We propose a complete axiomatization for the total variation distance of finite labelled Markov chains. Our axiomatization is given in the form of a quantitative deduction system, a framework recently proposed by Mardare, Panangaden, and Plotkin (LICS 2016) to extend classical equational deduction systems by means of inferences of equality relations t ≡ε s indexed by rationals, expressing that ...

CP violation in the neutral kaon system is known to be dominated by the mixing of K 0 and K 0. Direct CP violation in the 2 pion decays of neutral kaons has been a controversial subject over the last decade. A strong experimental effort has been devoted to the precise measurement of the direct CP violation parameter ℜe (ε ′ /ε). After 10 years of detector development, data collection and analys...

We present a detailed analysis of ε/ε within the Standard Model, taking into account the strong enhancement through final–state interactions identified in refs. [1] and [2]. The relevant hadronic matrix elements are fixed at leading order in the 1/NC expansion, through a matching procedure between the effective short–distance Lagrangian and its corresponding low–energy description in Chiral Per...

I discuss the comparison of the current theoretical calculations of ε/ε with the experimental data. Lacking reliable “first principle” calculations, phenomenological approaches may help in understanding correlations among different contributions and available experimental data. In particular, in the chiral quark model approach the same dynamics which underlies the ∆I = 1/2 selection rule in kao...

We extend the study of the complexity of computing an εapproximate Nash equilibrium in symmetric congestion games from the case of positive delay functions to delays of arbitrary sign. Our results show that with this extension the complexity has a richer structure, and it depends on the exact nature of the signs allowed. We first prove that in symmetric games with increasing delay functions and...

It is well known that Huxley’s density estimates [5] for the zeros of the Riemann zeta-function yield J(x, h) = o(xh2(log x)−2), but only for h ≥ x1/6(log x) , for some C > 0. The weaker result with h ≥ x1/6+ε is proved in Saffari and Vaughan [8], Lemma 5, and in [13], where an identity of Heath-Brown (Lemma 1 of [3]) is used. This paper is inspired by Heath-Brown’s extension [4] of Huxley’s Th...

By introducing the concept of -convertibility, we extend Nielsen’s and Vidal’s theorems to the entanglement transformation of infinite-dimensional systems. Using an infinitedimensional version of Vidal’s theorem we derive a new stochastic-LOCC (SLOCC) monotone which can be considered as an extension of the Schmidt rank. We show that states with polynomially-damped Schmidt coefficients belong to...

We present a general method for counting and packing Hamilton cycles in dense graphs and oriented graphs, based on permanent estimates. We utilize this approach to prove several extremal results. In particular, we show that every nearly cn-regular oriented graph on n vertices with c > 3/8 contains (cn/e)(1 + o(1)) directed Hamilton cycles. This is an extension of a result of Cuckler, who settle...

We consider two basic types of coarse-graining: the Ehrenfest’s coarsegraining and its extension to a general principle of non-equilibrium thermodynamics, and the coarse-graining based on uncertainty of dynamical models and ε-motions (orbits). Non-technical discussion of basic notions and main coarse-graining theorems are presented: the theorem about entropy overproduction for the Ehrenfest’s c...