Counting dependent and independent strings

The paper gives estimations for the sizes of the the following sets: (1) the set of strings that have a given dependency with a fixed string, (2) the set of strings that are pairwise \alpha independent, (3) the set of strings that are mutually \alpha independent. The relevant definitions are as follows: C(x) is the Kolmogorov complexity of the string x. A string y has \alpha -dependency with a string x if C(y) - C(y|x) \geq \alpha. A set of strings {x_1, \ldots, x_t} is pairwise \alpha-independent if for all i different from j, C(x_i) - C(x_i | x_j) \leq \alpha. A tuple of strings (x_1, \ldots, x_t) is mutually \alpha-independent if C(x_{\pi(1)} \ldots x_{\pi(t)}) \geq C(x_1) + \ldots + C(x_t) - \alpha, for every permutation \pi of [t]

Impossibility of independence amplification in Kolmogorov complexity theory

The paper studies randomness extraction from sources with bounded independence and the issue of independence amplification of sources, using the framework of Kolmogorov complexity. The dependency of strings $x$ and $y$ is ${\rm dep}(x,y) = \max\{C(x) - C(x \mid y), C(y) - C(y\mid x)\}$, where $C(\cdot)$ denotes the Kolmogorov complexity. It is shown that there exists a computable Kolmogorov extractor $f$ such that, for any two $n$-bit strings with complexity $s(n)$ and dependency $\alpha(n)$, it outputs a string of length $s(n)$ with complexity $s(n)- \alpha(n)$ conditioned by any one of the input strings. It is proven that the above are the optimal parameters a Kolmogorov extractor can achieve. It is shown that independence amplification cannot be effectively realized. Specifically, if (after excluding a trivial case) there exist computable functions $f_1$ and $f_2$ such that ${\rm dep}(f_1(x,y), f_2(x,y)) \leq \beta(n)$ for all $n$-bit strings $x$ and $y$ with ${\rm dep}(x,y) \leq \alpha(n)$, then $\beta(n) \geq \alpha(n) - O(\log n)$

Simple extractors via constructions of cryptographic pseudo-random generators

Trevisan has shown that constructions of pseudo-random generators from hard functions (the Nisan-Wigderson approach) also produce extractors. We show that constructions of pseudo-random generators from one-way permutations (the Blum-Micali-Yao approach) can be used for building extractors as well. Using this new technique we build extractors that do not use designs and polynomial-based error-correcting codes and that are very simple and efficient. For example, one extractor produces each output bit separately in $O(\log^2 n)$ time. These extractors work for weak sources with min entropy $\lambda n$, for arbitrary constant $\lambda > 0$, have seed length $O(\log^2 n)$, and their output length is $\approx n^{\lambda/3}$.Comment: 21 pages, an extended abstract will appear in Proc. ICALP 2005; small corrections, some comments and references adde

Is Independence an Exception?

Gödel's Incompleteness Theorem asserts that any sufficiently rich, sound, and recursively axiomatizable theory is incomplete. We show that, in a quite general topological sense, incompleteness is a rather common phenomenon: With respect to any reasonable topology the set of true and unprovable statements of such a theory is dense and in many cases even co-rare

Counterimmunoelectrophoresis in diagnosís of visceral leishmaniasis with ant1gens o- l. cfonovoni, l. brasiliensis and "leptomonas pessoai". Previous note

Submitted by Marlene Santos ([email protected]) on 2017-02-10T19:29:02Z No. of bitstreams: 2 Artigo - William Barbosa - 1973.pdf: 2612813 bytes, checksum: 7ca443b895eaf31baff494af2b689727 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)Approved for entry into archive by Luciana Ferreira ([email protected]) on 2017-02-20T15:03:59Z (GMT) No. of bitstreams: 2 Artigo - William Barbosa - 1973.pdf: 2612813 bytes, checksum: 7ca443b895eaf31baff494af2b689727 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)Approved for entry into archive by Luciana Ferreira ([email protected]) on 2017-02-20T15:05:05Z (GMT) No. of bitstreams: 2 Artigo - William Barbosa - 1973.pdf: 2612813 bytes, checksum: 7ca443b895eaf31baff494af2b689727 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)Made available in DSpace on 2017-02-20T15:05:15Z (GMT). No. of bitstreams: 2 Artigo - William Barbosa - 1973.pdf: 2612813 bytes, checksum: 7ca443b895eaf31baff494af2b689727 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 1973-12Soros de 11 pacientes de Calazar, comprovados parasitologicamente e acompanhados clinicamente, foram estudados pela técnica de contra-imunoeletroforese com os antígenos de L. braslliensls, L. pessoal e L. donovani. Os resultados positivos foram, respectivamente, da ordem de 90,9%, 72,7% e 96,6%. Dos soros testemunhas: (16 de doença de Chagas, 12 de Leishmaniose tegumentar, 12 de Tuberculose, 12 de Blastomicose Sul Americana e 8 de outras doenças) apenas 5, sendo 4 de Tuberculose e l de Blastomicose Sul Americana, deram reação cruzada com o antígeno de L. pessoai. O método, se revelou de grande sensibilidade e elevada especificidade além de ser muito prático e económico.Será from 11 patients with visceral leishmaniasis, confirmei! by parasítologie examination and clinicai control were studied by counterimmunoelectrophoresis using antigens of Leishmania brasiliensis, Leptomonas pessoal and L. donovanl. Positive results were 90,0%; 72,7% and 96,6% respectively. Among 60 control será tested (16 of Chagas' disease, 12 of mucocutaneous leishmaniasis, 12 of tuberculosis, 12 of South American blastomycosis and 8 of several other diseases) only 4 of tuberculosis and l of South American blastomycosis gave cross reaction with the aniigen of L. pessoai. The method is very practical and cheap and showed high sensitivity and great specificity

On Generating Independent Random Strings

Abstract. It is shown that from two strings that are partially random and independent (in the sense of Kolmogorov complexity) it is possible to effectively construct polynomially many strings that are random and pairwise independent. If the two initial strings are random, then the above task can be performed in polynomial time. It is also possible to construct in polynomial time a random string, from two strings that have constant randomness rate