COUNTING SMALL INDUCED SUBGRAPHS WITH HEREDITARY PROPERTIES

We study the computational complexity of the problem \#INDSUB(\Phi) of counting k-vertex induced subgraphs of a graph G that satisfy a graph property \Phi. Our main result establishes an exhaustive and explicit classification for all hereditary properties, including tight conditional lower bounds under the Exponential Time Hypothesis (ETH): If a hereditary property \Phi is true for all graphs, or if it is true only for finitely many graphs, then \#INDSUB(\Phi) is solvable in polynomial time. Otherwise, \#INDSUB(\Phi) is \#\sansW[\sansone]-complete when parameterized by k, and, assuming ETH, it cannot be solved in time f(k) \cdot |G|o(k) for any function f. This classification features a wide range of properties for which the corresponding detection problem (as classified by Khot and Raman [Theoret. Comput. Sci., 289 (2002), pp. 997-1008]) is tractable but counting is hard. Moreover, even for properties which are already intractable in their decision version, our results yield significantly stronger lower bounds for the counting problem. As an additional result, we also present an exhaustive and explicit parameterized complexity classification for all properties that are invariant under homomorphic equivalence. By covering one of the most natural and general notions of closure, namely, closure under vertex-deletion (hereditary), we generalize some of the earlier results on this problem. For instance, our results fully subsume and strengthen the existing classification of \#INDSUB(\Phi) for monotone (subgraph-closed) properties due to Roth, Schmitt, and Wellnitz [SIAM J. Comput., (2022), pp. FOCS20-139-FOCS20-174]

Rapid Profiling of Marine Notches Using a Handheld Laser Distance Meter

A rapid, single-user profiling method for rocky shores is described. The Leica Disto D8 handheld laser distance meter measures distance up to 100 m and inclination in 360 degrees. It automatically calculates horizontal distance and vertical elevation. Memory storage accommodates data for 30 measurement points, allowing easy plotting of shore profiles. This technique allows even inaccessible, dangerous, and overhanging cliff faces to be evaluated faithfully and within minutes. It is a major improvement over standard methods that often involve risky coasteering and climbing. Examples are given from marine notches in Thailand

Beyond the Dipole Approximation: Angular-Distribution Effects in the 1s Photoemission from Small Molecules

Over the past two decades, the dipole approximation has facilitated a basic understanding of the photoionization process in atoms and molecules. Recent experiments on the 1s inner shells of small molecules at relatively low photon energies (⩽ 1000 eV) show strong nondipole effects. They are significant and measurable at energies close to threshold, in conflict with a common assumption that the dipole approximation is valid for photon energies below 1 keV

Large Nondipole Effects in the Angular Distributions of K-Shell Photoelectrons from Molecular Nitrogen

Measurements of angular distributions of K-shell electrons photoejected from molecular nitrogen are reported which reveal large deviations at relatively low photon energies ( ħω≤500eV) from emission patterns anticipated from the dipole approximation to interactions between radiation and matter. A concomitant theoretical analysis incorporating the effects of electromagnetic retardation attributes the observed large nondipole behaviors in N2 to bond-length-dependent terms in the E1⊗(E2,M1) photoelectron emission amplitudes which are indicative of a potentially universal nondipole behavior in molecular photoionization

Defining Meyer's loop-temporal lobe resections, visual field deficits and diffusion tensor tractography

Anterior temporal lobe resection is often complicated by superior quadrantic visual field deficits (VFDs). In some cases this can be severe enough to prohibit driving, even if a patient is free of seizures. These deficits are caused by damage to Meyer's loop of the optic radiation, which shows considerable heterogeneity in its anterior extent. This structure cannot be distinguished using clinical magnetic resonance imaging sequences. Diffusion tensor tractography is an advanced magnetic resonance imaging technique that enables the parcellation of white matter. Using seed voxels antero-lateral to the lateral geniculate nucleus, we applied this technique to 20 control subjects, and 21 postoperative patients. All patients had visual fields assessed with Goldmann perimetry at least three months after surgery. We measured the distance from the tip of Meyer's loop to the temporal pole and horn in all subjects. In addition, we measured the size of temporal lobe resection using postoperative T1-weighted images, and quantified VFDs. Nine patients suffered VFDs ranging from 22% to 87% of the contralateral superior quadrant. In patients, the range of distance from the tip of Meyer's loop to the temporal pole was 24–43 mm (mean 34 mm), and the range of distance from the tip of Meyer's loop to the temporal horn was –15 to +9 mm (mean 0 mm). In controls the range of distance from the tip of Meyer's loop to the temporal pole was 24–47 mm (mean 35 mm), and the range of distance from the tip of Meyer's loop to the temporal horn was –11 to +9 mm (mean 0 mm). Both quantitative and qualitative results were in accord with recent dissections of cadaveric brains, and analysis of postoperative VFDs and resection volumes. By applying a linear regression analysis we showed that both distance from the tip of Meyer's loop to the temporal pole and the size of resection were significant predictors of the postoperative VFDs. We conclude that there is considerable variation in the anterior extent of Meyer's loop. In view of this, diffusion tensor tractography of the optic radiation is a potentially useful method to assess an individual patient's risk of postoperative VFDs following anterior temporal lobe resection

Personalized connectome fingerprints: Their importance in cognition from childhood to adult years

Structural neural network architecture patterns in the human brain could be related to individual differences in phenotype, behavior, genetic determinants, and clinical outcomes from neuropsychiatric disorders. Recent studies have indicated that a personalized neural (brain) fingerprint can be identified from structural brain connectomes. However, the accuracy, reproducibility and translational potential of personalized fingerprints in terms of cognition is not yet fully determined. In this study, we introduce a dynamic connectome modeling approach to identify a critical set of white matter subnetworks that can be used as a personalized fingerprint. Several individual variable assessments were performed that demonstrate the accuracy and practicality of personalized fingerprint, specifically predicting the identity and IQ of middle age adults, and the developmental quotient in toddlers. Our findings suggest the fingerprint found by our dynamic modeling approach is sufficient for differentiation between individuals, and is also capable of predicting general intellectual ability across human development. © 2020 The AuthorsSignificance Statement We demonstrate that white matter connections obtained from high resolution medical imaging data form a personalized fingerprint is capable of estimating individual identity and neurodevelopmental variables across human life-span. This important finding provides strong evidence to support the concept of neurological identity and function through human brain connectome mapping