Asymptotics for a special solution to the second member of the Painleve I hierarchy

We study the asymptotic behavior of a special smooth solution y(x,t) to the second member of the Painleve I hierarchy. This solution arises in random matrix theory and in the study of Hamiltonian perturbations of hyperbolic equations. The asymptotic behavior of y(x,t) if x\to \pm\infty (for fixed t) is known and relatively simple, but it turns out to be more subtle when x and t tend to infinity simultaneously. We distinguish a region of algebraic asymptotic behavior and a region of elliptic asymptotic behavior, and we obtain rigorous asymptotics in both regions. We also discuss two critical transitional asymptotic regimes.Comment: 19 page

The existence of a real pole-free solution of the fourth order analogue of the Painleve I equation

We establish the existence of a real solution y(x,T) with no poles on the real line of the following fourth order analogue of the Painleve I equation, x=Ty-({1/6}y^3+{1/24}(y_x^2+2yy_{xx})+{1/240}y_{xxxx}). This proves the existence part of a conjecture posed by Dubrovin. We obtain our result by proving the solvability of an associated Riemann-Hilbert problem through the approach of a vanishing lemma. In addition, by applying the Deift/Zhou steepest-descent method to this Riemann-Hilbert problem, we obtain the asymptotics for y(x,T) as x\to\pm\infty.Comment: 27 pages, 5 figure

Optimal urine culture diagnostic stewardship practice- Results from an expert modified-Delphi procedure

BACKGROUND: Urine cultures are nonspecific and often lead to misdiagnosis of urinary tract infection and unnecessary antibiotics. Diagnostic stewardship is a set of procedures that modifies test ordering, processing, and reporting in order to optimize diagnosis and downstream treatment. In this study, we aimed to develop expert guidance on best practices for urine culture diagnostic stewardship. METHODS: A RAND-modified Delphi approach with a multidisciplinary expert panel was used to ascertain diagnostic stewardship best practices. Clinical questions to guide recommendations were grouped into three thematic areas (ordering, processing, reporting) in practice settings of emergency department, inpatient, ambulatory, and long-term care. Fifteen experts ranked recommendations on a 9-point Likert scale. Recommendations on which the panel did not reach agreement were discussed during a virtual meeting, then a second round of ranking by email was completed. After secondary review of results and panel discussion, a series of guidance statements was developed. RESULTS: One hundred and sixty-five questions were reviewed. The panel reaching agreement on 104, leading to 18 overarching guidance statements. The following strategies were recommended to optimize ordering urine cultures: requiring documentation of symptoms, sending alerts to discourage ordering in the absence of symptoms, and cancelling repeat cultures. For urine culture processing, conditional urine cultures and urine white blood cell count as criteria were supported. For urine culture reporting, appropriate practices included nudges to discourage treatment under specific conditions and selective reporting of antibiotics to guide therapy decisions. CONCLUSIONS: These 18 guidance statements can optimize use of urine cultures for better patient outcomes

Campholenic aldehyde ozonolysis: a mechanism leading to specific biogenic secondary organic aerosol constituents

In the present study, campholenic aldehyde ozonolysis was performed to investigate pathways leading to specific biogenic secondary organic aerosol (SOA) marker compounds. Campholenic aldehyde, a known α-pinene oxidation product, is suggested to be a key intermediate in the formation of terpenylic acid upon α-pinene ozonolysis. It was reacted with ozone in the presence and absence of an OH radical scavenger, leading to SOA formation with a yield of 0.75 and 0.8, respectively. The resulting oxidation products in the gas and particle phases were investigated employing a denuder/filter sampling combination. Gas-phase oxidation products bearing a carbonyl group, which were collected by the denuder, were derivatised by 2,4-dinitrophenylhydrazine (DNPH) followed by liquid chromatography/negative ion electrospray ionisation time-of-flight mass spectrometry analysis and were compared to the gas-phase compounds detected by online proton-transfer-reaction mass spectrometry. Particle-phase products were also analysed, directly or after DNPH derivatisation, to derive information about specific compounds leading to SOA formation. Among the detected compounds, the aldehydic precursor of terpenylic acid was identified and its presence was confirmed in ambient aerosol samples from the DNPH derivatisation, accurate mass data, and additional mass spectrometry (MS² and MS³ fragmentation studies). Furthermore, the present investigation sheds light on a reaction pathway leading to the formation of terpenylic acid, involving α-pinene, α-pinene oxide, campholenic aldehyde, and terpenylic aldehyde. Additionally, the formation of diaterpenylic acid acetate could be connected to campholenic aldehyde oxidation. The present study also provides insights into the source of other highly functionalised oxidation products (e.g. <i>m</i> / <i>z</i> 201, C₉H₁₄O₅ and <i>m</i> / <i>z</i> 215, C₁₀H₁₆O₅), which have been observed in ambient aerosol samples and smog chamber-generated monoterpene SOA. The <i>m</i> / <i>z</i> 201 and 215 compounds were tentatively identified as a C₉- and C₁₀-carbonyl-dicarboxylic acid, respectively, based on reaction mechanisms of campholenic aldehyde and ozone, as well as detailed interpretation of mass spectral data, in conjunction with the formation of corresponding DNPH derivatives

Mesoscopic colonization of a spectral band

We consider the unitary matrix model in the limit where the size of the matrices become infinite and in the critical situation when a new spectral band is about to emerge. In previous works the number of expected eigenvalues in a neighborhood of the band was fixed and finite, a situation that was termed "birth of a cut" or "first colonization". We now consider the transitional regime where this microscopic population in the new band grows without bounds but at a slower rate than the size of the matrix. The local population in the new band organizes in a "mesoscopic" regime, in between the macroscopic behavior of the full system and the previously studied microscopic one. The mesoscopic colony may form a finite number of new bands, with a maximum number dictated by the degree of criticality of the original potential. We describe the delicate scaling limit that realizes/controls the mesoscopic colony. The method we use is the steepest descent analysis of the Riemann-Hilbert problem that is satisfied by the associated orthogonal polynomials.Comment: 17 pages, 2 figures, minor corrections and addition

Chemical characterisation of atmospheric aerosols during a 2007 summer field campaign at Brasschaat, Belgium : sources and source processes of biogenic secondary organic aerosol

Measurements of organic marker compounds and inorganic species were performed on PM2.5 aerosols from a Belgian forest site that is severely impacted by urban pollution ("De Inslag", Brasschaat, Belgium) during a 2007 summer period within the framework of the "Formation mechanisms, marker compounds, and source apportionment for biogenic atmospheric aerosols (BIOSOL)" project. The measured organic species included (i) low-molecular weight (MW) dicarboxylic acids (LMW DCAs), (ii) methanesulfonate (MSA), (iii) terpenoic acids originating from the oxidation of alpha-pinene, beta-pinene, d-limonene and Delta(3)-carene, and (iv) organosulfates related to secondary organic aerosol from the oxidation of isoprene and alpha-pinene. The organic tracers explained, on average, 5.3% of the organic carbon (OC), of which 0.7% was due to MSA, 3.4% to LMW DCAs, 0.6% to organosulfates, and 0.6% to terpenoic acids. The highest atmospheric concentrations of most species were observed during the first five days of the campaign, which were characterised by maximum day-time temperatures >22 degrees C. Most of the terpenoic acids and the organosulfates peaked during day-time, consistent with their local photochemical origin. High concentrations of 3-methyl-1,2,3-butanetricarboxylic acid (MBTCA) and low concentrations of cis-pinonic acid were noted during the first five days of the campaign, indicative of an aged biogenic aerosol. Several correlations between organic species were very high (r>0.85), high (0.70.7) and showed an Arrhenius-type relationship, consistent with their formation through OH radical chemistry

Joint distribution of the first and second eigenvalues at the soft edge of unitary ensembles

The density function for the joint distribution of the first and second eigenvalues at the soft edge of unitary ensembles is found in terms of a Painlev\'e II transcendent and its associated isomonodromic system. As a corollary, the density function for the spacing between these two eigenvalues is similarly characterized.The particular solution of Painlev\'e II that arises is a double shifted B\"acklund transformation of the Hasting-McLeod solution, which applies in the case of the distribution of the largest eigenvalue at the soft edge. Our deductions are made by employing the hard-to-soft edge transitions to existing results for the joint distribution of the first and second eigenvalue at the hard edge \cite{FW_2007}. In addition recursions under $a \mapsto a+1$ of quantities specifying the latter are obtained. A Fredholm determinant type characterisation is used to provide accurate numerics for the distribution of the spacing between the two largest eigenvalues.Comment: 26 pages, 1 Figure, 2 Table

On bulk singularities in the random normal matrix model

We extend the method of rescaled Ward identities of Ameur-Kang-Makarov to study the distribution of eigenvalues close to a bulk singularity, i.e. a point in the interior of the droplet where the density of the classical equilibrium measure vanishes. We prove results to the effect that a certain "dominant part" of the Taylor expansion determines the microscopic properties near a bulk singularity. A description of the distribution is given in terms of a special entire function, which depends on the nature of the singularity (a Mittag-Leffler function in the case of a rotationally symmetric singularity).Comment: This version clarifies on the proof of Theorem

The formation, properties and impact of secondary organic aerosol: current and emerging issues

Secondary organic aerosol (SOA) accounts for a significant fraction of ambient tropospheric aerosol and a detailed knowledge of the formation, properties and transformation of SOA is therefore required to evaluate its impact on atmospheric processes, climate and human health. The chemical and physical processes associated with SOA formation are complex and varied, and, despite considerable progress in recent years, a quantitative and predictive understanding of SOA formation does not exist and therefore represents a major research challenge in atmospheric science. This review begins with an update on the current state of knowledge on the global SOA budget and is followed by an overview of the atmospheric degradation mechanisms for SOA precursors, gas-particle partitioning theory and the analytical techniques used to determine the chemical composition of SOA. A survey of recent laboratory, field and modeling studies is also presented. The following topical and emerging issues are highlighted and discussed in detail: molecular characterization of biogenic SOA constituents, condensed phase reactions and oligomerization, the interaction of atmospheric organic components with sulfuric acid, the chemical and photochemical processing of organics in the atmospheric aqueous phase, aerosol formation from real plant emissions, interaction of atmospheric organic components with water, thermodynamics and mixtures in atmospheric models. Finally, the major challenges ahead in laboratory, field and modeling studies of SOA are discussed and recommendations for future research directions are proposed