Genus Two Modular Bootstrap

We study the Virasoro conformal block decomposition of the genus two partition function of a two-dimensional CFT by expanding around a Z3-invariant Riemann surface that is a three-fold cover of the Riemann sphere branched at four points, and explore constraints from genus two modular invariance and unitarity. In particular, we find 'critical surfaces' that constrain the structure constants of a CFT beyond what is accessible via the crossing equation on the sphere.Comment: 23 pages, 6 figures. v2: updated references, typos corrected. v3-v5: minor typos correcte

Recursive Representations of Arbitrary Virasoro Conformal Blocks

We derive recursive representations in the internal weights of N-point Virasoro conformal blocks in the sphere linear channel and the torus necklace channel, and recursive representations in the central charge of arbitrary Virasoro conformal blocks on the sphere, the torus, and higher genus Riemann surfaces in the plumbing frame.Comment: 39 pages, 8 figures, v2: comments on references added, reference added, typos corrected, v3: comments on the relation between the plumbing and the Schottky parameters added, v4: typos correcte

Bootstrap, Markov Chain Monte Carlo, and LP/SDP Hierarchy for the Lattice Ising Model

Bootstrap is an idea that imposing consistency conditions on a physical system may lead to rigorous and nontrivial statements about its physical observables. In this work, we discuss the bootstrap problem for the invariant measure of the stochastic Ising model defined as a Markov chain where probability bounds and invariance equations are imposed. It is described by a linear programming (LP) hierarchy whose asymptotic convergence is shown by explicitly constructing the invariant measure from the convergent sequence of moments. We also discuss the relation between the LP hierarchy for the invariant measure and a recently introduced semidefinite programming (SDP) hierarchy for the Gibbs measure of the statistical Ising model based on reflection positivity and spin-flip equations.Comment: 28 page

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School of Energy and Chemical Engineering (Chemical Engineering)An artificial cathode-electrolyte interphase (CEI) layer was employed on graphite to improve the anion intercalation reversibility for dual ion batteries (DIBs). An interesting LiF morphology feature was developed to have a nanometer-thick LiF skin on each graphite particle with a micrometer-thick LiF deposit on the electrode. The LiF skin/deposit nexus assembly on graphite played a role of: (1) facilitating anion intercalation kinetics, (2) alleviating volume expansion of graphite cathode and (3) suppressing electrolyte decomposition. Resultantly, it prolonged the cycling durability up to 86% capacity retention after 3000 cycles for the DIB cells having the natural graphite with the LiF-rich skin as the cathode with lithium metal anode (NG@LiFLi). Also, there was an insignificant capacity decay when the NG@LiFLi cell was charged even at 30C. Furthermore, the dual graphite battery (DGB) cell with NG@LiF cathode showed 97 % capacity retention up to 400 cycles.ope

Rolling tachyon and the Phase Space of Open String Field Theory

We construct the symplectic form on the covariant phase space of the open string field theory on a ZZ-brane in c=1 string theory, and determine the energy of the rolling tachyon solution, confirming Sen's earlier proposal based on boundary conformal field theory and closed string considerations.Comment: 33 pages, 6 figure

Out-of-Distribution Adaptation in Offline RL: Counterfactual Reasoning via Causal Normalizing Flows

Despite notable successes of Reinforcement Learning (RL), the prevalent use of an online learning paradigm prevents its widespread adoption, especially in hazardous or costly scenarios. Offline RL has emerged as an alternative solution, learning from pre-collected static datasets. However, this offline learning introduces a new challenge known as distributional shift, degrading the performance when the policy is evaluated on scenarios that are Out-Of-Distribution (OOD) from the training dataset. Most existing offline RL resolves this issue by regularizing policy learning within the information supported by the given dataset. However, such regularization overlooks the potential for high-reward regions that may exist beyond the dataset. This motivates exploring novel offline learning techniques that can make improvements beyond the data support without compromising policy performance, potentially by learning causation (cause-and-effect) instead of correlation from the dataset. In this paper, we propose the MOOD-CRL (Model-based Offline OOD-Adapting Causal RL) algorithm, which aims to address the challenge of extrapolation for offline policy training through causal inference instead of policy-regularizing methods. Specifically, Causal Normalizing Flow (CNF) is developed to learn the transition and reward functions for data generation and augmentation in offline policy evaluation and training. Based on the data-invariant, physics-based qualitative causal graph and the observational data, we develop a novel learning scheme for CNF to learn the quantitative structural causal model. As a result, CNF gains predictive and counterfactual reasoning capabilities for sequential decision-making tasks, revealing a high potential for OOD adaptation. Our CNF-based offline RL approach is validated through empirical evaluations, outperforming model-free and model-based methods by a significant margin.Comment: Submitted for review at IEEE: Neural Networks and Learning System

Facial emotion-recognition deficits in patients with schizophrenia and unaffected first-degree relatives

IntroductionThis study aimed to determine trait- and state-dependent markers of schizophrenia by investigating facial emotion-recognition (FER) deficits in remitted patients with schizophrenia and their first-degree relatives (FR).MethodsThree groups were included: the Schizophrenia group (n=66), their unaffected FR group (n=40), and healthy controls (n=50) who were matched for age, sex, and years of education. A facial-labeling task was used to examine FER deficits using the following eight standardized expressions: happy, fearful, disgusted, angry, sad, contemptuous, surprised, and neutral.ResultsThere was a poorer accuracy in the recognition of sadness and anger in the Schizophrenia group as well as in contempt in both the Schizophrenia and FR groups compared with healthy controls. The response times for the recognition of contempt, sadness, and neutral emotion were delayed in the Schizophrenia group and those for fear were delayed in the Schizophrenia and FR groups compared with healthy controls.ConclusionConcerning the accuracy in FER, sadness and anger can be considered state-dependent markers of remitted schizophrenia, and contempt is a trait-dependent marker of schizophrenia. Similarly, for response times in FER, contempt, sadness, and neutral emotion can be considered state-dependent markers of remitted schizophrenia, while fear is considered a trait-dependent marker of schizophrenia. These findings may contribute to the early diagnosis of schizophrenia and the development of relevant therapeutic interventions

Sparsity-based Safety Conservatism for Constrained Offline Reinforcement Learning

Reinforcement Learning (RL) has made notable success in decision-making fields like autonomous driving and robotic manipulation. Yet, its reliance on real-time feedback poses challenges in costly or hazardous settings. Furthermore, RL\u27s training approach, centered on on-policy sampling, doesn\u27t fully capitalize on data. Hence, Offline RL has emerged as a compelling alternative, particularly in conducting additional experiments is impractical, and abundant datasets are available. However, the challenge of distributional shift (extrapolation), indicating the disparity between data distributions and learning policies, also poses a risk in offline RL, potentially leading to significant safety breaches due to estimation errors (interpolation). This concern is particularly pronounced in safety-critical domains, where real-world problems are prevalent. To address both extrapolation and interpolation errors, numerous studies have introduced additional constraints to confine policy behavior, steering it towards more cautious decision-making. While many studies have addressed extrapolation errors, fewer have focused on providing effective solutions for tackling interpolation errors. For example, some works tackle this issue by incorporating potential cost-maximizing optimization by perturbing the original dataset. However, this, involving a bi-level optimization structure, may introduce significant instability or complicate problem-solving in high-dimensional tasks. This motivates us to pinpoint areas where hazards may be more prevalent than initially estimated based on the sparsity of available data by providing significant insight into constrained offline RL. In this paper, we present conservative metrics based on data sparsity that demonstrate the high generalizability to any methods and efficacy compared to using bi-level cost-ub-maximization

Temperature effects on electromechanical response of deposited piezoelectric sensors used in structural health monitoring of aerospace structures

Turbomachine components used in aerospace and power plant applications preferably require continuous structural health monitoring at various temperatures. The structural health of pristine and damaged superalloy compressor blades of a gas turbine engine was monitored using real electro-mechanical impedance of deposited thick film piezoelectric transducers at 20 and 200 °C. IVIUM impedance analyzer was implemented in laboratory conditions for damage detection in superalloy blades, while a custom-architected frequency-domain transceiver circuit was used for semi-field circumstances. Recorded electromechanical impedance signals at 20 and 200 °C acquired from two piezoelectric wafer active sensors bonded to an aluminum plate, near and far from the damage, were initially utilized for accuracy and reliability verification of the transceiver at temperatures >20 °C. Damage formation in both the aluminum plate and blades showed a peak shift in the swept frequency along with an increase in the amplitude and number of impedance peaks. The thermal energy at 200 °C, on the other hand, enforces a further subsequent peak shift in the impedance signal to pristine and damaged parts such that the anti-resonance frequency keeps reducing as the temperature increases. The results obtained from the impedance signals of both piezoelectric wafers and piezo-films, revealed that increasing the temperature somewhat decreased the real impedance amplitude and the number of anti-resonance peaks, which is due to an increase in permittivity and capacitance of piezo-sensors. A trend is also presented for artificial intelligence training purposes to distinguish the effect of the temperature versus damage formation in sample turbine compressor blades. Implementation of such a monitoring system provides a distinct advantage to enhance the safety and functionality of critical aerospace components working at high temperatures subjected to crack, wear, hot-corrosion and erosion