The Lax pair for C_2-type Ruijsenaars-Schneider model

We study the C_2 Ruijsenaars-Schneider(RS) model with interaction potential of trigonometric type. The Lax pairs for the model with and without spectral parameter are constructed. Also given are the involutive Hamiltonians for the system. Taking nonrelativistic limit, we obtain the Lax pair of C_2 Calogero-Moser model.Comment: LaTeX2e, 10 pages, some misprints corrected and sections rearrange

Resource-Efficient Replication and Migration of Virtual Machines.

Continuous replication and live migration of Virtual Machines (VMs) are two vital tools in a virtualized environment, but they are resource-expensive. Continuously replicating a VM's checkpointed state to a backup host maintains high-availability (HA) of the VM despite host failures, but checkpoint replication can generate significant network traffic. Each replicated VM also incurs a 100% memory overhead, since the backup unproductively reserves the same amount of memory to hold the redundant VM state. Live migration, though being widely used for load-balancing, power-saving, etc., can also generate excessive network traffic, by transferring VM state iteratively. In addition, it can incur a long completion time and degrade application performance. This thesis explores ways to replicate VMs for HA using resources efficiently, and to migrate VMs fast, with minimal execution disruption and using resources efficiently. First, we investigate the tradeoffs in using different compression methods to reduce the network traffic of checkpoint replication in a HA system. We evaluate gzip, delta and similarity compressions based on metrics that are specifically important in a HA system, and then suggest guidelines for their selection. Next, we propose HydraVM, a storage-based HA approach that eliminates the unproductive memory reservation made in backup hosts. HydraVM maintains a recent image of a protected VM in a shared storage by taking and consolidating incremental VM checkpoints. When a failure occurs, HydraVM quickly resumes the execution of a failed VM by loading a small amount of essential VM state from the storage. As the VM executes, the VM state not yet loaded is supplied on-demand. Finally, we propose application-assisted live migration, which skips transfer of VM memory that need not be migrated to execute running applications at the destination. We develop a generic framework for the proposed approach, and then use the framework to build JAVMM, a system that migrates VMs running Java applications skipping transfer of garbage in Java memory. Our evaluation results show that compared to Xen live migration, which is agnostic of running applications, JAVMM can reduce the completion time, network traffic and application downtime caused by Java VM migration, all by up to over 90%.PhDComputer Science and EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/111575/1/karenhou_1.pd

Expect the Unexpected: Deciphering Exoplanetary Signals with Machine Learning Techniques

The field of exoplanets has enjoyed unprecedented growth in the past decades, planets are being discovered at an exponential rate. With the launch of next-generation facilities in the coming decades, the arrival of high-quality spectroscopic data is expected to bring about yet another revolutionary change in our understanding of these remote worlds. The field has been actively developing tools to comprehend the large stream of incoming data, and among them, Machine Learning techniques are building up momentum as an alternative to conventional approaches. In this work, I developed methodologies to uncover potential biases in the interpretation of the exoplanetary atmosphere introduced during data analysis. I showed that naively combining observations from different instruments might lead to biased results, and in some extreme cases like WASP-96 b, it is impossible to com- bine observations. A new scheme of retrieval framework, namely the L - retrieval, holds the potential to detect incompatibility among different datasets by combining light-curve fitting with atmospheric radiative transfer modelling. This work also documents the application of ML techniques to two distinct fields of exoplanetary science: a planet signal detection pipeline for direct imaging data and a suite of diagnostic tools designed for the characterisation of exoplanets. In both approaches, I pioneered the integration of Explainable AI techniques to improve the reliability of the deep learning models. Initial successes of these novel methodologies have provided an exciting prospect to tackle upcoming challenges with the use of Artificial Intelligence. How- ever, significant work remains to progress these models from their current proof-of- concept stage to general application framework. In this thesis, I will discuss their current limitations, potential future, and the next steps required

Threshold Effects in the Decay of Heavy b' and t' Quarks

A sequential fourth generation is still viable, but the t' and b' quarks are constrained to be not too far apart in mass. The t'{\to}bW and b'{\to}tW decay channels are still being pursued at the Tevatron, which would soon be surpassed by the LHC. We use a convolution method with up to five-body final state to study t' and b' decays. We show how the two decay branches for m_{b'} below the tW threshold, b'{\to}tW^* and t^*W, merge with b'{\to}tW above the threshold. We then consider the heavy-to-heavy transitions b'{\to}t^{\prime(*)}W^{(*)} (or t'{\to}b^{\prime(*)}W^{(*)}), as they are not suppressed by quark mixing. We find that, because of the threshold sensitivity of the branching fraction of t'{\to}b'W^* (or b'{\to}t'W^*), it is possible to measure the strength of the CKM mixing element V_{t'b} (or V_{tb'}), especially when it is rather small. We urge the experiments to pursue and separate the t'{\to}b'W^* (or b'{\to}t'W^*) decay in their search program

ESA-Ariel Data Challenge NeurIPS 2022: introduction to exo-atmospheric studies and presentation of the Atmospheric Big Challenge (ABC) Database

This is an exciting era for exo-planetary exploration. The recently launched JWST, and other upcoming space missions such as Ariel, Twinkle, and ELTs are set to bring fresh insights to the convoluted processes of planetary formation and evolution and its connections to atmospheric compositions. However, with new opportunities come new challenges. The field of exoplanet atmospheres is already struggling with the incoming volume and quality of data, and machine learning (ML) techniques lands itself as a promising alternative. Developing techniques of this kind is an inter-disciplinary task, one that requires domain knowledge of the field, access to relevant tools and expert insights on the capability and limitations of current ML models. These stringent requirements have so far limited the developments of ML in the field to a few isolated initiatives. In this paper, We present the Atmospheric Big Challenge Database (ABC Database), a carefully designed, organized, and publicly available data base dedicated to the study of the inverse problem in the context of exoplanetary studies. We have generated 105 887 forward models and 26 109 complementary posterior distributions generated with Nested Sampling algorithm. Alongside with the data base, this paper provides a jargon-free introduction to non-field experts interested to dive into the intricacy of atmospheric studies. This data base forms the basis for a multitude of research directions, including, but not limited to, developing rapid inference techniques, benchmarking model performance, and mitigating data drifts. A successful application of this data base is demonstrated in the NeurIPS Ariel ML Data Challenge 2022