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We analyze the local dynamics of magnetotail reconnection onset using Magnetospheric Multiscale (MMS) data. In conjunction with MMS, the macroscopic dynamics of this event were captured by a number of other ground and space-based observatories, as is reported in a companion paper. We find that the local dynamics of the onset were characterized by the rapid thinning of the cross-tail current sheet below the ion inertial scale, accompanied by the growth of flapping waves and the subsequent onset of electron tearing. Multiple kinetic-scale magnetic islands were detected coincident with the growth of an initially sub-Alfv\'enic, demagnetized tailward ion exhaust. The onset and rapid enhancement of parallel electron inflow at the exhaust boundary was a remote signature of the intensification of reconnection Earthward of the spacecraft. Two secondary reconnection sites are found embedded within the exhaust from a primary X-line. The primary X-line was designated as such on the basis that (1) while multiple jet reversals were observed in the current sheet, only one reversal of the electron inflow was observed at the high-latitude exhaust boundary, (2) the reconnection electric field was roughly 5 times larger at the primary X-line than the secondary X-lines, and (3) energetic electron fluxes increased and transitioned from anti-field-aligned to isotropic during the primary X-line crossing, indicating a change in magnetic topology. The results are consistent with the idea that a primary X-line mediates the reconnection of lobe magnetic field lines and accelerates electrons more efficiently than its secondary X-line counterparts., Comment: In press, JGR Space Physics, JGRA58162

We analyze a magnetotail reconnection onset event on 3 July 2017 that was observed under otherwise quiescent magnetospheric conditions by a fortuitous conjunction of six space and ground-based observatories. The study investigates the large-scale coupling of the solar wind - magnetosphere system that precipitated the onset of the magnetotail reconnection, focusing on the processes that thinned and stretched the cross-tail current layer in the absence of significant flux loading during a two-hour-long preconditioning phase. It is demonstrated with data in the (1) upstream solar wind, (2) at the low-latitude magnetopause, (3) in the high-latitude polar cap, and (4) in the magnetotail that the typical picture of solar wind-driven current sheet thinning via flux loading does not appear relevant for this particular event. We find that the current sheet thinning was, instead, initiated by a transient solar wind pressure pulse and that the current sheet thinning continued even as the magnetotail and solar wind pressures decreased. We suggest that field line curvature induced scattering (observed by Magnetospheric Multiscale (MMS)) and precipitation (observed by Defense Meteorological Satellite Program (DMSP)) of high-energy thermal protons may have evacuated plasma sheet thermal energy, which may require a thinning of the plasma sheet to preserve pressure equilibrium with the solar wind., Comment: In press, JGR space physics, JGRA58161

We present EUV solar observations showing evidence for omnipresent jetting activity driven by small-scale magnetic reconnection at the base of the solar corona. We argue that the physical mechanism that heats and drives the solar wind at its source is ubiquitous magnetic reconnection in the form of small-scale jetting activity (i.e., a.k.a. jetlets). This jetting activity, like the solar wind and the heating of the coronal plasma, are ubiquitous regardless of the solar cycle phase. Each event arises from small-scale reconnection of opposite polarity magnetic fields producing a short-lived jet of hot plasma and Alfv\'en waves into the corona. The discrete nature of these jetlet events leads to intermittent outflows from the corona, which homogenize as they propagate away from the Sun and form the solar wind. This discovery establishes the importance of small-scale magnetic reconnection in solar and stellar atmospheres in understanding ubiquitous phenomena such as coronal heating and solar wind acceleration. Based on previous analyses linking the switchbacks to the magnetic network, we also argue that these new observations might provide the link between the magnetic activity at the base of the corona and the switchback solar wind phenomenon. These new observations need to be put in the bigger picture of the role of magnetic reconnection and the diverse form of jetting in the solar atmosphere., Comment: 10 pages, 4 figures

The fast solar wind that fills the heliosphere originates from deep within regions of open magnetic field on the Sun called coronal holes. The energy source responsible for accelerating the plasma to high speeds is widely debated, however there is evidence that it is ultimately magnetic in nature with candidate mechanisms including wave heating^(1,2) and interchange reconnection^(3,4,5). The coronal magnetic field near the solar surface is structured on scales associated with supergranulation convection cells, where descending flows create intense fields. The energy density in these network magnetic field bundles is a likely candidate as an energy source of the wind. Here we report measurements of fast solar wind streams from the Parker Solar Probe (PSP) spacecraft^6 which provides strong evidence for the interchange reconnection mechanism. We show that supergranulation structure at the coronal hole base remains imprinted in the near-Sun solar wind resulting in asymmetric patches of magnetic 'switchbacks'^(7,8) and bursty wind streams with power law-like energetic ion spectra to beyond 100 keV. Computer simulations of interchange reconnection support key features of the observations, including the ion spectra. Important characteristics of interchange reconnection in the low corona are inferred from the data including that the reconnection is collisionless and that the energy release rate is sufficient to power the fast wind. In this scenario, open magnetic flux undergoes continuous reconnection and the wind is driven both by the resulting plasma pressure and the radial Alfvenic flow bursts., Comment: 15 pages, 4 figures. Nature, 2023

We observe that many of the 2-complexes constructed by Freedman-Krushkal-Teichner in their paper on the incompleteness of the van Kampen embedding obstruction can actually be PL immersed in $\mathbb{R}^4$ in such a way that the images of the interiors of distinct cells are disjoint. In other words, they PL almost-embed in $\mathbb{R}^4$ with singularities occurring only as self intersections of some 2-cells. This note is written in (not necessarily modern) German., Comment: 3 pages, in German

We present statistical analysis of 11,200 proton kinetic-scale current sheets (CS) observed by Parker Solar Probe during 10 days around the first perihelion. The CS thickness $\lambda$ is in the range from a few to 200 km with the typical value around 30 km, while current densities are in the range from 0.1 to 10\;$\mu {\rm A/m^2}$ with the typical value around 0.7\;$\mu {\rm A/m^2}$. These CSs are resolved thanks to magnetic field measurements at 73--290 Samples/s resolution. In terms of proton inertial length $\lambda_{p}$, the CS thickness $\lambda$ is in the range from about $0.1$ to $10\lambda_{p}$ with the typical value around 2$\lambda_{p}$. The magnetic field magnitude does not substantially vary across the CSs and, accordingly, the current density is dominated by the magnetic field-aligned component. The CSs are typically asymmetric with statistically different magnetic field magnitudes at the CS boundaries. The current density is larger for smaller-scale CSs, $J_0\approx 0.15 \cdot (\lambda/100\;{\rm km})^{-0.76}$ $\mu {\rm A/m^2}$, but does not statistically exceed the Alfv\'en current density $J_A$ corresponding to the ion-electron drift of local Alfv\'{e}n speed. The CSs exhibit remarkable scale-dependent current density and magnetic shear angles, $J_0/J_{A}\approx 0.17\cdot (\lambda/\lambda_{p})^{-0.67}$ and $\Delta \theta\approx 21^{\circ}\cdot (\lambda/\lambda_{p})^{0.32}$. Based on these observations and comparison to recent studies at 1 AU, we conclude that proton kinetic-scale CSs in the near-Sun solar wind are produced by turbulence cascade and they are automatically in the parameter range, where reconnection is not suppressed by the diamagnetic mechanism, due to their geometry dictated by turbulence cascade.

In this paper we examine a low-energy SEP event observed by IS$\odot$IS's Energetic Particle Instrument-Low (EPI-Lo) inside 0.18 AU on September 30, 2020. This small SEP event has a very interesting time profile and ion composition. Our results show that the maximum energy and peak in intensity is observed mainly along the open radial magnetic field. The event shows velocity dispersion, and strong particle anisotropies are observed throughout the event showing that more particles are streaming outward from the Sun. We do not see a shock in the in-situ plasma or magnetic field data throughout the event. Heavy ions, such as O and Fe were detected in addition to protons and 4He, but without significant enhancements in 3He or energetic electrons. Our analysis shows that this event is associated with a slow streamer-blowout coronal mass ejection (SBO-CME) and the signatures of this small CME event are consistent with those typical of larger CME events. The time-intensity profile of this event shows that PSP encountered the western flank of the SBO-CME. The anisotropic and dispersive nature of this event in a shockless local plasma give indications that these particles are most likely accelerated remotely near the Sun by a weak shock or compression wave ahead of the SBO-CME. This event may represent direct observations of the source of low-energy SEP seed particle population., Comment: 25 pages, 8 figures

We present observations of >10-100 keV/nucleon suprathermal (ST) H, He, O, and Fe ions associated with crossings of the heliospheric current sheet (HCS) at radial distances <0.1 au from the Sun. Our key findings are: 1) very few heavy ions are detected during the 1st full crossing, the heavy ion intensities are reduced during the 2nd partial crossing and peak just after the 2nd crossing; 2) ion arrival times exhibit no velocity dispersion; 3) He pitch-angle distributions track the magnetic field polarity reversal and show up to ~10:1 anti-sunward, field-aligned flows and beams closer to the HCS that become nearly isotropic further from the HCS; 4) the He spectrum steepens either side of the HCS and the He, O, and Fe spectra exhibit power-laws of the form ~E^4-6; and 5) maximum energies EX increase with the ion's charge-to-mass (Q/M) ratio as EX/EH proportional to [(QX/MX)]^alpha where alpha~0.65-0.76, assuming that the average Q-states are similar to those measured in gradual and impulsive solar energetic particle events at 1 au. The absence of velocity dispersion in combination with strong field-aligned anisotropies closer to the HCS appears to rule out solar flares and near-sun coronal mass ejection-driven shocks. These new observations present challenges not only for mechanisms that employ direct parallel electric fields and organize maximum energies according to E/Q, but also for local diffusive and magnetic reconnection-driven acceleration models. Re-evaluation of our current understanding of the production and transport of energetic ions is necessary to understand this near-solar, current-sheet-associated population of ST ions., Comment: 4 Figures, 2 Tables

Context. Spacecraft observations early revealed frequent multiple proton populations in the solar wind. Decades of research on their origin have focused on processes such as magnetic reconnection in the low corona and wave-particle interactions in the corona and locally in the solar wind.Aims.This study aims to highlight that multiple proton populations and beams are also produced by magnetic reconnection occurring locally in the solar wind. Methods. We use high resolution Solar Orbiter proton velocity distribution function measurements, complemented by electron and magnetic field data, to analyze the association of multiple proton populations and beams with magnetic reconnection during a period of slow Alfv\'enic solar wind on 16 July 2020. Results. At least 6 reconnecting current sheets with associated multiple proton populations and beams, including a case of magnetic reconnection at a switchback boundary, are found during this day. This represents 2% of the measured distribution functions. We discuss how this proportion may be underestimated, and how it may depend on solar wind type and distance from the Sun. Conclusions. Although suggesting a likely small contribution, but which remains to be quantitatively assessed, Solar Orbiter observations show that magnetic reconnection must be considered as one of the mechanisms that produce multiple proton populations and beams locally in the solar wind.

A major discovery of Parker Solar Probe (PSP) was the presence of large numbers of localized increases in the radial solar wind speed and associated sharp deflections of the magnetic field - switchbacks (SB). A possible generation mechanism of SBs is through magnetic reconnection between open and closed magnetic flux near the solar surface, termed interchange reconnection that leads to the ejection of flux ropes (FR) into the solar wind. Observations also suggest that SBs undergo merging, consistent with a FR picture of these structures. The role of FRs merging in controlling the structure of SB in the solar wind is explored through direct observations, through analytic analysis, and numerical simulations. Analytic analysis reveals key features of the structure of FR and their scaling with the heliocentric distance R that are consistent with observations and that reveal the critical role of merging in controlling the SB structure. FR merging is shown to be energetically favorable to reduce the strength of the wrapping magnetic field and drive the observed elongation of SBs. A further consequence is the resulting dominance of the axial magnetic field within SBs that leads to the characteristic sharp rotation of the magnetic field into the axial direction at the SB boundary that is revealed in observations. Finally, the radial scaling of the SB area in the FR model of SBs suggests that the observational probability of SB identification should be insensitive to R, which is consistent with the most recent statistical analysis of SB observations from PSP., Comment: 21 pages, 9 figures

One of the striking observations from the Parker Solar Probe (PSP) spacecraft is the prevalence in the inner heliosphere of large amplitude, Alfv\'enic magnetic field reversals termed 'switchbacks'. These $\delta B_R/B \sim \mathcal{O}(1$) fluctuations occur on a range of timescales and in {\em patches} separated by intervals of quiet, radial magnetic field. We use measurements from PSP to demonstrate that patches of switchbacks are localized within the extensions of plasma structures originating at the base of the corona. These structures are characterized by an increase in alpha particle abundance, Mach number, plasma $\beta$ and pressure, and by depletions in the magnetic field magnitude and electron temperature. These intervals are in pressure-balance, implying stationary spatial structure, and the field depressions are consistent with overexpanded flux tubes. The structures are asymmetric in Carrington longitude with a steeper leading edge and a small ($\sim$1$^\circ$) edge of hotter plasma and enhanced magnetic field fluctuations. Some structures contain suprathermal ions to $\sim$85 keV that we argue are the energetic tail of the solar wind alpha population. The structures are separated in longitude by angular scales associated with supergranulation. This suggests that these switchbacks originate near the leading edge of the diverging magnetic field funnels associated with the network magnetic field - the primary wind sources. We propose an origin of the magnetic field switchbacks, hot plasma and suprathermals, alpha particles in interchange reconnection events just above the solar transition region and our measurements represent the extended regions of a turbulent outflow exhaust., Comment: 18 pages, 9 figures, submitted to Astrophys. J

Given an ACM set $\mathbb{X}$ of points in a multiprojective space $\mathbb{P}^m\times\mathbb{P}^n$ over a field of characteristic zero, we are interested in studying the K\"ahler different and the Cayley-Bacharach property for $\mathbb{X}$. In $\mathbb{P}^1\times\mathbb{P}^1$, the Cayley-Bacharach property agrees with the complete intersection property and it is characterized by using the K\"ahler different. However, this result fails to hold in $\mathbb{P}^m\times\mathbb{P}^n$ for $n>1$ or $m>1$. In this paper we start an investigation of the K\"ahler different and its Hilbert function and then prove that $\mathbb{X}$ is a complete intersection of type $(d_1,...,d_m,d'_1,...,d'_n)$ if and only if it has the Cayley-Bachrach property and the K\"ahler different is non-zero at a certain degree. When $\mathbb{X}$ has the $(\star)$-property, we characterize the Cayley-Bacharach property of $\mathbb{X}$ in terms of its components under the canonical projections., Comment: 18 pages, 1 figure

We give examples of finite, simplicial $2$-complexes that do not PL embed in $\mathbb{R}^4$ and exhibit, for each such complex, a family of PL immersions into $\mathbb{R}^4$ that hide the obstruction to embedding in "higher and higher order Milnor invariants". In addition, we show that the embedding obstructions defined by Krushkal in [8] vanish for our examples. We also answer a question in a paper of Avramidi-Okun-Schreve., Comment: New in this version: we show that the embedding obstructions defined by Krushkal in [8] vanish for our examples. 21 pages, 12 figures

Magnetic reconnection underlies many explosive phenomena in the heliosphere and in laboratory plasmas. The new research capabilities in theory/simulations, observations, and laboratory experiments provide the opportunity to solve the grand scientific challenges summarized in this whitepaper. Success will require enhanced and sustained investments from relevant funding agencies, increased interagency/international partnerships, and close collaborations of the solar, heliospheric, and laboratory plasma communities. These investments will deliver transformative progress in understanding magnetic reconnection and related explosive phenomena including space weather events., Comment: 4 pages (including a title page), white paper submitted to Helio2050 workshop at https://www.hou.usra.edu/meetings/helio2050/. arXiv admin note: substantial text overlap with arXiv:2004.00079

The structure of magnetic flux ropes injected into the solar wind during reconnection in the coronal atmosphere is explored with particle-in-cell simulations and compared with in situ measurements of magnetic "switchbacks" from the Parker Solar Probe. We suggest that multi-x-line reconnection between open and closed flux in the corona injects flux ropes into the solar wind and that these flux ropes convect outward over long distances before eroding due to reconnection. Simulations that explore the magnetic structure of flux ropes in the solar wind reproduce the following key features of the switchback observations: a rapid rotation of the radial magnetic field into the transverse direction, which is a consequence of reconnection with a strong guide field; and the potential to reverse the radial field component. The potential implication of the injection of large numbers of flux ropes in the coronal atmosphere for understanding the generation of the solar wind is discussed.

This white paper summarizes major scientific challenges and opportunities in understanding magnetic reconnection and related explosive phenomena as a fundamental plasma process., Comment: 6 pages, 1 figure, white paper submitted to both Plasma 2020 and Astro 2020 Decadal Surveys

Magnetospheric Multiscale (MMS) encountered the primary low-latitude magnetopause reconnection site when the inter-spacecraft separation exceeded the upstream ion inertial length. Classical signatures of the ion diffusion region (IDR), including a sub-ion-Alfv\'enic de-magnetized ion exhaust, a super-ion-Alfv\'enic magnetized electron exhaust, and Hall electromagnetic fields, are identified. The opening angle between the magnetopause and magnetospheric separatrix is $30^\circ\pm5^\circ$. The exhaust preferentially expands sunward, displacing the magnetosheath. Intense pileup of reconnected magnetic flux occurs between the magnetosheath separatrix and the magnetopause in a narrow channel intermediate between the ion and electron scales. The strength of the pileup (normalized values of 0.3-0.5) is consistent with the large angle at which the magnetopause is inclined relative to the overall reconnection coordinates. MMS-4, which was two ion inertial lengths closer to the X-line than the other three spacecraft, observed intense electron-dominated currents and kinetic-to-electromagnetic-field energy conversion within the pileup. MMS-1, 2, and 3 did not observe the intense currents nor the particle-to-field energy conversion but did observe the pileup, indicating that the edge of the generation region was contained within the tetrahedron. Comparisons with particle-in-cell simulations reveal that the electron currents and large inclination angle of the magnetopause are interconnected features of the asymmetric Hall effect. Between the separatrix and the magnetopause, high-density inflowing magnetosheath electrons brake and turn into the outflow direction, imparting energy to the normal magnetic field and generating the pileup. The findings indicate that electron dynamics are likely an important influence on the magnetic field structure within the ion diffusion region., Comment: Submitted to the Journal of Geophysical Research: Space Physics

Magnetic reconnection in current sheets converts magnetic energy into particle energy. The process may play an important role in the acceleration and heating of the solar wind close to the Sun. Observations from Parker Solar Probe provide a new opportunity to study this problem, as it measures the solar wind at unprecedented close distances to the Sun. During the 1st orbit, PSP encountered a large number of current sheets in the solar wind through perihelion at 35.7 solar radii. We performed a comprehensive survey of these current sheets and found evidence for 21 reconnection exhausts. These exhausts were observed in heliospheric current sheets, coronal mass ejections, and regular solar wind. However, we find that the majority of current sheets encountered around perihelion, where the magnetic field was strongest and plasma beta was lowest, were Alfv\'enic structures associated with bursty radial jets and these current sheets did not appear to be undergoing local reconnection. We examined conditions around current sheets to address why some current sheets reconnected, while others did not. A key difference appears to be the degree of plasma velocity shear across the current sheets: The median velocity shear for the 21 reconnection exhausts was 24% of the Alfv\'en velocity shear, whereas the median shear across 43 Alfv\'enic current sheets examined was 71% of the Alfv\'en velocity shear. This finding could suggest that large, albeit sub-Alfv\'enic, velocity shears suppress reconnection. An alternative interpretation is that the Alfv\'enic current sheets are isolated rotational discontinuities which do not undergo local reconnection., Comment: In Press (accepted by ApJS on 2019-11-08) This paper is part of the Parker Solar Probe ApJS Special Issue Current citation: Phan, T. D., S. D. Bale, J. P. Eastwood, et al. (2019), Parker Solar Probe In-Situ Observations of Magnetic Reconnection Exhausts During Encounter 1, ApJS., in press, doi: 10.3847/1538-4365/ab55ee

We show that all PL manifolds of dimension $\geq 3$ have spines similar to Bing's house with two rooms. Beyond this we explore approximation rigidity and an $h$-principle., Comment: 13 pages, 8 figures

We construct Bing houses in all dimensions $n \geq 3$, obtaining non-separating PL immersions of $\mathbb{S}^n \rightarrow\mathbb{R}^{n+1}$., Comment: 16 pages, 17 figures. Appendix added

The Boosted Difference of Convex functions Algorithm (BDCA) has been recently introduced to accelerate the performance of the classical Difference of Convex functions Algorithm (DCA). This acceleration is achieved thanks to an extrapolation step from the point computed by DCA via a line search procedure. In this work, we propose an extension of BDCA that can be applied to difference of convex functions programs with linear constraints, and prove that every cluster point of the sequence generated by this algorithm is a Karush--Kuhn-Tucker point of the problem if the feasible set has a Slater point. When the objective function is quadratic, we prove that any sequence generated by the algorithm is bounded and R-linearly (geometrically) convergent. Finally, we present some numerical experiments where we compare the performance of DCA and BDCA on some challenging problems: to test the copositivity of a given matrix, to solve one-norm and infinity-norm trust-region subproblems, and to solve piecewise quadratic problems with box constraints. Our numerical results demonstrate that this new extension of BDCA outperforms DCA.

Let $f\colon \mathbb{S}^1\rightarrow G$ be a surjective map from the standard unit circle to a graph $G$ such that the pre-image of each point has diameter less than $\varepsilon$. If $\varepsilon$ is small enough, does $f$ split as a free factor in $\pi_1(G)$?, Comment: 4 pages, 2 figures

The Difference of Convex functions Algorithm (DCA) is widely used for minimizing the difference of two convex functions. A recently proposed accelerated version, termed BDCA for Boosted DC Algorithm, incorporates a line search step to achieve a larger decrease of the objective value at each iteration. Thanks to this step, BDCA usually converges much faster than DCA in practice. The solutions found by DCA are guaranteed to be critical points of the problem, but these may not be local minima. Although BDCA tends to improve the objective value of the solutions it finds, these are frequently just critical points as well. In this paper we combine BDCA with a simple Derivative-Free Optimization (DFO) algorithm to force the d-stationarity (lack of descent direction) at the point obtained. The potential of this approach is illustrated through some computational experiments on a Minimum-Sum-of-Squares clustering problem. Our numerical results demonstrate that the new method provides better solutions while still remains faster than DCA in the majority of test cases.

Using kinetic particle-in-cell (PIC) simulations, we simulate reconnection conditions appropriate for the magnetosheath and solar wind, i.e., plasma beta (ratio of gas pressure to magnetic pressure) greater than 1 and low magnetic shear (strong guide field). Changing the simulation domain size, we find that the ion response varies greatly. For reconnecting regions with scales comparable to the ion Larmor radius, the ions do not respond to the reconnection dynamics leading to ''electron-only'' reconnection with very large quasi-steady reconnection rates. The transition to more traditional ''ion-coupled'' reconnection is gradual as the reconnection domain size increases, with the ions becoming frozen-in in the exhaust when the magnetic island width in the normal direction reaches many ion inertial lengths. During this transition, the quasi-steady reconnection rate decreases until the ions are fully coupled, ultimately reaching an asymptotic value. The scaling of the ion outflow velocity with exhaust width during this electron-only to ion-coupled transition is found to be consistent with a theoretical model of a newly reconnected field line. In order to have a fully frozen-in ion exhaust with ion flows comparable to the reconnection Alfv\'en speed, an exhaust width of at least several ion inertial lengths is needed. In turbulent systems with reconnection occurring between magnetic bubbles associated with fluctuations, using geometric arguments we estimate that fully ion-coupled reconnection requires magnetic bubble length scales of at least several tens of ion inertial lengths.

Using observations of Earth's bow shock by the Magnetospheric Multiscale mission, we show for the first time that active magnetic reconnection is occurring at current sheets embedded within the quasi-parallel shock's transition layer. We observe an electron jet and heating but no ion response, suggesting we have observed an electron-only mode. The lack of ion response is consistent with simulations showing reconnection onset on sub-ion timescales. We also discuss the impact of electron heating in shocks via reconnection.

The Boosted Difference of Convex functions Algorithm (BDCA) was recently proposed for minimizing smooth difference of convex (DC) functions. BDCA accelerates the convergence of the classical Difference of Convex functions Algorithm (DCA) thanks to an additional line search step. The purpose of this paper is twofold. Firstly, to show that this scheme can be generalized and successfully applied to certain types of nonsmooth DC functions, namely, those that can be expressed as the difference of a smooth function and a possibly nonsmooth one. Secondly, to show that there is complete freedom in the choice of the trial step size for the line search, which is something that can further improve its performance. We prove that any limit point of the BDCA iterative sequence is a critical point of the problem under consideration, and that the corresponding objective value is monotonically decreasing and convergent. The global convergence and convergent rate of the iterations are obtained under the Kurdyka-Lojasiewicz property. Applications and numerical experiments for two problems in data science are presented, demonstrating that BDCA outperforms DCA. Specifically, for the Minimum Sum-of-Squares Clustering problem, BDCA was on average sixteen times faster than DCA, and for the Multidimensional Scaling problem, BDCA was three times faster than DCA.

We present two globally convergent Levenberg-Marquardt methods for finding zeros of H\"{o}lder metrically subregular mappings that may have non-isolated zeros. The first method unifies the Levenberg- Marquardt direction and an Armijo-type line search, while the second incorporates this direction with a nonmonotone trust-region technique. For both methods, we prove the global convergence to a first-order stationary point of the associated merit function. Furthermore, the worst-case global complexity of these methods are provided, indicating that an approximate stationary point can be computed in at most $\mathcal{O}(\varepsilon^{-2})$ function and gradient evaluations, for an accuracy parameter $\varepsilon>0$. We also study the conditions for the proposed methods to converge to a zero of the associated mappings. Computing a moiety conserved steady state for biochemical reaction networks can be cast as the problem of finding a zero of a H\"{o}lder metrically subregular mapping. We report encouraging numerical results for finding a zero of such mappings derived from real-world biological data, which supports our theoretical foundations., Comment: 28 pages, 3 figures