Modular Invariance, Tauberian Theorems, and Microcanonical Entropy

We analyze modular invariance drawing inspiration from tauberian theorems. Given a modular invariant partition function with a positive spectral density, we derive lower and upper bounds on the number of operators within a given energy interval. They are most revealing at high energies. In this limit we rigorously derive the Cardy formula for the microcanonical entropy together with optimal error estimates for various widths of the averaging energy shell. We identify a new universal contribution to the microcanonical entropy controlled by the central charge and the width of the shell. We derive an upper bound on the spacings between Virasoro primaries. Analogous results are obtained in holographic 2d CFTs. We also study partition functions with a UV cutoff. Control over error estimates allows us to probe operators beyond the unity in the modularity condition. We check our results in the 2d Ising model and the Monster CFT and find perfect agreement.Comment: 39 pages, 9 figure

Unification of Flavor, CP, and Modular Symmetries

Flavor symmetry plays a crucial role in the standard model of particle physics but its origin is still unknown. We develop a new method (based on outer automorphisms of the Narain space group) to determine flavor symmetries within compactified string theory. A picture emerges where traditional (discrete) flavor symmetries, CP-like symmetries and modular symmetries (like T-duality) of string theory combine to unified flavor symmetries. The groups depend on the geometry of compact space and the geographical location of fields in the extra dimensions. We observe a phenomenon of "local flavor groups" with potentially different flavor symmetries for the various sectors of quarks and leptons. This should allow interesting connections to existing bottom-up attempts in flavor model building.Comment: 18 pages, 3 figures; v2: minor changes, version accepted by PL

A transparent framework towards the context-sensitive recognition of conversational engagement

Modelling and recognising affective and mental user states is an urging topic in multiple research fields. This work suggests an approach towards adequate recognition of such states by combining state-of-the-art behaviour recognition classifiers in a transparent and explainable modelling framework that also allows to consider contextual aspects in the inference process. More precisely, in this paper we exemplify the idea of our framework with the recognition of conversational engagement in bi-directional conversations. We introduce a multi-modal annotation scheme for conversational engagement. We further introduce our hybrid approach that combines the accuracy of state-of-the art machine learning techniques, such as deep learning, with the capabilities of Bayesian Networks that are inherently interpretable and feature an important aspect that modern approaches are lacking - causal inference. In an evaluation on a large multi-modal corpus of bi-directional conversations, we show that this hybrid approach can even outperform state-of-the-art black-box approaches by considering context information and causal relations

New examples of defective secant varieties of Segre-Veronese varieties

We prove the existence of defective secant varieties of three-factor and four-factor Segre-Veronese varieties embedded in certain multi-degree. These defective secant varieties were previously unknown and are of importance in the classification of defective secant varieties of Segre-Veronese varieties with three or more factors.Comment: 10 page

Prostate Cancer Nodal Staging: Using Deep Learning to Predict 68Ga-PSMA-Positivity from CT Imaging Alone

Lymphatic spread determines treatment decisions in prostate cancer (PCa) patients. 68Ga-PSMA-PET/CT can be performed, although cost remains high and availability is limited. Therefore, computed tomography (CT) continues to be the most used modality for PCa staging. We assessed if convolutional neural networks (CNNs) can be trained to determine 68Ga-PSMA-PET/CT-lymph node status from CT alone. In 549 patients with 68Ga-PSMA PET/CT imaging, 2616 lymph nodes were segmented. Using PET as a reference standard, three CNNs were trained. Training sets balanced for infiltration status, lymph node location and additionally, masked images, were used for training. CNNs were evaluated using a separate test set and performance was compared to radiologists' assessments and random forest classifiers. Heatmaps maps were used to identify the performance determining image regions. The CNNs performed with an Area-Under-the-Curve of 0.95 (status balanced) and 0.86 (location balanced, masked), compared to an AUC of 0.81 of experienced radiologists. Interestingly, CNNs used anatomical surroundings to increase their performance, "learning" the infiltration probabilities of anatomical locations. In conclusion, CNNs have the potential to build a well performing CT-based biomarker for lymph node metastases in PCa, with different types of class balancing strongly affecting CNN performance

I see what you did there: understanding when to trust a ML model with NOVA

In this demo paper we present NOVA, a machine learning and explanation interface that focuses on the automated analysis of social interactions. NOVA combines Cooperative Machine Learning (CML) and explainable AI (XAI) methods to reduce manual labelling efforts while simultaneously generating an intuitive understanding of the learning process of a classification system. Therefore, NOVA features a semi-automated labelling process in which users are provided with immediate visual feedback on the predictions, which gives insights into the strengths and weaknesses of the underlying classification system. Following an interactive and exploratory workflow, the performance of the model can be improved by manual revision of the predictions

Secants of Lagrangian Grassmannians

We study the dimensions of secant varieties of the Grassmannian of Lagrangian subspaces in a symplectic vector space. We calculate these dimensions for third and fourth secant varieties. Our result is obtained by providing a normal form for four general points on such a Grassmannian and by explicitly calculating the tangent spaces at these four points

Evaluation of T1 relaxation time in prostate cancer and benign prostate tissue using a Modified Look-Locker inversion recovery sequence

Purpose of this study was to evaluate the diagnostic performance of T1 relaxation time (T1) for differentiating prostate cancer (PCa) from benign tissue as well as high- from low-grade PCa. Twenty-three patients with suspicion for PCa were included in this prospective study. 3 T MRI including a Modified Look-Locker inversion recovery sequence was acquired. Subsequent targeted and systematic prostate biopsy served as a reference standard. T1 and apparent diffusion coefficient (ADC) value in PCa and reference regions without malignancy as well as high- and low-grade PCa were compared using the Mann-Whitney U test. The performance of T1, ADC value, and a combination of both to differentiate PCa and reference regions was assessed by receiver operating characteristic (ROC) analysis. T1 and ADC value were lower in PCa compared to reference regions in the peripheral and transition zone (p < 0.001). ROC analysis revealed high AUCs for T1 (0.92; 95%-CI, 0.87-0.98) and ADC value (0.97; 95%-CI, 0.94 to 1.0) when differentiating PCa and reference regions. A combination of T1 and ADC value yielded an even higher AUC. The difference was statistically significant comparing it to the AUC for ADC value alone (p = 0.02). No significant differences were found between high- and low-grade PCa for T1 (p = 0.31) and ADC value (p = 0.8). T1 relaxation time differs significantly between PCa and benign prostate tissue with lower T1 in PCa. It could represent an imaging biomarker for PCa

A String Theory of Flavor and CP

Modular transformations of string theory (including the well-known stringy dualities) play a crucial role in the discussion of discrete flavor symmetries in the Standard Model. They are at the origin of CP transformations and provide a unification of CP with traditional flavor symmetries. Here, we present a novel, fully systematic method to reliably compute the unified flavor symmetry of the low-energy effective theory, including enhancements from the modular transformations of string theory. The unified flavor group is non-universal in moduli space and exhibits the phenomenon of "Local Flavor Unification" where different sectors of the theory can be subject to different flavor structures.Comment: 38 pages, 2 figure