Manifold Paths Research Articles

Specular Manifold Bisection Sampling for Caustics Rendering

AbstractWe propose Specular Manifold Bisection Sampling (SMBS), an improved version of Specular Manifold Sampling (SMS) [ZGJ20]. SMBS is inspired by the small and large mutations in Metropolis Light Transport (MLT) [VG97]. While the Jacobian Matrix of the original SMS method performs well in local convergence (the small mutation), it might fail to find a valid manifold path when the ray deviates too much from the light or bounces from a complex surface. Our proposed SMBS method adds a large mutation step to avoid such a problematic convergence to the local minimum. The results show SMBS can find valid manifold paths in fewer iterations and also find more valid manifold paths. In scenes with complex reflective or refractive surfaces, our method achieves nearly twice or more improvement when measured in manifold walk success rate (SR) and root mean square error (RMSE).

A Path Integral Formalism for Non-equilibrium Hamiltonian Statistical Systems

A path integral formalism for non-equilibrium systems is proposed based on a manifold of quasi-equilibrium densities. A generalized Boltzmann principle is used to weight manifold paths with the exponential of minus the information discrepancy of a particular manifold path with respect to full Liouvillean evolution. The likelihood of a manifold member at a particular time is termed a consistency distribution and is analogous to a quantum wavefunction. The Lagrangian here is of modified generalized Onsager-Machlup form. For large times and long slow timescales the thermodynamics is of Oettinger form. The proposed path integral has connections with those occuring in the quantum theory of a particle in an external electromagnetic field. It is however entirely of a Wiener form and so practical to compute. Finally it is shown that providing certain reasonable conditions are met then there exists a unique steady-state consistency distribution.

Membrane proteins in microglia and exposure to cholesterol: manifold paths of influence

Membrane proteins in microglia and exposure to cholesterol: manifold paths of influence

Caveat emptor: limitations of the automated reconstruction of metabolic pathways in Plasmodium

The functional reconstruction of metabolic pathways from an annotated genome is a tedious and demanding enterprise. Automation of this endeavor using bioinformatics algorithms could cope with the ever-increasing number of sequenced genomes and accelerate the process. Here, the manual reconstruction of metabolic pathways in the functional genomic database of Plasmodium falciparum--Malaria Parasite Metabolic Pathways--is described and compared with pathways generated automatically as they appear in PlasmoCyc, metaSHARK and the Kyoto Encyclopedia for Genes and Genomes. A critical evaluation of this comparison discloses that the automatic reconstruction of pathways generates manifold paths that need an expert manual verification to accept some and reject most others based on manually curated gene annotation.

Hybridization produces novelty when the mapping of form to function is many to one

BackgroundEvolutionary biologists want to explain the origin of novel features and functions. Two recent but separate lines of research address this question. The first describes one possible outcome of hybridization, called transgressive segregation, where hybrid offspring exhibit trait distributions outside of the parental range. The second considers the explicit mapping of form to function and illustrates manifold paths to similar function (called many to one mapping, MTOM) when the relationship between the two is complex. Under this scenario, functional novelty may be a product of the number of ways to elicit a functional outcome (i.e., the degree of MTOM). We fuse these research themes by considering the influence of MTOM on the production of transgressive jaw biomechanics in simulated hybrids between Lake Malawi cichlid species.ResultsWe characterized the component links and functional output (kinematic transmission, KT) of the 4-bar mechanism in the oral jaws of Lake Malawi cichlids. We demonstrated that the input and output links, the length of the lower jaw and the length of the maxilla respectively, have consistent but opposing relationships with KT. Based on these data, we predicted scenarios in which species with different morphologies but similar KT (MTOM species) would produce transgressive function in hybrids. We used a simple but realistic genetic model to show that transgressive function is a likely outcome of hybridization among Malawi species exhibiting MTOM. Notably, F2 hybrids are transgressive for function (KT), but not the component links that contribute to function. In our model, transgression is a consequence of recombination and assortment among alleles specifying the lengths of the lower jaw and maxilla.ConclusionWe have described a general and likely pervasive mechanism that generates functional novelty. Simulations of hybrid offspring among Lake Malawi cichlids exhibiting MTOM produce transgressive function in the majority of cases, and at appreciable frequency. Functional transgression (i) is a product of recombination and assortment between alleles controlling the lengths of the lower jaw and the maxilla, (ii) occurs in the absence of transgressive morphology, and (iii) can be predicted from the morphology of parents. Our genetic model can be tested by breeding Malawi cichlid hybrids in the laboratory and examining the resulting range of forms and functions.

Reparametrization of paths in manifolds

We discuss some aspects of the construction of the principal fiber bundleEiI→EiI/Aut(I), whereEiI is the space of free and injective paths in an arbitrary topological spaceE, and Aut(I) is the group of automorphisms of the interval. The connection with quantum mechanics in the path integral formalism is presented, and it is qualitatively shown the naturalness of the ghost fields.

The image of man in psychotherapy

Ernst Kretschmer, the pioneer in the study of the relationship between body structure and character, in a letter to Karen Horney in which he invited her to join the editorial board of the Zeitschrift fur Psychotherapie, wrote: "Your ideas are in full agreement with my own views on psychotherapy which you know from my book Psychotherapeutische Studien. I wholly sympathize not only with your broadminded, undogmatic view of the manifold paths of psychotherapy--so rarely found today--but also particularly with such concepts as "'curative psychic forces," and "self-realization." Ernst Kretschmer is professor of psychiatry and director of the Neuropsychiatric Department of Ti~bingen University, He is president of the Allgemeine Aerztliche Gesellschaft ffir Psychotherapie. Among his numerous books are Der sensitive Beziehungswahn, KOrperbau und Character (Body Structure and Character), Medizinische Psychologie, Geniale Menschen (The Personality of Men of Genius), and Hysterie, Reflex und Instinkt, Psychotherapeutische Studien. The following article, chapter 8 of Dr. Kretschmer's Psychotherapeutische Studien, is published here with the kind permission of the author and the publisher, Georg Thieme Verlag, Stuttgart. It was translated by Heinz and Ruth Norden.