Causal Inference by Stochastic Complexity

The algorithmic Markov condition states that the most likely causal direction between two random variables X and Y can be identified as that direction with the lowest Kolmogorov complexity. Due to the halting problem, however, this notion is not computable. We hence propose to do causal inference by stochastic complexity. That is, we propose to approximate Kolmogorov complexity via the Minimum Description Length (MDL) principle, using a score that is mini-max optimal with regard to the model class under consideration. This means that even in an adversarial setting, such as when the true distribution is not in this class, we still obtain the optimal encoding for the data relative to the class. We instantiate this framework, which we call CISC, for pairs of univariate discrete variables, using the class of multinomial distributions. Experiments show that CISC is highly accurate on synthetic, benchmark, as well as real-world data, outperforming the state of the art by a margin, and scales extremely well with regard to sample and domain sizes

QED and Electroweak Corrections to Deep Inelastic Scattering

We describe the state of the art in the field of radiative corrections for deep inelastic scattering. Different methods of calculation of radiative corrections are reviewed. Some new results for QED radiative corrections for polarized deep inelastic scattering at HERA are presented. A comparison of results obtained by the codes POLRAD and HECTOR is given for the kinematic regime of the HERMES experiment. Recent results on radiative corrections to deep inelastic scattering with tagged photons are briefly discussed.Comment: 22 pages Latex, including 6 eps-figures; to appear in the Proceedings of the 3rd International Symposium on Radiative Corrections, Cracow, August 1-5, 1996, Acta Phys. Polonica

On Some Schützenberger Conjectures

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A non-ambiguous decomposition of regular languages and factorizing codes

AbstractGiven languages Z,L⊆Σ∗,Z is L-decomposable (finitely L-decomposable, resp.) if there exists a non-trivial pair of languages (finite languages, resp.) (A,B), such that Z=AL+B and the operations are non-ambiguous. We show that it is decidable whether Z is L-decomposable and whether Z is finitely L-decomposable, in the case Z and L are regular languages. The result in the case Z=L allows one to decide whether, given a finite language S⊆Σ∗, there exist finite languages C,P such that SC∗P=Σ∗ with non-ambiguous operations. This problem is related to Schützenberger's Factorization Conjecture on codes. We also construct an infinite family of factorizing codes

Secure and linear cryptosystems using error-correcting codes

A public-key cryptosystem, digital signature and authentication procedures based on a Gallager-type parity-check error-correcting code are presented. The complexity of the encryption and the decryption processes scale linearly with the size of the plaintext Alice sends to Bob. The public-key is pre-corrupted by Bob, whereas a private-noise added by Alice to a given fraction of the ciphertext of each encrypted plaintext serves to increase the secure channel and is the cornerstone for digital signatures and authentication. Various scenarios are discussed including the possible actions of the opponent Oscar as an eavesdropper or as a disruptor