相关论文: On the optimal form of branching supply and collec…
Network models of large-scale electricity systems feature only a limited spatial resolution, either due to lack of data or in order to reduce the complexity of the problem with respect to numerical calculations. In such cases, both the…
Many living and physical systems such as cell aggregates, tissues or bacterial colonies behave as unconventional systems of particles that are strongly constrained by volume exclusion and shape interactions. Understanding how these…
The existence and stability of the universality class associated to local minimal energy landscapes is investigated. Using extensive numerical simulations, we first study the dependence on a parameter $\gamma$ of a partial differential…
We study spatial networks that are designed to distribute or collect a commodity, such as gas pipelines or train tracks. We focus on the cost of a network, as represented by the total length of all its edges, and its efficiency in terms of…
Emerging applications of machine learning in numerous areas involve continuous gathering of and learning from streams of data. Real-time incorporation of streaming data into the learned models is essential for improved inference in these…
Cardiovascular networks span the body by branching across many generations of vessels. The resulting structure delivers blood over long distances to supply all cells with oxygen via the relatively short-range process of diffusion at the…
We formally extend the energy landscape approach for the thermodynamics of liquids to account for saddle points. By considering the extensive nature of macroscopic potential energies, we derive the scaling behavior of saddles with system…
Mixing is relevant to many areas of science and engineering, including the pharmaceutical and food industries, oceanography, atmospheric sciences, and civil engineering. In all these situations one goal is to quantify and often then to…
Highly-optimized complex transport networks serve crucial functions in many man-made and natural systems such as power grids and plant or animal vasculature. Often, the relevant optimization functional is non-convex and characterized by…
In real-world applications, observations are often constrained to a small fraction of a system. Such spatial subsampling can be caused by the inaccessibility or the sheer size of the system, and cannot be overcome by longer sampling.…
The best techniques for the constrained maximum-entropy sampling problem, a discrete-optimization problem arising in the design of experiments, are via a variety of concave continuous relaxations of the objective function. A standard…
The low energy regime of cosmological BPS-brane configurations with a bulk scalar field is studied. We construct a systematic method to obtain five-dimensional solutions to the full system of equations governing the geometry and dynamics of…
A useful approach to the mathematical analysis of large-scale biological networks is based upon their decompositions into monotone dynamical systems. This paper deals with two computational problems associated to finding decompositions…
Landscapes evolve toward surfaces with complex networks of channels and ridges in response to climatic and tectonic forcing. Here we analyze variational principles giving rise to minimalist models of landscape evolution as a system of…
The growth and scaling of organs is a fundamental aspect of animal development. However, how organs grow to the right size and shape required by physiological demands, remains largely unknown. Here, we provide a framework combining theory…
The origin of allometric scaling patterns that are multiples of 1/4 has long fascinated biologists. While not universal, scaling relationships with exponents that are close to multiples of 1/4 are common and have been described in all major…
This paper investigates the role of size in biological organisms. More specifically, how the energy demand, expressed by the metabolic rate, changes according to the mass of an organism. Empirical evidence suggests a power-law relation…
We study the emergence of a power law distribution in the systems which can be characterized by a hierarchically organized supplying network. It is shown that conservation laws on the branches of the network can, at some approximation,…
This paper is concerned with a shape optimization problem, where the functional to be maximized describes the total sunlight collected by a distribution of tree leaves, minus the cost for transporting water and nutrient from the base of the…
We derive a linear recursion relation for the species abundance distribution in a statistical model of ecology and demonstrate the existence of a scaling solution.