Simply-connected Research Articles

Gauge Theory Without Principal Fiber Bundles

Abstract In general relativity, the strong equivalence principle is underpinned by a geometrical account of fields on spacetime, by which all fields and bodies probe the same geometry. This geometric account implies that the parallel transport of all spacetime tensors and spinors is dictated by a single affine connection. No similar account of gauge theory is put forward by standard textbooks, which use principal bundles to coordinate the parallel transport of different, interacting particles. Nonetheless, here I argue that gauge theory does afford such a geometric account, obviating the need for principal bundles.

Онтологические аспекты философии А.А. Козлова

The article examines the ontological views of Alexei Alexandrovich Kozlov, a prominent representative of Russian idealist philosophy. It emphasizes that the Russian philosopher transforms Gottfried Leibniz’s monadology in the spirit of a unique doctrine he refers to as “panpsychism”. A.A. Kozlov rejects the radical boundary between mind and matter, asserting that matter is merely a lower level of spirit. Moreover, the philosopher highlights that it is impossible to conceive of actions without an actor and delineates a concept of multiple “substantial doers”. Regarding time, A.A. Kozlov introduces the notion of a “prospective series”, i.e., an order that we perceive precisely as development. The philosopher refers to this position as the concept of a timeless development. As for space, A.A. Kozlov believes that we see a symbol that real substances exist not in isolation, but interrelated, in a single connection. The author of the article concludes that the direction of “panpsychism”, with A.A. Kozlov as one of its brightest representatives, remains relevant. In a world where digital technologies are becoming significant, panpsychism can help in finding new ways for humans to interact with artificial intelligence.

Spatial localisation and sensing in two dimensions via metasurfaces

In this study, we introduce a two-dimensional metasurface sensor designed to detect, locate and distinguish between different objects placed in its near field. When an object is placed on the metasurface, local changes can be detected in one or more of the structure’s meta-atoms. This interaction generally modifies the inductance of the meta-atom, resulting in changes to the overall input impedance of the surface. We derive the properties of the structure and its behaviour in terms of superposition and demonstrate that observing the meta-surface from a single point is sufficient for unambiguous localisation and identification. To model these changes effectively and identify the position of an object, we employ a neural network machine learning algorithm. Our approach enables accurate localisation of all studied objects, with a precision exceeding 98%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$98\\%$$\\end{document}. Additionally, the distinct signatures of the objects allow for separation between them with an accuracy of over 97%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$97\\%$$\\end{document}. The potential applications of this platform extend to foreign object detection on metasurfaces for wireless power transfer, providing proximity detection for many surfaces such as clothing, car bodies and robotic carapaces. Furthermore, our research suggests the feasibility of implementing a touchscreen type interface requiring only a single waveguide connection.

Isoperimetric inequalities for inner parallel curves

We prove weighted isoperimetric inequalities for smooth, bounded, and simply-connected domains. More precisely, we show that the moment of inertia of inner parallel curves for domains with fixed perimeter attains its maximum for a disk. This inequality, which was previously only known for convex domains, allows us to extend an isoperimetric inequality for the magnetic Robin Laplacian to non-convex centrally symmetric domains. Furthermore, we extend our isoperimetric inequality for moments of inertia, which are second moments, to p -th moments for all p smaller than or equal to two. We also show that the disk is a strict local maximiser in the nearly circular, centrally symmetric case for all p strictly less than three, and that the inequality fails for all p strictly bigger than three.

Localized space-time Trefftz method for diffusion equations in complex domains

This paper introduces an advanced localized space-time Trefftz method tackling boundary value predicaments within complex two-dimensional domains governed by diffusion equations. In contrast to the widespread space-time collocation Trefftz method, which typically produces dense and ill-conditioned matrices, the proposed strategy employs a localized collocation scheme to remove these constraints. In particular, this is beneficial in multi-connected configurations or when dealing with significant variations in field values. To the best of our knowledge, this is the first space-time collocation Trefftz method adaptation, which is referred to as the localized space-time Trefftz method in this paper. The latter combines the space-time collocation Trefftz method principles, which allows to eliminate the need for mesh and numerical quadrature in its application. The localized space-time Trefftz method represents each interior node expressed as a linear blend of its immediate neighbors, while the space-time collocation Trefftz method applies numerical techniques within distinct subdomains. A sparse system of linear algebraic equations with internal points satisfying the governing equation, and boundary points satisfying the boundary conditions, allows to obtain numerical solutions using matrix systems. The localized space-time Trefftz method retains the easy-to-use properties and mesh-free structure of the space-time collocation Trefftz method, and it mitigates its ill-conditioning characteristics. Due to the localization principle and the consideration of overlapping subdomains, the solutions in the proposed localized space-time Trefftz method are more simply and compactly expressed compared with those in the space-time collocation Trefftz method, especially when dealing with multiply-connected domains. Numerical examples for simply-connected and multiply-connected domains are then provided to demonstrate the high precision and simplicity of the proposed localized space-time Trefftz method. The obtained results show that the latter has very high accuracy in solving two-dimensional diffusion problems. Compared with the traditional space-time collocation Trefftz method, the proposed mesh-free strategy yields solutions with higher precision while significantly reducing the instability.

Comparative analysis of performance of different types of Tesla valves

Abstract The Tesla valve is a valve with no moving parts. Its special configuration also allows the pressure drop of fluid passing through the Tesla valve from the reverse inlet to be much greater than the pressure drop of fluid passing through the Tesla valve from the forward inlet. Therefore, the Tesla valve has a certain degree of single pilot connectivity and pressure reduction capability. This article selected 8 common types of Tesla valves, By using numerical calculation method through Fluent simulation, the differences of resistance coefficient, pressure drop and Di value of 8 types of single-stage Tesla valves under three different working conditions were compared. In order to explore the performance of 8 kinds of Tesla valves under the three working conditions. At the same time, the relationship between the flow state and the structure of each part of the fluid before and after passing through the distributary pipe is analyzed. The simulation results show that due to the different structure of various Tesla valves, the flow rate, pressure and turbulent kinetic energy of the fluid inside the valve also have different changes. At the same time, there are many similarities in the flow state of some Tesla valves with similar structural types. Finally, according to the calculation results, the advantages and disadvantages of various types of Tesla valves and their applications are analyzed.

Load-bearing capacity of single and multi-anchor connections – theory vs results of experimental research (part 1)

Load-bearing capacity of single and multi-anchor connections – theory vs results of experimental research (part 1)

Test and simulation of high temperature resistant polyamide composite with single lap single bolt connection

Test and simulation of high temperature resistant polyamide composite with single lap single bolt connection

FunMaps: a method for parcellating functional brain networks using resting-state functional MRI data.

Parcellations of resting-state functional magnetic resonance imaging (rs-fMRI) data are widely used to create topographical maps of functional networks in the human brain. While such network maps are highly useful for studying brain organization and function, they usually require large sample sizes to make them, thus creating practical limitations for researchers that would like to carry out parcellations on data collected in their labs. Furthermore, it can be difficult to quantitatively evaluate the results of a parcellation since networks are usually identified using a clustering algorithm, like principal components analysis, on the results of a single group-averaged connectivity map. To address these challenges, we developed the FunMaps method: a parcellation routine that intrinsically incorporates stability and replicability of the parcellation by keeping only network distinctions that agree across halves of the data over multiple random iterations. Here, we demonstrate the efficacy and flexibility of FunMaps, while describing step-by-step instructions for running the program. The FunMaps method is publicly available on GitHub (https://github.com/persichetti-lab/FunMaps). It includes source code for running the parcellation and auxiliary code for preparing data, evaluating the parcellation, and displaying the results.

Macromolecular sensing motors from conducting polymers: Polyaniline/methylcellulose composites as stable current sensing supercapacitors

Sensing motors and supercapacitors are pivotal in empowering smart systems, honing energy management, and facilitating the seamless integration of responsive electronics. Harnessing the electrochemistry of methylcellulose-polyaniline (MC/PANI) composites, this research delves into their potential applications as reactive current sensing supercapacitors with single connectivity. The electrochemical traits of pristine polyaniline (PANI) and MC/PANI composites were analyzed and assessed for their potential applications in sensors and energy storage devices. With a specific capacitance of 300Fg−1, the MC/PANI_B3 composite-based device retained 87.01 % capacitance after 2000 cycles. Besides, based on electrical energy as the sensing parameter, the composite exhibited augmented cathodic and anodic current sensitivity of 8.77 mJmA−1 and -8.86 mJmA−1, respectively. The ameliorated supercapacitor and current sensing parameters of MC/PANI_B3 are ascribed to the percolation threshold content of the conducting phase, which is endowed with optimal hydrogen bond-mediated interactions with methylcellulose (MC), thus confers an expanded chain conformation.

Experimental study on low-cycle fatigue performance of high-strength bolted shear connections

In strong earthquakes, low-cycle fatigue fractures may occur in the bolted connections of steel braced frames. Ensuring a high low-cycle fatigue life for high-strength bolted connections is of paramount significance in enhancing the overall safety and collapse resistance of steel structures. Despite substantial research on plate fatigue failure within bolted connections, there remains a research gap regarding low-cycle fatigue failure of high-strength bolts in these connections. This study aims to address the aforementioned shortcomings by conducting 34 sets of low-cycle fatigue tests on high-strength bolted connections. The test specimens all experienced low-cycle shear fatigue fracture at the threaded or unthreaded portion of the bolt shank as the dominant failure mode. Residual deformations were observed in the holes of connection plates. Based on the test data, ultimate shear capacity of a single shear connection is around 0.61Fy (tensile yield bearing capacity of bolt) when the shear force passes through the unthreaded portion and drops to 0.54Fy for the shear force at the thread. The untreated Q355 (minimum yield strength of 355 MPa) steel surface has an average anti-slip coefficient of around 0.37, while milling reduces it to approximately 0.30. The influence patterns of loading amplitude, bolt material, minimum plate thickness, bolt diameter, shear force position and connection type on low-cycle fatigue life are given by range analysis. Among them, variance analysis shows that loading amplitude and bolt material are the primary influencing factors. The correlation coefficient between loading amplitude and low-cycle fatigue life is −0.92, indicating a strong negative correlation. The degradation amount and rate of anti-slip capacity and shear capacity of bolted connections are also investigated. To propose reliable life prediction method, three models were used to establish the relationship between dimensionless shear deformation and low-cycle fatigue life of 10.9-grade high-strength bolted connections. It is not appropriate to use the fatigue categories defined in current standards to predict the low-cycle shear fatigue life of high-strength bolted connections.

Switching in microseconds: design of a 5 × 5 non-blocking free space optical switch at 1550nm with a piezo-actuator and beam-steering lens system

Modern data center networks (DCNs) require optical switches with ultra-low loss, ultra-fast reconfiguration speed, high throughput, and high extinction ratio performances. In this work, we propose the design of a 5 × 5 optical switch at 1550 nm based on a piezo-actuator serving as a translating input optical source, and a beam-steering system built of spherical lenses to complete the switching behaviour. An ultra-fast actuator switching speed is estimated as 1.55 μs latency for a single connection with a demo circuit. We further simulate the beam-steering system end-to-end in a commercial optical design software CODE V and demonstrate a theoretical 2.16 dB insertion loss for a single connection in the switch at optimum alignment.

CNN-based Network Intrusion Detection and Classification Model for Cyber-Attacks

A Convolution Neural Network (CNN)-based Network Intrusion Detection Model for Cyber-attacks is of great value in identifying and classifying attacks on any network. The Knowledge Discovery in Database Cup '99 dataset containing approximately 4,900,000 single connection vectors was divided into two phases; 75% of the total dataset was used during the learning process of the machine learning technique, while 25% was used on a fully trained model to validate and evaluate its performance. The model's performance indicated that it can detect and classify different classes of attacks with an accuracy of 98% with 20 epochs at a 0.001 learning rate using machine learning. The model loss for the training and validation was 7.48% and 7.98%, respectively, over 20 epochs, which implies that the model performed better on the training dataset. This study demonstrated that the convolutional Neural network-based Network Intrusion Detection and classification model shows high detection and low false negative rates. The CNN model offers a high detection rate and fidelity to unknown attacks, i.e., it can differentiate between already-seen attacks and new zero-day attacks. At the end of the experiment, the proposed approach is suitable in modeling the network IDS for detecting intrusion attacks on computer networks thereby enabling a secured environment for the proper functioning of the system

Small-time global approximate controllability for incompressible MHD with coupled Navier slip boundary conditions

We study the small-time global approximate controllability for incompressible magnetohydrodynamic (MHD) flows in smoothly bounded two- or three-dimensional domains. The controls act on arbitrary nonempty open portions of each connected boundary component, while linearly coupled Navier slip-with-friction conditions are imposed along the uncontrolled parts of the boundary. Some choices for the friction coefficients give rise to interacting velocity and magnetic field boundary layers. We obtain sufficient dissipation properties of these layers by a detailed analysis of the corresponding asymptotic expansions. For certain friction coefficients, or if the obtained controls are not compatible with the induction equation, an additional pressure-like term appears. We show that such a term does not exist for problems defined in planar simply-connected domains and various choices of Navier slip-with-friction boundary conditions.

Context-invariant beliefs are supported by dynamic reconfiguration of single unit functional connectivity in prefrontal cortex of male macaques

Natural behaviors occur in closed action-perception loops and are supported by dynamic and flexible beliefs abstracted away from our immediate sensory milieu. How this real-world flexibility is instantiated in neural circuits remains unknown. Here, we have male macaques navigate in a virtual environment by primarily leveraging sensory (optic flow) signals, or by more heavily relying on acquired internal models. We record single-unit spiking activity simultaneously from the dorsomedial superior temporal area (MSTd), parietal area 7a, and the dorso-lateral prefrontal cortex (dlPFC). Results show that while animals were able to maintain adaptive task-relevant beliefs regardless of sensory context, the fine-grain statistical dependencies between neurons, particularly in 7a and dlPFC, dynamically remapped with the changing computational demands. In dlPFC, but not 7a, destroying these statistical dependencies abolished the area’s ability for cross-context decoding. Lastly, correlational analyses suggested that the more unit-to-unit couplings remapped in dlPFC, and the less they did so in MSTd, the less were population codes and behavior impacted by the loss of sensory evidence. We conclude that dynamic functional connectivity between neurons in prefrontal cortex maintain a stable population code and context-invariant beliefs during naturalistic behavior.

Single entanglement connection architecture between multi-layer bipartite hardware efficient ansatz

Variational quantum algorithms are among the most promising algorithms to achieve quantum advantages in the noisy intermediate-scale quantum (NISQ) era. One important challenge in implementing such algorithms is to construct an effective parameterized quantum circuit (also called an ansatz). In this work, we propose a single entanglement connection architecture (SECA) for a bipartite hardware efficient ansatz (HEA) by balancing its expressibility, entangling capability, and trainability. Numerical simulations with a one-dimensional Heisenberg model and quadratic unconstrained binary optimization (QUBO) issues were conducted. Our results indicate the superiority of SECA over the common full entanglement connection architecture in terms of computational performance. Furthermore, combining SECA with gate-cutting technology to construct distributed quantum computation (DQC) can efficiently expand the size of NISQ devices under low overhead. We also demonstrated the effectiveness and scalability of the DQC scheme. Our study is a useful indication for understanding the characteristics associated with an effective training circuit.

Comparative basolateral amygdala connectomics reveals dissociable single-neuron projection patterns to frontal cortex in macaques and mice

Basolateral amygdala (BLA) is a key hub for affect in the brain,1,2,3 and dysfunction within this area contributes to a host of psychiatric disorders.4,5 BLA is extensively and reciprocally interconnected with frontal cortex,6,7,8,9 and some aspects of its function are evolutionarily conserved across rodents, anthropoid primates, and humans.10 Neuron density in BLA is substantially lower in primates compared to murine rodents,11 and frontal cortex (FC) is dramatically expanded in primates, particularly the more anterior granular and dysgranular areas.12,13,14 Yet, how these anatomical differences influence the projection patterns of single BLA neurons to frontal cortex across rodents and primates is unknown. Using a barcoded connectomic approach, we assessed the single BLA neuron connections to frontal cortex in mice and macaques. We found that BLA neurons are more likely to project to multiple distinct parts of FC in mice than in macaques. Further, while single BLA neuron projections to nucleus accumbens were similarly organized in mice and macaques, BLA-FC connections differed substantially. Notably, BLA connections to subcallosal anterior cingulate cortex (scACC) in macaques were least likely to branch to other medial frontal cortex areas compared to perigenual ACC (pgACC). This pattern of connections was reversed in the mouse homologues of these areas, infralimbic and prelimbic cortex (IL and PL), mirroring functional differences between rodents and non-human primates. Taken together, these results indicate that BLA connections to FC are not linearly scaled from mice to macaques and instead the organization of single-neuron BLA connections is distinct between these species.

Patterns of stability in complex contagions

Contagions refer to the spread or transmission of diseases, behaviors, beliefs, or emotions. While some contagions easily propagate throughout entire populations, others seem to be more constrained and propagate only within specific parts of the population. This arises not just because of different transmission rates but because of qualitative differences in the mechanisms with which contagions propagate throughout a network. Diseases typically propagate through single connections, while behaviors and beliefs often necessitate multiple connections for further propagation, termed complex contagions. In this paper, we propose a graph reduction method to reduce a network to include only connections immediately relevant to the propagation of a complex contagion. Through repeated application, we obtain structures that remain stable under the reduction, allowing us to define and measure for any given network, (i) strongly contagious components, (ii) weakly contagious components, and (iii) bridge components. Information about the size and location of these components can be used as a meaningful basis to assess and prevent the potential spread of harmful contagions as well as incentivize the spread of beneficial contagions.

Decentralized Navigation with Optimality for Multiple Holonomic Agents in Simply Connected Workspaces.

Multi-agent systems are utilized more often in the research community and industry, as they can complete tasks faster and more efficiently than single-agent systems. Therefore, in this paper, we are going to present an optimal approach to the multi-agent navigation problem in simply connected workspaces. The task involves each agent reaching its destination starting from an initial position and following an optimal collision-free trajectory. To achieve this, we design a decentralized control protocol, defined by a navigation function, where each agent is equipped with a navigation controller that resolves imminent safety conflicts with the others, as well as the workspace boundary, without requesting knowledge about the goal position of the other agents. Our approach is rendered sub-optimal, since each agent owns a predetermined optimal policy calculated by a novel off-policy iterative method. We use this method because the computational complexity of learning-based methods needed to calculate the global optimal solution becomes unrealistic as the number of agents increases. To achieve our goal, we examine how much the yielded sub-optimal trajectory deviates from the optimal one and how much time the multi-agent system needs to accomplish its task as we increase the number of agents. Finally, we compare our method results with a discrete centralized policy method, also known as a Multi-Agent Poli-RRT* algorithm, to demonstrate the validity of our method when it is attached to other research algorithms.

The Intrinsic Geometry of Simply and Rectifiably Connected Plane Sets

AbstractWe prove that the metric completion of the intrinsic length space associated with a simply and rectifiably connected plane set is a Hadamard space. We also characterize when such a space is Gromov hyperbolic.