Duistermaat-Heckman measure and the mixture of quantum states

In this paper, we present a general framework to solve a fundamental problem in Random Matrix Theory (RMT), i.e., the problem of describing the joint distribution of eigenvalues of the sum \bsA+\bsB of two independent random Hermitian matrices \bsA and \bsB. Some considerations about the mixture of quantum states are basically subsumed into the above mathematical problem. Instead, we focus on deriving the spectral density of the mixture of adjoint orbits of quantum states in terms of Duistermaat-Heckman measure, originated from the theory of symplectic geometry. Based on this method, we can obtain the spectral density of the mixture of independent random states. In particular, we obtain explicit formulas for the mixture of random qubits. We also find that, in the two-level quantum system, the average entropy of the equiprobable mixture of $n$ random density matrices chosen from a random state ensemble (specified in the text) increases with the number $n$. Hence, as a physical application, our results quantitatively explain that the quantum coherence of the mixture monotonously decreases statistically as the number of components $n$ in the mixture. Besides, our method may be used to investigate some statistical properties of a special subclass of unital qubit channels.Comment: 40 pages, 10 figures, LaTeX, the final version accepted for publication in J. Phys.

Online Influence Maximization in Non-Stationary Social Networks

Social networks have been popular platforms for information propagation. An important use case is viral marketing: given a promotion budget, an advertiser can choose some influential users as the seed set and provide them free or discounted sample products; in this way, the advertiser hopes to increase the popularity of the product in the users' friend circles by the world-of-mouth effect, and thus maximizes the number of users that information of the production can reach. There has been a body of literature studying the influence maximization problem. Nevertheless, the existing studies mostly investigate the problem on a one-off basis, assuming fixed known influence probabilities among users, or the knowledge of the exact social network topology. In practice, the social network topology and the influence probabilities are typically unknown to the advertiser, which can be varying over time, i.e., in cases of newly established, strengthened or weakened social ties. In this paper, we focus on a dynamic non-stationary social network and design a randomized algorithm, RSB, based on multi-armed bandit optimization, to maximize influence propagation over time. The algorithm produces a sequence of online decisions and calibrates its explore-exploit strategy utilizing outcomes of previous decisions. It is rigorously proven to achieve an upper-bounded regret in reward and applicable to large-scale social networks. Practical effectiveness of the algorithm is evaluated using both synthetic and real-world datasets, which demonstrates that our algorithm outperforms previous stationary methods under non-stationary conditions.Comment: 10 pages. To appear in IEEE/ACM IWQoS 2016. Full versio

The Faster the Better? Innovation Speed and User Interest in Open Source Software

It is often believed that for open source software (OSS) projects the faster the release, the better for attracting user interest in the software. Whether this is true, however, is still open to question. There is considerable information asymmetry between OSS projects and potential users as project quality is unobservable to users. We suggest that innovation speed of OSS project can signal the unobservable project quality and attract users’ interest in downloading and using the software. We contextualize innovation speed of OSS projects as initial release speed and update speed and examine their impacts on user interest. Drawing on the signaling theory, we propose a signaling effect through which a higher initial release speed or update speed increases user interest, while the effect diminishes as initial release or update speed increases. Using a large-scale panel data set from 7442 OSS projects on SourceForge between 2007 and 2010, our results corroborate the inverted U-shaped relationships between initial release speed and user downloads and between update speed and user downloads

A Churn for the Better: Localizing Censorship using Network-level Path Churn and Network Tomography

Recent years have seen the Internet become a key vehicle for citizens around the globe to express political opinions and organize protests. This fact has not gone unnoticed, with countries around the world repurposing network management tools (e.g., URL filtering products) and protocols (e.g., BGP, DNS) for censorship. However, repurposing these products can have unintended international impact, which we refer to as "censorship leakage". While there have been anecdotal reports of censorship leakage, there has yet to be a systematic study of censorship leakage at a global scale. In this paper, we combine a global censorship measurement platform (ICLab) with a general-purpose technique -- boolean network tomography -- to identify which AS on a network path is performing censorship. At a high-level, our approach exploits BGP churn to narrow down the set of potential censoring ASes by over 95%. We exactly identify 65 censoring ASes and find that the anomalies introduced by 24 of the 65 censoring ASes have an impact on users located in regions outside the jurisdiction of the censoring AS, resulting in the leaking of regional censorship policies

Online Job Scheduling in Distributed Machine Learning Clusters

Nowadays large-scale distributed machine learning systems have been deployed to support various analytics and intelligence services in IT firms. To train a large dataset and derive the prediction/inference model, e.g., a deep neural network, multiple workers are run in parallel to train partitions of the input dataset, and update shared model parameters. In a shared cluster handling multiple training jobs, a fundamental issue is how to efficiently schedule jobs and set the number of concurrent workers to run for each job, such that server resources are maximally utilized and model training can be completed in time. Targeting a distributed machine learning system using the parameter server framework, we design an online algorithm for scheduling the arriving jobs and deciding the adjusted numbers of concurrent workers and parameter servers for each job over its course, to maximize overall utility of all jobs, contingent on their completion times. Our online algorithm design utilizes a primal-dual framework coupled with efficient dual subroutines, achieving good long-term performance guarantees with polynomial time complexity. Practical effectiveness of the online algorithm is evaluated using trace-driven simulation and testbed experiments, which demonstrate its outperformance as compared to commonly adopted scheduling algorithms in today's cloud systems

Dynamic Survival Transformers for Causal Inference with Electronic Health Records

In medicine, researchers often seek to infer the effects of a given treatment on patients' outcomes. However, the standard methods for causal survival analysis make simplistic assumptions about the data-generating process and cannot capture complex interactions among patient covariates. We introduce the Dynamic Survival Transformer (DynST), a deep survival model that trains on electronic health records (EHRs). Unlike previous transformers used in survival analysis, DynST can make use of time-varying information to predict evolving survival probabilities. We derive a semi-synthetic EHR dataset from MIMIC-III to show that DynST can accurately estimate the causal effect of a treatment intervention on restricted mean survival time (RMST). We demonstrate that DynST achieves better predictive and causal estimation than two alternative models.Comment: Accepted to the NeurIPS 2022 Workshop on Learning from Time Series for Healt

Sequence-Level Certainty Reduces Hallucination In Knowledge-Grounded Dialogue Generation

Model hallucination has been a crucial interest of research in Natural Language Generation (NLG). In this work, we propose sequence-level certainty as a common theme over hallucination in NLG, and explore the correlation between sequence-level certainty and the level of hallucination in model responses. We categorize sequence-level certainty into two aspects: probabilistic certainty and semantic certainty, and reveal through experiments on Knowledge-Grounded Dialogue Generation (KGDG) task that both a higher level of probabilistic certainty and a higher level of semantic certainty in model responses are significantly correlated with a lower level of hallucination. What's more, we provide theoretical proof and analysis to show that semantic certainty is a good estimator of probabilistic certainty, and therefore has the potential as an alternative to probability-based certainty estimation in black-box scenarios. Based on the observation on the relationship between certainty and hallucination, we further propose Certainty-based Response Ranking (CRR), a decoding-time method for mitigating hallucination in NLG. Based on our categorization of sequence-level certainty, we propose 2 types of CRR approach: Probabilistic CRR (P-CRR) and Semantic CRR (S-CRR). P-CRR ranks individually sampled model responses using their arithmetic mean log-probability of the entire sequence. S-CRR approaches certainty estimation from meaning-space, and ranks a number of model response candidates based on their semantic certainty level, which is estimated by the entailment-based Agreement Score (AS). Through extensive experiments across 3 KGDG datasets, 3 decoding methods, and on 4 different models, we validate the effectiveness of our 2 proposed CRR methods to reduce model hallucination

Die Struktur und Funktion von mimischen Emotikons in Deutschland und in China

In den letzten zwei Jahrzehnten haben sich Emotikons zu einem der effizientesten Mittel für den Ausdruck von Emotionen in geschriebenen Texten entwickelt. Besonders beliebt sind Emotikons, in denen lachende und lächelnde Gesichter dargestellt werden. Der vorliegende Beitrag analysiert die Ergebnisse einer vergleichenden Studie von chinesischen und deutschen Emotikons unter besonderer Berücksichtigung der Beziehung zwischen Zeichen und Objekten.In the last two decades emoticons have become one of the most efficient means for the expression of emotions in written texts. Especially popular are emoticons with the facial traits of laughing and smiling persons. The present article analyzes the results of a comparative study of Chinese and German emoticons with special consideration of the relation between signs and objects