Related papers: A note on the capacity of the binary perceptron
Shannon gave a lower bound in 1959 on the binary rate of spherical codes of given minimum Euclidean distance $\rho$. Using nonconstructive codes over a finite alphabet, we give a lower bound that is weaker but very close for small values of…
In this paper, capacity bounds for the two-user Interference Channel (IC) with cooperative receivers via conferencing links of finite capacities is investigated. The capacity results known for this communication scenario are limited to a…
We introduce the notion of \textit{Perron capacity} of a set of slopes $\Omega \subset \mathbb{R}$. Precisely, we prove that if the Perron capacity of $\Omega$ is finite then the directional maximal operator associated $M_\Omega$ is not…
There is a clear dearth of very eccentric binaries among those for which individual eccentricities can be measured. In this paper we report on observations of the two nearby, bright and very eccentric visual binaries Zeta Bo\"otis ($\zeta$…
We employ the chiral nucleon-nucleon potential derived in ref.[1] to study bound and scattering states in the two-nucleon system. At next-to-leading order, this potential is the sum of renormalized one-pion and two-pion exchange and contact…
In the large $N_c$ limit, the $\Lambda_b$ and $\Lambda_c$ can be treated as bound states of chiral solitons and mesons containing a heavy quark. We show that the soliton and heavy meson are bound in an attractive harmonic oscillator…
Let $D(n)$ be the maximal determinant for $n \times n$ $\{\pm 1\}$-matrices, and ${\mathcal R}(n) = D(n)/n^{n/2}$ be the ratio of $D(n)$ to the Hadamard upper bound. We give several new lower bounds on ${\mathcal R}(n)$ in terms of $d$,…
The mass spectrum of $c \bar b$ meson is investigated with an effective quark-antiquark potential of the form $\frac{-\alpha_c}{r}$ + $A r^{\nu}$ with $\nu$ varying from 0.5 to 2.0. The S and P-wave masses, pseudoscalar decay constant, weak…
A strong converse bound for the classical identification capacity of a quantum channel is an upper bound on the asymptotic identification rate of classical messages sent through the channel, such that, above this rate, the probability of an…
We place the first constraints on binary planets and exomoons from Doppler monitoring of directly imaged exoplanets. We model radial velocity observations of HR 8799 b, c, and d from Ruffio et al. (2021) and determine upper limits on the…
For any elements b,c of a number field K, let G(b,c) denote the backwards orbit of b under the map f_c: C-->C given by f_c(x)=x^2+c. We prove an upper bound on the number of elements of G(b,c) whose degree over K is at most some constant B.…
We interpret the newly discovered pentaquark $P_c(4450)$ as a bound state of charmonium $\psi(2S)$ and the nucleon. The binding potential is due to charmonium-nucleon interaction that in the heavy quark approximation is proportional to the…
Berlekamp and Zigangirov completely determined the capacity error function for binary error correcting codes with noiseless feedback. It is still an unsolved problem if the upper bound for the capacity error function in the non-binary case…
The notion of the capacity of a polynomial was introduced by Gurvits around 2005, originally to give drastically simplified proofs of the Van der Waerden lower bound for permanents of doubly stochastic matrices and Schrijver's inequality…
We study observational bounds in a class of scalar-tensor gravity theories recently proposed. Either an upper or lower bound on a conformal factor in these theories is derived from null observation in composition dependent fifth force…
This work investigates the secrecy capacity of the Wiretap Broadcast Channel (WBC) with an external eavesdropper where a source wishes to communicate two private messages over a Broadcast Channel (BC) while keeping them secret from the…
We investigate numerically how accurately one could constrain the strengths of different short-range contributions to neutrino-less double beta decay in effective field theory. Depending on the outcome of near-future experiments yielding…
We prove, under suitable conditions, a lower bound on the number of pinned distances determined by small subsets of two-dimensional vector spaces over fields. For finite subsets of the Euclidean plane we prove an upper bound for their…
The upper bound on the capacity of a 3-node discrete memoryless relay channel is considered, where a source X wants to send information to destination Y with the help of a relay Z. Y and Z are independent given X, and the link from Z to Y…
The existing upper and lower bounds between entropy and error probability are mostly derived from the inequality of the entropy relations, which could introduce approximations into the analysis. We derive analytical bounds based on the…