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We give a class of domains for which Fridman invariant and injectivity radius function coincide with respect to Carath\'eodory metric. We give explicit expressions of the squeezing functions for these domains and investigate some of their properties., Comment: 10 pages, work in progress, comments are welcome

We provide explicit expression of squeezing function for infinitely connected planar domain obtained by removing a convergent sequence of points from the unit disk converging to the boundary of unit disk. We also discuss Fridman invariant associated with this domain as well as some examples of squezzing functions corresponding to polydisk., Comment: 9 pages, work in progress, comments are welcome; In the new version, we have included one remark and corrected some typos

Minimal, open quantum systems that are governed by non-Hermitian Hamiltonians have been realized across multiple platforms in the past two years. Here we investigate the dynamics of open systems with Hermitian or anti-Hermitian Hamiltonians, both of which can be implemented in such platforms. For a single system subject to unitary and thermal dynamics in a periodic manner, we show that the corresponding Floquet Hamiltonian has a rich phase diagram with numerous exceptional-point (EP) degeneracy contours. This protocol can be used to realize a quantum Hatano-Nelson model that is characterized by asymmetric tunneling. For one unitary and one thermal qubit, we show that the concurrence is maximized at the EP that is controlled by the strength of Hermitian coupling between them. Surprisingly, the entropy of each qubit is also maximized at the EP. Our results point to the multifarious phenomenology of systems undergoing unitary and thermal dynamics., Comment: 8 pages, 3 figures

In the present article, we further investigate the properties of squeezing function corresponding to polydisk. We work out some explicit expressions of squeezing function corresponding to polydisk., Comment: 7 pages, work in progress, comments are welcome; In the new version, we have corrected typos and layout of the statements to enhance the readability of paper

Binary "YES-NO" notions of process compliance are not very helpful to managers for assessing the operational performance of their company because a large number of cases fall in the grey area of partial compliance. Hence, it is necessary to have ways to quantify partial compliance in terms of metrics and be able to classify actual cases by assigning a numeric value of compliance to them. In this paper, we formulate an evaluation framework to quantify the level of compliance of business processes across different levels of abstraction (such as task,trace and process level) and across multiple dimensions of each task (such as temporal, monetary, role-, data-, and quality-related) to provide managers more useful information about their operations and to help them improve their decision making processes. Our approach can also add social value by making social services provided by local, state and federal governments more flexible and improving the lives of citizens., Comment: 15 page, 4 figures, 2 tables; Under consideration at AICOL 2020, co-located with Jurix

Process consistency checking (PCC), an interdiscipline of natural language processing (NLP) and business process management (BPM), aims to quantify the degree of (in)consistencies between graphical and textual descriptions of a process. However, previous studies heavily depend on a great deal of complex expert-defined knowledge such as alignment rules and assessment metrics, thus suffer from the problems of low accuracy and poor adaptability when applied in open-domain scenarios. To address the above issues, this paper makes the first attempt that uses deep learning to perform PCC. Specifically, we proposed TraceWalk, using semantic information of process graphs to learn latent node representations, and integrates it into a convolutional neural network (CNN) based model called TraceNet to predict consistencies. The theoretical proof formally provides the PCC's lower limit and experimental results demonstrate that our approach performs more accurately than state-of-the-art baselines.

Process model extraction (PME) is a recently emerged interdiscipline between natural language processing (NLP) and business process management (BPM), which aims to extract process models from textual descriptions. Previous process extractors heavily depend on manual features and ignore the potential relations between clues of different text granularities. In this paper, we formalize the PME task into the multi-grained text classification problem, and propose a hierarchical neural network to effectively model and extract multi-grained information without manually-defined procedural features. Under this structure, we accordingly propose the coarse-to-fine (grained) learning mechanism, training multi-grained tasks in coarse-to-fine grained order to share the high-level knowledge for the low-level tasks. To evaluate our approach, we construct two multi-grained datasets from two different domains and conduct extensive experiments from different dimensions. The experimental results demonstrate that our approach outperforms the state-of-the-art methods with statistical significance and further investigations demonstrate its effectiveness., Comment: Accepted to CAiSE-2020

Sharing process models on the web has emerged as a common practice. Users can collect and share their experimental process models with others. However, some users always feel confused about the shared process models for lack of necessary guidelines or instructions. Therefore, several process translators have been proposed to explain the semantics of process models in natural language (NL). We find that previous studies suffer from information loss and generate semantically erroneous descriptions that diverge from original model behaviors. In this paper, we propose a novel process translator named BePT (Behavior-based Process Translator) based on the encoder-decoder paradigm, encoding a process model into a middle representation and decoding the representation into NL descriptions. Our theoretical analysis demonstrates that BePT satisfies behavior correctness, behavior completeness and description minimality. The qualitative and quantitative experiments show that BePT outperforms the state-of-the-art baselines.