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The cones of nonnegative polynomials and sums of squares arise as central objects in convex algebraic geometry and have their origin in the seminal work of Hilbert ([Hil88]). Depending on the number of variables n and the degree d of the polynomials, Hilbert famously characterizes all cases of equality between the cone of nonnegative polynomials and the cone of sums of squares. This equality precisely holds for bivariate forms, quadratic forms and ternary quartics ([Hil88]). Since then, a lot of work has been done in understanding the difference between these two cones, which has major consequences for many practical applications such as for polynomial optimization problems. Roughly speaking, minimizing polynomial functions (constrained as well as unconstrained) can be done efficiently whenever certain nonnegative polynomials can be written as sums of squares (see Section 2.3 for the precise relationship). The underlying reason is the fundamental difference that checking nonnegativity of polynomials is an NP-hard problem whenever the degree is greater or equal than four ([BCSS98]), whereas checking whether a polynomial can be written as a sum of squares is a semidefinite feasibility problem (see Section 2.2). Although the complexity status of the semidefinite feasibility problem is still an open problem, it is polynomial for fixed number of variables. Hence, understanding the difference between nonnegative polynomials and sums of squares is highly desirable both from a theoretical and a practical viewpoint.
Trust in policy makers fluctuates signi
cantly over the cycle and affects the transmission mechanism. Despite this it is absent from the literature. We build a monetary model embedding trust cycles; the latter emerge as an equilibrium phenomenon of a game-theoretic interaction between atomistic agents and the monetary authority. Trust affects agents' stochastic discount factors, namely the price of future risk, and through this it interacts with the monetary transmission mechanism. Using data from the Eurobarometer surveys, we analyze the link between trust and the transmission mechanism of macro and monetary shocks: Empirical results are in line with theoretical ones.
We document and study international differences in both ownership and holdings of stocks, private businesses, homes, and mortgages among households aged fifty or more in thirteen countries, using new and comparable survey data. We employ counterfactual techniques to decompose observed differences across the Atlantic, within the US, and within Europe into those arising from differences in population characteristics and differences in economic environments. We then correlate the latter differences to country-level indicators. Ownership across the range of the assets considered tends to be more widespread among US households. We document that shortly prior to the current crisis, US households tended to invest larger amounts in stocks and smaller ones in homes, and to have larger mortgages in older age, even controlling for characteristics. This is consistent with the high prevalence of negative equity associated with the current crisis. More generally, we find that differences in household characteristics often play a small role, while differences in economic environments tend to explain most of the observed differences in ownership rates and in amounts held. The latter differences are much more pronounced among European countries than among US regions, suggesting further potential for harmonization of policies and institutions.
Regulation of investor access to financial products is often based on product familiarity indicated by previous use. The underlying premise that lack of familiarity with a product class causes unwarranted participation is difficult to test. This paper uses household-level data from the ‘experiment’ of German reunification that (exogenously) offered to East Germans access to capitalist products (exogenously) unfamiliar to them. We compare the evolution of post-unification participation of former East and West Germans in financial products, controlling for relevant household characteristics. We vary familiarity differentials by considering (i) both unfamiliar ‘capitalist’ products (stocks, bonds, and consumer credit) and ones available in the East (savings accounts and life insurance); and (ii) cohorts with different exposure to capitalism. We find that East Germans participated immediately in unfamiliar risky securities, at rates comparable to West Germans of similar characteristics. They phased out disproportionate participation in previously familiar assets as familiarity with capitalist products grew. They were more likely to use consumer debt, partly to catch up with richer new peers. We find no signs of abrupt participation drops that could suggest mistakes or regret related to lack of familiarity.
In this paper we investigate the implications of providing loan officers with a compensation structure that rewards loan volume and penalizes poor performance versus a fixed wage unrelated to performance. We study detailed transaction information for more than 45,000 loans issued by 240 loan officers of a large commercial bank in Europe. We examine the three main activities that loan officers perform: monitoring, originating, and screening. We find that when the performance of their portfolio deteriorates, loan officers increase their effort to monitor existing borrowers, reduce loan origination, and approve a higher fraction of loan applications. These loans, however, are of above-average quality. Consistent with the theoretical literature on multitasking in incomplete contracts, we show that loan officers neglect activities that are not directly rewarded under the contract, but are in the interest of the bank. In addition, while the response by loan officers constitutes a rational response to a time allocation problem, their reaction to incentives appears myopic in other dimensions.
Euro area data show a positive connection between sovereign and bank risk, which increases with banks’ and sovereign long run fragility. We build a macro model with banks subject to moral hazard and liquidity risk (sudden deposit withdrawals): banks invest in risky government bonds as a form of capital buffer against liquidity risk. The model can replicate the positive connection between sovereign and bank risk observed in the data. Central bank liquidity policy, through full allotment policy, is successful in stabilizing the spiraling feedback loops between bank and sovereign risk.
We study the dispersion of debt maturities across time, which we call "granularity of corporate debt,'' using a model in which a firm's inability to roll over expiring debt causes inefficiencies, such as costly asset sales or underinvestment. Since multiple small asset sales are less costly than a single large one, firms diversify debt rollovers across maturity dates. We construct granularity measures using data on corporate bond issuers for the 1991-2012 period and establish a number of novel findings. First, there is substantial variation in granularity in that we observe both very concentrated and highly dispersed maturity structures. Second, observed variation in granularity supports the model's predictions, i.e. maturities are more dispersed for larger and more mature firms, for firms with better investment oppo
Juvenile neuronal ceroid lipofuscinosis (JNCL) is caused by mutations in the CLN3 gene, which encodes for a putative lysosomal transmembrane protein with thus far undescribed structure and function. Here we investigate the membrane topology of human CLN3 protein with a combination of advanced molecular cloning, spectroscopy, and in silico computation. Using the transposomics cloning method we first created a library of human CLN3 cDNA clones either with a randomly inserted eGFP, a myc-tag, or both. The functionality of the clones was evaluated by assessing their ability to revert a previously reported lysosomal phenotype in immortalized cerebellar granular cells derived from Cln3Δex7/8 mice (CbCln3Δex7/8). The double-tagged clones were expressed in HeLa cells, and FRET was measured between the donor eGFP and an acceptor DyLight547 coupled to a monoclonal α-myc antibody to assess their relative membrane orientation. The data were used together with previously reported experimental data to compile a constrained membrane topology model for hCLN3 using TOPCONS consensus membrane prediction algorithm. Our model with six transmembrane domains and cytosolic N- and C-termini largely agrees with those previously suggested but differs in terms of the transmembrane domain positions as well as in the size of the luminal loops. This finding improves understanding the function of the native hCLN3 protein.
High-throughput metabarcoding studies on fungi and other eukaryotic microorganisms are rapidly becoming more frequent and more complex, requiring researchers to handle ever increasing amounts of raw sequence data. Here, we provide a flexible pipeline for pruning and analyzing fungal barcode (ITS rDNA) data generated as paired-end reads on Illumina MiSeq sequencers. The pipeline presented includes specific steps fine-tuned for ITS, that are mostly missing from pipelines developed for prokaryotes. It (1) employs state of the art programs and follows best practices in fungal high-throughput metabarcoding; (2) consists of modules and scripts easily modifiable by the user to ensure maximum flexibility with regard to specific needs of a project or future methodological developments; and (3) is straightforward to use, also in classroom settings. We provide detailed descriptions and revision techniques for each step, thus giving the user maximum control over data treatment and avoiding a black-box approach. Employing this pipeline will improve and speed up the tedious and error-prone process of cleaning fungal Illumina metabarcoding data.
Guanine quadruplex (G-quadruplex) motifs in the 5′ untranslated region (5′-UTR) of mRNAs were recently shown to influence the efficiency of translation. In the present study, we investigate the interaction between cellular proteins and the G-quadruplexes located in two mRNAs (MMP16 and ARPC2). Formation of the G-quadruplexes was confirmed by biophysical characterization and the inhibitory activity on translation was shown by luciferase reporter assays. In experiments with whole cell extracts from different eukaryotic cell lines, G-quadruplex-binding proteins were isolated by pull-down assays and subsequently identified by matrix-assisted laser desorption ionization-time of flight mass spectrometry. The binding partners of the RNA G-quadruplexes we discovered included several heterogenous nuclear ribonucleoproteins, ribosomal proteins, and splicing factors, as well as other proteins that have previously not been described to interact with nucleic acids. While most of the proteins were specific for either of the investigated G-quadruplexes, some of them bound to both motifs. Selected candidate proteins were subsequently produced by recombinant expression and dissociation constants for the interaction between the proteins and RNA G-quadruplexes in the low nanomolar range were determined by surface plasmon resonance spectroscopy. The present study may thus help to increase our understanding of the mechanisms by which G-quadruplexes regulate translation.