Maximums of the Additive Differential Probability of Exclusive-Or

At FSE 2004, Lipmaa et al. studied the additive differential probability adp⊕(α,β → γ) of exclusive-or where differences α,β,γ ∈ Fn2 are expressed using addition modulo 2n. This probability is used in the analysis of symmetric-key primitives that combine XOR and modular addition, such as the increasingly popular Addition-Rotation-XOR (ARX) constructions. The focus of this paper is on maximal differentials, which are helpful when constructing differential trails. We provide the missing proof for Theorem 3 of the FSE 2004 paper, which states that maxα,βadp⊕(α,β → γ) = adp⊕(0,γ → γ) for all γ. Furthermore, we prove that there always exist either two or eight distinct pairs α,β such that adp⊕( α,β → γ) = adp⊕(0,γ → γ), and we obtain recurrence formulas for calculating adp⊕. To gain insight into the range of possible differential probabilities, we also study other properties such as the minimum value of adp⊕(0,γ → γ), and we find all γ that satisfy this minimum value

Relativistic Hadron-Hadron Collisions in the Ultra-Relativistic Quantum Molecular Dynamics Model (UrQMD)

Hadron-hadron collisions at high energies are investigated in the Ultra-relativistic-Quantum-Molecular-Dynamics approach (UrQMD). This microscopic transport model is designed to study pp, pA and A+A collisions. It describes the phenomenology of hadronic interactions at low and intermediate energies ($\sqrt s <5$ GeV) in terms of interactions between known hadrons and their resonances. At high energies, $\sqrt s >5$ GeV, the excitation of color strings and their subsequent fragmentation into hadrons dominates the multiple production of particles in the UrQMD model. The model shows a fair overall agreement with a large body of experimental h-h data over a wide range of h-h center-of-mass energies. Hadronic reaction data with higher precision would be useful to support the use of the UrQMD model for relativistic heavy ion collisions.Comment: 66 pages, Download the UrQMD model from http://www.th.physik.uni-frankfurt.de/~urqmd/urqmd.htm

Absolute Branching Fraction Measurements for D^+ and D^0 Inclusive Semileptonic Decays

We present measurements of the inclusive branching fractions for the decays D^+ -> X e^+ nu_e and D^0 -> X e^+ nu_e, using 281 pb^-1 of data collected on the psi(3770) resonance with the CLEO-c detector. We find Br(D^0 ->Xe^+\nu_e) = (6.46 \pm 0.17 \pm 0.13)% and Br((D^+ -> Xe^+nu_e) = (16.13 \pm 0.20 \pm 0.33)%. Using the known D meson lifetimes, we obtain the ratio Gamma{D^+}^sl/Gamma_{D^0}^sl= 0.985\pm 0.028\pm 0.015, confirming isospin invariance at the level of 3%. The positron momentum spectra from D^+ and D^0 have consistent shapes.Comment: 6 pages postscript,also available through this http://www.lns.cornell.edu/public/CLNS/2006

There are no universal rules for induction

In a material theory of induction, inductive inferences are warranted by facts that prevail locally. This approach, it is urged, is preferable to formal theories of induction in which the good inductive inferences are delineated as those conforming to universal schemas. An inductive inference problem concerning indeterministic, nonprobabilistic systems in physics is posed, and it is argued that Bayesians cannot responsibly analyze it, thereby demonstrating that the probability calculus is not the universal logic of induction. Copyright 2010 by the Philosophy of Science Association.All right reserved

Multiplicative noise: A mechanism leading to nonextensive statistical mechanics

A large variety of microscopic or mesoscopic models lead to generic results that accommodate naturally within Boltzmann-Gibbs statistical mechanics (based on $S_1\equiv -k \int du p(u) \ln p(u)$). Similarly, other classes of models point toward nonextensive statistical mechanics (based on $S_q \equiv k [1-\int du [p(u)]^q]/[q-1]$, where the value of the entropic index $q\in\Re$ depends on the specific model). We show here a family of models, with multiplicative noise, which belongs to the nonextensive class. More specifically, we consider Langevin equations of the type $\dot{u}=f(u)+g(u)\xi(t)+\eta(t)$, where $\xi(t)$ and $\eta(t)$ are independent zero-mean Gaussian white noises with respective amplitudes $M$ and $A$. This leads to the Fokker-Planck equation $\partial_t P(u,t) = -\partial_u[f(u) P(u,t)] + M\partial_u\{g(u)\partial_u[g(u)P(u,t)]\} + A\partial_{uu}P(u,t)$. Whenever the deterministic drift is proportional to the noise induced one, i.e., $f(u) =-\tau g(u) g'(u)$, the stationary solution is shown to be $P(u, \infty) \propto \bigl\{1-(1-q) \beta [g(u)]^2 \bigr\}^{\frac{1}{1-q}}$ (with $q \equiv \frac{\tau + 3M}{\tau+M}$ and $\beta=\frac{\tau+M}{2A}$). This distribution is precisely the one optimizing $S_q$ with the constraint $_q \equiv \{\int du [g(u)]^2[P(u)]^q \}/ \{\int du [P(u)]^q \}=$constant. We also introduce and discuss various characterizations of the width of the distributions.Comment: 3 PS figure