Related papers: Clocks are $e$-positive

All clocks, classical or quantum, are open non equilibrium irreversible systems subject to the constraints of thermodynamics. Using examples I show that these constraints necessarily limit the performance of clocks and that good clocks…

Suppose that D is an acyclic orientation of a graph G. An arc of D is called dependent if its reversal creates a directed cycle. Let m and M denote the minimum and the maximum of the number of dependent arcs over all acyclic orientations of…

One of the characteristic features of categorical systems theory is that the behavior of systems can be characterized by certain morphisms into them. In other words, behaviors form a representable covariant functor to Set. And more…

We show that a graph has an orientation under which every circuit of even length is clockwise odd if and only if the graph contains no subgraph which is, after the contraction of at most one circuit of odd length, an even subdivision of…

We introduce two classes of graphs - suns and dumbbells, both with few variations and explore their chromatic symmetric function and its $e$-positivity. We also give many connections of these two classes with other classes of connected…

Optical lattice clocks are the prospective devices that can probe many subtle physics including temporal variation of the fine structure constant ($\alpha_e$). These studies necessitate high-precision measurements of atomic clock frequency…

A long standing problem in the area of error correcting codes asks whether there exist good cyclic codes. Most of the known results point in the direction of a negative answer. The uncertainty principle is a classical result of harmonic…

In 2004, Karo\'nski, \L uczak and Thomason proposed $1$-$2$-$3$-conjecture: For every nice graph $G$ there is an edge weighting function $ w:E(G)\rightarrow\{1,2,3\} $ such that the induced vertex coloring is proper. After that, the total…

For simple electromagnetic models of a rod and a clock, a change of the shape of the rod and of the rate of the clock when they are set in uniform motion is calculated exactly, employing the correct equation of motion of a charged particle…

On a chassis of gear model, we have offered a quantitative description for our method to synthesize a chemical clock signal with various duty cycles in Part I. As Part II of the study, this paper devotes itself in proposing a design…

The clockwork is a mechanism for generating light particles with exponentially suppressed interactions in theories which contain no small parameters at the fundamental level. We develop a general description of the clockwork mechanism valid…

Kauffman's clock theorem provides a distributive lattice structure on the set of states of a four-valent graph in the plane. We prove two distinct generalisations of this theorem, for four-valent graphs embedded in more general compact…

The Thermal Time Hypotheis (TTH) has been proposed as a general method for identifying a time variable from within background-free theories which do not come equipped with a pre-defined clock variable. Here, we explore some implications of…

The bloom clock is a space-efficient, probabilistic data structure designed to determine the partial order of events in highly distributed systems. The bloom clock, like the vector clock, can autonomously detect causality violations by…

Our study is motivated by the prospect of several metastable states in the Sb$ ^{+} $, Au$ ^{+} $, and Hg$ ^{2+} $ ions being used as possible candidates for optical clocks. We calculate several atomic properties relevant to the development…

We prove that the chromatic symmetric function of any $n$-vertex tree containing a vertex of degree $d\geq \log _2n +1$ is not $e$-positive, that is, not a positive linear combination of elementary symmetric functions. Generalizing this, we…

It is shown that the graph obtained by merging two vertices of two 4-cycles is not a $\Theta$-graceful partial cube, thus answering in the negative a question by Bre\v{s}ar and Klav\v{z}ar from [1], who asked whether every partial cube is…

In classical music and in any genre of contemporary music, the tonal elements or notes used for playing are the same. The numerous possibilities of chords for a given instance in a piece make the playing, in general, very intricate, and…

Consider a $C_0$-semigroup $(e^{tA})_{t \ge 0}$ on a function space or, more generally, on a Banach lattice $E$. We prove a sufficient criterion for the operators $e^{tA}$ to be positive for all sufficiently large times $t$, while the…

Being able to measure time, whether directly or indirectly, is a significant advantage for an organism. It permits it to predict regular events, and prepare for them on time. Thus, clocks are ubiquitous in biology. In the present paper, we…