Related papers: Random Polynomials and the Friendly Landscape
We derive a class of space homogeneous Landau-like equations from stochastic interacting particles. Through the use of relative entropy, we obtain quantitative bounds on the distance between the solution of the N-particle Liouville equation…
This paper is a basis of a part of my set of lectures, subject:`Formal methods in solving differential equations and constructing models of physical phenomena'. Addressed, mainly: postgraduates and related readers. Content: a discussion of…
The statistical properties of the energy landscape of the low autocorrelated binary string problem (LABSP) are studied numerically and compared with those of several classic disordered models. Using two global measures of landscape…
This essay advocates the view that any problem that has a meaningful empirical content, can be formulated in constructive, more definitely, finite terms. We consider combinatorial models of dynamical systems and approaches to statistical…
In agricultural landscapes, the composition and spatial configuration of cultivated and semi-natural elements strongly impact species dynamics, their interactions and habitat connectivity. To allow for landscape structural analysis and…
This is a short exposition--mostly by way of the toy models ``double logarithm'' and ``triple logarithm''--which should serve as an introduction to a forthcoming article in which we establish a connection between multiple polylogarithms,…
We explore the possibility that quantum cosmology considerations could provide a selection principle in the landscape of string vacua. We propose that the universe emerged from the string era in a thermally excited state and determine,…
In this study, Hamiltonian and Lagrangian theories, which are mathematical models of mechanical systems, are structured on the horizontal and the vertical distributions of tangent and cotangent bundles. In the end, the geometrical and…
A stationary random sequence admits under some assumptions a representation as the sum of two others: one of them is a martingale difference sequence, and another is a so-called coboundary. Such a representation can be used for proving some…
We review the structure of local Lagrangians and field equations for free bosonic and fermionic gauge fields of mixed symmetry in flat space. These are first presented in a constrained setting and then the ($\g$-)trace constraints on fields…
We construct simple Lagrangians of vector fields which involve second derivatives, but nevertheless lead to second order field equations. These vector fields are, therefore, analogs of generalized Galileons. Our construction is given first…
In this paper, we explore the string theory landscape obtained from type IIB and F-theory flux compactifications. We first give a comprehensive introduction to a number of mathematical finiteness theorems, indicate how they have been…
When a new heavy particle is discovered at the LHC or at a future high-energy collider, it will be interesting to study its decays into Standard Model particles using an effective field-theory framework. We point out that the proper…
A new class of ``toy models'' for subaqueous bedform formation are proposed and examined. These models all show a similar mechanism of wavelength selection via bedform unification, and they may have applications to bedform stratigraphy. The…
Given a monotone Lagrangian submanifold invariant under a loop of Hamiltonian diffeomorphisms, we compute a piece of the closed-open string map into the Hochschild cohomology of the Lagrangian which captures the homology class of the loop's…
We review recent work in which compactifications of string and M theory are constructed in which all scalar fields (moduli) are massive, and supersymmetry is broken with a small positive cosmological constant, features needed to reproduce…
By analogy with Weinstein's neighbourhood theorem, we prove a uniqueness result for symplectic neighbourhoods of a large family of stratified subspaces. This result generalizes existing constructions, e.g., in the search for exotic…
By means of an analogy with Classical Mechanics and Geometrical Optics, we are able to reduce Lagrangians to a kinetic term only. This form enables us to examine the extended solution set of field theories by finding the geodesics of this…
Using effective-lagrangian techniques we perform a systematic survey of the lowest-dimension effective interactions through which heavy physics might manifest itself in present experiments. We do not restrict ourselves to special classes of…
We introduce the notion of linearly representable games. Broadly speaking, these are TU games that can be described by as many parameters as the number of players, like weighted voting games, airport games, or bankruptcy games. We show that…