Automated Lemma Synthesis in Symbolic-Heap Separation Logic

The symbolic-heap fragment of separation logic has been actively developed and advocated for verifying the memory-safety property of computer programs. At present, one of its biggest challenges is to effectively prove entailments containing inductive heap predicates. These entailments are usually proof obligations generated when verifying programs that manipulate complex data structures like linked lists, trees, or graphs. To assist in proving such entailments, this paper introduces a lemma synthesis framework, which automatically discovers lemmas to serve as eureka steps in the proofs. Mathematical induction and template-based constraint solving are two pillars of our framework. To derive the supporting lemmas for a given entailment, the framework firstly identifies possible lemma templates from the entailment's heap structure. It then sets up unknown relations among each template's variables and conducts structural induction proof to generate constraints about these relations. Finally, it solves the constraints to find out actual definitions of the unknown relations, thus discovers the lemmas. We have integrated this framework into a prototype prover and have experimented it on various entailment benchmarks. The experimental results show that our lemma-synthesis-assisted prover can prove many entailments that could not be handled by existing techniques. This new proposal opens up more opportunities to automatically reason with complex inductive heap predicates

Problems of QCD factorization in exclusive decays of B meson to charmonium

We study the exclusive decays of $B$ meson into P-wave charmonium states $\chi_{cJ}(J=0,1)$ in the QCD factorization approach with light-cone distribution functions describing the mesons in the processes. For $B \to \chi_{c1} K$ decay, we find that there are logarithmic divergences arising from nonfactorizable spectator interactions even at twist-2 order and the decay rate is too small to accommodate the experimental data. For $B\to \chi_{c0} K$ decay, we find that aside from the logarithmic divergences arising from spectator interactions at leading-twist order, more importantly, the factorization will break down due to the infrared divergence arising from nonfactorizable vertex corrections, which is independent of the specific form of the light-cone distribution functions. Our results may indicate that QCD factorization in the present form may not be safely applied to $B$-meson exclusive decays to charmonium states.Comment: Latex, 7 pages, 1 eps figure, final version to appear in Phys.Lett.B; a few references are added, the expression of chi_c1 decay constant is give

On-demand Multipath Routing Protocols for Mobile Ad-Hoc Networks: A Comparative Survey

A Mobile Ad Hoc Network (MANET) is an infrastructure-less, self-organized and multi-hop network with a rapidly changing topology causing the wireless links to be broken at any time. Routing in such a network is challenging due to the mobility of its nodes and the challenge becomes more difficult when the network size increases. Due to the limited capacity of a multi-hop path and the high dynamics of wireless links, the single-path routing approach is unable to provide efficient high data rate transmission in MANETs. The multipath routing is the routing technique of using multiple alternative paths through a network. Furthermore, whenever a link failure is detected on a primary route, the source node can select the optimal route among multiple available routes. Therefore, the multipath routing approach is broadly utilized as one of the possible solutions to overcome the single-path limitation. Most of the multipath routing protocols are based on Ad Hoc On-Demand Distance Vector (AODV). The objective of this paper is to provide a survey and compare sets of multipath routing protocols for mobile ad-hoc networks. This survey will motivate the design of new multipath routing protocols, which overcome the weaknesses identified in this paper

Aggregation induced photodynamic therapy enhancement based on linear and nonlinear excited FRET of fluorescent organic nanoparticles

A binary molecule can self-assemble to form fluorescent organic nanoparticles (FONs) based on the Aggregation-Induced Emission Enhancement (AIEE) property and subsequently, presents an efficient fluorescence resonance energy transfer (FRET) to generate singlet oxygen under linear and nonlinear light sources. Biologically, this FON-photosensitizer is much more phototoxic to cancer cells than to normal cells without significant dark toxicity. Eventually, a new approach, called FON FRET-PDT or AIEE FRET-PDT, to promote the PDT effect is expected

Regulation of axon repulsion by MAX-1 SUMOylation and AP-3.

During neural development, growing axons express specific surface receptors in response to various environmental guidance cues. These axon guidance receptors are regulated through intracellular trafficking and degradation to enable navigating axons to reach their targets. In Caenorhabditis elegans, the UNC-5 receptor is necessary for dorsal migration of developing motor axons. We previously found that MAX-1 is required for UNC-5-mediated axon repulsion, but its mechanism of action remained unclear. Here, we demonstrate that UNC-5-mediated axon repulsion in C. elegans motor axons requires both max-1 SUMOylation and the AP-3 complex β subunit gene, apb-3 Genetic interaction studies show that max-1 is SUMOylated by gei-17/PIAS1 and acts upstream of apb-3 Biochemical analysis suggests that constitutive interaction of MAX-1 and UNC-5 receptor is weakened by MAX-1 SUMOylation and by the presence of APB-3, a competitive interactor with UNC-5. Overexpression of APB-3 reroutes the trafficking of UNC-5 receptor into the lysosome for protein degradation. In vivo fluorescence recovery after photobleaching experiments shows that MAX-1 SUMOylation and APB-3 are required for proper trafficking of UNC-5 receptor in the axon. Our results demonstrate that SUMOylation of MAX-1 plays an important role in regulating AP-3-mediated trafficking and degradation of UNC-5 receptors during axon guidance

Neural plasticity in common forms of chronic headaches

Headaches are universal experiences and among the most common disorders. While headache may be physiological in the acute setting, it can become a pathological and persistent condition.The mechanisms underlying the transition from episodic to chronic pain have been the subject of intense study. Using physiological and imaging methods, researchers have identified a number of different forms of neural plasticity associated with migraine and other headaches, including peripheral and central sensitization, and alterations in the endogenous mechanisms of pain modulation. While these changes have been proposed to contribute to headache and pain chronification, some findings are likely the results of repetitive noxious stimulation, such as atrophy of brain areas involved in pain perception and modulation. In this review, we provide a narrative overview of recent advances on the neuroimaging, electrophysiological and genetic aspects of neural plasticity associated with the most common forms of chronic headaches, including migraine, cluster headache, tension-type headache, and medication overuse headache

Fermion masses in the economical 3-3-1 model

We show that, in frameworks of the economical 3-3-1 model, all fermions get masses. At the tree level, one up-quark and two down-quarks are massless, but the one-loop corrections give all quarks the consistent masses. This conclusion is in contradiction to the previous analysis in which, the third scalar triplet has been introduced. This result is based on the key properties of the model: First, there are three quite different scales of vacuum expectation values: \om \sim {\cal O}(1) \mathrm{TeV}, v \approx 246 \mathrm{GeV} and $u \sim {\cal O}(1) \mathrm{GeV}$. Second, there exist two types of Yukawa couplings with different strengths: the lepton-number conserving couplings $h$'s and the lepton-number violating ones $s$'s satisfying the condition in which the second are much smaller than the first ones: $s \ll h$. With the acceptable set of parameters, numerical evaluation shows that in this model, masses of the exotic quarks also have different scales, namely, the $U$ exotic quark ($q_U = 2/3$) gains mass $m_U \approx 700$ GeV, while the D_\al exotic quarks (q_{D_\al} = -1/3) have masses in the TeV scale: m_{D_\al} \in 10 \div 80 TeV.Comment: 20 pages, 8 figure