Singular components of spectral measures for ergodic Jacobi matrices

For ergodic 1d Jacobi operators we prove that the random singular components of any spectral measure are almost surely mutually disjoint as long as one restricts to the set of positive Lyapunov exponent. In the context of extended Harper's equation this yields the first rigorous proof of the Thouless' formula for the Lyapunov exponent in the dual regions.Comment: to appear in the Journal of Mathematical Physics, vol 52 (2011

Программные решения организации работы с ЭМК на мобильных устройствах в off-line режиме

The article deals with software solutions for e-health card under the access to the services of a medical information system. Consideration of some cross-platform solution for e-health card, as well as highlights the main approaches to the development of this service

Counting Small Induced Subgraphs with Edge-monotone Properties

We study the parameterized complexity of #IndSub($\Phi$), where given a graph $G$ and an integer $k$, the task is to count the number of induced subgraphs on $k$ vertices that satisfy the graph property $\Phi$. Focke and Roth [STOC 2022] completely characterized the complexity for each $\Phi$ that is a hereditary property (that is, closed under vertex deletions): #IndSub($\Phi$) is #W[1]-hard except in the degenerate cases when every graph satisfies $\Phi$ or only finitely many graphs satisfy $\Phi$. We complement this result with a classification for each $\Phi$ that is edge monotone (that is, closed under edge deletions): #IndSub($\Phi$) is #W[1]-hard except in the degenerate case when there are only finitely many integers $k$ such that $\Phi$ is nontrivial on $k$-vertex graphs. Our result generalizes earlier results for specific properties $\Phi$ that are related to the connectivity or density of the graph. Further, we extend the #W[1]-hardness result by a lower bound which shows that #IndSub($\Phi$) cannot be solved in time $f(k) \cdot |V(G)|^{o(\sqrt{\log k/\log\log k})}$ for any function $f$, unless the Exponential-Time Hypothesis (ETH) fails. For many natural properties, we obtain even a tight bound $f(k) \cdot |V(G)|^{o(k)}$; for example, this is the case for every property $\Phi$ that is nontrivial on $k$-vertex graphs for each $k$ greater than some $k_0$

Collusive market allocations

Collusive schemes by suppliers often take the form of allocating customers or markets among cartel members. We analyze incentives for suppliers to initiate and sustain such a collusive schemes in a repeated procurement setting. We show that, contrary to some prevailing beliefs, staggered (versus synchronized) purchasing does not make collusion more difficult to sustain or initiate. Buyer defensive measures include synchronized rather than staggered purchasing, first-price rather than second-price auctions, more aggressive or secrete reserve prices, longer contract lengths, withholding information, and avoiding observable registration procedures. Inefficiency induced by defensive measures is an often unrecognized social cost of collusive conduct

Building A Big Data Analytical Pipeline With Hadoop For Processing Enterprise XML Data

The current paper shows an end-to-end approach how to process XML files in the Hadoop ecosystem. The work demonstrates a way how to handle problems faced during the analysis of a large amounts of XML files. The paper presents a completed Extract, Load and Transform (ELT) cycle, which is based on the open source software stack Apache Hadoop, which became a standard for processing of a huge amounts of data. This work shows that applying open source solutions to a particular set of problems could not be enough. In fact, most of big data processing open source tools were implemented only to address a limited number of the use cases. This work explains and shows, why exactly specific use cases may require significant extension with a self-developed multiple software components. The use case described in the paper deals with huge amounts of semi-structured XML files, which supposed to be persisted and processed daily

Improving epidemic malaria planning, preparedness and response in Southern Africa

Malaria is a major public health problem for countries in the Southern Africa Development Community (SADC). While the endemicity of malaria varies enormously across this region, many of the countries have districts that are prone to periodic epidemics, which can be regional in their extent, and to resurgent outbreaks that are much more localized. These epidemics are frequently triggered by climate anomalies and often follow periods of drought. Many parts of Southern Africa have suffered rainfall deficit over the past three years and countries expect to see increased levels of malaria when the rains return to more 'normal' levels. Problems with drug and insecticide resistance are documented widely and the region contains countries with the highest rates of HIV prevalence to be found anywhere in the world. Consequently, many communities are vulnerable to severe disease outcomes should epidemics occur. The SADC countries have adopted the Abuja targets for Roll Back Malaria in Africa, which include improved epidemic detection and response, i.e., that 60% of epidemics will be detected within two weeks of onset, and 60% of epidemics will be responded to within two weeks of detection. The SADC countries recognize that to achieve these targets they need improved information on where and when to look for epidemics. The WHO integrated framework for improved early warning and early detection of malaria epidemics has been recognized as a potentially useful tool for epidemic preparedness and response planning. Following evidence of successful adoption and implementation of this approach in Botswana, the SADC countries, the WHO Southern Africa Inter-Country Programme on Malaria Control, and the SADC Drought Monitoring Centre decided to organize a regional meeting where countries could gather to assess their current control status and community vulnerability, consider changes in epidemic risk, and develop a detailed plan of action for the forthcoming 2004–2005 season. The following is a report on the 1(st )Southern African Regional Epidemic Outlook Forum, which was held in Harare, Zimbabwe, 26(th)–29(th )September, 2004

The contribution of the German building sector to achieve the 1.5 °C target

The melting greenhouse gas emissions budget of the German building sector for the 1.5 °C target requires fast counteraction. In this paper, an analysis of the applicable legal and regulatory framework, the funding situation as well as national and international strategies on a transformation towards climate neutrality elucidates that the suggested approaches do not take a holistic view into account. They neglect, that embodied emissions from construction and emissions from operations phases of buildings must be oriented on the remaining budget, as well as material and human resources associated with the required actions. Therefore a framework to decarbonise the German building sector with eleven recommendations for action, which addresses these findings, is developed with a panel of experts. The results clarify, that the focus must be on adapting the existing building stock since renovation processes release significantly fewer emissions than the construction of new buildings. Stricter legal requirements for building envelopes have no significant effect on the reduction of emissions. Instead, fast-acting measures, such as the usage of district heating, photovoltaics, heat pumps, the optimisation of building operation and digitalisation, must be implemented in a prioritised manner to save resources and maintain the emissions budget longer. To be able to align effective measures it is necessary to engage all Stakeholders and to establish reliable political guidance down to the building level