The Phantom Dark Matter Halos of the Local Volume in the Context of Modified Newtonian Dynamics

We explore the predictions of Milgromian gravity (MOND) in the local universe by considering the distribution of the “phantom” dark matter (PDM) that would source the MOND gravitational field in Newtonian gravity, allowing an easy comparison with the dark matter framework. For this, we specifically deal with the quasi-linear version of MOND (QUMOND). We compute the “stellar-to-(phantom)halo mass relation” (SHMR), a monotonically increasing power law resembling the SHMR observationally deduced from spiral galaxy rotation curves in the Newtonian context. We show that the gas-to-(phantom)halo mass relation is flat. We generate a map of the Local Volume in QUMOND, highlighting the important influence of distant galaxy clusters, in particular Virgo. This allows us to explore the scatter of the SHMR and the average density of PDM around galaxies in the Local Volume, ΩPDM ≈ 0.1, below the average cold dark matter density in a ΛCDM universe. We provide a model of the Milky Way in its external field in the MOND context, which we compare to an observational estimate of the escape velocity curve. Finally, we highlight the peculiar features related to the external field effect in the form of negative PDM density zones in the outskirts of each galaxy, and test a new analytic formula for computing galaxy rotation curves in the presence of an external field in QUMOND. While we show that the negative PDM density zones would be difficult to detect dynamically, we quantify the weak-lensing signal they could produce for lenses at z ∼ 0.3.

Bose–Einstein Condensation Processes with Nontrivial Geometric Multiplicities Realized via 𝒫𝒯−Symmetric and Exactly Solvable Linear-Bose–Hubbard Building Blocks

It is well known that, using the conventional non-Hermitian but PT−symmetric Bose–Hubbard Hamiltonian with real spectrum, one can realize the Bose–Einstein condensation (BEC) process in an exceptional-point limit of order N. Such an exactly solvable simulation of the BEC-type phase transition is, unfortunately, incomplete because the standard version of the model only offers an extreme form of the limit, characterized by a minimal geometric multiplicity K = 1. In our paper, we describe a rescaled and partitioned direct-sum modification of the linear version of the Bose–Hubbard model, which remains exactly solvable while admitting any value of K≥1. It offers a complete menu of benchmark models numbered by a specific combinatorial scheme. In this manner, an exhaustive classification of the general BEC patterns with any geometric multiplicity is obtained and realized in terms of an exactly solvable generalized Bose–Hubbard model.

Comparison of a Short Linear Antimicrobial Peptide with Its Disulfide-Cyclized and Cyclotide-Grafted Variants against Clinically Relevant Pathogens

According to the World Health Organization (WHO) the development of resistance against antibiotics by microbes is one of the most pressing health concerns. The situation will intensify since only a few pharmacological companies are currently developing novel antimicrobial compounds. Discovery and development of novel antimicrobial compounds with new modes of action are urgently needed. Antimicrobial peptides (AMPs) are known to be able to kill multidrug-resistant bacteria and, therefore, of interest to be developed into antimicrobial drugs. Proteolytic stability and toxicities of these peptides are challenges to overcome, and one strategy frequently used to address stability is cyclization. Here we introduced a disulfide-bond to cyclize a potent and nontoxic 9mer peptide and, in addition, as a proof-of-concept study, grafted this peptide into loop 6 of the cyclotide MCoTI-II. This is the first time an antimicrobial peptide has been successfully grafted onto the cyclotide scaffold. The disulfide-cyclized and grafted cyclotide showed moderate activity in broth and strong activity in 1/5 broth against clinically relevant resistant pathogens. The linear peptide showed superior activity in both conditions. The half-life time in 100% human serum was determined, for the linear peptide, to be 13 min, for the simple disulfide-cyclized peptide, 9 min, and, for the grafted cyclotide 7 h 15 min. The addition of 10% human serum led to a loss of antimicrobial activity for the different organisms, ranging from 1 to >8-fold for the cyclotide. For the disulfide-cyclized version and the linear version, activity also dropped to different degrees, 2 to 18-fold, and 1 to 30-fold respectively. Despite the massive difference in stability, the linear peptide still showed superior antimicrobial activity. The cyclotide and the disulfide-cyclized version demonstrated a slower bactericidal effect than the linear version. All three peptides were stable at high and low pH, and had very low hemolytic and cytotoxic activity.

Standard model from a supergravity model with a naturally small cosmological constant

Guided by the naturalness criterion for an exponentially small cosmological constant, we present a string theory motivated 4-dimensional $$ \mathcal{N} $$ N = 1 non-linear supergravity model (or its linear version with a nilpotent superfield) with spontaneous supersymmetry breaking. The model encompasses the minimal supersymmetric standard model, the racetrack Kähler uplift, and the KKLT anti-D3-branes, and use the nilpotent superfield to project out the undesirable interaction terms as well as the unwanted degrees of freedom to end up with the standard model (not the supersymmetric version) of strong and electroweak interactions.

Cascaded Complementary Filter Architecture for Sensor Fusion in Attitude Estimation

Attitude estimation is the process of computing the orientation angles of an object with respect to a fixed frame of reference. Gyroscope, accelerometer, and magnetometer are some of the fundamental sensors used in attitude estimation. The orientation angles computed from these sensors are combined using the sensor fusion methodologies to obtain accurate estimates. The complementary filter is one of the widely adopted techniques whose performance is highly dependent on the appropriate selection of its gain parameters. This paper presents a novel cascaded architecture of the complementary filter that employs a nonlinear and linear version of the complementary filter within one framework. The nonlinear version is used to correct the gyroscope bias, while the linear version estimates the attitude angle. The significant advantage of the proposed architecture is its independence of the filter parameters, thereby avoiding tuning the filter’s gain parameters. The proposed architecture does not require any mathematical modeling of the system and is computationally inexpensive. The proposed methodology is applied to the real-world datasets, and the estimation results were found to be promising compared to the other state-of-the-art algorithms.

Measuring Spinal Mobility Using an Inertial Measurement Unit System: A Reliability Study in Axial Spondyloarthritis

The objectives of this study were to evaluate the reliability of wearable inertial motion unit (IMU) sensors in measuring spinal range of motion under supervised and unsupervised conditions in both laboratory and ambulatory settings. A secondary aim of the study was to evaluate the reliability of composite IMU metrology scores (IMU-ASMI (Amb)). Forty people with axSpA participated in this clinical measurement study. Participant spinal mobility was assessed by conventional metrology (Bath Ankylosing Spondylitis Metrology Index, linear version—BASMILin) and by a wireless IMU sensor-based system which measured lumbar flexion-extension, lateral flexion and rotation. Each sensor-based movement test was converted to a normalized index and used to calculate IMU-ASMI (Amb) scores. Test-retest reliability was evaluated using intra-class correlation coefficients (ICC). There was good to excellent agreement for all spinal range of movements (ICC > 0.85) and IMU-ASMI (Amb) scores (ICC > 0.87) across all conditions. Correlations between IMU-ASMI (Amb) scores and conventional metrology were strong (Pearson correlation ≥ 0.85). An IMU sensor-based system is a reliable way of measuring spinal lumbar mobility in axSpA under supervised and unsupervised conditions. While not a replacement for established clinical measures, composite IMU-ASMI (Amb) scores may be reliably used as a proxy measure of spinal mobility.

Do Domestic Dogs (Canis lupus familiaris) Perceive Numerosity Illusions?

Recent studies have showed that domestic dogs are only scantly susceptible to visual illusions, suggesting that the perceptual mechanisms might be different in humans and dogs. However, to date, none of these studies have utilized illusions that are linked to quantity discrimination. In the current study, we tested whether dogs are susceptible to a linear version of the Solitaire illusion, a robust numerosity illusion experienced by most humans. In the first experiment, we tested dogs’ ability to discriminate items in a 0.67 and 0.75 numerical ratio. The results showed that dogs’ quantity discrimination abilities fall in between these two ratios. In Experiment 2, we presented the dogs with the Solitaire illusion pattern using a spontaneous procedure. No evidence supporting any numerosity misperception was found. This conclusion was replicated in Experiment 3, where we manipulated dogs’ initial experience with the stimuli and their contrast with the background. The lack of dogs’ susceptibility to the Solitaire illusion suggests that numerical estimation of dogs is not influenced by the spatial arrangement of the items to be enumerated. In view of the existing evidence, the effect may be extended to dogs’ quantitative abilities at large.

Periodically Forced Nonlinear Oscillators With Hysteretic Damping

We perform a detailed study of the dynamics of a nonlinear, one-dimensional oscillator driven by a periodic force under hysteretic damping, whose linear version was originally proposed and analyzed by Bishop (1955, “The Treatment of Damping Forces in Vibration Theory,” Aeronaut. J., 59(539), pp. 738–742). We first add a small quadratic stiffness term in the constitutive equation and construct the periodic solution of the problem by a systematic perturbation method, neglecting transient terms as t→∞. We then repeat the analysis replacing the quadratic by a cubic term, which does not allow the solutions to escape to infinity. In both cases, we examine the dependence of the amplitude of the periodic solution on the different parameters of the model and discuss the differences with the linear model. We point out certain undesirable features of the solutions, which have also been alluded to in the literature for the linear Bishop's model, but persist in the nonlinear case as well. Finally, we discuss an alternative hysteretic damping oscillator model first proposed by Reid (1956, “Free Vibration and Hysteretic Damping,” Aeronaut. J., 60(544), pp. 283–283), which appears to be free from these difficulties and exhibits remarkably rich dynamical properties when extended in the nonlinear regime.

Asymmetric Interest Rate Transmission in an Inflation Targeting Framework: The Case of Colombia

After adopting an inflation targeting framework for monetary policy at the turn of the century, the Central Bank of Colombia started actively using the monetary policy interest rate as its key policy tool. In this regard, this paper examines the interest rate pass-through from the monetary policy rate to the retail rates in Colombia and explores asymmetries in the adjustment process within the framework of a non-linear version of the ARDL (NARDL) model developed by Shin et al. (2014). Our findings show that the policy rate plays a key role in determining deposit and lending retail rates but the nature of the pass-through varies across different types of lending products. In the case of lending rates, the pass-through is usually a full one, and takes around 12 months to be nearly complete. Our results capture an asymmetric positive pass-through in deposit rates and an upward rigidity in the lending rates of consumer and ordinary corporate loans, key segments of the credit market. These findings imply that most retail lending rates respond more to policy rate cuts than to hikes, indicating that financial intermediaries are more reluctant to raise interest rates than to decrease them following policy adjustments.

Shape optimization of a Dirichlet type energy for semilinear elliptic partial differential equations

Minimizing the so-called “Dirichlet energy” with respect to the domain under a volume constraint is a standard problem in shape optimization which is now well understood. This article is devoted to a prototypal non-linear version of the problem, where one aims at mini- mizing a Dirichlet-type energy involving the solution to a semilinear elliptic PDE with respect to the domain, under a volume constraint. One of the main differences with the standard version of this problem rests upon the fact that the criterion to minimize does not write as the minimum of an energy, and thus most of the usual tools to analyze this problem cannot be used. By using a relaxed version of this problem, we first prove the existence of optimal shapes under several assumptions on the problem parameters. We then analyze the stability of the ball, expected to be a good candidate for solving the shape optimization problem, when the coefficients of the involved PDE are radially symmetric.