A class of well-posed parabolic final value problems

This paper focuses on parabolic final value problems, and well-posedness is proved for a large class of these. The clarification is obtained from Hilbert spaces that characterise data that give existence, uniqueness and stability of the solutions. The data space is the graph normed domain of an unbounded operator that maps final states to the corresponding initial states. It induces a new compatibility condition, depending crucially on the fact that analytic semigroups always are invertible in the class of closed operators. Lax--Milgram operators in vector distribution spaces constitute the main framework. The final value heat conduction problem on a smooth open set is also proved to be well posed, and non-zero Dirichlet data are shown to require an extended compatibility condition obtained by adding an improper Bochner integral.Comment: 16 pages. To appear in "Applied and numerical harmonic analysis"; a reference update. Conference contribution, based on arXiv:1707.02136, with some further development

Spin-dynamic field coupling in strongly THz driven semiconductors : local inversion symmetry breaking

We study theoretically the optics in undoped direct gap semiconductors which are strongly driven in the THz regime. We calculate the optical sideband generation due to nonlinear mixing of the THz field and the near infrared probe. Starting with an inversion symmetric microscopic Hamiltonian we include the THz field nonperturbatively using non-equilibrium Green function techniques. We find that a self induced relativistic spin-THz field coupling locally breaks the inversion symmetry, resulting in the formation of odd sidebands which otherwise are absent.Comment: 8 pages, 6 figure

Selective cooling of the brain in reindeer

Selective cooling of the brain during hyper-thermia has been demonstrated in several species of mammals (Baker 1979, 1982). Such cooling is achieved by heat exchange between the cooled venous blood returning from the nasal mucosa and the warmer arterial blood entering the brain via the carotid rete. Spot measurements of brain temperature (Tbr) and carotid blood temperature (TCar) were made within 1 min. of death in 40 wild reindeer (Rangifer tarandus tarandus). At Tear lower than 40.5°C Tbr was higher than T c a r. With increasing Tear above 40.5°C Tbr remained at approxima-tely 40.5°C, indicating that selective cooling of the brain had occurred

Overvåking av forurensningssituasjonen i indre Oslofjord 1997

Vannkvaliteten i fjordens overflatelag sommeren 1997 var omtrent like bra som i 1996, som var et meget bra år sammenlignet med 1994 og 1995, hvor overløp og flom (1995) preget forholdene. Den milde vinteren var lite gunstig for dypvannsfornyelsen og det var meget liten vannfornyelse i Bunnefjorden. Det ble allikevel registrert oksygen i dypvannet selv om konsentrasjonene ble meget lave på høsten og klart lavere enn gjennomsnittlige forhold i perioden før det siste store anlegget med kjemisk rensing ble startet i 1982. I Vestfjorden var oksygenforholdene om høsten noe bedre. I Drøbaksundet ble det observert lave oksygenkonsentrasjoner sammenlignet med tidligere observasjoner, selv om nivået, som vanlig, var betydelig høyere enn i indre Oslofjord. Årsaken til de relativt lave oksygenkonsentrasjonene var en ekstra lang stagnasjonperiode. Observasjonene i 1997 bekrefter tidligere trender i fjordens forurensningsutvikling. Vannkvaliteten i overflatelaget har blitt bedre etter gjennomførte rensetiltak og det har vært en liten men positiv utvikling i dypvannet i Vestfjorden, men ikke i Bunnefjorden. På mellomdyp i Vestfjorden er det fortsatt ofte registrert dårligere oksygenforhold. De observerte forandringer skyldes ikke bare rensetiltak men også variasjoner i dypvannsfornyelser og andre klimaavhengige variasjoner

Affective Flexibility: Evaluative Processing Goals Shape Amygdala Activity

Although early research implicated the amygdala in automatic processing of negative information, more recent research suggests that it plays a more general role in processing the motivational relevance of various stimuli, suggesting that the relation between valence and amygdala activation may depend on contextual goals. This study provides experimental evidence that the relation between valence and amygdala activity is dynamically modulated by evaluative goals. During functional magnetic resonance imaging, participants evaluated the positive, negative, or overall (positive plus negative) aspects of famous people. When participants were providing overall evaluations, both positive and negative names were associated with amygdala activation. When they were evaluating positivity, positive names were associated with amygdala activity, and when they were evaluating negativity, negative names were associated with amygdala activity. Evidence for a negativity bias was found; modulation was more pronounced for positive than for negative information. These data suggest that the amygdala flexibly processes motivationally relevant evaluative information in accordance with current processing goals, but processes negative information less flexibly than positive information

Manifold Contrastive Learning with Variational Lie Group Operators

Self-supervised learning of deep neural networks has become a prevalent paradigm for learning representations that transfer to a variety of downstream tasks. Similar to proposed models of the ventral stream of biological vision, it is observed that these networks lead to a separation of category manifolds in the representations of the penultimate layer. Although this observation matches the manifold hypothesis of representation learning, current self-supervised approaches are limited in their ability to explicitly model this manifold. Indeed, current approaches often only apply augmentations from a pre-specified set of "positive pairs" during learning. In this work, we propose a contrastive learning approach that directly models the latent manifold using Lie group operators parameterized by coefficients with a sparsity-promoting prior. A variational distribution over these coefficients provides a generative model of the manifold, with samples which provide feature augmentations applicable both during contrastive training and downstream tasks. Additionally, learned coefficient distributions provide a quantification of which transformations are most likely at each point on the manifold while preserving identity. We demonstrate benefits in self-supervised benchmarks for image datasets, as well as a downstream semi-supervised task. In the former case, we demonstrate that the proposed methods can effectively apply manifold feature augmentations and improve learning both with and without a projection head. In the latter case, we demonstrate that feature augmentations sampled from learned Lie group operators can improve classification performance when using few labels

Excitonic Dynamical Franz-Keldysh Effect

The Dynamical Franz-Keldysh Effect is exposed by exploring near-bandgap absorption in the presence of intense THz electric fields. It bridges the gap between the DC Franz- Keldysh effect and multi-photon absorption and competes with the THz AC Stark Effect in shifting the energy of the excitonic resonance. A theoretical model which includes the strong THz field non-perturbatively via a non-equilibrium Green Functions technique is able to describe the Dynamical Franz-Keldysh Effect in the presence of excitonic absorption.Comment: 4 pages in revtex with 5 figures included using epsf. Submitted to Physical Review Letter

No alignment of cattle along geomagnetic field lines found

This paper presents a study of the body orientation of domestic cattle on free pastures in several European states, based on Google satellite photographs. In sum, 232 herds with 3412 individuals were evaluated. Two independent groups participated in our study and came to the same conclusion that, in contradiction to the recent findings of other researchers, no alignment of the animals and of their herds along geomagnetic field lines could be found. Several possible reasons for this discrepancy should be taken into account: poor quality of Google satellite photographs, difficulties in determining the body axis, selection of herds or animals within herds, lack of blinding in the evaluation, possible subconscious bias, and, most importantly, high sensitivity of the calculated main directions of the Rayleigh vectors to some kind of bias or to some overlooked or ignored confounder. This factor could easily have led to an unsubstantiated positive conclusion about the existence of magnetoreception.Comment: Added electronic supplement with source dat