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The size of large cliff failures may be described in several ways, for instance considering the horizontal eroded area at the cliff top and the maximum local retreat of the coastline. Field studies suggest that, for large failures, the…
Patent systems vary widely in how rigorously they define and enforce inventors' rights. On one hand, formal statutes ("law on the books") set the scope of what can be patented and outline procedural safeguards. On the other hand, actual…
Reinforced random walks are random walks on graphs whose transition probabilities along edges from a vertex are proportional to the weights of those edges, but where the weight of an edge evolves in a way that depends on the past traversals…
The partial differential equations describing compressible fluid flows can be notoriously difficult to resolve on a pragmatic scale and often require the use of high performance computing systems and/or accelerators. However, these systems…
Are large scale research programs that include many projects more productive than smaller ones with fewer projects? This problem of economy of scale is particularly relevant for understanding recent mergers in particular in the…
Quantum information science currently poses a troubling contradiction. It can be summarized as: (1) To factor efficiently, quantum computers must perform exponentially precise energy estimation. (2) Exponentially precise energy estimation…
Newton's law of motion relative to an inertial frame ("the laboratory") for a particle subject to a force acting at a certain time may be interpreted in either of two ways: (1) The force acting on the particle during an infinitesimal time…
Industrial domains such as automotive, robotics, and aerospace are rapidly evolving to satisfy the increasing demand for machine-learning-driven Autonomy, Connectivity, Electrification, and Shared mobility (ACES). This paradigm shift…
The second law of thermodynamics states that entropy increases (or does not change) by time in an isolated system. As microscopic physical laws are reversible, the origin of irreversibility is not straightforward. Although the outcome of a…
We consider a random walk on the support of a stationary simple point process on $R^d$, $d\geq 2$ which satisfies a mixing condition w.r.t.the translations or has a strictly positive density uniformly on large enough cubes. Furthermore the…
The second law of thermodynamics places a limitation into which states a system can evolve into. For systems in contact with a heat bath, it can be combined with the law of energy conservation, and it says that a system can only evolve into…
When a quantity reaches a value higher (or lower) than its value at any time before, it is said to have made a record. We numerically study the statistical properties of records in the time series of order parameters in different models…
Policymakers often assess the growth of science in a country and compare it with that of other countries to set future planning for scientific research focusing on the sustainable development and economic growth of the country. Here, we…
There are many astrophysical scenarios where extreme mass ratio inspiral (EMRI) binaries can be surrounded by matter distribution. The distribution of mass can affect the dynamical properties (e.g. orbital frequency, average energy…
We describe the Reversibility Error Method (REM) and its applications to planetary dynamics. REM is based on the time-reversibility analysis of the phase-space trajectories of conservative Hamiltonian systems. The round-off errors break the…
Probabilities of the outcomes of consecutive quantum measurements can be obtained by construction probability amplitudes, thus implying unitary evolution of the measured system, broken each time a measurement is made. In practice, the…
In statistical thermodynamics the 2nd law is properly spelled out in terms of conditioned probabilities. As such it makes the statement, that `entropy increases with time' without preferring a time direction. In this paper I try to explain…
Politicians world-wide frequently promise a better life for their citizens. We find that the probability that a country will increase its {\it per capita} GDP ({\it gdp}) rank within a decade follows an exponential distribution with decay…
The persistence phenomenon is studied in the Japanese financial market by using a novel mapping of the time evolution of the values of shares quoted on the Nikkei Index onto Ising spins. The method is applied to historical end of day data…
Optimization and expansion are two modes of staged evolution of complex systems where macroscopic observables change at a decreasing, respectively increasing, rate. A prime example of evolutionary expansion, Gross Domestic Product (GDP)…