An exploratory prospective clinical study to assess the combined effect of Virechana and Raktamokshana in Vicharchika - A Case Study

Vicharchika is one of the Kshudra Kushta (skin disease). Kashyapa mentioned it as Sadhya Vyadhi. Almost all symptoms are Vata-Pitta or Kapha-Pitta predominant and even Tridosha involvement and it is specifically located at lower extremities. The choice of treatment is Virechana (purgation) and Raktamokshan (bloodletting). We can use this modality as per requirement. Kandu (itching), Pidika (pimples), Bahusrava (discharge) get relieved completely (100%) after Virechana. Mild effect was noticed in Shyava (blackish discoloration) and Rukshata (dryness) i.e. (33.33%). Highly significant result found after both the therapies (Virechana and Raktamokshana) and marked improvement was seen in Shyava and Rukshata after Raktamokshana. It shows over all Ayurvedic modality gives very good result in Vicharchika

Limits on Parameter Estimation of Quantum Channels

The aim of this thesis is to develop a theoretical framework to study parameter estimation of quantum channels. We begin by describing the classical task of parameter estimation that we build upon. In its most basic form, parameter estimation is the task of obtaining an estimate of an unknown parameter from some experimental data. This experimental data can be seen as a number of samples of a parameterized probability distribution. In general, the goal of such a task is to obtain an estimate of the unknown parameter while minimizing its error. We study the task of estimating unknown parameters which are encoded in a quantum channel. A quantum channel is a map that describes the evolution of the state of a quantum system. We study this task in the sequential setting. This means that the channel in question is used multiple times, and each channel use happens subsequent to the previous one. A sequential strategy is the most general way to use, or process, a channel multiple times. Our goal is to establish lower bounds on the estimation error in such a task. These bounds are called Cramer--Rao bounds. Quantum channels encompass all possible dynamics allowed by quantum mechanics, and sequential estimation strategies capture the most general way to process multiple uses of a channel. Therefore, the bounds we develop are universally applicable. We consider the use of catalysts to enhance the power of a channel estimation strategy. This is termed amortization. The reason we do so is to investigate if an n-round sequential estimation strategy does better than a simpler parallel strategy. Quantitatively, the power of a channel for a particular estimation task is determined by the channel\u27s Fisher information. Thus, we study how much a catalyst quantum state can enhance the Fisher information of a quantum channel by defining the amortized Fisher information. In the quantum setting, there are many Fisher information quantities that can be defined. We limit our study to two particular ones: the symmetric logarithmic derivative (SLD) Fisher information and the right logarithmic derivative (RLD) Fisher information. We establish our Cramer--Rao bounds by proving that for certain Fisher information quantities, catalyst states do not improve the performance of a sequential estimation protocol. The technical term for this is an amortization collapse. We show how such a collapse leads directly to a corresponding Cramer--Rao bound. We establish bounds both when estimating a single parameter and when estimating multiple parameters simultaneously. For the single parameter case, we establish Cramer--Rao bounds for general quantum channels using both the SLD and RLD Fisher information. The task of estimating multiple parameters simultaneously is more involved than the single parameter case. In the multiparameter case, Cramer--Rao bounds take the form of matrix inequalities. We provide a method to obtain scalar Cramer--Rao bounds from the corresponding matrix inequalities. We then establish a scalar Cramer--Rao bound using the RLD Fisher information. Our bounds apply universally and we also show how they are efficiently computable by casting them as optimization problems. In the single parameter case, we recover the so-called Heisenberg scaling\u27\u27 using our SLD-based bound. On the other hand, we provide a no-go condition for Heisenberg scaling using our RLD-based bound for both the single and multiparameter settings. Finally, we apply our bounds to the example of estimating the parameters of a generalized amplitude damping channel

Entropic Energy-Time Uncertainty Relation

Energy-time uncertainty plays an important role in quantum foundations and technologies, and it was even discussed by the founders of quantum mechanics. However, standard approaches (e.g., Robertson's uncertainty relation) do not apply to energy-time uncertainty because, in general, there is no Hermitian operator associated with time. Following previous approaches, we quantify time uncertainty by how well one can read off the time from a quantum clock. We then use entropy to quantify the information-theoretic distinguishability of the various time states of the clock. Our main result is an entropic energy-time uncertainty relation for general time-independent Hamiltonians, stated for both the discrete-time and continuous-time cases. Our uncertainty relation is strong, in the sense that it allows for a quantum memory to help reduce the uncertainty, and this formulation leads us to reinterpret it as a bound on the relative entropy of asymmetry. Due to the operational relevance of entropy, we anticipate that our uncertainty relation will have information-processing applications.Comment: 6 + 9 pages, 2 figure

RLD Fisher information bound for multiparameter estimation of quantum channels

One of the fundamental tasks in quantum metrology is to estimate multiple parameters embedded in a noisy process, i.e. a quantum channel. In this paper, we study fundamental limits to quantum channel estimation via the concept of amortization and the right logarithmic derivative (RLD) Fisher information value. Our key technical result is the proof of a chain-rule inequality for the RLD Fisher information value, which implies that amortization, i.e. access to a catalyst state family, does not increase the RLD Fisher information value of quantum channels. This technical result leads to a fundamental and efficiently computable limitation for multiparameter channel estimation in the sequential setting, in terms of the RLD Fisher information value. As a consequence, we conclude that if the RLD Fisher information value is finite, then Heisenberg scaling is unattainable in the multiparameter setting

MaxGap Bandit: Adaptive Algorithms for Approximate Ranking

This paper studies the problem of adaptively sampling from K distributions (arms) in order to identify the largest gap between any two adjacent means. We call this the MaxGap-bandit problem. This problem arises naturally in approximate ranking, noisy sorting, outlier detection, and top-arm identification in bandits. The key novelty of the MaxGap-bandit problem is that it aims to adaptively determine the natural partitioning of the distributions into a subset with larger means and a subset with smaller means, where the split is determined by the largest gap rather than a pre-specified rank or threshold. Estimating an arm's gap requires sampling its neighboring arms in addition to itself, and this dependence results in a novel hardness parameter that characterizes the sample complexity of the problem. We propose elimination and UCB-style algorithms and show that they are minimax optimal. Our experiments show that the UCB-style algorithms require 6-8x fewer samples than non-adaptive sampling to achieve the same error

The Shading Effect of Poplar (Populus Deltoides) on Wheat Crop

This study was conducted in different villages of the district Saharanpur. The poplar tree (Populus deltoides) is used as the tree component and wheat crops are used as intercrops in an agrisilvicultural system. In this study, the different effects of poplar (Populus deltoides) on wheat crops were discussed. The parameters which are recorded were grain yield and biological yield. In the district Saharanpur, there are two patterns of tree growing with crops, block plantation and boundary plantation. It was observed that the yield with block plantation is less than boundary plantation. It was also recorded that 95% of farmers are doing boundary plantation in the district Saharanpur. In shaded areas, grain and straw yields were also drastically lowered by poplar border plantations. All villages saw a significant decline in grain yield due to the shading effect of poplar trees. It is observed that in the villages of district Saharanpur most of the farmers are practicing agroforestry with poplar (Populus deltoides). There are multiple effects of shading on agricultural crops. For this study, those farmers were surveyed who are growing poplar trees with different crops. Trees and crops both were analyzed for the survey

Pseudoaneurysm of profunda femoris artery: a rare complication after intramedullary fixation for an intertrochanteric femur fracture

Intertrochanteric fracture fixation with a trochanteric femoral nail rarely leads to any vascular or neurological complications. The aim of this case report is to identify a patient with post-operative Pseudoaneurysm of profunda femoris artery and how to manage it. We report a case of 79-year-old male who developed a Pseudoaneurysm of the profunda femoris artery 3 days after intramedullary femoral nailing for a intertrochanteric femur fracture. Percutaneous embolization was performed with subsequent resolution of the symptoms. Diagnosis of vascular complications after hip surgery may be very challenging because symptoms are often nonspecific. Despite their rarity, it is important to know this type of complications to address the diagnostic pathway in the right direction and to treat them promptly