A minimal-variable symplectic method for isospectral flows

Isospectral flows are abundant in mathematical physics; the rigid body, the the Toda lattice, the Brockett flow, the Heisenberg spin chain, and point vortex dynamics, to mention but a few. Their connection on the one hand with integrable systems and, on the other, with Lie--Poisson systems motivates the research for optimal numerical schemes to solve them. Several works about numerical methods to integrate isospectral flows have produced a large varieties of solutions to this problem. However, many of these algorithms are not intrinsically defined in the space where the equations take place and/or rely on computationally heavy transformations. In the literature, only few examples of numerical methods avoiding these issues are known, for instance, the \textit{spherical midpoint method} on \SO(3). In this paper we introduce a new minimal-variable, second order, numerical integrator for isospectral flows intrinsically defined on quadratic Lie algebras and symmetric matrices. The algorithm is isospectral for general isospectral flows and Lie--Poisson preserving when the isospectral flow is Hamiltonian. The simplicity of the scheme, together with its structure-preserving properties, makes it a competitive alternative to those already present in literature.Comment: 17 pages, 9 figure

I want to, but...

I want to see the concert, but I don’t want to take the long drive. Both of these desire ascriptions are true, even though I believe I’ll see the concert if and only if I take the drive.Yet they, and strongly conflicting desire ascriptions more generally, are predicted incompatible by the standard semantics, given two standard constraints. There are two proposed solutions. I argue that both face problems because they misunderstand how what we believe influences what we desire. I then sketch my own solution: a coarse-worlds semantics that captures the extent to which belief influences desire. My semantics models what I call some-things-considered desire. Considering what the concert would be like, but ignoring the drive, I want to see the concert; considering what the drive would be like, but ignoring the concert, I don’t want to take the drive

Anankastic conditionals are still a mystery

‘If you want to go to Harlem, you have to take the A train’ doesn’t look special. Yet a compositional account of its meaning, and the meaning of anankastic conditionals more generally, has proven an enigma. Semanticists have responded by assigning anankastics a unique status, distinguishing them from ordinary indicative conditionals. Condoravdi & Lauer (2016) maintain instead that “anankastic conditionals are just conditionals.” I argue that Condoravdi and Lauer don’t give a general solution to a well-known problem: the problem of conflicting goals. They rely on a special, “effective preference” interpretation for want on which an agent cannot want two things that conflict with her beliefs. A general solution, though, requires that the goals cannot conflict with the facts. Condoravdi and Lauer’s view fails. Yet they show, I believe, that previous accounts fail too. Anankastic conditionals are still a mystery

Financial Development, Entrepreneurship, and Job Satisfaction.

This paper shows that utility differences between the self-employed and employees increase with financial development. This effect is not explained by increased profits but by an increased value of non- monetary benefits, in particular job independence. We interpret these findings by building a simple occupational choice model in which financial constraints may impede the creation of firms and depress labor demand, thereby pushing some individuals into self-employment for lack of salaried jobs. In this setting, financial development favors a better matching between individual motivation and occupation, thereby increasing entrepreneurial utility despite increasing competition and so reducing profits.Financial development; job satisfaction; entrepreneurship;

Financial development, entrepreneurship and job satisfaction

This paper shows that utility differences between the self-employed and the employees increase with financial development. This effect is not explained by increased profits but by an increased value of non- monetary benefits, in particular job independence. We interpret these findings by building a simple occupational choice model in which financial constraints may impede firms' creation and depress labor demand, thereby pushing some individuals into self-employment for lack of salaried jobs. In this setting, financial development favors a better matching between individual motivation and occupation, thereby increasing entrepreneurial utility despite increasing competition and so reducing profits.financial development ; entrepreneurship ; job satisfaction

Credit Constraints, Entrepreneurial Talent, and Economic Development

In this paper, we formalize the view that economic development requires high rates of productive entrepreneurship, and this requires an efficient matching between entrepreneurial talent and production echnologies. We first explore the role of financial development in promoting such efficient allocation of talent, which results in higher production, job creation and social mobility. We then show how different levels of financial development may endogenously arise in a setting in which financial constraints depend on individual incentives to misbehave, these incentives depend on how many jobs are available, and this in turn depends on the level of financial development. Such complementarity between labour market and financial marketdevelopment may generate highly divergent development paths even for countries with very similar initialcredit constraints; allocation of entrepreneurial talent; productive and unproductive entrepreneurs; economic development

Immigration policy and self-selecting migrants

I build a simple theory of self-selection into migration and immigration policy formation. I show that any immigration policy affects immigrants skill composition, and this effect may drive the policy outcome in the receiving country. For example, restricting immigration when it is low skilled may worsen immigrants' self-selection and thus the receiving country skill distribution. Hence, understanding the migration decision becomes crucial for analyzing the political economy of immigration. By this composition effect, some natives may support further restrictions even though current immigrants are not harmful for them, and immigration restrictions may be optimal even in a purely utilitarian world.immigrant self-selection ; political economy of immigration ; immigration policy preferences

Immigration Policy and Self-Selecting Migrants

We explore the implications of migrants' self-selection for the determination of immigration policy in a simple model where incentives and resources to migrate vary with skills. We show how self-selection determines the response of potential migrants to immigration policy changes, which is crucial for predicting the effects of such policy in the receiving country. For example, restricting immigration when it is low skilled may worsen self-selection and thus the receiving country skill distribution. These selection effects may lead low skilled natives to support a more restrictive policy even though current immigrants are not harmful for them, and the receiving country government to impose significant restrictions even in a purely utilitarian world.Immigrant self-selection; immigration policy preferences; political economy of immigration.

Credit Constraints, Entrepreneurial Talent, and Economic Development

In this paper, we formalize the view that economic development requires high rates of productive entrepreneurship, and this requires an e¢ cient matching between entrepreneurial talent and production technologies. We …rst explore the role of …nancial development in promoting such e¢ cient allocation of talent, which results in higher production, job creation and social mobility. We then show how di¤er- ent levels of …nancial development may endogenously arise in a setting in which …nancial constraints depend on individual incentives to mis- behave, these incentives depend on how many jobs are available, and this in turn depends on the level of …nancial development. Such com- plementarity between labor market and …nancial market development may generate highly divergent development paths even for countries with very similar initial conditions.Credit constraints, allocation of entrepreneurial talent, productive and unproductive entrepreneurs, economic development.