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We present ${\sim}0.2$ arcsec ($\sim$80 au) resolution observations of the CO (2-1) and SiO (5-4) lines made with the Atacama large millimeter/submillimeter array toward an extremely young intermediate-mass protostellar source (t$_{\rm dyn}<$1000 years), MMS 1 located in the Orion Molecular Cloud-3 region. We have successfully imaged a very compact CO molecular outflow associated with MMS 1, having deprojected lobe sizes of $\sim$18000 au (red-shifted lobe) and $\sim$35000 au (blue-shifted lobe). We have also detected an extremely compact ($\lesssim$1000 au) and collimated SiO protostellar jet within the CO outflow. The maximum deprojected jet speed is measured to be as high as 93 km s$^{-1}$. The SiO jet wiggles and displays a chain of knots. Our detection of the molecular outflow and jet is the first direct evidence that MMS 1 already hosts a protostar. The position-velocity diagram obtained from the SiO emission shows two distinct structures: (i) bow-shocks associated with the tips of the outflow, and (ii) a collimated jet, showing the jet velocities linearly increasing with the distance from the driving source. Comparisons between the observations and numerical simulations quantitatively share similarities such as multiple-mass ejection events within the jet and Hubble-like flow associated with each mass ejection event. Finally, while there is a weak flux decline seen in the 850 $\mu$m light curve obtained with JCMT/SCUBA 2 toward MMS 1, no dramatic flux change events are detected. This suggests that there has not been a clear burst event within the last 8 years., Comment: 19 pages, 9 figures, Accepted for publication in ApJ

Maximin share (MMS) allocations are a popular relaxation of envy-free allocations that have received wide attention in the fair division of indivisible items. Although MMS allocations of goods can fail to exist, previous work has found conditions under which they exist. Specifically, MMS allocations of goods exist whenever $m \leq n+5$, and this bound is tight in the sense that they can fail to exist when $m = n+6$. The techniques used to obtain these results do not apply to the mixed manna setting, leaving the question of whether similar results hold for the general setting. This paper addresses this by introducing new techniques to handle these settings. In particular, we are able to answer this question completely for the chores setting, and partially for the mixed manna setting. An agent $i$ is a {\em chores agent} if it considers every item to be a chore and a {\em non-negative agent} if its MMS guarantee is non-negative. In this paper, we prove that an MMS allocation exists as long as $m \leq n+5$ and either (i) every agent is a chores agent, or (ii) there exists a non-negative agent. In addition, for $n \leq 3$, we also prove that an MMS allocation exists as long as $m \leq n+5$, regardless of the types of agents. To the best of our knowledge, these are the first non-trivial results pertaining to the existence of exact MMS allocations in the mixed manna setting., Comment: 8 pages. To appear in ECAI 2024

We study fair distribution of a collection of m indivisible goods among a group of n agents, using the widely recognized fairness principles of Maximin Share (MMS) and Any Price Share (APS). These principles have undergone thorough investigation within the context of additive valuations. We explore these notions for valuations that extend beyond additivity. First, we study approximate MMS under the separable (piecewise-linear) concave (SPLC) valuations, an important class generalizing additive, where the best known factor was 1/3-MMS. We show that 1/2-MMS allocation exists and can be computed in polynomial time, significantly improving the state-of-the-art. We note that SPLC valuations introduce an elevated level of intricacy in contrast to additive. For instance, the MMS value of an agent can be as high as her value for the entire set of items. Further, the equilibrium computation problem, which is polynomial-time for additive valuations, becomes intractable for SPLC. We use a relax-and-round paradigm that goes through competitive equilibrium and LP relaxation. Our result extends to give (symmetric) 1/2-APS, a stronger guarantee than MMS. APS is a stronger notion that generalizes MMS by allowing agents with arbitrary entitlements. We study the approximation of APS under submodular valuation functions. We design and analyze a simple greedy algorithm using concave extensions of submodular functions. We prove that the algorithm gives a 1/3-APS allocation which matches the current best-known factor. Concave extensions are hard to compute in polynomial time and are, therefore, generally not used in approximation algorithms. Our approach shows a way to utilize it within analysis (while bypassing its computation), and might be of independent interest., Comment: To appear in AAAI Conference on Artificial Intelligence, 2024

I propose an alternative algorithm to compute the MMS voting rule. Instead of using linear programming, in this new algorithm the maximin support value of a committee is computed using a sequence of maximum flow problems., Comment: 8 pages

Based on the Magnetospheric Multiscale (MMS) mission we look at magnetic field fluctuations in the Earth's magnetosheath. We apply the statistical analysis using a Fokker-Planck equation to investigate processes responsible for stochastic fluctuations in space plasmas. As already known, turbulence in the inertial range of hydromagnetic scales exhibits Markovian features. We have extended the statistical approach to much smaller scales in space, where kinetic theory should be applied. Here we study in detail and compare the characteristics of magnetic fluctuations behind the bow shock, inside the magnetosheath, and near the magnetopause. It appears that the first Kramers- Moyal coefficient is linear and the second term is quadratic function of magnetic increments, which describe drift and diffusion, correspondingly, in the entire magnetosheath. This should correspond to a generalization of Ornstein-Uhlenbeck process. We demonstrate that the second order approximation of the Fokker-Planck equation leads to non-Gaussian kappa distributions of the probability density functions. In all cases in the magnetosheath, the approximate power-law distributions are recovered. For some moderate scales we have the kappa distributions described by various peaked shapes with heavy tails. In particular, for large values of the kappa parameter this shape is reduced to the normal Gaussian distribution. It is worth noting that for smaller kinetic scales the rescaled distributions exhibit a universal global scale-invariance, consistently with the stationary solution of the Fokker-Planck equation. These results, especially on kinetic scales, could be important for a better understanding of the physical mechanism governing turbulent systems in space and astrophysical plasmas., Comment: 13 pages, 7 figures

Collisionless shocks play a key role in the heliosphere at planetary bow shocks by governing the conversion of the upstream bulk kinetic energy of the solar wind flow to other forms of energy in the downstream, including bulk plasma heat, acceleration of particles, and magnetic energy. Here we present the first observational identification of the velocity-space signature of shock-drift acceleration of ions at a perpendicular collisionless shock, previously predicted using kinetic numerical simulations, using a field-particle correlation analysis of Magnetospheric Multiscale (\emph{MMS}) observations of Earth's bow shock. Furthermore, by resolving the ion energization rates as a function of particle velocity, the field-particle correlation technique facilitates a clean quantitative separation of the energization rate of the reflected ions from that of the incoming ion beam, enabling a more complete characterization of the energy conversion at the shock.

The evolution of plasma entropy and the process of plasma energy re-distribution at the collisionless plasma shock front are evaluated based on the high temporal resolution data from the four MMS spacecraft during the crossing of the terrestrial bow shock. The ion distribution function has been separated into the populations with different characteristic behavior in the vicinity of the shock: the upstream core population, the reflected ions; the gyrating ions; the ions trapped in the vicinity of the shock, and the downstream core population. The values of ion and electron moments (density, bulk velocity, and temperature) have been determined separately for these populations. It was shown that the solar wind core population bulk velocity slows down mainly in the ramp with the electrostatic potential increase but not in the foot region as it was supposed. The reflected ion population determine the foot region properties, so that the proton temperature peak in the foot region is the effect of the relative motion of the different ion populations, rather than an actual increase in the thermal speed of any of the ion population. The ion entropy evaluated showed a significant increase across the shock the enhancement of the ion entropy occurs in the foot of the shock front and at the ramp, where the reflected ions are emerging in addition to the upstream solar wind ions, the anisotropy growing to generate the bursts of ion-scales electrostatic waves. The entropy of electrons across the shock doesn't show significant change - electron heating goes almost adiabatically.

We consider the problem of fairly allocating a sequence of indivisible items that arrive online in an arbitrary order to a group of n agents with additive normalized valuation functions. We consider both the allocation of goods and chores and propose algorithms for approximating maximin share (MMS) allocations. When agents have identical valuation functions the problem coincides with the semi-online machine covering problem (when items are goods) and load balancing problem (when items are chores), for both of which optimal competitive ratios have been achieved. In this paper, we consider the case when agents have general additive valuation functions. For the allocation of goods, we show that no competitive algorithm exists even when there are only three agents and propose an optimal 0.5-competitive algorithm for the case of two agents. For the allocation of chores, we propose a (2-1/n)-competitive algorithm for n>=3 agents and a square root of 2 (approximately 1.414)-competitive algorithm for two agents. Additionally, we show that no algorithm can do better than 15/11 (approximately 1.364)-competitive for two agents., Comment: 29 pages, 1 figure (to appear in ICML 2023)

We consider the problem of fairly allocating a set of indivisible goods among $n$ agents with additive valuations, using the popular fairness notion of maximin share (MMS). Since MMS allocations do not always exist, a series of works provided existence and algorithms for approximate MMS allocations. The Garg-Taki algorithm gives the current best approximation factor of $(\frac{3}{4} + \frac{1}{12n})$. Most of these results are based on complicated analyses, especially those providing better than $2/3$ factor. Moreover, since no tight example is known of the Garg-Taki algorithm, it is unclear if this is the best factor of this approach. In this paper, we significantly simplify the analysis of this algorithm and also improve the existence guarantee to a factor of $(\frac{3}{4} + \min(\frac{1}{36}, \frac{3}{16n-4}))$. For small $n$, this provides a noticeable improvement. Furthermore, we present a tight example of this algorithm, showing that this may be the best factor one can hope for with the current techniques.

We study the problem of allocating indivisible chores to agents under the Maximin share (MMS) fairness notion. The chores are embedded on a graph and each bundle of chores assigned to an agent should be connected. Although there is a simple algorithm for MMS allocations of goods on trees, it remains open whether MMS allocations of chores on trees always exist or not, which is a simple but annoying problem in chores allocation. In this paper, we introduce a new method for chores allocation with connectivity constraints, called the group-satisfied method, that can show the existence of MMS allocations of chores on several subclasses of trees. Even these subcases are non-trivial and our results can be considered as a significant step to the open problem. We also consider MMS allocations of chores on cycles where we get the tight approximation ratio for three agents. Our result was obtained via the linear programming (LP) method, which enables us not only to compute approximate MMS allocations but also to construct tight examples of the nonexistence of MMS allocations without complicated combinatorial analysis. These two proposed methods, the group-satisfied method and the LP method, have the potential to solve more related problems.