ProbNV: probabilistic verification of network control planes

ProbNV is a new framework for probabilistic network control plane verification that strikes a balance between generality and scalability. ProbNV is general enough to encode a wide range of features from the most common protocols (eBGP and OSPF) and yet scalable enough to handle challenging properties, such as probabilistic all-failures analysis of medium-sized networks with 100-200 devices. When there are a small, bounded number of failures, networks with up to 500 devices may be verified in seconds. ProbNV operates by translating raw CISCO configurations into a probabilistic and functional programming language designed for network verification. This language comes equipped with a novel type system that characterizes the sort of representation to be used for each data structure: concrete for the usual representation of values; symbolic for a BDD-based representation of sets of values; and multi-value for an MTBDD-based representation of values that depend upon symbolics. Careful use of these varying representations speeds execution of symbolic simulation of network models. The MTBDD-based representations are also used to calculate probabilistic properties of network models once symbolic simulation is complete. We implement the language and evaluate its performance on benchmarks constructed from real network topologies and synthesized routing policies.

Probabilistic theories and reconstructions of quantum theory

These lecture notes provide a basic introduction to the framework of generalized probabilistic theories (GPTs) and a sketch of a reconstruction of quantum theory (QT) from simple operational principles. To build some intuition for how physics could be even more general than quantum, I present two conceivable phenomena beyond QT: superstrong nonlocality and higher-order interference. Then I introduce the framework of GPTs, generalizing both quantum and classical probability theory. Finally, I summarize a reconstruction of QT from the principles of Tomographic Locality, Continuous Reversibility, and the Subspace Axiom. In particular, I show why a quantum bit is described by a Bloch ball, why it is three-dimensional, and how one obtains the complex numbers and operators of the usual representation of QT.

New realizations of algebras of the Askey–Wilson type in terms of Lie and quantum algebras

The Askey–Wilson algebra is realized in terms of the elements of the quantum algebras [Formula: see text] or [Formula: see text]. A new realization of the Racah algebra in terms of the Lie algebras [Formula: see text] or [Formula: see text] is also given. Details for different specializations are provided. The advantage of these new realizations is that one generator of the Askey–Wilson (or Racah) algebra becomes diagonal in the usual representation of the quantum algebras whereas the second one is tridiagonal. This allows us to recover easily the recurrence relations of the associated orthogonal polynomials of the Askey scheme. These realizations involve rational functions of the Cartan generator of the quantum algebras, where they are linear with respect to the other generators and depend on the Casimir element of the quantum algebras.

The homologies and evolutionary reduction of the pelvis and hindlimbs in snakes, with the first report of ossified pelvic vestiges in an anomalepidid (Liotyphlops beui)

We report the first example of ossified pelvic vestiges in an anomalepidid snake, Liotyplophs beui, and provide a review of the diversity of limb and pelvic elements within Serpentes. We trace the evolution, homology and reduction of the pelvic elements and hindlimbs from the oldest known snakes through to living forms. Evolutionary analysis of the pelvic and limb data shows that the most recent common ancestor of all living snakes (Serpentes) most probably retained all three pelvic elements and rudimentary hindlimbs (femoral spurs). Subsequently, there have been multiple losses of ossified pelvic and hindlimb elements and regaining of ossified pelvic elements. Reduction of the pelvis has followed different routes in the two primary groups of living snakes (scolecophidians and alethinophidians). The single remaining rod-like element in some scolecophidians is the ischium, whereas the single remaining rod-like element in many basal alethinophidians is the pubis. Notably, many basal alethinophidians share a distinctive configuration of cloacal spur (claw), femur and a sizeable pubis, which is likely to be related functionally to the widespread use of the hindlimbs in mating and courtship, rather than the usual representation of the bones as non-functional vestiges.

One Step Further in the Characterization of Synthetic Polymers by Ion Mobility Mass Spectrometry: Evaluating the Contribution of End-groups

Several families of polymers possessing various end-groups are characterized by ion mobility mass spectrometry (IMMS). A significant contribution of the end-groups to the ion collision cross section (CCS) is observed, although their role is neglected in current fitting models described in literature. Comparing polymers prepared from different synthetic procedures might thus, be misleading with the current theoretical treatments. We show that this issue is alleviated by comparing the CCS of various polymer ions (polyesters and polyethers) as a function of the number of atoms in the macroion instead of the usual representation involving the degree of polymerization. Finally, we extract the atom number density from the spectra which gives us the possibility to evaluate the compaction of polymer ions, and by extension to discern isomeric polymers.

Egyptianism

Summary When dealing with Isis, Serapis and the other members of the so-called ‘gens isiaca’, scholars have hesitated whether to emphasize their (indisputable) historico-geographic origin in the Nile valley or their (no less indisputable) character as Graeco-Roman cults. We thus find these deities referred to as ‘Egyptian’, ‘Graeco-Egyptian’, ‘Graeco-Roman’, ‘Greek’, ‘Roman’ and, again, ‘Oriental’, ‘Orientalized Roman’, and so on. Each of these definitions is evidently partial, which is one reason for the growing preference for the less specific terms ‘Isiac gods’ and ‘Isiac cults’. Yet even these elide the problem of how these cults were perceived in relation to Egypt. This article aims to challenge the terms of the conventional dichotomy between Egyptian and Graeco-Roman, by exploring the many specific contexts in which ‘Egypt’ was appropriated, for example, by institutions, intellectuals (e.g. ‘Middle-’ and Neo-Platonists), Christian apologists, late-antique encyclopedists, etc. Starting with the comparandum ‘Persianism’ recently highlighted in relation to the cult of Mithras, the paper will explore the various interests and aims involved in the construction of ideas of Egypt, which might even involve more than one ‘Egyptianism’ at the same time. Each of our nine suggested ‘Egyptianisms’ is the creation of numerous ‘producers’, who adapted what they knew of ‘Egypt’ (‘foreign’, ‘exotic’, ‘other’) to create their own religious offers. Our basic model is derived from the Erfurt project Lived Ancient Religions, which inverts the usual representation of ancient religion as collective (‘polis religion’, ‘civic religion’) in favour of a perspective that stresses individual agency, sense-making and appropriation within a range of broader constraints.

Counting, Generating, Analyzing and Sampling Tree Alignments

Pairwise ordered tree alignment are combinatorial objects that appear in important applications, such as RNA secondary structure comparison. However, the usual representation of tree alignments as supertrees is ambiguous, i.e. two distinct supertrees may induce identical sets of matches between identical pairs of trees. This ambiguity is uninformative, and detrimental to any probabilistic analysis. In this work, we consider tree alignments up to equivalence. Our first result is a precise asymptotic enumeration of tree alignments, obtained from a context-free grammar by mean of basic analytic combinatorics. Our second result focuses on alignments between two given ordered trees [Formula: see text] and [Formula: see text]. By refining our grammar to align specific trees, we obtain a decomposition scheme for the space of alignments, and use it to design an efficient dynamic programming algorithm for sampling alignments under the Gibbs-Boltzmann probability distribution. This generalizes existing tree alignment algorithms, and opens the door for a probabilistic analysis of the space of suboptimal alignments.

Application of AC Impedance Spectroscopy for Characterization of BiNbO4 Ceramics

Impedance spectroscopy is known as an important technique used for describing the electrical processes occurring in a system on applying an ac signal as input perturbation. In the present paper results of a study of BiNbO4 ceramics fabricated by mixed oxide method and sintered by free sintering are reported. Results on the ac response of the electroceramic samples by impedance spectroscopy at temperature T= 100 – 400 °C are given. The usual representation (i.e. Z” vs. Z’ where Z’ and Z” are the real and imaginary parts of the complex impedance, respectively) as well as the alternative representations of the impedance measurement (electrical modulus representation) was used to interpret the impedance spectra of BiNbO4 ceramics in order to obtain separate contributions of the bulk, grain boundary and electrode processes. The Kramers-Kronig data validation test was employed in the impedance data analysis. Experimental data of impedance spectroscopy were fitted to the corresponding equivalent circuit using the complex non-linear least squares method. Agreement between experimental and simulated data was established.

Manufacturing datatypes

This article describes a general framework for designing purely functional datatypes that automatically satisfy given size or structural constraints. Using the framework we develop implementations of different matrix types (for example, square matrices) and implementations of several tree types (for example, Braun trees and 2-3 trees). Consider representing square n×n matrices. The usual representation using lists of lists fails to meet the structural constraints: there is no way to ensure that the outer list and the inner lists have the same length. The main idea of our approach is to solve in a first step a related, but simpler problem, namely to generate the multiset of all square numbers. To describe this multiset we employ recursion equations involving finite multisets, multiset union, addition and multiplication lifted to multisets. In a second step we mechanically derive from these recursion equations datatype definitions that enforce the ‘squareness’ constraint. The transformation makes essential use of parameterized types.

An ab initio study on the magnetic susceptibility and magnetically induced current density distribution of the bicyclo[3.2.1]octa-3,6-dien-2-yl anion

The molecular susceptibility and the atomic contributions including the basin and surface components calculated at the RHF/6-31+G(d)//6-31+G(d) level of theory along with vector current densities obtained at the 6-31++G(d,p)//6-31+G(d) and 6-31+G(d)//6-31+G(d) levels are reported for benzene (1) and correlated - the agreement is excellent - with the results obtained by Keith and Bader with the 6-311++G(2d,2p) basis. This validates our similar studies on the bicyclo[3.2.1]octa-3,6-dien-2-yl anion (2) - initially considered to be a bishomoaromatic species - its parent hydrocarbon bicyclo[3.2.1]octa-2,5-diene (3), the bicyclo[3.2.1]oct-3-ene-2-yl anion (4), and 5, the lithium complex of 2. While a magnetic susceptibility exhalation is found in going from 4 to 2, the increase in atomic surface contribution to Δχ arises predominately (42.6%) from the ethenyl bridge carbons C6 and C7, with C2 + C4 and C3 exhibiting substantially smaller increases (27.4 and 8.3%, respectively). This result, in conjunction with the nature of the vector current density maps of 2 and 4, provides further evidence that 2 does not possess a ring current as depicted in 2-bh, the usual representation of "bishomoaromatic" 2.Key words: ab initio calculations, IGAIM, CSGT, magnetic susceptibility, induced current density distributions, bicyclo[3.2.1]octa-3,6-dien-2-yl anion.