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Context. Trojan asteroids of Mars date from an early phase of solar system evolution. Based on a sample of <10 asteroids, MT distribution has been previously shown to be both asymmetric and inhomogeneous with population evolution dominated by thermal radiation forces acting over timescales of Gyr. Remarkably, a single asteroid family associated with (5261) Eureka (H~16) at L5 contains most MTs and all members of the stable population fainter than H=18. Aims. Using the currently available sample of MTs and their orbits, we take a fresh look at this population to re-evaluate these earlier conclusions and to search for additional features diagnostic of the evolutionary history of MTs and the Eureka family in particular. Methods. We perform harmonic analysis on numerical time series of the osculating elements to compile a new proper element catalogue comprising 16 L5 and 1 L4 Mars Trojan asteroids. We then combine sample variance analysis with statistical hypothesis testing to identify clusters in the distribution of orbits and assess their significance. Results. We identify two small clusterings significant at 95% confidence of three H=20-21 asteroids each and investigate their likely origin. One of the clusters is probably the result of rotational breakup of a Eureka family asteroid ~10^8 yr ago. The significantly higher tadpole libration width of asteroids in the other cluster is more consistent with an origin as impact ejecta from Eureka itself and on a timescale comparable to the ~1 Gyr age of its family. We further confirm the previously reported correlations in Eureka family orbital distribution attributed to the long-term action of radiation-driven forces and torques on the asteroids., Comment: 10 pages,9 figures, accepted in A&A with minor corrections

Global challenges such as food supply chain disruptions, public health crises, and natural hazard responses require access to and integration of diverse datasets, many of which are geospatial. Over the past few years, a growing number of (geo)portals have been developed to address this need. However, most existing (geo)portals are stacked by separated or sparsely connected data "silos" impeding effective data consolidation. A new way of sharing and reusing geospatial data is therefore urgently needed. In this work, we introduce KnowWhereGraph, a knowledge graph-based data integration, enrichment, and synthesis framework that not only includes schemas and data related to human and environmental systems but also provides a suite of supporting tools for accessing this information. The KnowWhereGraph aims to address the challenge of data integration by building a large-scale, cross-domain, pre-integrated, FAIR-principles-based, and AI-ready data warehouse rooted in knowledge graphs. We highlight the design principles of KnowWhereGraph, emphasizing the roles of space, place, and time in bridging various data "silos". Additionally, we demonstrate multiple use cases where the proposed geospatial knowledge graph and its associated tools empower decision-makers to uncover insights that are often hidden within complex and poorly interoperable datasets.

Power distribution networks are evolving due to the integration of DERs and increased customer participation. To maintain optimal operation, minimize losses, and meet varying load demands, frequent network reconfiguration is necessary. Traditionally, the reconfiguration task relies on optimization software and expert operators, but as systems grow more complex, faster and more adaptive solutions are required without expert intervention. Data-driven reconfiguration is gaining traction for its accuracy, speed, and robustness against incomplete network data. LLMs, with their ability to capture complex patterns, offer a promising approach for efficient and responsive network reconfiguration in evolving complex power networks. In this work, we introduce LLM4DistReconfig, a deep learning-based approach utilizing a fine-tuned LLM to solve the distribution network reconfiguration problem. By carefully crafting prompts and designing a custom loss function, we train the LLM with inputs representing network parameters such as buses, available lines, open lines, node voltages, and system loss. The model then predicts optimal reconfigurations by outputting updated network configurations that minimize system loss while meeting operational constraints. Our approach significantly reduces inference time compared to classical algorithms, allowing for near real-time optimal reconfiguration after training. Experimental results show that our method generates optimal configurations minimizing system loss for five individual and a combined test dataset. It also produces minimal invalid edges, no cycles, or subgraphs across all datasets, fulfilling domain-specific needs. Additionally, the generated responses contain less than 5% improper outputs on seen networks and satisfactory results on unseen networks, demonstrating its effectiveness and reliability for the reconfiguration task., Comment: Accepted in NAACL 2025 Conference Main Track

We consider a class of optimization problems over stochastic variables where the algorithm can learn information about the value of any variable through a series of costly steps; we model this information acquisition process as a Markov Decision Process (MDP). The algorithm's goal is to minimize the cost of its solution plus the cost of information acquisition, or alternately, maximize the value of its solution minus the cost of information acquisition. Such bandit superprocesses have been studied previously but solutions are known only for fairly restrictive special cases. We develop a framework for approximate optimization of bandit superprocesses that applies to arbitrary processes with a matroid (and in some cases, more general) feasibility constraint. Our framework establishes a bound on the optimal cost through a novel cost amortization; it then couples this bound with a notion of local approximation that allows approximate solutions for each component MDP in the superprocess to be composed without loss into a global approximation. We use this framework to obtain approximately optimal solutions for several variants of bandit superprocesses for both maximization and minimization. We obtain new approximations for combinatorial versions of the previously studied Pandora's Box with Optional Inspection and Pandora's Box with Partial Inspection; as well as approximation algorithms for a new problem that we call the Weighing Scale problem.

Knowledge graphs (KGs) are increasingly utilized for data integration, representation, and visualization. While KG population is critical, it is often costly, especially when data must be extracted from unstructured text in natural language, which presents challenges, such as ambiguity and complex interpretations. Large Language Models (LLMs) offer promising capabilities for such tasks, excelling in natural language understanding and content generation. However, their tendency to ``hallucinate'' can produce inaccurate outputs. Despite these limitations, LLMs offer rapid and scalable processing of natural language data, and with prompt engineering and fine-tuning, they can approximate human-level performance in extracting and structuring data for KGs. This study investigates LLM effectiveness for the KG population, focusing on the Enslaved.org Hub Ontology. In this paper, we report that compared to the ground truth, LLM's can extract ~90% of triples, when provided a modular ontology as guidance in the prompts.

Geospatial Knowledge Graphs (GeoKGs) have become integral to the growing field of Geospatial Artificial Intelligence. Initiatives like the U.S. National Science Foundation's Open Knowledge Network program aim to create an ecosystem of nation-scale, cross-disciplinary GeoKGs that provide AI-ready geospatial data aligned with FAIR principles. However, building this infrastructure presents key challenges, including 1) managing large volumes of data, 2) the computational complexity of discovering topological relations via SPARQL, and 3) conflating multi-scale raster and vector data. Discrete Global Grid Systems (DGGS) help tackle these issues by offering efficient data integration and representation strategies. The KnowWhereGraph utilizes Google's S2 Geometry -- a DGGS framework -- to enable efficient multi-source data processing, qualitative spatial querying, and cross-graph integration. This paper outlines the implementation of S2 within KnowWhereGraph, emphasizing its role in topologically enriching and semantically compressing data. Ultimately, this work demonstrates the potential of DGGS frameworks, particularly S2, for building scalable GeoKGs.

KnowWhereGraph is one of the largest fully publicly available geospatial knowledge graphs. It includes data from 30 layers on natural hazards (e.g., hurricanes, wildfires), climate variables (e.g., air temperature, precipitation), soil properties, crop and land-cover types, demographics, and human health, various place and region identifiers, among other themes. These have been leveraged through the graph by a variety of applications to address challenges in food security and agricultural supply chains; sustainability related to soil conservation practices and farm labor; and delivery of emergency humanitarian aid following a disaster. In this paper, we introduce the ontology that acts as the schema for KnowWhereGraph. This broad overview provides insight into the requirements and design specifications for the graph and its schema, including the development methodology (modular ontology modeling) and the resources utilized to implement, materialize, and deploy KnowWhereGraph with its end-user interfaces and public query SPARQL endpoint.

Time-series forecasting has seen significant advancements with the introduction of token prediction mechanisms such as multi-head attention. However, these methods often struggle to achieve the same performance as in language modeling, primarily due to the quadratic computational cost and the complexity of capturing long-range dependencies in time-series data. State-space models (SSMs), such as Mamba, have shown promise in addressing these challenges by offering efficient solutions with linear RNNs capable of modeling long sequences with larger context windows. However, there remains room for improvement in accuracy and scalability. We propose the use of Test-Time Training (TTT) modules in a parallel architecture to enhance performance in long-term time series forecasting. Through extensive experiments on standard benchmark datasets, we demonstrate that TTT modules consistently outperform state-of-the-art models, including the Mamba-based TimeMachine, particularly in scenarios involving extended sequence and prediction lengths. Our results show significant improvements in Mean Squared Error (MSE) and Mean Absolute Error (MAE), especially on larger datasets such as Electricity, Traffic, and Weather, underscoring the effectiveness of TTT in capturing long-range dependencies. Additionally, we explore various convolutional architectures within the TTT framework, showing that even simple configurations like 1D convolution with small filters can achieve competitive results. This work sets a new benchmark for time-series forecasting and lays the groundwork for future research in scalable, high-performance forecasting models.

Acute lymphoblastic leukemia (ALL) is a form of blood cancer that affects the white blood cells. ALL constitutes approximately 25% of pediatric cancers. Early diagnosis and treatment of ALL are crucial for improving patient outcomes. The task of identifying immature leukemic blasts from normal cells under the microscope can prove challenging, since the images of a healthy and cancerous cell appear similar morphologically. In this study, we propose a binary image classification model to assist in the diagnostic process of ALL. Our model takes as input microscopic images of blood samples and outputs a binary prediction of whether the sample is normal or cancerous. Our dataset consists of 10661 images out of 118 subjects. Deep learning techniques on convolutional neural network architectures were used to achieve accurate classification results. Our proposed method achieved 94.3% accuracy and could be used as an assisting tool for hematologists trying to predict the likelihood of a patient developing ALL.

Meteor and bolide phenomena caused by the atmospheric ablation of incoming meteoroids are predicted to occur at the planet Venus. Their systematic observation would allow to measure and compare the sub-mm to m meteoroid flux at different locations in the solar system. Using a physical model of atmospheric ablation, we demonstrate that Venus meteors would be brighter, shorter-lived, and appear higher in the atmosphere than Earth meteors. To investigate the feasibility of meteor detection at Venus from an orbiter, we apply the SWARMS survey simulator tool to sets of plausible meteoroid population parameters, atmospheric models and instrument designs suited to the task, such as the Mini-EUSO camera operational on the ISS since 2019. We find that such instrumentation would detect meteors at Venus with a 1.5x to 2.5x higher rate than at Earth. The estimated Venus-Earth detection ratio remains insensitive to variations in the chosen observation orbit and detector characteristics, implying that a meteor survey from Venus orbit is feasible, though contingent on the availability of suitable algorithms and methods for efficient on-board processing and downlinking of the meteor data to Earth. We further show that a hypothetical camera onboard the upcoming EnVision mission to Venus similar to the ISS instrument should detect many times more meteors than needed for an initial characterisation of the large meteoroid population at 0.7 au from the Sun., Comment: Accepted for publication in Icarus

We study multi-buyer multi-item sequential item pricing mechanisms for revenue maximization with the goal of approximating a natural fractional relaxation -- the ex ante optimal revenue. We assume that buyers' values are subadditive but make no assumptions on the value distributions. While the optimal revenue, and therefore also the ex ante benchmark, is inapproximable by any simple mechanism in this context, previous work has shown that a weaker benchmark that optimizes over so-called ``buy-many" mechanisms can be approximable. Approximations are known, in particular, for settings with either a single buyer or many unit-demand buyers. We extend these results to the much broader setting of many subadditive buyers. We show that the ex ante buy-many revenue can be approximated via sequential item pricings to within an $O(\log^2 m)$ factor, where $m$ is the number of items. We also show that a logarithmic dependence on $m$ is necessary. Our approximation is achieved through the construction of a new multi-dimensional Online Contention Resolution Scheme (OCRS), that provides an online rounding of the optimal ex ante solution. Chawla et al. arXiv:2204.01962 previously constructed an OCRS for revenue for unit-demand buyers, but their construction relied heavily on the ``almost single dimensional" nature of unit-demand values. Prior to that work, OCRSes have only been studied in the context of social welfare maximization for single-parameter buyers. For the welfare objective, constant-factor approximations have been demonstrated for a wide range of combinatorial constraints on item allocations and classes of buyer valuation functions. Our work opens up the possibility of a similar success story for revenue maximization., Comment: 39 pages

In the recent Astro2020 Decadal Report, ''Pathways to Discovery in Astronomy and Astrophysics for the 2020s'' Adaptive Optics (AO) was identified as a crucial technology for a variety of reasons. These included an emphasis on high-contrast imaging and AO systems as being part of future technology development especially with application to the two US ELT projects. Instrument upgrades were also identified for existing 4m to 10m class telescopes which would incorporate upgrades to existing AO systems. As noted in the Report: (1) ''the central role of AO instrumentation and the importance of further development are rapidly growing, with novel concepts pushing toward wider area'', (2) ''Visible AO has high potential scientific return by opening up an entire wavelength regime to high angular resolution studies. The goal is to exploit the smaller diffraction limit of telescopes in the optical, yet both the coherence length and time decrease at shorter wavelengths requiring wavefront sensing at high spatial and temporal frequencies that are currently technologically challenging. This is an important developing area for the 2020s - 2030s.'', and (3) ''Such investments in AO systems development is a key risk mitigation strategy for ELTs, whose full resolution and sensitivity potential can only be realized with AO, and which is recognized as the most important technical risk for both GMT and TMT''. A workshop was held in May, 2023 to develop a Community Response document (this document) to provide feedback and suggested priorities to various funding agencies, such as NSF, NASA, and DoE, as to the AO Research and Development priorities to meet the technical and science objectives outlined in Astro2020 for ground-based AO, both stand-alone and in support of space missions., Comment: 66 Total Pages with 26 pages of response to ASTRO2020 and the remainder being supporting and context information in the form of Appendices

The hybridisation of robot-assisted gait training and functional electrical stimulation (FES) can provide numerous physiological benefits to neurological patients. However, the design of an effective hybrid controller poses significant challenges. In this over-actuated system, it is extremely difficult to find the right balance between robotic assistance and FES that will provide personalised assistance, prevent muscle fatigue and encourage the patient's active participation in order to accelerate recovery. In this paper, we present an adaptive hybrid robot-FES controller to do this and enable the triadic collaboration between the patient, the robot and FES. A patient-driven controller is designed where the voluntary movement of the patient is prioritised and assistance is provided using FES and the robot in a hierarchical order depending on the patient's performance and their muscles' fitness. The performance of this hybrid adaptive controller is tested in simulation and on one healthy subject. Our results indicate an increase in tracking performance with lower overall assistance, and less muscle fatigue when the hybrid adaptive controller is used, compared to its non adaptive equivalent. This suggests that our hybrid adaptive controller may be able to adapt to the behaviour of the user to provide assistance as needed and prevent the early termination of physical therapy due to muscle fatigue.

Methods: Broad- and narrow-band imaging of AFGL 5180 was made in the NIR with the LBT, in both seeing-limited ($\sim0.5\arcsec$) and high angular resolution ($\sim0.09\arcsec$) Adaptive Optics (AO) modes, as well as with HST. Archival ALMA continuum data was also utilized. Results: At least 40 jet knots were identified via NIR emission from H$_2$ and [FeII] tracing shocked gas. Bright jet knots outflowing from the central most massive protostar, S4, are detected towards the east of the source and are resolved in fine detail with the AO imaging. Additional knots are distributed throughout the field, likely indicating the presence of multiple driving sources. Sub-millimeter sources detected by ALMA are shown to be grouped in two main complexes, AFGL 5180 M and a small cluster $\sim15\arcsec$ to the south, AFGL 5180 S. From our NIR continuum images we identify YSO candidates down to masses of $\sim 0.1\:M_\odot$. Combined with the sub-mm sources, this yields a surface number density of such YSOs of $N_* \sim 10^3 {\rm pc}^{-2}$ within a projected radius of about 0.1 pc. Such a value is similar to those predicted by models of both Core Accretion from a turbulent clump environment and Competitive Accretion. The radial profile of $N_*$ is relatively flat on scales out to 0.2~pc, with only modest enhancement around the massive protostar inside 0.05~pc. Conclusions: This study demonstrates the utility of high-resolution NIR imaging, in particular with AO, for detecting outflow activity and YSOs in distant regions. The presented images reveal the complex morphology of outflow-shocked gas within the large-scale bipolar flow of a massive protostar, as well as clear evidence for several other outflow driving sources in the region. Finally, this work presents a novel approach to compare the observed YSO surface number density from our study against different models of massive star formation., Comment: Accepted to Astronomy & Astrophysics (A&A)

Most tourist destinations are facing regular and consistent seasonality with significant economic and social impacts. This phenomenon is more pronounced in the post-covid era, where demand for travel has increased but unevenly among different geographic areas. To counter these problems that both customers and hoteliers are facing, we have developed two auctioning systems that allow hoteliers of lower popularity tier areas or during low season periods to auction their rooms in what we call a forward auction model, and also allows customers to initiate a bidding process whereby hoteliers in an area may make offers to the customer for their rooms, in what constitutes a reverse auction model initiated by the customer, similar to the bidding concept of priceline.com. We develop mathematical programming models that define explicitly both types of auctions, and show that in each type, there are significant benefits to be gained both on the side of the hotelier as well as on the side of the customer. We discuss algorithmic techniques for the approximate solution of these optimization problems, and present results using exact optimization solvers to solve them to guaranteed optimality. These techniques could be beneficial to both customer and hotelier reducing seasonality during middle and low season and providing the customer with attractive offers., Comment: 21 pages, 7 figures

The SOUL systems at the Large Bincoular Telescope can be seen such as precursor for the ELT SCAO systems, combining together key technologies such as EMCCD, Pyramid WFS and adaptive telescopes. After the first light of the first upgraded system on September 2018, going through COVID and technical stops, we now have all the 4 systems working on-sky. Here, we report about some key control improvements and the system performance characterized during the commissioning. The upgrade allows us to correct more modes (500) in the bright end and increases the sky coverage providing SR(K)>20% with reference stars G$_{RP}$<17, opening to extragalcatic targets with NGS systems. Finally, we review the first astrophysical results, looking forward to the next generation instruments (SHARK-NIR, SHARK-Vis and iLocater), to be fed by the SOUL AO correction., Comment: 13 pages, 10 figures, Adaptive Optics for Extremely Large Telescopes 7th Edition, 25-30 Jun 2023 Avignon (France)

The asteroid belt is a unique source of information on some of the most important questions facing solar system science. These questions include the sizes, numbers, types and orbital distributions of the planetesimals that formed the planets, and the identification of those asteroids that are the sources of meteorites and near-Earth asteroids. Answering these questions requires an understanding of the dynamical evolution of the asteroid belt, but this evolution is governed by a complex interplay of mechanisms that include catastrophic disruption, orbital evolution driven by Yarkovsky radiation forces, and chaotic orbital evolution driven by gravitational forces. While the timescales of these loss mechanisms have been calculated using estimates of some critical parameters that include the thermal properties, strengths and mean densities of the asteroids, we argue here that the uncertainties in these parameters are so large that deconvolution of the structure of the asteroid belt must be guided primarily by observational constraints. We argue that observations of the inner asteroid belt indicate that the size-frequency distribution is not close to the equilibrium distribution postulated by Dohnanyi (1969). We also discuss the correlations observed between the sizes and the orbital elements of the asteroids. While some of these correlations are significant and informative, others are spurious and may arise from the limitations of the Hierarchical Clustering Method that is currently used to define family membership., Comment: 11 pages, 10 figures, to appear in Proc. of IAUS 382: Complex Planetary Systems II (CPS II) 2023

We investigate the low-lying baryon spectrum using three $N_f$=2+1+1 ensembles simulated with physical values of the quark masses and lattice spacings of 0.080, 0.069, and 0.057 fm. The ensembles are generated using twisted mass clover-improved fermions and the Iwasaki gauge action. The spatial length is kept approximately the same at about 5.1 fm to 5.5 fm fulfilling the condition $m_\pi L$> 3.6. We investigate isospin splitting within isospin multiples and verify that for most cases the isospin splitting for these lattice spacing is consistent with zero. In the couple of cases, for which there is a non-zero value, in the continuum limit, the mass splitting goes to zero. The baryon masses are extrapolated to the continuum limit using the three $N_f$=2+1+1 ensembles and are compared to other recent lattice QCD results. For the strange and charm quark masses, we find, respectively, $m_s$(2 GeV)=99.2(2.7) MeV and $m_c$(3 GeV)=1.015(39) GeV. The values predicted for the masses of the doubly charmed $\Xi_{cc}^\star$, $\Omega_{cc}$ and $\Omega_{cc}^\star$ baryons are 3.676(55) GeV, 3.703(51) GeV and 3.803(50) GeV, respectively, and for the triply charmed $\Omega_{ccc}$ baryon is 4.785(71) GeV., Comment: accepted version, 15 pages, 18 figures, 10 tables

Network coordination across multiple domains is a complex task requiring seamless communication between network entities. Network operators target to minimize costs while ensuring the requirements of the user requests. Such efforts are highly challenging in decentralized environments with diverse network operators, where only partial knowledge of the complete network is available. Intent-driven multi-domain coordination offers various benefits, some inherent to Intent-Based Networking (IBN) and others stemming from the standardization of the Northbound Interface (NBI). As standardization is still missing, there has not been a substantial initiative to develop tools that leverage this paradigm. MINDFul.jl is a Julia library that fills this gap and provides the means to accelerate research in this area, both at the architectural and the algorithmic level. It provides a stateful, modular representation of common metro/core IP-optical network equipment as well as the common intent operations. Finally, it facilitates event-based simulations with a hackable interface and offers visualization support.

During the last few years, there have been concentrated efforts toward intent-driven networking. While relying upon Software-Defined Networking (SDN), Intent-Based Networking (IBN) pushes the frontiers of efficient networking by decoupling the intentions of a network operator (i.e., what is desired to be done) from the implementation (i.e., how is it achieved). The advantages of such a paradigm have long been argued and include, but are not limited to, the reduction of human errors, reduced expertise requirements among operator personnel, and faster business plan adaptation. In previous work, we have shown how incorporating IBN in multi-domain networks can have a significantly positive impact as it can enable decentralized operation, accountability, and confidentiality. The pillar of our previous contribution is the compilation of intents using system-generated intent trees. In this work, we extend the architecture to enable grooming among the user intents. Therefore, separate intents can now end up using the same network resources. While this makes the intent system reasonably more complex, it indisputably improves resource allocation. To represent the intent relationships of the newly enhanced architecture, we use Directed Acyclic Graphs (DAGs). Furthermore, we appropriately adapt an advanced established technique from the literature to solve the Routing, Modulation, and Spectrum Assignment (RMSA) problem for the intent compilation. We demonstrate a realistic scenario in which we evaluate our architecture and the intent compilation strategy. Our current approach successfully consolidates the advantages of having an intent-driven architecture and, at the same time, flexibly choosing among advanced resource allocation techniques.

In the Time-Windows TSP (TW-TSP) we are given requests at different locations on a network; each request is endowed with a reward and an interval of time; the goal is to find a tour that visits as much reward as possible during the corresponding time window. For the online version of this problem, where each request is revealed at the start of its time window, no finite competitive ratio can be obtained. We consider a version of the problem where the algorithm is presented with predictions of where and when the online requests will appear, without any knowledge of the quality of this side information. Vehicle routing problems such as the TW-TSP can be very sensitive to errors or changes in the input due to the hard time-window constraints, and it is unclear whether imperfect predictions can be used to obtain a finite competitive ratio. We show that good performance can be achieved by explicitly building slack into the solution. Our main result is an online algorithm that achieves a competitive ratio logarithmic in the diameter of the underlying network, matching the performance of the best offline algorithm to within factors that depend on the quality of the provided predictions. The competitive ratio degrades smoothly as a function of the quality and we show that this dependence is tight within constant factors., Comment: 31 pages, 1 figure

We exploit the increased sensitivity of the recently installed AO SOUL at the LBT to obtain new high-spatial-resolution NIR images of the massive young stellar object IRAS20126+4104 and its outflow. We aim to derive the jet proper motions and kinematics, as well as to study its photometric variability by combining the novel performances of SOUL together with previous NIR images. We used both broad-band ($K_{s}$, $K'$) and narrow-band (Br$\gamma$, H2) observations from a number of NIR cameras (UKIRT/UFTI,SUBARU/CIAO,TNG/NICS,LBT/PISCES,and LBT/LUCI1) to derive maps of the continuum and the H$_2$ emission in the 2.12 $\mu$m line. Three sets of images, obtained with AO systems (CIAO,2003; FLAO,2012; SOUL,2020), allowed us to derive the proper motions of a large number of H$_2$ knots along the jet. Photometry from all images was used to study the jet variability. We derived knot proper motions in the range of 1.7-20.3 mas yr$^{-1}$ (i.e. 13-158 km s$^{-1}$ at 1.64 kpc, avg. outflow tangential velocity $\sim$ 80 km s$^{-1}$). The derived knot dynamical age spans a $\sim$ 200-4000 yr interval. A ring-like H$_2$ feature near the protostar location exhibits peculiar kinematics and may represent the outcome of a wide-angle wind impinging on the outflow cavity. Both H$_2$ geometry and velocities agree with those inferred from proper motions of the H$_2$O masers, located at a smaller distance from the protostar. Although the total H$_2$ line emission from the knots does not exhibit time variations at a $\widetilde{>}$ 0.3 mag level, we have found a clear continuum flux variation (radiation scattered by the dust in the cavity opened by the jet) which is anti-correlated between the blue-shifted and red-shifted lobes and may be periodic (with a period of $\sim$ 12-18 yr). We suggest that the continuum variability might be related to inner-disc oscillations which have also caused the jet precession., Comment: 26 pages, 22 figures, 2 mpeg files, accepted by Astronomy & Astrophysics