Continuity Results and Estimates for the Lyapunov Exponent of Brownian Motion in Random Potential

We collect some applications of the variational formula established by Schr\"oder (1988) and Rue\ss (2013) for the quenched Lyapunov exponent of Brownian motion in stationary and ergodic nonnegative potential. We show for example that the Lyapunov exponent for nondeterministic potential is strictly lower than the Lyapunov exponent for the averaged potential. The behaviour of the Lyapunov exponent under independent perturbations of the underlying potential is examined. And with the help of counterexamples we are able to give a detailed picture of the continuity properties of the Lyapunov exponent.Comment: 20 pages, 1 figure, some references update

Effect of emerging technology on a convertible, business/interceptor, supersonic-cruise jet

This study was initiated to assess the feasibility of an eight-passenger, supersonic-cruise long range business jet aircraft that could be converted into a military missile carrying interceptor. The baseline passenger version has a flight crew of two with cabin space for four rows of two passenger seats plus baggage and lavatory room in the aft cabin. The ramp weight is 61,600 pounds with an internal fuel capacity of 30,904 pounds. Utilizing an improved version of a current technology low-bypass ratio turbofan engine, range is 3,622 nautical miles at Mach 2.0 cruise and standard day operating conditions. Balanced field takeoff distance is 6,600 feet and landing distance is 5,170 feet at 44,737 pounds. The passenger section from aft of the flight crew station to the aft pressure bulkhead in the cabin was modified for the interceptor version. Bomb bay type doors were added and volume is sufficient for four advanced air-to-air missiles mounted on a rotary launcher. Missile volume was based on a Phoenix type missile with a weight of 910 pounds per missile for a total payload weight of 3,640 pounds. Structural and equipment weights were adjusted and result in a ramp weight of 63,246 pounds with a fuel load of 30,938 pounds. Based on a typical intercept mission flight profile, the resulting radius is 1,609 nautical miles at a cruise Mach number of 2.0

The theology of god and the gentile mission in acts

The present study aims to investigate Luke's theology of God in the accounts of the mission to the Gentiles in Acts. In Acts, God is portrayed as the cause of the mission. It is God who inaugurates and guides the Gentile mission. For Luke, God who acts is God who has fixed the times and seasons. The mission is described as part of God's times, past, present and future. It is mission by God. The Gentile mission is also mission about God. The "cause" of the mission becomes the content'. This fact is not widely recognised by studies in Luke-Acts. God' is prominent in the speeches in the Gentile mission narratives of Samaria (8: 4-25), Caesarea (10: 33- 43), Lystra (14: 8-18), Athens (17: 16-34) and Ephesus (19: 21- 41). We examine these narratives to analyse the speeches in their immediate contexts provided in the narrative itself. Except in Ac. 10, Luke's contexts contain details concerning Gentiles" belief and worship of god/goddess/gods which in Luke's view represent false notions about God. The fundamental issue in the theology of God in all these narratives is confusion of the human with the divine. That men and works of men are neither God nor manifestations of God is the essence of the theological kerygma. In Ac. 10, Peter's own wrong notion of God is corrected and his new knowledge about God leads to the conversion of the Gentiles. God who is proclaimed to the Gentiles is God who does 'mighty acts". We consider two more narratives, 12: 21-24 and 28: 1-10, in which Gentile notions of god are presented without kerygma attached to them. The former can be classified with the mission narratives since all of them function as model settings to Luke's readers, illustrating how mission ought to take place in circumstances in which similar false understandings of God are found. The latter episode is an example of Luke's positive use of Gentile notions of god as 'justice' to attest the innocence of Paul, the prisoner and missionary to Rome. In the description of the Gentile mission in Acts, Luke emerges as a theologian of God

Spatial point pattern analysis with application to confocal microscopy data

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Discrete duality principle in different random graph models

For a given random graph, a connected component that contains a finite fraction of the entire graph's vertices is called giant. The study of these components started with the \ER model, where it has been proven that removing the (unique) giant component from a random graph is essentially equivalent to another random graph in the same model with different known parameters. This is called the discrete duality principle. In this report we aim at presenting this principle in its historical \ER settings, and then to present more recent generalisations made on random graphs with given degree sequences

Chromatin organization in relation to the nuclear periphery

AbstractIn the limited space of the nucleus, chromatin is organized in a dynamic and non-random manner. Three ways of chromatin organization are compaction, formation of loops and localization within the nucleus. To study chromatin localization it is most convenient to use the nuclear envelope as a fixed viewpoint. Peripheral chromatin has both been described as silent chromatin, interacting with the nuclear lamina, and active chromatin, interacting with nuclear pore proteins. Current data indicate that the nuclear envelope is a reader as well as a writer of chromatin state, and that its influence is not limited to the nuclear periphery

Reflections and Insights on the Evolution of the Biological Remediation of Contaminated Soils

The field of soil biological remediation was initially focused on the use of microorganisms. For organic contaminants, biostimulation and bioaugmentation were the strategies of choice. For heavy metals, bioremediation was centered on the feasibility of using microorganisms to reduce metal toxicity. Partly due to the impossibility to degrade metals, phytoremediation emerged proposing the use of plants to extract them (phytoextraction) or reduce their bioavailability (phytostabilization). Later, microbial-assisted phytoremediation addressed the inoculation of plant growth-promoting microorganisms to improve phytoremediation efficiency. Similarly, plant-assisted bioremediation examined the stimulatory effect of plant growth on the microbial degradation of soil contaminants. The combination of plants and microorganisms is nowadays often recommended for mixed contaminated soils. Finally, phytomanagement emerged as a phytotechnology focused on the use of plants and associated microorganisms to decrease contaminant linkages, maximize ecosystem services, and provide economic revenues. Although biological remediation methods have been in use for decades, the truth is that they have not yet yielded the expected results. Here, we claim that much more research is needed to make the most of the many ways that microorganisms have evolutionary developed to access the contaminants and to better understand the soil microbial networks responsible, to a great extent, for soil functioning.This work was supported by the European Union through the Interreg SUDOE Program (Project Phy2SUDOE SOE4/P5/E1021)

Learning Structured Distributions: Power-Law and Low-Rank

Utilizing the structure of a probabilistic model can significantlyincrease its compression efficiency and learning speed. We considerthese potential improvements under two naturally-omnipresentstructures.Power-Law: English words and many other natural phenomena arewell-known to follow a power-law distribution. Yet this ubiquitousstructure has never been shown to help compress or predict thesephenomena. It is known that the class of unrestricted distributionsover alphabet of size k and blocks of length n can never becompressed with diminishing per-symbol redundancy, when k>n. Weshow that under power-law structure, in expectation we can compresswith diminishing per-symbol redundancy for k growing as large assub-exponential in n.For learning a power-law distribution, we rigorously explain theefficacy of the absolute-discount estimator using less pessimisticnotions. We show that (1) it is adaptive to an effectivedimension and (2) it is stronglyrelated to the Good--Turing estimator and inherits itscompetitive properties.Low-Rank: We study learning low-rank conditional probabilitymatrices under expected KL-risk. This choice accentuates smoothing,the careful handling of low-probability elements. We define a lossfunction, determine sample-complexity bound for its global minimizer,and show that this bound is optimal up to logarithmic terms. Wepropose an iterative algorithm that extends classical non-negativematrix factorization to naturally incorporate additive smoothing andprove that it converges to the stationary points of our loss function.Power-Law and Low-Rank: We consider learning distributions inthe presence of both low-rank and power-law structures. We studyKneser-Ney smoothing, a successful estimator for the N-gram languagemodels through the lens of competitive distribution estimation. Wefirst establish some competitive properties for the contextualprobability estimation problem. This leads to Partial Low Rank,a powerful generalization of Kneser-Ney that we conjecture to haveeven stronger competitive properties. Empirically, it significantlyimproves the performance on language modeling, even matching thefeed-forward neural models, and gives similar gains on the task ofpredicting attack types for the Global Terrorism Database