In this paper we discuss lower bounds for convergence of convex optimization methods of high order and attainability of this bounds. We formulate a hypothesis that covers all the cases. It is ...noticeable that we provide this statement without a proof. Newton method is the most famous method that uses gradient and Hessian of optimized function. However, it converges locally even for strongly convex functions. Global convergence can be achieved with cubic regularization of Newton method Nesterov, Polyak, 2006, whose iteration cost is comparable with iteration cost of Newton method and is equivalent to inversion of Hessian of optimized function. Yu.Nesterov proposed accelerated variant of Newton method with cubic regularization in 2008 Nesterov, 2008. R.Monteiro and B. Svaiter managed to improve global convergence of cubic regularized method in 2013 Monteiro, Svaiter, 2013. Y.Arjevani, O. Shamir and R. Shiff showed that convergence bound of Monteiro and Svaiter is optimal (cannot be improved by more than logarithmic factor with any second order method) in 2017 Arjevani et al., 2017. They also managed to find bounds for convex optimization methods of p-th order for $p 2$. However, they got bounds only for first and second order methods for strongly convex functions. In 2018 Yu.Nesterov proposed third order convex optimization methods with rate of convergence that is close to this lower bounds and with similar to Newton method cost of iteration Nesterov, 2018. Consequently, it was showed that high order methods can be practical. In this paper we formulate lower bounds for p-th order methods for $p 3$ for strongly convex unconstrained optimization problems. This paper can be viewed as a little survey of state of the art of high order optimization methods.
The Iron Princess Helfferich, Tryntje
2013, 2013-06-03, 2013-07-01
eBook
In the bloodiest conflict Europe had ever experienced, Amalia Elisabeth fought to save her tiny German state, her Calvinist church, and her children's inheritance. Tryntje Helfferich reveals how this ...embattled ruler used diplomacy to play the European powers against one another, while raising one of the continent's most effective fighting forces.
Hesse Decker, Gunnar; Lewis, Peter
2018, 2018-11-30
eBook
Against Nazi dictatorship, the disillusionment of Weimar, and Christian austerity, Hermann Hesse's stories inspired a nonconformist yearning for universal values to supplant fanaticism in all its ...guises. He reenters our world through Gunnar Decker's biography—a champion of spiritual searching in the face of mass culture and the disenchanted life.
Alfred Nobels Testament wohnt eine Dynamik inne, die alljährlich für internationale Kontroversen sorgt. Die Schwedische Akademie, die diese Auszeichnung verleiht, versucht seit Beginn ihrer ...Tätigkeit, die von Nobel festgelegten Richtlinien vor dem Hintergrund gegenwärtiger literarischer Strömungen bzw. Tendenzen auszulegen. Die vorliegende Untersuchung setzt sich mit dem Literaturnobelpreis und seinen deutschsprachigen Preisträgern der ersten Hälfte des 20. Jahrhunderts auseinander. Anhand von Archivmaterial (Nominierungen, Gutachten, offiziellen Schreiben und privaten Briefen) wird gezeigt, auf welch vielfältige Weise das Auswahlverfahren funktioniert. Die dabei gewonnenen Einblicke in die Abläufe machen die hinter den jeweiligen Entscheidungen stehenden auch auβerliterarischen Zusammenhänge deutlich.
Teleconnections in spatial modelling Behrens, Thorsten; MacMillan, Robert A.; Viscarra Rossel, Raphael A. ...
Geoderma,
11/2019, Letnik:
354
Journal Article
Recenzirano
In pedology, spatial context is relevant to soil-landscape systems on at least three different scales: i) the scale of quasi-local processes, which are independent of influence from the direct or ...wider neighborhood, ii) the scale of short-range processes for example on the local hillslope or catena, and iii) the scale of long-range processes, or teleconnected systems. We can represent the effects of teleconnections using existing tools and covariates, but we cannot easily infer or identify their controls, landscape processes or landscape units. We consider that an ability to identify the relevant controls in teleconnected systems would greatly improve pedological interpretation and understanding. Such understanding relates to the interaction of environmental factors and processes in the spatial context, which is relevant for environmental mapping generally. Here we show that teleconnected systems can be disassembled and interpreted using contextual modelling in such a way that the controls, i.e. the cause, can be localized in space. We present examples of how teleconnected systems can be deciphered. The methodology is based on the previously described ConMap approach in combination with Random Forest's measures of local feature importance. ConMap uses elevation differences, computed along multiple rays radiating out from a center grid cell, as predictors instead of complex surface derivatives or decomposed scales of a digital elevation model (DEM) or terrain attribute. Using synthetic and real-world data sets, we show how to identify and interpret teleconnections in soil environmental systems. In the synthetic example, elevation peaks are shown to produce larger values of soil properties, while, in contrast, a valley-mountain system is the main control of soil texture in the real-world example. Our analyses of teleconnected soil environmental systems illustrate that the stochastic component of the universal model of spatial variation is an integral but typically unresolved part of the deterministic component.
•The three most important contextual environmental process systems are defined.•The term teleconnection is introduced for digital soil mapping and pedology.•A method is presented that makes it possible to decode teleconnected systems.•The control of a teleconnected system can be determined and spatially localized.
Veneration and revolt Stephenson, Barry
Veneration and revolt,
c2009, 2009, 2009-02-24, Letnik:
33
eBook
One of the most widely read German authors in the world, Hermann Hesse (1877-1962) won the Nobel Prize for Literature in 1946. After his death, his novels enjoyed a revival of popularity, becoming a ...staple of popular religion and spirituality in Europe and North America. Veneration and Revolt: Hermann Hesse and Swabian Pietism is the first comprehensive study of the impact of German Pietism (the religion of Hesse's family and native Swabia) on Hesse's life and literature. Hesse's literature bears witness to a lifelong conversation with his religious heritage despite that in adolescence he rejected his family's expectation that he become a theologian, cleric, and missionary. Hesse's Pietist upbringing and broader Swabian heritage contributed to his moral and political views, his pacifism and internationalism, the confessional and autobiographical style of his literature, his romantic mysticism, his suspicion of bourgeois culture, his ecumenical outlook, and, in an era scarred by two world wars, his hopes for the future. Veneration and Revolt offers a unique perspective on the life and works of one of the twentieth century's most influential writers.
In the focus of this study are the sedimentary characteristics, chronology, magnitude, and causes of past soil erosion dynamics of an agriculturally intensively used glacial lowland landscape. From ...the mesoscale Quillow river catchment, sedimentary sections bearing colluvial sediments from different landforms were analysed to explore their geoarchive potential and to establish a local chronology of Late Holocene soil erosion. Sections from footslopes contain a rather simple stratigraphy with one topping colluvial horizon of up to 1 m thickness burying a palaeosol. In contrast glacial kettle holes preserve more complex sequences partly having several colluvial layers with intercalating palaeosols. The most complex stratigraphy is associated with a kettle hole being the ultimate sediment trap for a dendritic gully system, forming a 4 m thick sequence of alternating peat and colluvial layers. Thirty OSL ages and 13 radiocarbon ages are used to reconstruct phases of soil erosion. Potentially human-induced soil erosion, which is corroborated by local archaeological and palynological data, can be traced back to the last c. 4000 years. The oldest colluvial deposits date back to the Late Bronze Age. Most datings, however, cluster within the last 600 years with a peak in the last 200 years, ascribing the main phase of local soil erosion to the recent past. Thus, although numerous archaeological finds are detected in the catchment since the Neolithic, considerable agricultural soil erosion does not occur before the last millennium. A compilation of OSL chronologies based on colluvial sediments from other regions in Central Europe shows a more complex erosion history there with a pronounced two- or three-phased distribution of ages primarily dating into the last c. 4000–5000 years. This study underlines that in northeastern Central Europe human impact on landscapes was effective apparently at a later stage as compared to some adjacent regions.
•The oldest colluvial deposits are linked with the Late Bronze Age.•No correlation to Neolithic cultures could be detected.•Broad dataset of published datings was established and compared with this study.•Soil erosion in northeastern Germany happened later than in adjacent regions.
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