Giant capacitance of a plane capacitor with a two-dimensional electron gas in a magnetic field

If a clean two-dimensional electron gas (2DEG) with small concentration $n$ comprises one (or both) electrodes of a plane capacitor, the resulting capacitance $C$ can be larger than the "geometric capacitance" $C_g$ determined by the physical separation $d$ between electrodes. A recent paper [1] argued that when the effective Bohr radius $a_B$ of the 2DEG satisfies $a_B << d$, one can achieve $C >> C_g$ at low concentration $nd^2 << 1$. Here we show that even for devices with $a_B > d$, including graphene, for which $a_B$ is effectively infinite, one also arrives at $C >> C_g$ at low electron concentration if there is a strong perpendicular magnetic field.Comment: 6 pages, 5 figures; updated discussion about bilayer systems; added discussion of fractional quantum Hall state

Declarative process modeling in BPMN

Traditional business process modeling notations, including the standard Business Process Model and Notation (BPMN), rely on an imperative paradigm wherein the process model captures all allowed activity flows. In other words, every flow that is not specified is implicitly disallowed. In the past decade, several researchers have exposed the limitations of this paradigm in the context of business processes with high variability. As an alternative, declarative process modeling notations have been proposed (e.g., Declare). These notations allow modelers to capture constraints on the allowed activity flows, meaning that all flows are allowed provided that they do not violate the specified constraints. Recently, it has been recognized that the boundary between imperative and declarative process modeling is not crisp. Instead, mixtures of declarative and imperative process modeling styles are sometimes preferable, leading to proposals for hybrid process modeling notations. These developments raise the question of whether completely new notations are needed to support hybrid process modeling. This paper answers this question negatively. The paper presents a conservative extension of BPMN for declarative process modeling, namely BPMN-D, and shows that Declare models can be transformed into readable BPMN-D models. © Springer International Publishing Switzerland 2015

Bubbling with L2L^2-almost constant mean curvature and an Alexandrov-type theorem for crystals

A compactness theorem for volume-constrained almost-critical points of elliptic integrands is proven. The result is new even for the area functional, as almost-criticality is measured in an integral rather than in a uniform sense. Two main applications of the compactness theorem are discussed. First, we obtain a description of critical points/local minimizers of elliptic energies interacting with a confinement potential. Second, we prove an Alexandrov-type theorem for crystalline isoperimetric problems

Predictive Monitoring of Business Processes

Modern information systems that support complex business processes generally maintain significant amounts of process execution data, particularly records of events corresponding to the execution of activities (event logs). In this paper, we present an approach to analyze such event logs in order to predictively monitor business goals during business process execution. At any point during an execution of a process, the user can define business goals in the form of linear temporal logic rules. When an activity is being executed, the framework identifies input data values that are more (or less) likely to lead to the achievement of each business goal. Unlike reactive compliance monitoring approaches that detect violations only after they have occurred, our predictive monitoring approach provides early advice so that users can steer ongoing process executions towards the achievement of business goals. In other words, violations are predicted (and potentially prevented) rather than merely detected. The approach has been implemented in the ProM process mining toolset and validated on a real-life log pertaining to the treatment of cancer patients in a large hospital

Interestingness of traces in declarative process mining: The janus LTLPf Approach

Declarative process mining is the set of techniques aimed at extracting behavioural constraints from event logs. These constraints are inherently of a reactive nature, in that their activation restricts the occurrence of other activities. In this way, they are prone to the principle of ex falso quod libet: they can be satisfied even when not activated. As a consequence, constraints can be mined that are hardly interesting to users or even potentially misleading. In this paper, we build on the observation that users typically read and write temporal constraints as if-statements with an explicit indication of the activation condition. Our approach is called Janus, because it permits the specification and verification of reactive constraints that, upon activation, look forward into the future and backwards into the past of a trace. Reactive constraints are expressed using Linear-time Temporal Logic with Past on Finite Traces (LTLp f). To mine them out of event logs, we devise a time bi-directional valuation technique based on triplets of automata operating in an on-line fashion. Our solution proves efficient, being at most quadratic w.r.t. trace length, and effective in recognising interestingness of discovered constraints