Related papers: Wiring Switches to Light Bulbs
This paper gives an heuristic lower bound for the number of integers connected to 1 and less than $x$, $\theta(x) > 0.9x,$ in the context of the $3n+1$ problem.
We compute the effects due to the virtual exchange (or the soft emission) of a scalar particle with generic couplings to the top quark in $t\bar t$ pair production at the LHC. We apply the results to two cases of interest, extending and…
It was conjectured by Levi, Hadwiger, Gohberg and Markus that the boundary of any convex body in ${\mathbb R}^n$ can be illuminated by at most $2^n$ light sources, and, moreover, $2^n-1$ light sources suffice unless the body is a…
The Gale-Berlekamp switching game is played on the following device: $G_n=\{1,2,\ldots,n\} \times \{1,2,\ldots,n\}$ is an $n \times n$ array of lights is controlled by $2n$ switches, one for each row or column. Given an (arbitrary) initial…
We investigate the stabilizability of discrete-time linear switched systems, when the sole control action of the controller is the switching signal, and when the controller has access to the state of the system in real time. Despite their…
The quantum interaction between free electrons and photons is fundamental to free-electron based light sources and free-electron quantum optics applications. A large coupling between free electrons and photons is generally desired. In this…
We consider the problem of carrying an initial Bloch vector to a final Bloch vector in a specified amount of time under the action of three control fields (a vector control field). We show that this control problem is solvable and therefore…
We show that there is a calculable upper limit on the mass of the lightest Higgs boson in any supersymmetric theory that remains perturbative up to a high scale . There are no restrictions on the Higgs sector, or the gauge group or particle…
We give an explicitly computable lower bound for the arithmetic self-intersection number of the dualizing sheaf on a large class of arithmetic surfaces. If some technical conditions are satisfied, then this lower bound is positive. In…
Given a large finite point set, $P\subset \mathbb R^2$, we obtain upper bounds on the number of triples of points that determine a given pair of dot products. That is, for any pair of positive real numbers, $(\alpha, \beta)$, we bound the…
Lights Out! is a game played on a $5 \times 5$ grid of lights, or more generally on a graph. Pressing lights on the grid allows the player to turn off neighboring lights. The goal of the game is to start with a given initial configuration…
A single-electron inverter was fabricated that switches from a high output to a low output when a fraction of an electron is added to the input. For the proper operation of the inverter, the two single-electron transistors that make up the…
A pebbling move on a graph removes two pebbles at a vertex and adds one pebble at an adjacent vertex. Rubbling is a version of pebbling where an additional move is allowed. In this new move, one pebble each is removed at vertices $v$ and…
We develop a general method to bound the ordered singular values (channel amplitudes) of the electromagnetic Green function for arbitrarily structured linear photonic systems. The approach yields computable, quantitatively predictive, upper…
The independence between few-body scales beyond the van der Waals universality is demonstrated for the extreme mass-imbalanced case of a specific many-boson system. This finding generalizes the scaling properties of universal tetramers to a…
We consider a subgroup of unitary transformations on a mode of light induced by a Mach-Zehnder Interferometer and an algebra of observables describing a photon-number detector proceeded by an interferometer. We explore the uncertainty…
We show that the cusp volume of a hyperbolic alternating knot can be bounded above and below in terms of the twist number of an alternating diagram of the knot. This leads to diagrammatic estimates on lengths of slopes, and has some…
Future power grids will offer enhanced controllability due to the increased availability of power flow control units (FACTS). As the installation of control units in the grid is an expensive investment, we are interested in using few…
We study the coupling between collective variables of atomic spin and light polarization in an ensemble of cold 87Rb probed with polarized light. The effects of multiple hyperfine levels manifest themselves as a rank-2 tensor…
Based on symmetry constraint that leads to the appearance of nodes in the wave functions of 3-electron systems at regular triangle configurations, it was found that, if the parameters of confinement are skillfully given and if a magnetic…