Constrained Type Families

We present an approach to support partiality in type-level computation without compromising expressiveness or type safety. Existing frameworks for type-level computation either require totality or implicitly assume it. For example, type families in Haskell provide a powerful, modular means of defining type-level computation. However, their current design implicitly assumes that type families are total, introducing nonsensical types and significantly complicating the metatheory of type families and their extensions. We propose an alternative design, using qualified types to pair type-level computations with predicates that capture their domains. Our approach naturally captures the intuitive partiality of type families, simplifying their metatheory. As evidence, we present the first complete proof of consistency for a language with closed type families.Comment: Originally presented at ICFP 2017; extended editio

On the Equivalence Between a Minimal Codomain Cardinality Riesz Basis Construction, a System of Hadamard–Sylvester Operators, and a Class of Sparse, Binary Optimization Problems

Piecewise, low-order polynomial, Riesz basis families are constructed such that they share the same coefficient functionals of smoother, orthonormal bases in a localized indexing subset. It is shown that a minimal cardinality basis codomain can be realized by inducing sparsity, via l1 regularization, in the distributional derivatives of the basis functions and that the optimal construction can be found numerically by constrained binary optimization over a suitably large dictionary. Furthermore, it is shown that a subset of these solutions are equivalent to a specific, constrained analytical solution, derived via Sylvester-type Hadamard operators

The Effect of Credit Constraints on the College Drop-Out Decision A Direct Approach Using a New Panel Study

A serious difficulty in determining the importance of credit constraints in education arises because standard data sources do not provide a direct way of identifying which students are credit constrained. This has forced researchers to adopt a variety of indirect approaches. This paper differentiates itself from previous work by taking a direct approach for providing evidence about this issue which is made possible by unique longitudinal data that have been collected specifically for this type of purpose. Our results suggest that, while credit constraints likely play an important role in the drop-out decisions of some students, the large majority of attrition of students from low income families should be primarily attributed to reasons other than credit constraints.

An anisotropic distribution of spin vectors in asteroid families

Current amount of ~500 asteroid models derived from the disk-integrated photometry by the lightcurve inversion method allows us to study not only the spin-vector properties of the whole population of MBAs, but also of several individual collisional families. We create a data set of 152 asteroids that were identified by the HCM method as members of ten collisional families, among them are 31 newly derived unique models and 24 new models with well-constrained pole-ecliptic latitudes of the spin axes. The remaining models are adopted from the DAMIT database or the literature. We revise the preliminary family membership identification by the HCM method according to several additional criteria - taxonomic type, color, albedo, maximum Yarkovsky semi-major axis drift and the consistency with the size-frequency distribution of each family, and consequently we remove interlopers. We then present the spin-vector distributions for eight asteroidal families. We use a combined orbital- and spin-evolution model to explain the observed spin-vector properties of objects among collisional families. In general, we observe for studied families similar trends in the (a_p, \beta) space: (i) larger asteroids are situated in the proximity of the center of the family; (ii) asteroids with \beta>0{\deg} are usually found to the right from the family center; (iii) on the other hand, asteroids with \beta<0{\deg} to the left from the center; (iv) majority of asteroids have large pole-ecliptic latitudes (|\beta|\gtrsim 30{\deg}); and finally (v) some families have a statistically significant excess of asteroids with \beta>0{\deg} or \beta<0{\deg}. Our numerical simulation of the long-term evolution of a collisional family is capable of reproducing well the observed spin-vector properties. Using this simulation, we also independently constrain the age of families Flora (1.0\pm0.5 Gyr) and Koronis (2.5-4 Gyr).Comment: Accepted for publication in A&A (September 16, 2013

Managing escalating demand for public services in a time of financial austerity: a case study of family interventions

The UK (along with many other countries) is facing the challenges of financial austerity with little or no growth in public funding for the foreseeable future. This creates particular challenges for public services as economic downturns often increase the demand for public services at a time when resources are constrained. A particular service of this type is the provision of support to ‘troubled’ families through what are termed family interventions, in one local authority area, and the impact of financial austerity on those services. It considers the strategic options available for dealing with the dilemma of increasing demand and declining resources, and assesses the implications of implementing these options. It also considers the key factors which inhibit the development and implementation of such approaches, in order to provide a starting point for developing a practical strategy for dealing with the challenges ahead. Finally, it considers how the findings related to family interventions can be applied to other services in a similar situation of increasing demand and decreasing resources

Gaia spectroscopy and application to asteroid families

openContext. The third data release by the Gaia mission of the European Space Agency (DR3) contains 60 518 asteroid reflectance spectra over the range 374 nm−1034 nm, representing a huge improvement in spectroscopic data compared to previous surveys available in the literature. Gaia spectra are however affected by systematic deviations in the near infrared when compared to ground-based and template spectra. Aims. I explored possible correlations of the deviations with several parameters of the observed objects, such as the magnitude and the spectral type, in order to assess the internal consistency of Gaia spectra. In addition, I explored different approaches able to mitigate the deviations and classify Gaia spectra into a consistent taxonomy scheme. Finally, I determined whether if asteroid families could be identified using Gaia spectra alone. Methods. In order to determine if the deviations were correlating with the magnitude, I quantified them for groups of asteroids of the same spectral type and different luminosity. To explore the correlation with the taxonomy class, I quantified the deviations for groups of objects of different spectral types. I then developed a procedure able to mitigate the deviations, which I tested with the classy Python tool. Finally, I tested a colorbased taxonomy, which by converting Gaia reflectance spectra in SDSS colors retrieves the spectral type of a specific asteroid given its position on a color-color diagram. With this taxonomy system I classified Gaia observations in specific regions of the Main Belt in order to identify the Tirela and Watsonia families. By converting the observations in diameters, I then fitted the slopes of the v-shapes in order to constrain the ages of the families. Results. I found that the systematic deviations in the near infrared correlate with the spectral type, being maximum for S- complex asteroids, intermediate for the C- complex and almost null for M- and P- types. Classifying Gaia observations with the color-based taxonomy, I identified the Tirela and the Watsonia families, whose memberships resulted to be in very good agreement with the literature. I then constrained the age of the Tirela family, which resulted to be 670 ± 570 Myr for the inner side and 688 ± 377 Myr for the outer side. The same analysis for the Watsonia family turned out to be less precise due to the limited number of objects observed by Gaia and resulted in an age of the order of 1 Gyr. Conclusions. Gaia spectra have been found to be internally coherent, such that asteroids of the same spectral type present similar spectra. In addition, I proved that asteroid families can be recognized using Gaia spectra alone. In particular, the Tirela and the Watsonia families were correctly identified. I then constrained their ages, showing one of the many possibilities in which Gaia spectra can be exploited.Context. The third data release by the Gaia mission of the European Space Agency (DR3) contains 60 518 asteroid reflectance spectra over the range 374 nm−1034 nm, representing a huge improvement in spectroscopic data compared to previous surveys available in the literature. Gaia spectra are however affected by systematic deviations in the near infrared when compared to ground-based and template spectra. Aims. I explored possible correlations of the deviations with several parameters of the observed objects, such as the magnitude and the spectral type, in order to assess the internal consistency of Gaia spectra. In addition, I explored different approaches able to mitigate the deviations and classify Gaia spectra into a consistent taxonomy scheme. Finally, I determined whether if asteroid families could be identified using Gaia spectra alone. Methods. In order to determine if the deviations were correlating with the magnitude, I quantified them for groups of asteroids of the same spectral type and different luminosity. To explore the correlation with the taxonomy class, I quantified the deviations for groups of objects of different spectral types. I then developed a procedure able to mitigate the deviations, which I tested with the classy Python tool. Finally, I tested a colorbased taxonomy, which by converting Gaia reflectance spectra in SDSS colors retrieves the spectral type of a specific asteroid given its position on a color-color diagram. With this taxonomy system I classified Gaia observations in specific regions of the Main Belt in order to identify the Tirela and Watsonia families. By converting the observations in diameters, I then fitted the slopes of the v-shapes in order to constrain the ages of the families. Results. I found that the systematic deviations in the near infrared correlate with the spectral type, being maximum for S- complex asteroids, intermediate for the C- complex and almost null for M- and P- types. Classifying Gaia observations with the color-based taxonomy, I identified the Tirela and the Watsonia families, whose memberships resulted to be in very good agreement with the literature. I then constrained the age of the Tirela family, which resulted to be 670 ± 570 Myr for the inner side and 688 ± 377 Myr for the outer side. The same analysis for the Watsonia family turned out to be less precise due to the limited number of objects observed by Gaia and resulted in an age of the order of 1 Gyr. Conclusions. Gaia spectra have been found to be internally coherent, such that asteroids of the same spectral type present similar spectra. In addition, I proved that asteroid families can be recognized using Gaia spectra alone. In particular, the Tirela and the Watsonia families were correctly identified. I then constrained their ages, showing one of the many possibilities in which Gaia spectra can be exploited

Saturated fusion systems with parabolic families

Let G be group; a finite p-subgroup S of G is a Sylow p-subgroup if every finite p-subgroup of G is conjugate to a subgroup of S. In this paper, we examine the relations between the fusion system over S which is given by conjugation in G and a certain chamber system C, on which G acts chamber transitively with chamber stabilizer N_G(S). Next, we introduce the notion of a fusion system with a parabolic family and we show that a chamber system can be associated to such a fusion system. We determine some conditions the chamber system has to fulfill in order to assure the saturation of the underlying fusion system. We give an application to fusion systems with parabolic families of classical type.Comment: 28 page

Genomic Selective Constraints in Murid Noncoding DNA

Recent work has suggested that there are many more selectively constrained, functional noncoding than coding sites in mammalian genomes. However, little is known about how selective constraint varies amongst different classes of noncoding DNA. We estimated the magnitude of selective constraint on a large dataset of mouse-rat gene orthologs and their surrounding noncoding DNA. Our analysis indicates that there are more than three times as many selectively constrained, nonrepetitive sites within noncoding DNA as in coding DNA in murids. The majority of these constrained noncoding sites appear to be located within intergenic regions, at distances greater than 5 kilobases from known genes. Our study also shows that in murids, intron length and mean intronic selective constraint are negatively correlated with intron ordinal number. Our results therefore suggest that functional intronic sites tend to accumulate toward the 5' end of murid genes. Our analysis also reveals that mean number of selectively constrained noncoding sites varies substantially with the function of the adjacent gene. We find that, among others, developmental and neuronal genes are associated with the greatest numbers of putatively functional noncoding sites compared with genes involved in electron transport and a variety of metabolic processes. Combining our estimates of the total number of constrained coding and noncoding bases we calculate that over twice as many deleterious mutations have occurred in intergenic regions as in known genic sequence and that the total genomic deleterious point mutation rate is 0.91 per diploid genome, per generation. This estimated rate is over twice as large as a previous estimate in murids