Distribution of Caustic-Crossing Intervals for Galactic Binary-Lens Microlensing Events

Detection of caustic crossings of binary-lens gravitational microlensing events is important because by detecting them one can obtain useful information both about the lens and source star. In this paper, we compute the distribution of the intervals between two successive caustic crossings, $f(t_{\rm cc})$, for Galactic bulge binary-lens events to investigate the observational strategy for the optimal detection and resolution of caustic crossings. From this computation, we find that the distribution is highly skewed toward short $t_{\rm cc}$ and peaks at $t_{\rm cc}\sim 1.5$ days. For the maximal detection of caustic crossings, therefore, prompt initiation of followup observations for intensive monitoring of events will be important. We estimate that under the strategy of the current followup observations with a second caustic-crossing preparation time of $\sim 2$ days, the fraction of events with resolvable caustic crossing is $\sim 80$. We find that if the followup observations can be initiated within 1 day after the first caustic crossing by adopting more aggressive observational strategies, the detection rate can be improved into $\sim 90$.Comment: total 6 pages, including 5 Figures and no Table, submitted to MNRA

\u3cem\u3eTherasense\u3c/em\u3e Nonsense

In Therasense v. Becton, Dickinson & Co., a sharply divided en banc Court of Appeals for the Federal Circuit pronounced a new standard for inequitable conduct. Despite the reasons set forth by the concurring and dissenting judges, the majority elevated the requirements for inequitable conduct. Specifically, the Therasense majority required two elements to be shown: (1) specific intent to deceive; and (2) but-for materiality. Specific intent is established if one can show proof of: (a) knowledge of the information; (b) knowledge of the materiality of the information; and (c) deliberate decision to withhold the information from the United States Patent and Trademark Office ( USPTO or PTO ). But-for materiality requires one to show that the patent would not have issued but-for the withheld information. This article analyzes the Therasense majority\u27s heightened requirement for inequitable conduct and shows why the requirement is not only impractical, but also logically impossible to meet

Multidimensional Signaling with a Resource Constraint

We study multidimensional signaling (cognitive/non-cognitive) as a sender's portfolio choice with a resource constraint. We establish the existence of a unique monotone D1 equilibrium where the cognitive (non-cognitive) signal increases (decreases) in sender type and the sum of the two increases in sender type. The equilibrium is characterized by two threshold sender types. The low threshold is one where a kink occurs in signaling. The constraint is binding only for sender types above it. The high threshold is the other one, above which all types spend all the resources in cognitive signal with pooling and discontinuity on the top