Using linear algebra in decomposition of Farkas interpolants

The use of propositional logic and systems of linear inequalities over reals is a common means to model software for formal verification. Craig interpolants constitute a central building block in this setting for over-approximating reachable states, e.g. as candidates for inductive loop invariants. Interpolants for a linear system can be efficiently computed from a Simplex refutation by applying the Farkas’ lemma. However, these interpolants do not always suit the verification task—in the worst case, they can even prevent the verification algorithm from converging. This work introduces the decomposed interpolants, a fundamental extension of the Farkas interpolants, obtained by identifying and separating independent components from the interpolant structure, using methods from linear algebra. We also present an efficient polynomial algorithm to compute decomposed interpolants and analyse its properties. We experimentally show that the use of decomposed interpolants in model checking results in immediate convergence on instances where state-of-the-art approaches diverge. Moreover, since being based on the efficient Simplex method, the approach is very competitive in general.

     

A Logic for Reasoning About Knowledge of Unawareness

In the most popular logics combining knowledge and awareness, it is not possible to express statements about knowledge of unawareness such as “Ann knows that Bill is aware of something Ann is not aware of”—without using a stronger statement such as “Ann knows that Bill is aware of \(p\) and Ann is not aware of \(p\) ”, for some particular \(p\) . In Halpern and Rêgo (Proceedings of KR 2006; Games Econ Behav 67(2):503–525, 2009b) Halpern and Rêgo introduced a logic in which such statements about knowledge of unawareness can be expressed. The logic extends the traditional framework with quantification over formulae, and is thus very expressive. As a consequence, it is not decidable. In this paper we introduce a decidable logic which can be used to reason about certain types of unawareness. Our logic extends the traditional framework with an operator expressing full awareness, i.e., the fact that an agent is aware of everything, and another operator expressing relative awareness, the fact that one agent is aware of everything another agent is aware of. The logic is less expressive than Halpern’s and Rêgo’s logic. It is, however, expressive enough to express all of the motivating examples in Halpern and Rêgo (Proceedings of KR 2006; Games Econ Behav 67(2):503–525, 2009b). In addition to proving that the logic is decidable and that its satisfiability problem is PSPACE-complete, we present an axiomatisation which we show is sound and complete.     

Polymeric prodrugs containing neridronate and ferrocene: Synthesis,characterization, and antimalarial activity

Polyamidoamine prodrugs containing ferrocene derivatives and neridronate were successfully synthesized and characterized by NMR, FTIR, SEM, and EDX analyses. Appearance of characteristic peaks in ¹H and ³¹P NMR or EDX spectra were used to confirm the presence of neridronate or ferrocene in the conjugates and co-conjugates. In vitro evaluation of the new materials revealed improved antimalarial activity, especially for conjugate 5 and corresponding co-conjugate 8, when compared with chloroquine and quinine. Hemolysis studies revealed that synthesized prodrugs had no effect on the integrity of the host red blood cell membrane; a direct effect on the intra-erythrocytic parasite was, however, noted.     

Nanoformulation of Brain‐Derived Neurotrophic Factor with Target Receptor‐Triggered‐Release in the Central Nervous System

Brain‐derived neurotrophic factor (BDNF) is identified as a potent neuroprotective and neuroregenerative agent for many neurological diseases. Regrettably, its delivery to the brain is hampered by poor serum stability and rapid brain clearance. Here, a novel nanoformulation is reported composed of a biocompatible polymer, poly(ethylene glycol)‐b‐poly(l ‐glutamic acid) (PEG‐PLE), that hosts the BDNF molecule in a nanoscale complex, termed here Nano‐BDNF. Upon simple mixture, Nano‐BDNF spontaneously forms uniform spherical particles with a core–shell structure. Molecular dynamics simulations suggest that binding between BDNF and PEG‐PLE is mediated through electrostatic coupling as well as transient hydrogen bonding. The formation of Nano‐BDNF complex stabilizes BDNF and protects it from nonspecific binding with common proteins in the body fluid, while allowing it to associate with its receptors. Following intranasal administration, the nanoformulation improves BDNF delivery throughout the brain and displays a more preferable regional distribution pattern than the native protein. Furthermore, intranasally delivered Nano‐BDNF results in superior neuroprotective effects in the mouse brain with lipopolysaccharides‐induced inflammation, indicating promise for further evaluation of this agent for the therapy of neurologic diseases.