Complex Scaling Research Articles

Unmet rehabilitation needs in the first 6 months post-injury in a trauma centre population with moderate-to-severe traumatic injuries.

To describe the needs for subacute inpatient rehabilitation and community-based healthcare services, rehabilitation, and social support in patients with moderate-to-severe traumatic injury in the first 6 months post-injury. Further, to explore associations between sociodemographic and clinical characteristics and unmet needs. Multicentre prospective cohort study. Of 601 persons (75% males), mean (standard deviation) age 47 (21) years, admitted to trauma centres in 2020 with moderate-to-severe injury, 501 patients responded at the 6-month follow-up and thus were included in the analyses. Sociodemographic and injury-related characteristics were recorded at inclusion. Estimation of needs was assessed with the Rehabilitation Complexity Scale Extended-Trauma and the Needs and Provision Complexity Scale on hospital discharge. Provision of services was recorded 6months post-injury. Multivariable logistic regressions explored associations between baseline variables and unmet inpatient rehabilitation and community-based service needs. In total, 20% exhibited unmet needs for subacute inpatient rehabilitation, compared with 60% for community-based services. Predictors for unmet community-based service needs included residing in less central areas, profound injury severity, severe head injury, and rehabilitation referral before returning home. Inadequate provision of healthcare and rehabilitation services, particularly in the municipalities, resulted in substantial unmet needs in the first 6 months following injury.

Complexity of fermionic states

How much information does a fermionic state contain? To address this fundamental question, we define the complexity of a particle-conserving many-fermion state as the entropy of its Fock space probability distribution, minimized over all Fock representations. The complexity characterizes the minimum computational and physical resources required to represent the state and store the information obtained from it by measurements. Alternatively, the complexity can be regarded as a Fock space entanglement measure describing the intrinsic many-particle entanglement in the state. We establish a universal lower bound for the complexity in terms of the single-particle correlation matrix eigenvalues and formulate a finite-size complexity scaling hypothesis. Remarkably, numerical studies on interacting lattice models suggest a general model-independent complexity hierarchy: ground states are exponentially less complex than average excited states, which, in turn, are exponentially less complex than generic states in the Fock space. Our work has fundamental implications on how much information is encoded in fermionic states. Published by the American Physical Society 2024

Crashworthiness Study of Functional Gradient Lattice-Reinforced Thin-Walled Tubes under Impact Loading.

Creating lightweight and impact-resistant box structures has been an enduring pursuit among researchers. A new energy-absorbing structure consisting of a bionic gradient lattice-enhanced thin-walled tube is presented in this article. The gradient lattice and thin-walled tube were prepared using selective laser melting (SLM) and wire-cutting techniques, respectively. To analyze the effects of gradient pattern, mass ratio, diameter range and impact speed on structural crashworthiness, low-speed impact at 4 m/s and finite element simulation experiments were conducted. The study demonstrates that the design of inward radial gradient lattice-reinforced thin-walled tubes can effectively enhance structure's energy-absorption efficiency and provide a more stable mode of deformation. It also shows a 17.44% specific energy-absorption advantage over the uniformly lattice-reinforced thin-walled tubes, with no significant overall gain in peak crushing force. A complex scale evaluation method was used to determine the optimum structure and the structure type with the best crashworthiness was found to be a gradient lattice-filled tube with a thickness of 0.9 mm and a slope index of 10. The gradient lattice-reinforced thin-walled tube suggested in this investigation offers guidance for designing a more efficient thin-walled energy-absorption structure.

The influence of SEN structure on the flow and solidification phenomena in ultra-large-section beam blank mould

Due to the complex cross-section and scale effects, surface and internal defects are prone to occur in the ultra-large-section beam blank. In this study, a coupled model of steel liquid flow and heat transfer within a 1300 × 510 × 140 mm cross-section beam blank mould was established. The results indicate that single-port SEN reduced the flow activity on the meniscus, and the three-ports SEN led to significant high temperature zones and re-melting of the solidified shell in the flange tip and web. The four-ports nozzle not only optimizes the internal flow behavior of the mould but also enhances the uniformity of temperature and solidification. The maximum circumferential difference in shell thickness under the four-ports SEN was only 8.1 mm, compared to 13.2 mm and 13.8 mm under the single-port and three-ports SEN, respectively.

Algorithm for Coal Mine Rock Foreign Object Detection Based on Enhanced YOLOv8

In addressing the challenge of suboptimal detection precision in coal mine rock foreign object detection due to complex environments and variable object scales, this paper proposes a coal mine rock foreign object detection algorithm based on YOLOv8. Initially, the incorporation of the BiFormer attention mechanism is advocated to refine the backbone network, augmenting the model's attention towards pivotal information regions, consequently enhancing localization and feature extraction capabilities. Secondly, a lightweight Content-Aware Recurrent Affine Feature Extraction (CARAFE) operator is utilized within the neck architecture to effectively capture and preserve intricate features at lower hierarchical levels. Finally, Wise-IoU v3 is adopted as the bounding box regression loss for the proposed algorithm, coupled with a prudent gradient allocation approach, thereby enhancing the model's localization capabilities. Empirical findings illustrate that compared to baseline algorithms, the proposed algorithm has fewer parameters, with an average mAP improvement of 2.5%, and a detection speed increase of 2fps/s.

Cut structures and an observable singularity in the three-body threshold dynamics: The Tcc+ case

The three-body threshold effect, the distinctive and intriguing nonperturbative dynamics in the low-energy hadron-hadron scattering, has acquired compelling significance in the wake of the recent observation of the double-charm tetraquark Tcc+. This dynamics is characterized by the emergence of singular points and branch cuts within the interaction potential, occurring when the on-shell condition of the mediated particle is satisfied. The presence of these potential singularities indicates that the system is no longer Hermitian and also poses intractable challenges in obtaining exact solutions for dynamical scattering amplitudes. In this work, we develop a complex scaled Lippmann-Schwinger equation as an operation of analytical continuation of the T matrix to resolve this problem. Through a practical application to the DD*→DD* process, we reveal complicated cut structures of the three-body threshold dynamics in the complex plane, primarily stemming from the one-pion exchange. Notably, our methodology succeeds in reproducing the Tcc+ structure, in alignment with the quasibound pole derived from the complex scaling method within the Schrödinger equation framework. More remarkably, after solving the on-shell T matrix on the positive real axis of momentum plane, we find an extra new structure in the DD* mass spectrum, which arises from a right-hand cut at a physical pion mass and should be observable in lattice QCD simulations and future high-energy experiments. Published by the American Physical Society 2024

Efficient multimode vectorial nonlinear propagation solver beyond the weak guidance approximation

In this paper, we present an efficient numerical model able to solve the vectorial nonlinear pulse propagation equation in circularly symmetric multimode waveguides. The algorithm takes advantage of the conservation of total angular momentum of light upon propagation and takes into account the vectorial nature of the propagating modes, making it particularly relevant for studies in ring-core fibers. While conventional propagation solvers exhibit a computational complexity scaling as Nmode4, where Nmode is the number of considered modes, the present solver scales as Nmode3/2. As a first example, it is shown that orbital angular momentum modulation instability processes take place in ring-core fibers in realistic conditions. Finally, it is predicted that the modulation instability process is followed by the appearance of breather-like angular structures.

Cell motility in cancer, crucial events, criticality, and Lévy walks

The analysis of glioblastoma (GB) cell locomotion and its modeling inspired by Lévy random walks is presented herein. We study such walks occurring on a two-dimensional plane where the walk is similar to the motion of a bird flying with a constant velocity, but with random changes of direction in time. The intelligence of the bird is signaled by the instantaneous changes of flying direction, which become invisible in the time series obtained by projecting the 2D walk either on the x-axis or y-axis. We establish that the projected 1D time series share the statistical complexity of time series frequently used to monitor physiological processes, shedding light on the role of crucial events (CE-s) in pathophysiology. Such CE-s are signified by abrupt changes of flying direction which are invisible in the 1D physiological time series. We establish a connection between the complex scaling index δ generated by the CE-s through μR=2−δ, where μR is the inverse power law index of the probability density function of the time interval between consecutive failures of the process of interest. We argue that the identification of empirical indices along with their theoretical relations afford important measures to control cancer.

Needs for Community-Based Rehabilitation Services and Support 12 Months After Moderate and Severe Physical Traumatic Injuries: A Brief Report.

Patients with physical traumatic injuries frequently require long-term rehabilitation services. To strengthen rehabilitation services in the postacute phase, we need to assess characteristics of this population and their healthcare and rehabilitation needs in the community. This brief report summarizes the frequency of unmet rehabilitation needs in community-based rehabilitation during the first year after moderate and severe trauma. Additionally, the associations between sociodemographic, injury severity factors and unmet needs were examined. Data from a prospective multicenter cohort study of patients with moderate and severe trauma (New Injury Severity Score > 9) of all ages, discharged alive from two regional trauma centers in 2020 were used. Needs were estimated using the Needs and Provision Complexity Scale. Overall, 46% of patients had unmet needs at 12-mo postinjury, particularly related to the provision of rehabilitation services, specialist follow-ups, and social and family support. The probability of unmet needs was associated with age, preinjury comorbidities, and impaired functioning. Our findings support strategies targeting younger patients, those with preinjury comorbidities, and those with higher levels of disability and provide a starting point for the development of standardized rehabilitation needs assessment and guidelines after injury.

Efficient Bayesian Physics Informed Neural Networks for inverse problems via Ensemble Kalman Inversion

Bayesian Physics Informed Neural Networks (B-PINNs) have gained significant attention for inferring physical parameters and learning the forward solutions for problems based on partial differential equations. However, the overparameterized nature of neural networks poses a computational challenge for high-dimensional posterior inference. Existing inference approaches, such as particle-based or variance inference methods, are either computationally expensive for high-dimensional posterior inference or provide unsatisfactory uncertainty estimates. In this paper, we present a new efficient inference algorithm for B-PINNs that uses Ensemble Kalman Inversion (EKI) for high-dimensional inference tasks. By reframing the setup of B-PINNs as a traditional Bayesian inverse problem, we can take advantage of EKI's key features: (1) gradient-free, (2) computational complexity scales linearly with the dimension of the parameter spaces, and (3) rapid convergence with typically O(100) iterations. We demonstrate the applicability and performance of the proposed method through various types of numerical examples. We find that our proposed method can achieve inference results with informative uncertainty estimates comparable to Hamiltonian Monte Carlo (HMC)-based B-PINNs with a much reduced computational cost. These findings suggest that our proposed approach has great potential for uncertainty quantification in physics-informed machine learning for practical applications.

Concatenated Nanopore DNA Codes.

In nanopore sequencers, single-stranded DNA molecules (or k-mers) enter a small opening in a membrane called a nanopore and modulate the ionic current through the pore, producing a channel output in the form of a noisy piecewise constant signal. An important problem in DNA-based data storage is finding a set of k-mers, i.e. a DNA code, that is robust against noisy sample duplication introduced by nanopore sequencers. Good DNA codes should contain as many k-mers as possible that produce distinguishable current signals (squiggles) as measured by the sequencer. The dissimilarity between squiggles can be estimated using a bound on their pairwise error probability, which is used as a metric for code design. Unfortunately, code construction using the union bound is limited to small k's due to the difficulty of finding maximum cliques in large graphs. In this paper, we construct large codes by concatenating codewords from a base code, thereby packing more information in a single strand while retaining the storage efficiency of the base code. To facilitate decoding, we include a circumfix in the base code to reduce the effect of the nanopore channel memory. We show that the decoding complexity scales as [Formula: see text], where m is the number of concatenated k-mers. Simulations show that the base code error rate is stable as m increases.

Calculation of DC Stark Resonances for the Ammonia Molecule.

A model potential previously developed for the ammonia molecule is treated in a single-center partial-wave approximation in analogy with a self-consistent field method developed by Moccia. The latter was used in a number of collision studies. The model potential is used to calculate DC Stark resonance parameters, i.e., resonance positions and shifts using the exterior complex scaling method for the radial coordinate. Three molecular valence orbitals are investigated for fields along the three Cartesian coordinates, i.e., along the molecular axis and in two perpendicular directions. The work extends previous work on the planar-geometry water molecule for which non-monotonic shifts were observed. We find such non-monotonic shifts for fields along the molecular axis. For perpendicular fields, we report the splitting of the 1e orbitals into a fast- and a slow-ionizing orbital.

Benchmark calculations of fully heavy compact and molecular tetraquark states

We calculate the mass spectrum of the S-wave fully heavy tetraquark systems QQQ¯Q¯(Q=c,b) with both normal (JPC=0++,1+−,2++) and exotic (JPC=0+−,1++,2+−) C-parities using three different quark potential models (AL1, AP1, BGS). The exotic C-parity systems refer to the ones that cannot be composed of two S-wave ground heavy quarkonia. We incorporate the molecular dimeson and compact diquark-antidiquark spatial correlations simultaneously, thereby discerning the actual configurations of the states. We employ the Gaussian expansion method to solve the four-body Schrödinger equation, and the complex scaling method to identify the resonant states. The mass spectra in three different models qualitatively agree with each other. We obtain several resonant states with JPC=0++,1+−,2++,1++ in the mass region (6.92,7.30) GeV, some of which are good candidates of the experimentally observed X(6900) and X(7200). We also obtain several exotic C-parity zero-width states with JPC=0+− and 2+−. These zero-width states have no corresponding S-wave diquarkonium threshold and can only decay strongly to final states with P-wave quarkonia. With the notation T4Q,J(C)(M), we deduce from the root mean square radii that the X(7200) candidates T4c,0(+)(7173),T4c,2(+)(7214) and the state T4c,1(−)(7191) look like molecular states although most of the resonant and zero-width states are compact states. Published by the American Physical Society 2024

Beyond Attention: Breaking the Limits of Transformer Context Length with Recurrent Memory

A major limitation for the broader scope of problems solvable by transformers is the quadratic scaling of computational complexity with input size. In this study, we investigate the recurrent memory augmentation of pre-trained transformer models to extend input context length while linearly scaling compute. Our approach demonstrates the capability to store information in memory for sequences of up to an unprecedented two million tokens while maintaining high retrieval accuracy. Experiments with language modeling tasks show perplexity improvement as the number of processed input segments increases. These results underscore the effectiveness of our method, which has significant potential to enhance long-term dependency handling in natural language understanding and generation tasks, as well as enable large-scale context processing for memory-intensive applications.

Classical shadows based on locally-entangled measurements

We study classical shadows protocols based on randomized measurements in n-qubit entangled bases, generalizing the random Pauli measurement protocol (n=1). We show that entangled measurements (n≥2) enable nontrivial and potentially advantageous trade-offs in the sample complexity of learning Pauli expectation values. This is sharply illustrated by shadows based on two-qubit Bell measurements: the scaling of sample complexity with Pauli weight k improves quadratically (from ∼3k down to ∼3k/2) for many operators, while others become impossible to learn. Tuning the amount of entanglement in the measurement bases defines a family of protocols that interpolate between Pauli and Bell shadows, retaining some of the benefits of both. For large n, we show that randomized measurements in n-qubit GHZ bases further improve the best scaling to ∼(3/2)k, albeit on an increasingly restricted set of operators. Despite their simplicity and lower hardware requirements, these protocols can match or outperform recently-introduced "shallow shadows" in some practically-relevant Pauli estimation tasks.

Research on cooling load estimation through optimal hybrid models based on Naive Bayes

Cooling load estimation is crucial for energy conservation in cooling systems, with applications like advanced air-conditioning control and chiller optimization. Traditional methods include energy simulation and regression analysis, but artificial intelligence outperforms them. Artificial intelligence models autonomously capture complex patterns, adapt, and scale with more data. They excel at predicting cooling loads influenced by various factors, like weather, building materials, and occupancy, leading to dynamic, responsive predictions and energy optimization. Traditional methods simplify real-world complexities, highlighting artificial intelligence’s role in precise cooling load forecasting for energy-efficient building management. This study evaluates Naive Bayes-based models for estimating building cooling load consumption. These models encompass a single model, one optimized with the Mountain Gazelle Optimizer and another optimized with the horse herd optimization algorithm. The training dataset consists of 70% of the data, which incorporates eight input variables related to the geometric and glazing characteristics of the buildings. Following the validation of 15% of the dataset, the performance of the remaining 15% is tested. Based on analysis through evaluation metrics, among the three candidate models, Naive Bayes optimized with the Mountain Gazelle Optimizer (NBMG) demonstrates remarkable accuracy and stability, reducing prediction errors by an average of 18% and 31% compared to the other two models (NB and NBHH) and achieving a maximum R2 value of 0.983 for cooling load prediction.

PolyARBerNN: A Neural Network Guided Solver and Optimizer for Bounded Polynomial Inequalities

Constraints solvers play a significant role in the analysis, synthesis, and formal verification of complex cyber-physical systems. In this article, we study the problem of designing a scalable constraints solver for an important class of constraints named polynomial constraint inequalities (also known as nonlinear real arithmetic theory). In this article, we introduce a solver named PolyARBerNN that uses convex polynomials as abstractions for highly nonlinears polynomials. Such abstractions were previously shown to be powerful to prune the search space and restrict the usage of sound and complete solvers to small search spaces. Compared with the previous efforts on using convex abstractions, PolyARBerNN provides three main contributions namely (i) a neural network guided abstraction refinement procedure that helps selecting the right abstraction out of a set of pre-defined abstractions, (ii) a Bernstein polynomial-based search space pruning mechanism that can be used to compute tight estimates of the polynomial maximum and minimum values which can be used as an additional abstraction of the polynomials, and (iii) an optimizer that transforms polynomial objective functions into polynomial constraints (on the gradient of the objective function) whose solutions are guaranteed to be close to the global optima. These enhancements together allowed the PolyARBerNN solver to solve complex instances and scales more favorably compared to the state-of-the-art nonlinear real arithmetic solvers while maintaining the soundness and completeness of the resulting solver. In particular, our test benches show that PolyARBerNN achieved 100X speedup compared with Z3 8.9, Yices 2.6, and PVS (a solver that uses Bernstein expansion to solve multivariate polynomial constraints) on a variety of standard test benches. Finally, we implemented an optimizer called PolyAROpt that uses PolyARBerNN to solve constrained polynomial optimization problems. Numerical results show that PolyAROpt is able to solve high-dimensional and high order polynomial optimization problems with higher speed compared to the built-in optimizer in the Z3 8.9 solver.

Unraveling power-law scaling through exponential cell division dynamics

A primary objective of biology is the development of universal laws that define how organic form develops and how it evolves as a function of size, both ontogenetically and across evolutionary time. Scaling theory has been essential in reaching this goal by giving a complete perspective point, particularly in illuminating the fundamental biological features produced within scaling exponents defining families of equations. Nonetheless, the theoretical basis of the allometric equation within scaling theory are inadequately explained, particularly when it comes to establishing links between micro-level processes at the cellular level and macro-level phenomena. We proposed an unlimited cell bipartition, resulting in an exponential growth in cell numbers during an individual’s lifespan, to bridge this conceptual gap between cellular processes and allometric scaling. The power-law scaling between body mass and organ weight was produced by the synchronous exponential increments and the allometric exponent is rate of logarithmic cell proliferation rate. Substituting organ weight for erythrocyte weight aided in the development of a power-law scaling relationship between body mass and metabolic rate. Furthermore, it is critical to understand how cell size affects the exponent in power-law scaling. We find that a bigger exponent will result from an increase in the average weight of organ cells or a decrease in the average weight of all cells. Furthermore, cell proliferation dynamics showed a complex exponential scaling between body mass and longevity, defying the previously reported power-law scaling. We discovered a quadratic link between longevity and logarithmic body mass. Notably, all of the parameters included in these relationships are explained by indices linked to cell division and embryonic development. This research adds to our understanding of the complex interaction between cellular processes and overarching scaling phenomena in biology.

Hidden-Charm Pentaquarks with Strangeness in a Chiral Quark Model

The LHCb collaboration has recently announced the discovery of two hidden-charm pentaquark states with strange quark content, Pcs(4338) and Pcs(4459); its analysis points towards having both hadrons’ isospins equal to zero and spin-parity quantum numbers 12− and 32−, respectively. Herein, we perform a systematical investigation of the qqscc¯(q=u,d) system by means of a chiral quark model, along with a highly accurate computational method, the Gaussian expansion approach combined with the complex scaling technique. baryon-meson configurations in both singlet- and hidden-color channels are considered. The Pcs(4338) and Pcs(4459) signals can be well identified as molecular bound states with dominant components ΛJ/ψ(60%) and ΞcD(23%) for the lowest-energy case and ΞcD∗(72%) for the highest-energy one. In addition, it seems that some narrow resonances can also be found in each allowed I(JP) channel in the energy region of 4.6–5.5 GeV, except for the 1(12−) channel where a shallow bound state with dominant Ξc∗D∗ structure is obtained at 4673 MeV with binding energy EB=−3 MeV. These exotic states are expected to be confirmed in future high-energy experiments.

Heterogeneous subpopulations of GABAAR-responding neurons coexist across neuronal network scales and developmental stages in health and disease

Gamma-aminobutyric acid (GABA) is the main inhibitory neurotransmitter in adults. Depolarizing GABA responses have been well characterized at neuronal-population average level during typical neurodevelopment and partially in brain disorders. However, no investigation has specifically assessed whether a mosaicism of cells with either depolarizing or hyperpolarizing/inhibitory GABAergic responses exists in animals in health/disease at diverse developmental stages, including adulthood. Here, we showed that such mosaicism is present in wild-type (WT) and down syndrome (DS) neuronal networks, as assessed at increasing scales of complexity (cultures, brain slices, behaving mice). Nevertheless, WT mice presented a much lower percentage of cells with depolarizing GABA than DS mice. Restoring the mosaicism of hyperpolarizing and depolarizing GABA-responding neurons to WT levels rescued anxiety behavior in DS mice. Moreover, we found heterogeneous GABAergic responses in developed control and trisomic human induced-pluripotent-stem-cells-derived neurons. Thus, a heterogeneous subpopulation of GABA-responding cells exists in physiological/pathological conditions in mouse and human neurons, possibly contributing to disease-associated behaviors.