We use the theta correspondence to study the equivalence between Godement–Jacquet and Jacquet–Langlands L-functions for ${\mathrm {GL}}(2)$. We show that the resulting comparison is in fact an expression of an exotic symmetric monoidal structure on the category of ${\mathrm {GL}}(2)$-modules. Moreover, this enables us to construct an abelian category of abstractly automorphic representations, whose irreducible objects are the usual automorphic representations. We speculate that this category is a natural setting for the study of automorphic phenomena for ${\mathrm {GL}}(2)$, and demonstrate its basic properties.

This paper is a part of the author’s thesis [4].

Salmonella spp. is a common zoonotic pathogen, causing gastrointestinal infections in people. Pigs and pig meat are a major source of infection. Although farm biosecurity is believed to be important for controlling Salmonella transmission, robust evidence is lacking on which measures are most effective. This study enrolled 250 pig farms across nine European countries. From each farm, 20 pooled faecal samples (or similar information) were collected and analysed for Salmonella presence. Based on the proportion of positive results, farms were categorised as at higher or lower Salmonella risk, and associations with variables from a comprehensive questionnaire investigated. Multivariable analysis indicated that farms were less likely to be in the higher-risk category if they had ‘<400 sows’; used rodent baits close to pig enclosures; isolated stay-behind (sick) pigs; did not answer that the hygiene lock/ anteroom was easy to clean; did not have a full perimeter fence; did apply downtime of at least 3 days between farrowing batches; and had fully slatted flooring in all fattener buildings. A principal components analysis assessed the sources of variation between farms, and correlation between variables. The study results suggest simple control measures that could be prioritised on European pig farms to control Salmonella.

Background: Circulating cell-free DNA (cfDNA) is a novel type of biomarker with a broad utility in diagnostic medicine, based on the release of DNA fragments from dying cells to the circulation. We developed an approach for identifying the tissue origins of cfDNA, using cell-type-specific DNA methylation patterns, based on a massive reference atlas of the genome-wide methylomes of multiple human tissues and cell types. Cancer inflicts damage to surrounding normal tissues, which can culminate in fatal organ failure. We demonstrated that brain cell death in CNS cancer can be detected by tissue-specific methylation patterns of circulating cfDNA. Methods: We developed a cocktail of brain-specific DNA methylation markers, and used it to assess the presence of brain-derived-cfDNA in the plasma of patients with brain metastasis. Results: We identified significantly elevated neuron-, oligodendrocyte-, and astrocyte-derived cfDNA (p<0.0001) in patients with brain metastases (n=29) compared with cancer patients without brain metastasis (n=113). Conclusions: We show a new set of biomarkers to identify brain damage with high specificity and resolution. We detected brain (neurons, oligodendrocytes, astrocytes) cfDNA in the plasma of patients with brain metastasis. Cell-type-specific cfDNA methylation markers allow the identification of collateral tissue damage, reveals the presence of metastases, and potentially assist in early cancer detection.

In Aizenbud et al. (2010, Annals of Mathematics 172, 1407–1434), a multiplicity one theorem is proved for general linear groups, orthogonal groups, and unitary groups ( $GL, O,$ and U) over p-adic local fields. That is to say that when we have a pair of such groups $G_n{\subseteq } G_{n+1}$ , any restriction of an irreducible smooth representation of $G_{n+1}$ to $G_n$ is multiplicity-free. This property is already known for $GL$ over a local field of positive characteristic, and in this paper, we also give a proof for $O,U$ , and $SO$ over local fields of positive odd characteristic. These theorems are shown in Gan, Gross, and Prasad (2012, Sur les Conjectures de Gross et Prasad. I, Société Mathématique de France) to imply the uniqueness of Bessel models, and in Chen and Sun (2015, International Mathematics Research Notice 2015, 5849–5873) to imply the uniqueness of Rankin–Selberg models. We also prove simultaneously the uniqueness of Fourier–Jacobi models, following the outlines of the proof in Sun (2012, American Journal of Mathematics 134, 1655–1678).

By the Gelfand–Kazhdan criterion, the multiplicity one property for a pair $H\leq G$ follows from the statement that any distribution on G invariant to conjugations by H is also invariant to some anti-involution of G preserving H. This statement for $GL, O$ , and U over p-adic local fields is proved in Aizenbud et al. (2010, Annals of Mathematics 172, 1407–1434). An adaptation of the proof for $GL$ that works over of local fields of positive odd characteristic is given in Mezer (2020, Mathematische Zeitschrift 297, 1383–1396). In this paper, we give similar adaptations of the proofs of the theorems on orthogonal and unitary groups, as well as similar theorems for special orthogonal groups and for symplectic groups. Our methods are a synergy of the methods used over characteristic 0 (Aizenbud et al. [2010, Annals of Mathematics 172, 1407–1434]; Sun [2012, American Journal of Mathematics 134, 1655–1678]; and Waldspurger [2012, Astérisque 346, 313–318]) and of those used in Mezer (2020, Mathematische Zeitschrift 297, 1383–1396).

OBJECTIVES/GOALS: Biliary atresia (BA) is a progressive congenital disease that is characterized by periductular inflammation and fibrosis that leads to bile duct destruction and cholestasis in neonates. Galectin-3 (Gal3) plays a key role in inflammation and fibrosis. The aim of this study was to evaluate plasma Gal3 levels in early and late BA. METHODS/STUDY POPULATION: Samples from our institutional Pediatric Liver Biobank were used for this study. Patients were categorized as early BA (at diagnosis), late BA (at liver transplant), early other cholestatic liver disease (CLD), late other CLD, or controls without cholestasis or structural liver disease. Plasma Gal3 levels were measured by standard ELISA. Inflammatory cytokines were measured in a subset of samples using MSD Proinflammatory Panel 1 multiplex ELISA. Liver fibrosis was categorized as none (Ishak or METAVIR 0), mild (Ishak 1-2 or METAVIR 1), moderate (Ishak 3-4 or METAVIR 2-3), and severe (Ishak 5-6 or METAVIR 4) based on histology. Data are presented as median (IQR) and compared using Kruskal-Wallis test. Spearmans correlation was used to assess the relationship between Gal3 and clinical and inflammatory markers. RESULTS/ANTICIPATED RESULTS: Samples from 10 controls, 26 early BA, 24 late BA, 13 early other CLD, and 8 late other CLD patients were used for this study. Gal3 levels in late BA (20.8 [12.4-30.5] ng/mL) and late other CLD (21.8 [16.9 – 27.2] ng/mL) were significantly higher than in controls (10.2 [7.6 – 14.5] ng/mL, p < 0.02) and early BA (11.3 [8.7 – 16.8] ng/mL, p < 0.01), but not significantly different from early other CLD (15.7 [11.9 – 21.4] ng/mL, p > 0.05). Gal3 positively correlated with fibrosis score (rho 0.3, p = 0.01), total bilirubin (rho 0.3, p = 0.002), ALT (rho 0.3, p = 0.01), AST (rho 0.3, p = 0.005), and APRI score (rho 0.3, p = 0.009), and negatively correlated with albumin (rho -0.3, p = 0.01). Out of the 10 cytokine proinflammatory panel, Gal3 was significantly correlated with IL-6 (rho 0.3, p = 0.006). DISCUSSION/SIGNIFICANCE: Gal3 is elevated in late BA and other CLD at time of transplant and correlated with degree of fibrosis, suggesting it may play a role in disease progression to cirrhosis. If targeted in the early disease stage, blocking Gal3 in pediatric cholestatic liver diseases may help delay the progression to cirrhosis and need for transplant.

The propagation of a normal shock wave along a coupled convex–concave surface of equal radii has been analysed experimentally and numerically in this study. The experimental and numerical studies were conducted using a similar geometry as of that used by Ram et al. (J. Fluid Mech., vol. 768, 2015, pp. 219–239) for studying the shock wave transition from regular reflection to Mach reflection. Many interesting flow features such as shock wave transitions over the ramp, characteristics of the induced flow behind the shock wave and the development of a stationary separation shock wave have been observed in the study. The numerical results are validated with experimental data. While the shock wave transitions over the ramp are found to depend mainly on the ramp geometry, the characteristics of the stationary shock wave and the flow separation in the concave region of the ramp surface have been found to vary with the shock wave Mach numbers.

Since their inception in the 1930s by von Neumann, operator algebras have been used to shed light on many mathematical theories. Classification results for self-adjoint and non-self-adjoint operator algebras manifest this approach, but a clear connection between the two has been sought since their emergence in the late 1960s. We connect these seemingly separate types of results by uncovering a hierarchy of classification for non-self-adjoint operator algebras and $C^{*}$-algebras with additional $C^{*}$-algebraic structure. Our approach naturally applies to algebras arising from $C^{*}$-correspondences to resolve self-adjoint and non-self-adjoint isomorphism problems in the literature. We apply our strategy to completely elucidate this newly found hierarchy for operator algebras arising from directed graphs.

Shock-wave reflection over concave surfaces poses a difficulty in its analysis due to the unsteady nature of the reflection process and the occurrence of various types of Mach reflections caused by it. In a pseudo-steady flow, the reflection's configuration is self-similar since the shock wave reflects over a surface with constant inclination. The unsteady Mach reflection introduces an additional complexity as it is affected by the changing inclination of the surface, forcing the reflection to continuously adjust itself to the varying boundary condition. In this study, validated simulations of Mach reflection (MR) over cylindrical concave surfaces with different radii were performed for three inviscid perfect gases with moderate incident shock Mach numbers (Ms) ranging from 1.3 to 1.5. The reflection was investigated up to the point of transition from MR to transitioned regular reflection. A similar behaviour of the configuration and evolution of the Mach stem was observed, one that is independent of the surface radius and type of gas. With regards to different gases, the speed of sound a0 is a dominant factor since it dictates the propagation of wall disturbances. A universal condition of the rate of surface change was found, accounting for different radii, different gases and Ms variation. Analysis based on shock dynamics is employed to explain how disturbances caused by surface variations play a significant role in the behaviour of the reflection. This method successfully supports the similarity that was demonstrated and facilitates a more informed perception of the MR process.

Adolescent suicide is a worldwide troubling phenomenon that has high comorbidity, including impulsivity, depression, and personality disorders. Attention Deficit Hyperactivity Disorder (ADHD) includes attention, impulsivity and hyperactivity. Comorbidity includes depression and substance abuse, and has a higher rate in adolescents and adults. Studies considering the association between these phenomena are surprisingly rare. This pilot study estimated the percentage of ADHD in a population of adolescents who attempted suicide. Population included all adolescents (12-18 yrs.) who were brought to local ER after attempting suicide. Assessment included an interview according to the DSM-IV criteria, the Strengths and Difficulties Questionnaire parents (SDQ-P) the Conners' Rating Scale parents (CRS-P), and Kiddie-SADS. Test Of Variables of Attention (TOVA) with methylphenidate (MPH) challenge was done after the clinical evaluation to those diagnosed as ADHD.

We examined the trends in prescribing psychotropic drugs to children and adolescents within an inpatients adolescent psychiatric ward in Israel. Data of 414 subjects, ranging from 12- to 22-year-old, covering the years 1997, 2002 and 2007, was examined retrospectively. Analyzed variables included the number and type of drug prescriptions per patient at discharge, the subjects’ age at discharge and the number of diagnoses per patient at discharge. Analysis of variance (ANOVA) with repeated measures was used to evaluate changes between the three calendar years, along the 10-year study period, while Pearson χ2 test was performed for categorical variables. Over the study period the mean age at discharge decreased significantly, by about a year and a half, the mean number of diagnoses increased significantly, from 1.6 to 2.4 diagnoses per patient and the total number of drugs prescribed at discharge increased significantly from 1.48 to 1.93 per patient. Overall, the number of patients who were prescribed mood stabilizers increased by 14%, those who were prescribed antidepressants increased by almost 24%, almost 16% in antipsychotics prescriptions and 51.5% in prescriptions of atypical antipsychotics. Typical antipsychotic prescriptions decreased by 35.5% and accordingly, the number of patients who were prescribed agents for the treatment of extra-pyramidal side effects decreased by almost 24%. Due to a low number of inpatients with attention deficit and hyperactivity disorder (ADHD), no significant statistical conclusion could be drawn regarding trends in psychostimulant prescriptions. Our findings agree with other published studies from the last two decades. The growing use of psychotropic agents in children and adolescents merit a continuous concern with regard to their effects on the developing brain and impact on quality of life and to authorizing these drugs for use in specific young age subgroups.

In this paper we show that every non-cycle finite transitive directed graph has a Cuntz–Krieger family whose WOT-closed algebra is $B(\mathcal {H})$. This is accomplished through a new construction that reduces this problem to in-degree 2-regular graphs, which is then treated by applying the periodic Road Colouring Theorem of Béal and Perrin. As a consequence we show that finite disjoint unions of finite transitive directed graphs are exactly those finite graphs which admit self-adjoint free semigroupoid algebras.

The aim of diagnostic diagrams is to classify galactic nuclei according to their photoionizing source using emission-line ratios, differentiating starburst regions from active galactic nuclei (AGN). However, the three traditional diagnostic diagrams can sometimes be ambiguous with regard to a single object. The main goal of the present work is to propose alternative diagnostic diagrams by using distinct combinations of emission lines ratios. We present these diagrams using data from the Sloan Digital Sky Survey. With these new diagrams, it is possible to better distinguish the ionizing source in nuclei of galaxies and also to study the parameters that are relevant when considering both kinds of objects, starbursts and AGN.

Interactions and mergers between dwarf galaxies are mostly gas-rich and should be marked by an intense star formation activity. But these processes, which are expected to be common at earlier times, are very difficult to observe at low redshifts. To investigate that, we look in the Sloan Digital Sky Survey (SDSS) for compact groups that contain one luminous compact galaxy (LCG) with very high specific star formation rate (sSFR) and at least two other blue galaxies. We found 24 groups that satisfy these criteria, among which 12 groups have SDSS spectroscopic data for at least 2 member galaxies. Here we want to investigate, using the tidal strength estimator Q, how interactions between neighbouring galaxies affect the sSFR and concentration of each LCG. Statistical tests reveal a correlation between Q and their sSFR, indicating that tidal forces between neighbouring galaxies might be inducing bursts of star formation in the LCGs.