Chromatic number of the product of graphs, graph homomorphisms, Antichains and cofinal subsets of posets without AC

We have observations concerning the set theoretic strength of the following combinatorial statements without the axiom of choice. 1. If in a partially ordered set, all chains are finite and all antichains are countable, then the set is countable. 2. If in a partially ordered set, all chains are finite and all antichains have size $\aleph_{\alpha}$, then the set has size $\aleph_{\alpha}$ for any regular $\aleph_{\alpha}$. 3. CS (Every partially ordered set without a maximal element has two disjoint cofinal subsets). 4. CWF (Every partially ordered set has a cofinal well-founded subset). 5. DT (Dilworth's decomposition theorem for infinite p.o.sets of finite width). 6. If the chromatic number of a graph $G_{1}$ is finite (say $k<\omega$), and the chromatic number of another graph $G_{2}$ is infinite, then the chromatic number of $G_{1}\times G_{2}$ is $k$. 7. For an infinite graph $G=(V_{G}, E_{G})$ and a finite graph $H=(V_{H}, E_{H})$, if every finite subgraph of $G$ has a homomorphism into $H$, then so has $G$. Further we study a few statements restricted to linearly-ordered structures without the axiom of choice.Comment: Revised versio

Radiation of scalar oscillons in 2 and 3 dimensions

The radiation loss of small-amplitude radially symmetric oscillons (long-living, spatially localized, time-dependent solutions) in two- and three-dimensional scalar field theories is computed analytically in the small-amplitude expansion. The amplitude of the radiation is beyond all orders in perturbation theory and it is determined using matched asymptotic series expansions and Borel summation. The general results are illustrated on the case of the two- and three-dimensional sine-Gordon theory and a two-dimensional $\phi^6$ model. The analytic predictions are found to be in good agreement with the results of numerical simulations of oscillons.Comment: 7 pages, 3 figure

Online Variance Reduction for Stochastic Optimization

Modern stochastic optimization methods often rely on uniform sampling which is agnostic to the underlying characteristics of the data. This might degrade the convergence by yielding estimates that suffer from a high variance. A possible remedy is to employ non-uniform importance sampling techniques, which take the structure of the dataset into account. In this work, we investigate a recently proposed setting which poses variance reduction as an online optimization problem with bandit feedback. We devise a novel and efficient algorithm for this setting that finds a sequence of importance sampling distributions competitive with the best fixed distribution in hindsight, the first result of this kind. While we present our method for sampling datapoints, it naturally extends to selecting coordinates or even blocks of thereof. Empirical validations underline the benefits of our method in several settings.Comment: COLT 201

Standard Bayes logic is not finitely axiomatizable

In the paper [http://philsci-archive.pitt.edu/14136] a hierarchy of modal logics have been defined to capture the logical features of Bayesian belief revision. Elements in that hierarchy were distinguished by the cardinality of the set of elementary propositions. By linking the modal logics in the hierarchy to Medvedev's logic of (in)finite problems it has been shown that the modal logic of Bayesian belief revision determined by probabilities on a finite set of elementary propositions is not finitely axiomatizable. However, the infinite case remained open. In this paper we prove that the modal logic of Bayesian belief revision determined by standard Borel spaces (these cover probability spaces that occur in most of the applications) is also not finitely axiomatizable

Tejsavbaktériumok szelektálása romlást okozó élesztők szaporodásának gátlására

Az emberiség régóta használja, kezdetben tudatlanul, későbbiekben már célirányosan a tejsavbaktériumokat - és köztük a Lactobacillus nemzetség tagjait –, azok széleskörű környezeti előfordulása és kedvező tevékenysége okán, élelmiszereinek kialakítására, tartósítására. A kezdetektől használt s kihasznált tartósító tulajdonságaik jelentősége egy időben háttérbe szorult, ám napjainkban a kevesebb tartósítószer alkalmazása, a kíméletesebb tartósító kezelések, összességében a „természetesebb” élelmiszer iránti fogyasztói igény hatására a tejsavbaktériumok és az általuk szintetizált antimikrobiális anyagok ismét előtérbe kerültek a biotartósítás zászlója alatt. Az élelmiszeriparban az élesztőgombák hasznos és nélkülözhetetlen szerepe kétségbevonhatatlan, azonban gyakran a nyersanyagok, a késztermékek káros, romlást okozó mikroorganizmusai is egyben. Sokféle élelmiszer romlását előidézhetik, nagy gazdasági veszteséget okozva, amelyet jól mutat, hogy becslések szerint a világ élelmiszertermelésének 5-10%-a az élesztők és penészek okozta romlás miatt vész kárba. Doktori disszertációmban tejsavbaktériumok élesztőgátló tulajdonságuk alapján történő szelekcióját, a gátló hatás hátterének feltárását és a hatékony törzsek, illetve ezekből kialakított vegyes kultúrák gyakorlati alkalmazás szempontjából történő vizsgálatát tűztem ki célul

Finite Jeffrey logic is not finitely axiomatizable

Bayes logics based on Bayes conditionalization as a probability updating mechanism have recently been introduced in [http://philsci-archive.pitt.edu/14136/]. It has been shown that the modal logic of Bayesian belief revision determined by probabilities on a finite set of elementary propositions or on a standard Borel space is not finitely axiomatizable [http://philsci-archive.pitt.edu/14136/]. Apart from Bayes conditionalization there are other methods, extensions of the standard one, of updating a probability measure. One such important method is Jeffrey's conditionalization. In this paper we consider the modal logic \JL_{<\omega} of probability updating based on Jeffrey's conditionalization where the underlying measurable space is finite. By relating this logic to the logic of absolute continuity and to Medvedev's logic of finite problems, we show that \JL_{<\omega} is not finitely axiomatizable. The result is significant because it indicates that axiomatic approaches to belief revision might be severely limited