and (ii) comparing our results with another available WQI. The CWQI outputs showed an optimal response with the number of variables exceeding the quality target with high correlation coefficients (r = 0.94; R2 = 0.89). Due to the simplicity of its computation, the absence of arbitrariness in the weightage of selected variables, and the independence of the proposed approach regarding the choice of the chemical parameters, CWQI can be easily and universally applied.

Mobility Support for MIMO-NOMA User Clustering in Next-Generation Wireless Networks

Non-Orthogonal Multiple Access (NOMA) is a promising technology for future-generation wireless systems, with potential to contribute to the improvement of spectral efficiency. NOMA groups users into clusters, based on channel gain-difference. However, user mobility continuously changes the channel gain, which often requires re-clustering. In this paper, we study a set of re-clustering methods: arbitrary, one-by-one and Kuhn-Munkres assignment algorithm (KMAA), that expedite link re-establishment and keep the clusters interference-free, taking into account the mobility of users. The methods are applied to automatically dissociate identified users within clusters, when the gain-difference is lower than a given threshold, followed by re-association procedure, which integrates users into different clusters, maintaining an appropriate gain-difference. Experimental results show that the KMAA method improves efficiency and capacity through minimizing the number of re-clustering events, improving resource utilization, and lowering signaling overhead. Other sets of results highlight the throughput and outage probability gains of the KMAA method across a wide range of mobility scenarios. We also provide an analysis of the KMAA algorithm when applied to MIMO-NOMA, encompassing link resiliency and maintenance of average gain-difference, among users in clusters.

B-089 Development of a Secondary Standard for Quantitation of IgG Antibodies to SARS-CoV-2 Proteins in a Multiplex Assay

Abstract Background Serological surveillance is essential for monitoring disease burden and vaccine uptake at an individual and population level. During the pandemic caused by severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2), several serological assays were developed and obtained emergency use authorization to detect antibodies after infection. At that time, the need was to differentiate the infected from the naïve population, and these qualitative assays played a critical role in disease management. In the wake of vaccinations, there is a need for the development of quantitative assays. The world health organization (WHO) developed an international standard for quantitation. We performed this study to develop and validate an in-house secondary standard for our multiplex assay based on this WHO standard. Methods We developed a novel multiplex assay for quantifying human IgG antibodies to four different SARS-CoV-2 antigens in human serum or plasma. We have used Luminex® xMAP® technology for this assay and immobilized four recombinant proteins, namely, the receptor-binding domain of S1(RBD), nucleocapsid protein (NP), S1 protein (S1), and trimeric Spike protein (trimer) on internally coded magnetic microspheres. We procured lyophilized WHO quantification standard 20/136 from the National Institute for Biological Standards and Control (NIBSC), which has the arbitrary assignment of 1000 BAU/mL after reconstitution in 0.25 mL. We tested this standard in the range of 10 to 0.01 BAU/mL for the standard curve. We tested NIBSC 20/162 control reagent using this assay for the linearity of dilution. Thirty-seven samples from the NIBSC verification panel were also tested for this evaluation. We also quantified IgG antibodies in 25 samples from vaccinated individuals, ten samples from vaccine breakthrough individuals, 25 samples from PCR-positive individuals, and 75 samples collected before 2019. Results The secondary standard was calibrated using the 20/136 standard. The NIBSC 20/136 and the secondary standard displayed a wide dynamic range of quantitation. The difference in the expected and actual concentrations was less than 20%. Multiple dilutions of the serum or plasma samples were used to get readings within the standard curve range. Excellent linearity was noted at various sample dilutions to get the correct quantification. We observed that vaccinated individuals had a higher concentration of binding antibodies to S1, Trimer, and RBD and were negative for NP antibodies. Conversely, the acute samples from infected individuals collected less than ten days post-positive PCR showed higher antibodies to NP than different spike proteins. The vaccine break-through infection samples showed lower NP antibodies than unvaccinated but infected individuals. Conclusion Our development of a secondary standard calibrated against WHO international standard is vital for quantitatively measuring different SARS-CoV-2 antibodies. A secondary standard can help manufacturers and users to normalize results from various assays and lots over a prolonged period.

Exploring the nature of the gender-congruency effect: implicit gender activation and social bias.

The aim of the study was to explore the nature of the gender-congruency effect, characterized by a facilitation on the processing of congruent words in grammatical gender. Moreover, we explored whether resemblances between gender identities and gender attitudes with grammatical gender modulated lexical processing. We designed a gender-priming paradigm in Spanish, in which participants decided the gender of a masculine or feminine pronoun preceded by three different primes: biological gender nouns (mapping biological sex), stereotypical nouns (mapping biological and stereotypical information), and epicene nouns (arbitrary gender assignment). We found faster processing of gender congruent pronouns independently of the type of prime, showing that the grammatical gender feature is active even when processing bare nouns that are not conceptually related to gender. This indicates that the gender-congruency effect is driven by the activation of the gender information at the lexical level, which is transferred to the semantic level. Interestingly, the results showed an asymmetry for epicene primes: the gender-congruency effect was smaller for epicene primes when preceding the feminine pronoun, probably driven by the grammatical rule of the masculine being the generic gender. Furthermore, we found that masculine oriented attitudes can bias language processing diminishing the activation of feminine gender, which ultimately could overshadow the female figure.

Solving simultaneous target assignment and path planning efficiently with time-independent execution

Real-time planning for a combined problem of target assignment and path planning for multiple agents, also known as the unlabeled version of multi-agent path finding (MAPF), is crucial for high-level coordination in multi-agent systems, such as pattern formation by robot swarms. This paper studies two aspects of unlabeled-MAPF: (1) offline scenario: solving large instances using centralized approaches with a small computation time, and (2) online scenario: executing unlabeled-MAPF, despite the timing uncertainties real robots face. For this purpose, we propose TSWAP, a novel sub-optimal complete algorithm that takes an arbitrary initial target assignment and then repeats one-timestep path planning with target swapping. TSWAP can adapt to both offline and online scenarios. We empirically demonstrate that offline TSWAP is highly scalable, and provides near-optimal solutions while reducing runtime by orders of magnitude compared with existing approaches. In addition, we present the benefits of online TSWAP, such as delay tolerance, through real-robot demonstrations.

On approximating shortest paths in weighted triangular tessellations

We study the quality of weighted shortest paths when a continuous 2-dimensional space is discretized by a weighted triangular tessellation. In order to evaluate how well the tessellation approximates the 2-dimensional space, we study three types of shortest paths: a weighted shortest path SPw(s,t), which is a shortest path from s to t in the space; a weighted shortest vertex path SVPw(s,t), which is an any-angle shortest path; and a weighted shortest grid path SGPw(s,t), which is a shortest path whose edges are edges of the tessellation. Given any arbitrary weight assignment to the faces of a triangular tessellation, thus extending recent results by Bailey et al. (2021) [6], we prove upper and lower bounds on the ratios ‖SGPw(s,t)‖‖SPw(s,t)‖, ‖SVPw(s,t)‖‖SPw(s,t)‖, ‖SGPw(s,t)‖‖SVPw(s,t)‖, which provide estimates on the quality of the approximation. It turns out, surprisingly, that our worst-case bounds are independent of any weight assignment. Our main result is that ‖SGPw(s,t)‖‖SPw(s,t)‖=23≈1.15 in the worst case, and this is tight. As a corollary, for the weighted any-angle path SVPw(s,t) we obtain the approximation result ‖SVPw(s,t)‖‖SPw(s,t)‖⪅1.15.

Assignment of the upper Bohl exponent for linear periodic control systems in Hilbert spaces

A linear continuous-time control system with time-varying linear bounded operator coefficients in a Hilbert space is considered. The controller in the system has the form of linear state feedback with a time-varying linear bounded gain operator function. We study the problem of arbitrary assignment of the upper Bohl exponent by state feedback control. The property of exact controllability for the open-loop system is studied, some necessary and sufficient conditions are obtained for exact controllability. For periodic systems, it is proved that if the open-loop system is exactly controllable then one can shift the upper Bohl exponent of the closed-loop system by any pregiven number with respect to the upper Bohl exponent of the free system by means of linear state feedback with a periodic gain operator function. This implies arbitrary assignability of the upper Bohl exponent by linear state feedback. Finally, an illustrative example is presented.

Solving Simultaneous Target Assignment and Path Planning Efficiently with Time-Independent Execution

Real-time planning for a combined problem of target assignment and path planning for multiple agents, also known as the unlabeled version of Multi-Agent Path Finding (MAPF), is crucial for high-level coordination in multi-agent systems, e.g., pattern formation by robot swarms. This paper studies two aspects of unlabeled-MAPF: (1) offline scenario: solving large instances by centralized approaches with small computation time, and (2) online scenario: executing unlabeled-MAPF despite timing uncertainties of real robots. For this purpose, we propose TSWAP, a novel sub-optimal complete algorithm, which takes an arbitrary initial target assignment then repeats one-timestep path planning with target swapping. TSWAP can adapt to both offline and online scenarios. We empirically demonstrate that Offline TSWAP is highly scalable; providing near-optimal solutions while reducing runtime by orders of magnitude compared to existing approaches. In addition, we present the benefits of Online TSWAP, such as delay tolerance, through real-robot demos.

Dynamic-Decoupled Active Damping Control Method for Improving Current Transient Behavior of LCL-Equipped High-Speed PMSMs

In this article, a novel dynamic-decoupled active damping current controller is proposed for an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LCL</i> -equipped high-speed permanent magnet synchronous machine. Compared with the conventional stationary current-control method for the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LCL</i> -type system, the proposed method is established in the synchronous rotating frame for improving the current transient performance. When taking the controller into the synchronous coordinate, there are two following challenges: first, the synchronous resonance frequency varying in a wide range because of the synchronous coordinate transformation, and second, eliminating the coupling between the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${dq}$</tex-math></inline-formula> coordinate. To address these issues, an improved synchronous capacitor-current-feedback active damping method is designed based on arbitrary pole assignment and is significantly effective for the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LCL</i> resonance within the Nyquist frequency. Moreover, a novel dynamic-decoupled motor-current controller is proposed to eliminate the coupling between the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${dq}$</tex-math></inline-formula> -axis motor current. The gain selection method is discussed to acquire sufficient phase margin and gain margin. Finally, the effectiveness of the proposed method is verified by driving the tested motor to 72 kr/min.

On Arbitrary Assignability of Initial Conditions for a Discrete Autonomous $n$-D System

The issue of initial/boundary conditions for a general system of partial difference equations – called a discrete <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$n$</tex-math></inline-formula> -D system – is resolved through the notion of characteristic sets: the restriction of a solution trajectory to a minimal characteristic set can be considered to be the initial/boundary condition to the corresponding trajectory. In the recent paper [8], it has been shown that every autonomous <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$n$</tex-math></inline-formula> -D system admits a minimal characteristic set that is the union of a sublattice (of rank equal to the Krull dimension of the system) and its finitely many parallel translates. Treating the restrictions of every solution trajectories to such a characteristic set as initial/boundary conditions, in this paper, we provide a full parametrization of the set of all initial/boundary conditions of a discrete autonomous <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$n$</tex-math></inline-formula> -D system. The key to this parametrization is that the set of allowable initial/boundary conditions itself can be viewed as a discrete <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$d$</tex-math></inline-formula> -D system, where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$d$</tex-math></inline-formula> is the Krull dimension of the system: we prove this result here. An upshot of this parametrization is the answer to free assignability of these initial/boundary conditions.

Algorithms for specifying initial data for discrete autonomous nD systems

For nD systems, initial data is obtained by specifying trajectories on special subsets of the domain, known as characteristic sets. In this paper, we consider a special class of systems that admits a union of a coordinate sublattice and finitely many parallel translates of it as a characteristic set; we call such systems as strongly relevant systems. Using the discrete Noether's normalization lemma, every discrete autonomous nD system can be transformed to a strongly relevant system. For a strongly relevant system, the set of allowable initial conditions, obtained by restricting trajectories on the characteristic set, is characterized. We then provide an implementable algorithm, based on Gröbner basis, for obtaining a representation of the set of allowable initial conditions. Once such a representation is obtained, important deductions, such as, arbitrary assignability of initial data can be easily made.

Enabling Workforce Optimization in Constrained Attribute-Based Access Control Systems.

Effective utilization of human capital is one of the key requirements for any successful business endeavor, with reorganization necessary if there are nonproductive employees or employees that are retiring. However, while reorganizing tasks for newer employees, it should be ensured that the employees have the requisite capabilities of handling the assigned tasks. Furthermore, security constraints forbid any arbitrary assignment of tasks to employees and also enforce major dependencies on other employees who have access to the same tasks. Since Attribute Based Access Control (ABAC) is poised to emerge as the de facto model for specifying access control policies in commercial information systems, we consider organizational policies and constraints to be modeled with ABAC. Given the increasing size and scale of organizations, both in terms of employees and resources that need to be managed, it is crucial that computational solutions are developed to automate the process of employee to task assignment. In this work, we define the Employee Replacement Problem (ERP) which answers the question of whether a given set of employees can be replaced by a smaller set of employees, while ensuring that the desired security constraints are not violated. We prove that the problem is NP-hard and use CNF-SAT to obtain a solution. An extensive experimental evaluation is carried out on diverse data sets to validate the efficiency of the proposed solution.

Reducing variability of breast cancer subtype predictors by grounding deep learning models in prior knowledge

Deep learning neural networks have improved performance in many cancer informatics problems, including breast cancer subtype classification. However, many networks experience underspecificationwheremultiplecombinationsofparametersachievesimilarperformance, bothin training and validation. Additionally, certain parameter combinations may perform poorly when the test distribution differs from the training distribution. Embedding prior knowledge from the literature may address this issue by boosting predictive models that provide crucial, in-depth information about a given disease. Breast cancer research provides a wealth of such knowledge, particularly in the form of subtype biomarkers and genetic signatures. In this study, we draw on past research on breast cancer subtype biomarkers, label propagation, and neural graph machines to present a novel methodology for embedding knowledge into machine learning systems. We embed prior knowledge into the loss function in the form of inter-subject distances derived from a well-known published breast cancer signature. Our results show that this methodology reduces predictor variability on state-of-the-art deep learning architectures and increases predictor consistency leading to improved interpretation. We find that pathway enrichment analysis is more consistent after embedding knowledge. This novel method applies to a broad range of existing studies and predictive models. Our method moves the traditional synthesis of predictive models from an arbitrary assignment of weights to genes toward a more biologically meaningful approach of incorporating knowledge.

Arbitrary Coefficient Assignment by Static Output Feedback for Linear Differential Equations with Non-Commensurate Lumped and Distributed Delays

We consider a linear control system defined by a scalar stationary linear differential equation in the real or complex space with multiple non-commensurate lumped and distributed delays in the state. In the system, the input is a linear combination of multiple variables and its derivatives, and the output is a multidimensional vector of linear combinations of the state and its derivatives. For this system, we study the problem of arbitrary coefficient assignment for the characteristic function by linear static output feedback with lumped and distributed delays. We obtain necessary and sufficient conditions for the solvability of the arbitrary coefficient assignment problem by the static output feedback controller. Corollaries on arbitrary finite spectrum assignment and on stabilization of the system are obtained. We provide an example illustrating our results.

Spectrum assignment and stabilization by static output feedback of linear difference equations with state variable delays

We study the problem of arbitrary eigenvalue spectrum assignment for a linear discrete-time control system with delays defined by a linear difference equation of the nth order with multiple inputs and multiple outputs via static output feedback with delays. Necessary and sufficient conditions are obtained for arbitrary eigenvalue spectrum assignment by linear static output feedback with delays. These conditions are expressed in terms of system coefficients. A corollary on stabilization is derived. An illustrative example is presented.

Necessary and Sufficient Conditions for Assignability of Dichotomy Spectrum of One-Sided Discrete Time-Varying Linear Systems

We consider a version of the pole placement problem for one-sided linear discrete time-varying linear systems. Our purpose is to prove that uniform complete controllability is equivalent to possibility of arbitrary assignment of the dichotomy spectrum.