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Given integers $n \geq k \geq d$, let $X_{n,k,d}$ be the moduli space of $n$-tuples of lines $(\ell_1, \dots, \ell_n)$ in $\mathbb{C}^k$ such that $\ell_1 + \cdots + \ell_n$ has dimension $d$. We give a quotient presentation of the torus-equivariant cohomology of $X_{n,k,d}$. The form of this presentation, and in particular the torus parameters appearing therein, will arise from the orbit harmonics method of combinatorial representation theory., Comment: 29 pages

Let $X$ be a complex manifold, and let $Y$ and $D$ be two reduced simple-normal-crossing (snc) divisors on $X$ with no common irreducible components. Given a proper locally K\"ahler morphism $\pi \colon X \to \Delta$ from $X$ to a complex analytic space $\Delta$, we prove Fujino's conjecture on the injectivity theorem in the relative setting in a generalized form. Specifically, we establish an injectivity result for the higher direct images under $\pi$ for the lc pairs $(X, D)$ as well as $(Y, D_Y)$, where $D_Y := D \cap Y$. As an application, this result immediately implies the injectivity theorem on holomorphically convex K\"ahler manifolds with reduced snc divisors. The main technique in the proof consists of the theory of harmonic integrals together with residue formulae associated with adjoint ideal sheaves, which are developed from our previous work for the absolute case (where $\Delta$ is a point and $X$ is compact). Additionally, we make use of the Takegoshi harmonic forms to deal with the non-compactness of $X$., Comment: 37 pages; see our previous related work at arXiv:2307.12025

In modern materials science, effective and high-volume data management across leading-edge experimental facilities and world-class supercomputers is indispensable for cutting-edge research. Such facilities and supercomputers are typically utilized by a wide range of researchers across different fields and organizations in academia and industry. However, existing integrated systems that handle data from these resources have primarily focused just on smaller-scale cross-institutional or single-domain operations. As a result, they often lack the scalability, efficiency, agility, and interdisciplinarity, needed for handling substantial volumes of data from various researchers. In this paper, we introduce ARIM-mdx data system, a nationwide data platform for materials science in Japan. The platform involves 8 universities and institutes all over Japan through the governmental materials science project. Currently in its trial phase, the ARIM-mdx data system is utilized by over 800 researchers from around 140 organizations in academia and industry, being intended to gradually expand its reach. The system employs a hybrid architecture, combining a peta-scale dedicated storage system for security and stability with a high-performance academic cloud for efficiency and scalability. Through direct network connections between them, the system achieves 4.7x latency reduction compared to a conventional approach, resulting in near real-time interactive data analysis. It also utilizes specialized IoT devices for secure data transfer from equipment computers and connects to multiple supercomputers via an academic ultra-fast network, achieving 4x faster data transfer compared to the public Internet. The ARIM-mdx data system, as a pioneering nationwide data platform, has the potential to contribute to the creation of new research communities and accelerates innovations., Comment: Under Review

In this paper, we extend the uniform $L^2$-estimate of $\bar{\partial}$-equations for flat nontrivial line bundles, proved for compact K\"ahler manifolds in the previous work, to compact complex manifolds. In the proof, by tracing the Dolbeault isomorphism in detail, we derive the desired $L^2$-estimate directly from Ueda's lemma.

A compact energy-recovery linac (cERL) has been un-der construction at KEK since 2009 to develop key technologies for the energy-recovery linac. The cERL began operating in 2013 to create a high-current beam with a low-emittance beam with stable continuous wave (CW) superconducting cavities. Owing to the development of critical components, such as the DC gun, superconducting cavities, and the design of ideal beam transport optics, we have successfully established approximately 1 mA stable CW operation with a small beam emittance and extremely small beam loss. This study presents the details of our key technologies and experimental results for achieving 100% energy recovery operation with extremely small beam loss during a stable, approximately 1 mA CW beam operation., Comment: 11 pages, 16 figures

To handle unintended changes in the environment by agents, we propose an environment-centric active inference EC-AIF in which the Markov Blanket of active inference is defined starting from the environment. In normal active inference, the Markov Blanket is defined starting from the agent. That is, first the agent was defined as the entity that performs the "action" such as a robot or a person, then the environment was defined as other people or objects that are directly affected by the agent's "action," and the boundary between the agent and the environment was defined as the Markov Blanket. This agent-centric definition does not allow the agent to respond to unintended changes in the environment caused by factors outside of the defined environment. In the proposed EC-AIF, there is no entity corresponding to an agent. The environment includes all observable things, including people and things conventionally considered to be the environment, as well as entities that perform "actions" such as robots and people. Accordingly, all states, including robots and people, are included in inference targets, eliminating unintended changes in the environment. The EC-AIF was applied to a robot arm and validated with an object transport task by the robot arm. The results showed that the robot arm successfully transported objects while responding to changes in the target position of the object and to changes in the orientation of another robot arm., Comment: 14 pages, 9 figures

We present here the current state of a collection of promising ultraviolet technologies in preparation for the Habitable Worlds Observatory. Working with experts representing a significant number of groups working in the ultraviolet, we summarize some of the leading science drivers, present an argument for a 100 nm blue wavelength cutoff, and gather current state of the art of UV technologies. We present the state of the art of contamination control, a crucial piece of the UV instrument plan. We explore next steps with individual technologies, as well as present paths forward with systems level testing and development.

GaN is expected to be a key material for next-generation electronics due to its interesting properties. However, the current collapse poses a challenge to the application of GaN FETs to electronic devices. In this study, we investigate the formation of quantum dots in GaN FETs under the current collapse. By comparing the Coulomb diamond between standard measurements and those under current collapse, we find that the gate capacitance is significantly decreased by the current collapse. This suggests that the current collapse changes the distribution of trapped electrons at the device surface, which is reported in the previous study by operando X-ray spectroscopy. Also, we show external control of quantum dot formation, previously challenging in an FET structure, by using current collapse., Comment: 11 pages, 4 figures

Large angular scale surveys in the absence of atmosphere are essential for measuring the primordial $B$-mode power spectrum of the Cosmic Microwave Background (CMB). Since this proposed measurement is about three to four orders of magnitude fainter than the temperature anisotropies of the CMB, in-flight calibration of the instruments and active suppression of systematic effects are crucial. We investigate the effect of changing the parameters of the scanning strategy on the in-flight calibration effectiveness, the suppression of the systematic effects themselves, and the ability to distinguish systematic effects by null-tests. Next-generation missions such as LiteBIRD, modulated by a Half-Wave Plate (HWP), will be able to observe polarisation using a single detector, eliminating the need to combine several detectors to measure polarisation, as done in many previous experiments and hence avoiding the consequent systematic effects. While the HWP is expected to suppress many systematic effects, some of them will remain. We use an analytical approach to comprehensively address the mitigation of these systematic effects and identify the characteristics of scanning strategies that are the most effective for implementing a variety of calibration strategies in the multi-dimensional space of common spacecraft scan parameters. We also present Falcons, a fast spacecraft scanning simulator that we developed to investigate this scanning parameter space.

A muon-flux measurement behind the beam dump of the J-PARC Hadron Experimental Facility was performed with a compact muon detector that can be inserted into a vertical observing hole which was dug underground with 81 mm in diameter. The flux of the muons penetrating the beam dump was scanned vertically at intervals of 0.5 m, showing a wide distribution with a maximum at the beam level. The muon flux was consistent with the expectation from a Monte-Carlo simulation at more than 1 m away from the beam axis, which is expected to be used for signal-loss evaluation in the future KOTO II experiment for measuring rare kaon decays. The data can also be used in improving the accuracy of shielding calculations in the radiation protection., Comment: 13 pages, 10 figures, submitted to Nuclear Instruments and Methods in Physics Research Section A

We assess the capabilities of the LiteBIRD mission to map the hot gas distribution in the Universe through the thermal Sunyaev-Zeldovich (SZ) effect. Our analysis relies on comprehensive simulations incorporating various sources of Galactic and extragalactic foreground emission, while accounting for specific instrumental characteristics of LiteBIRD, such as detector sensitivities, frequency-dependent beam convolution, inhomogeneous sky scanning, and $1/f$ noise. We implement a tailored component-separation pipeline to map the thermal SZ Compton $y$-parameter over 98% of the sky. Despite lower angular resolution for galaxy cluster science, LiteBIRD provides full-sky coverage and, compared to the Planck satellite, enhanced sensitivity, as well as more frequency bands to enable the construction of an all-sky $y$-map, with reduced foreground contamination at large and intermediate angular scales. By combining LiteBIRD and Planck channels in the component-separation pipeline, we obtain an optimal $y$-map that leverages the advantages of both experiments, with the higher angular resolution of the Planck channels enabling the recovery of compact clusters beyond the LiteBIRD beam limitations, and the numerous sensitive LiteBIRD channels further mitigating foregrounds. The added value of LiteBIRD is highlighted through the examination of maps, power spectra, and one-point statistics of the various sky components. After component separation, the $1/f$ noise from LiteBIRD is effectively mitigated below the thermal SZ signal at all multipoles. Cosmological constraints on $S_8=\sigma_8\left(\Omega_{\rm m}/0.3\right)^{0.5}$ obtained from the LiteBIRD-Planck combined $y$-map power spectrum exhibits a 15% reduction in uncertainty compared to constraints from Planck alone. This improvement can be attributed to the increased portion of uncontaminated sky available in the LiteBIRD-Planck combined $y$-map., Comment: 38 pages, 13 figures, abstract shortened, submitted to JCAP

In this study, we investigate the decoherence of a spatially superposed electrically neutral spin-$\frac12$ particle in the presence of a relativistic quantum electromagnetic field in Minkowski spacetime. We demonstrate that decoherence due to the spin-magnetic field coupling can be categorized into two distinct factors: local decoherence, originating from the two-point correlation functions along each branch of the superposed trajectories, and nonlocal decoherence, which arises from the correlation functions between the two superposed trajectories. These effects are linked to phase damping and amplitude damping. We also show that if the quantum field is prepared in a thermal state, decoherence monotonically increases with the field temperature., Comment: (v1)17 pages, 4 figures

We propose a constrained generalized method of moments estimator (GMM) incorporating theoretical conditions for the unique existence of equilibrium prices for estimating conduct parameters in a log-linear model with homogeneous goods markets. First, we derive such conditions. Second, Monte Carlo simulations confirm that in a log-linear model, incorporating the conditions resolves the problems of implausibly low or negative values of conduct parameters., Comment: 7 pages, 12 page appendix

In this paper, we consider a proper K\"ahler fibration $f \colon X \to Y$ and a singular Hermitian line bundle $(L, h)$ on $X$ with semi-positive curvature. We prove that the direct image sheaf $f_{*}(\mathcal{O}_{X}(K_{X/Y}+L) \otimes \mathcal{I}(h))$, equipped with the Narasimhan-Simha metric, is singular Nakano semi-positive in the sense that the $\overline{\partial}$-equation can be solved with optimal $L^{2}$-estimate. Our proof does not rely on the theory of Griffiths positivity for the direct image sheaf., Comment: v2: 24 pages; added Section 4 to discuss the direct images of puri-canonical bundles; included an Appendix to summarize approximations of singular Hermitian metrics

We present the overview and first results from the North-PHASE Legacy Survey, which follows six young clusters for five years, using the 2 deg$^2$ FoV of the JAST80 telescope from the Javalambre Observatory (Spain). North-PHASE investigates stellar variability on timescales from days to years for thousands of young stars distributed over entire clusters. This allows us to find new YSO, characterise accretion and study inner disk evolution within the cluster context. Each region (Tr37, CepOB3, IC5070, IC348, NGC2264, and NGC1333) is observed in six filters (SDSS griz, u band, and J0660, which covers H$\alpha$), detecting cluster members as well as field variable stars. Tr37 is used to prove feasibility and optimise the variability analysis techniques. In Tr37, variability reveals 50 new YSO, most of them proper motion outliers. North-PHASE independently confirms the youth of astrometric members, efficiently distinguishes accreting and non-accreting stars, reveals the extent of the cluster populations along Tr37/IC1396 bright rims, and detects variability resulting from rotation, dips, and irregular bursts. The proper motion outliers unveil a more complex star formation history than inferred from Gaia alone, and variability highlights previously hidden proper motion deviations in the surrounding clouds. We also find that non-YSO variables identified by North-PHASE cover a different variability parameter space and include long-period variables, eclipsing binaries, RR Lyr, and $\delta$ Scuti stars. These early results also emphasize the power of variability to complete the picture of star formation where it is missed by astrometry., Comment: Accepted by MNRAS

Automatically assessing classroom discussion quality is becoming increasingly feasible with the help of new NLP advancements such as large language models (LLMs). In this work, we examine how the assessment performance of 2 LLMs interacts with 3 factors that may affect performance: task formulation, context length, and few-shot examples. We also explore the computational efficiency and predictive consistency of the 2 LLMs. Our results suggest that the 3 aforementioned factors do affect the performance of the tested LLMs and there is a relation between consistency and performance. We recommend a LLM-based assessment approach that has a good balance in terms of predictive performance, computational efficiency, and consistency., Comment: EDM 2024 Short Paper

LiteBIRD, the next-generation cosmic microwave background (CMB) experiment, aims for a launch in Japan's fiscal year 2032, marking a major advancement in the exploration of primordial cosmology and fundamental physics. Orbiting the Sun-Earth Lagrangian point L2, this JAXA-led strategic L-class mission will conduct a comprehensive mapping of the CMB polarization across the entire sky. During its 3-year mission, LiteBIRD will employ three telescopes within 15 unique frequency bands (ranging from 34 through 448 GHz), targeting a sensitivity of 2.2\,$\mu$K-arcmin and a resolution of 0.5$^\circ$ at 100\,GHz. Its primary goal is to measure the tensor-to-scalar ratio $r$ with an uncertainty $\delta r = 0.001$, including systematic errors and margin. If $r \geq 0.01$, LiteBIRD expects to achieve a $>5\sigma$ detection in the $\ell=$2-10 and $\ell=$11-200 ranges separately, providing crucial insight into the early Universe. We describe LiteBIRD's scientific objectives, the application of systems engineering to mission requirements, the anticipated scientific impact, and the operations and scanning strategies vital to minimizing systematic effects. We will also highlight LiteBIRD's synergies with concurrent CMB projects., Comment: 23 pages, 9 figures, 1 table, SPIE Astronomical Telescopes + Instrumentation 2024

We report the feasibility of detecting the gravity-induced entanglement (GIE) with optomechanical systems, which is the first investigation that clarifies the feasible experimental parameters to achieve a signal-to-noise ratio of S/N=1. Our proposal focuses on GIE generation between optomechanical mirrors, coupled via gravitational interactions, under continuous measurement, feedback control, and Kalman filtering process, which matured in connection with the field of gravitational wave observations. We solved the Riccati equation to evaluate the time evolution of the conditional covariance matrix for optomechanical mirrors that estimated the minimum variance of the motions. The results demonstrate that GIE is generated faster than a well-known time scale without optomechanical coupling. The fast generation of entanglement is associated with quantum-state squeezing by the Kalman filtering process, which is an advantage of using optomechanical systems to experimentally detect GIE., Comment: 5 pages, 4 figures

We investigated the magnetic helicity of the triple-$q$ magnetic structure of the triangular skyrmion lattice in the ``A-phase" of EuPtSi for a magnetic field along the [111] axis by resonant x-ray diffraction using a circularly polarized beam. We show that all three Fourier components of the triple-$q$ structure are perpendicular to the respective $q$ vectors and have the same helicity. They are connected by the rotation operations about the [111] axis. The helicity is the same as that of the single-$q$ helimagnetic phase at low fields, suggesting that the antisymmetric exchange interaction inherent in the chiral structure supports the formation of the triangular skyrmion lattice. We also observe that the helical plane in the helimagnetic phase is tilted to the magnetic field to form a conical structure before the first-order transition to the skyrmion lattice phase., Comment: 9 pages, 8 figures, Accepted for publication in Phys. Rev. B

Defects in semiconductors, traditionally seen as detrimental to electronic device performance, have emerged as potential assets in quantum technologies due to their unique quantum properties. This study investigates the interaction between defects and quantum electron transport in GaN/AlGaN field-effect transistors, highlighting the observation of Fano resonances at low temperatures. We observe the resonance spectra and their dependence on gate voltage and magnetic fields. To explain the observed behavior, we construct the possible scenario as a Fano interferometer with finite width. Our findings reveal the potential of semiconductor defects to contribute to the development of quantum information processing, providing their role to key components in next-generation quantum devices., Comment: 14 pages, 6 figures

In this paper, we solve the abundance conjecture for minimal projective klt varieties $X$ satisfying Miyaoka's equality $3c_2(X) = c_{1}(X)^{2}$. Specifically, we prove that the canonical divisor $K_{X}$ is semi-ample and the Kodaira dimension $\kappa(K_{X})$ is either $0$, $1$, or $2$. Moreover, according to the Kodaira dimension, we reveal the structure of the Iitaka fibration of $X$ up to quasi-\'etale covers. Additionally, we show similar results for projective klt varieties with nef anti-canonical divisor., Comment: v2: 33pages; minor revison (We revised Introduction and added references) v1: 32 pages; comments are welcome

The sense of touch is fundamental to how we interact with the physical and digital world. Conventional interactive surfaces and tactile interfaces use electronic sensors embedded into objects, however this approach poses serious challenges both for environmental sustainability and a future of truly ubiquitous interaction systems where information is encoded into everyday objects. In this work, we present Biodegradable Interactive Materials: backyard-compostable interactive interfaces that leverage information encoded in material properties. Inspired by natural systems, we propose an architecture that programmatically encodes multidimensional information into materials themselves and combines them with wearable devices that extend human senses to perceive the embedded data. We combine unrefined biological matter from plants and algae like chlorella with natural minerals like graphite and magnetite to produce materials with varying electrical, magnetic, and surface properties. We perform in-depth analysis using physics models, computational simulations, and real-world experiments to characterize their information density and develop decoding methods. Our passive, chip-less materials can robustly encode 12 bits of information, equivalent to 4096 unique classes. We further develop wearable device prototypes that can decode this information during touch interactions using off-the-shelf sensors. We demonstrate sample applications such as customized buttons, tactile maps, and interactive surfaces. We further demonstrate the natural degradation of these interactive materials in degrade outdoors within 21 days and perform a comparative environmental analysis of the benefits of this approach.

The formation history of Jupiter has been of interest due to its ability to shape the solar system's history. Yet little attention has been paid to the formation and growth of Saturn and the other giant planets. Here, we explore the implications of the simplest disc and pebble accretion model with steady-state accretion on the formation of giant planets in the solar system through N-body simulations. We conducted a statistical survey of different disc parameters and initial conditions of the protoplanetary disc to establish which combination best reproduces the present outer solar system. We examined the effect of the initial planetesimal disc mass, the number of planetesimals and their size-frequency distribution slope, pebble accretion prescription, and sticking efficiency on the likelihood of forming gas giants and their orbital distribution. The results reveal that the accretion sticking efficiency is the most sensitive parameter for controlling the final masses and number of giant planets. We have been unable to replicate the formation of all three types of giant planets in the solar system in a single simulation. The probability distribution of the final location of the giant planets is approximately constant in $\log r$, suggesting there is a slight preference for formation closer to the Sun but no preference for more massive planets to form closer. The eccentricity distribution has a higher mean for more massive planets, indicating that systems with more massive planets are more violent. The formation timescales of the cores of the gas giants are distinct, suggesting that they formed sequentially., Comment: 17 pages, 18 figures, 1 table

We propose methods and an architecture to conduct measurements and optimize newly installed optical fiber line systems semi-automatically using integrated physics-aware technologies in a data center interconnection (DCI) transmission scenario. We demonstrate, for the first time, digital longitudinal monitoring (DLM) and optical line system (OLS) physical parameter calibration working together in real-time to extract physical link parameters for transmission performance optimization. Our methodology has the following advantages over traditional design: a minimized footprint at user sites, accurate estimation of the necessary optical network characteristics via complementary telemetry technologies, and the capability to conduct all operation work remotely. The last feature is crucial, as it enables remote operation to implement network design settings for immediate response to quality of transmission (QoT) degradation and reversion in the case of unforeseen problems. We successfully performed semi-automatic line system provisioning over field fiber networks facilities at Duke University, Durham, NC. The tasks of parameter retrieval, equipment setting optimization, and system setup/provisioning were completed within 1 hour. The field operation was supervised by on-duty personnel who could access the system remotely from different time zones. By comparing Q-factor estimates calculated from the extracted link parameters with measured results from 400G transceivers, we confirmed that our methodology has a reduction in the QoT prediction errors (+-0.3 dB) over existing design (+-10.6 dB).

Self-report measures (e.g., Likert scales) are widely used to evaluate subjective health perceptions. Recently, the visual analog scale (VAS), a slider-based scale, has become popular owing to its ability to precisely and easily assess how people feel. These data can be influenced by the response style (RS), a user-dependent systematic tendency that occurs regardless of questionnaire instructions. Despite its importance, especially in between-individual analysis, little attention has been paid to handling the RS in the VAS (denoted as response profile (RP)), as it is mainly used for within-individual monitoring and is less affected by RP. However, VAS measurements often require repeated self-reports of the same questionnaire items, making it difficult to apply conventional methods on a Likert scale. In this study, we developed a novel RP characterization method for various types of repeatedly measured VAS data. This approach involves the modeling of RP as distributional parameters ${\theta}$ through a mixture of RS-like distributions, and addressing the issue of unbalanced data through bootstrap sampling for treating repeated measures. We assessed the effectiveness of the proposed method using simulated pseudo-data and an actual dataset from an empirical study. The assessment of parameter recovery showed that our method accurately estimated the RP parameter ${\theta}$, demonstrating its robustness. Moreover, applying our method to an actual VAS dataset revealed the presence of individual RP heterogeneity, even in repeated VAS measurements, similar to the findings of the Likert scale. Our proposed method enables RP heterogeneity-aware VAS data analysis, similar to Likert-scale data analysis., Comment: Accepted to IEEE Access. Accessible at https://ieeexplore.ieee.org/document/10638535

Superconductivity was recently reported in several quasicrystalline systems. These are materials which are structurally ordered, but since they are not translationally invariant, the usual BCS theory does not apply. At the present time, the underlying mechanism and the properties of the superconducting phase are insufficiently understood. To gain a better understanding of quasiperiodic superconductors, we consider the attractive Hubbard model on the Fibonacci chain, and examine its low-temperature superconducting phase in detail using the Bogoliubov-de Gennes mean-field approach. We obtain superconducting solutions as a function of the parameters controlling the physical properties of the system: the strength of the Hubbard attraction $U$, the chemical potential $\mu$, and the strength of the modulation of the Fibonacci Hamiltonian, $w$. We find that there is a bulk transition at a critical temperature that obeys a power law in $U$. The local superconducting order parameter is self-similar both in real and perpendicular space. The local densities of states vary from site to site, however, the width of the superconducting gap is the same on all sites. The interplay between the Hubbard attraction and the intrinsic gaps of the Fibonacci chain results in a complex zero-temperature $\mu$-$U$ phase diagram with insulating domes surrounded by superconducting regions. Finally, we show that tuning $w$ from weak to strong quasicrystalline modulation gives rise to qualitatively different thermodynamic behaviors as could be observed by measuring the specific heat.

The Simons Observatory (SO) experiment is a cosmic microwave background (CMB) experiment located in the Atacama Desert, Chile. The SO' s small aperture telescopes (SATs) consist of three telescopes designed for precise CMB polarimetry at large angular scales. Each SAT uses a cryogenic rotating half-wave plate (HWP) as a polarization modulator to mitigate atmospheric 1/f noise and other systematics. To realize efficient polarization modulation over the observation bands, we fabricated an achromatic HWP (AHWP) consisting of three sapphire plates with anti-reflection coatings. The AHWP is designed to have broadband modulation efficiency and transmittance. This paper reports on the design and the preliminary characterization of the AHWPs for SATs.

This paper studies the approximation of singular Hermitian metrics on vector bundles using smooth Hermitian metrics with Nakano semi-positive curvature on Zariski open sets. We show that singular Hermitian metrics capable of this approximation satisfy Nakano semi-positivity as defined through the $\overline{\partial} $-equation with optimal $L^2$-estimates. Furthermore, for a projective fibration $f \colon X \to Y$ with a line bundle $L$ on $X$, we provide a specific condition under which the Narasimhan-Simha metric on the direct image sheaf $f_{*}\mathcal{O}_{X}(K_{X/Y}+L)$ admits this approximation. As an application, we establish several vanishing theorems., Comment: 18 pages; comments are welcome

We report 850 $\mu$m continuum polarization observations toward the filamentary high-mass star-forming region NGC 2264, taken as part of the B-fields In STar forming Regions Observations (BISTRO) large program on the James Clerk Maxwell Telescope (JCMT). These data reveal a well-structured non-uniform magnetic field in the NGC 2264C and 2264D regions with a prevailing orientation around 30 deg from north to east. Field strengths estimates and a virial analysis for the major clumps indicate that NGC 2264C is globally dominated by gravity while in 2264D magnetic, gravitational, and kinetic energies are roughly balanced. We present an analysis scheme that utilizes the locally resolved magnetic field structures, together with the locally measured gravitational vector field and the extracted filamentary network. From this, we infer statistical trends showing that this network consists of two main groups of filaments oriented approximately perpendicular to one another. Additionally, gravity shows one dominating converging direction that is roughly perpendicular to one of the filament orientations, which is suggestive of mass accretion along this direction. Beyond these statistical trends, we identify two types of filaments. The type-I filament is perpendicular to the magnetic field with local gravity transitioning from parallel to perpendicular to the magnetic field from the outside to the filament ridge. The type-II filament is parallel to the magnetic field and local gravity. We interpret these two types of filaments as originating from the competition between radial collapsing, driven by filament self-gravity, and the longitudinal collapsing, driven by the region's global gravity., Comment: Accepted for publication in the Astrophysical Journal. 43 pages, 32 figures, and 4 tables (including Appendix)