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The Laplace operator encodes the behavior of physical systems at vastly different scales, describing heat flow, fluids, as well as electric, gravitational, and quantum fields. A key input for the Laplace equation is the curvature of space. Here we discuss and experimentally demonstrate that the spectral ordering of Laplacian eigenstates for hyperbolic (negatively curved) and flat two-dimensional spaces has a universally different structure. We use a lattice regularization of hyperbolic space in an electric-circuit network to measure the eigenstates of a ‘hyperbolic drum’, and in a time-resolved experiment we verify signal propagation along the curved geodesics. Our experiments showcase both a versatile platform to emulate hyperbolic lattices in tabletop experiments, and a set of methods to verify the effective hyperbolic metric in this and other platforms. The presented techniques can be utilized to explore novel aspects of both classical and quantum dynamics in negatively curved spaces, and to realise the emerging models of topological hyperbolic matter. Spaces with negative curvature are difficult to realise and investigate experimentally, but they can be emulated with synthetic matter. Here, the authors show how to do this using an electric circuit network, and present a method to characterize and verify the hyperbolic nature of the implemented model.

Curved spaces play a fundamental role in many areas of modern physics, from cosmological length scales to subatomic structures related to quantum information and quantum gravity. In tabletop experiments, negatively curved spaces can be simulated with hyperbolic lattices. Here we introduce and experimentally realize hyperbolic matter as a paradigm for topological states through topolectrical circuit networks relying on a complex-phase circuit element. The experiment is based on hyperbolic band theory that we confirm here in an unprecedented numerical survey of finite hyperbolic lattices. We implement hyperbolic graphene as an example of topologically nontrivial hyperbolic matter. Our work sets the stage to realize more complex forms of hyperbolic matter to challenge our established theories of physics in curved space, while the tunable complex-phase element developed here can be a key ingredient for future experimental simulation of various Hamiltonians with topological ground states. Hyperbolic lattices emulate particle dynamics equivalent to those in negatively curved space, with connections to general relativity. Here, the authors use electric circuits with a novel complex-phase circuit element to simulate hyperbolic graphene with negligible boundary contributions.

Knots are intricate structures that cannot be unambiguously distinguished with any single topological invariant. Momentum space knots, in particular, have been elusive due to their requisite finely tuned long-ranged hoppings. Even if constructed, probing their intricate linkages and topological \"drumhead” surface states will be challenging due to the high precision needed. In this work, we overcome these practical and technical challenges with RLC circuits, transcending existing theoretical constructions which necessarily break reciprocity, by pairing nodal knots with their mirror image partners in a fully reciprocal setting. Our nodal knot circuits can be characterized with impedance measurements that resolve their drumhead states and image their 3D nodal structure. Doing so allows for reconstruction of the Seifert surface and hence knot topological invariants like the Alexander polynomial. We illustrate our approach with large-scale simulations of various nodal knots and an experiment which maps out the topological drumhead region of a Hopf-link. Topological phases with knotted configurations in momentum space have been challenging to realize. Here, Lee et al. provide a systematic design and measurement of a three-dimensional knotted nodal structure, and resolve its momentum space drumhead states via a topolectrical RLC-type circuit.

Light-matter superposition states obtained via strong coupling play a decisive role in quantum information processing, but the deleterious effects of material dissipation and environment-induced decoherence inevitably destroy coherent light-matter polaritons over time. Here, we propose the use of coherent perfect absorption under near-field driving to prepare and protect the polaritonic states of a single quantum emitter interacting with a plasmonic nanocavity at room temperature. Our scheme of quantum nanoplasmonic coherent perfect absorption leverages an inherent frequency specificity to selectively initialize the coupled system in a chosen plasmon-emitter dressed state, while the coherent, unidirectional and non-perturbing near-field energy transfer from a proximal plasmonic waveguide can in principle render the dressed state robust against dynamic dissipation under ambient conditions. Our study establishes a previously unexplored paradigm for quantum state preparation and coherence preservation in plasmonic cavity quantum electrodynamics, offering compelling prospects for elevating quantum nanophotonic technologies to ambient temperatures. Quantum states are incredibly sensitive to their environment, making them perfect for ultrasensitive quantum detection—if they can be maintained long enough. Here, the authors showed that they can ‘immortalize’ the excited state of a coupled light-matter system using a technique called ‘coherent perfect absorption’.

A graph on at least ${{k+1}}$ vertices is uniformly $k$-connected if each pair of its vertices is connected by $k$ and not more than $k$ independent paths. We reinvestigate a recent constructive characterization of uniformly $3$-connected graphs and obtain a more detailed result that relates the number of vertices to the operations involved in constructing a respective uniformly $3$-connected graph. Furthermore, we investigate how crossing numbers and treewidths behave under the mentioned constructions. We demonstrate how these results can be utilized to study the structure and properties of uniformly $3$-connected graphs with minimum number of vertices of minimum degree.

NUCB2/nesfatin-1 is an anorexigenic hormone with elevated levels in obese and decreased levels in anorexia nervosa (AN) patients. Moreover, a role in the regulation of stress and emotions was suggested by several rodent and preliminary human studies. Since anxiety and depression are common comorbidities in AN, we investigated the association of NUCB2/nesfatin-1 with anxiety, depression and perceived stress in AN. We analyzed circulating NUCB2/nesfatin-1 levels in 64 female inpatients diagnosed with anorexia nervosa (body mass index, BMI; mean±SD, 14.7±2.3 kg/m2). At the same time anxiety (GAD-7), depression (PHQ-9), stress (PSQ-20) and disordered eating (EDI-2) were measured psychometrically. No correlation was observed between NUCB2/nesfatin-1 and BMI (r = 0.06, p = 0.70). The study population was divided in patients with low anxiety (n = 32, GAD-7 scores, mean±SD, 7.5±3.3) and high anxiety (n = 32, 16.0±3.0, p<0.001). Patients with high anxiety scores displayed 65% higher NUCB2/nesfatin-1 levels (p = 0.04). This was reflected by a positive correlation of GAD-7 and NUCB2/nesfatin-1-levels (r = 0.32, p = 0.04). Scores of PSQ-20 (73.3±14.3 vs. 48.6±17.2) and PHQ-9 (18.8±5.0 vs. 10.3±5.1) were higher in the high anxiety group (p<0.001) but did not correlate with NUCB2/nesfatin-1 (p>0.05). EDI-2 total score was also higher in the high anxiety group (52.3±14.1 vs. 40.2±16.0, p = 0.02), while no correlations of EDI-2-scores with plasma NUCB2/nesfatin-1 were observed (p>0.05). Circulating NUCB2/nesfatin-1 levels correlated positively with perceived anxiety, whereas no association with BMI or eating disorder symptoms was observed. NUCB2/nesfatin-1 might be primarily involved in the modulation of anxiety and subsequently in the regulation of eating habits and body weight in AN.

Quantum graphs are ideally suited to studying the spectral statistics of chaotic systems. Depending on the boundary conditions at the vertices, there are Neumann and Dirichlet graphs. The latter ones correspond to totally disassembled graphs with a spectrum being the superposition of the spectra of the individual bonds. According to the interlacing theorem, Neumann and Dirichlet eigenvalues on average alternate as a function of the wave number, with the consequence that the Neumann spectral statistics deviate from random matrix predictions. There is, e.g., a strict upper bound for the spacing of neighboring Neumann eigenvalues given by the number of bonds (in units of the mean level spacing). Here, we present analytic expressions for level spacing distribution and number variance for ensemble averaged spectra of Dirichlet graphs in dependence of the bond number, and compare them with numerical results. For a number of small Neumann graphs, numerical results for the same quantities are shown, and their deviations from random matrix predictions are discussed.

Neurotensin and xenin are two closely related anorexigenic neuropeptides synthesized in the small intestine that exert diverse peripheral and central functions. Both act via the neurotensin-1-receptor. In animal models of obesity reduced central concentrations of these peptides have been found. Dysregulations of the acute and chronic stress response are associated with development and maintenance of obesity. Until now, associations of both peptides with stress, anxiety, depressiveness, and eating disorder symptoms have not been investigated. The aim of the present study was to examine associations of neurotensin and xenin with these psychological characteristics under conditions of obesity. From 2010 to 2016 we consecutively enrolled 160 inpatients (63 men and 97 women), admitted due to obesity and its mental and somatic comorbidities. Blood withdrawal und psychometric tests (PSQ-20, GAD-7, PHQ-9, and EDI-2) occurred within one week after admission. We measured levels of neurotensin and xenin in plasma by ELISA. Mean body mass index was 47.2 ± 9.5 kg/m . Concentrations of neurotensin and xenin positively correlated with each other (women: = 0.788, < 0.001; men: = 0.731, < 0.001) and did not significantly differ between sexes ( > 0.05). Women generally displayed higher psychometric values than men (PSQ-20: 58.2 ± 21.7 vs. 47.0 ± 20.8, = 0.002; GAD-7: 9.7 ± 5.8 vs. 7.1 ± 5.3, = 0.004; PHQ-9: 11.6 ± 6.6 vs. 8.8 ± 5.9, = 0.008; EDI-2: 50.5 ± 12.8 vs. 39.7 ± 11.9, < 0.001). Only women showed positive correlations of both neuropeptides with stress (neurotensin: = 0.231, = 0.023; xenin: = 0.254, = 0.013), anxiety (neurotensin: = 0.265, = 0.009; xenin: = 0.257, = 0.012), depressiveness (neurotensin: = 0.281, = 0.006; xenin: = 0.241, = 0.019) and eating disorder symptoms (neurotensin: = 0.276, = 0.007; xenin: = 0.26, = 0.011), whereas, men did not ( > 0.05). Neurotensin and xenin plasma levels of female obese patients are positively correlated with perceived stress, anxiety, depressiveness, and eating disorder symptoms. These associations could be influenced by higher prevalence of mental disorders in women and by sex hormones. In men, no correlations were observed, which points toward a sex-dependent regulation.

Neuropeptide Y (NPY), peptide tyrosine tyrosine (PYY) and pancreatic polypeptide (PP) are important mediators in the bidirectional communication along the gut-brain-axis. Best known for their role in the regulation of appetite and food intake they are considered to play a crucial role in the development of obesity. Additionally, mounting evidence indicates a regulatory function in anxiety, mood and stress resilience with potential sex differences. In the present study, we examined the associations of NPY, PYY and PP plasma levels with anxiety, depressiveness and perceived stress in obese patients. We analyzed 144 inpatients (90 female, 54 male, BMI mean: 49.4 kg/m2) who received medical treatment for obesity and its somatic and mental comorbidities. Fasting blood samples were taken, and patients completed psychometric self-assessment questionnaires (GAD-7, PHQ-9, PSQ-20) within the first week after admission and before discharge. Plasma concentrations of the peptides were measured by ELISA. Women showed significant higher anxiety (GAD-7: 8.13±5.67 vs. 5.93±5.42, p=0.04) and stress scores (PSQ-20: 52.62±23.5 vs. 41.23±22.53, p=0.01) than men. In the longitudinal analysis women with a clinically relevant improvement of anxiety (≥5 points on GAD-7, p<0.001) also showed significant improvements in depression (PHQ-9: 38%, p=0.002) and PSQ-20 scores (23%, p=0.005) while anxiety-improved male patients only improved in the subscale tension of the PSQ-20 (34%, p=0.02). In men we observed a positive correlation of PP with anxiety scores (GAD-7: r=0.41, p=0.007) and with age (r=0.49, p=0.001) on admission while NPY negatively correlated with age (r=-0.38, p=0.01). In contrast, there were no significant associations (p>0.05) in female subjects in the cross-sectional as well as in the longitudinal analysis. In conclusion, women suffering from morbid obesity showed greater psychological comorbidity and considerable interactions among them. Despite that we solely observed associations of PP with anxiety and age with NPY and PP in men, suggesting a possible influence of sex hormones on the NPY system. However, improvement of anxiety scores did not lead to significant changes in NPY.

While ample data demonstrate the effectiveness of inpatient psychosomatic treatment, clinical observation and empirical evidence demonstrate that not all patients benefit equally from established therapeutic methods. Especially patients with a comorbid personality disorder often show reduced therapeutic success compared to other patient groups. Due to the heterogeneous and categorical personality assessment, previous studies indicated no uniform direction of this influence. This complicates the derivation of therapeutic recommendations for mental disorders with comorbid personality pathology. Analyzing n = 2094 patients from German university hospitals enrolled in the prospective “MEPP” study, we tested the dynamic interaction between dimensionally assessed personality functioning and psychopathology of anxiety and depression. Longitudinal structural equation modelling replicated the finding that the severity of symptoms at admission predicts symptom improvement within the same symptom domain. In addition, we here report a significant coupling parameter between the baseline level of personality function and the change in general psychopathology - and vice versa. These results imply that personality pathology at admission hinders the therapeutic improvement in anxiety and depression, and that improvement of personality pathology is hindered by general psychopathology. Furthermore, the covariance between both domains supports the assumption that personality functioning and general psychopathology cannot be clearly distinguished and adversely influence each other. A dimensional assessment of the personality pathology is therefore recommendable for psychotherapy research and targeted therapeutic treatment. [Display omitted] •Representative sample of 2,094 patients receiving treatment at German hospitals for psychotherapy and psychosomatic medicine.•Longitudinal structural equation approach using dimensional assessments of personality and general psychopathology.•High personality pathology at admission impedes therapeutic progress in treating anxiety and depression and vice versa.•Symptoms of anxiety and depression show a high covariance with personality pathology at admission and for therapeutic change.•Personality and general psychopathology seem not clearly distinguishable and adversely influence each other.