Three Families of Lie Algebras of Exponential Growth from Vertex Operator Algebras

We study three families of infinite-dimensional Lie algebras defined from Vertex Operator Algebras and their properties. For $N=0$ VOAs, we review the construction of the Fock space $V_L$ from an even lattice $L$ and provide an algebraic description of the Lie algebra $g_{II_{25,1}}$ from the perspective of $24$ different Niemeier lattices $N$ via the decomposition $II_{25,1} = N \oplus II_{1,1}$ using the no-ghost theorem. For $N=1$ SVOAs we review the construction of the Fock space $V_{NS}$ and provide an explicit basis for the spectrum-generating algebra of the Lie algebra $g_{NS}$. For $N=2$ SVOAs, we describe the structure of $g^{(2)}_{NS}$ explicitly as a $\mathbb{Q}$-graded Lie algebra and we lift a left and right $SL(2,\mathbb{Z})$ action on $II_{2,2}$ to $g^{(2)}_{NS}$.Comment: PhD dissertation, 2021, 152 page

Availability and affordability of treatment for Human African Trypanosomiasis.

Human African Trypanosomiasis (HAT) is a re-emerging disease whose usual treatments are becoming less efficient because of the increasing parasite resistance. Availability of HAT drugs is poor and their production in danger because of technical, ecological and economic constraints. In view of this dramatic situation, a network involving experts from NGOs, WHO and pharmaceutical producers was commissioned with updating estimates of need for each HAT drug for the coming years; negotiations with potential producers of new drugs such as eflornithine; securing sustainable manufacturing of existing drugs; clinical research into new combinations of these drugs for first and second-line treatments; centralizing drug purchases and their distribution through a unique non-profit entity; and addressing regulatory and legal issues concerning new drugs

Caractérisation des sous-unités principales et auxiliaires des canaux sodium dépendant du potentiel exprimées dans le système nerveux central de l'insecte Periplaneta americana (Thèse de Doctorat d'Université)

In insects, only one gene encodes the α pore-forming subunit of voltage-gated sodium channel (Nav). In addition, four to five genes encode the β auxiliary subunits. Although the American cockroach, Periplaneta americana, is a model in insect neurophysiology, few data describe the molecular structures at the base of the Nav. The aim of our study was to characterize the subunits expressed in the nerve cord (NC), the terminal abdominal ganglion (TAG) and DUM neurons of this particular species. First, we showed that the molecular diversity of the α subunit is generated by alternative splicing in NC and TAG. The main alternative exons identified in the cloned cDNA are A (loop L1), EFGHG1129 (loop L2) and G1 (IIIS3-S4). Despite of the molecular diversity, only one 6153-bp cDNA encoding PaNav1 has been identified. This isoform is characterized by the alternative exons (J, A; E; F; G1129, H and G1) highly expressed in the NC and TAG. On the opposite, only one type of cDNA has been identified in DUM neurons. Altogether, these results show that molecular diversity is lower at the cellular level. Moreover, a bioinformatic analysis showed the optional exons I and F are the most divergent currently known exons between insect orders. In addition, we discovered two full-length cDNAs encoding atypical α subunits named PaFPC1 and PaFPC2. They contain 1553 amino acid residues and differ from each other by eight punctual mutations. They share 59% protein identity with PaNav1. The absence of the inactivation particle MFMT suggests that these novel subunits mediate original electrophysiological properties. However, a detailed phylogenetic analysis puts forward that PaFPC is a novel member of the insect Nav channels. Hence; this discovery shows for the first time the existence of an ancestral duplication event of the Nav gene in insects. Finally, we cloned two cDNA populations encoding auxiliary subunits named PaTEH1.1 and PaTEH1.2. A phylogenetic analysis clarifies the relationships between the different families of insect auxiliary subunit. Moreover, a preliminary electrophysiological study showed that PaTEH1.1 increased significatively the expression of the pore-forming subunit of insect Nav in Xenopus oocytes. In conclusion, our results constitute new insights in insect ion channels field. In addition, they open new research perspectives for understanding the molecular basis of the membrane excitability in insects

How does calcium-dependent intracellular regulation of voltage-dependent sodium current increase the sensitivity to the oxadiazine insecticide indoxacarb metabolite decarbomethoxylated JW062 (DCJW) in insect pacemaker neurons

Decarbomethoxylated JW062 (DCJW), the active component of the oxadiazine insecticide (S)-methyl 7-chloro-2,5-dihydro-2-[[(methoxycarbonyl)[4-(trifluoromethoxy)phenyl] amino]carbonyl] indeno[1,2-e][1,3,4]oxadiazine-4a(3H)-carboxylate (DPX-JW062) (indoxacarb), was tested on 2 inward voltage-dependent sodium currents (named INa1 and INa2) expressed in short-term cultured dorsal unpaired median neurons of the cockroach Periplaneta americana. Under whole-cell voltage-clamp conditions, application of DCJW resulted in a biphasic dose-dependent inhibition of the global sodium current amplitude illustrating the differing sensitivity of sodium channels to DCJW. INa2 was less sensitive to DCJW [half-maximal inhibitory concentration (IC(50)) = 1.6 microM] compared with INa1 (IC(50) = 1.7 nM). Although a previous study demonstrated that INa1 was regulated by the cAMP/protein kinase A cascade, we showed that INa2 was mainly regulated in an opposite way by the activation of calcium-calmodulin-dependent protein phosphatase 2B (PP2B) and calcium-calmodulin-dependent protein kinase II (CaM-kinase II). Furthermore, we demonstrated that activation of CaM-kinase II by intracellular calcium via the calcium-calmodulin complex affected the sensitivity of INa2 channels to DCJW. By increasing the intracellular calcium concentration and/or using 1,2-bis(o-aminophenoxy)ethane-N,N,N\u27,N\u27-tetraacetic acid (BAPTA) (a calcium chelator), N-(6-aminohexyl)-5-chloro-1-naphthalenesulfonamide hydrochloride (W7) (a calmodulin inhibitor), cyclosporine A (a PP2B inhibitor), and 1-[N,O-bis(5-isoquinolinesulfonyl)-N-methyl-L-tyrosyl]-4-phenylpiperazine (KN-62) (a CaM-kinase II inhibitor), we revealed that activation of CaM-kinase II was involved in the modulation of the voltage dependence of steady-state inactivation and that the CaM-kinase II pathway activated by elevation of the intracellular calcium concentration might render INa2 channels approximately 3000-fold more sensitive to DCJW. These results indicated that manipulating specific intracellular signaling pathways involved in the regulation of sodium channels might have fundamental consequences for the sensitivity of insects to insecticides. This finding reveals an exciting research area that could lead to improvement in the efficiency of insecticides

Call centers with a postponed callback offer

We study a call center model with a postponed callback option. A customer at the head of the queue whose elapsed waiting time achieves a given threshold receives a voice message mentioning the option to be called back later. This callback option differs from the traditional ones found in the literature where the callback offer is given at customer’s arrival. We approximate this system by a two-dimensional Markov chain, with one dimension being a unit of a discretization of the waiting time. We next show that this approximation model converges to the exact one. This allows us to obtain explicitly the performance measures without abandonment and to compute them numerically otherwise. From the performance analysis, we derive a series of practical insights and recommendations for a clever use of the callback offer. In particular, we show that this time-based offer outperforms traditional ones when considering the waiting time of inbound calls