Steady and Stable: Numerical Investigations of Nonlinear Partial Differential Equations

Excerpt: Mathematics is a language which can describe patterns in everyday life as well as abstract concepts existing only in our minds. Patterns exist in data, functions, and sets constructed around a common theme, but the most tangible patterns are visual. Visual demonstrations can help undergraduate students connect to abstract concepts in advanced mathematical courses. The study of partial differential equations, in particular, benefits from numerical analysis and simulation

The Modular Approach to Micro, Small, and Medium Enterprise Insolvency

Historically, insolvency systems have been designed with larger enterprises in mind. They assume an extensive insolvency estate of significant worth, and the presence of creditors and other stakeholders with sufficient value at stake that they participate in and oversee the process. These assumptions undergird mechanisms by which creditors and other stakeholders may ensure that the insolvency process faithfully serves their interests, for an independent professional to run the business undergoing an insolvency process, and for extensive judicial oversight. These assumptions and features are incongruent with the reality of micro, small, and medium enterprises (\u27MSMEs\u27). Mirroring the general population of businesses and reflecting the particular fragility associated with smaller asset bases and relative absence of risk diversification, the vast majority of businesses entering insolvency proceedings are MSMEs. On MSME insolvency, little or no value is available for distribution to anyone other than secured creditors in a significant proportion of insolvency estates, and secured creditors tend to have effective collection methods under non-insolvency law. Correspondingly, most secured and unsecured creditors, as well as other stakeholders, are rationally disinterested in the insolvency process. In many cases, it is not worthwhile for either the estate or most stakeholders to engage lawyers to represent them in court. Estates may possess inadequate value even to pay an independent insolvency professional. Such incongruence between the design of insolvency regimes and the nature of most of the businesses to which they apply leaves the insolvency process unbalanced, inadequately supervised, non-efficacious, and sometimes, simply unfeasible. Policy-makers and legislators have often responded through ad hoc changes to the ‘standard’ regime, such as by shearing some elements of the insolvency process when applied to smaller businesses, by shortening statutory timelines, and by dispensing with the necessary participation of certain stakeholders. The resulting processes have been marked by arbitrary boundaries, rigid preconditions for availability, and limited effectiveness. This paper systematically rethinks the treatment of distressed MSMEs. At its core is a new ‘Modular Approach’ to MSME insolvency. This approach is modular in two ways: (i) it allows national policy makers to choose from a range of available options including in terms of the involvement of appropriate institutions; (ii) subject to national authorities’ design decisions, the Modular Approach provides an essential ‘core’ process in each case, and allows relevant stakeholders to invoke additional tools (‘modules’) if and when the benefits of wielding those tools in the particular case outweigh the costs. The Modular Approach shares with ‘standard’ insolvency regimes the core objectives of preserving and maximizing the value in the insolvency estate, ensuring distribution over an appropriate period of time of the highest feasible proportion of that value to those entitled to it, providing due accountability for any wrongdoing connected with the insolvency, and enabling discharge of over-indebted natural persons. The Modular Approach differs in the way it pursues these objectives. Its basic assumption is that the parties to a particular insolvency case are best placed to select the tools appropriate to that case. The role of the legal regime should be to provide these tools in a maximally flexible way, while creating the correct incentives for their deployment. Traditionally, legal systems provide particular ‘packages’ or combinations of these tools and label them ‘workout’, ‘liquidation’ and ‘restructuring’. The Modular Approach unpacks those combinations. It assumes a core process, geared towards enabling the entrepreneur to propose a restructuring of the business’ liabilities and to obtain discharge of any unrepayable obligations. The entrepreneur, who may operate through a legal entity or as a sole trader, may access any of the full range of insolvency law mechanisms to enable attainment of these objectives. At the same time, creditors and other stakeholders have the right to adequate notification of each step in the process, coupled with the power to override the entrepreneur’s choices where a sufficient proportion of them consider it appropriate to do so. Judicial involvement is not required as a matter of course, though, again, it may be requested by the stipulated proportion of creditors. The process may obtain and retain momentum by virtue of the presumptions that stakeholders who have not positively objected to a step in the process have consented to that step, and that the non-exercise of procedural rights within the process precludes the relevant stakeholders from objecting to the part of the process to which the unexercised rights relate. Stakeholders are divided into appropriate classes; they must act by stipulated majority by value; and stipulated majorities by value of a class may bind dissenting minorities. The Modular Approach is designed to provide appropriate incentives for the entrepreneur and other stakeholders alike. Entrepreneurs have positive incentives to commence the insolvency process in a timely manner: they do not have to declare the business insolvent; they may, in principle, retain its management; and they have the right to propose how the insolvency should proceed. Entrepreneurs also face negative incentives that discourage non-timely commencement of insolvency proceedings, in that the Modular Approach imposes personal liability for any additional loss suffered by the business’ creditors because of blameworthy delay in commencement. The Modular Approach acknowledges that in many MSME insolvencies, unsecured creditors are rationally disinterested, given their limited economic stake and the very limited likelihood of any recovery in the process. They need not actively participate in the process if, upon due notification, they do not consider it worth the time and expense of participating. As noted, their abstention is deemed approval, and the insolvency process may continue apace. Negative incentives for creditors arise because the non-exercise of procedural rights amounts to a waiver of such rights. Positive incentives arise in creditors’ ability, acting with others who together hold a sufficiently large proportion of the claims against the enterprise, to override the entrepreneur’s choice of tools and to select a destiny for the business different to the one favoured by the entrepreneur. The Modular Approach also responds to differences in the economic, social and legal circumstances of different countries. It does so by guiding national policymakers with respect to the factors relevant to determining the proper boundaries between ‘standard’ and MSME insolvency regimes, and by identifying three functions: management, administrative and judicial. The Approach explains the costs and benefits of assigning those functions to different entities

Dynamic clonal progression in xenografts of acute lymphoblastic leukemia with intrachromosomal amplification of chromosome 21

Intrachromosomal amplification of chromosome 21 is a heterogeneous chromosomal rearrangement occurring in 2% of childhood precursor B-cell acute lymphoblastic leukemia. There are no cell lines with iAMP21 and these abnormalities are too complex to faithfully engineer in animal models. As a resource for future functional and pre-clinical studies, we have created xenografts from intrachromosomal amplification of chromosome 21 leukemia patient blasts and characterised them by in-vivo and ex-vivo luminescent imaging, FLOW immunophenotyping, and histological and ultrastructural analysis of bone marrow and the central nervous system. Investigation of up to three generations of xenografts revealed phenotypic evolution, branching genomic architecture and, compared with other B-cell acute lymphoblastic leukemia genetic subtypes, greater clonal diversity of leukemia initiating cells. In support of intrachromosomal amplification of chromosome 21 as a primary genetic abnormality, it was always retained through generations of xenografts, although we also observed the first example of structural evolution of this rearrangement. Clonal segregation in xenografts revealed convergent evolution of different secondary genomic abnormalities implicating several known tumour suppressor genes and a region, containing the B-cell adaptor, PIK3AP1, and nuclear receptor co-repressor, LCOR, in the progression of B-ALL. Tracking of mutations in patients and derived xenografts provided evidence for co-operation between abnormalities activating the RAS pathway in B-ALL and for their aggressive clonal expansion in the xeno-environment. Bi-allelic loss of the CDKN2A/B locus was recurrently maintained or emergent in xenografts and also strongly selected as RNA sequencing demonstrated a complete absence of reads for genes associated with the deletions

Measurement of neutron detection efficiency between 22 and 174 MeV using two different kinds of Pb-scintillating fiber sampling calorimeters

We exposed a prototype of the lead-scintillating fiber KLOE calorimeter to neutron beam of 21, 46 and 174 MeV at The Svedberg Laboratory, Uppsala, to study its neutron detection efficiency. This has been found larger than what expected considering the scintillator thickness of the prototype. %To check our method, we measured also the neutron %detection efficiency of a 5 cm thick NE110 scintillator. We show preliminary measurement carried out with a different prototype with a larger lead/fiber ratio, which proves the relevance of passive material to neutron detection efficiency in this kind of calorimeters

Measurement of the neutron detection efficiency of a 80% absorber - 20% scintillating fibers calorimeter

The neutron detection efficiency of a sampling calorimeter made of 1 mm diameter scintillating fibers embedded in a lead/bismuth structure has been measured at the neutron beam of the The Svedberg Laboratory at Uppsala. A significant enhancement of the detection efficiency with respect to a bulk organic scintillator detector with the same thickness is observed.Comment: 10 pages, 7 figure

Characterization and Performance of PADME's Cherenkov-Based Small-Angle Calorimeter

The PADME experiment, at the Laboratori Nazionali di Frascati (LNF), in Italy, will search for invisible decays of the hypothetical dark photon via the process $e^+e^-\rightarrow \gamma A'$, where the $A'$ escapes detection. The dark photon mass range sensitivity in a first phase will be 1 to 24 MeV. We report here on measurement and simulation studies of the performance of the Small-Angle Calorimeter, a component of PADME's detector dedicated to rejecting 2- and 3-gamma backgrounds. The crucial requirement is a timing resolution of less than 200 ps, which is satisfied by the choice of PbF$_2$ crystals and the newly released Hamamatsu R13478UV photomultiplier tubes (PMTs). We find a timing resolution of 81 ps (with double-peak separation resolution of 1.8 ns) and a single-crystal energy resolution of 5.7%/$\sqrt{E}$ with light yield of 2.07 photo-electrons per MeV, using 100 to 400 MeV electrons at the Beam Test Facility of LNF. We also propose the investigation of a two-PMT solution coupled to a single PbF$_2$ crystal for higher-energy applications, which has potentially attractive features.Comment: 12 pages, 19 figures. v2: added section on radiation damage studie

First national intercomparison of solar ultraviolet radiometers in Italy

A blind intercomparison of ground-based ultraviolet (UV) instruments has been organized for the first time in Italy. The campaign was coordinated by the Environmental Protection Agency of Aosta Valley (ARPA Valle d'Aosta) and took place in Saint-Christophe (45.8 degrees N, 7.4 degrees E, 570 m a.s.l.), in the Alpine region, from 8 to 23 June 2010. It involved 8 institutions, 10 broadband radiometers, 2 filter radiometers and 2 spectroradiometers. Synchronized measurements of downward global solar UV irradiance at the ground were collected and the raw series were then individually processed by the respective operators on the base of their own procedures and calibration data. A radiative transfer model was successfully applied as an interpretative tool. The input parameters and output results are described in detail. The comparison was performed in terms of global solar UV Index and integrated UV-A irradiance against a well-calibrated double monochromator spectroradiometer as reference. An improved algorithm for comparing broadband data and spectra has been developed and is discussed in detail. For some instruments, we found average deviations ranging from -16% up to 20% relative to the reference and diurnal variations as large as 15% even in clear days. Remarkable deviations were found for the instruments calibrated in the manufacturers' facilities and never involved in field intercomparison. Finally, some recommendations to the UV operators based on the campaign results are proposed

The Mu2e undoped CsI crystal calorimeter

The Mu2e experiment at Fermilab will search for Charged Lepton Flavor Violating conversion of a muon to an electron in an atomic field. The Mu2e detector is composed of a tracker, an electromagnetic calorimeter and an external system, surrounding the solenoid, to veto cosmic rays. The calorimeter plays an important role to provide: a) excellent particle identification capabilities; b) a fast trigger filter; c) an easier tracker track reconstruction. Two disks, located downstream of the tracker, contain 674 pure CsI crystals each. Each crystal is read out by two arrays of UV-extended SiPMs. The choice of the crystals and SiPMs has been finalized after a thorough test campaign. A first small scale prototype consisting of 51 crystals and 102 SiPM arrays has been exposed to an electron beam at the BTF (Beam Test Facility) in Frascati. Although the readout electronics were not the final, results show that the current design is able to meet the timing and energy resolution required by the Mu2e experiment.Comment: 6 pages, 8 figures, proceedings of the "Calorimetry for the high energy frontier (CHEF17)" conference, 2-6 October 2017, Lyon, Franc

Quality Assurance on a custom SiPMs array for the Mu2e experiment

The Mu2e experiment at Fermilab will search for the coherent $\mu \to e$ conversion on aluminum atoms. The detector system consists of a straw tube tracker and a crystal calorimeter. A pre-production of 150 Silicon Photomultiplier arrays for the Mu2e calorimeter has been procured. A detailed quality assur- ance has been carried out on each SiPM for the determination of its own operation voltage, gain, dark current and PDE. The measurement of the mean-time-to-failure for a small random sample of the pro-production group has been also completed as well as the determination of the dark current increase as a function of the ioninizing and non-ioninizing dose.Comment: 4 pages, 10 figures, conference proceeding for NSS-MIC 201