Solving Non-homogeneous Nested Recursions Using Trees

The solutions to certain nested recursions, such as Conolly's C(n) = C(n-C(n-1))+C(n-1-C(n-2)), with initial conditions C(1)=1, C(2)=2, have a well-established combinatorial interpretation in terms of counting leaves in an infinite binary tree. This tree-based interpretation, which has a natural generalization to a k-term nested recursion of this type, only applies to homogeneous recursions, and only solves each recursion for one set of initial conditions determined by the tree. In this paper, we extend the tree-based interpretation to solve a non-homogeneous version of the k-term recursion that includes a constant term. To do so we introduce a tree-grafting methodology that inserts copies of a finite tree into the infinite k-ary tree associated with the solution of the corresponding homogeneous k-term recursion. This technique can also be used to solve the given non-homogeneous recursion with various sets of initial conditions.Comment: 14 page

Peripheral and central neuroplasticity in a mouse model of endometriosis

OnlinePublChronic pelvic pain (CPP) is the most debilitating symptom of gynaecological disorders such as endometriosis. However, it remains unclear how sensory neurons from pelvic organs affected by endometriosis, such as the female reproductive tract, detect and transmit nociceptive events and how these signals are processed within the central nervous system (CNS). Using a previously characterized mouse model of endometriosis, we investigated whether the increased pain sensitivity occurring in endometriosis could be attributed to (i) changes in mechanosensory properties of sensory afferents innervating the reproductive tract, (ii) alterations in sensory input from reproductive organs to the spinal cord or (iii) neuroinflammation and sensitization of spinal neural circuits. Mechanosensitivity of vagina-innervating primary afferents was examined using an ex vivo single-unit extracellular recording preparation. Nociceptive signalling from the vagina to the spinal cord was quantified by phosphorylated MAP kinase ERK1/2 immunoreactivity. Immunohistochemistry was used to determine glial and neuronal circuit alterations within the spinal cord. We found that sensory afferents innervating the rostral, but not caudal portions of the mouse vagina, developed mechanical hypersensitivity in endometriosis. Nociceptive signalling from the vagina to the spinal cord was significantly enhanced in mice with endometriosis. Moreover, mice with endometriosis developed microgliosis, astrogliosis and enhanced substance P neurokinin-1 receptor immunoreactivity within the spinal cord, suggesting the development of neuroinflammation and sensitization of spinal circuitry in endometriosis. These results demonstrate endometriosis-induced neuroplasticity occurring at both peripheral and central sites of sensory afferent pathways. These findings may help to explain the altered sensitivity to pain in endometriosis and provide a novel platform for targeted pain relief treatments for this debilitating disorder.Joel Castro, Jessica Maddern, Andelain Erickson, Andrea M. Harrington, Stuart M. Brierle

Quintessential Maldacena-Maoz Cosmologies

Maldacena and Maoz have proposed a new approach to holographic cosmology based on Euclidean manifolds with disconnected boundaries. This approach appears, however, to be in conflict with the known geometric results [the Witten-Yau theorem and its extensions] on spaces with boundaries of non-negative scalar curvature. We show precisely how the Maldacena-Maoz approach evades these theorems. We also exhibit Maldacena-Maoz cosmologies with [cosmologically] more natural matter content, namely quintessence instead of Yang-Mills fields, thereby demonstrating that these cosmologies do not depend on a special choice of matter to split the Euclidean boundary. We conclude that if our Universe is fundamentally anti-de Sitter-like [with the current acceleration being only temporary], then this may force us to confront the holography of spaces with a connected bulk but a disconnected boundary.Comment: Much improved exposition, exponent in Cai-Galloway theorem fixed, axionic interpretation of scalar explained, JHEP version. 33 pages, 3 eps figure

Schwinger boson theory of anisotropic ferromagnetic ultrathin films

Ferromagnetic thin films with magnetic single-ion anisotropies are studied within the framework of Schwinger bosonization of a quantum Heisenberg model. Two alternative bosonizations are discussed. We show that qualitatively correct results are obtained even at the mean-field level of the theory, similar to Schwinger boson results for other magnetic systems. In particular, the Mermin-Wagner theorem is satisfied: a spontaneous magnetization at finite temperatures is not found if the ground state of the anisotropic system exhibits a continuous degeneracy. We calculate the magnetization and effective anisotropies as functions of exchange interaction, magnetic anisotropies, external magnetic field, and temperature for arbitrary values of the spin quantum number. Magnetic reorientation transitions and effective anisotropies are discussed. The results obtained by Schwinger boson mean-field theory are compared with the many-body Green's function technique.Comment: 14 pages, including 7 EPS figures, minor changes, final version as publishe

Answering a Basic Objection to Bang/Crunch Holography

The current cosmic acceleration does not imply that our Universe is basically de Sitter-like: in the first part of this work we argue that, by introducing matter into *anti-de Sitter* spacetime in a natural way, one may be able to account for the acceleration just as well. However, this leads to a Big Crunch, and the Euclidean versions of Bang/Crunch cosmologies have [apparently] disconnected conformal boundaries. As Maldacena and Maoz have recently stressed, this seems to contradict the holographic principle. In the second part we argue that this "double boundary problem" is a matter not of geometry but rather of how one chooses a conformal compactification: if one chooses to compactify in an unorthodox way, then the appearance of disconnectedness can be regarded as a *coordinate effect*. With the kind of matter we have introduced here, namely a Euclidean axion, the underlying compact Euclidean manifold has an unexpectedly non-trivial topology: it is in fact one of the 75 possible underlying manifolds of flat compact four-dimensional Euclidean spaces.Comment: 29 pages, 3 figures, added references and comparison with "cyclic" cosmology, JHEP versio

Assessing the mechanisms of common Pb incorporation into titanite

Common Pb, the portion of non-radiogenic Pb within a U bearing mineral, needs to be accurately accounted for in order to subtract its effect on U-Pb isotopic ratios so that meaningful ages can be calculated. The propensity to accommodate common Pb during crystallization, or later, is different across the range of U bearing minerals used for geochronology. Titanite frequently accommodates significant amounts of common Pb. However, the most appropriate method to correct for this requires knowledge on the mechanism and timing of common Pb incorporation; information that is commonly difficult to extract. In this study, the spatial and compositional distribution of trace elements (including Pb) in metamorphic titanites from a Greenland amphibolite is investigated on the grain- to nano-scale. Titanites have an isotopically similar signature for both common and radiogenic-Pb in all grains but significantly different quantities of the non-radiogenic component. Microstructural and compositional examination of these grains reveals undeformed, but high common Pb (F207%) titanites have homogeneous element distributions on the atomic scale suggesting common Pb is incorporated into titanite during its growth and not during later processes. In contrast, deformed titanite comprising low-angle boundaries, formed by subgrain rotation recrystallization, comprise networks of dislocations that are enriched in Mg, Al, K and Fe. Smaller cations may migrate due to elastic strain in the vicinity of the dislocation network, yet the larger K cations more likely reflect the mobility of externally-derived K along the orien tation interface. The absence of Pb enrichment along the boundary indicates that either Pb was too large to fit into migrating lattice dislocations or static low-angle boundaries and/or that there was no external Pb available to diffuse along the grain boundary. As the common Pb composition is distinctly different to regional Pb models, the metamorphic titanite grew in a homogeneous Pb reservoir dominated by the break-down of precursor U-bearing phases. The different quantity of common Pb in the titanite grains indicates a mineral-driven element partitioning in an isotopically homogeneous metamorphic reservoir, consistent with low U, low total REE and flat LREE signatures in high F207% analyses. These results have implications for the selection of appropriate common Pb corrections in titanite and other accessory phases

The parent?infant dyad and the construction of the subjective self

Developmental psychology and psychopathology has in the past been more concerned with the quality of self-representation than with the development of the subjective agency which underpins our experience of feeling, thought and action, a key function of mentalisation. This review begins by contrasting a Cartesian view of pre-wired introspective subjectivity with a constructionist model based on the assumption of an innate contingency detector which orients the infant towards aspects of the social world that react congruently and in a specifically cued informative manner that expresses and facilitates the assimilation of cultural knowledge. Research on the neural mechanisms associated with mentalisation and social influences on its development are reviewed. It is suggested that the infant focuses on the attachment figure as a source of reliable information about the world. The construction of the sense of a subjective self is then an aspect of acquiring knowledge about the world through the caregiver's pedagogical communicative displays which in this context focuses on the child's thoughts and feelings. We argue that a number of possible mechanisms, including complementary activation of attachment and mentalisation, the disruptive effect of maltreatment on parent-child communication, the biobehavioural overlap of cues for learning and cues for attachment, may have a role in ensuring that the quality of relationship with the caregiver influences the development of the child's experience of thoughts and feelings

Randomized Trial of Metformin, Ivermectin, and Fluvoxamine for Covid-19

BACKGROUND Early treatment to prevent severe coronavirus disease 2019 (Covid-19) is an important component of the comprehensive response to the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) pandemic. METHODS In this phase 3, double-blind, randomized, placebo-controlled trial, we used a 2-by-3 factorial design to test the effectiveness of three repurposed drugs - metformin, ivermectin, and fluvoxamine - in preventing serious SARS-CoV-2 infection in nonhospitalized adults who had been enrolled within 3 days after a confirmed diagnosis of infection and less than 7 days after the onset of symptoms. The patients were between the ages of 30 and 85 years, and all had either overweight or obesity. The primary composite end point was hypoxemia (≤93% oxygen saturation on home oximetry), emergency department visit, hospitalization, or death. All analyses used controls who had undergone concurrent randomization and were adjusted for SARSCoV-2 vaccination and receipt of other trial medications. RESULTS A total of 1431 patients underwent randomization; of these patients, 1323 were included in the primary analysis. The median age of the patients was 46 years; 56% were female (6% of whom were pregnant), and 52% had been vaccinated. The adjusted odds ratio for a primary event was 0.84 (95% confidence interval [CI], 0.66 to 1.09; P=0.19) with metformin, 1.05 (95% CI, 0.76 to 1.45; P=0.78) with ivermectin, and 0.94 (95% CI, 0.66 to 1.36; P=0.75) with fluvoxamine. In prespecified secondary analyses, the adjusted odds ratio for emergency department visit, hospitalization, or death was 0.58 (95% CI, 0.35 to 0.94) with metformin, 1.39 (95% CI, 0.72 to 2.69) with ivermectin, and 1.17 (95% CI, 0.57 to 2.40) with fluvoxamine. The adjusted odds ratio for hospitalization or death was 0.47 (95% CI, 0.20 to 1.11) with metformin, 0.73 (95% CI, 0.19 to 2.77) with ivermectin, and 1.11 (95% CI, 0.33 to 3.76) with fluvoxamine. CONCLUSIONS None of the three medications that were evaluated prevented the occurrence of hypoxemia, an emergency department visit, hospitalization, or death associated with Covid-19