Dimensional Space Research Articles

Holographic phenomenology via overlapping degrees of freedom

Abstract The holographic principle suggests that regions of space contain fewer physical degrees of freedom than would be implied by conventional quantum field theory. Meanwhile, in Hilbert spaces of large dimension $2^n$, it is possible to define $N \gg n$ Pauli algebras that are nearly anti-commuting (but not quite) and which can be thought of as ``overlapping degrees of freedom". We propose to model the phenomenology of holographic theories by allowing field-theory modes to be overlapping, and derive potential observational consequences. In particular, we build a Fermionic quantum field whose effective degrees of freedom approximately obey area scaling and satisfy a cosmic Bekenstein bound, and compare predictions of that model to cosmic neutrino observations. Our implementation of holography implies a finite lifetime of plane waves, which depends on the overall UV cutoff of the theory. To allow for neutrino flux from blazar TXS 0506+056 to be observable, our model needs to have a cutoff $k_{\mathrm{UV}} \lesssim 500\, k_{\mathrm{LHC}}\,$. This is broadly consistent with current bounds on the energy spectrum of cosmic neutrinos from IceCube, but high energy neutrinos are a potential challenge for our model of holography. We motivate our construction via quantum mereology, \ie using the idea that EFT degrees of freedom should emerge from an abstract theory of quantum gravity by finding quasi-classical Hilbert space decompositions. We also discuss how to extend the framework to Bosons. Finally, using results from random matrix theory we derive an analytical understanding of the energy spectrum of our theory.\ \ The numerical tools used in this work are publicly available within the \verb|GPUniverse| package, \url{https://github.com/OliverFHD/GPUniverse}~.

Quantum exploration of high-dimensional canyon landscapes

Canyon landscapes in high dimension can be described as manifolds of small, but extensive dimension, immersed in a higher dimensional ambient space and characterized by a zero potential energy on the manifold. Here we consider the problem of a quantum particle exploring a prototype of a high-dimensional random canyon landscape. We characterize the thermal partitionfunction and show that around the point where the classical phase space has a satisfiability transition so that zero potential energy canyons disappear, moderate quantum fluctuations have a deleterious effect: they induce glassy phasesat temperature where classical thermal fluctuations alone would thermalize the system. Surprisingly we show that even when, classically, diffusion is expected to be unbounded in space, the interplay between quantum fluctuations and the randomness of the canyon landscape conspire to have a confining effect.

Approximation of a two‐dimensional Gross–Pitaevskii equation with a periodic potential in the tight‐binding limit

AbstractThe Gross–Pitaevskii (GP) equation is a model for the description of the dynamics of Bose–Einstein condensates. Here, we consider the GP equation in a two‐dimensional setting with an external periodic potential in the ‐direction and a harmonic oscillator potential in the ‐direction in the so‐called tight‐binding limit. We prove error estimates which show that in this limit the original system can be approximated by a discrete nonlinear Schrödinger equation. The paper is a first attempt to generalize the results from [19] obtained in the one‐dimensional setting to higher space dimensions and more general interaction potentials. Such a generalization is a non‐trivial task due to the oscillations in the external periodic potential which become singular in the tight‐binding limit and cause some irregularity of the solutions which are harder to handle in higher space dimensions. To overcome these difficulties, we work in anisotropic Sobolev spaces. Moreover, additional non‐resonance conditions have to be satisfied in the two‐dimensional case.

Reinforced steering Evolutionary Markov Chain for high-dimensional feature selection

The increasing accessibility of extensive datasets has amplified the importance of extracting insights from high-dimensional data. However, the task of selecting relevant features in these high-dimensional spaces is made more difficult due to the curse of dimensionality. Although Evolutionary Algorithms (EAs) have shown promise in the literature for feature selection, creating EAs for high dimensions is still challenging. To address the problem of feature selection in high dimensions, a novel concept of Evolutionary Reinforced Markov Chain is proposed in this paper. The proposed work has the following contributions and merits: (i) The paradigms of evolutionary computation, reinforcement learning, and Markov chain are incorporated into an integrational framework for feature selection in high dimensional spaces in a recursive manner. (ii) To support the global convergence of the algorithm and manage its computational complexity, a restricted group of the most effective agents is maintained within the evolutionary population. (iii) The dynamic Markov chain process efficiently manages agent evolution and communication, ensuring effective navigation through the search space. (iv) Agents moving in the right way are rewarded with an increase in their associated transition probability, while the agents going in the wrong direction are discouraged with a decrease in their associated transition probabilities; this promotes the establishment of an equilibrium state and leads to convergence. (v) The effective size of successful agents is reduced recursively while progressing through different states to further facilitate the speed of convergence and decrease the number of features. (vi) The performance comparison with state-of-the-art feature selection methods shows a significant improvement and promise of the proposed method over the existing methods.

Bounds of Different Integral Operators in Tensorial Hilbert and Variable Exponent Function Spaces

In dynamical systems, Hilbert spaces provide a useful framework for analyzing and solving problems because they are able to handle infinitely dimensional spaces. Many dynamical systems are described by linear operators acting on a Hilbert space. Understanding the spectrum, eigenvalues, and eigenvectors of these operators is crucial. Functional analysis typically involves the use of tensors to represent multilinear mappings between Hilbert spaces, which can result in inequality in tensor Hilbert spaces. In this paper, we study two types of function spaces and use convex and harmonic convex mappings to establish various operator inequalities and their bounds. In the first part of the article, we develop the operator Hermite–Hadamard and upper and lower bounds for weighted discrete Jensen-type inequalities in Hilbert spaces using some relational properties and arithmetic operations from the tensor analysis. Furthermore, we use the Riemann–Liouville fractional integral and develop several new identities which are used in operator Milne-type inequalities to develop several new bounds using different types of generalized mappings, including differentiable, quasi-convex, and convex mappings. Furthermore, some examples and consequences for logarithm and exponential functions are also provided. Furthermore, we provide an interesting example of a physics dynamical model for harmonic mean. Lastly, we develop Hermite–Hadamard inequality in variable exponent function spaces, specifically in mixed norm function space (lq(·)(Lp(·))). Moreover, it was developed using classical Lebesgue space (Lp) space, in which the exponent is constant. This inequality not only refines Jensen and triangular inequality in the norm sense, but we also impose specific conditions on exponent functions to show whether this inequality holds true or not.

New procedure for evaluation of U(3) coupling and recoupling coefficients

A simple method to calculate Wigner coupling coefficients and Racah recoupling coefficients for U(3) in two group–subgroup chains is presented. While the canonical U(3)⊃U(2)⊃U(1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\rm U(3)\\supset U(2)\\supset U(1)$$\\end{document} coupling and recoupling coefficients are applicable to any system that respects U(3) symmetry, the U(3)⊃SO(3)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\rm U(3) \\supset SO(3)$$\\end{document} coupling coefficients are more specific to nuclear structure studies. This new procedure precludes the use of binomial coefficients and alternating sums which were used in the 1973 formulation of Draayer and Akiyama, and in so doing provides a faster and more accurate determination of any and all required results. The resolution of the outer multiplicity is based on the null space concept of the U(3) generators proposed by Alex et al., whereas the inner multiplicity in the angular momentum subgroup chain is obtained from the dimension of the null space of the SO(3) raising operator. It is anticipated that a C++ library will ultimately be available for determining generic coupling and recoupling coefficients associated with both the canonical and the physical group–subgroup chains of U(3).

Joint computation offloading and resource allocation for end-edge collaboration in internet of vehicles via multi-agent reinforcement learning

Vehicular edge computing (VEC), a promising paradigm for the development of emerging intelligent transportation systems, can provide lower service latency for vehicular applications. However, it is still a challenge to fulfill the requirements of such applications with stringent latency requirements in the VEC system with limited resources. In addition, existing methods focus on handling the offloading task in a certain time slot with statically allocated resources, but ignore the heterogeneous tasks’ different resource requirements, resulting in resource wastage. To solve the real-time task offloading and heterogeneous resource allocation problem in VEC system, we propose a decentralized solution based on the attention mechanism and recurrent neural networks (RNN) with a multi-agent distributed deep deterministic policy gradient (AR-MAD4PG). First, to address the partial observability of agents, we construct a shared agent graph and propose a periodic communication mechanism that enables edge nodes to aggregate information from other edge nodes. Second, to help agents better understand the current system state, we design an RNN-based feature extraction network to capture the historical state and resource allocation information of the VEC system. Thirdly, to tackle the challenges of excessive joint observation-action space and ineffective information interference, we adopt the multi-head attention mechanism to compress the dimension of the observation-action space of agents. Finally, we build a simulation model based on the actual vehicle trajectories, and the experimental results show that our proposed method outperforms the existing approaches.

The eLTER research infrastructure: Current design and coverage of environmental and socio-ecological gradients

Addressing global change requires standardised observations across all ecosystem spheres. To that end, the distributed Integrated European Long-Term Ecosystem, critical zone and socio-ecological Research Infrastructure (eLTER RI) strives for an optimal observational design of its over 200 in-situ facilities. Their spatial distribution should be unbiased to scale local data to its continental target region.Therefore, we assessed biases in the emerging eLTER RI in-situ facility network. We (i) conducted a survey describing the emerging eLTER RI, (ii) detected critical gaps in its coverage of Reference Parameters by identifying biases in a six-dimensional thematic space and determined regions, where these biases cluster spatially, and (iii) derived recommendations to further develop the eLTER RI network.Three distinct gaps were identified: the Iberian, Eastern and Nordic Gap. They resulted mainly from underrepresentation of agricultural lands, mesic and dry regions with low economic density and the Mediterranean, Continental and Boreal biogeoregions. The patterns of underrepresentation are driven by various factors including the thematic context of site establishment over the past decades, operations logistics and funding constraints. We consider closing these gaps of highest priority for spatial network development.Mitigating the biases in the eLTER RI network is crucial to enable confident scaling of local data to the European scale. This will allow the eLTER RI to provide a comprehensive foundation for scientists, policy and decision makers to face global change. Next, a comprehensive dataset of possible additional research sites over Europe must be analysed to derive site- and country-specific recommendations for cost-efficient gap mitigation.

Chaotic LLM billiards

We study null geodesics of the ten-dimensional LLM geometries. In particular, we show that there are a subset of these null geodesics that are confined to the LLM plane. The effective dynamics of these in-plane geodesics is that of a Hamiltonian system with two degrees of freedom (a phase space of dimension 4). We show that these are chaotic. In the two-coloring of the LLM plane, if they start in the empty region, they cannot penetrate the filled region and viceversa. The dynamical problem is therefore very similar to that of a billiards problem with fixed obstacles. We study to what extent LLM geometries with many droplets may be treated as an incipient black hole and draw analogies with the fuzzball proposal. We argue that for in-plane null geodesics deep in the interior of a region with a lot of droplets, in order to exit towards the AdS boundary they will need to undergo a process that resembles diffusion. This mechanism can account for signals getting lost in the putative black hole for a very long time.

Statistical mechanics of stochastic quantum control: d-adic Rényi circuits.

The dynamics of quantum information in many-body systems with large onsite Hilbert space dimension admits an enlightening description in terms of effective statistical mechanics models. Motivated by this fact, we reveal a connection between three separate models: the classically chaotic d-adic Rényi map with stochastic control, a quantum analog of this map for qudits, and a Potts model on a random graph. The classical model and its quantum analog share a transition between chaotic and controlled phases, driven by a randomly applied control map that attempts to order the system. In the quantum model, the control map necessitates measurements that concurrently drive a phase transition in the entanglement content of the late-time steady state. To explore the interplay of the control and entanglement transitions, we derive an effective Potts model from the quantum model and use it to probe information-theoretic quantities that witness both transitions. The entanglement transition is found to be in the bond-percolation universality class, consistent with other measurement-induced phase transitions, while the control transition is governed by a classical random walk. These two phase transitions can be made to coincide by varying a parameter in the model, producing a picture consistent with behavior observed in previous small-size numerical studies of the quantum model.

A conditional latent autoregressive recurrent model for generation and forecasting of beam dynamics in particle accelerators

Particle accelerators are complex systems that focus, guide, and accelerate intense charged particle beams to high energy. Beam diagnostics present a challenging problem due to limited non-destructive measurements, computationally demanding simulations, and inherent uncertainties in the system. We propose a two-step unsupervised deep learning framework named as Conditional Latent Autoregressive Recurrent Model (CLARM) for learning the spatiotemporal dynamics of charged particles in accelerators. CLARM consists of a Conditional Variational Autoencoder transforming six-dimensional phase space into a lower-dimensional latent distribution and a Long Short-Term Memory network capturing temporal dynamics in an autoregressive manner. The CLARM can generate projections at various accelerator modules by sampling and decoding the latent space representation. The model also forecasts future states (downstream locations) of charged particles from past states (upstream locations). The results demonstrate that the generative and forecasting ability of the proposed approach is promising when tested against a variety of evaluation metrics.

Early warning signals for bifurcations embedded in high dimensions

Recent work has highlighted the utility of methods for early warning signal detection in dynamic systems approaching critical tipping thresholds. Often these tipping points resemble local bifurcations, whose low dimensional dynamics can play out on a manifold embedded in a much higher dimensional state space. In many cases of practical relevance, the form of this embedding is poorly understood or entirely unknown. This paper explores how measurement of the critical phenomena that generically precede such bifurcations can be used to make inferences about some properties of their embeddings, and, conversely, how prior knowledge about the mechanism of bifurcation can robustify predictions of an oncoming tipping event. These modes of analysis are first demonstrated on a simple fluid flow system undergoing a Hopf bifurcation. The same approach is then applied to data associated with the West African monsoon shift, with results corroborated by existing models of the same system. This example highlights the effectiveness of the methodology even when applied to complex climate data, and demonstrates how a well-resolved spatial structure associated with the onset of atmospheric instability can be inferred purely from time series measurements.

Radially symmetric solutions of the ultra-relativistic Euler equations in several space dimensions

The ultra-relativistic Euler equations for an ideal gas are described in terms of the pressure, the spatial part of the dimensionless four-velocity and the particle density. Radially symmetric solutions of these equations are studied in two and three space dimensions. Of particular interest in the solutions are the formation of shock waves and a pressure blow up. For the investigation of these phenomena we develop a one-dimensional scheme using radial symmetry and integral conservation laws. We compare the numerical results with solutions of multi-dimensional high-order numerical schemes for general initial data in two space dimensions. The presented test cases and results may serve as interesting benchmark tests for multi-dimensional solvers.

Global stability of the Dirac–Klein–Gordon system in two and three space dimensions

Global stability of the Dirac–Klein–Gordon system in two and three space dimensions

Navigating Social Services from the Perspective of Finnish Older Adults with Complex Needs: An Examination of Different Dimensions of Access

This study aims to increase understanding of accessing social services for older adults with complex needs. Individual interviews (18) with older clients of gerontological social work and diaconal social work in Finland were analyzed using abductive content analysis. The conceptual framework of access to services, consisting of five interrelated dimensions by Penchansky and Thomas (1981) and the sixth dimension, awareness, by Saurman (2016), was used as a basis for analysis and reporting of results. The findings showed that accessing services was affected by all six dimensions and factors related to both the service system and the clients. The main results showed that available services did not always meet the needs of older adults (Availability), or they did not have enough information about the services (Awareness). Attitudes toward both the service system and older adults affected their experiences (Acceptability), as well as the perceived approachability of the services (Accommodation). In addition, mobility of services and physical abilities of clients (Accessibility), together with the perceived worth of services in relation to their cost (Affordability), influenced older adults’ access to services. Overall, this study emphasizes the significance of considering different aspects of access in service design and policies for services for older adults.

Optimization and realignment of OAM mode excitation in ring-core optical fibers using machine learning.

Light beams carrying orbital angular momentum (OAM) in free space or within optical fibers have a wide range of applications in optics; however, exciting these modes with both high purity and low loss generally requires demanding optimization of excitation conditions in a high dimensional space. Furthermore, mechanical drift can significantly degrade the mode purity over time, which may limit practical deployment of OAM modes in concrete applications. Here, combining an iterative wavefront matching approach and a genetic algorithm, we demonstrate rapid and automated excitation of OAM modes with optimized purity and reduced loss. Our approach allows for systematic computational realignment of the system enabling drift compensation over extended durations. Our experimental results indicate that OAM purity can be optimized and maintained over periods exceeding 24 h, paving the way for the applications of stable OAM beams in optics.

Asymptotic stability of the nonlocal diffusion equation with nonlocal delay

This work focuses on the asymptotic stability of nonlocal diffusion equations in ‐dimensional space with nonlocal time‐delayed response term. To begin with, we prove and ‐decay estimates for the fundamental solution of the linear time‐delayed equation by Fourier transform. For the considered nonlocal diffusion equation, we show that if , then the solution converges globally to the trivial equilibrium time‐exponentially. If , then the solution converges globally to the trivial equilibrium time‐algebraically. Furthermore, it can be proved that when , the solution converges globally to the positive equilibrium time‐exponentially, and when , the solution converges globally to the positive equilibrium time‐algebraically. Here, , and are the coefficients of each term contained in the linear part of the nonlinear term . All convergence rates above are and ‐decay estimates. The comparison principle and low‐frequency and high‐frequency analyses are significantly effective in proofs. Finally, our theoretical results are supported by numerical simulations in different situations.

The future of work of academics in the age of Artificial Intelligence: State-of-the-art and a research roadmap

The Future of Work (FoW) has garnered significant attention among scholars and practitioners, with the advent of Artificial Intelligence (AI) playing an important role in shaping this discourse. Despite the common perception that intelligent machines pose a threat to workers in routine roles, AI technologies are increasingly being utilized for advanced tasks carried out by knowledge workers. Drawing on state-of-the-art research and real-life examples we develop an integrated framework to explore the future of academic work. Our focus is on academics, an essential yet under-researched group of knowledge workers, and we discuss their work in relation to AI across space, time, and task dimensions. Our analysis reveals that the usage of AI technologies can have implications for the research, teaching, and service activities of academics and thereby also for the creation, acquisition, dissemination, and application of knowledge. Based on our framework we develop scenarios and propose a future research roadmap.

Humans use local spectrotemporal correlations to detect rising and falling pitch.

To discern speech or appreciate music, the human auditory system detects how pitch increases or decreases over time. However, the algorithms used to detect changes in pitch, or pitch motion, are incompletely understood. Here, using psychophysics, computational modeling, functional neuroimaging, and analysis of recorded speech, we ask if humans detect pitch motion using computations analogous to those used by the visual system. We adapted stimuli from studies of vision to create novel auditory correlated noise stimuli that elicited robust pitch motion percepts. Crucially, these stimuli possess no persistent features across frequency or time, but do possess positive or negative local spectrotemporal correlations in intensity. In psychophysical experiments, we found clear evidence that humans judge pitch direction based on both positive and negative spectrotemporal correlations. The observed sensitivity to negative correlations is a direct analogue of illusory "reverse-phi" motion in vision, and thus constitutes a new auditory illusion. Our behavioral results and computational modeling led us to hypothesize that human auditory processing employs pitch direction opponency. fMRI measurements in auditory cortex supported this hypothesis. To link our psychophysical findings to real-world pitch perception, we analyzed recordings of English and Mandarin speech and discovered that pitch direction was robustly signaled by the same positive and negative spectrotemporal correlations used in our psychophysical tests, suggesting that sensitivity to both positive and negative correlations confers ecological benefits. Overall, this work reveals that motion detection algorithms sensitive to local correlations are deployed by the central nervous system across disparate modalities (vision and audition) and dimensions (space and frequency).

Sensitivity analysis and robust optimization to high-dimensional uncertainties of compressors with active subspace method

The performance of compressors often deviates significantly from the design value due to the substantial geometric deviations arising from manufacturing errors and in-service degradation. Robust design optimization (RDO) plays a crucial role in ensuring the high performance and reliability of compressors. The study proposes an active subspace-based dimensionality-reduction RDO method for high-dimensional uncertainties of compressors. By employing the active subspace (AS) method, a dimensionality-reduction artificial neural network (ANN) is raised to solve the "dimension disaster" problem for high-dimensional uncertainty quantification (UQ) analysis. Additionally, to decrease the computation cost of the original AS method, a data-driven method is utilized to calculate the gradient of the quantity of interest (QoI) within the AS dimensionality-reduction framework. Furthermore, Shapley method is applied to study the sensitivity of geometric variables and their variation direction on the mean and variance of the performance, and the robustness improvement method by only modifying key geometric variables based on Shapley results is discussed. The RDO of high dimensional geometrical uncertainties of a transonic compressor stage is studied by using this method. The results demonstrate a reduction from the original 24-dimensional uncertainties to a 4-dimensional space, achieved through this method. Consequently, the required sample size is reduced by 75 % while maintaining nearly unchanged model accuracy. Furthermore, the findings reveal that after RDO, the mean efficiency increases by 1.04 %, with a 42 % reduction in variance. Compared to RDO, which requires simultaneous optimization of all 24 geometric variables, the robustness improvement based on Shapley only necessitates modifying 4 key geometric variables, resulting in a substantial increase in both the mean and variance of efficiency.