The spin-glass phase-transition in the Hopfield model with p-spin interactions

We study the Hopfield model with pure $p$-spin interactions with even $p\geq 4$, and a number of patterns, M(N) growing with the system size, $N$, as M(N) = \a N^{p-1}. We prove the existence of a critical temperature \b_p characterized as the first time quenched and annealed free energy differ. We prove that as $p\uparrow\infty$, \b_p\to\sqrt {\a 2\ln 2}. Moreover, we show that for any \a>0 and for all inverse temperatures \b, the free energy converges to that of the REM at inverse temperature \b/\sqrt\a. Moreover, above the critical temperature the distribution of the replica overlap is concentrated at zero. We show that for large enough \a, there exists a non-empty interval of in the low temperature regime where the distribution has mass both near zero and near $\pm 1$. As was first shown by M. Talagrand in the case of the $p$-spin SK model, this implies the the Gibbs measure at low temperatures is concentrated, asymptotically for large $N$, on a countable union of disjoint sets, no finite subset of which has full mass. Finally, we show that there is \a_p\sim 1/p! such that for \a>\a_p the set carrying almost all mass does not contain the original patterns. In this sense we describe a genuine spin glass transition. Our approach follows that of Talagrand's analysis of the $p$-spin SK-model. The more complex structure of the random interactions necessitates, however, considerable technical modifications. In particular, various results that follow easily in the Gaussian case from integration by parts fromulas have to be derived by expansion techniques.Comment: 58 pages, AMS-TE

Szlovák-magyar kapcsolatok a diplomáciai iratok tükrében 1939-1944 között = Slovakian-hungarian relation in diplomatic documents between 1939-44

A dokumentumok kiválogatása szisztematikus levéltári kutatások révén valósult meg a tárgykörhöz tartozó levéltári fondok módszeres átnézésével és a kigyűjtött anyag válogatásával. Terveimben szerepel, hogy amennyiben sikerül a forráskiadvány nyomdai munkáihoz anyagi támogatást szereznem, azt szlovák és magyar nyelven is megjelentetem. Munkámat a szlovák és magyar fél közötti eddigi feszült viszony oldására szeretném felhasználni. Szeretném elérni, hogy a korábbi történelmi félreértések és ferdítések végre tisztázódjanak és a két nép közötti közeledést, múltjuk és történelmük objektív feltárásával elősegíthessem. A forráskiadványom időszerűségét növeli, hogy az 1939-1944 közötti szlovák-magyar kapcsolatok tudományos feltárása csak bizonyos résztémák földolgozásaként készült el. A szlovák-magyar kapcsolatok kutatása e rövid időszakra vonatkozólag a mai napig sem történt meg. A két érdekelt állam történészei a szlovák-magyar diplomáciai kapcsolatok témakörében eddig nem jelenthettek meg forráskiadványt, így munkám hiánypótlás lenne, másik eredménye pedig az, hogy a kutatók, történészek, illetve a téma iránt érdeklődő nagyközönség munkáját is megkönnyítem, mivel így mindenki számára használhatóvá és elérhetővé válhatnak ezek a dokumentumok. | In the centre of the planned publication of sources will be the antecedents of the development of policy of reciprocity and its tragic impact. In my work, I would like to compare and reconstruct how the principle of reciprocity developed in the minority policy of the two countries and how it prevailed during the war. How big and what kind of scope for action was ensured by the great powers to the two small countries, for their domestic and foreign policy between 1939 and 1944. In the publication of sources, I would like to describe the life of minorities of the two countries, which is easy to follow in the battles of diplomatic documents. The minorities living in the two countries were both hostages and trumps in the hands of the leaders of Slovak and Hungarian political life, which could be used any time to achieve their political goals. In connection with the research of the countries' relations, I would like to describe the background of strengthening of the Slovak revision claims, as well as the steps of the Hungarian diplomacy to prevent these

Stochastic symmetry-breaking in a gaussian Hopfield model

We study a ``two-pattern'' Hopfield model with Gaussian disorder. We find that there are infinitely many pure states at low temperatures in this model, and we find that the metastate is supported on an infinity of symmetric pairs of pure states. The origin of this phenomenon is the random breaking of a rotation symmetry of the distribution of the disorderComment: 31pp, AMSTe

Thematic Working Group 7: Indicators of Quality Technology: Enhanced Learning and Teaching

EDUsummIT 2015 was co-hosted by UNESCO Bangkok (the Asia and Pacific regional bureau of UNESCO) and Curtin Universitypublished_or_final_versio

A Multilevel System of Quality Technology-Enhanced Learning and Teaching Indicators

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High-resolution esophageal long-term ECG allows detailed atrial wave morphology analysis in case of atrial ectopic beats

Detection of arrhythmic atrial beats in surface ECGs can be challenging when they are masked by the R or T wave, or do not affect the RR-interval. Here, we present a solution using a high-resolution esophageal long-term ECG that offers a detailed view on the atrial electrical activity. The recorded ECG shows atrial ectopic beats with long coupling intervals, which can only be successfully classified using additional morphology criteria. Esophageal high-resolution ECGs provide this information, whereas surface long-term ECGs show poor atrial signal quality. This new method is a promising tool for the long-term rhythm monitoring with software-based automatic classification of atrial beat