Action minimizing orbits in the n-body problem with simple choreography constraint

In 1999 Chenciner and Montgomery found a remarkably simple choreographic motion for the planar 3-body problem (see \cite{CM}). In this solution 3 equal masses travel on a eight shaped planar curve; this orbit is obtained minimizing the action integral on the set of simple planar choreographies with some special symmetry constraints. In this work our aim is to study the problem of $n$ masses moving in \RR^d under an attractive force generated by a potential of the kind $1/r^\alpha$, $\alpha >0$, with the only constraint to be a simple choreography: if $q_1(t),...,q_n(t)$ are the $n$ orbits then we impose the existence of x \in H^1_{2 \pi}(\RR,\RR^d) such that q_i(t)=x(t+(i-1) \tau), i=1,...,n, t \in \RR, where $\tau = 2\pi / n$. In this setting, we first prove that for every d,n \in \NN and $\alpha>0$, the lagrangian action attains its absolute minimum on the planar circle. Next we deal with the problem in a rotating frame and we show a reacher phenomenology: indeed while for some values of the angular velocity minimizers are still circles, for others the minima of the action are not anymore rigid motions.Comment: 24 pages; 4 figures; submitted to Nonlinearit

Financial Crisis and New Dimensions of Liquidity Risk: Rethinking Prudential Regulation and Supervision

This paper aims to stress the importance of market liquidity for the stability of the financial system, emphasizing the pivotal role played by liquidity risk in the development of the current financial crisis, pointing out the flaws of regulation and supervision and stressing the need for their reform. We first investigate the evolution of the concept of liquidity and the nexus between the transformations of financial systems and their increased vulnerability to liquidity risks. Then we focus on the causes of the emergence of liquidity risk in the ongoing financial crisis. We point out two intertwined processes: firstly, the huge increase in financial assets stemming from the shift to an \u201coriginate-to-distribute\u201d intermediation model; secondly, the growth of a parallel financial circuit. After this, we focus on the main lessons for regulation and supervision: first of all we address the case for adjustments to or reform of Basel 2 in view of the nexus between solvency and liquidity. Further crucial points relate to market liquidity and OTC markets, scale and scope of LLR function, architecture of supervisory authorities and perimeter of controls. Finally we stress the need for harmonization, or at least coordination, of national liquidity regimes, at least for cross-border group

Birds of a feather flock together and get money from the crowd

In constructing online alternative finance instruments as a new form of financial democratization and financial inclusion, this article aims at verifying the presence of similarity effect in equity crowdfunding investments. Discussion focuses on ethnic and gender similarity between the seekers and investors that sustained the project. Our analysis is based on 5,996 personal investors that have participated in 81 equity crowdfunding campaigns, on Crowdcube, a British equity crowdfunding platform from 2011 and 2016. Results show that in equity crowdfunding gender and ethnic similarities play different role based on investors’ characteristics - gender, ethnicity and the combination of two. In particular, ethnic similarity positively influence the level of amount invested by both female and male investors belonging to an ethnic minority. Even if female investors tend to prefer male company, their preference changes if a female proponent belonging to an ethnic minority runs the company. From a practical perspective, our findings shed new light on how individual characteristics can be important factor in financing situations. Results allow entrepreneurs and equity crowdfunding platforms to understand better potential investor behaviour and highlights the role of equity crowdfunding as tool for minorities’ financial inclusion and women entrepreneur empowerment

How did COVID-19 affect medical and cardiology journals? A pandemic in literature

BACKGROUND AND AIMS: The spreading speed of the COVID-19 pandemic forced the medical community to produce efforts in updating and sharing the evidence about this new disease, trying to preserve the accuracy of the data but at the same time avoiding the potentially harmful delay from discovery to implementation. The aim of our analysis was to assess the impact of the COVID-19 pandemic on medical literature in terms of proportion of COVID-19-related published papers and temporal patterns of publications within a sample of general/internal medicine and cardiology journals. METHODS: We searched through PubMed scientific papers published from 1 January 2020 to 31 January 2021 about COVID-19 in ten major medical journals, of which five were in general/internal medicine and five in the cardiology field. We analyzed the proportion of COVID-19-related papers, and we examined temporal trends in the number of published papers. RESULTS: Overall, the proportion of COVID-19-related papers was 18.5% (1986/10 756). This proportion was higher among the five selected general/internal medicine journals, compared with cardiology journals (23.8% vs 9.5%). The vast majority of papers were not original articles; in particular, in cardiology journals, there were 28% 'original articles', 17% 'review articles' and 55.1% 'miscellaneous', compared with 20.2%, 5.1% and 74.7% in general/internal medicine journals, respectively. CONCLUSIONS: Our analysis highlights the big impact of the COVID-19 pandemic on international scientific literature. General and internal medicine journals were mainly involved, with cardiology journals only at a later time

Exploring Network-Related Optimization Problems Using Quantum Heuristics

Network-related connectivity optimization problems are underlying a wide range of applications and are also of high computational complexity. We consider studying network optimization problems using two types of quantum heuristics.One is quantum annealing, and the other Quantum Alternating Operator Ansatz, an extension of the Quantum Approximate Optimization Algorithms for gate-model quantum computation, in which a cost-function based unitary and a non-commuting mixing unitary are applied alternately. We present problem mappings for problems of finding the spanning-tree or spanning-graph of a graph that optimizes certain costs, and a variant that further requires the spanning-tree be degree-bounded. With quantum annealing, all constraints are cast into penalty terms in the cost Hamiltonian, and the solution is encoded as the ground state of the Hamiltonian. We provide three mappings to the quadratic unconstrained binary optimization (QUBO) form, compare the resource requirements, and analyze the tradeoffs. For QAOA, we give special focus on the design of mixers based on the constraints presented in the problem, such that the system evolution remains in a subspace of the full Hilbert space where all constraints are satisfied. In the spanning-tree problem, one such hard constraint is that a mixer applied to a spanning-tree needs also be a spanning tree. This involves checking the connectivity of a subgraph, which is a global condition common for most network-related problems. We show how this feature can be efficiently represented in the mixer in a quantum coherent way, based on manipulation of a descendant-matrix and an adjacent matrix. We further develop a mixer for the spanning-graphs based on the spanning-tree mixer