From coinductive proofs to exact real arithmetic: theory and applications

Based on a new coinductive characterization of continuous functions we extract certified programs for exact real number computation from constructive proofs. The extracted programs construct and combine exact real number algorithms with respect to the binary signed digit representation of real numbers. The data type corresponding to the coinductive definition of continuous functions consists of finitely branching non-wellfounded trees describing when the algorithm writes and reads digits. We discuss several examples including the extraction of programs for polynomials up to degree two and the definite integral of continuous maps

Adsorption of benzene on Si(100) from first principles

Adsorption of benzene on the Si(100) surface is studied from first principles. We find that the most stable configuration is a tetra-$\sigma$-bonded structure characterized by one C-C double bond and four C-Si bonds. A similar structure, obtained by rotating the benzene molecule by 90 degrees, lies slightly higher in energy. However, rather narrow wells on the potential energy surface characterize these adsorption configurations. A benzene molecule impinging on the Si surface is most likely to be adsorbed in one of three different di-$\sigma$-bonded, metastable structures, characterized by two C-Si bonds, and eventually converts into the lowest-energy configurations. These results are consistent with recent experiments.Comment: 4 pages, RevTex, 2 PostScript gzipped figure

Polynomial function intervals for floating-point software verification

The focus of our work is the verification of tight functional properties of numerical programs, such as showing that a floating-point implementation of Riemann integration computes a close approximation of the exact integral. Programmers and engineers writing such programs will benefit from verification tools that support an expressive specification language and that are highly automated. Our work provides a new method for verification of numerical software, supporting a substantially more expressive language for specifications than other publicly available automated tools. The additional expressivity in the specification language is provided by two constructs. First, the specification can feature inclusions between interval arithmetic expressions. Second, the integral operator from classical analysis can be used in the specifications, where the integration bounds can be arbitrary expressions over real variables. To support our claim of expressivity, we outline the verification of four example programs, including the integration example mentioned earlier. A key component of our method is an algorithm for proving numerical theorems. This algorithm is based on automatic polynomial approximation of non-linear real and real-interval functions defined by expressions. The PolyPaver tool is our implementation of the algorithm and its source code is publicly available. In this paper we report on experiments using PolyPaver that indicate that the additional expressivity does not come at a performance cost when comparing with other publicly available state-of-the-art provers. We also include a scalability study that explores the limits of PolyPaver in proving tight functional specifications of progressively larger randomly generated programs

The RACE Project: Robustness by Autonomous Competence Enhancement

This paper reports on the aims, the approach, and the results of the European project RACE. The project aim was to enhance the behavior of an autonomous robot by having the robot learn from conceptualized experiences of previous performance, based on initial models of the domain and its own actions in it. This paper introduces the general system architecture; it then sketches some results in detail regarding hybrid reasoning and planning used in RACE, and instances of learning from the experiences of real robot task execution. Enhancement of robot competence is operationalized in terms of performance quality and description length of the robot instructions, and such enhancement is shown to result from the RACE system

An ontology-based multi-level robot architecture for learning from experiences

One way to improve the robustness and flexibility of robot performance is to let the robot learn from its experiences. In this paper, we describe the architecture and knowledge-representation framework for a service robot being developed in the EU project RACE, and present examples illustrating how learning from experiences will be achieved. As a unique innovative feature, the framework combines memory records of low-level robot activities with ontology-based high-level semantic descriptions

Distributed optimization with arbitrary local solvers

With the growth of data and necessity for distributed optimization methods, solvers that work well on a single machine must be re-designed to leverage distributed computation. Recent work in this area has been limited by focusing heavily on developing highly specific methods for the distributed environment. These special-purpose methods are often unable to fully leverage the competitive performance of their well-tuned and customized single machine counterparts. Further, they are unable to easily integrate improvements that continue to be made to single machine methods. To this end, we present a framework for distributed optimization that both allows the flexibility of arbitrary solvers to be used on each (single) machine locally, and yet maintains competitive performance against other state-of-the-art special-purpose distributed methods. We give strong primal-dual convergence rate guarantees for our framework that hold for arbitrary local solvers. We demonstrate the impact of local solver selection both theoretically and in an extensive experimental comparison. Finally, we provide thorough implementation details for our framework, highlighting areas for practical performance gains

Paleogeographic evolution of the Southern Pannonian Basin: 40Ar/39Ar age constraints on the Miocene continental series of notthern Croatia

The Pannonian Basin, originating during the Early Miocene, is a large extensional basin incorporated between Alpine, Carpathian and Dinaride fold-thrust belts. Back-arc extensional tectonics triggered deposition of up to 500-m-thick continental fluvio-lacustrine deposits distributed in numerous sub-basins of the Southern Pannonian Basin. Extensive andesitic and dacitic volcanism accompanied the syn-rift deposition and caused a number of pyroclastic intercalations. Here, we analyze two volcanic ash layers located at the base and top of the continental series. The lowermost ash from Mt. Kalnik yielded an 40Ar/39Ar age of 18.07 ± 0.07 Ma. This indicates that the marine-continental transition in the Slovenia-Zagorje Basin, coinciding with the onset of rifting tectonics in the Southern Pannonian Basin, occurs roughly at the Eggenburgian/ Ottnangian boundary of the regional Paratethys time scale. This age proves the synchronicity of initial rifting in the Southern Pannonian Basin with the beginning of sedimentation in the Dinaride Lake System. Beside geodynamic evolution, the two regions also share a biotic evolutionary history: both belong to the same ecoregion, which we designate here as the Illyrian Bioprovince. The youngest volcanic ash level is sampled at the Glina and Karlovac sub-depressions, and both sites yield the same 40Ar/39Ar age of 15.91 ± 0.06 and 16.03 ± 0.06 Ma, respectively. This indicates that lacustrine sedimentation in the Southern Pannonian Basin continued at least until the earliest Badenian. The present results provide not only important bench marks on duration of initial synrift in the Pannonian Basin System, but also deliver substantial backbone data for paleogeographic reconstructions in Central and Southeastern Europe around the Early–Middle Miocene transition

Postavenie Rusínskej a Ukrajinskej menšiny na Slovensku v podmienkach Československa (1918–1992)

Štúdia formou stručnej syntézy prezentuje vývoj v postavení rusínskej a ukrajinskej menšiny žijúcej na východnom Slovensku v období existencie Československej republiky. V úvodnej časti autori charakterizujú menšinu a poukazujú na faktory a okolnosti, ktoré ju spojili s československým štátom. Historická kontinuita a určité súvislosti s problematikou Podkarpatskej Rusi priniesli Rusínom na Slovensku v medzivojnovom období isté zvláštnosti v jednotlivých oblastiach života spoločnosti. Inštitúty demokratického štátu však využívali v prospech rozvoja životnej a kultúrnej úrovne komunity. Po obnovení Československa a definitívnom oddelení od väčšiny etnika dochádza v nových politických podmienkach k umelým zásahom do etnogenézy minority, ktoré viedli k poklesu jej početnosti a oslabeniu národných atribútov. Po páde komunistického režimu je rozvoj menšiny limitovaný najmä jej rozdelením a niektorými prechodnými dôsledkami spoločenskej transformácie na Slovensku.The authors of the study present the development of legal and social status of the ethnic minority of Ruthenians and Ukrainians in Slovakia during the existence of the Czechoslovak state. Based on recent scholarship, in the first part of the study the authors characterize basic features of the minority and explain factors and circumstances which contributed to the annexation of the territories populated by this minority by the Czechoslovak state. The fact that Ruthenians and Ukrainians lived continuously on the annexed territory, as well as the factor of establishing of the formally autonomous region of Subcarpathian Ruthenia, meant that members of this minority were characterized by several specifics which are dealt with in detail in the study. The democratic regime of the Czechoslovak Republic (1918–1938) enabled development of self-governed minority bodies in the benefit of the members of the community. After the restoration of Czechoslovakia and the definitive separation from the majority of ethnicities, the new political conditions leads to artificial interventions in the ethnic minority ethnogenesis. This has led to a decline in its number and weakening of national attributes. After the collapse of the communist regime, the development of the minority is limited, especially, by its partition and some temporary consequences of social transformation in Slovakia