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Published work

32 published item(s)

preprint2026arXiv

Beyond Direct Generation: A Decomposed Approach to Well-Crafted Screenwriting with LLMs

The screenplay serves as the foundation for television production, defining narrative structure, character development, and dialogue. While Large Language Models (LLMs) show great potential in creative writing, direct end-to-end generation approaches often fail to produce well-crafted screenplays. We argue this failure stems from forcing a single model to simultaneously master two disparate capabilities: creative narrative construction and rigid format adherence. The resulting outputs may mimic superficial style but lack the deep structural integrity and storytelling substance required for professional use. To enable LLMs to generate high-quality screenplays, we introduce Dual-Stage Refinement (DSR), a decomposed framework that decouples creative narrative generation from format conversion. The first stage transforms a brief outline into rich, novel-style prose. The second stage refines this narrative into a professionally formatted screenplay. This separation enables the model to specialize in one distinct capability at each stage. A key challenge in implementing DSR is the scarcity of paired outline-to-novel training data. We address this through hybrid data synthesis: reverse synthesis deconstructs existing screenplays into structured inputs, while forward synthesis leverages these inputs to generate high-quality narrative texts as training targets. Blind evaluations by professional screenwriters show that DSR achieves a 75% win rate against strong baselines like Gemini-2.5-Pro and reaches 82.7% of human-level performance. Our work demonstrates that decomposed generation architecture with tailored data synthesis effectively specializes LLMs in complex creative domains.

preprint2026arXiv

CAX-Agent: A Lightweight Agent Harness for Reliable APDL Automation

Large language models deployed for MAPDL finite-element simulation face practical reliability challenges: without structured execution control, tool encapsulation, and fault recovery, outputs may be inconsistent and task failures are common. The Agent Harness paradigm addresses this by inserting domain-specific orchestration middleware that manages tool lifecycles, workflow state, and recovery escalation. This paper presents the architecture of CAX-Agent, a lightweight agent harness purpose-built for MAPDL automation, and empirically evaluates one of its core components -- the recovery policy.CAX-Agent organizes execution into three layers -- LLM service, agent harness, and solver backend -- with a recovery ladder that escalates from deterministic rule patching through model-driven regeneration to context enrichment and human intervention. We evaluate three recovery strategies (no_recovery, rule_only, and model_only) on 50 standard structural benchmarks with three repeated runs per strategy (450 case-runs total). Two independent human raters score task completion under blind conditions; inter-rater agreement is strong (quadratic weighted Cohen's kappa = 0.84, 96 percent of score pairs within one point). Model_only achieves the best completion rate (0.9267), task score (3.59/4), total score (9.16/10), and zero-intervention rate (0.84), outperforming rule_only (0.7733, 3.17/4, 7.03/10, 0.00) and no_recovery (0.6933, 2.74/4, 5.60/10, 0.00) with large effect sizes (Cliff's delta = 0.81-0.87). The benchmark uses deliberately simple geometries to isolate recovery-policy effects; we discuss the scope of these findings and directions for broader validation.

preprint2026arXiv

Rewarding Creativity: A Human-Aligned Generative Reward Model for Reinforcement Learning in Storytelling

While Large Language Models (LLMs) can generate fluent text, producing high-quality creative stories remains challenging. Reinforcement Learning (RL) offers a promising solution but faces two critical obstacles: designing reliable reward signals for subjective storytelling quality and mitigating training instability. This paper introduces the Reinforcement Learning for Creative Storytelling (RLCS) framework to systematically address both challenges. First, we develop a Generative Reward Model (GenRM) that provides multi-dimensional analysis and explicit reasoning about story preferences, trained through supervised fine-tuning on demonstrations with reasoning chains distilled from strong teacher models, followed by GRPO-based refinement on expanded preference data. Second, we introduce an entropy-based reward shaping strategy that dynamically prioritizes learning on confident errors and uncertain correct predictions, preventing overfitting on already-mastered patterns. Experiments demonstrate that GenRM achieves 68\% alignment with human creativity judgments, and RLCS significantly outperforms strong baselines including Gemini-2.5-Pro in overall story quality. This work provides a practical pipeline for applying RL to creative domains, effectively navigating the dual challenges of reward modeling and training stability.

preprint2022arXiv

A Survey of ADMM Variants for Distributed Optimization: Problems, Algorithms and Features

By coordinating terminal smart devices or microprocessors to engage in cooperative computation to achieve systemlevel targets, distributed optimization is incrementally favored by both engineering and computer science. The well-known alternating direction method of multipliers (ADMM) has turned out to be one of the most popular tools for distributed optimization due to many advantages, such as modular structure, superior convergence, easy implementation and high flexibility. In the past decade, ADMM has experienced widespread developments. The developments manifest in both handling more general problems and enabling more effective implementation. Specifically, the method has been generalized to broad classes of problems (i.e.,multi-block, coupled objective, nonconvex, etc.). Besides, it has been extensively reinforced for more effective implementation, such as improved convergence rate, easier subproblems, higher computation efficiency, flexible communication, compatible with inaccurate information, robust to communication delays, etc. These developments lead to a plentiful of ADMM variants to be celebrated by broad areas ranging from smart grids, smart buildings, wireless communications, machine learning and beyond. However, there lacks a survey to document those developments and discern the results. To achieve such a goal, this paper provides a comprehensive survey on ADMM variants. Particularly, we discern the five major classes of problems that have been mostly concerned and discuss the related ADMM variants in terms of main ideas, main assumptions, convergence behaviors and main features. In addition, we figure out several important future research directions to be addressed. This survey is expected to work as a tutorial for both developing distributed optimization in broad areas and identifying existing theoretical research gaps.

preprint2021arXiv

The TESS Faint Star Search: 1,617 TOIs from the TESS Primary Mission

We present the detection of 1,617 new transiting planet candidates, identified in the Transiting Exoplanet Survey Satellite (TESS) full-frame images (FFIs) observed during the Primary Mission (Sectors 1 - 26). These candidates were initially detected by the Quick-Look Pipeline (QLP), which extracts FFI lightcurves for and searches all stars brighter than TESS magnitude T = 13.5 mag in each sector. However, QLP heavily relies on manual inspection for the identification of planet candidates, limiting vetting efforts to planet-hosting stars brighter than T = 10.5 mag and leaving millions of potential transit signals un-vetted. We describe an independent vetting pipeline applied to QLP transit search results, incorporating both automated vetting tests and manual inspection to identify promising planet candidates around these fainter stars. The new candidates discovered by this ongoing project will allow TESS to significantly improve the statistical power of demographics studies of giant, close-in exoplanets.

preprint2020arXiv

A Giant Planet Candidate Transiting a White Dwarf

Astronomers have discovered thousands of planets outside the solar system, most of which orbit stars that will eventually evolve into red giants and then into white dwarfs. During the red giant phase, any close-orbiting planets will be engulfed by the star, but more distant planets can survive this phase and remain in orbit around the white dwarf. Some white dwarfs show evidence for rocky material floating in their atmospheres, in warm debris disks, or orbiting very closely, which has been interpreted as the debris of rocky planets that were scattered inward and tidally disrupted. Recently, the discovery of a gaseous debris disk with a composition similar to ice giant planets demonstrated that massive planets might also find their way into tight orbits around white dwarfs, but it is unclear whether the planets can survive the journey. So far, the detection of intact planets in close orbits around white dwarfs has remained elusive. Here, we report the discovery of a giant planet candidate transiting the white dwarf WD 1856+534 (TIC 267574918) every 1.4 days. The planet candidate is roughly the same size as Jupiter and is no more than 14 times as massive (with 95% confidence). Other cases of white dwarfs with close brown dwarf or stellar companions are explained as the consequence of common-envelope evolution, wherein the original orbit is enveloped during the red-giant phase and shrinks due to friction. In this case, though, the low mass and relatively long orbital period of the planet candidate make common-envelope evolution less likely. Instead, the WD 1856+534 system seems to demonstrate that giant planets can be scattered into tight orbits without being tidally disrupted, and motivates searches for smaller transiting planets around white dwarfs.

preprint2020arXiv

A Node Embedding Framework for Integration of Similarity-based Drug Combination Prediction

Motivation: Drug combination is a sensible strategy for disease treatment by improving the efficacy and reducing concomitant side effects. Due to the large number of possible combinations among candidate compounds, exhaustive screening is prohibitive. Currently, a plenty of studies have focused on predicting potential drug combinations. However, these methods are not entirely satisfactory in performance and scalability. Results: In this paper, we proposed a Network Embedding framework in Multiplex Networks (NEMN) to predict synthetic drug combinations. Based on a multiplex drug similarity network, we offered alternative methods to integrate useful information from different aspects and to decide quantitative importance of each network. To explain the feasibility of NEMN, we applied our framework to the data of drug-drug interactions, on which it showed better performance in terms of AUPR and ROC. For Drug combination prediction, we found seven novel drug combinations which have been validated by external sources among the top-ranked predictions of our model.

preprint2020arXiv

Identification and Validation of the SNV Biomarkers Based on Multi-Dimensional Patterns

Background: Single nucleotide variants (SNVs) are detected as different distributions of DNA samples of distinct types of cancer patients. Even though, it is an exacting task to select the appropriate method to identify cancer to the greatest extent of SNVs. Results: In this paper, we proposed a biomarker concept based on SNV patterns in different feature dimensions. Raw dataset (2761 samples) consisting of twelve different cancers was obtained from TCGA (The Cancer Genome Atlas). After preliminary screening of 562,321 DNA mutation sites in the samples, the mutation sites were extracted and characterized by cancer types in six different SNV feature dimensions. In this study, we found that the extracted features showed similar distribution in the cluster center of the disease type of the samples. After the initial processing of the raw data, the sample was more focused on the subtype distribution of the cancer or the cancer at the SNV level. We used k-nearest neighbors (KNN) to classify the extracted features and Leave-One-Out cross verified them. The accuracy of classifying is stable at around 97% and reached 97.43% at the highest. During the validation phase, we found validated oncogenes in the loci of the features with the highest importance among nine cancers. Conclusions: In summary, the samples showed consistent patterns according to the cancer in which it belongs. It is feasible to classify the cancer of the sample by the distribution of different dimensions of the SNVs and has a high accuracy. And has potential implications for the discovery of cancer-causing genes.

preprint2020arXiv

Multi-Agent Deep Reinforcement Learning for HVAC Control in Commercial Buildings

In commercial buildings, about 40%-50% of the total electricity consumption is attributed to Heating, Ventilation, and Air Conditioning (HVAC) systems, which places an economic burden on building operators. In this paper, we intend to minimize the energy cost of an HVAC system in a multi-zone commercial building under dynamic pricing with the consideration of random zone occupancy, thermal comfort, and indoor air quality comfort. Due to the existence of unknown thermal dynamics models, parameter uncertainties (e.g., outdoor temperature, electricity price, and number of occupants), spatially and temporally coupled constraints associated with indoor temperature and CO2 concentration, a large discrete solution space, and a non-convex and non-separable objective function, it is very challenging to achieve the above aim. To this end, the above energy cost minimization problem is reformulated as a Markov game. Then, an HVAC control algorithm is proposed to solve the Markov game based on multi-agent deep reinforcement learning with attention mechanism. The proposed algorithm does not require any prior knowledge of uncertain parameters and can operate without knowing building thermal dynamics models. Simulation results based on real-world traces show the effectiveness, robustness and scalability of the proposed algorithm.

preprint2020arXiv

TOI 694 b and TIC 220568520 b: Two Low-Mass Companions Near the Hydrogen Burning Mass Limit Orbiting Sun-like Stars

We report the discovery of TOI 694 b and TIC 220568520 b, two low-mass stellar companions in eccentric orbits around metal-rich Sun-like stars, first detected by the Transiting Exoplanet Survey Satellite (TESS). TOI 694 b has an orbital period of 48.05131$\pm$0.00019 days and eccentricity of 0.51946$\pm$0.00081, and we derive a mass of 89.0$\pm$5.3 $M_J$ (0.0849$\pm$0.0051 $M_\odot$) and radius of 1.111$\pm$0.017 $R_J$ (0.1142$\pm$0.0017 $R_\odot$). TIC 220568520 b has an orbital period of 18.55769$\pm$0.00039 days and eccentricity of 0.0964$\pm$0.0032, and we derive a mass of 107.2$\pm$5.2 $M_J$ (0.1023$\pm$0.0050 $M_\odot$) and radius of 1.248$\pm$0.018 $R_J$ (0.1282$\pm$0.0019 $R_\odot$). Both binary companions lie close to and above the Hydrogen burning mass threshold that separates brown dwarfs and the lowest mass stars, with TOI 694 b being 2-$σ$ above the canonical mass threshold of 0.075 $M_\odot$. The relatively long periods of the systems mean that the magnetic fields of the low-mass companions are not expected to inhibit convection and inflate the radius, which according to one leading theory is common in similar objects residing in short-period tidally-synchronized binary systems. Indeed we do not find radius inflation for these two objects when compared to theoretical isochrones. These two new objects add to the short but growing list of low-mass stars with well-measured masses and radii, and highlight the potential of the TESS mission for detecting such rare objects orbiting bright stars.

preprint2016arXiv

Doppler Monitoring of five K2 Transiting Planetary Systems

In an effort to measure the masses of planets discovered by the NASA {\it K2} mission, we have conducted precise Doppler observations of five stars with transiting planets. We present the results of a joint analysis of these new data and previously published Doppler data. The first star, an M dwarf known as K2-3 or EPIC~201367065, has three transiting planets ("b", with radius $2.1~R_{\oplus}$; "c", $1.7~R_{\oplus}$; and "d", $1.5~R_{\oplus}$). Our analysis leads to the mass constraints: $M_{b}=8.1^{+2.0}_{-1.9}~M_{\oplus}$ and $M_{c}$ < $ 4.2~M_{\oplus}$~(95\%~conf.). The mass of planet d is poorly constrained because its orbital period is close to the stellar rotation period, making it difficult to disentangle the planetary signal from spurious Doppler shifts due to stellar activity. The second star, a G dwarf known as K2-19 or EPIC~201505350, has two planets ("b", $7.7~R_{\oplus}$; and "c", $4.9~R_{\oplus}$) in a 3:2 mean-motion resonance, as well as a shorter-period planet ("d", $1.1~R_{\oplus}$). We find $M_{b}$= $28.5^{+5.4}_{-5.0} ~M_{\oplus}$, $M_{c}$= $25.6^{+7.1}_{-7.1} ~M_{\oplus}$ and $M_{d}$ < $14.0~M_{\oplus} $~(95\%~conf.). The third star, a G dwarf known as K2-24 or EPIC~203771098, hosts two transiting planets ("b", $5.7~R_{\oplus}$; and "c", $7.8~R_{\oplus}$) with orbital periods in a nearly 2:1 ratio. We find $M_{b}$= $19.8^{+4.5}_{-4.4} ~M_{\oplus}$ and $M_{c}$ = $26.0^{+5.8}_{-6.1}~M_{\oplus}$.....

preprint2016arXiv

The K2-ESPRINT Project III: A Close-in Super-Earth around a Metal-rich Mid-M Dwarf

We validate a $R_p=2.32\pm 0.24R_\oplus$ planet on a close-in orbit ($P=2.260455\pm 0.000041$ days) around K2-28 (EPIC 206318379), a metal-rich M4-type dwarf in the Campaign 3 field of the K2 mission. Our follow-up observations included multi-band transit observations from the optical to the near infrared, low-resolution spectroscopy, and high-resolution adaptive-optics (AO) imaging. We perform a global fit to all the observed transits using a Gaussian process-based method and show that the transit depths in all passbands adopted for the ground-based transit follow-ups ($r'_2, z_\mathrm{s,2}, J, H, K_\mathrm{s}$) are within $\sim 2σ$ of the K2 value. Based on a model of the background stellar population and the absence of nearby sources in our AO imaging, we estimate the probability that a background eclipsing binary could cause a false positive to be $< 2\times 10^{-5}$. We also show that K2-28 cannot have a physically associated companion of stellar type later than M4, based on the measurement of almost identical transit depths in multiple passbands. There is a low probability for a M4 dwarf companion ($\approx 0.072_{-0.04}^{+0.02}$), but even if this were the case, the size of K2-28b falls within the planetary regime. K2-28b has the same radius (within $1σ$) and experiences a similar irradiation from its host star as the well-studied GJ~1214b. Given the relative brightness of K2-28 in the near infrared ($m_\mathrm{Kep}=14.85$ mag and $m_H=11.03$ mag) and relatively deep transit ($0.6-0.7\%$), a comparison between the atmospheric properties of these two planets with future observations would be especially interesting.

preprint2016arXiv

The K2-ESPRINT Project IV: A Hot Jupiter in a Prograde Orbit with a Possible Stellar Companion

We report on the detection and early characterization of a hot Jupiter in a 3-day orbit around K2-34 (EPIC~212110888), a metal-rich F-type star located in the K2 Cycle 5 field. Our follow-up campaign involves precise radial velocity (RV) measurements and high-contrast imaging using multiple facilities. The absence of a bright nearby source in our high-contrast data suggests that the transit-like signals are not due to light variations from such a companion star. Our intensive RV measurements show that K2-34b has a mass of $1.773\pm0.086M_J$, confirming its status as a planet. We also detect the Rossiter-McLaughlin effect for K2-34b and show that the system has a good spin-orbit alignment ($λ=-1_{-9}^{+10}$ degrees). High-contrast images obtained by the HiCIAO camera on the Subaru 8.2-m telescope reveal a faint companion candidate ($Δm_H=6.19\pm 0.11$ mag) at a separation of $0\farcs36$. Follow-up observations are needed to confirm that the companion candidate is physically associated with K2-34. K2-34b appears to be an example of a typical "hot Jupiter," albeit one which can be precisely characterized using a combination of K2 photometry and ground-based follow-up.

preprint2016arXiv

The K2-ESPRINT Project V: a short-period giant planet orbiting a subgiant star

We report on the discovery and characterization of the transiting planet K2-39b (EPIC 206247743b). With an orbital period of 4.6 days, it is the shortest-period planet orbiting a subgiant star known to date. Such planets are rare, with only a handful of known cases. The reason for this is poorly understood, but may reflect differences in planet occurrence around the relatively high-mass stars that have been surveyed, or may be the result of tidal destruction of such planets. K2-39 is an evolved star with a spectroscopically derived stellar radius and mass of $3.88^{+0.48}_{-0.42}~\mathrm{R_\odot}$ and $1.53^{+0.13}_{-0.12}~\mathrm{M_\odot}$, respectively, and a very close-in transiting planet, with $a/R_\star = 3.4$. Radial velocity (RV) follow-up using the HARPS, FIES and PFS instruments leads to a planetary mass of $50.3^{+9.7}_{-9.4}~\mathrm{M_\oplus}$. In combination with a radius measurement of $8.3 \pm 1.1~\mathrm{R_\oplus}$, this results in a mean planetary density of $0.50^{+0.29}_{-0.17}$ g~cm$^{-3}$. We furthermore discover a long-term RV trend, which may be caused by a long-period planet or stellar companion. Because K2-39b has a short orbital period, its existence makes it seem unlikely that tidal destruction is wholly responsible for the differences in planet populations around subgiant and main-sequence stars. Future monitoring of the transits of this system may enable the detection of period decay and constrain the tidal dissipation rates of subgiant stars.

preprint2015arXiv

Tests of the planetary hypothesis for PTFO 8-8695b

The T Tauri star PTFO 8-8695 exhibits periodic fading events that have been interpreted as the transits of a giant planet on a precessing orbit. Here we present three tests of the planet hypothesis. First, we sought evidence for the secular changes in light-curve morphology that are predicted to be a consequence of orbital precession. We observed 28 fading events spread over several years, and did not see the expected changes. Instead we found that the fading events are not strictly periodic. Second, we attempted to detect the planet's radiation, based on infrared observations spanning the predicted times of occultations. We ruled out a signal of the expected amplitude. Third, we attempted to detect the Rossiter-McLaughlin effect by performing high-resolution spectroscopy throughout a fading event. No effect was seen at the expected level, ruling out most (but not all) possible orientations for the hypothetical planetary orbit. Our spectroscopy also revealed strong, time-variable, high-velocity Hα and Ca H & K emission features. All these observations cast doubt on the planetary hypothesis, and suggest instead that the fading events represent starspots, eclipses by circumstellar dust, or occultations of an accretion hotspot.

preprint2015arXiv

The Influence of Mergers on Scatter and Evolution in Sunyaev-Zel'dovich Effect Scaling Relations

The Sunyaev-Zel'dovich effect (SZE) observable-mass (Y-M) scaling relation is a promising technique for obtaining mass estimates for large samples of galaxy clusters and holds a key to studying the nature of dark matter and dark energy. However, cosmological inference based on SZE cluster surveys is limited by our incomplete knowledge of bias, scatter, and evolution in the Y-M relation. In this work, we investigate the effects of galaxy cluster mergers on the scaling relation using the Omega500 high-resolution cosmological hydrodynamic simulation. We show that the non-thermal pressure associated with merger-induced gas motions contributes significantly to the bias, scatter, and evolution of the scaling relation. After the merger, the kinetic energy of merging systems is slowly converted into thermal energy through dissipation of turbulent gas motions, which causes the thermal SZE signal to increase steadily with time. This post-merger evolution is one of the primary source of bias and scatter in the Y-M relation. However, we show that when the missing non-thermal energy is accounted for, the resulting relation exhibits little to no redshift evolution and the scatter around the scaling relation is ~20-30 % smaller than that of the thermal SZE signal alone. Our work opens up a possibility to further improve the current robust mass proxy, Y, by accounting for the missing non-thermal pressure component. We discuss future prospect of measuring internal gas motions in galaxy clusters and its implication for cluster-based cosmological tests.

preprint2014arXiv

Weighing Galaxy Clusters with Gas. II. On the Origin of Hydrostatic Mass Bias in LambdaCDM Galaxy Clusters

The use of galaxy clusters as cosmological probes hinges on our ability to measure their masses accurately and with high precision. Hydrostatic mass is one of the most common methods for estimating the masses of individual galaxy clusters, which suffer from biases due to departures from hydrostatic equilibrium. Using a large, mass-limited sample of massive galaxy clusters from a high-resolution hydrodynamical cosmological simulation, in this work we show that in addition to turbulent and bulk gas velocities, acceleration of gas introduces biases in the hydrostatic mass estimate of galaxy clusters. In unrelaxed clusters, the acceleration bias is comparable to the bias due to non-thermal pressure associated with merger-induced turbulent and bulk gas motions. In relaxed clusters, the mean mass bias due to acceleration is small (<3%), but the scatter in the mass bias can be reduced by accounting for gas acceleration. Additionally, this acceleration bias is greater in the outskirts of higher redshift clusters where mergers are more frequent and clusters are accreting more rapidly. Since gas acceleration cannot be observed directly, it introduces an irreducible bias for hydrostatic mass estimates. This acceleration bias places limits on how well we can recover cluster masses from future X-ray and microwave observations. We discuss implications for cluster mass estimates based on X-ray, Sunyaev-Zeldovich effect, and gravitational lensing observations and their impact on cluster cosmology.

preprint2013arXiv

Digital breadcrumbs: Detecting urban mobility patterns and transport mode choices from cellphone networks

Many modern and growing cities are facing declines in public transport usage, with few efficient methods to explain why. In this article, we show that urban mobility patterns and transport mode choices can be derived from cellphone call detail records coupled with public transport data recorded from smart cards. Specifically, we present new data mining approaches to determine the spatial and temporal variability of public and private transportation usage and transport mode preferences across Singapore. Our results, which were validated by Singapore's quadriennial Household Interview Travel Survey (HITS), revealed that there are 3.5 (HITS: 3.5 million) million and 4.3 (HITS: 4.4 million) million inter-district passengers by public and private transport, respectively. Along with classifying which transportation connections are weak or underserved, the analysis shows that the mode share of public transport use increases from 38 percent in the morning to 44 percent around mid-day and 52 percent in the evening.

preprint2013arXiv

Displacement induced electric force and natural self-oscillation of a free electron

We show that a kind of displacement induced temporary electric force of a single point charge can be derived by using Maxwell stress analysis. This force comes from the variation of the charge's electric intensities that follow Coulomb's inverse square law, and it is a kind of displacement dependent temporary restoring force. We also show the possible existence of natural self-oscillation of a free electron which is driven by this restoring self-force of its own electric fields.

preprint2013arXiv

On the existence of natural self-oscillation of a free electron

The possibility of the existence of natural self-oscillation of a free electron is suggested. This oscillation depends on the interaction of the electron with its own electromagnetic fields. Suitable standing wave solutions of the electromagnetic fields are chosen. A kind of displacement dependent electric potential and mechanism of energy exchange between velocity and acceleration dependent electromagnetic fields are analyzed. Conditions for the existence of natural self-oscillation are given.

preprint2012arXiv

Serial Symmetrical Relocation Algorithm for the Equal Sphere Packing Problem

For dealing with the equal sphere packing problem, we propose a serial symmetrical relocation algorithm, which is effective in terms of the quality of the numerical results. We have densely packed up to 200 equal spheres in spherical container and up to 150 equal spheres in cube container. All results are rigorous because of a fake sphere trick. It was conjectured impossible to pack 68 equal spheres of radius 1 into a sphere of radius 5. The serial symmetrical relocation algorithm has proven wrong this conjecture by finding one such packing.

preprint2011arXiv

Asymptotic Analysis of the Wigner $3j$-Symbol in the Bargmann Representation

We derive the leading asymptotic limit of the Wigner $3j$-symbol from a stationary phase approximation of a twelve dimensional integral, obtained from an inner product between two exact Bargmann wavefunctions. We show that, by the construction of the Bargmann inner product, the stationary phase conditions have a geometric description in terms of the Hopf fibration of ${\mathbb C}^6$ into ${\mathbb R}^3 \times {\mathbb R}^3 \times {\mathbb R}^3$. In addition, we find that, except for the usual modification of the quantum numbers by 1/2, the imaginary part of the logarithm of a Bargmann wavefunction, evaluated at the stationary points, is equal to the asymptotic phase of the $3j$-symbol.

preprint2011arXiv

Asymptotic Limits of the Wigner $12J$-Symbol in Terms of the Ponzano-Regge Phases

There are two types of asymptotic formulas for the $12j$ symbol with one small and 11 large angular momenta. We have derived the first type of formula previously in [L. Yu, Phys. Rev. A84 022101 (2011)]. We will derive the second type in this paper. We find that this second asymptotic formula for the $12j$ symbol is expressed in terms of the vector diagram associated with two $6j$ symbols, namely, the vector diagram of two adjacent tetrahedra sharing a common face. As a result, two sets of Ponzano-Regge phases appear in the asymptotic formula. This work contributes another asymptotic formula of the Wigner $12j$ symbol to the re-coupling theory of angular momenta.

preprint2011arXiv

Asymptotic Limits of the Wigner $15J$-Symbol with Small Quantum Numbers

We present new asymptotic formulas for the Wigner $15j$-symbol with two, three, or four small quantum numbers, and provide numerical evidence of their validity. These formulas are of the WKB form and are of a similar nature as the Ponzano-Regge formula for the Wigner $6j$-symbol. They are expressed in terms of edge lengths and angles of geometrical figures associated with angular momentum vectors. In particular, the formulas for the $15j$-symbol with two, three, and four small quantum numbers are based on the geometric figures of the $9j$-, $6j$-, and $3j$-symbols, respectively, The geometric nature of these new asymptotic formulas pave the way for further analysis of the semiclassical limits of vertex amplitudes in loop quantum gravity models.

preprint2011arXiv

Semiclassical Analysis of the Wigner $12j$ Symbol with One Small Angular Momentum

We derive an asymptotic formula for the Wigner $12j$ symbol, in the limit of one small and 11 large angular momenta. There are two kinds of asymptotic formulas for the $12j$ symbol with one small angular momentum. We present the first kind of formula in this paper. Our derivation relies on the techniques developed in the semiclassical analysis of the Wigner $9j$ symbol [L. Yu and R. G. Littlejohn, Phys. Rev. A 83, 052114 (2011)], where we used a gauge-invariant form of the multicomponent WKB wave-functions to derive asymptotic formulas for the $9j$ symbol with small and large angular momenta. When applying the same technique to the $12j$ symbol in this paper, we find that the spinor is diagonalized in the direction of an intermediate angular momentum. In addition, we find that the geometry of the derived asymptotic formula for the $12j$ symbol is expressed in terms of the vector diagram for a $9j$ symbol. This illustrates a general geometric connection between asymptotic limits of the various $3nj$ symbols. This work contributes the first known asymptotic formula for the $12j$ symbol to the quantum theory of angular momentum, and serves as a basis for finding asymptotic formulas for the Wigner $15j$ symbol with two small angular momenta.

preprint2011arXiv

Semiclassical Analysis of the Wigner $9J$-Symbol with Small and Large Angular Momenta

We derive a new asymptotic formula for the Wigner $9j$-symbol, in the limit of one small and eight large angular momenta, using a novel gauge-invariant factorization for the asymptotic solution of a set of coupled wave equations. Our factorization eliminates the geometric phases completely, using gauge-invariant non-canonical coordinates, parallel transports of spinors, and quantum rotation matrices. Our derivation generalizes to higher $3nj$-symbols. We display without proof some new asymptotic formulas for the $12j$-symbol and the $15j$-symbol in the appendices. This work contributes a new asymptotic formula of the Wigner $9j$-symbol to the quantum theory of angular momentum, and serves as an example of a new general method for deriving asymptotic formulas for $3nj$-symbols.

preprint2011arXiv

Semiclassical Mechanics of the Wigner 6j-Symbol

The semiclassical mechanics of the Wigner 6j-symbol is examined from the standpoint of WKB theory for multidimensional, integrable systems, to explore the geometrical issues surrounding the Ponzano-Regge formula. The relations among the methods of Roberts and others for deriving the Ponzano-Regge formula are discussed, and a new approach, based on the recoupling of four angular momenta, is presented. A generalization of the Yutsis-type of spin network is developed for this purpose. Special attention is devoted to symplectic reduction, the reduced phase space of the 6j-symbol (the 2-sphere of Kapovich and Millson), and the reduction of Poisson bracket expressions for semiclassical amplitudes. General principles for the semiclassical study of arbitrary spin networks are laid down; some of these were used in our recent derivation of the asymptotic formula for the Wigner 9j-symbol.

preprint2011arXiv

Uniform Approximation from Symbol Calculus on a Spherical Phase Space

We use symbol correspondence and quantum normal form theory to develop a more general method for finding uniform asymptotic approximations. We then apply this method to derive a result we announced in an earlier paper, namely, the uniform approximation of the $6j$-symbol in terms of the rotation matrices. The derivation is based on the Stratonovich-Weyl symbol correspondence between matrix operators and functions on a spherical phase space. The resulting approximation depends on a canonical, or area preserving, map between two pairs of intersecting level sets on the spherical phase space.

preprint2009arXiv

Uniform Semiclassical Approximation for the Wigner $6j$ Symbol in Terms of Rotation Matrices

A new uniform asymptotic approximation for the Wigner $6j$ symbol is given in terms of Wigner rotation matrices ($d$-matrices). The approximation is uniform in the sense that it applies for all values of the quantum numbers, even those near caustics. The derivation of the new approximation is not given, but the geometrical ideas supporting it are discussed and numerical tests are presented, including comparisons with the exact $6j$-symbol and with the Ponzano-Regge approximation.

preprint2007arXiv

Semiclassical analysis of Wigner $3j$-symbol

We analyze the asymptotics of the Wigner $3j$-symbol as a matrix element connecting eigenfunctions of a pair of integrable systems, obtained by lifting the problem of the addition of angular momenta into the space of Schwinger's oscillators. A novel element is the appearance of compact Lagrangian manifolds that are not tori, due to the fact that the observables defining the quantum states are noncommuting. These manifolds can be quantized by generalized Bohr-Sommerfeld rules and yield all the correct quantum numbers. The geometry of the classical angular momentum vectors emerges in a clear manner. Efficient methods for computing amplitude determinants in terms of Poisson brackets are developed and illustrated.