1,356,148 research outputs found
Heat and mass transfer from the mantle: heat flow and He-isotope constraints
No full textTerrestrial heat flow density, q, is inversely correlated with the age, t, of tectono-magmatic activity in the Earth's
crust (Polyak and Smirnov, 1966; etc.). «Heat flow-age dependence» indicates unknown temporal heat sources in
the interior considered a priori as the mantle-derived diapirs. The validity of this hypothesis is demonstrated by
studying the helium isotope ratio, 3He/4He = R, in subsurface fluids. This study discovered the positive correlation
between the regionally averaged (background) estimations of R- and q-values (Polyak et al., 1979a). Such a correlation
manifests itself in both pan-regional scales (Norhtern Eurasia) and separate regions, e.g., Japan (Sano et al.,
1982), Eger Graben (Polyak et al., 1985) Eastern China rifts (Du, 1992), Southern Italy (Italiano et al., 2000), and
elsewhere. The R-q relation indicates a coupled heat and mass transfer from the mantle into the crust. From considerations
of heat-mass budget this transfer can be provided by the flux consisting of silicate matter rather than He
or other volatiles. This conclusion is confirmed by the correlation between 3He/ 4He and 87Sr/86Sr ratios in the products
of the volcanic and hydrothermal activity in Italy (Polyak et al., 1979b; Parello et al., 2000) and other places.
Migration of any substance through geotemperature field transports thermal energy accumulated within this substance,
i.e. represents heat and mass transfer. Therefore, only the coupled analysis of both material and energy
aspects of this transfer makes it possible to characterise the process adequately and to decipher an origin of terrestrial
heat flow observed in upper parts of the earth crust. An attempt of such kind is made in this paper.PublishedJCR Journalope
Complexity Guarantees for Polyak Steps with Momentum
No full textIn smooth strongly convex optimization, or in the presence of H\"olderian error bounds, knowledge of the curvature parameter is critical for obtaining simple methods with accelerated rates. In this work, we study a class of methods, based on Polyak steps, where this knowledge is substituted by that of the optimal value, . We first show slightly improved convergence bounds than previously known for the classical case of simple gradient descent with Polyak steps, we then derive an accelerated gradient method with Polyak steps and momentum, along with convergence guarantees
Polyak Minorant Method for Convex Optimization
No full textIn 1963 Boris Polyak suggested a particular step size for gradient descent
methods, now known as the Polyak step size, that he later adapted to
subgradient methods. The Polyak step size requires knowledge of the optimal
value of the minimization problem, which is a strong assumption but one that
holds for several important problems. In this paper we extend Polyak's method
to handle constraints and, as a generalization of subgradients, general
minorants, which are convex functions that tightly lower bound the objective
and constraint functions. We refer to this algorithm as the Polyak Minorant
Method (PMM). It is closely related to cutting-plane and bundle methods.Comment: 28 pages, 4 figure
Replication Data for: Silent Losers of Export Surpluses
No full textGermany’s excessive current account surpluses mirror domestic problems. They are rooted in inequality and a weak home market, creating an overdependence on exports. Why, then, are policymakers so reluctant to reduce them? This paper argues that a contributing factor is the public misrepresentation of surpluses’ domestic costs. Imbalances are narrated as distributional conflicts between countries, not within them; and bilateral trade is framed as a competition, where surplus countries win. The analysis reconstructs stakeholders’ positions and discursive strategies through media narratives and Bundestag debates, using an original dataset of public statements. It finds evidence for a systematic bias disregarding the domestic losers of surpluses. Whenever imbalances are discussed, the triggering event is outside criticism, mainly from the European Commission and the United States. The ensuing debate follows an ‘us versus them’ logic, where foreign critics clash with domestic defenders – mainly the government and export-sector organizations. The success narrative and identitarian discourse about an ‘export nation’ limits left-wing actors’ room to move beyond incremental criticism. The analysis finds an effect of European integration exacerbating imbalances. Germans fend off critics by an arena-shifting strategy: pointing out that exchange rates and trade are European-level prerogatives, disregarding internal policy levers for rebalancing
Accelerating Level-Value Adjustment for the Polyak Stepsize
No full textThe Polyak stepsize formula has been widely used for convex optimization.
However, stepsize computations require the generally unknown optimal value.
Dynamic estimations of the optimal value are thus usually needed. In this
paper, guided by a decision-based procedure through a novel easy-to-solve
``Polyak Stepsize Violation Detector'' (PSVD) linear constraint satisfaction
problem, a series of level values is constructed to successively estimate the
optimal value to guarantee convergence for subgradient as well as for
approximate subgradient methods. Through a series of empirical tests of convex
optimization problems with diverse characteristics, we illustrate the practical
advantages of our approach as compared to existing methods
On the Polyak–Viro Vassiliev Invariant of Degree 4
No full textAbstractUsing the Polyak–Viro Gauss diagram formula for the degree-4 Vassiliev invariant, we extend some previous results on positive knots and the non-triviality of the Jones polynomial of untwisted Whitehead doubles.</jats:p
Investigation of early medieval pottery production in Lower Austria: an archaeological science approach
No full textThis thesis aims to contribute to a better understanding of early medieval pottery production
in Lower Austria by the scientific analysis of ceramics. The investigation is based on 135
potsherds, including graphite-containing ceramics, which originate from the Erlauf Valley and
other sites of Lower Austria and Vienna. The ceramics are dated to the 1st–12th centuries AD,
with a majority of samples (n=123) from the 6th–11th centuries AD. The potsherds are studied,
in addition to macroscopic analysis, by four scientific methods: petrographic thin section
analysis, scanning electron microscopy (SEM), inductively coupled plasma optical emission
spectrometry (ICP-OES) and X-ray diffraction (XRD). These methods are used to identify and characterise the origin and manufacturing technology
of the ceramics in order to gain insight into wider aspects of pottery production such as the
organisation of production, technological choices, traditions and innovation. The compositions
of the studied ceramics are consistent with different parts of one geological unit, the
Bohemian Massif. This information, together with the distribution of the pots, provides details
about connectivity and suggests the presence of local, regional and supra-regional
trade/exchange networks within the study area. Traces of the applied production techniques
indicate a relatively low level of standardisation for most of the ceramics; observations in this
regard along with scale, degree of control and specialisation are used to discuss organisation of
production. Through the reconstruction of the ceramic making process, technological choices
are examined, such as the use of a new raw material, graphite, from the 8th/9th centuries. The
analysis of the manufacturing steps also sheds light on practices of different periods and
reveals, for example, differences in raw material preparation between the 1st–7
th and 8th–9
th
centuries, which suggest a more sophisticated technology of pottery production in the former
than in the latter period in the Erlauf Valley
Michael Polyak
No full text. The classical Whitney formula relates the algebraic number of selfintersections of a generic plane curve to its winding number. We generalize it to an infinite family of identities, expressing the winding number in terms of the internal geometry of a plane curve. This enables us to split the Whitney formula by some characteristic of double points. It turns out, that only crossings of a very specific type contribute to the computation of the winding number. We also provide a "difference integration" of these formulae, establishing a new family of simple formulae with the base point pushed off the curve. Similar new identities are obtained for Arnold's invariant Strangeness of plane curves. 1. Whitney formula and its generalizations 1.1. Introduction. The classical Whitney formula [4] relates the algebraic number of times that a generic immersed plane curve intersects itself to the Whitney index, or winding number, of this curve. Since it was discovered in 1937, this formula remained m..
Levitin-Polyak well-posedness of completely generalized mixed variational inequalities in reflexive banach spaces
No full textLet be a real reflexive Banach space. In this paper, we first introduce the concept of Levitin-Polyak well-posedness of a completely generalized mixed variational inequality in , and establish some characterizations of its Levitin-Polyak well-posedness. Under suitable conditions, we prove that the Levitin-Polyak well-posedness of a completely generalized mixed variational inequality is equivalent both to the Levitin-Polyak well-posedness of a corresponding inclusion problem and to the Levitin-Polyak well-posedness of a corresponding fixed point problem. We also derive some conditions under which a completely generalized mixed variational inequality in is Levitin-Polyak well-posed. Our results improve, extend and develop the early and recent ones in the literature.</jats:p
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