Formal Computations and Methods

We present formal verification methods and procedures for finding bounds of linear programs and proving nonlinear inequalities. An efficient implementation of formal arithmetic computations is also described. Our work is an integral part of the Flyspeck project (a formal proof of the Kepler conjecture) and we show how developed formal procedures solve formal computational problems in this project. We also introduce our implementation of SSReflect language (originally developed by G. Gonthier in Coq) in HOL Light

A New Species of the Genus Parasa Moore (Lepidoptera: Limacodidae) from Yemen

A new species Parasa dusii Solovyev and Saldaitis from northern Yemen is described (holotype in Museum Witt, Munich; Germany). The species has tendency to lose the green pigment typical for other congeners. It is provisionally placed into the genus Parasa Moore, 1859 where it is closely related to P. divisa West, 1940, P. catori Bethune-Baker, 1911, P. marginata West, 1940, P. thamia Rungs, 1951, P. dentina Hering, 1932, P. ananii Karsch, 1896, and P. semiochracea Hering, 1933. The relationship of the new species to these African species suggests its secondary penetration into the Arabian Peninsula from an origin in tropical Africa. The problems of monophyly of the genus Parasa and several associated genera are briefly discussed. All important characters of the new species, and some related species, are illustrated

A Dynamic View of Trauma/Hemorrhage-Induced Inflammation in Mice: Principal Drivers and Networks

Background: Complex biological processes such as acute inflammation induced by trauma/hemorrhagic shock/ (T/HS) are dynamic and multi-dimensional. We utilized multiplexing cytokine analysis coupled with data-driven modeling to gain a systems perspective into T/HS. Methodology/Principal Findings: Mice were subjected to surgical cannulation trauma (ST) ± hemorrhagic shock (HS; 25 mmHg), and followed for 1, 2, 3, or 4 h in each case. Serum was assayed for 20 cytokines and NO2-/NO3-. These data were analyzed using four data-driven methods (Hierarchical Clustering Analysis [HCA], multivariate analysis [MA], Principal Component Analysis [PCA], and Dynamic Network Analysis [DyNA]). Using HCA, animals subjected to ST vs. ST + HS could be partially segregated based on inflammatory mediator profiles, despite a large overlap. Based on MA, interleukin [IL]-12p40/p70 (IL-12.total), monokine induced by interferon-γ (CXCL-9) [MIG], and IP-10 were the best discriminators between ST and ST/HS. PCA suggested that the inflammatory mediators found in the three main principal components in animals subjected to ST were IL-6, IL-10, and IL-13, while the three principal components in ST + HS included a large number of cytokines including IL-6, IL-10, keratinocyte-derived cytokine (CXCL-1) [KC], and tumor necrosis factor-α [TNF-α]. DyNA suggested that the circulating mediators produced in response to ST were characterized by a high degree of interconnection/complexity at all time points; the response to ST + HS consisted of different central nodes, and exhibited zero network density over the first 2 h with lesser connectivity vs. ST at all time points. DyNA also helped link the conclusions from MA and PCA, in that central nodes consisting of IP-10 and IL-12 were seen in ST, while MIG and IL-6 were central nodes in ST + HS. Conclusions/Significance: These studies help elucidate the dynamics of T/HS-induced inflammation, complementing other forms of dynamic mechanistic modeling. These methods should be applicable to the analysis of other complex biological processes

Hybrid Equation/Agent-Based Model of Ischemia-Induced Hyperemia and Pressure Ulcer Formation Predicts Greater Propensity to Ulcerate in Subjects with Spinal Cord Injury

Pressure ulcers are costly and life-threatening complications for people with spinal cord injury (SCI). People with SCI also exhibit differential blood flow properties in non-ulcerated skin. We hypothesized that a computer simulation of the pressure ulcer formation process, informed by data regarding skin blood flow and reactive hyperemia in response to pressure, could provide insights into the pathogenesis and effective treatment of post-SCI pressure ulcers. Agent-Based Models (ABM) are useful in settings such as pressure ulcers, in which spatial realism is important. Ordinary Differential Equation-based (ODE) models are useful when modeling physiological phenomena such as reactive hyperemia. Accordingly, we constructed a hybrid model that combines ODEs related to blood flow along with an ABM of skin injury, inflammation, and ulcer formation. The relationship between pressure and the course of ulcer formation, as well as several other important characteristic patterns of pressure ulcer formation, was demonstrated in this model. The ODE portion of this model was calibrated to data related to blood flow following experimental pressure responses in non-injured human subjects or to data from people with SCI. This model predicted a higher propensity to form ulcers in response to pressure in people with SCI vs. non-injured control subjects, and thus may serve as novel diagnostic platform for post-SCI ulcer formation. © 2013 Solovyev et al

A formal proof of the Kepler conjecture

This article describes a formal proof of the Kepler conjecture on dense sphere packings in a combination of the HOL Light and Isabelle proof assistants. This paper constitutes the official published account of the now completed Flyspeck project

Lassie: HOL4 Tactics by Example

Proof engineering efforts using interactive theorem proving have yielded several impressive projects in software systems and mathematics. A key obstacle to such efforts is the requirement that the domain expert is also an expert in the low-level details in constructing the proof in a theorem prover. In particular, the user needs to select a sequence of tactics that lead to a successful proof, a task that in general requires knowledge of the exact names and use of a large set of tactics. We present Lassie, a tactic framework for the HOL4 theorem prover that allows individual users to define their own tactic language by example and give frequently used tactics or tactic combinations easier-to-remember names. The core of Lassie is an extensible semantic parser, which allows the user to interactively extend the tactic language through a process of definitional generalization. Defining tactics in Lassie thus does not require any knowledge in implementing custom tactics, while proofs written in Lassie retain the correctness guarantees provided by the HOL4 system. We show through case studies how Lassie can be used in small and larger proofs by novice and more experienced interactive theorem prover users, and how we envision it to ease the learning curve in a HOL4 tutorial

Search for dark matter produced in association with bottom or top quarks in √s = 13 TeV pp collisions with the ATLAS detector

A search for weakly interacting massive particle dark matter produced in association with bottom or top quarks is presented. Final states containing third-generation quarks and miss- ing transverse momentum are considered. The analysis uses 36.1 fb−1 of proton–proton collision data recorded by the ATLAS experiment at √s = 13 TeV in 2015 and 2016. No significant excess of events above the estimated backgrounds is observed. The results are in- terpreted in the framework of simplified models of spin-0 dark-matter mediators. For colour- neutral spin-0 mediators produced in association with top quarks and decaying into a pair of dark-matter particles, mediator masses below 50 GeV are excluded assuming a dark-matter candidate mass of 1 GeV and unitary couplings. For scalar and pseudoscalar mediators produced in association with bottom quarks, the search sets limits on the production cross- section of 300 times the predicted rate for mediators with masses between 10 and 50 GeV and assuming a dark-matter mass of 1 GeV and unitary coupling. Constraints on colour- charged scalar simplified models are also presented. Assuming a dark-matter particle mass of 35 GeV, mediator particles with mass below 1.1 TeV are excluded for couplings yielding a dark-matter relic density consistent with measurements