Theoretical Complexity Research Articles

Doing Critical Race Theory in Perilous Times: Engaging Critical Race Legal Scholarship for Higher Education and Beyond

Abstract: Misinterpretations and caricatures of Critical Race Theory (CRT) abound in popular media and in higher education scholarship. Given the confusion surrounding what CRT is and is not, I write this conceptual essay as an invitation to engage seriously with CRT’s legal foundations. I offer four guideposts to aid scholars in engaging the legal roots of CRT on a deeper level: thinking with and beyond tenets, leveraging the scope of CRT work by legal scholars, understanding the CRT critique of Critical Legal Studies, and appreciating CRT’s theoretical depth and complexity. Further, I highlight characteristics of CRT legal scholarship that are not always explicit in higher education research. Specifically, I describe CRT as an anti-subordination project, a materialist project, a critical intellectual project, and an activist project. Through engaging with CRT’s legal scholarship, I demonstrate how higher education scholars’ understanding and employment of CRT will be enriched.

Reactivity umpolung (reversal) of ligands in transition metal complexes.

The success and power of homogeneous catalysis derives in large part from the wide choice of transition metal ions and their ligands. This tutorial review introduces examples where the reactivity of a ligand is completely reversed (umpolung) from Lewis basic/nucleophilic to acidic/electrophilic or vice versa on changing the metal and co-ligands. Understanding this phenomenon will assist in the rational design of catalysts and the understanding of metalloenzyme mechanisms. Labelling a metal and ligand with Seebach donor and acceptor labels helps to identify whether a reaction involving the intermolecular attack on the ligand is displaying native reactivity or reactivity umpolung. This has been done for complexes of nitriles, carbonyls, isonitriles, dinitrogen, Fischer carbenes, alkenes, alkynes, hydrides, methyls, methylidenes and alkylidenes, silylenes, oxides, imides/nitrenes, alkylidynes, methylidynes, and nitrides. The electronic influence of the metal and co-ligands is discussed in terms of the energy of (HOMO) d electrons. The energy can be related to the pKLACa (LAC is ligand acidity constant) of the theoretical hydride complexes [H-[M]-L]+ formed by the protonation of pair of valence d electrons on the metal in the [M-L] complex. Preliminary findings indicate that a negative pKLACa indicates that nucleophilic attack by a carbanion or amine on the ligand will likely occur while a positive pKLACa indicates that electrophilic attack by strong acids on the ligand will usually occur when the ligand is nitrile, carbonyl, isonitrile, alkene and η6-arene.

A nonlinear relaxation-strategy-based algorithm for solving sum-of-linear-ratios problems

<p>This paper mainly studies the sum-of-linear-ratios problems, which have important applications in finance, economy and computational vision. In this process, we first propose a new method to re-represent the original problem as an equivalent problem (EP). Secondly, by relaxing these constraints, a nonlinear relaxation subproblem is constructed for EP. In view of the special structure of the relaxation, it is reconstructed as a second-order cone programming (SOCP) problem, which is essentially a SOCP relaxation of EP. Thirdly, through the structural characteristics of the objective function of EP, a region reduction technique is designed to accelerate the termination of the algorithm as much as possible. By integrating the SOCP relaxation and acceleration strategy into the branch and bound framework, a new global optimization algorithm is developed. Further, the theoretical convergence and computational complexity of the algorithm are analyzed. Numerical experiment results reveal that the algorithm is effective and feasible.</p>

Predictive processing as a theoretical complex in the cognitive sciences

Predictive processing as a theoretical complex in the cognitive sciences

CR‐Net: Robot grasping detection method integrating convolutional block attention module and residual module

AbstractGrasping detection, which involves identifying and assessing the grasp ability of objects by robotic systems, has garnered significant attention in recent years due to its pivotal role in the development of robotic systems and automated assembly processes. Despite notable advancements in this field, current methods often grapple with both practical and theoretical challenges that hinder their real‐world applicability. These challenges encompass low detection accuracy, the burden of oversized model parameters, and the inherent complexity of real‐world scenarios. In response to these multifaceted challenges, a novel lightweight grasping detection model that not only addresses the technical aspects but also delves into the underlying theoretical complexities is introduced. The proposed model incorporates attention mechanisms and residual modules to tackle the theoretical challenges posed by varying object shapes, sizes, materials, and environmental conditions. To enhance its performance in the face of these theoretical complexities, the proposed model employs a Convolutional Block Attention Module (CBAM) to extract features from RGB and depth channels, recognising the multifaceted nature of object properties. Subsequently, a feature fusion module effectively combines these diverse features, providing a solution to the theoretical challenge of information integration. The model then processes the fused features through five residual blocks, followed by another CBAM attention module, culminating in the generation of three distinct images representing capture quality, grasping angle, and grasping width. These images collectively yield the final grasp detection results, addressing the theoretical complexities inherent in this task. The proposed model's rigorous training and evaluation on the Cornell Grasp dataset demonstrate remarkable detection accuracy rates of 98.44% on the Image‐wise split and 96.88% on the Object‐wise split. The experimental results strongly corroborate the exceptional performance of the proposed model, underscoring its ability to overcome the theoretical challenges associated with grasping detection. The integration of the residual module ensures rapid training, while the attention module facilitates precise feature extraction, ultimately striking an effective balance between detection time and accuracy.

Halin’s infinite ray theorems: Complexity and reverse mathematics

Halin in 1965 proved that if a graph has [Formula: see text] many pairwise disjoint rays for each [Formula: see text] then it has infinitely many pairwise disjoint rays. We analyze the complexity of this and other similar results in terms of computable and proof theoretic complexity. The statement of Halin’s theorem and the construction proving it seem very much like standard versions of compactness arguments such as König’s Lemma. Those results, while not computable, are relatively simple. They only use arithmetic procedures or, equivalently, finitely many iterations of the Turing jump. We show that several Halin-type theorems are much more complicated. They are among the theorems of hyperarithmetic analysis. Such theorems imply the ability to iterate the Turing jump along any computable well ordering. Several important logical principles in this class have been extensively studied beginning with work of Kreisel, H. Friedman, Steel and others in the 1960s and 1970s. Until now, only one purely mathematical example was known. Our work provides many more and so answers Question 30 of Montalbán’s Open Questions in Reverse Mathematics in 2011. Some of these theorems including ones in Halin in 1965 are also shown to have unusual proof theoretic strength as well.

Robust, revocable, forward and backward adaptively secure attribute-based encryption with outsourced decryption1

Attribute based encryption (ABE) is a cryptographic technique allowing fine-grained access control by enabling one-to-many encryption. Existing ABE constructions suffer from at least one of the following limitations. First, single point of failure on security meaning that, once an authority is compromised, an adversary can either easily break the confidentiality of the encrypted data or effortlessly prevent legitimate users from accessing data; second, the lack of user and/or attribute revocation mechanism achieving forward and backward secrecy; third, a heavy computation workload is placed on data user; last but not least, the lack of adaptive security in standard models. In this paper, we propose the first single-point-of-failure free multi-authority ciphertext-policy ABE that simultaneously (1) ensures robustness for both decryption key issuing and access revocation while achieving both backward and forward secrecy; (2) enables outsourced decryption to reduce the decryption overhead for data users that have limited computational resources; and (3) achieves adaptive (full) security in standard models. The provided theoretical complexity comparison as well as the conducted experiments show that our construction introduces linear storage and computation overheads that occurs only once during its setup phase, which we believe to be a reasonable price to pay to achieve all previous features.

Improved Linear Decomposition of Majority and Threshold Boolean Functions

To support efficient design automation for emerging computing fabrics, novel data structures for logic synthesis and technology mapping are being intensively studied. It has been shown that for several promising computing technologies intermediate forms like Majority-Inverter Graph (MIG), and Xor-Majority Graph (XMG) can be particularly beneficial. This has propelled the Boolean majority operator at the forefront of research. Though these structures primarily utilise 3-input Majority nodes, the efficacy of n-input Majority operators has been demonstrated as well. A long-standing research problem, in that context and also for theoretical circuit complexity, is to determine efficient decomposition of an n-input Majority (Majn) function in terms of 3-input Majority (Maj3) operator. In this manuscript, we make two significant advances in this topic. First, a practically realizable linear decomposition is provided, thus improving the previously reported quadratic bounds. Second, the theoretical upper bound of decomposing Majn, in terms of Maj3, is reduced from 5.884n to 3n. The erstwhile theoretical upper bound of 5.884n also lacked a practical construction for Majn decomposition, presumably due to the presence of sequential elements in the algorithm. The proof of the linearity, detailed construction procedure along with experimental studies using state-of-the-art synthesis flows to validate the aforementioned claims are presented in this work. The results are applicable to threshold Boolean functions, too.

Effective Two-Phase Heuristic and Lower Bounds for Multi-Stage Flexible Flow Shop Scheduling Problem with Unloading Times

This paper addresses the flexible flow shop scheduling problem with unloading operations, which commonly occurs in modern manufacturing processes like sand casting. Although only a few related works have been proposed in the literature, the significance of this problem motivates the need for efficient algorithms and the exploration of new properties. One interesting property established is the symmetry of the problem, where scheduling from the first stage to the last or vice versa yields the same optimal solution. This property enhances solution quality. Considering the problem’s theoretical complexity as strongly NP-Hard, approximate solutions are preferable, especially for medium and large-scale instances. To address this, a new two-phase heuristic is proposed, consisting of a constructive phase and an improvement phase. This heuristic builds upon an existing efficient heuristic for the parallel machine-scheduling problem and extends it to incorporate unloading times efficiently. The selection of the two-phase heuristic is justified by its ability to generate high-quality schedules at each stage. Moreover, new efficient lower bounds based on estimating minimum idle time in each stage are presented, utilizing the polynomial parallel machine-scheduling problem with flow time minimization in the previous stage. These lower bounds contribute to assessing the performance of the two-phase heuristic over the relative gap performance measure. Extensive experiments are conducted on benchmark test problems, demonstrating the effectiveness of the proposed algorithms. The results indicate an average computation time of 9.92 s and a mean relative gap of only 2.80% for several jobs up to 200 and several stages up to 10.

Concordance between pharmacotherapeutic complexity calculated and perceived by HIV+ patients with antiretroviral treatment

ObjectiveTo determine the difference between the pharmacotherapeutic complexity index by Medication Regimen Complexity Index and it's perceived by patients through a visual analogue scale in patients HIV+ with antiretroviral treatment. MethodProspective, observational study of patients HIV+ > 18 years of age with stable antiretroviral treatment in the last three months, followed up by external consultations of pharmaceutical care between October’17 and February’18. The main variable of the study was the concordance between the median of the score obtained in the pharmacotherapeutic complexity perceived by the patients using the visual analog scale whose range of values oscillates between 0–10, categorized in low complexity (0–1) and high complexity (2–10), and the median of the score obtained for the theoretical pharmacotherapeutic complexity using the Medication Regimen Complexity Index tool whose ranges of values oscillate between 1 and infinity, categorized in low complexity (0–11) and high complexity > 11. The overall complexity was calculated: antiretroviral treatment and concomitant treatment. Results: We included 236 patients in the study. There was a discrete concordance between the pharmacotherapeutic complexity perceived by the patients and that calculated according to the Medication Regimen Complexity Index tool (Cohen's Kappa index 0.203). The median of the Medication Regimen Complexity Index of the total medication was 6 (interquartile range: 4–10) versus the median of the Complexity Index measured by visual analog scale of 2 (interquartile range: 0–4). ConclusionsPatients perceive a pharmacotherapeutic complexity lower than that calculated. Therefore, we must include the two scales in pharmaceutical care for a better understanding of the patient's perception.

Dynamic probabilistic risk assessment with K-shortest-paths planning for generating discrete dynamic event trees

Conventional risk assessment methods are often not well suited for fast-changing dynamic and complex systems since the results from the analysis may be averages or valid for a short time before the system’s state changes. A response to this problem is dynamic probabilistic risk assessment (DPRA), which considers the ever-changing nature of such systems and how their dynamic behavior affects the likelihood of future accident scenarios. Performing DPRA is difficult for complex systems — i.e., systems with many interconnected subsystems and components, for example, autonomous systems. There is a combinatorial “explosion” when considering how component failures affect one another and the overall system performance, known in the DPRA literature as the “state explosion problem”, causing DPRA methods to have poor computational performance for large-scale systems. Although solutions to state explosion alleviate the average-case performance, most DPRA methods remain computationally expensive, with exponential worst-case time complexities. In this paper, a method for solving DPRA problems with K-Shortest-Paths planning algorithms is proposed. The method, called KPRA, consists in framing a subset of DPRA problems as relaxed versions of the K-Shortest-Paths (KSP) planning problem, allowing these DPRA problems to be solved by a graph search algorithm called K*, which has a theoretical log-linear worst-case complexity. Therefore, in theory, KPRA with K* solves DPRA problems with computational performance better than exponential. KPRA was implemented and applied to a case study of DPRA for an autonomous ship for validation and comparison with conventional DPRA methods. The case study consists of two ships, one of them autonomous, in a crossing encounter with a possible collision risk. The task is to find the most critical situations for the autonomous ship, i.e., the scenarios where its collision risk is the highest. KPRA’s performance in solving the case study is compared with two conventional DPRA methods. The results show that the KPRA implementation in this work can solve the case study, i.e., produce an output equivalent to the other methods, with a polynomial worst-case computational complexity, i.e., more efficiently than the other methods with exponential complexities.

Maximizing truck platooning participation with preferences

Truck platooning refers to trucks traveling in convoy with longitudinal proximity. By reducing aerodynamic drag, platooning cuts truck energy use and operating cost along with other benefits to the freight transportation system. This research proposes a platform-based platooning system to maximize the participation of truck platooning considering stability of the formed platoons that arises from truck preferences of platooning partners. Preference-based platooning is of both scientific interest and practical importance to the trucking sector, which is highly fragmented especially in the US. The preferences depend on the benefits of fuel saving and schedule adjustment to coordinate the time for platoon formation. The formed platoons are stable in the sense that no two trucks in two platoons want to break away from their current platoons and platoon with each other. Tackling this operation planning problem, the proposed system involves a platform interacting with individual trucks in a way that reduces truck communication and computation burdens, mitigates truck privacy concerns, and overcomes trucks misreporting private information. The central methodological investigation of the interactive process is on how to solve the Maximum Stable Truck Platooning Participation (MS-TPP) problem, for which a two-phase algorithmic approach is proposed. The underlying idea of this approach is to progressively reduce the lengths of truck preference lists, by eliminating truck pairs that do not affect the MS-TPP solution presence and separating trucks in odd rotations – which are key constructs in this approach – from the rest of the truck population. Theoretical properties and computational complexity of this two-phase algorithmic approach are investigated, along with a comparison with an integer programming approach and extensive numerical experiments in the context of a northern Illinois road network in the US. We find that the proposed two-phase algorithmic approach is very efficient compared to the integer programming approach in forming a maximum number of truck platoons while ensuring stability. In addition, the percentage of trucks that end up platooning by solving MS-TPP is much greater than using a greedy approach. The algorithmic approach is computationally scalable for solving large problem instances. The advantages of MS-TPP, in terms of the percentage of trucks in platooning and the average utility gain, become even more prominent as we deal with a larger system with more trucks.

Hardware architecture of Dillon’s APN permutation for different primitive polynomials

Cryptographically strong functions used as S-boxes in block cyphers are fundamental for the cypher’s security. Their representation as lookup tables is possible for functions of small dimension. For larger dimensions, this is infeasible, especially if resources are limited. An alternative is representing the function as a polynomial over a finite field, and constructing a circuit evaluating this polynomial. We study how the choice of primitive polynomial affects the efficiency of hardware implementations. We take Dillon’s permutation on 6 bits (the only known permutation in even dimension from the cryptographically optimal Almost Perfect Nonlinear functions) as a relevant example, and present hardware architectures, polynomial representations and hardware theoretical complexities for all primitive polynomials of degree six. To compare the efficiency, we report on results obtained from FPGA (Field Programmable Gate Array) implementations. To the best of our knowledge, no similar study has been given in the literature. We observe that using the primitive trinomial y6+y+1 reduces the number of 2-input XOR gates up to 11.7% and the number of XOR gates × Delay metrics up to 13.2% with respect to the worst-case implementation. Therefore, the choice of primitive polynomial can profoundly impact the efficiency of such an implementation, and should be carefully considered.

Influencing factors of self-management behavior in cancer patients based on a theoretical domain framework: a literature review.

To explore the factors that influence self-management behavior in cancer patients based on the theoretical domain framework. Studies in Chinese and English-language about factors influencing self-management behavior in cancer patients were searched from Wanfang DATA, CNKI, VIP, Sinomed, Pubmed, EMbase, CINAHL, Web of Science Core Collection, Cochrane library and Medline from inception to June 2022. Two investigators independently identified, extracted data, and collected characteristics and methodology of the studies. Factors were analyzed with Nvivo12, and theoretical domain framework was mapped to theoretical domain; then the secondary node was generalized by the theme analysis; finally, the specific influencing factors were summarized and analyzed. Thirty-four studies were included for analysis. A total of 194 factors were mapped to 13 theoretical domains, and 31 secondary nodes were summarized. The top three factors were mapped to the three theoretical domains, which were environmental context and resources, social/professional role and identity, and beliefs about consequences. Knowledge, age, self-efficacy, social support gender, economic status and physical status were the most influential factors for self-management in cancer patients. The influencing factors of self-management of cancer patients involve most of the theoretical domains, and are intersectional, multi-source and complex. It is important to further explore the key factors to provide the basis for the intervention of self-management behavior in cancer patients.

Quality of medical care and patient safety, and clinical simulation: A goal for faculty at the faculty of medicine, BUAP

The medical training involving theoretical and practical complexity requires settings that contribute to patient safety. It emerged with the evolution and complexity of healthcare systems, resulting in an increase in patient harm within healthcare facilities. The main objective is to prevent and reduce risks, errors, and damages experienced by patients during medical care. The cornerstone of this discipline is continuous improvement, based on learning from mistakes and adverse events. The aim of this study is to analyze the significance of healthcare quality and patient safety, along with clinical simulation in medical education, through a literature review, from the perspective of developing professional competencies. Materials and Methods: Through a review of scientific literature in databases, websites, scientific journals, books, and others, the selection criteria encompassed articles in Spanish from the last 5 years related to the topics of healthcare quality, patient safety, and analysis of clinical simulation within the Faculty of Medicine at BUAP. Results: It was evident that the quality of healthcare and patient safety during healthcare delivery is directly influenced by the quality of education students receive in universities. There's a consensus that clinical simulation contributes to better professional training, serving as an innovative teaching strategy that enables the enhancement of students' and professionals' skills and abilities. The Faculty of Medicine at BUAP includes the subject of healthcare quality and patient safety, as well as clinical simulation, in its curriculum at various levels, which has piqued significant interest among instructors for its implementation. Moreover, the institution is in the process of expanding its clinical simulation hospital, which aims to contribute to significant knowledge. Conclusion: Healthcare quality, patient safety, and clinical simulation play a pivotal role as teaching methods in medical education, significantly contributing to student and physician learning. This orientation toward safe medical practice ultimately impacts the enhancement of patient healthcare. These elements are already partially implemented within BUAP's Faculty of Medicine.

Augmented tour construction heuristics for the travelling salesman problem

Tour construction heuristics serve as fundamental techniques in optimizing the routes of a traveling salesman. These heuristics remain significant as foundational methods for generating initial solutions to the Traveling Salesman Problem (TSP), facilitating subsequent applications of tour improvement heuristics. These heuristics effectively comprise the iterative application of city node selection and insertion. However, thus far, no attempts have been made to enhance the basic structure of tour construction heuristics to bring a better initial solution for the advanced heuristics. This study aims to enhance tour construction heuristics without compromising their theoretical complexity. Specifically, an iterative step of partial tour deconstruction has been introduced to the existing heuristics. This additional step has been implemented and evaluated with three highly performing tour construction heuristics: the farthest insertion heuristic, the max difference insertion heuristic, and the fast max difference insertion heuristic. The results demonstrate that augmenting these heuristics with the partial tour deconstruction step improves the best, worst, and average solutions while preserving their theoretical complexity

Output-space branch-and-bound reduction algorithm for generalized linear fractional-multiplicative programming problem

In this paper, we investigate a class of linear fractional-multiplicative programs with exponents, which have important applications in finance and economy. By introducing p variables, the problem is re-represented as an equivalent problem. Immediately, two new linear relaxation strategies are proposed and embedded in the branch-and-bound framework, and the corresponding new global optimization algorithms are developed in combination with an acceleration technique. Furthermore, the theoretical convergence and computational complexity of the algorithms are elucidated. Numerical experiment results illustrate that both algorithms are effective and feasible.

Empirical validation of task-related component analysis reformulation for computational complexity reduction

The task-related component analysis (TRCA) is a data-driven method for extracting reproducible components across multiple data segments from multivariate data. TRCA has been proven effective in enhancing the signal-to-noise ratio of neuroimaging data in previous studies. However, its original form requires a computational cost of O(N2) to compute the sum of cross-covariance matrices, indicating that the computational time increases rapidly as the number of data segments N increases. This study aims to empirically validate that the reformulated form of TRCA can reduce its computational complexity. This study estimated that the reformulation can reduce the computational complexity from O(N2) to O(N) without distorting its outputs by reducing the number of matrix multiplications in computing the sum of cross-covariance matrices. A series of computer simulations using computer-generated synthetic, functional near-infrared spectroscopy (fNIRS), and electroencephalogram (EEG) data were conducted to verify the theoretical computation complexity and consistency of the outputs between the original and reformulated TRCA. The computation reduction was validated through an experimental comparison of the original and reformulated TRCA with synthetic and real data of various sizes (e.g., data segments, dimensions, and lengths). In addition, the two algorithms output almost exactly identical results with only floating-point errors. The reformulation would considerably benefit practical applications, especially when applying the TRCA to large-scale computations. The code is available at https://github.com/mnakanishi/TRCA-SSVEP.

On transformations of ellipsoidal (triaxial) orthogonal curvilinear coordinates

Ellipsoidal orthogonal curvilinear coordinates referred to a triaxial reference ellipsoid are not used in geodesy perhaps because of their theoretical complexity. However, many surveying and geodetic problems could be resolved by simply transforming variables between local frames. Herein it is shown that the computations of local displacements and variance-covariance matrices referred to currently used local curvilinear geodetic coordinate frames gives approximately the same answers than when referred to local ellipsoidal (triaxial) curvilinear frames. The theoretical procedures to obtain the required transformations between local geodetic and local ellipsoidal (triaxial) frames are introduced and examples explained.

Jouissance and affective neuroscience: a critical neuropsychoanalytic integration

ABSTRACT Jouissance is a multifaceted Lacanian concept that refers to a paradoxical blend of pleasure and unpleasure, an excess of pleasure that becomes traumatic. While jouissance appears as a pinnacle of Lacanian theoretical complexity, it has been critiqued as a nebulous descriptor that shuts down questions rather than deepening rigor. Specifically, Darian Leader has charged the Lacanian use of jouissance as theoretically imprecise, ignoring vicissitudes of bodily innervation, obscuring the relationship with the Other, and implicitly maintaining problematic Freudian quantitative, homeostatic ideas. I propose that affective neuroscience, when interpreted within a Lacanian neuropsychoanalytic framework, offers tools to answer some of these critiques of jouissance. At the same time, an integration of jouissance with affective neuroscience draws out radical perspectives in neuropsychoanalysis – specifically against a straightforward application of homeostasis – that demonstrate the importance of maintaining the concept of jouissance as excess. This article attempts to advance interdisciplinary dialogue in Lacanian neuropsychoanalysis.