On the geometric structure of fMRI searchlight-based information maps

Information mapping is a popular application of Multivoxel Pattern Analysis (MVPA) to fMRI. Information maps are constructed using the so called searchlight method, where the spherical multivoxel neighborhood of every voxel (i.e., a searchlight) in the brain is evaluated for the presence of task-relevant response patterns. Despite their widespread use, information maps present several challenges for interpretation. One such challenge has to do with inferring the size and shape of a multivoxel pattern from its signature on the information map. To address this issue, we formally examined the geometric basis of this mapping relationship. Based on geometric considerations, we show how and why small patterns (i.e., having smaller spatial extents) can produce a larger signature on the information map as compared to large patterns, independent of the size of the searchlight radius. Furthermore, we show that the number of informative searchlights over the brain increase as a function of searchlight radius, even in the complete absence of any multivariate response patterns. These properties are unrelated to the statistical capabilities of the pattern-analysis algorithms used but are obligatory geometric properties arising from using the searchlight procedure.Comment: 15 pages, 7 figure

Caustic Structures and Detectability of Circumbinary Planets in Microlensing

Recent discoveries of circumbinary planets in Kepler data show that there is a viable channel of planet formation around binary main sequence stars. Motivated by these discoveries, we have investigated the caustic structures and detectability of circumbinary planets in microlensing events. We have produced a suite of animations of caustics as a function of the projected separation and angle of the binary host to efficiently explore caustic structures over the entire circumbinary parameter space. Aided by these animations, we have derived a semi-empirical analytic expression for the location of planetary caustics, which are displaced in circumbinary lenses relative to those of planets with a single host. We have used this expression to show that the dominant source of caustic motion will be due to the planet's orbital motion and not that of the binary star. Finally, we estimate the fraction of circumbinary microlensing events that are recognizable as such to be significant (5-50 percent) for binary projected separations in the range 0.1-0.5 in units of Einstein radii.Comment: 15 pages, 1 table, 18 figures. Accepted for publication in Ap

Self-Assembly of Arbitrary Shapes Using RNAse Enzymes: Meeting the Kolmogorov Bound with Small Scale Factor (extended abstract)

We consider a model of algorithmic self-assembly of geometric shapes out of square Wang tiles studied in SODA 2010, in which there are two types of tiles (e.g., constructed out of DNA and RNA material) and one operation that destroys all tiles of a particular type (e.g., an RNAse enzyme destroys all RNA tiles). We show that a single use of this destruction operation enables much more efficient construction of arbitrary shapes. In particular, an arbitrary shape can be constructed using an asymptotically optimal number of distinct tile types (related to the shape's Kolmogorov complexity), after scaling the shape by only a logarithmic factor. By contrast, without the destruction operation, the best such result has a scale factor at least linear in the size of the shape, and is connected only by a spanning tree of the scaled tiles. We also characterize a large collection of shapes that can be constructed efficiently without any scaling

Characterizing and correcting for the effect of sensor noise in the dynamic mode decomposition

Dynamic mode decomposition (DMD) provides a practical means of extracting insightful dynamical information from fluids datasets. Like any data processing technique, DMD's usefulness is limited by its ability to extract real and accurate dynamical features from noise-corrupted data. Here we show analytically that DMD is biased to sensor noise, and quantify how this bias depends on the size and noise level of the data. We present three modifications to DMD that can be used to remove this bias: (i) a direct correction of the identified bias using known noise properties, (ii) combining the results of performing DMD forwards and backwards in time, and (iii) a total least-squares-inspired algorithm. We discuss the relative merits of each algorithm, and demonstrate the performance of these modifications on a range of synthetic, numerical, and experimental datasets. We further compare our modified DMD algorithms with other variants proposed in recent literature

Exploring exoplanetary systems beyond 1AU with WFIRST

The Wide Field InfraRed Survey Telescope (WFIRST) was the top ranked large space mission of the New Worlds, New Horizons Decadal Survey, and is currently under active study by NASA. Its primary instrument will be a large-format high-resolution near-infrared imager and slitless spectrometer. A primary goal of WFIRST will be to perform a high-cadence microlensing survey of the Galactic bulge to search for low-mass exoplanets beyond the ice line. We highlight some of the expected results of the WFIRST exoplanet survey. For example, the survey will probe the abundance of Earth-mass planets from less than 1 AU outwards, including free-floating planets. In its peak sensitivity range of ~2-5 AU, WFIRST will be sensitive to planets with masses lower than Mercury, and even down to the mass of Ganymede. Overall, WFIRST is expected to detect several thousand bound planets, in addition to several thousand free-floating planets. WFIRST will complete the exoplanet census begun by Kepler, enabling an unprecedented understanding of planetary systems and their formation. Copyright © 2013, International Astronomical Union

SIGNS INSCRIBED ON A GATE: THE IMPACT OF VAN BUREN V. UNITED STATES ON CIVIL CLAIMS UNDER THE COMPUTER FRAUD AND ABUSE ACT

This Article addresses the impact of the U.S. Supreme Court’s June 2021 decision in Van Buren v. United States on what constitutes“ authorization” to access a computer under the Federal Computer Fraud and Abuse Act (CFAA)—a law that imposes both criminal and private civil liability for violations—and concludes that, so far, the Van Buren decision has not rendered the CFAA toothless. The Introduction briefly explains the history of the CFAA, a summary of why it was enacted, how organizations have relied upon it as an important tool to protect themselves from computer hackers and increased cybersecurity risks, and a Circuit of Appeals split about what it means to “exceed authorization.” The Article then, in a section titled “Exceeding Authorized Access: All That Is Not Permitted Is Forbidden,” tells the sordid tale of what happened to Van Buren and how the U.S. Supreme Court resolved his case, ultimately by reversing the Court of Appeals’s ruling affirming his CFAA conviction in an attempt to resolve the circuit split. It concludes in “Protecting Systems with a Sign on the Doorposts” by examining the two cases that, through December 2021, considered the authorization issue and what they indicate about the future of the post-Van Buren CFAA