Theoretical Complexity Research Articles

Defense of Integrative Pluralism in the Cognitive Sciences

This article considers the opposition between the pluralist and unificationist stances in the philosophy of cognitive sciences. The choice between pluralism and unificationism is important both in terms of discussing the current methodological practices and with respect to the debates about the future of the cognitive studies. As a starting point, the author takes his own idea of theoretical complexes. One of its most significant normative consequences is theoretical pluralism. There have been a number of skeptical arguments against pluralism, including the fear of generating many useless theories and dissipating of efforts, as well as the doubts about the differences between pluralism and relativism. One of the most recent objections states that integrative pluralism implies a tension, an instability, if one prioritizes the epistemic quality of explanatory depth. The author addresses each of these objections in turn. The constructive variety of pluralism is distinguished from unbridled pluralism and relativism by its commitment to the idea of improving explanatory, predictive, and other characteristics of a theory through the presence of alternatives and their collisions, mutual criticisms. Integrative pluralism does not entail instability, since the values of unification and explanatory depth cannot be prescribed to the cognitive sciences ex cathedra, without taking into account the character of the cognitive process revealed in empirical studies. The pluralist stance appears to be incompatible with radical projects of unification of the cognitive studies, though there are many opportunities for more moderate integrative initiatives. One such initiative is the recent idea of integrative experiment design, which involves constructing a space of experiments for a particular problem. Testing theories by selectively sampling points in this space and then updating them accordingly may be a key to the integration of experimental observations.

Improving Systematic Generalization of Linear Transformer Using Normalization Layers and Orthogonality Loss Function

A Linear Transformer linearizes the attention mechanism of the vanilla Transformer architecture, significantly improving efficiency and achieving linear theoretical complexity with respect to sequence length. However, few studies have explored the capabilities of the Linear Transformer beyond its efficiency. In this work, we investigate the systematic generalization capability of the Linear Transformer, a crucial property for strong generalization to unseen data. Through preliminary experiments, we identify two major issues contributing to its unstable systematic generalization performance: (i) unconstrained norms of Queries and Keys, and (ii) high correlation among Values across the sequence. To address these issues, we propose two simple yet effective methods: normalization layers for Queries and Keys, and an orthogonality loss function applied to Values during training. In experiments, we demonstrate that applying these methods to the Linear Transformer significantly improves its stability and systematic generalization performance across several well-known tasks. Furthermore, our proposed methods outperform the vanilla Transformer on specific systematic generalization tasks, such as the sort-of-CLEVR and SCAN tasks.

On Interdicting Dense Clusters in a Network

Given a vertex-weighted undirected graph with blocking costs of its vertices and edges, we seek a minimum cost subset of vertices and edges to block such that the weight of any γ-quasi-clique in the interdicted graph is at most some predefined threshold parameter. The value of [Formula: see text] specifies the edge density of cohesive vertex groups of interest in the network. The considered weighted γ-quasi-clique interdiction problem can be viewed as a natural generalization of several variations of the clique blocker problem previously studied in the literature. From the application perspective, this setting is primarily motivated by the problem of disrupting adversarial (“dark”) networks (e.g., social or communication networks), where γ-quasi-cliques represent “tightly knit” groups of adversaries that we aim to dismantle. We first address the theoretical computational complexity of the problem. We then exploit some basic characterization of its feasible solutions to derive a linear integer programming (IP) formulation. This linear IP model can be solved using a lazy-fashioned branch-and-cut scheme. We also propose a combinatorial branch-and-bound algorithm for solving this problem. The computational performance of the developed exact solution schemes is studied using a test bed of randomly generated and real-life networks. Finally, some interesting insights and observations are also provided using a well-known example of a terrorist network. History: Accepted by Russel Bent, Area Editor for Network Optimization: Algorithms & Applications. Funding: The work of S. Butenko was partially supported by the Air Force Office of Scientific Research under Award FA9550-23-1-0300. The work of O. A. Prokopyev was partially supported by the Office of Naval Research under Award ONR N00014-22-1-2678. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.0027 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2023.0027 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ . The online appendix is available at https://doi.org/10.1287/ijoc.2023.0027 .

A generalization of Lehman’s method

AbstractA new deterministic algorithm for finding square divisors, and finding r-power divisors in general, is presented. This algorithm is based on Lehman’s method for integer factorization and is straightforward to implement. While the theoretical complexity of the new algorithm is far from best known, the algorithm becomes especially effective if even a loose bound on a square divisor is known. Additionally, we answer a question by D. Harvey and M. Hittmeir on whether their recent deterministic algorithm for integer factorization can be adapted to finding r-power divisors.

The Square-Root Unscented and the Square-Root Cubature Kalman Filters on Manifolds.

Estimating the state of a system by fusing sensor data is a major prerequisite in many applications. When the state is time-variant, derivatives of the Kalman filter are a popular choice for solving that task. Two variants are the square-root unscented Kalman filter (SRUKF) and the square-root cubature Kalman filter (SCKF). In contrast to the unscented Kalman filter (UKF) and the cubature Kalman filter (CKF), they do not operate on the covariance matrix but on its square root. In this work, we modify the SRUKF and the SCKF for use on manifolds. This is particularly relevant for many state estimation problems when, for example, an orientation is part of a state or a measurement. In contrast to other approaches, our solution is both generic and mathematically coherent. It has the same theoretical complexity as the UKF and CKF on manifolds, but we show that the practical implementation can be faster. Furthermore, it gains the improved numerical properties of the classical SRUKF and SCKF. We compare the SRUKF and the SCKF on manifolds to the UKF and the CKF on manifolds, using the example of odometry estimation for an autonomous car. It is demonstrated that all algorithms have the same localization performance, but our SRUKF and SCKF have lower computational demands.

Securing Democracy? The National Security State Revisited

ABSTRACT The “national security state” concept traditionally examines the interplay between security imperatives and democratic governance in the United States. While research has expanded it, further refinement is needed. This paper advocates for its universal relevance to democracies, shedding light on political reorganization driven by national security objectives. A qualitative analysis of prior studies reveals six core attributes of the concept, enhanced to formulate a robust definition that embodies its theoretical and analytical complexities in the disciplinary history of security studies. The resulting framework is instrumental in exploring how states balance the quest for security with democratic principles.

Symmetry Breaking in a Triferrous Extended Metal Atom Chain.

Semilocal and random phase approximation (RPA) density functional theory (DFT) and complete active space (CASSCF + NEVPT2) methodologies were applied to investigate a new class of extended metal atom chain (EMAC) complexes. A novel triferrous complex has been synthesized recently that does not utilize the usual 2,2'-dipyridylamine (dpa) ligand framework, which essentially always results in a tetragonal coordination environment and general formula M3(dpa)4X2, where X is an anion. Instead, the triferrous complex utilizes a dianionic, 2,6-bis(trimethylsilylamido)pyridine ligand (L2-) resulting in the formation of trigonal complexes with general formula Fe3L3. To better understand the electronic structure of this complex, calculations were utilized to explore the experimentally isolated Fe3L3, and a smaller theoretical complex, in order to compare and contrast with the traditional dpa-based EMACs. Due to the absence of anionic, axial ligands, the sigma nonbonding orbitals formed from the metal d orbitals are lower in energy than in the dpa complexes, and compete with the pi bonding orbitals for occupation in the Fe3L3 complex. While the idealized geometry of these complexes is D3h, a helical distortion of the ligands and subsequent electronic symmetry breaking due to Jahn-Teller distortions are predicted utilizing both semilocal and RPA DFT methods, ending in a C2 structure that closely matches the reported crystal structure. Predicted Mössbauer isomer shifts and ultraviolet/visible (UV/vis) spectra also agree with the experimental data available in the literature. Magnetic coupling constants also indicate ferromagnetic coupling between nearest neighbor irons. Two-dimensional (2D) potential energy surfaces were calculated for a range of fixed Fe-Fe bond lengths, revealing a flat potential energy surface over a wide range of Fe-Fe bond lengths and verifying the ability of RPA to act as a higher-level check on semilocal DFT results. In order to verify the predicted high-spin ground state, CASSCF + NEVPT2 was applied to selected molecular configurations and confirmed the predictions made by DFT. These calculations shed light on the physical ground state electron configuration of Fe3L3 and correlate this electronic configuration with the available experimental data.

Unraveling the Complexity of the N e/N c Ratio for Conservation of Large and Widespread Pelagic Fish Species: Current Status and Challenges.

Estimating and understanding the ratio between effective population size (N e) and census population size (N c) are pivotal in the conservation of large marine pelagic fish species, including bony fish such as tunas and cartilaginous fish such as sharks, given the challenges associated with obtaining accurate estimates of their abundance. The difficulties inherent in capturing and monitoring these species in vast and dynamic marine environments often make direct estimation of their population size challenging. By focusing on N e, it is conceivable in certain cases to approximate census size once the N e/N c ratio is known, although this ratio can vary and does not always increase linearly, as it is influenced by various ecological and evolutionary factors. Thus, this ratio presents challenges and complexities in the context of pelagic species conservation. To delve deeper into these challenges, firstly, we recall the diverse types of effective population sizes, including contemporary and historical sizes, and their implications in conservation biology. Secondly, we outline current knowledge about the influence of life history traits on the N e/N c ratio in the light of examples drawn from large and abundant pelagic fish species. Despite efforts to document an increasing number of marine species using recent technologies and statistical methods, establishing general rules to predict N e/N c remains elusive, necessitating further research and investment. Finally, we recall statistical challenges in relating N e and N c emphasizing the necessity of aligning temporal and spatial scales. This last part discusses the roles of generation and reproductive cycle effective population sizes to predict genetic erosion and guiding management strategies. Collectively, these sections underscore the multifaceted nature of effective population size estimation, crucial for preserving genetic diversity and ensuring the long-term viability of populations. By navigating statistical and theoretical complexities, and addressing methodological challenges, scientists should be able to advance our understanding of the N e/N c ratio.

Forward variable selection enables fast and accurate dynamic system identification with Karhunen-Loève decomposed Gaussian processes

A promising approach for scalable Gaussian processes (GPs) is the Karhunen-Loève (KL) decomposition, in which the GP kernel is represented by a set of basis functions which are the eigenfunctions of the kernel operator. Such decomposed kernels have the potential to be very fast, and do not depend on the selection of a reduced set of inducing points. However KL decompositions lead to high dimensionality, and variable selection thus becomes paramount. This paper reports a new method of forward variable selection, enabled by the ordered nature of the basis functions in the KL expansion of the Bayesian Smoothing Spline ANOVA kernel (BSS-ANOVA), coupled with fast Gibbs sampling in a fully Bayesian approach. It quickly and effectively limits the number of terms, yielding a method with competitive accuracies, training and inference times for tabular datasets of low feature set dimensionality. Theoretical computational complexities are O ( N P 2 ) in training and O ( P ) per point in inference, where N is the number of instances and P the number of expansion terms. The inference speed and accuracy makes the method especially useful for dynamic systems identification, by modeling the dynamics in the tangent space as a static problem, then integrating the learned dynamics using a high-order scheme. The methods are demonstrated on two dynamic datasets: a ‘Susceptible, Infected, Recovered’ (SIR) toy problem, along with the experimental ‘Cascaded Tanks’ benchmark dataset. Comparisons on the static prediction of time derivatives are made with a random forest (RF), a residual neural network (ResNet), and the Orthogonal Additive Kernel (OAK) inducing points scalable GP, while for the timeseries prediction comparisons are made with LSTM and GRU recurrent neural networks (RNNs) along with the SINDy package.

NEURAL NETWORKS AND DEEP LEARNING: ENHANCING AI THROUGH NEURAL NETWORK OPTIMIZATION

Neural networks and deep learning have profoundly impacted artificial intelligence (AI), driving advancements across numerous applications. However, optimizing these networks remains a critical challenge, necessitating sophisticated techniques and methodologies. This article explores the state-of-the-art in neural network optimization, delving into advanced gradient descent variants, regularization methods, learning rate schedulers, batch normalization, and cutting-edge architectures. We discuss their theoretical underpinnings, implementation complexities, and empirical results, providing insights into how these optimization strategies contribute to the development of high-performance AI systems. Case studies in image classification and natural language processing illustrate practical applications and outcomes. The article concludes with an examination of current challenges and future directions in neural network optimization, emphasizing the need for scalable, interpretable, and robust solutions.

Plasma centrifugation method for separation of the nuclear waste

The high-throughput, plasma-based, mass separation techniques of nuclear waste are still an active research topic due to the theoretical and practical complexity of processing such waste. The nuclear waste can be separated according to its masses by plasma centrifugation technique. Because of this, the present research has been performed by setting up E → × B → rotation in cold cylindrical plasma surrounded by an ideally conducting homogenous shell inside a plasma centrifuge device. The results obtained are useful in analyzing the magneto-rotational instability (MRI) and trajectories of the plasma particles which are beneficial for improving the throughput and separation factor of the device.

Optimizing network insights: AI-Driven approaches to circulant graph based on Laplacian spectra

The study of Laplacian and signless Laplacian spectra extends across various fields, including theoretical chemistry, computer science, electrical networks, and complex networks, providing critical insights into the structures of real-world networks and enabling the prediction of their structural properties. A key aspect of this study is the spectrum-based analysis of circulant graphs. Through these analyses, important network measures such as mean-first passage time, average path length, spanning trees, and spectral radius are derived. This research enhances our understanding of the relationship between graph spectra and network characteristics, offering a comprehensive perspective on complex networks. Consequently, it supports the ability to make predictions and conduct analyses across a wide range of scientific disciplines.

Structural Chemistry Simulation Experiments: A Case Study on Conjugated Alkene Molecules

As a core branch of chemistry, structural chemistry presents challenges in teaching due to its theoretical constructs and complex mathematical derivations. The application of quantum mechanics is particularly difficult for students. This paper analyzes the limitations of traditional experimental teaching and proposes simulation experiments as an effective supplementary method. Simulation experiments, by reducing costs, improving safety, and enhancing intuitiveness, help students deeply understand the theoretical knowledge of structural chemistry and cultivate their critical thinking and problem-solving skills. This study designs a series of simulation experiment teaching activities aimed at enhancing students' understanding of the structural characteristics of conjugated alkene molecules and their impact on molecular properties. Through case analysis, interactive discussions, and feedback evaluation, the study demonstrates the advantages of simulation experiments in improving student engagement, knowledge mastery, and practical abilities. Additionally, it points out the shortcomings of simulation experiments in terms of authenticity and technological dependence and proposes corresponding improvement suggestions. Finally, it emphasizes the importance of combining practical experimental operations with cultivating students' autonomous learning abilities, aiming to provide a more comprehensive strategy for structural chemistry teaching.

A model is worth tens of thousands of examples for estimation and thousands for classification

Traditional signal processing methods relying on mathematical data generation models have been cast aside in favour of deep neural networks, which require vast amounts of data. Since the theoretical sample complexity is nearly impossible to evaluate, these amounts of examples are usually estimated with crude rules of thumb. However, these rules only suggest when the networks should work, but do not relate to the traditional methods. In particular, an interesting question is: how much data is required for neural networks to be on par or outperform, if possible, the traditional model-based methods? In this work, we empirically investigate this question in three simple examples covering estimation and classification, where the data is generated according to precisely defined mathematical models, and where well-understood optimal or state-of-the-art mathematical data-agnostic solutions are known. A first problem is deconvolving one-dimensional Gaussian signals, a second one is estimating a circle’s radius and location in random grayscale images of disks, and a third one both classifies the presence of a line and locates it when present in a binary random dot image. By training various networks, either naive custom designed or well-established ones, with various amounts of training data, we find that networks require tens of thousands of examples for estimation in comparison to the traditional methods and thousands for classification, whether the networks are trained from scratch or even with transfer-learning or finetuning.

An optimized design of delay-and energy-efficient Booth multiplier

Multipliers are essential computation units in virtually all computing systems, including processors and numerous AI accelerator architectures. This paper presents an optimized architecture for a Booth multiplier, targeting high performance while minimizing energy consumption and area utilization. The design optimization focuses on all three multiplier stages: partial product generation, reduction, and summation. To enhance delay and energy efficiency in the partial product generation stage, we first employed a simplified configuration comprising inverters and a sign selection unit instead of complex binary-to-two's complement circuitry. Next, to achieve further delay and area efficiency at this stage, logic optimization is applied at the partial product's generation circuitry by designing Booth encoders to remove redundant logic in multiplexers circuitry. Moreover, we introduced specialized sign compressors tailored for carry-save compression in the compression stage. Compared to conventional counterparts, these compressors offered lower power consumption and reduced critical path delay with only two XOR logic gates. Finally, in the summation stage, we proposed an optimized design segment for Carry Look-Ahead Adder for the final summation stage, designed to deliver swift throughput with minimal fan-in logic gates, even in the context of high bit-width configurations. This segment is cascaded to make a 13-bit final adder for the summation stage in the proposed design. The proposed architecture undergoes ASIC-targeted synthesis in Cadence Genus employing FreePDK CMOS 45 nm process technology. Synthesized results, along with theoretical design complexity comparison, demonstrate that the proposed design surpasses state-of-the-art 8 × 8 multiplier designs by critical metrics, including delay, power consumption, area utilization, power delay product, and area delay product.

Median and small parsimony problems on RNA trees.

Noncoding RNAs (ncRNAs) express their functions by adopting molecular structures. Specifically, RNA secondary structures serve as a relatively stable intermediate step before tertiary structures, offering a reliable signature of molecular function. Consequently, within an RNA functional family, secondary structures are generally more evolutionarily conserved than sequences. Conversely, homologous RNA families grouped within an RNA clan share ancestors but typically exhibit structural differences. Inferring the evolution of RNA structures within RNA families and clans is crucial for gaining insights into functional adaptations over time and providing clues about the Ancient RNA World Hypothesis. We introduce the median problem and the small parsimony problem for ncRNA families, where secondary structures are represented as leaf-labeled trees. We utilize the Robinson-Foulds (RF) tree distance, which corresponds to a specific edit distance between RNA trees, and a new metric called the Internal-Leafset (IL) distance. While the RF tree distance compares sets of leaves descending from internal nodes of two RNA trees, the IL distance compares the collection of leaf-children of internal nodes. The latter is better at capturing differences in structural elements of RNAs than the RF distance, which is more focused on base pairs. We also consider a more general tree edit distance that allows the mapping of base pairs that are not perfectly aligned. We study the theoretical complexity of the median problem and the small parsimony problem under the three distance metrics and various biologically relevant constraints, and we present polynomial-time maximum parsimony algorithms for solving some versions of the problems. Our algorithms are applied to ncRNA families from the RFAM database, illustrating their practical utility. https://github.com/bmarchand/rna\_small\_parsimony.

Mobility as a Service: An exploration of exact and heuristic algorithms for a new multi-modal multi-objective journey planning problem

Mobility as a Service (MaaS) is a term coined for the development and implementation of multi-modal trip planner recommendation systems. Multi-modal journeys can include public transport, private transport and hire-able e-scooters which can beneficially augment public transport journeys. This study proposes and tackles a new and more general multi-modal multi-objective journey planning problem than considered previously. Our aim is to generate Pareto sets of multi-modal journeys which minimise the objectives of cost, travel time, inconvenience, CO2 emissions, and calorie expenditure, as well as find journeys that optimally balance the trade-offs between them. Commuters can then choose between green, cheap, fast, car-free or convenient journeys. This work proposes implicit enumeration and heuristic algorithms which are analysed in terms of their theoretical time complexity, empirically in terms of solution time and optimality gap using a series of Manhattan and random structure transport networks. We show that our algorithms can generate solutions of equal quality to RAPTOR—a prominent existing journey planning algorithm. For this problem we reveal that the number of network nodes is a huge computational bottleneck, leading to the suggestion that future research can benefit from limiting the number of network nodes that are considered as transfer points. While our heuristic can generate good quality Pareto sets quicker than the enumeration procedure for the largest instances considered, we show that the enumeration procedure with pruning rules can still be the most effective strategy for this particular problem.

Scorn Not Its Simplicity: Examining the Effectiveness of Simple Generalist Treatment for Personality Disorders.

Treatment guidelines for personality disorders have typically recommended specialized psychotherapeutic interventions. In this review, the author suggests that an intervention's effectiveness may be determined less by the specific method than by therapist competence, team culture, clinical process structure, and institutional context. The author argues that these elements determine variance in effectiveness between and within methods. Whereas initial studies of a specialized treatment may reflect the exceptional competencies of the treatment's developers and early adopters, in daily clinical practice, therapists with an average level of skill may struggle with the theoretical and methodological complexities of these treatments, which can hinder genuine connection with patients. This interference may particularly affect treatment outcomes when therapists encounter the intense emotions and interpersonal hypersensitivity experienced by patients with personality disorders. Most therapists would benefit from a set of simple generalist principles that determine the context for their work and offer a framework for dealing with clinical challenges while enabling them to be true to themselves and use their previously learned competencies. The Guideline-Informed Treatment for Personality Disorders is an enhanced common-factors approach that summarizes the core principles of effective treatment and can be feasibly implemented by most therapists.

Energy Complexity of Convolutional Neural Networks.

The energy efficiency of hardware implementations of convolutional neural networks (CNNs) is critical to their widespread deployment in low-power mobile devices. Recently, a number of methods have been proposed for providing energy-optimal mappings of CNNs onto diverse hardware accelerators. Their estimated energy consumption is related to specific implementation details and hardware parameters, which does not allow for machine-independent exploration of CNN energy measures. In this letter, we introduce a simplified theoretical energy complexity model for CNNs, based on only a two-level memory hierarchy that captures asymptotically all important sources of energy consumption for different CNN hardware implementations. In this model, we derive a simple energy lower bound and calculate the energy complexity of evaluating a CNN layer for two common data flows, providing corresponding upper bounds. According to statistical tests, the theoretical energy upper and lower bounds we present fit asymptotically very well with the real energy consumption of CNN implementations on the Simba and Eyeriss hardware platforms, estimated by the Timeloop/Accelergy program, which validates the proposed energy complexity model for CNNs.

A Review of Foreign Languages in Advertising and Product Packaging: Socio-and Psycholinguistic Perspectives

Research on the use of foreign languages in advertising and packaging identifies English as a medium due to its modern universal appeal. As advertising vehicles become more numerous and diverse, foreign languages have veered from their purely linguistic function to assuming a more active role in influencing consumers’ cognitions and behaviors. Research allows companies to tap into the implicit emotional connections and associations that foreign languages evoke in consumers and better assist companies in adjusting their consumer culture positioning strategies to various local markets. This review aims to encapsulate the theoretical complexities underpinning the mechanism of how foreign languages function and how understanding them may help advertisers and brand managers in influencing consumer behavior and perception. The existing body of research shows a surging interest in multilingual advertising and product packaging. The former is more consolidated with validated experimental designs and a wider application of relevant theories whereas the latter is still at its infancy and lacks the generalizability to diverse markets. The authors conclude that foreign languages are widespread. Drawing on the theories of linguistics, sociolinguistics and psycholinguistics, alongside considering markets' cultural sensitivities, the authors recommend employing foreign language cues in both advertising and packaging.