Properties of dyons in N=4{\cal N}=4 theories at small charges

We study three properties of $1/4$ BPS dyons at small charges in string compactifications which preserve ${\cal N}=4$ supersymmetry. We evaluate the non-trivial constant present in the one loop statistical entropy for ${\cal N}=4$ compactifications of type IIB theory on $K3\times T^2$ orbifolded by an order $\mathbb{Z}_N$ freely acting orbifold $g'$ including all CHL compactifications. This constant is trivial for the un-orbifolded model but we show that it contributes crucially to the entropy of low charge dyons in all the orbifold models. We then show that the meromorphic Jacobi form which captures the degeneracy of $1/4$ BPS states for the first two non-trivial magnetic charges can be decomposed into an Appell-Lerch sum and a mock Jacobi form transforming under $\Gamma_0(N)$. This generalizes the earlier observation of Dabholkar-Murthy-Zagier to the orbifold models. Finally we study the sign of the Fourier coefficients of the inverse Siegel modular form which counts the index of $1/4$ BPS dyons in ${\cal N}=4$ models obtained by freely acting $\mathbb{Z}_2$ and $\mathbb{Z}_3$ orbifolds of type II theory compactified on $T^6$. We show that sign of the index for sufficiently low charges and ensuring that it counts single centered black holes, violates the positivity conjecture of Sen which indicates that these states posses non-trivial hair

Gravitational couplings in N=2{\cal N}=2 string compactifications and Mathieu Moonshine

We evaluate the low energy gravitational couplings, $F_g$ in the heterotic $E_8\times E_8$ string theory compactified on orbifolds of $K3\times T^2$ by $g'$ which acts as a $\mathbb{Z}_N$ automorphisim on $K3$ together with a $1/N$ shift along $T^2$. The orbifold $g'$ corresponds to the conjugacy classes of the Mathieu group $M_{24}$. The holomorphic piece of $F_g$ is given in terms of a polylogarithim with index $3-2g$ and predicts the Gopakumar-Vafa invariants in the corresponding dual type II Calabi-Yau compactifications. We show that low lying Gopakumar-Vafa invariants for each of these compactifications including the twisted sectors are integers. We observe that the conifold singularity for all these compactifications occurs only when states in the twisted sectors become massless and the strength of the singularity is determined by the genus zero Gopakumar-Vafa invariant at this point in the moduli space.Comment: 54 pages, Mathematica code included in the source file, minor typos fixed, one reference adde

Dyon degeneracies from Mathieu moonshine

We construct the Siegel modular forms associated with the theta lift of twisted elliptic genera of $K3$ orbifolded with $g'$ corresponding to the conjugacy classes of the Mathieu group $M_{24}$. We complete the construction for all the classes which belong to $M_{23} \subset M_{24}$ and two other classes outside the subgroup $M_{23}$. For this purpose we provide the explicit expressions for all the twisted elliptic genera in all the sectors of these classes. We show that the Siegel modular forms satisfy the required properties for them to be generating functions of $1/4$ BPS dyons of type II string theories compactified on $K3\times T^2$ and orbifolded by $g'$ which acts as a $\mathbb{Z}_N$ automorphism on $K3$ together with a $1/N$ shift on a circle of $T^2$. In particular the inverse of these Siegel modular forms admit a Fourier expansion with integer coefficients together with the right sign as predicted from black hole physics. Our analysis completes the construction of the partition function for dyons as well as the twisted elliptic genera for all the $7$ CHL compactifications.Comment: Section on comparison with earlier literature added, References adde

Spectrophotometric Determination of Dissociation Constants of 3-Mercuri-5-sulphosalicylic Acid & Stability Constant of Its Fe(III) Complex

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A Dynamic Model of Interactions of Ca^(2+), Calmodulin, and Catalytic Subunits of Ca^(2+)/Calmodulin-Dependent Protein Kinase II

During the acquisition of memories, influx of Ca^(2+) into the postsynaptic spine through the pores of activated N-methyl-D-aspartate-type glutamate receptors triggers processes that change the strength of excitatory synapses. The pattern of Ca^(2+) influx during the first few seconds of activity is interpreted within the Ca^(2+)-dependent signaling network such that synaptic strength is eventually either potentiated or depressed. Many of the critical signaling enzymes that control synaptic plasticity, including Ca^(2+)/calmodulin-dependent protein kinase II (CaMKII), are regulated by calmodulin, a small protein that can bind up to 4 Ca^(2+) ions. As a first step toward clarifying how the Ca^(2+)-signaling network decides between potentiation or depression, we have created a kinetic model of the interactions of Ca^(2+), calmodulin, and CaMKII that represents our best understanding of the dynamics of these interactions under conditions that resemble those in a postsynaptic spine. We constrained parameters of the model from data in the literature, or from our own measurements, and then predicted time courses of activation and autophosphorylation of CaMKII under a variety of conditions. Simulations showed that species of calmodulin with fewer than four bound Ca^(2+) play a significant role in activation of CaMKII in the physiological regime, supporting the notion that processing ofCa^(2+) signals in a spine involves competition among target enzymes for binding to unsaturated species of CaM in an environment in which the concentration of Ca^(2+) is fluctuating rapidly. Indeed, we showed that dependence of activation on the frequency of Ca^(2+) transients arises from the kinetics of interaction of fluctuating Ca^(2+) with calmodulin/CaMKII complexes. We used parameter sensitivity analysis to identify which parameters will be most beneficial to measure more carefully to improve the accuracy of predictions. This model provides a quantitative base from which to build more complex dynamic models of postsynaptic signal transduction during learning

Dynamic Remodeling of Dendritic Arbors in GABAergic Interneurons of Adult Visual Cortex

Despite decades of evidence for functional plasticity in the adult brain, the role of structural plasticity in its manifestation remains unclear. To examine the extent of neuronal remodeling that occurs in the brain on a day-to-day basis, we used a multiphoton-based microscopy system for chronic in vivo imaging and reconstruction of entire neurons in the superficial layers of the rodent cerebral cortex. Here we show the first unambiguous evidence (to our knowledge) of dendrite growth and remodeling in adult neurons. Over a period of months, neurons could be seen extending and retracting existing branches, and in rare cases adding new branch tips. Neurons exhibiting dynamic arbor rearrangements were GABA-positive non-pyramidal interneurons, while pyramidal cells remained stable. These results are consistent with the idea that dendritic structural remodeling is a substrate for adult plasticity and they suggest that circuit rearrangement in the adult cortex is restricted by cell type–specific rules

Oxytocin Signaling in Mouse Taste Buds

The neuropeptide, oxytocin (OXT), acts on brain circuits to inhibit food intake. Mutant mice lacking OXT (OXT knockout) overconsume salty and sweet (i.e. sucrose, saccharin) solutions. We asked if OXT might also act on taste buds via its receptor, OXTR.Using RT-PCR, we detected the expression of OXTR in taste buds throughout the oral cavity, but not in adjacent non-taste lingual epithelium. By immunostaining tissues from OXTR-YFP knock-in mice, we found that OXTR is expressed in a subset of Glial-like (Type I) taste cells, and also in cells on the periphery of taste buds. Single-cell RT-PCR confirmed this cell-type assignment. Using Ca2+ imaging, we observed that physiologically appropriate concentrations of OXT evoked [Ca2+]i mobilization in a subset of taste cells (EC50 approximately 33 nM). OXT-evoked responses were significantly inhibited by the OXTR antagonist, L-371,257. Isolated OXT-responsive taste cells were neither Receptor (Type II) nor Presynaptic (Type III) cells, consistent with our immunofluorescence observations. We also investigated the source of OXT peptide that may act on taste cells. Both RT-PCR and immunostaining suggest that the OXT peptide is not produced in taste buds or in their associated nerves. Finally, we also examined the morphology of taste buds from mice that lack OXTR. Taste buds and their constituent cell types appeared very similar in mice with two, one or no copies of the OXTR gene.We conclude that OXT elicits Ca2+ signals via OXTR in murine taste buds. OXT-responsive cells are most likely a subset of Glial-like (Type I) taste cells. OXT itself is not produced locally in taste tissue and is likely delivered through the circulation. Loss of OXTR does not grossly alter the morphology of any of the cell types contained in taste buds. Instead, we speculate that OXT-responsive Glial-like (Type I) taste bud cells modulate taste signaling and afferent sensory output. Such modulation would complement central pathways of appetite regulation that employ circulating homeostatic and satiety signals

A Missense Mutation in a Highly Conserved Alternate Exon of Dynamin-1 Causes Epilepsy in Fitful Mice

Dynamin-1 (Dnm1) encodes a large multimeric GTPase necessary for activity-dependent membrane recycling in neurons, including synaptic vesicle endocytosis. Mice heterozygous for a novel spontaneous Dnm1 mutation—fitful—experience recurrent seizures, and homozygotes have more debilitating, often lethal seizures in addition to severe ataxia and neurosensory deficits. Fitful is a missense mutation in an exon that defines the DNM1a isoform, leaving intact the alternatively spliced exon that encodes DNM1b. The expression of the corresponding alternate transcripts is developmentally regulated, with DNM1b expression highest during early neuronal development and DNM1a expression increasing postnatally with synaptic maturation. Mutant DNM1a does not efficiently self-assemble into higher order complexes known to be necessary for proper dynamin function, and it also interferes with endocytic recycling in cell culture. In mice, the mutation results in defective synaptic transmission characterized by a slower recovery from depression after trains of stimulation. The DNM1a and DNM1b isoform pair is highly conserved in vertebrate evolution, whereas invertebrates have only one isoform. We speculate that the emergence of more specialized forms of DNM1 may be important in organisms with complex neuronal function