Spectral function of the U→∞U \rightarrow \infty one dimensional Hubbard model at finite temperature and the crossover to the spin incoherent regime

The physics of the strongly interacting Hubbard chain (with $t/U \ll 1$) at finite temperatures undergoes a crossover to a spin incoherent regime when the temperature is very small relative to the Fermi energy, but larger than the characteristic spin energy scale. This crossover can be understood by means of Ogata and Shiba's factorized wave function, where charge and spin are totally decoupled, and assuming that the charge remains in the ground state, while the spin is thermally excited and at an effective "spin temperature". We use the time-dependent density matrix renormalization group method (tDMRG) to calculate the dynamical contributions of the spin, to reconstruct the single-particle spectral function of the electrons. The crossover is characterized by a redistribution of spectral weight both in frequency and momentum, with an apparent shift by $k_F$ of the minimum of the dispersion.Comment: 4+pages, 3 fig

Class of variational Ansätze for the spin-incoherent ground state of a Luttinger liquid coupled to a spin bath

Interacting one-dimensional electron systems are generally referred to as “Luttinger liquids”, after the effective low-energy theory in which spin and charge behave as separate degrees of freedom with independent energy scales. The “spin-incoherent Luttinger liquid” describes a finite-temperature regime that is realized when the temperature is very small relative to the Fermi energy, but larger than the characteristic spin energy scale. Similar physics can take place in the ground-state, when a Luttinger Liquid is coupled to a spin bath, which effectively introduces a “spin temperature”through its entanglement with the spin degree of freedom. We show that the spin-incoherent state can be exactly written as a factorized wave-function, with a spin wave-function that can be described within a valence bond formalism. This enables us to calculate exact expressions for the momentum distribution function and the entanglement entropy. This picture holds not only for two antiferromagnetically coupled t−J chains, but also for the t−J-Kondo chain with strongly interacting conduction electrons. We argue that this theory is quite universal and may describe a family of problems that could be dubbed “spin-incoherent”.Accepted manuscrip

Pick the Right Tactics When Online Sales Go Live: An Empirical Analysis of Livestreaming for Amazon Sellers

Using livestreaming to boost sales has become an essential strategy to achieve deeper interactions with customers for many large e-commerce platforms worldwide. Existing livestreaming literature has looked at multiple Chinese e-commerce platforms but not enough attention has been paid to the U.S. market. This study investigates consumer behaviors and the promotion efficacy in the Livestream setting on Amazon Live. We analyze the time patterns of customer engagement and explain why sellers should use different promotion strategies for weekdays and for weekend streamers. Besides, we present evidence that the average video display time per product is crucial for the livestream promotion efficacy and suggest optimal time-exposure intervals as a benchmark for sellers to align with

Pan-cancer classifications of tumor histological images using deep learning

Histopathological images are essential for the diagnosis of cancer type and selection of optimal treatment. However, the current clinical process of manual inspection of images is time consuming and prone to intra- and inter-observer variability. Here we show that key aspects of cancer image analysis can be performed by deep convolutional neural networks (CNNs) across a wide spectrum of cancer types. In particular, we implement CNN architectures based on Google Inception v3 transfer learning to analyze 27815 H&E slides from 23 cohorts in The Cancer Genome Atlas in studies of tumor/normal status, cancer subtype, and mutation status. For 19 solid cancer types we are able to classify tumor/normal status of whole slide images with extremely high AUCs (0.995±0.008). We are also able to classify cancer subtypes within 10 tissue types with AUC values well above random expectations (micro-average 0.87±0.1). We then perform a cross-classification analysis of tumor/normal status across tumor types. We find that classifiers trained on one type are often effective in distinguishing tumor from normal in other cancer types, with the relationships among classifiers matching known cancer tissue relationships. For the more challenging problem of mutational status, we are able to classify TP53 mutations in three cancer types with AUCs from 0.65-0.80 using a fully-trained CNN, and with similar cross-classification accuracy across tissues. These studies demonstrate the power of CNNs for not only classifying histopathological images in diverse cancer types, but also for revealing shared biology between tumors. We have made software available at: https://github.com/javadnoorb/HistCNNFirst author draf

Deep learning-based cross-classifications reveal conserved spatial behaviors within tumor histological images.

Histopathological images are a rich but incompletely explored data type for studying cancer. Manual inspection is time consuming, making it challenging to use for image data mining. Here we show that convolutional neural networks (CNNs) can be systematically applied across cancer types, enabling comparisons to reveal shared spatial behaviors. We develop CNN architectures to analyze 27,815 hematoxylin and eosin scanned images from The Cancer Genome Atlas for tumor/normal, cancer subtype, and mutation classification. Our CNNs are able to classify TCGA pathologist-annotated tumor/normal status of whole slide images (WSIs) in 19 cancer types with consistently high AUCs (0.995 ± 0.008), as well as subtypes with lower but significant accuracy (AUC 0.87 ± 0.1). Remarkably, tumor/normal CNNs trained on one tissue are effective in others (AUC 0.88 ± 0.11), with classifier relationships also recapitulating known adenocarcinoma, carcinoma, and developmental biology. Moreover, classifier comparisons reveal intra-slide spatial similarities, with an average tile-level correlation of 0.45 ± 0.16 between classifier pairs. Breast cancers, bladder cancers, and uterine cancers have spatial patterns that are particularly easy to detect, suggesting these cancers can be canonical types for image analysis. Patterns for TP53 mutations can also be detected, with WSI self- and cross-tissue AUCs ranging from 0.65-0.80. Finally, we comparatively evaluate CNNs on 170 breast and colon cancer images with pathologist-annotated nuclei, finding that both cellular and intercellular regions contribute to CNN accuracy. These results demonstrate the power of CNNs not only for histopathological classification, but also for cross-comparisons to reveal conserved spatial behaviors across tumors

Deep learning-based cross-classifications reveal conserved spatial behaviors within tumor histological images

Histopathological images are a rich but incompletely explored data type for studying cancer. Manual inspection is time consuming, making it challenging to use for image data mining. Here we show that convolutional neural networks (CNNs) can be systematically applied across cancer types, enabling comparisons to reveal shared spatial behaviors. We develop CNN architectures to analyze 27,815 hematoxylin and eosin scanned images from The Cancer Genome Atlas for tumor/normal, cancer subtype, and mutation classification. Our CNNs are able to classify TCGA pathologist-annotated tumor/normal status of whole slide images (WSIs) in 19 cancer types with consistently high AUCs (0.995 ± 0.008), as well as subtypes with lower but significant accuracy (AUC 0.87 ± 0.1). Remarkably, tumor/normal CNNs trained on one tissue are effective in others (AUC 0.88 ± 0.11), with classifier relationships also recapitulating known adenocarcinoma, carcinoma, and developmental biology. Moreover, classifier comparisons reveal intra-slide spatial similarities, with an average tile-level correlation of 0.45 ± 0.16 between classifier pairs. Breast cancers, bladder cancers, and uterine cancers have spatial patterns that are particularly easy to detect, suggesting these cancers can be canonical types for image analysis. Patterns for TP53 mutations can also be detected, with WSI self- and cross-tissue AUCs ranging from 0.65-0.80. Finally, we comparatively evaluate CNNs on 170 breast and colon cancer images with pathologist-annotated nuclei, finding that both cellular and intercellular regions contribute to CNN accuracy. These results demonstrate the power of CNNs not only for histopathological classification, but also for cross-comparisons to reveal conserved spatial behaviors across tumors.R01 CA230031 - NCI NIH HHSPublished versio

Class of variational Ansätze for the spin-incoherent ground state of a Luttinger liquid coupled to a spin bath

Interacting one-dimensional electron systems are generally referred to as "Luttinger liquids", after the effective low-energy theory in which spin and charge behave as separate degrees of freedom with independent energy scales. The "spin-incoherent Luttinger liquid" describes a finite-temperature regime that is realized when the temperature is very small relative to the Fermi energy, but larger than the characteristic spin energy scale. Similar physics can take place in the ground-state, when a Luttinger Liquid is coupled to a spin bath, which effectively introduces a "spin temperature" through its entanglement with the spin degree of freedom. We show that the spin-incoherent state can be written as a factorized wave-function, with a spin wave-function that can be described within a valence bond formalism. This enables us to calculate exact expressions for the momentum distribution function and the entanglement entropy. This picture holds not only for two antiferromagnetically coupled t-J chains, but also for the t-J-Kondo chain with strongly interacting conduction electrons. We argue that this theory is quite universal and may describe a family of problems that could be dubbed "spin-incoherent".Comment: Accepted for publication in PR