Harmonic coordinates in the string and membrane equations

In this note, we first show that the solutions to Cauchy problems for two versions of relativistic string and membrane equations are diffeomorphic. Then we investigate the coordinates transformation presented in Ref. [9] (see (2.20) in Ref. [9]) which plays an important role in the study on the dynamics of the motion of string in Minkowski space. This kind of transformed coordinates are harmonic coordinates, and the nonlinear relativistic string equations can be straightforwardly simplified into linear wave equations under this transformation

Monte Carlo Hamiltonian: the Linear Potentials

We further study the validity of the Monte Carlo Hamiltonian method. The advantage of the method, in comparison with the standard Monte Carlo Lagrangian approach, is its capability to study the excited states. We consider two quantum mechanical models: a symmetric one $V(x) = |x|/2$; and an asymmetric one $V(x)=\infty$, for $x < 0$ and $V(x)=x$, for $x \ge 0$. The results for the spectrum, wave functions and thermodynamical observables are in agreement with the analytical or Runge-Kutta calculations.Comment: Latex file, 8 figure

Monte Carlo Hamiltonian

We suggest how to construct an effective low energy Hamiltonian via Monte Carlo starting from a given action. We test it by computing thermodynamical observables like average energy and specific heat for simple quantum systems.Comment: Contribution to Lattice'99 (Theoretical developments) Text (LaTeX file) + 2 figures (ps files

Learning with Noisily-labeled Class-imbalanced Data

Real-world large-scale datasets are both noisily labeled and class-imbalanced. The issues seriously hurt the generalization of trained models. It is hence significant to address the simultaneous incorrect labeling and class-imbalance, i.e., the problem of learning with noisy labels on long-tailed data. Previous works develop several methods for the problem. However, they always rely on strong assumptions that are invalid or hard to be checked in practice. In this paper, to handle the problem and address the limitations of prior works, we propose a representation calibration method RCAL. Specifically, RCAL works with the representations extracted by unsupervised contrastive learning. We assume that without incorrect labeling and class imbalance, the representations of instances in each class conform to a multivariate Gaussian distribution, which is much milder and easier to be checked. Based on the assumption, we recover underlying representation distributions from polluted ones resulting from mislabeled and class-imbalanced data. Additional data points are then sampled from the recovered distributions to help generalization. Moreover, during classifier training, representation learning takes advantage of representation robustness brought by contrastive learning, which further improves the classifier performance. Experiments on multiple benchmarks justify our claims and confirm the superiority of the proposed method

Toward Transparent Sequence Models with Model-Based Tree Markov Model

In this study, we address the interpretability issue in complex, black-box Machine Learning models applied to sequence data. We introduce the Model-Based tree Hidden Semi-Markov Model (MOB-HSMM), an inherently interpretable model aimed at detecting high mortality risk events and discovering hidden patterns associated with the mortality risk in Intensive Care Units (ICU). This model leverages knowledge distilled from Deep Neural Networks (DNN) to enhance predictive performance while offering clear explanations. Our experimental results indicate the improved performance of Model-Based trees (MOB trees) via employing LSTM for learning sequential patterns, which are then transferred to MOB trees. Integrating MOB trees with the Hidden Semi-Markov Model (HSMM) in the MOB-HSMM enables uncovering potential and explainable sequences using available information

The Drosophila caspase Ice is important for many apoptotic cell deaths and for spermatid individualization, a nonapoptotic process

Caspase family proteases play important roles in the regulation of apoptotic cell death. Initiator caspases are activated in response to death stimuli, and they transduce and amplify these signals by cleaving and thereby activating effector caspases. In Drosophila, the initiator caspase Nc (previously Dronc) cleaves and activates two short-prodomain caspases, Dcp-1 and Ice (previously Drice), suggesting these as candidate effectors of Nc killing activity. dcp-1-null mutants are healthy and possess few defects in normally occurring cell death. To explore roles for Ice in cell death, we generated and characterized an Ice null mutant. Animals lacking Ice show a number of defects in cell death, including those that occur during embryonic development, as well as during formation of adult eyes, arista and wings. Ice mutants exhibit subtle defects in the destruction of larval tissues, and do not prevent destruction of salivary glands during metamorphosis. Cells from Ice animals are also markedly resistant to several stresses, including X-irradiation and inhibition of protein synthesis. Mutations in Ice also suppress cell death that is induced by expression of Rpr, Wrinkled (previously Hid) and Grim. These observations demonstrate that Ice plays an important non-redundant role as a cell death effector. Finally, we demonstrate that Ice participates in, but is not absolutely required for, the non-apoptotic process of spermatid differentiation

Dopamine D1 receptor-mediated NMDA receptor insertion depends on Fyn but not Src kinase pathway in prefrontal cortical neurons

<p>Abstract</p> <p>Background</p> <p>Interactions between dopamine and glutamate in the prefrontal cortex are essential for cognitive functions such as working memory. Modulation of N-methyl-D-aspartic acid (NMDA) receptor functions by dopamine D1 receptor is believed to play a critical role in these functions. The aim of the work reported here is to explore the signaling pathway underlying D1 receptor-mediated trafficking of NMDA receptors in cultured rat prefrontal cortical neurons.</p> <p>Results</p> <p>Activation of D1 receptor by selective agonist SKF-81297 significantly increased the expression of NR2B subunits. This effect was completely blocked by small interfering RNA knockdown of Fyn, but not Src. Under control conditions, neither Fyn nor Src knockdown exhibited significant effect on basal NR2B expression. D1 stimulation significantly enhanced NR2B insertion into plasma membrane in cultured PFC neurons, a process obstructed by Fyn, but not Src, knockdown.</p> <p>Conclusions</p> <p>Dopamine D1 receptor-mediated increase of NMDA receptors is thus Fyn kinase dependent. Targeting this signaling pathway may be useful in treating drug addiction and schizophrenia.</p