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The structure of an Al(111)3x3-Si surface was examined by combining data from positron diffraction and core-level photoemission spectroscopy. Analysis of the diffraction rocking curves indicated that the overlayer had a flat honeycomb lattice structure. Simulations of Si core-level spectra calculated via the first-principles indicated that one of the Si atoms in the unit cell was replaced by an Al atom. The surface superstructure was thus a two-dimensional layer of Al-embedded silicene on Al(111).

Robots operating in the real world face significant but unavoidable issues in object localization that must be dealt with. A typical approach to address this is the addition of compliance mechanisms to hardware to absorb and compensate for some of these errors. However, for fine-grained manipulation tasks, the location and choice of appropriate compliance mechanisms are critical for success. For objects to be inserted in a target site on a flat surface, the object must first be successfully aligned with the opening of the slot, as well as correctly oriented along its central axis, before it can be inserted. We developed the Four-Axis Adaptive Finger Hand (FAAF hand) that is equipped with fingers that can passively adapt in four axes (x, y, z, yaw) enabling it to perform insertion tasks including lid fitting in the presence of significant localization errors. Furthermore, this adaptivity allows the use of simple control methods without requiring contact sensors or other devices. Our results confirm the ability of the FAAF hand on challenging insertion tasks of square and triangle-shaped pegs (or prisms) and placing of container lids in the presence of position errors in all directions and rotational error along the object's central axis, using a simple control scheme., Comment: 8 pages. Accepted at IEEE IROS 2024. An accompanying video is available at https://www.youtube.com/watch?v=s3yf2MQ5Pag

We mathematically show an equality between the index of a Dirac operator on a flat continuum torus and the $\eta$ invariant of the Wilson Dirac operator with a negative mass when the lattice spacing is sufficiently small. Unlike the standard approach, our formulation using $K$-theory does not require the Ginsparg-Wilson relation or the modified chiral symmetry on the lattice. We prove that a one-parameter family of continuum massive Dirac operators and the corresponding Wilson Dirac operators belong to the same equivalence class of the $K^1$ group at a finite lattice spacing. Their indices, which are evaluated by the spectral flow or equivalently by the $\eta$ invariant at finite masses, are proved to be equal., Comment: 51 pages, 3 figures

We report on ALMA ACA observations of a high-density region of the Corona Australis cloud forming a young star cluster, and the results of resolving internal structures. In addition to embedded Class 0/I protostars in continuum, a number of complex dense filamentary structures are detected in the C18O and SO lines by the 7m array. These are sub-structures of the molecular clump that are detected by the TP array as the extended emission. We identify 101 and 37 filamentary structures with a few thousand AU widths in C18O and SO, respectively, called as feathers. The typical column density of the feathers in C18O is about 10^{22} cm^{-2}, and the volume density and line mass are ~ 10^5 cm^{-3}, and a few times M_{sun} pc^{-1}, respectively. This line mass is significantly smaller than the critical line mass expected for cold and dense gas. These structures have complex velocity fields, indicating a turbulent internal property. The number of feathers associated with Class 0/I protostars is only ~ 10, indicating that most of them do not form stars but rather being transient structures. The formation of feathers can be interpreted as a result of colliding gas flow as the morphology well reproduced by MHD simulations, supported by the the presence of HI shells in the vicinity. The colliding gas flows may accumulate gas and form filaments and feathers, and trigger the active star formation of the R CrA cluster., Comment: 24 pages, 13 figures; Accepted for publication in ApJ

Acquiring accurate depth information of transparent objects using off-the-shelf RGB-D cameras is a well-known challenge in Computer Vision and Robotics. Depth estimation/completion methods are typically employed and trained on datasets with quality depth labels acquired from either simulation, additional sensors or specialized data collection setups and known 3d models. However, acquiring reliable depth information for datasets at scale is not straightforward, limiting training scalability and generalization. Neural Radiance Fields (NeRFs) are learning-free approaches and have demonstrated wide success in novel view synthesis and shape recovery. However, heuristics and controlled environments (lights, backgrounds, etc) are often required to accurately capture specular surfaces. In this paper, we propose using Visual Foundation Models (VFMs) for segmentation in a zero-shot, label-free way to guide the NeRF reconstruction process for these objects via the simultaneous reconstruction of semantic fields and extensions to increase robustness. Our proposed method Segmentation-AIDed NeRF (SAID-NeRF) shows significant performance on depth completion datasets for transparent objects and robotic grasping., Comment: 8 pages. An accompanying video is available at https://www.youtube.com/watch?v=S4NCoUq4bmE

We investigate supercurrent nonreciprocal effects in a superconducting weak-link hosting distinct types of vortices. We demonstrate how the winding number of the vortex, its spatial configuration and the shape of the superconducting lead can steer the sign and amplitude of the supercurrent rectification. We find a general criterion for the vortex pattern to maximize the rectification amplitude of the supercurrent. The underlying strategy is the search of specific vortex core position yielding a vanishing amplitude of the supercurrent first harmonic. We also prove that supercurrent nonreciprocal effects can be used to diagnose high-winding vortex and to distinguish between different types of vorticity. Our results thus provide a toolkit to control the supercurrent rectification by means of vortex phase textures and nonreciprocal signatures to detect vortex states with nonstandard phase patterns., Comment: 7 pages and 3 figures + 9 pages and 6 figures

Recent Atacama Large Millimeter/submillimeter Array (ALMA) observations have revealed an increasing number of compact protostellar disks with radii of less than a few tens of astronomical units and that young Class 0/I objects have an intrinsic size diversity. To deepen our understanding of the origin of such tiny disks, we performed the highest-resolution configuration observations with ALMA at a beam size of $\sim$0$''$03 (4 au) on the very low-luminosity Class 0 protostar embedded in the Taurus dense core MC 27/L1521F. The 1.3 mm continuum measurement successfully resolved a tiny, faint ($\sim$1 mJy) disk with a major axis length of $\sim$10 au, one of the smallest examples in the ALMA protostellar studies. In addition, we detected spike-like components in the northeastern direction at the disk edge. Gravitational instability or other fragmentation mechanisms cannot explain the structures, given the central stellar mass of $\sim$0.2 $M_{\odot}$ and the disk mass of $\gtrsim$10$^{-4}$ $M_{\odot}$. Instead, we propose that these small spike structures were formed by a recent dynamic magnetic flux transport event due to interchange instability that would be favorable to occur if the parental core has a strong magnetic field. The presence of complex arc-like structures on a larger ($\sim$2000 au) scale in the same direction as the spike structures suggests that the event was not single. Such episodic, dynamical events may play an important role in maintaining the compact nature of the protostellar disk in the complex gas envelope during the main accretion phase., Comment: 13 pages, 5 figures, Accepted for publication in ApJ

This is a corrigendum of Lemma 9.1 of the paper [FOOO3] in the title. This lemma is not correct as pointed out by A. Daemi and a referee of the paper [DF]. The corrigendum does not affect the applications of this lemma in [FOOO3] and other papers and exactly the same proofs as therein apply if one replaces the statement of [FOOO3,Lemma 9.1] by Lemma 2 of the present note., Comment: 7 pages

We show that under appropriate assumptions, a blown-up corona of a relatively hyperbolic group is equivariant and the compactification of the universal space for proper action by the blown-up corona is contractible. As a corollary, we establish the formula to determine the covering dimension of the blown-up corona by the cohomological dimension of the group. We also show that the blown-up corona of a hyperbolic group with respect to an almost malnormal family of quasiconvex subgroups is homeomorphic to the Gromov boundary of the group., Comment: 32 pages

In the standard lattice domain-wall fermion formulation, one needs two flat domain-walls where both of the left- and right-handed massless modes appear. In this work we investigate a single domain-wall system with a nontrivial curved background. Specifically we consider a massive fermion on a $3D$ square lattice, whose domain-wall is a $2D$ sphere. In the free theory, we find that a single Weyl fermion is localized at the wall and it feels gravity through the induced spin connection. With a topologically nontrivial $U(1)$ link gauge field, however, we find a zero mode with the opposite chirality localized at the center where the gauge field is singular. In the latter case, the low-energy effective theory is not chiral but vectorlike. We discuss how to circumvent this obstacle in formulating lattice chiral gauge theory in the single domain-wall fermion system., Comment: 26 pages, 12 figures, minor corrections, published version

In this paper, we compute (co)homologies of ideal boundaries of free products of geodesic coarsely convex spaces in terms of those of each of the components. The (co)homology theories we consider are, $K$-theory, Alexander-Spanier cohomology, $K$-homology, and Steenrod homology. These computations led to the computation of $K$-theory of the Roe algebra of free products of geodesic coarsely convex spaces via the coarse Baum-Connes conjecture., Comment: 32 pages, 3 figures

We study the $U(1)_A$ anomaly at high temperatures of $N_f=2+1$ lattice QCD with chiral fermions. Gauge ensembles are generated with M\"obius domain-wall (MDW) fermions, and the measurements are reweighted to those with overlap fermions. We report on the results for the Dirac spectra, the $U(1)_A$ susceptibility, and the topological susceptibility in the temperature range of $T=136$, $153$, $175$, and $204$ MeV, where the up and down quark masses are set to be near the physical point as well as at lighter or heavier masses., Comment: 10 pages, 4 figures, 1 table; Proceedings of the 40th International Symposium on Lattice Field Theory (Lattice 2023), July 31st - August 4th, 2023, Fermilab, Batavia, Illinois, USA

Based on simulations of 2+1 flavor lattice QCD with M\"obius domain wall fermions at high temperatures, we compute a series of spatial correlation functions to study the screening masses in mesonic states. We compare these masses with the symmetry relations for various quark masses and lattice sizes at temperatures above the critical point. Using these spatial correlation functions we examine the $SU(2)_L \times SU(2)_R$ symmetry as well as the anomalously broken axial $U(1)_A$ symmetry. Additionally we explore a possible and emergent chiral-spin symmetry $SU(2)_{CS}$., Comment: 10 pages, 5 figures, Contribution to the 40th International Symposium on Lattice Field Theory (Lattice 2023)

We investigate relations between the chiral susceptibility and axial $U(1)$ anomaly in lattice QCD at high temperatures. Employing the exactly chiral symmetric Dirac operator, we separate the purely axial $U(1)$ breaking effect in the connected and disconnected chiral susceptibilites in a theoretically clean manner. Preliminary results for two-flavor lattice QCD near the critical temperature are presented., Comment: 9 pages, 3 figures, LATTICE2023, minor corrections

In this article, we analyze a magnetic monopole in topological insulators. The monopole obtain a fractional electric charge because of the Witten effect. We consider this system with a microscopic view by adding the Wilson term to the ordinary Dirac Hamiltonian. The Wilson term yields the positive mass shift to the effective mass of the electrons, then the curved domain-wall is dynamically generated around the monopole. The zero-modes of the electrons are localized on the domain-wall, which can be identified as the source of the electric charge., Comment: 9 pages, contribution to the 40th International Symposium on Lattice Field Theory (Lattice2023), July 31st - August 4th, 2023, Fermi National Accelerator Laboratory

We report on a lattice fermion formulation with a curved domain-wall mass term to nonperturbatively describe fermions in a gravitational background. In our previous work in 2022, we showed under the time-reversal symmetry that the edge-localized massless Dirac fermion appears on one and two-dimensional spherical domain-walls and the spin connection is induced on the lattice in a consistent way with continuum theory. In this work, we extend our study to the Shamir type curved domain-wall fermions without the time-reversal symmetry. We find in the free fermion case that a single Weyl fermion appears on the edge, and feels gravity through the induced spin connection. With a topologically nontrivial $U(1)$ gauge potential, however, we find an oppositely chiral zero mode at the center where the gauge field is singular., Comment: 9 pages, 6 figures. Talk presented at the 40th International Symposium on Lattice Field Theory (Lattice2023), 31 July - 4 August 2023, Fermi National Accelerator Laboratory, minor corrections

Back-action refers to a response that retro-acts on a system to tailor its properties with respect to an external stimulus. This self-induced effect generally belongs to both the natural and technological realm, ranging from neural networks to optics and electronic circuitry. In electronics, back-action mechanisms are at the heart of many classes of devices such as amplifiers, oscillators, and sensors. Here, we demonstrate that back-action can be successfully exploited to achieve $\textit{non-reciprocal}$ transport in superconducting circuits. Our device realizes a supercurrent diode, since the dissipationless current flows in one direction whereas dissipative transport occurs in the opposite direction. Supercurrent diodes presented so far rely on magnetic elements or vortices to mediate charge transport or external magnetic fields to break time-reversal symmetry. In our implementation, back-action solely turns a conventional reciprocal superconducting weak link with no asymmetry between the current bias directions into a diode, where the critical current amplitude depends on the bias sign. The self-interaction of the supercurrent with the device stems from the gate tunability of the critical current, which uniquely promotes up to $\sim$88% of magnetic field-free signal rectification and diode functionality with selectable polarity. The concept we introduce is very general and can be applied directly to a large variety of devices, thereby opening novel functionalities in superconducting electronics.

Procedural content generation (PCG) can be applied to a wide variety of tasks in games, from narratives, levels and sounds, to trees and weapons. A large amount of game content is comprised of graphical assets, such as clouds, buildings or vegetation, that do not require gameplay function considerations. There is also a breadth of literature examining the procedural generation of such elements for purposes outside of games. The body of research, focused on specific methods for generating specific assets, provides a narrow view of the available possibilities. Hence, it is difficult to have a clear picture of all approaches and possibilities, with no guide for interested parties to discover possible methods and approaches for their needs, and no facility to guide them through each technique or approach to map out the process of using them. Therefore, a systematic literature review has been conducted, yielding 200 accepted papers. This paper explores state-of-the-art approaches to graphical asset generation, examining research from a wide range of applications, inside and outside of games. Informed by the literature, a conceptual framework has been derived to address the aforementioned gaps.

Micro well-plates are an apparatus commonly used in chemical and biological experiments that are a few centimeters thick and contain wells or divets. In this paper, we aim to solve the task of placing the well-plate onto a well-plate holder (referred to as holder). This task is challenging due to the holder's raised grooves being a few millimeters in height, with a clearance of less than 1 mm between the well-plate and holder, thus requiring precise control during placing. Our placing task has the following challenges: 1) The holder's detected pose is uncertain; 2) the required accuracy is at the millimeter to sub-millimeter level due to the raised groove's shallow height and small clearance; 3) the holder is not fixed to a desk and is susceptible to movement from external forces. To address these challenges, we developed methods including a) using tactile sensors for accurate pose estimation of the grasped well-plate to handle issue (1); b) sliding the well-plate onto the target holder while maintaining contact with the holder's groove and estimating its orientation for accurate alignment. This allows for high precision control (addressing issue (2)) and prevents displacement of the holder during placement (addressing issue (3)). We demonstrate a high success rate for the well-plate placing task, even under noisy observation of the holder's pose., Comment: 8 pages, 8 figures, an accompanying video is available at the following link: https://www.youtube.com/watch?v=noyxIYfVxq0

Transferring a significant fraction of the magnetic flux from a dense cloud core is essential in the star formation process. A ring-like structure produced by magnetic flux loss has been predicted theoretically, but no observational identification has been presented. We have performed ALMA observations of the Class I protostar IRS 2 in the Corona Australis star-forming region and resolved a distinctive gas ring in the C$^{18}$O ($J$ = 2-1) line emission. The center of this gas ring is $\sim$5,000 au away from the protostar, with a diameter of $\sim$7,000 au. The radial velocity of the gas is $\lesssim1$ km s$^{-1}$ blueshifted from that of the protostar, with a possible expanding feature judged from the velocity-field (moment 1) map and position-velocity diagram. These features are either observationally new or have been discovered but not discussed in depth because they are difficult to explain by well-studied protostellar phenomena such as molecular outflows and accretion streamers. A plausible interpretation is a magnetic wall created by the advection of magnetic flux which is theoretically expected in the Class 0/I phase during star formation as a removal mechanism of magnetic flux. Similar structures reported in the other young stellar sources could likely be candidates formed by the same mechanism, encouraging us to revisit the issue of magnetic flux transport in the early stages of star formation from an observational perspective., Comment: 9 pages, 3 figures, Accepted for publication in the Astronomical Journal Letters

A problem that plagues robotic grasping is the misalignment of the object and gripper due to difficulties in precise localization, actuation, etc. Under-actuated robotic hands with compliant mechanisms are used to adapt and compensate for these inaccuracies. However, these mechanisms come at the cost of controllability and coordination. For instance, adaptive functions that let the fingers of a two-fingered gripper adapt independently may affect the coordination necessary for grasping small objects. In this work, we develop a two-fingered robotic hand capable of grasping objects that are offset from the gripper's center, while still having the requisite coordination for grasping small objects via a novel gear-type synchronization mechanism with a magnet. This gear synchronization mechanism allows the adaptive finger's tips to be aligned enabling it to grasp objects as small as toothpicks and washers. The magnetic component allows this coordination to automatically turn off when needed, allowing for the grasping of objects that are offset/misaligned from the gripper. This equips the hand with the capability of grasping light, fragile objects (strawberries, creampuffs, etc) to heavy frying pan lids, all while maintaining their position and posture which is vital in numerous applications that require precise positioning or careful manipulation., Comment: 8 pages. Accepted at IEEE IROS 2023. An accompanying video is available at https://www.youtube.com/watch?v=RAO7Qb2ZGNs

This is a survey of various types of Floer theories (both in symplectic geometry and gauge theory) and relations among them., Comment: 56 pages 12 Figures

We calculate the form factors for the $B \to D^*\ell\nu_\ell$ decay in 2+1 flavor lattice QCD. For all quark flavors, we employ the M\"obius domain-wall action, which preserves chiral symmetry to a good precision. Our gauge ensembles are generated at three lattice cutoffs $a^{-1} \sim 2.5$, 3.6 and 4.5 GeV with pion masses as low as $M_\pi \sim 230$ MeV. The physical lattice size $L$ satisfies the condition $M_\pi L \geq 4$ to control finite volume effects (FVEs), while we simulate a smaller size at the smallest $M_\pi$ to directly examine FVEs. The bottom quark masses are chosen in a range from the physical charm quark mass to $0.7 a^{-1}$ to control discretization effects. We extrapolate the form factors to the continuum limit and physical quark masses based on heavy meson chiral perturbation theory at next-to-leading order. Then the recoil parameter dependence is parametrized using a model independent form leading to our estimate of the decay rate ratio between the tau ($\ell = \tau$) and light lepton ($\ell = e,\mu$) channels $R(D^*) = 0.252(22)$ in the Standard Model. A simultaneous fit with recent data from the Belle experiment yields $|V_{cb}| = 39.19(91)\times 10^{-3}$, which is consistent with previous exclusive determinations, and shows good consistency in the kinematical distribution of the differential decay rate between the lattice and experimental data., Comment: 45 pages, 19 figures; v2: version published in PRD

Supercurrent diodes are nonreciprocal electronic elements whose switching current depends on their flow direction. Recently, a variety of composite systems combining different materials and engineered asymmetric superconducting devices have been proposed. Yet, ease of fabrication and tunable sign of supercurrent rectification joined to large efficiency have not been assessed in a single platform so far. We demonstrate that all-metallic superconducting Dayem nanobridges naturally exhibit nonreciprocal supercurrents under an external magnetic field, with a rectification efficiency up to $\sim 27\%$. Our niobium nanostructures are tailored so that the diode polarity can be tuned by varying the amplitude of an out-of-plane magnetic field or the temperature in a regime without magnetic screening. We show that sign reversal of the diode effect may arise from the high-harmonic content of the current phase relation in combination with vortex phase windings present in the bridge or an anomalous phase shift compatible with anisotropic spin-orbit interactions.

We consider a double power nonlinear Schr\"odinger equation which possesses the algebraically decaying stationary solution $\phi_0$ as well as exponentially decaying standing waves $e^{i\omega t}\phi_\omega(x)$ with $\omega>0$. It is well-known from the general theory that stability properties of standing waves are determined by the derivative of $\omega\mapsto M(\omega):=\frac{1}{2}\|\phi_\omega\|_{L^2}^2$; namely $e^{i\omega t}\phi_\omega$ with $\omega>0$ is stable if $M'(\omega)>0$ and unstable if $M'(\omega)<0$. However, the stability/instability of stationary solutions is outside the general theory from the viewpoint of spectral properties of linearized operators. In this paper we prove the instability of the stationary solution $\phi_0$ in one dimension under the condition $M'(0):=\lim_{\omega\downarrow 0}M'(\omega)\in[-\infty, 0)$. The key in the proof is the construction of the one-sided derivative of $\omega\mapsto\phi_\omega$ at $\omega=0$, which is effectively used to construct the unstable direction of $\phi_0$., Comment: 26 pages, 2 figures

The Witten effect predicts that a magnetic monopole acquires a fractional electric charge inside topological insulators. In this work, we give a microscopic description of this phenomenon, as well as an analogous two-dimensional system with a vortex. We solve the Dirac equation of electron field both analytically in continuum and numerically on a lattice, by adding the Wilson term and smearing the gauge field within a finite range to regularize the short-distance behavior of the system. Our results reveal that the Wilson term induces a strong positive mass shift, creating a domain-wall around the monopole/vortex. This small, yet finite-sized domain-wall localizes the chiral zero modes and ensures their stability through the Atiyah-Singer index theorem, whose cobordism invariance is crucial in explaining why the electric charge is fractional., Comment: 40 pages, 10 figures, minor corrections, references added, published version

The first author and Oguni introduced a wide class of metric spaces, called coarsely convex spaces. It includes Gromov hyperbolic metric spaces, CAT(0) spaces, systolic complexes, proper injective metric spaces. We introduce the notion of free products of metric spaces and show that free products of symmetric geodesic coarsely convex spaces are also symmetric geodesic coarsely convex spaces. As an application, it follows that free products of symmetric geodesic coarsely convex spaces satisfy the coarse Baum-Connes conjecture., Comment: 30 pages, 11 figures

We report on our finite temperature 2+1 flavor lattice QCD simulation to study the thermodynamic properties of QCD near the (pseudo) critical point employing $N_T=12$ and $16$. The simulation points are chosen along the lines of constant physics. The quark mass for M\"obius domain-wall fermion are tuned by taking into account the residual mass either by fine-tuning the input quark masses or by post-process using reweighting. In this talk, we focus on simulation details and present some preliminary results., Comment: 8 pages, contribution to the 39th International Symposium on Lattice Field theory (LATTICE2022), 8th-13th August, 2022, Bonn, Germany

We investigate the effect of $U (1)$ gauge field on lattice fermion systems with a curved domain-wall mass term. In the same way as the conventional flat domain-wall fermion, the chiral edge modes appear localized at the wall, whose Dirac operator contains the induced gravitational potential as well as the $U(1)$ vector potential. In the case of $S^1$ domain-wall fermion on a two-dimensional flat lattice, we find a competition between the Aharonov-Bohm(AB) effect and gravitational gap in the Dirac eigenvalue spectrum, which leads to anomaly of the time-reversal ($T$) symmetry. Our numerical result shows a good consistency with the Atiyah-Patodi-Singer index theorem on a disk inside the $S^1$ domain-wall, which describes the cancellation of the $T$ anomaly between the bulk and edge. When the $U(1)$ flux is squeezed inside one plaquette, and the AB phase takes a quantized value $\pi$ mod $2\pi\mathbb{Z}$, the anomaly inflow drastically changes: the strong flux creates another domain-wall around the flux to make the two zero modes coexist. This phenomenon is also observed in the $S^2$ domain-wall fermion in the presence of a magnetic monopole. We find that the domain-wall creation around the monopole microscopically explains the Witten effect., Comment: 30 pages, 13 figures, minor corrections

Understanding the initial conditions of star formation requires both observational studies and theoretical works taking into account the magnetic field, which plays an important role in star formation processes. Herein, we study the young nearby dense cloud core L1521 F ($n$(H$_2$) $\sim 10^{4-6}$ cm$^{-3}$) in the Taurus Molecular Cloud. This dense core hosts a 0.2 $M_\odot$ protostar, categorized as a Very Low Luminosity Objects with complex velocity structures, particularly in the vicinity of the protostar. To trace the magnetic field within the dense core, we conducted high sensitivity submillimeter polarimetry of the dust continuum at $\lambda$= 850 $\mu$m and 450 $\mu$m using the POL-2 polarimeter situated in front of the SCUBA-2 submillimeter bolometer camera on James Clerk Maxwell Tetescope. This was compared with millimeter polarimetry taken at $\lambda$= 3.3 mm with ALMA. The magnetic field was detected at $\lambda$= 850 $\mu$m in the peripheral region, which is threaded in a north-south direction, while the central region traced at $\lambda$= 450 $\mu$m shows a magnetic field with an east-west direction, i.e., orthogonal to that of the peripheral region. Magnetic field strengths are estimated to be $\sim$70 $\mu$G and 200 $\mu$G in the peripheral- and central-regions, respectively, using the Davis-Chandrasekhar-Fermi method. The resulting mass-to-flux ratio of 3 times larger than that of magnetically critical state for both regions indicates that L1521 F is magnetically supercritical, i.e., gravitational forces dominate over magnetic turbulence forces. Combining observational data with MHD simulations, detailed parameters of the morphological properties of this puzzling object are derived for the first time., Comment: 9 pages, 7 figures

This is the third paper in a series of papers studying intersection Floer theory of Lagrangians in the complement of a smooth divisor. We complete the construction of Floer homology for such Lagrangians., Comment: 56 pages, 8 figures. This paper is born out of the revisions of 1808.08915 and 1809.03409, where some parts of the older versions of 1808.08915 and 1809.03409 are moved here. We also added a brief speculative discussion at the end about a generalization of our construction to the case of non-compact Lagrangians and its formal similarity to the definition of monopole Floer homology