Accountability and Intervening Agency: An Asymmetry between Upstream and Downstream Actors

Suppose someone (P1) does something that is wrongful only in virtue of the risk that it will enable another person (P2) to commit a wrongdoing. Suppose further that P1’s conduct does indeed turn out to enable P2’s wrongdoing. The resulting wrong is agentially mediated: P1 is an enabling agent and P2 is an intervening agent. Whereas the literature on intervening agency focuses on whether P2’s status as an intervening agent makes P1’s conduct less bad, I turn this issue on its head by investigating whether P1’s status as an enabling agent makes P2’s conduct more bad. I argue that it does: P2 wrongs not just the victims of ϕ but P1 as well, by acting in a way that wrongfully makes P1 accountable for ϕ. This has serious implications for compensatory and defensive liability in cases of agentially mediated wrongs

Higgs algebra of curves and loop crystals

We define the Higgs algebra $\mathcal{H}_\P1$ of the projective line, as a convolution algebra of constructible functions on the global nilpotent cone $\underline{\Lambda}_\P1$, a lagrangian substack of the Higgs bundle T^*\Coh_\P1, where \Coh_\P1 is the stack of coherent sheaves on $\P1$. We prove that $\mathcal{H}_\P1$ is isomorphic to (some completion of) $U^+(\hat{sl}_2)$. We use this geometric realization to define a semicanonical basis of $U^+(\hat{sl}_2)$, indexed by irreducible components of $\underline{\Lambda}_\P1$. We also construct a combinatorial data on this set of irreducible components in the spirit of \cite{KS}, which is an affine analog of a crystal. We call it a loop crystal and give some of its properties

On the restriction of the Fourier transform to polynomial curves

We prove a Fourier restriction theorem on curves parametrised by the mapping P(t) = (P1(t),..., Pn(t)), where each of the P1,..., Pn is a real-valued polynomial and t belongs to an interval on which each of the P1,..., Pn "resembles" a monomial

Singular normal form for the Painlev\'e equation P1

We show that there exists a rational change of coordinates of Painlev\'e's P1 equation $y''=6y^2+x$ and of the elliptic equation $y''=6y^2$ after which these two equations become analytically equivalent in a region in the complex phase space where $y$ and $y'$ are unbounded. The region of equivalence comprises all singularities of solutions of P1 (i.e. outside the region of equivalence, solutions are analytic). The Painlev\'e property of P1 (that the only movable singularities are poles) follows as a corollary. Conversely, we argue that the Painlev\'e property is crucial in reducing P1, in a singular regime, to an equation integrable by quadratures

Selective Activation of Alternative MYC Core Promoters by Wnt-Responsive Enhancers.

In Metazoans, transcription of most genes is driven by the use of multiple alternative promoters. Although the precise regulation of alternative promoters is important for proper gene expression, the mechanisms that mediates their differential utilization remains unclear. Here, we investigate how the two alternative promoters (P1, P2) that drive MYC expression are regulated. We find that P1 and P2 can be differentially regulated across cell-types and that their selective usage is largely mediated by distal regulatory sequences. Moreover, we show that in colon carcinoma cells, Wnt-responsive enhancers preferentially upregulate transcription from the P1 promoter using reporter assays and in the context of the endogenous Wnt induction. In addition, multiple enhancer deletions using CRISPR/Cas9 corroborate the regulatory specificity of P1. Finally, we show that preferential activation between Wnt-responsive enhancers and the P1 promoter is influenced by the distinct core promoter elements that are present in the MYC promoters. Taken together, our results provide new insight into how enhancers can specifically target alternative promoters and suggest that formation of these selective interactions could allow more precise combinatorial regulation of transcription initiation

Sum of squared logarithms - An inequality relating positive definite matrices and their matrix logarithm

Let y1, y2, y3, a1, a2, a3 > 0 be such that y1 y2 y3 = a1 a2 a3 and y1 + y2 + y3 >= a1 + a2 + a3, y1 y2 + y2 y3 + y1 y3 >= a1 a2 + a2 a3 + a1 a3. Then the following inequality holds (log y1)^2 + (log y2)^2 + (log y3)^2 >= (log a1)^2 + (log a2)^2 + (log a3)^2. This can also be stated in terms of real positive definite 3x3-matrices P1, P2: If their determinants are equal det P1 = det P2, then tr P1 >= tr P2 and tr Cof P1 >= tr Cof P2 implies norm(log P1) >= norm(log P2), where log is the principal matrix logarithm and norm(P) denotes the Frobenius matrix norm. Applications in matrix analysis and nonlinear elasticity are indicated

Fragmentation at the Earliest Phase of Massive Star Formation

We present 1.3mm continuum and spectral line images of two massive molecular clumps P1 and P2 in the G28.34+0.06 region with the Submillimeter Array. While the two clumps contain masses of 1000 and 880 \msun, respectively, P1 has a luminosity $< 10^2$ \lsun, and a lower gas temperature and smaller line width than P2. Thus, P1 appears to be at a much earlier stage of massive star formation than P2. The high resolution SMA observations reveal two distinctive cores in P2 with masses of 97 and 49 \msun, respectively. The 4 GHz spectral bandpass captures line emission from CO isotopologues, SO, CH$_3$OH, and CH$_3$CN, similar to hot molecular cores harboring massive young stars. The P1 clump, on the other hand, is resolved into five cores along the filament with masses from 22 to 64 \msun and an average projected separation of 0.19 pc. Except $^{12}$CO, no molecular line emission is detected toward the P1 cores at a 1$\sigma$ rms of 0.1 K. Since strong $^{12}$CO and C$^{18}$O emissions are seen with the single dish telescope at a resolution of 11$''$, the non-detection of these lines with the SMA indicates a depletion factor upto $10^3$. While the spatial resolution of the SMA is better than the expected Jeans length, the masses in P1 cores are much larger than the thermal Jeans mass, indicating the importance of turbulence and/or magnetic fields in cloud fragmentation. The hierarchical structures in the P1 region provide a glimpse of the initial phase of massive star and cluster formation.Comment: 17 pages, 4 figures. Accepted for publication in Ap

Milk Chemical Composition of Dairy Cows Fed Rations Containing Protected Omega-3 Fatty Acids and Fermented Rice Bran

The research was conducted to investigate the effect of ration containing protected omega-3 and fermented rice bran on chemical composition of dairy milk. The research employed 10 female PFH dairy cows of 2-4 years old with body weight 300-375 kg. The research was assigned in randomized complete block design. The treatment consisted of P0= control ration, P1= P0 + 20% fermented rice bran, P2= P1 + 4% soya bean oil, P3= P1 + 4% protected tuna fish oil and P4= P1 + 4% protected lemuru fish oil. The results showed that the effects of fish oil supplementation in the rations significantly (P&lt;0.01) decreased feed consumption, cholesterol, low density lipoprotein, lipids, and saturated fatty acids. Meanwhile, it increased milk production, content of high density lipoprotein, omega-3, omega-6 and unsaturated fatty acids in the dairy cows milk. It is concluded that the inclusion of 4% protected fish oil in the rations can produce healthy milk by decreasing milk cholesterol and increasing omega-3 fatty acids content