Related papers: The high-d landscapes paradigm: spin-glasses, and …

The topological organization of several world cities are studied according to respective representations by complex networks. As a first step, the city maps are processed by a recently developed methodology that allows the most significant…

If the gradient of a probability distribution on a landscape of vacua aligns with the variation of some fundamental parameter, the parameter may be likely to take some non-generic value. Such non-generic values can be associated to critical…

Framed combinatorial topology is a novel theory describing combinatorial phenomena arising at the intersection of stratified topology, singularity theory, and higher algebra. The theory synthesizes elements of classical combinatorial…

A good deal of current research in complex networks involves the characterization and/or classification of the topological properties of given structures, which has motivated several respective measurements. This letter proposes a framework…

The local minima (inherent structures) of a system and their associated transition links give rise to a network. Here we consider the topological and distance properties of such a network in the context of spin glasses. We use steepest…

Technological innovations have revolutionized the process of scientific research and knowledge discovery. The availability of massive data and challenges from frontiers of research and development have reshaped statistical thinking, data…

This expository paper explores the interaction of group ordering with topological questions, especially in dimensions 2 and 3. Among the topics considered are surfaces, braid groups, 3-manifolds and their structures such as foliations and…

There has been some debate as to whether the landscape does or does not predict low energy supersymmetry. We argue that under rather mild assumptions, the landscape seems to favor such breaking, quite possibly at a very low scale. Some of…

We discuss and review recent developments in the area of applied algebraic topology, such as persistent homology and barcodes. In particular, we discuss how these are related to understanding more about manifold learning from random point…

Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical…

Many real-world networks of interest are embedded in physical space. We present a new random graph model aiming to reflect the interplay between the geometries of the graph and of the underlying space. The model favors configurations with…

Describing the complex landscape of infinite-dimensional free energy is generally a challenging problem. This difficulty arises from the existence of numerous minimizers and, consequently, a vast number of saddle points. These factors make…

In this paper, we connect some recent papers on smoothing of energy landscapes and scored-based generative models of machine learning to classical work in stochastic control. We clarify these connections providing rigorous statements and…

Science in the 21st century seems to be governed by novel approaches involving interdisciplinary work, systemic perspectives and complexity theory concepts. These new paradigms force us to leave aside our elder mechanistic approaches and…

In this paper we follow up the study of 'complex complex landscapes,' rugged landscapes of many complex variables. Unlike real landscapes, the classification of saddles by index is trivial. Instead, the spectrum of fluctuations at…

Transport in crowded, complex environments occurs across many spatial scales. Geometric restrictions can hinder the motion of individuals and, combined with crowding between individuals, can have drastic effects on global transport…

Landscape is one of the key notions in literature on biological processes and physics of complex systems with both deterministic and stochastic dynamics. The large deviation theory (LDT) provides a possible mathematical basis for the…

Landscape paradigm is ubiquitous in physics and other natural sciences, but it has to be supplemented with both quantitative and qualitatively meaningful tools for analyzing the topography of a given landscape. We here consider dynamic…

We consider recent reports on small-world topologies of interaction networks derived from the dynamics of spatially extended systems that are investigated in diverse scientific fields such as neurosciences, geophysics, or meteorology. With…

In this work, we introduce the problem of scenic routes among points in Rd. The key development is the nature of the problem in terms of both defining the concept of scenic points and scenic routes and then coming up with algorithms that…