Numerical Verification of Affine Systems with up to a Billion Dimensions

Affine systems reachability is the basis of many verification methods. With further computation, methods exist to reason about richer models with inputs, nonlinear differential equations, and hybrid dynamics. As such, the scalability of affine systems verification is a prerequisite to scalable analysis for more complex systems. In this paper, we improve the scalability of affine systems verification, in terms of the number of dimensions (variables) in the system. The reachable states of affine systems can be written in terms of the matrix exponential, and safety checking can be performed at specific time steps with linear programming. Unfortunately, for large systems with many state variables, this direct approach requires an intractable amount of memory while using an intractable amount of computation time. We overcome these challenges by combining several methods that leverage common problem structure. Memory is reduced by exploiting initial states that are not full-dimensional and safety properties (outputs) over a few linear projections of the state variables. Computation time is saved by using numerical simulations to compute only projections of the matrix exponential relevant for the verification problem. Since large systems often have sparse dynamics, we use Krylov-subspace simulation approaches based on the Arnoldi or Lanczos iterations. Our method produces accurate counter-examples when properties are violated and, in the extreme case with sufficient problem structure, can analyze a system with one billion real-valued state variables

The intrinsic vulnerability of networks to epidemics

Contact networks are convenient models to investigate epidemics, with nodes and links representing potential hosts and infection pathways, respectively. The outcomes of outbreak simulations on networks are driven both by the underlying epidemic model, and by the networks’ structural properties, so that the same pathogen can generate different epidemic dynamics on different networks. Here we ask whether there are general properties that make a contact network intrinsically vulnerable to epidemics (that is, regardless of specific epidemiological parameters). By conducting simulations on a large set of modelled networks, we show that, when a broad range of network topologies is taken into account, the effect of specific network properties on outbreak magnitude is stronger than that of fundamental pathogen features such as transmission rate, infection duration, and immunization ability. Then, by focusing on a large set of real world networks of the same type (potential contacts between field voles, Microtus agrestis), we showed how network structure can be used to accurately assess the relative, intrinsic vulnerability of networks towards a specific pathogen, even when those have limited topological variability. These results have profound implications for how we prevent disease outbreaks; in many real world situations, the topology of host contact networks can be described and used to infer intrinsic vulnerability. Such an approach can increase preparedness and inform preventive measures against emerging diseases for which limited epidemiological information is available, enabling the identification of priority targets before an epidemic event

Ignition and combustion characteristics of n-butanol and FPBO/n-butanol blends with addition of ignition improver

In this study, the ignition and combustion characteristics of fast pyrolysis bio-oil (FPBO) are investigated in a commercially available combustion research unit (CRU) system, which is mainly composed of a constant-volume combustion chamber. To make the unmodified CRU system realizable for FPBO combustion, n-butanol and EHN are used to improve the atomization and ignition properties of the fuel blends, respectively. The study first determines an appropriate proportion of EHN additive into n-butanol to arrive at a good balance between the ignition improvement and the amount of EHN addition. Then, the effects of FPBO content in FPBO/n-butanol blends with the same EHN addition are investigated. The effects of chamber wall temperature are also studied. Experimental results show that the low-temperature and high-temperature heat release phases can be observed in all tested cases. For n-butanol with addition of EHN, the increase of EHN proportion could effectively advance the low-temperature heat release phase and shorten the ignition delay, while the chamber wall temperature is the dominant factor for combustion phasing and combustion duration. For FPBO/n-butanol blends with addition of EHN, FPBO proportion has negligible effects on the ignition delay. The increase of FPBO proportion results in a delayed combustion phasing and prolonged combustion duration, while these effects become less obvious at the elevated chamber wall temperature.<br/

New solutions in the ferrates(VI) process with the use of SnО₂–modified electrodes

Изучены особенности образования ферратов(VI) из соединений Fe(III) в растворах с различным ионным составом на инертных SnО₂-электродах, легированных Ru, Pt, Pd и Sb. Установлено, что изменением природы и содержания легирующего металла можно целенаправленно регулировать электро-каталитические свойства анодов, в частности величину перенапряжения выделения О₂. Показана принципиальная возможность электрохимического окисления на поверхности электрода и химического окисления в объеме раствора частиц Fe(ОН)₃ и Fe(ОН)₄. Разработаны рекомендации для синтеза ферратов(VI) с использованием анодов, обеспечивающих длительный режим работы без ухудшения их эксплуатационных характеристик.Disadvantages of traditional synthesis methods of ferrates (VI) - promising green oxidants - stimulate the search of new technological solutions which meet the requirements of modern production. The purpose of this work was to study the ferrates (VI) formation from Fe (III) compounds in solutions with different pH on inert SnО₂ electrodes doped with Pt, Ru, Pd, and Sb. The influence of the nature and the content of the alloying metal on the electrocatalytic properties of the electrode was studied by the stationary voltammetry method, as well as by determining the current yields of hypochlorite and sodium chlorate during the electrolysis of a slightly alkaline NaCl solution. Coatings based on SnО₂, doped with palladium and platinum, show maximal electrocatalytic activity according to ClO – synthesis. It has been established that the oxygen evolution overvoltage on the electrodes with comparable dopant concentrations increases in the Ru-Pd-Pt-Sb series. It has been shown that for effective synthesis of ferrates (VI), flat Ti anodes of a large area with an electroactive layer based on SnО₂-Sb2О₃ should be used. It is noted that electrochemical oxidation of Fe (III) in Fe (VI) is more energetically favorable on these electrodes than О₂ evolution, which opens up new possibilities for these processes in ferrate (VI) synthesis technology. We have shown the principal possibility of increasing the productivity of the Fe (VI) process due to the direct interaction of the Fe(ОН)₃ and Fe(ОН)₄− particles in the solution volume with ClO− anions generated on an inert electrode when Сl− anions are preliminarily added to the system. Technological solutions have been proposed to increase the life of inert electrodes when 5-10% TiO2 is introduced into the SnО₂ matrix, providing a long-term operating mode without degradation of their performance characteristics

Unveiling spatial inequalities: Exploring county-level disaster damages and social vulnerability on public disaster assistance in contiguous US

Understanding the dynamics between public disaster assistance, disaster damages, and social vulnerability at county-level is crucial for designing effective disaster mitigation strategies. This study utilized the Local Bivariate Moran Index (LBMI) and geographically weighted regression (GWR) models to examine spatial patterns and relationships between disaster damages, social vulnerability, and public disaster assistance in contiguous US counties from 2001 to 2021. LBMI results reveal that public disaster assistance has predominantly been directed towards post-disaster recovery efforts, with a particular focus on coastal communities affected by major declared disasters. However, the distributions of public assistance and individual housing assistance, which are the two primary sources of public disaster assistance, do not adequately cover physically and socially vulnerable communities. The distribution of pre-disaster risk mitigation also falls short of sufficiently covering vulnerable communities. Results further indicate the complex interactions between different categories of natural disasters and public assistances. The GWR model results demonstrate spatial variations in predicting each category of public disaster assistance. These findings indicate the need to address disparities in accessing public disaster assistance in the US, and advocate for more equitable disaster mitigation strategies

Dynamics of false vacuum bubbles: beyond the thin shell approximation

We numerically study the dynamics of false vacuum bubbles which are inside an almost flat background; we assumed spherical symmetry and the size of the bubble is smaller than the size of the background horizon. According to the thin shell approximation and the null energy condition, if the bubble is outside of a Schwarzschild black hole, unless we assume Farhi-Guth-Guven tunneling, expanding and inflating solutions are impossible. In this paper, we extend our method to beyond the thin shell approximation: we include the dynamics of fields and assume that the transition layer between a true vacuum and a false vacuum has non-zero thickness. If a shell has sufficiently low energy, as expected from the thin shell approximation, it collapses (Type 1). However, if the shell has sufficiently large energy, it tends to expand. Here, via the field dynamics, field values of inside of the shell slowly roll down to the true vacuum and hence the shell does not inflate (Type 2). If we add sufficient exotic matters to regularize the curvature near the shell, inflation may be possible without assuming Farhi-Guth-Guven tunneling. In this case, a wormhole is dynamically generated around the shell (Type 3). By tuning our simulation parameters, we could find transitions between Type 1 and Type 2, as well as between Type 2 and Type 3. Between Type 2 and Type 3, we could find another class of solutions (Type 4). Finally, we discuss the generation of a bubble universe and the violation of unitarity. We conclude that the existence of a certain combination of exotic matter fields violates unitarity.Comment: 40 pages, 41 figure

ac Josephson effect in the resonant tunneling through mesoscopic superconducting junctions

We investigate ac Josephson effect in the resonant tunneling through mesoscopic superconducting junctions. In the presence of microwave irradiation, we show that the trajectory of multiple Andreev reflections can be closed by emitting or absorbing photons. Consequently, photon-assisted Andreev states are formed and play the role of carrying supercurrent. On the Shapiro steps, dc component appears when the resonant level is near a series of positions with spacing of half of the microwave frequency. Analytical result is derived in the limit of infinite superconducting gap, based on which new features of ac Josephson effect are revealed.Comment: 11 pages, 3 figure

Distribution of graph-distances in Boltzmann ensembles of RNA secondary structures

Large RNA molecules often carry multiple functional domains whose spatial arrangement is an important determinant of their function. Pre-mRNA splicing, furthermore, relies on the spatial proximity of the splice junctions that can be separated by very long introns. Similar effects appear in the processing of RNA virus genomes. Albeit a crude measure, the distribution of spatial distances in thermodynamic equilibrium therefore provides useful information on the overall shape of the molecule can provide insights into the interplay of its functional domains. Spatial distance can be approximated by the graph-distance in RNA secondary structure. We show here that the equilibrium distribution of graph-distances between arbitrary nucleotides can be computed in polynomial time by means of dynamic programming. A naive implementation would yield recursions with a very high time complexity of O(n^11). Although we were able to reduce this to O(n^6) for many practical applications a further reduction seems difficult. We conclude, therefore, that sampling approaches, which are much easier to implement, are also theoretically favorable for most real-life applications, in particular since these primarily concern long-range interactions in very large RNA molecules.Comment: Peer-reviewed and presented as part of the 13th Workshop on Algorithms in Bioinformatics (WABI2013