Mathematical Analysis of a System for Biological Network Formation

Motivated by recent physics papers describing rules for natural network formation, we study an elliptic-parabolic system of partial differential equations proposed by Hu and Cai. The model describes the pressure field thanks to Darcy's type equation and the dynamics of the conductance network under pressure force effects with a diffusion rate $D$ representing randomness in the material structure. We prove the existence of global weak solutions and of local mild solutions and study their long term behaviour. It turns out that, by energy dissipation, steady states play a central role to understand the pattern capacity of the system. We show that for a large diffusion coefficient $D$, the zero steady state is stable. Patterns occur for small values of $D$ because the zero steady state is Turing unstable in this range; for $D=0$ we can exhibit a large class of dynamically stable (in the linearized sense) steady states

How does digitalization affect headquarters and what does it mean for CEE-focused headquarters in Austria?

Headquarters (HQs) represent central units within corporationsi and their goal is to add value to the firm and its respective subunits. They do so by taking over various responsibilities, such as allocating resources within the firm, coordinating and monitoring subunits, and identifying and realizing synergies, among others. HQs are also important for the economy of the countries they are located in, as they offer for example high-value employment, increased demand for related business services (e.g., legal and financial services), and represent a non-trivial source of tax income. Additionally, there is scientific evidence suggesting that the location of the HQ influences its investment decisions and consequently adjacent economies (e.g., investments that are in regions close to the HQ are favoured). Thus, many countries consider it important to attract and maintain HQsii. In this article, we will focus on a topic that has not received much attention yet. Specifically, we discuss how digitalization (i.e., recent advancements in areas such as big data analytics, automation, artificial intelligence, the internet of things, etc.) influences HQs in Austria, most of which have a strong focus on CEE countries. Companies are dealing with a variety of issues stemming from digitalization, which results in changes to business models, firm processes, and company culturesiii. Yet, digitalization also affects the role and value added of the HQs but we still lack a clear understanding of thativ. In the following, we first discuss Austria as a location for HQs, then the impact of digitalization on HQs, and finally, we explore how the digitalization might influence the attractiveness of Austria for CEE-oriented HQs. Thereby, we refer to recent empirical material that we have collected

Notes on a PDE System for Biological Network Formation

We present new analytical and numerical results for the elliptic-parabolic system of partial differential equations proposed by Hu and Cai, which models the formation of biological transport networks. The model describes the pressure field using a Darcy's type equation and the dynamics of the conductance network under pressure force effects. Randomness in the material structure is represented by a linear diffusion term and conductance relaxation by an algebraic decay term. The analytical part extends the results of Haskovec, Markowich and Perthame regarding the existence of weak and mild solutions to the whole range of meaningful relaxation exponents. Moreover, we prove finite time extinction or break-down of solutions in the spatially onedimensional setting for certain ranges of the relaxation exponent. We also construct stationary solutions for the case of vanishing diffusion and critical value of the relaxation exponent, using a variational formulation and a penalty method. The analytical part is complemented by extensive numerical simulations. We propose a discretization based on mixed finite elements and study the qualitative properties of network structures for various parameters values. Furthermore, we indicate numerically that some analytical results proved for the spatially one-dimensional setting are likely to be valid also in several space dimensions.Comment: 33 pages, 12 figure

Delimited continuations for Prolog

Delimited continuations are a famous control primitive that originates in the functional programming world. It allows the programmer to suspend and capture the remaining part of a computation in order to resume it later. We put a new Prolog-compatible face on this primitive and specify its semantics by means of a meta-interpreter. Moreover, we establish the power of delimited continuations in Prolog with several example definitions of high-level language features. Finally, we show how to easily and effectively add delimited continuations support to the WAM

1/fα1/f^\alpha spectra in elementary cellular automata and fractal signals

We systematically compute the power spectra of the one-dimensional elementary cellular automata introduced by Wolfram. On the one hand our analysis reveals that one automaton displays $1/f$ spectra though considered as trivial, and on the other hand that various automata classified as chaotic/complex display no $1/f$ spectra. We model the results generalizing the recently investigated Sierpinski signal to a class of fractal signals that are tailored to produce $1/f^{\alpha}$ spectra. From the widespread occurrence of (elementary) cellular automata patterns in chemistry, physics and computer sciences, there are various candidates to show spectra similar to our results.Comment: 4 pages (3 figs included

Sea glider guidance around a circle using distance measurements to a drifting acoustic source

International audienceThis paper describes a simple yet robust sea glider guidance method in a constellation of Lagrangian drifters under the polar ice cap. The glider has to perform oceanographic measurements, mainly conductivity, temperature and depth, in the area enclosed by the drifters and can not rely on GNSS (Global Navigation Satellite System) positionning data as the polar ice cap makes it impossible to surface. The originality of the presented method resides in 2 points. First, a very simple PID (Proportional, Integral and Derivative) controller based on a basic kinematic model is tuned. Second, the method does not use a localization algorithm to estimate state space model data but interval analysis methods are performed to bound the errors in range to the transponder and its derivative. Moreover, only one acoustic beacon is used. Validation is then performed through simulations

How corporate headquarters add value in the digital age

How will digitalization influence the role of corporate headquarters (CHQs) and their relationships with their operating units? We recently asked 67 senior CHQ managers this question. The results suggest that CHQs expect to become more powerful and more involved in their operating units. These conclusions seem to be driven by perceptions that the ongoing digitalization will provide CHQ managers with more timely and better information. In this "Point of View", we discuss the potential pitfalls of such a narrative. We also offer ideas for how to avoid mistakes and ensure that CHQs increase their value-added in times of digitalization. In particular, we suggest that CHQs place emphasis on social interactions for data to be effectively collected and analyzed, for decision-making power to be adequately allocated, and for CHQ involvement to be informed and necessary

First-principle study of paraelectric and ferroelectric CsH2_2PO4_4 including dispersion forces: stability and related vibrational, dielectric and elastic properties

Using density functional theory (DFT) and density functional perturbation theory (DFPT), we investigate the stability and response functions of CsH$_2$PO$_4$, a ferroelectric material at low temperature. This material cannot be described properly by the usual (semi-)local approximations within DFT. The long-range e$^-$-e$^-$ correlation needs to be properly taken into account, using, for instance, Grimme's DFT-D methods, as investigated in this work. We find that DFT-D3(BJ) performs the best for the members of the dihydrogenated alkali phosphate family (KH$_2$PO$_4$, RbH$_2$PO$_4$, CsH$_2$PO$_4$), leading to experimental lattice parameters reproduced with an average deviation of 0.5 %. With these DFT-D methods, the structural, dielectric, vibrational and mechanical properties of CsH$_2$PO$_4$ are globally in excellent agreement with the available experiments ($<$ 2% MAPE for Raman-active phonons). Our study suggests the possible existence of a new low-temperature phase for CsH$_2$PO$_4$, not yet reported experimentally. Finally, we report the implementation of DFT-D contributions to elastic constants within DFPT.Comment: This paper was published in Physical Review B the 25 January 2017 (21 pages, 4 figures