Related papers: Fundamental Limits to Moore's Law
In this paper, we establish an almost sure central limit theorem for a general random sequence under a strong approximation condition. Additionally, we derive the law of the iterated logarithm for the center of mass corresponding to a…
Some limit theorems of the type $\int_{\Omega}f_n dm_n -- --> \int_{\Omega}f dm$ are presented for scalar, (vector), (multi)-valued sequences of m_n-integrable functions f_n. The convergences obtained, in the vector and multivalued…
The ultimate limits of computation are not just logical, but physical. We investigate the physical resources -- time, energy, entropy, and free energy -- required to perform computational work. We apply the resulting measures of physical…
Computers are physical systems: what they can and cannot do is dictated by the laws of physics. In particular, the speed with which a physical device can process information is limited by its energy and the amount of information that it can…
Different aspects of critical behaviour of magnetic materials are presented and discussed. The scaling ideas are shown to arise in the context of purely magnetic properties as well as in that of thermal properties as demonstrated by…
Scaling laws arise and are eulogized across disciplines from natural to social sciences for providing pithy, quantitative, `scale-free', and `universal' power law relationships between two variables. On a log-log plot, the power laws…
An elementary system leading to the notions of fractional integrals and derivatives is considered. Various physical situations whose description is associated with fractional differential equations of motion are discussed.
We study the finite-size scaling behaviour at the critical point, resulting from the addition of a homogeneous size-dependent perturbation, decaying as an inverse power of the system size. The scaling theory is first formulated in a general…
We give tight lower and upper bounds on the expected missing mass for distributions over finite and countably infinite spaces. An essential characterization of the extremal distributions is given. We also provide an extension to totally…
Universal scaling laws of fluctuations (the $\Delta$-scaling laws) can be derived for equilibrium and off-equilibrium systems when combined with the finite-size scaling analysis. In any system in which the second-order critical behavior can…
We investigate necessary and sufficient conditions for the extendibility and boundedness of Gaussian curvature, Mean curvature and principal curvatures near all types of singularities on fronts. We also study the convergence to infinite…
We show that the scaling limit exists and is invariant to dilations and rotations. We give some tools that might be useful to show universality.
Moore's Law has been used by semiconductor industry as predicative indicators of the industry and it has become a self-fulfilling prophecy. Now more people tend to agree that the original Moore's Law started to falter. This paper proposes a…
This paper explores the fundamental causal limits on how much of the universe we can observe or affect. It distinguishes four principal regions: the affectable universe, the observable universe, the eventually observable universe, and the…
Newtonian limit of Extended Theories of Gravity (in particular, higher--order and scalar--tensor theories) is theoretically discussed taking into account recent observational and experimental results.
Mass scaling is widely used in finite element models of structural dynamics for increasing the critical time step of explicit time integration methods. While the field has been flourishing over the years, it still lacks a strong theoretical…
Partial descriptions of the Universe are presented in the form of linear equations considered in the free (full, super) Fock space. The universal properties of these equations are discussed. The closure problem caused by computational and…
We consider biased random walks in positive random conductances on the d-dimensional lattice in the zero-speed regime and study their scaling limits. We obtain a functional Law of Large Numbers for the position of the walker, properly…
We apply the Principle of Maximum Entropy to the study of a general class of deterministic fractal sets. The scaling laws peculiar to these objects are accounted for by means of a constraint concerning the average content of information in…
As it is pretty sure that Moore's law will end some day, questioning about the post-Moore era is more than interesting. Similarly, looking for new computing paradigms that could provide solutions is important. Revisiting the history of…