In this paper, we consider a general distributed system with multiple agents who select and then implement actions in the system. The system has an operator with a centralized objective. The agents, ...on the other hand, are self-interested and strategic in the sense that each agent optimizes its own individual objective. The operator aims to mitigate this misalignment by designing an incentive scheme for the agents. The problem is difficult due to the cost functions of the agents being coupled, the objective of the operator not being social welfare, and the operator having no direct control over actions being implemented by the agents. This problem has been studied in many fields, particularly in mechanism design and cost allocation. However, mechanism design typically assumes that the objective of the operator is social welfare and the actions being implemented by the operator. On the other hand, cost allocation classically assumes that agents do not anticipate the effect of their actions on the incentive that they obtain. We remove these assumptions and present an incentive rule for this setup by bridging the gap between mechanism design and classical cost allocation. We analyze whether the proposed design satisfies various desirable properties such as social optimality, budget balance, participation constraint, and so on. We also analyze which of these properties can be satisfied if the assumptions on cost functions of the agents being private and the agents being anticipatory are relaxed.
Meningitis after spine surgery is a rare complication. In this report, we aim to discuss the case of a male patient who developed this rare condition after undergoing cervical spine surgery with ...devastating outcomes. We also engage in a review of the relevant literature. A 17-year-old boy presented with post-traumatic cervical kyphotic deformity with signs of cord compression. He was operated in three stages, all conducted in a single sitting. There was an incidental cerebrospinal fluid (CSF) leak, which was primarily repaired. On the fourth postoperative day, the patient developed altered sensorium and seizures. Evaluations for clinical signs of meningitis such as neck rigidity and Kernig's sign were inconclusive. CSF analysis confirmed the diagnosis of meningitis. Thereafter, the patient developed hydrocephalus and intractable infection, for which multiple procedures were done. Finally, we succeeded in controlling the infection, but the patient developed a neurological deficit, which did not resolve even after 2.5 years of follow-up. The clinical signs and symptoms of meningitis after cervical spine surgery are not very clear or suggestive. A strong index of suspicion should be maintained for the early detection of this condition to prevent devastating complications that result from it.
Policy Iteration (PI) is a widely used family of algorithms to compute optimal policies for Markov Decision Problems (MDPs). We derive upper bounds on the running time of PI on Deterministic MDPs ...(DMDPs): the class of MDPs in which every state-action pair has a unique next state. Our results include a non-trivial upper bound that applies to the entire family of PI algorithms, and affirmation that a conjecture regarding Howard's PI on MDPs is true for DMDPs. Our analysis is based on certain graph-theoretic results, which may be of independent interest.
This paper presents EinsteinPy (version 0.3), a community-developed Python package for gravitational and relativistic astrophysics. Python is a free, easy to use a high-level programming language ...which has seen a huge expansion in the number of its users and developers in recent years. Specifically, a lot of recent studies show that the use of Python in Astrophysics and general physics has increased exponentially. We aim to provide a very high level of abstraction, an easy to use interface and pleasing user experience. EinsteinPy is developed keeping in mind the state of a theoretical gravitational physicist with little or no background in computer programming and trying to work in the field of numerical relativity or trying to use simulations in their research. Currently, EinsteinPy supports simulation of time-like and null geodesics and calculates trajectories in different background geometries some of which are Schwarzschild, Kerr, and KerrNewmann along with coordinate inter-conversion pipeline. It has a partially developed pipeline for plotting and visualization with dependencies on libraries like Plotly, matplotlib, etc. One of the unique features of EinsteinPy is a sufficiently developed symbolic tensor manipulation utilities which are a great tool in itself for teaching yourself tensor algebra which for many beginner students can be overwhelmingly tricky. EinsteinPy also provides few utility functions for hypersurface embedding of Schwarzschild spacetime which further will be extended to model gravitational lensing simulation.
A procedure is developed to automatically correct the bit flip and the arbitrary phase change errors in Generalized Bell states (GBS). The phase and parity characteristics of the GBS are encoded in ...ancilla bits without altering the state under consideration. The same information is then used to correct the state at a different point, through appropriate unitrary control operations. It is also shown that the distributed/indirect measurements on ancilla can yield the error syndrome. The restricted error correction circuit obtained for N-qubit entangled states of the Bell type, are generalized for the corresponding higher dimensions, thus opening up the possibility of designing of task specific error correction circuits.
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