Constant Scaling Research Articles

Entanglement – nonstabilizerness separation in hybrid quantum circuits

Nonstabilizerness describes the distance of a quantum state to its closest stabilizer state. It is—like entanglement—a necessary resource for a quantum advantage over classical computing. We study nonstabilizerness, quantified by stabilizer entropy, in a hybrid quantum circuit with projective measurements and a controlled injection of non-Clifford resources. We discover a phase transition between a power law and constant scaling of nonstabilizerness with system size controlled by the rate of measurements. The same circuit also exhibits a phase transition in entanglement that appears, however, at a different critical measurement rate. This mechanism shows how, from the viewpoint of a quantum advantage, hybrid circuits can host multiple distinct transitions where not only entanglement, but also other nonlinear properties of the density matrix come into play. Published by the American Physical Society 2024

Constant isometric scaling of soil carbon to nitrogen in Moso bamboo-invaded evergreen broadleaf forests in subtropical China

Constant isometric scaling of soil carbon to nitrogen in Moso bamboo-invaded evergreen broadleaf forests in subtropical China

Long head of biceps tendon augmentation in rotator cuff repair enhances tendon healing, shoulder function and patient-reported outcomes one-year post-surgery.

The aim is to determine the effect on healing and functionality of patients after 1 year of biceps augmentation of a rotator cuff repair (RCR) compared to RCR plus long head of the biceps (LHB) tenotomy. In addition, to analyse the main factors involved in the recovery after the surgery. A prospective, comparative, non-randomized study (Level of Evidence III) was conducted. Patients with repairable rotator cuff tears were allocated to either the control group, with a double row transosseous equivalent RCR with LHB tenotomy, or the RCR+augmentation with LHB group. Patients were evaluated for radiological (MRI), clinical (cuff size, Patte and Goutallier scales) and functional variables (Constant and American Shoulder and Elbow Surgeons [ASES] scales) before the intervention. At 1-year follow-up cuff healing was confirmed through MRI and functional evaluation with Constant, ASES, simple shoulder test [SST] and Disabilities of the Arm, Shoulder and Hand scales. Seventy-seven patients underwent control or RCR+augmentation with LHB, there were no preoperative differences between the groups. After 1 year of the surgery, re-rupture occurred in 38.5% and 16% of the patients in control and RCR+augmentation with LHB groups, respectively (p = .026). Total functionality was higher (p < .05) in RCR+augmentation with LHB than in the control group: Constant, SST and ASES scales. Among the explored factors involved in healing, re-rupture occurred in 100% of the cases with high fatty degeneration. Besides, higher initial functionality (Constant scale) and RCR+augmentation with LHB increased the odds of healing (odds ratio [OR] = 1.12 [1.04-1.21]; OR = 5 [1, 61], respectively), while higher cuff length had a detrimental effect (OR = 0.92 [0.85-0.99]). RCR+augmentation with LHB achieves a higher healing percentage and a better functional evolution than RCR+LHB tenotomy, 1 year after cuff repair. Fatty degeneration, cuff length and initial functionality are the main factors involved in cuff healing. Level III randomized controlled trial.

Thermal preconditioning of membrane stress to control the shapes of ultrathin crystals.

We employ the phospholipid bilayer membranes of giant unilamellar vesicles as a free-standing environment for the growth of membrane-integrated ultrathin phospholipid crystals possessing a variety of shapes with 6-fold symmetry. Crystal growth within vesicle membranes, where more elaborate shapes grow on larger vesicles is dominated by the bending energy of the membrane itself, creating a means to manipulate crystal morphology. Here we demonstrate how cooling rate preconditions the membrane tension before nucleation, in turn regulating nucleation and growth, and directing the morphology of crystals by the time they are large enough to be visualized. The crystals retain their shapes during further growth through the two phase region. Experiments demonstrate this behavior for single crystals growing within the membrane of each vesicle, ultimately comprising up to 13% of the vesicle area and length scales of up to 50 microns. A model for stress evolution, employing only physical property data, reveals how the competition between thermal membrane contraction and water diffusion from tensed vesicles produces a size- and time-dependence of the membrane tension as a result of cooling history. The tension, critical in the contribution of bending energy in the fluid membrane regions, in turn selects for crystal shape for vesicles of a given size. The model reveals unanticipated behaviors including a low steady state tension on small vesicles that allows compact domains to develop, rapid tension development on large vesicles producing flower-shaped domains, and a stress relaxation through water diffusion across the membrane with a time constant scaling as the square of the vesicle radius, consistent with measurable tensions only in the largest vesicles.

A Model-Driven Framework for Composition-Based Quantum Circuit Design

Quantum programming languages support the design of quantum applications. However, to create such programs, one needs to understand the fundamental characteristics of quantum computing and quantum information theory. Furthermore, quantum algorithms frequently make use of abstract operations with a hidden low-level realization (e.g., Quantum Fourier Transform). Thus, turning from elementary quantum operations to a higher-level view of quantum circuit design not only reduces the development effort but also lowers the entry barriers for non-quantum computing experts. To this end, this paper proposes a modeling language and design framework for quantum circuits. This allows the definition of composite operators to advocate a higher-level quantum algorithm design, together with automated code generation for the circuit execution. To demonstrate the benefits of the proposed approach, coined Composition-Based Quantum Circuit Designer , we applied it for realizing the Quantum Counting algorithm and the Quantum Approximate Optimization Algorithm. Our evaluation results show that, compared to an existing state-of-the-art editor, the proposed approach allows for the realization of both quantum algorithms on a high level with a substantially reduced development effort. In particular, the proposed approach shows constant scaling when increasing the size of the investigated quantum circuits and a lower change criticality when evolving existing quantum circuits.

Cosmographic analysis of holographic nonzero torsion framework

In this paper, we use the cosmographic approach to discuss Friedmann space-time in the presence of torsion. For this, we explore equations of motion that explain creation in an isotropic and homogeneous cosmic backdrop with nonzero torsion. Here, we consider the energy density of holographic dark energy model [Formula: see text] where [Formula: see text] is a dimensionless parameter depending on redshift parameter [Formula: see text] is the reduced Planck mass and [Formula: see text] represents the holographic length scale. We examine this dark energy model with both constant and variable holographic length scales in terms of Hubble parameter to determine the best-fit scale. The interaction between dark sector components is taken to evaluate cosmographic parameters, like Hubble, equation of state, deceleration, jerk, snap, lerk and statefinder parameters. We consider four [Formula: see text] parametrizations, which are Chevallier–Polarski–Linder, Jassal–Bagla–Padmanabhan, Wetterich and Ma–Zhang for both cases. We obtain consistent results for specific choices of constant parameters in the underlying scenario.

Vibration Study of Functionally Graded Microcantilever Beams in Fluids Based on Modified Couple Stress Theory by Considering the Physical Neutral Plane

Theoretical studies on the vibration of microcantilever beams in fluids, which are commonly used in micro- and nanoelectromechanical systems (MEMS/NEMS). When microcantilever beams are subjected to photo-thermal excitation, they show that the material properties such as the dynamic response and the one-dimensional temperature field will show significant differences from the macroscopic properties when the size appearance of the microbeam decreases to the scale below a dozen micrometers. In this paper, by correcting the scale constants of the beams, the photothermal vibration model of the microbeam is established using the physical neutral plane theory. The one-dimensional heat transfer equations and scale-corrected temperature field of the microcantilever beam under laser excitation are derived, which are solved by Galerkin’s method, based on the theory of thermoelasticity, the hydrodynamic model of the beams vibrating in incompressible liquids proposed by Sader et al. and the theory of Euler–Bernoulli beams. The equations governing the vibration of micro-cantilever beams corrected for scale effects in different fluids when subjected to photothermal excitation are obtained. The results show that the temperature field, resonant frequency, and quality factor of the microbeam will have a significant upward drift when the size of the microbeam is close to the scale parameter, and the scale effect has a non-negligible influence on the macroscopic performance parameters; the upward drift is gradually weakening when the thickness to scale ratio gradually increases. Finally, the property of the beam is almost the same as that of the theory when the thickness of the beam is 10 times the scale constant. The correction of the theory by the scale effect is insignificant.

Good Gottesman-Kitaev-Preskill codes from the NTRU cryptosystem

We introduce a new class of random Gottesman-Kitaev-Preskill (GKP) codes derived from the cryptanalysis of the so-called NTRU cryptosystem. The derived codes are good in that they exhibit constant rate and average distance scaling &amp;#x0394;&amp;#x221D;n with high probability, where n is the number of bosonic modes, which is a distance scaling equivalent to that of a GKP code obtained by concatenating single mode GKP codes into a qubit-quantum error correcting code with linear distance. The derived class of NTRU-GKP codes has the additional property that decoding for a stochastic displacement noise model is equivalent to decrypting the NTRU cryptosystem, such that every random instance of the code naturally comes with an efficient decoder. This construction highlights how the GKP code bridges aspects of classical error correction, quantum error correction as well as post-quantum cryptography. We underscore this connection by discussing the computational hardness of decoding GKP codes and propose, as a new application, a simple public key quantum communication protocol with security inherited from the NTRU cryptosystem.

Scaling Energy Transfer in Ball Mills: A Scale-Agnostic Approach through a Universal Scaling Constant

Ball mills are widely used for size reduction in mineral processing, but effective scaling from laboratory to industrial scale remains challenging. This study introduces a novel scaling constant approach to replicate energy transfer to ore during milling across different scales by adjusting rotational speed and grinding medium size distribution. The scaling constant encapsulates parameters like the number of balls per working area, rotational speed, and an average ball’s maximum potential and kinetic energies. Experiments were conducted using a laboratory ball mill with interchangeable drum sizes (300, 400, and 500 mm) and a Design of Experiments methodology. Statistical analysis revealed that the scaling constant was more effective at maintaining consistent specific energy and energy per rotation across scales than size reduction, especially in dry milling. Wet milling results showed no significant differences in all metrics across scales. The dominant charge motion shifted from centrifuging to cascading as the mill diameter increased, highlighting the complex scaling dynamics. While the scaling constant shows promise for maintaining energy utilization, additional factors like charge motion and particle breakage mechanisms should be considered. The findings provide insights for improving ball mill design and optimization in mineral processing.

Superior capsular reconstruction with the long head of the biceps tendon achieves excellent clinical results and low rotator cuff rerupture rates one year after cuff repair surgery.

To analyze the clinical one-year evolution of healed and rerupture lesions in patients who received a rotator cuff repair plus Superior Capsular Reconstruction (SCR) with the long head of the biceps (LHB). Moreover, to compare this evolution between men and women. A pilot study was conducted on patients who underwent a rotator cuff repair plus SCR with LHB between February 2021 and June 2022. All patients completed pre-operative and one-year post-operative evaluations for tendon type of tear and tendon integrity using Magnetic Resonance Imaging (MRI)after one year of the surgery. Besides, functionality was evaluated with the American Shoulder and Elbow Surgeons (ASES) score; the visual analog scale for pain (VAS); and the Constant score. A total of 38 patients completed the one-year final evaluation, they presented an increased functionality score to 83 and 86 in Constant and ASES scales (p < .001), respectively. Besides, 84% of the patients presented a healed cuff, while rerupture occurred in 16% of the patients. There were differences between the healed and rerupture patients in the total Constant score, with a remarkable increase in the strength subscale, almost double for patients with healed cuff (p < .001); in the same way, daily life activity score, and balance subscale increased, while pain score decreased in the healed cuff group (p < .05). There was no difference in functionality between men and women (p > .05). Besides, almost all patients achieved the MCID in both ASES and Constant total scores, irrespectively of the healing group. The cuff repair using SCR with the LHB achieved a low percentage of rerupture and a functional improvement after one year of follow-up. Patients who healed the lesion presented more strength and better performance in daily life activities than those with cuff repurture. Thus, SCR + LHB procedure can be considered an efficient technique for rotator cuff repair surgery for both men and women. Although a comparison with a control group is needed to confirm these findings.

Maximizing discrimination capability of knowledge distillation with energy function

To apply the latest computer vision techniques that require a large computational cost in real industrial applications, knowledge distillation methods (KDs) are essential. Existing logit-based KDs apply the constant temperature scaling to all samples in dataset, limiting the utilization of knowledge inherent in each sample individually. In our approach, we classify the dataset into two categories (i.e., low energy and high energy samples) based on their energy score. Through experiments, we have confirmed that low energy samples exhibit high confidence scores, indicating certain predictions, while high energy samples yield low confidence scores, meaning uncertain predictions. To distill optimal knowledge by adjusting non-target class predictions, we apply a higher temperature to low energy samples to create smoother distributions and a lower temperature to high energy samples to achieve sharper distributions. When compared to previous logit-based and feature-based methods, our energy-based KD (Energy KD) achieves better performance on various datasets. Especially, Energy KD shows significant improvements on CIFAR-100-LT and ImageNet datasets, which contain many challenging samples. Furthermore, we propose high energy-based data augmentation (HE-DA) for further improving the performance. We demonstrate that higher performance improvement could be achieved by augmenting only a portion of the dataset rather than the entire dataset, suggesting that it can be employed on resource-limited devices. To the best of our knowledge, this paper represents the first attempt to make use of energy function in knowledge distillation and data augmentation, and we believe it will greatly contribute to future research.

A Case-Study on the Photophysics of Chalcogen-Substituted Zinc(II) Phthalocyanines.

Singlet dioxygen has been widely applied in different disciplines such as medicine (photodynamic therapy or blood sterilization), remediation (wastewater treatment) or industrial processes (fine chemicals synthesis). Particularly, it can be conveniently generated by energy transfer between a photosensitizer's triplet state and triplet dioxygen upon irradiation with visible light. Among the best photosensitizers, substituted zinc(II) phthalocyanines are prominent due to their excellent photophysical properties, which can be tuned by structural modifications, such as halogen- and chalcogen-atom substitution. These patterns allow for the enhancement of spin-orbit coupling, commonly attributed to the heavy atom effect, which correlates with the atomic number ( ) and the spin-orbit coupling constant ( ) of the introduced heteroatom. Herein, a fully systematic analysis of the effect exerted by chalcogen atoms on the photophysical characteristics (absorption and fluorescence properties, lifetimes and singlet dioxygen photogeneration), involving 30 custom-made β-tetrasubstituted chalcogen-bearing zinc(II) phthalocyanines is described and evaluated regarding the heavy atom effect. Besides, the intersystem crossing rate constants are estimated by several independent methods and a quantitative profile of the heavy atom is provided by using linear correlations between relative intersystem crossing rates and relative atomic numbers. Good linear trends for both intersystem crossing rates (S1-T1 and T1-S0) were obtained, with a dependency on the atomic number and the spin-orbit coupling constant scaling as and , respectively The trend shows to be independent of the solvent and temperature.

Efficient Algorithms for Non-gaussian Single Index Models with Generative Priors

In this work, we focus on high-dimensional single index models with non-Gaussian sensing vectors and generative priors. More specifically, our goal is to estimate the underlying signal from i.i.d. realizations of the semi-parameterized single index model, where the underlying signal is contained in (up to a constant scaling) the range of a Lipschitz continuous generative model with bounded low-dimensional inputs, the sensing vector follows a non-Gaussian distribution, the noise is a random variable that is independent of the sensing vector, and the unknown non-linear link function is differentiable. Using the first- and second-order Stein's identity, we introduce efficient algorithms to obtain estimated vectors that achieve the near-optimal statistical rate. Experimental results on image datasets are provided to support our theory.

Impact of Coracohumeral Ligament Release on Treatment Outcomes in Patients with Idiopathic Adhesive Capsulitis

Background. The coracohumeral ligament restricts external rotation of the shoulder joint and, along with the upper, middle, and lower glenohumeral ligaments, participates in stabilizing the shoulder joint. There is ongoing debate regarding the division of this anatomical structure in patients with limited external rotation. Objective: to compare the treatment outcomes of patients with idiopathic adhesive capsulitis who underwent coracohumeral ligament release along with selective capsulotomy to those who underwent only partial coracohumeral ligament release. Material and Methods. We treated 85 patients with idiopathic adhesive capsulitis, who were divided into two groups: group 1 underwent selective anterior capsulotomy of the shoulder joint with the division of the middle and lower glenohumeral ligaments, biceps long head tenotomy, subacromial decompression, and partial coracohumeral ligament release; group 2 underwent a similar surgical procedure with complete coracohumeral ligament excision. The average age of the patients was 47.9±19.1 years. The function of the shoulder joint was assessed using the Constant Shoulder Score and VAS scales before surgery and at 3 and 6 months postoperatively. Results. At 3 months postoperatively, group 2 showed a slightly better functional outcome according to the Constant Shoulder Score (12.2±6.9 points) compared to group 1 (18.1±6.4 points, p=0.038). At 6 months postoperatively, group 1 had a mean Constant Shoulder Score of 15.1±7 points, while group 2 had a score of 10.1±6.3 points (p=0.02). Conclusions. Excision of the coracohumeral ligament in patients with idiopathic adhesive capsulitis allows for better functional outcomes according to the Constant Shoulder Score and VAS at both 3 and 6 months postoperatively.

Analysis of Successive Doubly Nested Mixed-Mode Oscillations

In previous works [Inaba &amp; Kousaka, 2020; Inaba &amp; Tsubone, 2020; Inaba et al., 2023], significant bifurcation structures referred to as nested Mixed-Mode Oscillations (MMOs) were found to be present in forced Bonhoeffer–van der Pol (BVP) oscillators. It is well known that unnested Mixed-Mode Oscillation-Incrementing Bifurcations (MMOIBs) can generate [Formula: see text] oscillations (i.e. [Formula: see text] followed by [Formula: see text] repeated [Formula: see text] times) for successive values of [Formula: see text], where [Formula: see text] and [Formula: see text] are adjacent fundamental simple MMOs, e.g. [Formula: see text] and [Formula: see text], where [Formula: see text] is an integer. Furthermore, it has been confirmed that MMOIBs can generate nested MMOs. Let two adjacent unnested MMOIB-generated MMOs be denoted [Formula: see text] and [Formula: see text]. Then, singly nested MMOIBs can generate [Formula: see text] for successive values of [Formula: see text], i.e. [Formula: see text] followed by [Formula: see text] repeated [Formula: see text] times, between the [Formula: see text]- and [Formula: see text]-generating regions. The sequential generation of singly nested MMOs has been investigated in detail in previous work [Ito et al., 2021]. Nested MMOs can, however, be at least doubly nested. In this study, we investigate doubly nested MMOs considering a constrained nonautonomous BVP oscillator containing an idealized diode. Based on the observed dynamics of this system, Poincaré return maps are rigorously constructed in one dimension. Therefore, we can solve the successive saddle-node bifurcations using a nested (i.e. double-loop) bisection method. We track 60 successive doubly nested MMOIBs and we do not rule out the possibility that the 58 scaling constants corresponding to the MMOIB intervals converge to unity. We note that because we solve the bifurcation equation avoiding the use of a method that requires the careful selection of the initial conditions (e.g. the Newton–Raphson), we can accurately track the saddle-node bifurcations without missing any doubly nested MMO sequences.

The GHP scaling limit of uniform spanning trees of dense graphs

AbstractWe consider dense graph sequences that converge to a connected graphon and prove that the GHP scaling limit of their uniform spanning trees (USTs) is Aldous' Brownian CRT. Furthermore, we are able to extract the precise scaling constant from the limiting graphon. As an example, we can apply this to the scaling limit of the USTs of the Erdös–Rényi sequence for any fixed , and sequences of dense expanders. A consequence of GHP convergence is that several associated quantities of the spanning trees also converge, such as the height, diameter and law of a simple random walk.

Stable laws for random dynamical systems

Abstract In this paper, we consider random dynamical systems formed by concatenating maps acting on the unit interval $[0,1]$ in an independent and identically distributed (i.i.d.) fashion. Considered as a stationary Markov process, the random dynamical system possesses a unique stationary measure $\nu $ . We consider a class of non-square-integrable observables $\phi $ , mostly of form $\phi (x)=d(x,x_0)^{-{1}/{\alpha }}$ , where $x_0$ is a non-recurrent point (in particular a non-periodic point) satisfying some other genericity conditions and, more generally, regularly varying observables with index $\alpha \in (0,2)$ . The two types of maps we concatenate are a class of piecewise $C^2$ expanding maps and a class of intermittent maps possessing an indifferent fixed point at the origin. Under conditions on the dynamics and $\alpha $ , we establish Poisson limit laws, convergence of scaled Birkhoff sums to a stable limit law, and functional stable limit laws in both the annealed and quenched case. The scaling constants for the limit laws for almost every quenched realization are the same as those of the annealed case and determined by $\nu $ . This is in contrast to the scalings in quenched central limit theorems where the centering constants depend in a critical way upon the realization and are not the same for almost every realization.

Modeling ants’ walks in patrolling multiple resources using stochastic approximation partial momentum refreshment

In the realm of ant foraging studies, researchers commonly map the movement of ant colonies to Markov Chain Monte Carlo (MCMC) models based on the probability matching strategy, aiming to achieve optimal foraging outcomes. When faced with multiple resources, ants often exhibit remarkable flexibility by patrolling over the foraging area and maximizing resource utilization. However, the regular MCMC models face challenges when resources are multimodally distributed as they struggle to efficiently explore the state space, particularly when modes are distantly separated. Building upon the existing partial momentum refreshment model, we propose a stochastic approximation partial momentum refreshment (SAPMR) model that not only performs equally well as regular MCMC models in bimodal distributions featuring two closely located modes but also overcomes energy barriers associated with multimodal distributions characterized by distantly separated modes. The synthetic data generated using SAPMR exhibits characteristics reminiscent of ants’ behavior such as Lévy-like patterns and maintaining a constant scaling function (≈1) when examining the relationship between the rescaled event speed and the rescaled time.

USING 3D PRINTING FOR OPEN REDUCTION OF CHRONIC POSTERIOR SHOULDER DISLOCATION (CASE FROM PRACTICE)

Objective. An example of the treatment of a patient with chronic posterior dislocation of the shoulder, previously operated on by the Latarge technique due to recurrence of anterior instability, is given. Methods. The patient presented with an old fixed posterior dislocation of the left shoulder joint, large bone defect of the front part of the head (reverse Hill-Sachs). The patient has already undergone 2 operations on the left shoulder due to chronic anterior dislocation of the humeral head: 2018 — arthroscopy and capsuloplasty according to Bankart; 2020 — arthrotomy with Latarje transposition (due to recurrence of anterior instability). The peculiarity of this case is a bone block with screws located on the front surface of the glenoid made a massive defect front part of the humeral head. Planning performed on the basis of a CT scan of the shoulder joint in the FreeformPlus program. Assessment of functioning performed on the QuickDASH and Constant scales. The results. To improve the performance of intraoperative osteoplasty of the defect, a plastic model of the humeral head was printed for simulating bone graft and osteosynthesis. According to the QuickDASH scale before the operation, the patient had 45 points, that is, a significant decrease in the function of the upper limb — constant discomfort, pain. After surgery for 2 days — 35 points, 6 weeks — 12, and 3 months. — 12 points, that is, the patientʼs quality of life has improved significantly. According to the Constant scale before the operation, there were 16 points, of which: pain — 6, household activity — 2, range of motion — 8. After surgery on the 2nd day, a total of 33 points: pain — 10, household activity — 7, range of motion (passive) — 16, after 6 weeks — 80 points, this result remained after 3 months. Conclusion. The use of three-dimensional planning and an individual tool greatly facilitated the main stages ofsurgical intervention in the case of chronic posterior dislocation of the humeral head and made it possible to quickly and conveniently prepare a bone graft and install it in the defect. The printed navigation made it possible to perform a stabilizing osteosynthesis, ensure high patient satisfaction and a good functional result.

Fostering Responsible Online Behavior through Digital Ethics in Bangladesh: An Exploration of Vulnerability, Facts, and Catalysts

This paper aims to explore the current Behavioral trends of Bangladeshi online users, vulnerability of different online security dimensions in Bangladesh, identify the impacts of different catalysts and roles of different institutes and stakeholder pursuing responsible online behavior. In this study, opinions of 10 general internet users and 5 E-entrepreneurs have been collected by using semi-structured questionnaire. Rank order scaling and constant sum scaling have been used to compare the data and form comparative analysis. It has been exhibited in this study that, authenticity, nonrepudiation and privacy are the most vulnerable dimensions of cyber security in Bangladesh. Digital ethics can pursue more responsible online behavior with the integration of legal influence and technological measures. Inclusion and collaboration of all the stakeholders like users, academics, E-entrepreneurs, government etc. might bring better digital environment in ethical concern. Family, Educational institutions and social community can play prominent role pursuing more responsible behavior in online by personality formation of tweens &amp; teens, knowledge buildings of young adults and including digital ethics in social norms. This study is an attempt to more quantification of the facts and catalysts through comparison. Despite having a very nominal sample size, this study can serve as a foundation for further rigorous research on the factors and catalysts that encourage more responsible online behavior.