Semi-basic 1-forms and Helmholtz conditions for the inverse problem of the calculus of variations

We use Fr\"olicher-Nijenhuis theory to obtain global Helmholtz conditions, expressed in terms of a semi-basic 1-form, that characterize when a semispray is locally Lagrangian. We also discuss the relation between these Helmholtz conditions and their classic formulation written using a multiplier matrix. When the semi-basic 1-form is 1-homogeneous (0-homogeneous) we show that two (one) of the Helmholtz conditions are consequences of the other ones. These two special cases correspond to two inverse problems in the calculus of variation: Finsler metrizability for a spray, and projective metrizability for a spray

Descending maps between slashed tangent bundles

Suppose $TM\setminus \{0\}$ and $T\widetilde M\setminus\{0\}$ are slashed tangent bundles of two smooth manifolds $M$ and $\widetilde M$, respectively. In this paper we characterize those diffeomorphisms $F\colon TM\setminus\{0\} \to T\widetilde M\setminus\{0\}$ that can be written as $F = (D\phi)|_{TM\setminus\{0\}}$ for a diffeomorphism \phi\colon M\to \wt M. When $F = (D\phi)|_{TM\setminus\{0\}}$ one say that $F$ \emph{descends}. If $M$ is equipped with two sprays, we use the characterization to derive sufficient conditions that imply that $F$ descends to a totally geodesic map. Specializing to Riemann geometry we also obtain sufficient conditions for $F$ to descent to an isometry

Aperiodic nano-photonic design

The photon scattering properties of aperiodic nano-scale dielectric structures can be tailored to closely match a desired response by using adaptive algorithms for device design. We show that broken symmetry of aperiodic designs provides access to device functions not available to conventional periodic photonic crystal structures.Comment: 23 pages, LaTex, 8 postscript figure

Hedge funds are heavily involved in the distressed debt market

Konstantinos (Kostas) E. Zachariadis and Ioan F. Olaru explain how this can affect the outcome of debt restructuring

Machine Learning Solvation Environments in Conductive Polymers: Application to ProDOT-2Hex with Solvent Swelling

Automated identification and classification of ion solvation sites in diverse chemical systems will improve the understanding and design of polymer electrolytes for battery applications. We introduce a machine learning approach to classify and characterize ion solvation environments based on feature vectors extracted from all-atom simulations. This approach is demonstrated in poly(3,4-propylenedioxythiophene), which is a promising candidate polymer binder for Li-ion batteries. In the dry polymer, four distinct Li⁺ solvation environments are identified close to the backbone of the polymer. Upon swelling of the polymer with propylene carbonate solvent, the nature of Li⁺ solvation changes dramatically, featuring a rapid diversification of solvation environments. This application of machine learning can be generalized to other polymer condensed-phase systems to elucidate the molecular mechanisms underlying ion solvation

Augmentation of Brain Function: Facts, Fiction and Controversy. Volume III: From Clinical Applications to Ethical Issues and Futuristic Ideas

The final volume in this tripartite series on Brain Augmentation is entitled “From Clinical Applications to Ethical Issues and Futuristic Ideas”. Many of the articles within this volume deal with translational efforts taking the results of experiments on laboratory animals and applying them to humans. In many cases, these interventions are intended to help people with disabilities in such a way so as to either restore or extend brain function. Traditionally, therapies in brain augmentation have included electrical and pharmacological techniques. In contrast, some of the techniques discussed in this volume add specificity by targeting select neural populations. This approach opens the door to where and how to promote the best interventions. Along the way, results have empowered the medical profession by expanding their understanding of brain function. Articles in this volume relate novel clinical solutions for a host of neurological and psychiatric conditions such as stroke, Parkinson’s disease, Huntington’s disease, epilepsy, dementia, Alzheimer’s disease, autism spectrum disorders (ASD), traumatic brain injury, and disorders of consciousness. In disease, symptoms and signs denote a departure from normal function. Brain augmentation has now been used to target both the core symptoms that provide specificity in the diagnosis of a disease, as well as other constitutional symptoms that may greatly handicap the individual. The volume provides a report on the use of repetitive transcranial magnetic stimulation (rTMS) in ASD with reported improvements of core deficits (i.e., executive functions). TMS in this regard departs from the present-day trend towards symptomatic treatment that leaves unaltered the root cause of the condition. In diseases, such as schizophrenia, brain augmentation approaches hold promise to avoid lengthy pharmacological interventions that are usually riddled with side effects or those with limiting returns as in the case of Parkinson’s disease. Brain stimulation can also be used to treat auditory verbal hallucination, visuospatial (hemispatial) neglect, and pain in patients suffering from multiple sclerosis. The brain acts as a telecommunication transceiver wherein different bandwidth of frequencies (brainwave oscillations) transmit information. Their baseline levels correlate with certain behavioral states. The proper integration of brain oscillations provides for the phenomenon of binding and central coherence. Brain augmentation may foster the normalization of brain oscillations in nervous system disorders. These techniques hold the promise of being applied remotely (under the supervision of medical personnel), thus overcoming the obstacle of travel in order to obtain healthcare. At present, traditional thinking would argue the possibility of synergism among different modalities of brain augmentation as a way of increasing their overall effectiveness and improving therapeutic selectivity. Thinking outside of the box would also provide for the implementation of brain-to-brain interfaces where techniques, proper to artificial intelligence, could allow us to surpass the limits of natural selection or enable communications between several individual brains sharing memories, or even a global brain capable of self-organization. Not all brains are created equal. Brain stimulation studies suggest large individual variability in response that may affect overall recovery/treatment, or modify desired effects of a given intervention. The subject’s age, gender, hormonal levels may affect an individual’s cortical excitability. In addition, this volume discusses the role of social interactions in the operations of augmenting technologies. Finally, augmenting methods could be applied to modulate consciousness, even though its neural mechanisms are poorly understood. Finally, this volume should be taken as a debate on social, moral and ethical issues on neurotechnologies. Brain enhancement may transform the individual into someone or something else. These techniques bypass the usual routes of accommodation to environmental exigencies that exalted our personal fortitude: learning, exercising, and diet. This will allow humans to preselect desired characteristics and realize consequent rewards without having to overcome adversity through more laborious means. The concern is that humans may be playing God, and the possibility of an expanding gap in social equity where brain enhancements may be selectively available to the wealthier individuals. These issues are discussed by a number of articles in this volume. Also discussed are the relationship between the diminishment and enhancement following the application of brain-augmenting technologies, the problem of “mind control” with BMI technologies, free will the duty to use cognitive enhancers in high-responsibility professions, determining the population of people in need of brain enhancement, informed public policy, cognitive biases, and the hype caused by the development of brain- augmenting approaches