Related papers: Fast optimization algorithms and the cosmological …
Fractional cosmology modifies the standard derivative to Caputo's fractional derivative of order $\mu$, generating changes in General Relativity. Friedmann equations are modified, and the evolution of the species densities depends on $\mu$…
We introduce the problem of finding a satisfying assignment to a CNF formula that must further belong to a prescribed input subspace. Equivalent formulations of the problem include finding a point outside a union of subspaces (the…
We investigate a $(n+1)$-dimensional generalized Randall-Sundrum model with an anisotropic metric which has three different scale factors. One obtain a positive effective cosmological constant $\Omega_{eff}\sim10^{-124}$ (in Planck unit)…
We consider a dynamical approach to the cosmological constant. There is a scalar field with a potential whose minimum occurs at a generic, but negative, value for the vacuum energy, and it has a non-standard kinetic term whose coefficient…
We present a quantum algorithm for finding the minimum of a function based on multistep quantum computation and apply it for optimization problems with continuous variables, in which the variables of the problem are discretized to form the…
The smallness of the cosmological constant is one of the basic problems in particle physics and cosmology. Various attempts have been made to explain this mystery, but no satisfactory solution has been found yet. The appearance of extra…
We consider the hardness of approximation of optimization problems from the point of view of definability. For many NP-hard optimization problems it is known that, unless P = NP, no polynomial-time algorithm can give an approximate solution…
Grothendieck constants $K_G(d)$ bound the advantage of $d$-dimensional strategies over $1$-dimensional ones in a specific optimisation task. They have applications ranging from approximation algorithms to quantum nonlocality. However, apart…
Finding the largest cardinality feasible subset of an infeasible set of linear constraints is the Maximum Feasible Subsystem problem (MAX FS). Solving this problem is crucial in a wide range of applications such as machine learning and…
In a recent work, Esmer et al. describe a simple method - Approximate Monotone Local Search - to obtain exponential approximation algorithms from existing parameterized exact algorithms, polynomial-time approximation algorithms and, more…
A range of cosmological observations demonstrate an accelerated expansion of the Universe, and the most likely explanation of this phenomenon is a cosmological constant. Given the importance of understanding the underlying physics, it is…
We present a general technique, based on parametric search with some twist, for solving a variety of optimization problems on a set of semi-algebraic geometric objects of constant complexity. The common feature of these problems is that…
Gradient-based (a.k.a. `first order') optimization algorithms are routinely used to solve large scale non-convex problems. Yet, it is generally hard to predict their effectiveness. In order to gain insight into this question, we revisit the…
Based on the assertion that the cosmological constant problem is essentially a quantum gravity problem, the framework which addresses the cosmological constant problem should also bear a picture for the ``quantum space-time''. In this talk…
We consider the popular $k$-means problem in $d$-dimensional Euclidean space. Recently Friggstad, Rezapour, Salavatipour [FOCS'16] and Cohen-Addad, Klein, Mathieu [FOCS'16] showed that the standard local search algorithm yields a…
A probable solution of the cosmological constant problem was recently found. We propose that dark energy of the Universe is vacuum energy. Our Universe during its expansion is spending its vacuum energy for creation of new quantum states,…
We consider further consequences of recently [1] revealed role of cosmological constant \Lambda as of a physical constant, along with the gravitational one to define the gravity i.e. the General Relativity and its low-energy limit. We now…
In this paper, we study the hard uniform capacitated $k$- median problem using local search heuristic. Obtaining a constant factor approximation for the \ckm problem is open. All the existing solutions giving constant-factor approximation,…
Optimization problems in disciplines such as machine learning are commonly solved with iterative methods. Gradient descent algorithms find local minima by moving along the direction of steepest descent while Newton's method takes into…
A diverse set of observations now compellingly suggest that Universe possesses a nonzero cosmological constant. In the context of quantum-field theory a cosmological constant corresponds to the energy density of the vacuum, and the wanted…