Stratification of moduli spaces of Lie algebras, similar matrices and bilinear forms

In this paper, the authors apply a stratification of moduli spaces of complex Lie algebras to analyzing the moduli spaces of nxn matrices under scalar similarity and bilinear forms under the cogredient action. For similar matrices, we give a complete description of a stratification of the space by some very simple projective orbifolds of the form P^n/G, where G is a subgroup of the symmetric group sigma_{n+1} acting on P^n by permuting the projective coordinates. For bilinear forms, we give a similar stratification up to dimension 4

Spontaneous visual exploration during locomotion in patients with phobic postural vertigo

BACKGROUND Earlier studies on stance and gait with posturographic and EMG-recordings and automatic gait analysis in patients with phobic postural vertigo (PPV) or visual height intolerance (vHI) revealed similar patterns of body stiffening with muscle co-contraction and a slow, cautious gait. Visual exploration in vHI patients was characterized by a freezing of gaze-in-space when standing and reduced horizontal eye and head movements during locomotion. OBJECTIVE Based on the findings in vHI patients, the current study was performed with a focus on visual control of locomotion in patients with PPV while walking along a crowded hospital hallway. METHODS Twelve patients with PPV and eleven controls were recruited. Participants wore a mobile infrared video eye-tracking system that continuously measured eye-in-head movements in the horizontal and vertical planes and head orientation and motion in the yaw, pitch, and roll planes. Visual exploration behavior of participants was recorded at the individually preferred speed for a total walking distance of 200 m. Gaze-in-space directions were determined by combining eye-in-head and head-in-space orientation. Walking speeds were calculated based on the trial duration and the total distance traversed. Participants were asked to rate their feelings of discomfort during the walk on a 4-point numeric rating scale. The examiners rated the crowdedness of the hospital hallway on a 4-point numeric rating scale. RESULTS The major results of visual exploration behavior in patients with PPV in comparison to healthy controls were: eye and head positions were directed more downward in the vertical plane towards the ground ahead with increased frequency of large amplitude vertical orientation movements towards the destination, the end of the ground straight ahead. The self-adjusted speed of locomotion was significantly lower in PPV. Particularly those patients that reported high levels of discomfort exhibited a specific visual exploration of their horizontal surroundings. The durations of fixating targets in the visual surroundings were significantly shorter as compared to controls. CONCLUSION Gaze control of locomotion in patients with PPV is characterized by a preferred deviation of gaze more downward and by horizontal explorations for suitable auxiliary means for potential postural support in order to prevent impending falls. These eye movements have shorter durations of fixation as compared to healthy controls and patients with vHI. Finally, the pathological alterations in eye-head coordination during locomotion correlate with a higher level of discomfort and anxiety about falling

A novel pathogenic CACNA1A variant causing episodic ataxia type 2 (EA2) spectrum phenotype in four family members and a novel combined therapy

Objective!#!The safety and efficacy of surgical microvascular decompression (MVD) in elderly patients with trigeminal neuralgia (TN) is controversially discussed in the literature. A widespread reluctance to expose this cohort to major intracranial surgery persists. Our aim was to compare the efficacy and safety between older and younger patients with TN.!##!Methods!#!In this cross-sectional study, 139 MVD procedures (103 patients < 70 and 36 patients ≥ 70) were included. Surgical fitness was assessed by the American Society of Anesthesiology (ASA) grade. The pain-free interval was evaluated using Kaplan-Meier analysis only in patients with a recent follow-up visit. Independent risk factors for recurrence in patients with a minimum 12-month follow-up were determined.!##!Results!#!Patients ≥ 70 showed a significantly higher number of comorbidities. Pain intensity, affection of trigeminal branches and symptom duration was similar between groups. No significant difference in treatment associated complications and permanent neurological deficits was shown. There was no treatment-related mortality. A tendency towards a lower recurrence rate in patients < 70 did not reach statistical significance (17.6% vs. 28.6%, P = 0.274). Pain-free interval was not different between both cohorts (78.7 vs. 73.5 months, P = 0.391).!##!Conclusion!#!Despite a higher prevalence of comorbidities in elderly patients, complication rates and neurological deficits after MVD were comparable to younger patients. Rates of immediate and long-term pain relief compared favorably to previous studies and were similar between elderly and younger patients. These data endorse MVD as a safe and effective first-line surgical procedure for elderly patients with TN and neurovascular conflict on MRI

Formal deformations, contractions and moduli spaces of Lie algebras

Jump deformations and contractions of Lie algebras are inverse concepts, but the approaches to their computations are quite different. In this paper, we contrast the two approaches, showing how to compute jump deformations from the miniversal deformation of a Lie algebra, and thus arrive at the contractions. We also compute contractions directly. We use the moduli spaces of real 3-dimensional and complex 3 and 4-dimensional Lie algebras as models for explaining a deformation theory approach to computation of contractions.Comment: 27 page

Matrix Factorizations, Minimal Models and Massey Products

We present a method to compute the full non-linear deformations of matrix factorizations for ADE minimal models. This method is based on the calculation of higher products in the cohomology, called Massey products. The algorithm yields a polynomial ring whose vanishing relations encode the obstructions of the deformations of the D-branes characterized by these matrix factorizations. This coincides with the critical locus of the effective superpotential which can be computed by integrating these relations. Our results for the effective superpotential are in agreement with those obtained from solving the A-infinity relations. We point out a relation to the superpotentials of Kazama-Suzuki models. We will illustrate our findings by various examples, putting emphasis on the E_6 minimal model.Comment: 32 pages, v2: typos corrected, v3: additional comments concerning the bulk-boundary crossing constraint, some small clarifications, typo

Star products made (somewhat) easier

We develop an approach to the deformation quantization on the real plane with an arbitrary Poisson structure which based on Weyl symmetrically ordered operator products. By using a polydifferential representation for deformed coordinates $\hat x^j$ we are able to formulate a simple and effective iterative procedure which allowed us to calculate the fourth order star product (and may be extended to the fifth order at the expense of tedious but otherwise straightforward calculations). Modulo some cohomology issues which we do not consider here, the method gives an explicit and physics-friendly description of the star products.Comment: 20 pages, v2, v3: comments and references adde

On operad structures of moduli spaces and string theory

Recent algebraic structures of string theory, including homotopy Lie algebras, gravity algebras and Batalin-Vilkovisky algebras, are deduced from the topology of the moduli spaces of punctured Riemann spheres. The principal reason for these structures to appear is as simple as the following. A conformal field theory is an algebra over the operad of punctured Riemann surfaces, this operad gives rise to certain standard operads governing the three kinds of algebras, and that yields the structures of such algebras on the (physical) state space naturally.Comment: 33 pages (An elaboration of minimal area metrics and new references are added

Single-cell sequencing reveals clonal expansions of pro-inflammatory synovial CD8 T cells expressing tissue-homing receptors in psoriatic arthritis.

Psoriatic arthritis (PsA) is a debilitating immune-mediated inflammatory arthritis of unknown pathogenesis commonly affecting patients with skin psoriasis. Here we use complementary single-cell approaches to study leukocytes from PsA joints. Mass cytometry demonstrates a 3-fold expansion of memory CD8 T cells in the joints of PsA patients compared to peripheral blood. Meanwhile, droplet-based and plate-based single-cell RNA sequencing of paired T cell receptor alpha and beta chain sequences show pronounced CD8 T cell clonal expansions within the joints. Transcriptome analyses find these expanded synovial CD8 T cells to express cycling, activation, tissue-homing and tissue residency markers. T cell receptor sequence comparison between patients identifies clonal convergence. Finally, chemokine receptor CXCR3 is upregulated in the expanded synovial CD8 T cells, while two CXCR3 ligands, CXCL9 and CXCL10, are elevated in PsA synovial fluid. Our data thus provide a quantitative molecular insight into the cellular immune landscape of psoriatic arthritis

Single-cell sequencing reveals clonal expansions of pro-inflammatory synovial CD8 T cells expressing tissue-homing receptors in psoriatic arthritis

Psoriatic arthritis (PsA) is a debilitating immune-mediated inflammatory arthritis of unknown pathogenesis commonly affecting patients with skin psoriasis. Here we use complementary single-cell approaches to study leukocytes from PsA joints. Mass cytometry demonstrates a 3-fold expansion of memory CD8 T cells in the joints of PsA patients compared to peripheral blood. Meanwhile, droplet-based and plate-based single-cell RNA sequencing of paired T cell receptor alpha and beta chain sequences show pronounced CD8 T cell clonal expansions within the joints. Transcriptome analyses find these expanded synovial CD8 T cells to express cycling, activation, tissue-homing and tissue residency markers. T cell receptor sequence comparison between patients identifies clonal convergence. Finally, chemokine receptor CXCR3 is upregulated in the expanded synovial CD8 T cells, while two CXCR3 ligands, CXCL9 and CXCL10, are elevated in PsA synovial fluid. Our data thus provide a quantitative molecular insight into the cellular immune landscape of psoriatic arthritis