Single Scaling Research Articles

A Fragmenting Protocol with Explicit Hydration for Calculation of Binding Enthalpies of Target-Ligand Complexes at a Quantum Mechanical Level.

Optimization of the enthalpy component of binding thermodynamics of drug candidates is a successful pathway of rational molecular design. However, the large size and missing hydration structure of target-ligand complexes often hinder such optimizations with quantum mechanical (QM) methods. At the same time, QM calculations are often necessitated for proper handling of electronic effects. To overcome the above problems, and help the QM design of new drugs, a protocol is introduced for atomic level determination of hydration structure and extraction of structures of target-ligand complex interfaces. The protocol is a combination of a previously published program MobyWat, an engine for assigning explicit water positions, and Fragmenter, a new tool for optimal fragmentation of protein targets. The protocol fostered a series of fast calculations of ligand binding enthalpies at the semi-empirical QM level. Ligands of diverse chemistry ranging from small aromatic compounds up to a large peptide helix of a molecular weight of 3000 targeting a leukemia protein were selected for systematic investigations. Comparison of various combinations of implicit and explicit water models demonstrated that the presence of accurately predicted explicit water molecules in the complex interface considerably improved the agreement with experimental results. A single scaling factor was derived for conversion of QM reaction heats into binding enthalpy values. The factor links molecular structure with binding thermodynamics via QM calculations. The new protocol and scaling factor will help automated optimization of binding enthalpy in future molecular design projects.

An SDR implementation of WiFi receiver for mitigating multiple co-channel ZigBee interferers

Machine-to-machine (M2M) communication is one of the vertical sectors that will benefit from 5G communication systems, but today, these systems are still dominated by technologies such as ZigBee and WiFi. An M2M scenario will experience dense deployment of ZigBee and WiFi nodes in order to route the data from one end to the other. In the 2.4 GHz industrial, scientific, and medical (ISM) band, both of the technologies perform co-channel overlapped operation and hence face severe cross technology co-channel interference (CCI). In contrast to cellular systems, which solve the CCI by centralized coordination through the base station, addressing CCI in the ISM band is non-trivial due to heterogeneous wireless technologies and the lack of centralized coordination. In this work, we first present interference mitigating receiver architectures for OFDM-based WiFi using single and multiple antennas. Our single antenna work is based on the localized estimation of excess noise caused by single and multiple co-channel narrowband interferers and scaling the log-likelihood ratios (LLRs) of the affected WiFi subcarriers. The simulation shows our method achieves a significant gain in SNR compared to the conventional method for a given packet error rate (PER) criterion. Next, we discuss maximal ratio combiner with LLR scaling (MLSC), which is a multi-antenna extension to our previous work. The simulation shows MLSC achieves diversity gain apart from the gain in SNR. Further, we propose soft-bit maximal ratio combiner with LLR scaling (SB-MLSC). SB-MLSC is an easy to implement version of MLSC. However, diversity combining in SB-MLSC is performed by combining the LLRs. Nonetheless, simulations show equivalence in performance by SB-MLSC and MLSC. Finally, as a significant part of this work, we implemented all our methods using a software-defined radio (SDR) and performed over-the-air (OTA) testing in the 2.4-GHz ISM band using standard WiFi and ZigBee frames. Results of OTA tests fall in complete agreement with our simulations indicating the practical applicability of our methods. Our methods apply to all the standards and related radio transmission techniques which are based on OFDM and face narrowband co-channel interference. Additionally, since our work focuses only on receiver side modifications, they can be integrated with the existing infrastructure with minimal modifications.

The critical behavior in antiperovskite compound Fe3.4In0.6N

Abstract The critical behavior of the antiperovskite crystal Fe3.4In0.6N has been systematically studied in this paper. We have used a modified Arrott plot, the Kouvel-Fisher method, and critical isotherm analysis to obtain the critical exponents (β, γ and δ) which suggest that a long-range magnetic coupling described by mean-field (MF) theoretical model is dominant in Fe3.4In0.6N. The experimental M−T−H relations below and above Curie temperature (Tc) collapse into two branches by the single scaling equation m = f±(h) (m and h are renormalized magnetization and field), respectively. The critical exponents are confirmed by the Widom scaling law δ = 1 + γβ−1. In addition, it is suggested that the ferromagnetic (FM), anti-ferromagnetic (AFM) interactions and the magnetic disorders result to the exchange distance which is obtained just as J(r)∝ r - 4.4 .

Prediction of volume of distribution in humans: analysis of eight methods and their application in drug discovery

The performance of eight different methods to predict human volume of distribution (VDss) using a large data set (N > 100) was evaluated.The accuracy was assessed by the end points % within two-fold and absolute average fold error (AAFE). The ability to rank order was accessed by the σ and bias was examined using average fold error. Significance of observed differences was established using statistical permutation testing.The Rodgers-Lukova equation, a tissue composition model, for acids and single species scaling based on rat for other ion classes showed the best results in absence of non-rodent data.The semimechanistic Øie-Tozer model based on all thee preclinical species showed the best performance overall (81% within two-fold, AAFE 1.55, σ 0.62). This was not statistically significantly better at the 95% confidence level than the same model based on two preclinical species or single species scaling from monkey. Thus, the use of primates appears difficult to justify when the sole goal is to extrapolate human volume of distribution.

A quantitative confidence signal detection model: 2. Confidence analysis.

Decision making is a fundamental subfield within neuroscience. While recent findings have yielded major advances in our understanding of decision making, confidence in such decisions remains poorly understood. In this paper, we present a confidence signal detection (CSD) model that combines a standard signal detection model yielding a noisy decision variable with a model of confidence. The CSD model requires quantitative measures of confidence obtained by recording confidence probability judgments. Specifically, we model confidence probability judgments for binary direction recognition (e.g., did I move left or right) decisions. We use our CSD model to study both confidence calibration (i.e., how does confidence compare with performance) and the distributions of confidence probability judgments. We evaluate two variants of our CSD model: a conventional model with two free parameters (CSD2) that assumes that confidence is well calibrated and our new model with three free parameters (CSD3) that includes an additional confidence scaling factor. On average, our CSD2 and CSD3 models explain 73 and 82%, respectively, of the variance found in our empirical data set. Furthermore, for our large data sets consisting of 3,600 trials per subject, correlation and residual analyses suggest that the CSD3 model better explains the predominant aspects of the empirical data than the CSD2 model, especially for subjects whose confidence is not well calibrated. Moreover, simulations show that asymmetric confidence distributions can lead traditional confidence calibration analyses to suggest "underconfidence" even when confidence is perfectly calibrated. These findings show that this CSD model can be used to help improve our understanding of confidence and decision making.NEW & NOTEWORTHY We make life-or-death decisions each day; our actions depend on our "confidence." Though confidence, accuracy, and response time are the three pillars of decision making, we know little about confidence. In a previous paper, we presented a new model - dependent on a single scaling parameter - that transforms decision variables to confidence. Here we show that this model explains the empirical human confidence distributions obtained during a vestibular direction recognition task better than standard signal detection models.

Structural Properties of Vicsek-like Deterministic Multifractals

Deterministic nano-fractal structures have recently emerged, displaying huge potential for the fabrication of complex materials with predefined physical properties and functionalities. Exploiting the structural properties of fractals, such as symmetry and self-similarity, could greatly extend the applicability of such materials. Analyses of small-angle scattering (SAS) curves from deterministic fractal models with a single scaling factor have allowed the obtaining of valuable fractal properties but they are insufficient to describe non-uniform structures with rich scaling properties such as fractals with multiple scaling factors. To extract additional information about this class of fractal structures we performed an analysis of multifractal spectra and SAS intensity of a representative fractal model with two scaling factors—termed Vicsek-like fractal. We observed that the box-counting fractal dimension in multifractal spectra coincide with the scattering exponent of SAS curves in mass-fractal regions. Our analyses further revealed transitions from heterogeneous to homogeneous structures accompanied by changes from short to long-range mass-fractal regions. These transitions are explained in terms of the relative values of the scaling factors.

Non-universal scaling transition of momentum cascade in wall turbulence

As a counterpart of energy cascade, turbulent momentum cascade (TMC) in the wall-normal direction is important for understanding wall turbulence. Here, we report an analytic prediction of non-universal Reynolds number ($Re_{\unicode[STIX]{x1D70F}}$) scaling transition of the maximum TMC located at $y_{p}$. We show that in viscous units,$y_{p}^{+}$(and$1+\overline{u^{\prime }v^{\prime }}_{p}^{+}$) displays a scaling transition from$Re_{\unicode[STIX]{x1D70F}}^{3/7}$($Re_{\unicode[STIX]{x1D70F}}^{-6/7}$) to$Re_{\unicode[STIX]{x1D70F}}^{3/5}$($Re_{\unicode[STIX]{x1D70F}}^{-3/5}$) in turbulent boundary layer, in sharp contrast to that from$Re_{\unicode[STIX]{x1D70F}}^{1/3}$($Re_{\unicode[STIX]{x1D70F}}^{-2/3}$) to$Re_{\unicode[STIX]{x1D70F}}^{1/2}$($Re_{\unicode[STIX]{x1D70F}}^{-1/2}$) in a channel/pipe, countering the prevailing view of a single universal near-wall scaling. This scaling transition reflects different near-wall motions in the buffer layer for small$Re_{\unicode[STIX]{x1D70F}}$and log layer for large $Re_{\unicode[STIX]{x1D70F}}$, with the non-universality being ascribed to the presence/absence of mean wall-normal velocity $V$. Our predictions are validated by a large set of data, and a probable flow state with a full coupling between momentum and energy cascades beyond a critical$Re_{\unicode[STIX]{x1D70F}}$is envisaged.

An experiment-oriented analysis of 2D spin-glass dynamics: a twelve time-decades scaling study

Recent high precision experimental results on spin-glass films ask for a detailed understanding of the domain-growth dynamics of two-dimensional spin glasses. To achieve this goal, we numerically simulate the out-equilibrium dynamics of the Ising spin glass for a time that spans close to twelve orders of magnitude (from picoseconds to order of a second), in systems large enough to avoid finite-size effects. We find that the time-growth of the size of the glassy domains is excellently described by a single scaling function. A single time-scale controls the dynamics. diverges upon approaching the T = 0 critical point. The divergence of is Arrhenius-like, with a barrier height that depends very mildly on temperature. The growth of this barrier-height is best described by critical dynamics. As a side product we obtain an impressive confirmation of universality of the equilibrium behavior of two-dimensional spin-glasses.

The influence of vitamin D supplementation on local and systemic inflammatory markers in periodontitis patients: A pilot study.

Vitamin D deficiency/insufficiency is a worldwide public health issue that has been linked to numerous inflammatory disorders, including periodontitis. There is increasing support for a role for adequate vitamin D levels in overall health. Populations with darker skin color have a higher prevalence of vitamin D deficiency/insufficiency and periodontitis. The purpose of this small pilot study was to investigate the influence of 12weeks of 25(OH)D vitamin D supplementation (VDS) on mediators of systemic inflammation in dark-skinned, periodontitis patients. A total of 23 patients with moderate to severe periodontitis were randomly assigned to the vitamin D group or placebo group and received intensive single visit scaling and root planning to elicit a systemic inflammatory response. Vitamin D supplementation increased serum 25(OH)D levels approximately 2-fold over baseline levels; moreover, VDS group had reduced peripheral blood CD3 and CD3+CD8+ cytotoxic T lymphocyte (CTLs) counts and reduced pro-inflammatory salivary cytokines. In contrast, VDS group had higher levels of the autophagy-related proteins and other proteins crucial for anti-microbial autophagy in whole blood PBMCs. In conclusion, VDS has multiple benefits for reducing systemic inflammation and promoting induction of autophagy-related proteins related to anti-microbial functions.

Connecting 1D and 2D Confined Polymer Dynamics to Its Bulk Behavior via Density Scaling.

Under confinement, the properties of polymers can be much different from the bulk. Because of the potential applications in technology and hope to reveal fundamental problems related to the glass-transition, it is important to realize whether the nanoscale and macroscopic behavior of polymer glass-formers are related to each other in any simple way. In this work, we have addressed this issue by studying the segmental dynamics of poly(4-chlorostyrene) (P4ClS) in the bulk and upon geometrical confinement at the nanoscale level, in either one- (thin films on Al substrate) or two- (within alumina nanopores) dimensions. The results demonstrate that the segmental relaxation time, irrespective of the confinement size or its dimensionality, can be scaled onto a single curve when plotted versus ργ/T with the same single scaling exponent, γ = 3.1, obtained via measurements at high pressures in bulk. The implication is that the macro- and nanoscale confined polymer dynamics are intrinsically connected and governed by the same underlying rules.

Assessment of the critical behavior near the FM to PM phase transition in nano-crystalline La0.7Ca0.3Mn1−xNixO3 (x = 0, 0.02, 0.07, 0.10) samples synthesized by auto-combustion

The structural and critical exponent analysis along with the universal behavior of the magnetocaloric effect in nano-crystalline La0.7Ca0.3Mn1−xNixO3 (x = 0.0, 0.02, 0.07, 0.10), manganites, exhibiting second order phase transition, are experimentally studied. Structural study using Rietveld refinement of X-ray diffraction patterns shows orthorhombic structure with Pnma space group. The Curie temperature could be tuned over a wide temperature range upon variation in the Ni2+ content. The nature of the transition was found to be of second order for all Ni2+-concentrations. Various techniques such as modified Arrott plots, Kouvel-Fisher method and critical isotherm were used to analyze the magnetic-field dependence of magnetization. Although the critical exponents beta (β), gamma (γ) and delta (δ) were analyzed with various theoretical models such as 3D-Ising model and 3D-Heisenberg model, the estimated critical exponents, obtained for different values of X, seemed to be consistent with those predicted by the mean-field theory. The critical exponents were further confirmed using the single scaling equation M(H,ε) = εβf ± (H/εγ+β). The achieved results indicated that the obtained values of the critical exponents were reliable and reasonably accurate.

Efficient automatic parallelization of a single GPU program for a multiple GPU system

Single GPU scaling is unable to keep pace with the soaring demand for high throughput computing. As such executing an application on multiple GPUs connected through an off-chip interconnect will become an attractive option to explore. However, much of the current code is written for a single GPU system. Porting such a code for execution on multiple GPUs is difficulty task. In particular, it requires programmer effort to determine how data is partitioned across multiple GPU cards and then launch the appropriate thread blocks that mostly accesses the data that is local to that card. Otherwise, cross-card data movement is an expensive operation. In this work we explore hardware support to efficiently parallelize a single GPU code for execution on multiple GPUs. In particular, our approach focuses on minimizing the number of remote memory accesses across the off-chip network without burdening the programmer to perform data partitioning and workload assignment. We propose a data-location aware thread block scheduler to schedule the thread blocks on the GPU that has most of its input data. The scheduler exploits well known observation that GPU workloads tend to launch a kernel multiple times iteratively to process large volumes of data. The memory accesses of the thread block across different iterations of a kernel launch exhibit correlated behavior. Our data location aware scheduler exploits this predictability to track memory access affinity of each thread block to a specific GPU card and stores this information to make scheduling decisions for future iterations. To further reduce the number of remote accesses we propose a hybrid mechanism that enables migrating or copying the pages between the memory of multiple GPUs based on their access behavior. Hence, most of the memory accesses are to the local GPU memory. Over an architecture consisting of two GPUs, our proposed schemes are able to improve the performance by 1.55× when compared to single GPU execution across widely used Rodinia [17], Parboil [18], and Graph [23] benchmarks.

Long-range persistence in sea surface temperature off the coast of central California

We estimate long-range persistence in ocean surface temperature off the coast of central California, a region where similar observations have not been made. The database consists of 20-year records of daily sea surface temperature from three locations: Pacific Grove and Granite Canyon along the coast, and Southeast Farallon Island located 40 km off the coast and slightly further north. Long-range persistence is important for a number of reasons: on the negative side, it can have serious detrimental effects for statistical inference and on the positive side, it provides access to the ocean’s memory which can lead to a greater understanding of the processes involved and thus to better prediction. Long-range persistence also provides important insights into the relationship between the scaling that is obtained and the time scales employed. The first step in the analysis was to remove the annual cycle from the data at each location because of its detrimental effect on estimating long-range persistence. Then detrended fluctuation analysis was used to calculate long-range persistence where a single scaling exponent is obtained that relates the magnitudes of the fluctuations in the data to the time scales involved. Similar scaling exponents were obtained for Granite Canyon and Pacific Grove with values of 1.04 and 1.05, respectively. At Southeast Farallon Island, a value of 1.16 was obtained. The increase in the scaling exponent at Southeast Farallon Island is consistent with observations made elsewhere and model results, which indicate that as coastal influence decreases further offshore, the scaling exponents for sea surface temperature tend to increase. Because Southeast Farallon Island is exposed to subarctic waters offshore, whereas Pacific Grove and Granite Canyon are exposed to warmer waters from the California Undercurrent along the coast, these exposures to different water masses may contribute to the observed change in scaling behavior.

Chain organization of human interphase chromosome determines the spatiotemporal dynamics of chromatin loci.

We investigate spatiotemporal dynamics of human interphase chromosomes by employing a heteropolymer model that incorporates the information of human chromosomes inferred from Hi-C data. Despite considerable heterogeneities in the chromosome structures generated from our model, chromatins are organized into crumpled globules with space-filling (SF) statistics characterized by a single universal scaling exponent (ν = 1/3), and this exponent alone can offer a quantitative account of experimentally observed, many different features of chromosome dynamics. The local chromosome structures, whose scale corresponds to that of topologically associated domains (∼ 0.1 − 1 Mb), display dynamics with a fast relaxation time (≲ 1 − 10 sec); in contrast, the long-range spatial reorganization of the entire chromatin ( Mb) occurs on a much slower time scale (≳ hour), providing the dynamic basis of cell-to-cell variability and glass-like behavior of chromosomes. Biological activities, modeled using stronger isotropic white noises added to active loci, accelerate the relaxation dynamics of chromatin domains associated with the low frequency modes and induce phase segregation between the active and inactive loci. Surprisingly, however, they do not significantly change the dynamics at local scales from those obtained under passive conditions. Our study underscores the role of chain organization of chromosome in determining the spatiotemporal dynamics of chromatin loci.

Universal dynamics in an isolated one-dimensional Bose gas far from equilibrium

Understanding the behaviour of isolated quantum systems far from equilibrium and their equilibration is one of the most pressing problems in quantum many-body physics1,2. There is strong theoretical evidence that sufficiently far from equilibrium a wide variety of systems-including the early Universe after inflation3-6, quark-gluon matter generated in heavy-ion collisions7-9, and cold quantum gases4,10-14-exhibit universal scaling in time and space during their evolution, independent of their initial state or microscale properties. However, direct experimental evidence is lacking. Here we demonstrate universal scaling in the time-evolving momentum distribution of an isolated, far-from-equilibrium, one-dimensional Bose gas, which emerges from a three-dimensional ultracold Bose gas by means of a strong cooling quench. Within the scaling regime, the time evolution of the system at low momenta is described by a time-independent, universal function and a single scaling exponent. The non-equilibrium scaling describes the transport of an emergent conserved quantity towards low momenta, which eventually leads to the build-up of a quasi-condensate. Our results establish universal scaling dynamics in an isolated quantum many-body system, which is a crucial step towards characterizing time evolution far from equilibrium in terms of universality classes. Universality would open the possibility of using, for example, cold-atom set-ups at the lowest energies to simulate important aspects of the dynamics of currently inaccessible systems at the highest energies, such as those encountered in the inflationary early Universe.

Critical behavior and magnetocaloric effect in La0.67Sr0.33MnO3.01 compounds

The polycrystalline La0.67Sr0.33MnO3.01 sample was synthesized by standard solid state technique. Crystal structure of sample belongs to rhombohedral system with space group R3−c. The parameters are a = 0.55003(2) and c = 1.33753(4) nm for indexing in hexagonal system and a′ = 0.54689 nm and α = 60.38° for indexing in rhombohedral system. In order to obviously reveal the magnetic interaction we study the critical behavior by the modified Arrott plot, the Kouvel-Fisher method and the critical isotherm technique. Three main critical exponents, β, γ and δ, are derived from different three methods mentioned above. The three critical exponents obey the Widom relation and are able to collapse the different isothermal magnetization data into two branches below and above TC based on the single scaling equation M(H, ε) = εβf±(H/εβ+γ). The critical exponents, β and γ, are on the verge of the theoretical prediction of a mean-field model, implying the existence of long-range magnetic interaction with magnetic exchange distance decaying as J(r) ≈ r−4.57. The exponent n in the power relation ΔSm∝Hn dependence of temperature increases with temperature decreasing and approaches to 1 well below TC and increases with temperature increasing and approaches to 2 well above TC. Near TC the n = 0.669 is very close to 2/3. These data support that the magnetic interaction can assign to mean-field model. The RCP increases with applied magnetic field and is about 40 J/kg under 1.2 T applied field.

Strongly Correlated Photon Transport in Waveguide Quantum Electrodynamics with Weakly Coupled Emitters.

We show that strongly correlated photon transport can be observed in waveguides containing optically dense ensembles of emitters. Remarkably, this occurs even for weak coupling efficiencies. Specifically, we compute the photon transport properties through a chirally coupled system of N two-level systems driven by a weak coherent field, where each emitter can also scatter photons out of the waveguide. The photon correlations arise due to an interplay of nonlinearity and coupling to a loss reservoir, which creates a strong effective interaction between transmitted photons. The highly correlated photon states are less susceptible to losses than uncorrelated photons and have a power-law decay with N. This is described using a simple universal asymptotic solution governed by a single scaling parameter which describes photon bunching and power transmission. We show numerically that, for randomly placed emitters, these results hold even in systems without chirality. The effect can be observed in existing tapered fiber setups with trapped atoms.

Weak disposability in nonparametric production analysis: A new taxonomy of reference technology sets

Adequate modeling of undesirable outputs in production processes plays an important role in management practice. Nonparametric models that assume jointly weak disposability of desirable and undesirable outputs have become prevalent in the literature although a consensus on how to implement this axiom has not been reached yet. Particularly, there is still an unresolved debate on whether to use a single or multiple scaling factors when applying weak disposability to real datasets in practice. In this paper, we shed some new light on the debate from various theoretical and practical viewpoints including disposability, convexity, returns to scale, and computational issues. Furthermore, we introduce a new model and unveil some interesting properties of the current ones, which then help to construct a comprehensive taxonomy of reference technology sets for activity analysis models under variable returns to scale.

Scaling law for slip flow of gases in nanoporous media from nanofluidics, rocks, and pore-scale simulations

In unconventional reservoirs, as the effective pore size becomes close to the mean free path of gas molecules, gas transport in porous media begins to deviate from Darcy’s law. The objective of this study is to explore the similarities of gas flows in nanochannels and core samples as well as those simulated by direct simulation BGK (DSBGK), a particle-based method that solves the Bhatnagar-Gross-Krook (BGK) equation.Due to difficulties in fabrication and experimentation, previous study on gas flow experiments in nanochannels is very limited. In this work, steady-state gas flow was measured in reactive-ion etched nanochannels with a controlled channel size on a sillicon wafer. A core-based permeability measurement apparatus was used to perform steady-state gas flow measurements on carbonate and shale samples. Klinkenberg permeability was obtained under varying pore pressures but constant temperature and effective stress. Methane was used in nanofluidic and rock experiments, making them directly comparable. Results from both experiments were then compared to gas flow simulations by DSBGK method carried out on several independently constructed geometry models. DSBGK uses hundreds of millions of simulated molecules to approximate gas flow inside the pore space. The intermolecular collisions are handled by directly integrating the BGK equation along each molecules trajectory, rather than through a sampling scheme like that in the direct simulation Monte-Carlo (DSMC) method. Consequently, the stochastic noise is significantly reduced, and simulation of nano-scale gas flows in complex geometries becomes computationally affordable.The slippage factors obtained from these independent studies varied across three orders of magnitude, yet they all appear to collapse on a single scaling relation where the slippage factor in the slip flow regime is inversely proportional to the square root of intrinsic permeability over porosity. Our correlation could also fit the data in the literature, which were often obtained using nitrogen, after correcting for temperature and gas properties. This study contributes to rock characterization, well testing analysis as well as the understanding of rarefied gas transport in porous media.

Eigenstate entanglement between quantum chaotic subsystems: Universal transitions and power laws in the entanglement spectrum

We derive universal entanglement entropy and Schmidt eigenvalue behaviors for the eigenstates of two quantum chaotic systems coupled with a weak interaction. The progression from a lack of entanglement in the noninteracting limit to the entanglement expected of fully randomized states in the opposite limit is governed by the single scaling transition parameter, $\Lambda$. The behaviors apply equally well to few- and many-body systems, e.g.\ interacting particles in quantum dots, spin chains, coupled quantum maps, and Floquet systems as long as their subsystems are quantum chaotic, and not localized in some manner. To calculate the generalized moments of the Schmidt eigenvalues in the perturbative regime, a regularized theory is applied, whose leading order behaviors depend on $\sqrt{\Lambda}$. The marginal case of the $1/2$ moment, which is related to the distance to closest maximally entangled state, is an exception having a $\sqrt{\Lambda}\ln \Lambda$ leading order and a logarithmic dependence on subsystem size. A recursive embedding of the regularized perturbation theory gives a simple exponential behavior for the von Neumann entropy and the Havrda-Charv{\' a}t-Tsallis entropies for increasing interaction strength, demonstrating a universal transition to nearly maximal entanglement. Moreover, the full probability densities of the Schmidt eigenvalues, i.e.\ the entanglement spectrum, show a transition from power laws and L\'evy distribution in the weakly interacting regime to random matrix results for the strongly interacting regime. The predicted behaviors are tested on a pair of weakly interacting kicked rotors, which follow the universal behaviors extremely well.