Author Q&A: Karan Patel
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Linear and non-linear response of quadratic Lindbladians
Quadratic Lindbladians encompass a rich class of dissipative electronic and bosonic quantum systems, which have been predicted to host new and exotic physics. In this study, we develop a Lindblad-Keldysh spectroscopic response formalism for open quantum systems that elucidates their steady-state response properties and dissipative phase transitions via finite-frequency linear and non-linear probes. As illustrative examples, we utilize this formalism to calculate the (1) density and dynamic spin susceptibilities of a boundary driven XY model at and near criticality, (2) linear and non-linear optical responses in Bernal bilayer graphene coupled to dissipative leads, and (3) steady state susceptibilities in a bosonic optical lattice. We find that the XY model spin density wavelength diverges with critical exponent 1/2, and there are gapless dispersive modes in the dynamic spin response that originate from the underlying spin density wave order; additionally the dispersing modes of the weak and ultra-strong dissipation limits exhibit a striking correspondence since the boundary dissipators couple only weakly to the bulk in both cases. In the optical response of the Bernal bilayer, we find that the diamagnetic response can decrease with increasing occupation, as opposed to in closed systems where the response increases monotonically with occupation; we study the effect of second harmonic generation and shift current and find that these responses, forbidden in centrosymmetric closed systems, can manifest in these open systems as a result of dissipation. We compare this formalism to its equilibrium counterpart and draw analogies between these non-interacting open systems and strongly interacting closed systems.
Stability and control analysis of COVID-19 spread in India using SEIR model
In this work, we investigate a mathematical model that depicts the dynamics of COVID-19, with an emphasis on the effectiveness of detection and diagnosis procedures as well as the impact of quarantine measures. Using data from May 1 to May 31, 2020, the current study compares three states: Tamil Nadu, Maharashtra, and Andhra Pradesh. A compartmental model has been developed in order to forecast the pandemic’s trajectory and devise an effective control strategy. The study then examines the dynamic progression of the pandemic by including important epidemiological factors into a modified SEIR (Susceptible, Exposed, Infectious, Recovered) model. Our method is a thorough analysis of the equilibria of the deterministic mathematical model in question. We use rigorous techniques to find these equilibrium points and then conduct a comprehensive investigation of their stability. Furthermore, an optimum control problem is applied to reduce the illness fatality, taking into account both pharmaceutical and nonpharmaceutical intervention options as control functions. With the aid of Pontryagin’s maximal principle, an objective functional has been created and solved in order to minimize the number of infected people and lower the cost of the controls. In terms of the basic reproduction number, the stability of biologically plausible equilibrium points and the qualitative behavior of the model are examined. We found that the disease transmission rate has an effect on reducing the spread of diseases after conducting sensitivity analysis with regard to the basic reproduction number. According to the findings, Tamil Nadu had the lowest reproduction number ((R_0 = 0.0334)) and Maharashtra the highest ((R_0 = 0.2170)), indicating regional differences in the efficacy of public health initiatives. Furthermore, it has been demonstrated that appropriate control strategies, such as vaccination ((M)), can successfully reduce infection levels and improve recovery rates. In our study compared to the other two states, Tamil Nadu is notable for its quick recovery and decrease in infection rates. In our findings are more dependable and applicable when mathematical analysis and numerical simulations are combined, which also helps to provide a more thorough understanding of the dynamics at work in the COVID-19 environment. This research also offers suggestions for how government agencies, health groups, and legislators can lessen the effects of COVID-19 and distribute resources as efficiently as possible . Finally, we conclude by discussing the optimal control strategy to contain the epidemic.
GenAI synthesis of histopathological images from Raman imaging for intraoperative tongue squamous cell carcinoma assessment
The presence of a positive deep surgical margin in tongue squamous cell carcinoma (TSCC) significantly elevates the risk of local recurrence. Therefore, a prompt and precise intraoperative assessment of margin status is imperative to ensure thorough tumor resection. In this study, we integrate Raman imaging technology with an artificial intelligence (AI) generative model, proposing an innovative approach for intraoperative margin status diagnosis. This method utilizes Raman imaging to swiftly and non-invasively capture tissue Raman images, which are then transformed into hematoxylin-eosin (H&E)-stained histopathological images using an AI generative model for histopathological diagnosis. The generated H&E-stained images clearly illustrate the tissue’s pathological conditions. Independently reviewed by three pathologists, the overall diagnostic accuracy for distinguishing between tumor tissue and normal muscle tissue reaches 86.7%. Notably, it outperforms current clinical practices, especially in TSCC with positive lymph node metastasis or moderately differentiated grades. This advancement highlights the potential of AI-enhanced Raman imaging to significantly improve intraoperative assessments and surgical margin evaluations, promising a versatile diagnostic tool beyond TSCC.
Stabilization of Kerr-cat qubits with quantum circuit refrigerator
A periodically driven superconducting nonlinear resonator can implement a Kerr-cat qubit, which provides a promising route to a quantum computer with a long lifetime. However, the system is vulnerable to pure dephasing, which causes unwanted excitations outside the qubit subspace. Therefore, we require a refrigeration technology that confines the system in the qubit subspace. We theoretically study on-chip refrigeration for Kerr-cat qubits based on photon-assisted electron tunneling at tunneling junctions, called quantum circuit refrigerators (QCR). Rates of QCR-induced deexcitations of the system can be changed by more than four orders of magnitude by tuning a bias voltage across the tunneling junctions. Unwanted QCR-induced bit flips are greatly suppressed due to quantum interference in the tunneling process, and thus the long lifetime is preserved. The QCR can serve as a tunable dissipation source that stabilizes Kerr-cat qubits.
An integrated perspective on single-cell and spatial transcriptomic signatures in high-grade gliomas
High-grade gliomas (HGG) are incurable brain malignancies in children and adults. Breakthrough advances in transcriptomic technologies unveiled the intricate diversity of cellular states and their spatial organization within HGGs. We qualitatively integrated 55 neoplastic transcriptomic signatures described in 17 single-cell and spatial RNA sequencing-based studies. Our review delineates a spectrum of cellular states, represented by the expression of specific genes, which can be conceptualized along a “reactive-developmental programs” axis. Additionally, we discussed the potential cues influencing these cellular states, including how spatial organization may impact transcriptomic dynamics. Leveraging these insightful discoveries, we discussed a novel, evolutive way to integrate the different transcriptomic signatures in two or three dimensions, incorporating developmental states, their proliferative capacity, and their possible transition towards reactive states. This integrated analysis illuminates the diverse cellular landscape of HGGs and provides a valuable resource for further elucidation of malignant mechanisms, and for the design of therapeutic endeavors.
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