اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدNew separation between $s(f)$ and $bs(f)$
117
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
In this note we give a new separation between sensitivity and block sensitivity of Boolean functions: $bs(f)=(2/3)s(f)^2-(1/3)s(f)$.
قيم البحث
اقرأ أيضاً
Andreev bound states are an expression of quantum coherence between particles and holes in hybrid structures composed of superconducting and non-superconducting metallic parts. Their spectrum carries important information on the nature of the pairing
, and determines the current in Josephson devices. Here I give a short review on Andreev bound states in systems involving superconductors and ferromagnets with strong spin-polarization. I show how the processes of spin-dependent scattering phase shifts and of triplet rotation influence Andreev point contact spectra, and provide a general framework for non-local Andreev phenomena in such structures in terms of coherence functions. Finally, I demonstrate how the concept of coherence functions cross-links wave-function and Green-function based theories, by showing that coherence functions fulfilling the equations of motion for quasiclassical Green functions can be used to derive a set of generalised Andreev equations.
We develop a rigorous and general framework for constructing information-theoretic divergences that subsume both $f$-divergences and integral probability metrics (IPMs), such as the $1$-Wasserstein distance. We prove under which assumptions these div
ergences, hereafter referred to as $(f,Gamma)$-divergences, provide a notion of `distance between probability measures and show that they can be expressed as a two-stage mass-redistribution/mass-transport process. The $(f,Gamma)$-divergences inherit features from IPMs, such as the ability to compare distributions which are not absolutely continuous, as well as from $f$-divergences, namely the strict concavity of their variational representations and the ability to control heavy-tailed distributions for particular choices of $f$. When combined, these features establish a divergence with improved properties for estimation, statistical learning, and uncertainty quantification applications. Using statistical learning as an example, we demonstrate their advantage in training generative adversarial networks (GANs) for heavy-tailed, not-absolutely continuous sample distributions. We also show improved performance and stability over gradient-penalized Wasserstein GAN in image generation.
We show that there exists a Boolean function $F$ which observes the following separations among deterministic query complexity $(D(F))$, randomized zero error query complexity $(R_0(F))$ and randomized one-sided error query complexity $(R_1(F))$: $R_
1(F) = widetilde{O}(sqrt{D(F)})$ and $R_0(F)=widetilde{O}(D(F))^{3/4}$. This refutes the conjecture made by Saks and Wigderson that for any Boolean function $f$, $R_0(f)=Omega({D(f)})^{0.753..}$. This also shows widest separation between $R_1(f)$ and $D(f)$ for any Boolean function. The function $F$ was defined by G{{o}}{{o}}s, Pitassi and Watson who studied it for showing a separation between deterministic decision tree complexity and unambiguous non-deterministic decision tree complexity. Independently of us, Ambainis et al proved that different variants of the function $F$ certify optimal (quadratic) separation between $D(f)$ and $R_0(f)$, and polynomial separation between $R_0(f)$ and $R_1(f)$. Viewed as separation results, our results are subsumed by those of Ambainis et al. However, while the functions considerd in the work of Ambainis et al are different variants of $F$, we work with the original function $F$ itself.
We study the anomalous Josephson effect, as well as the dependence on the direction of the critical Josephson current, in an S/N/S junction, where the normal part is realized by alternating spin-orbit coupled and ferromagnetic layers. We show that to
observe these effects it is sufficient to break spin rotation and time reversal symmetry in spatially separated regions of the junction. Moreover, we discuss how to further improve these effects by engineering multilayers structures with more that one couple of alternating layers.
In this presentation the new physics implications of the $B$-meson decay anomalies, observed at LHCb, are discussed. In the first part of the talk a brief overview of the experimental status is presented. In the second part, a class of semi-local F-t
heory GUT models with additional neutral gauge bosons are proposed which are capable of accounting for the anomalous $B$-decay ratios $R_{K}$ and $R_{K^*}$
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
