Categorical notions of fibration

Fibrations over a category $B$, introduced to category theory by Grothendieck, encode pseudo-functors $B^{op} \rightsquigarrow {\bf Cat}$, while the special case of discrete fibrations encode presheaves $B^{op} \to {\bf Set}$. A two-sided discrete variation encodes functors $B^{op} \times A \to {\bf Set}$, which are also known as profunctors from $A$ to $B$. By work of Street, all of these fibration notions can be defined internally to an arbitrary 2-category or bicategory. While the two-sided discrete fibrations model profunctors internally to ${\bf Cat}$, unexpectedly, the dual two-sided codiscrete cofibrations are necessary to model $\cal V$-profunctors internally to $\cal V$-$\bf Cat$.Comment: These notes were initially written by the second-named author to accompany a talk given in the Algebraic Topology and Category Theory Proseminar in the fall of 2010 at the University of Chicago. A few years later, the now first-named author joined to expand and improve in minor ways the exposition. To appear on "Expositiones Mathematicae

t-structures are normal torsion theories

We characterize $t$-structures in stable $\infty$-categories as suitable quasicategorical factorization systems. More precisely we show that a $t$-structure $\mathfrak{t}$ on a stable $\infty$-category $\mathbf{C}$ is equivalent to a normal torsion theory $\mathbb{F}$ on $\mathbf{C}$, i.e. to a factorization system $\mathbb{F}=(\mathcal{E},\mathcal{M})$ where both classes satisfy the 3-for-2 cancellation property, and a certain compatibility with pullbacks/pushouts.Comment: Minor typographical corrections from v1; 25 pages; to appear in "Applied Categorical Structures

Multivariate Lévy Models by Linear Combination: Estimation

In this paper we propose a simple and effective two-step procedure to estimate the multivariate Lévy model introduced by Ballotta and Bonfiglioli (2012). We assess our estimation approach via simulations, comparing the results with those obtained through a standard but more computationally intensive one-step maximum likelihood estimation. The proposed method is then applied to the computation of the intra-horizon Value at Risk for a portfolio of assets following the model under consideration

Human Cytomegalovirus Inhibitor AL18 Also Possesses Activity against Influenza A and B Viruses

AL18, an inhibitor of human cytomegalovirus DNA polymerase, was serendipitously found to also block the interaction between the PB1 and PA polymerase subunits of influenza A virus. Furthermore, AL18 effectively inhibited influenza A virus polymerase activity and the overall replication of influenza A and B viruses. A molecular model to explain the binding of AL18 to both cytomegalovirus and influenza targets is proposed. Thus, AL18 represents an interesting lead for the development of new antivirals

Binding Parameters and Thermodynamics of the Interaction of the Human Cytomegalovirus DNA Polymerase Accessory Protein, UL44, with DNA: Implications for the Processivity Mechanism

The mechanisms of processivity factors of herpesvirus DNA polymerases remain poorly understood. The proposed processivity factor for human cytomegalovirus DNA polymerase is a DNA-binding protein, UL44. Previous findings, including the crystal structure of UL44, have led to the hypothesis that UL44 binds DNA as a dimer via lysine residues. To understand how UL44 interacts with DNA, we used filter-binding and electrophoretic mobility shift assays and isothermal titration calorimetry (ITC) analysis of binding to oligonucleotides. UL44 bound directly to double-stranded DNA as short as 12 bp, with apparent dissociation constants in the nanomolar range for DNAs > 18 bp, suggesting a minimum DNA length for UL44 interaction. UL44 also bound single-stranded DNA, albeit with lower affinity, and for either single- or double-stranded DNA, there was no apparent sequence specificity. ITC analysis revealed that UL44 binds to duplex DNA as a dimer. Binding was endothermic, indicating an entropically driven process, likely due to release of bound ions. Consistent with this hypothesis, analysis of the relationship between binding and ionic strength indicated that, on average, $4 \pm 1$ monovalent ions are released in the interaction of each monomer of UL44 with DNA. The results taken together reveal interesting implications for how UL44 may mediate processivity