Integral representation of the density matrix of the XXZ chain at finite temperatures

We present an integral formula for the density matrix of a finite segment of the infinitely long spin-1/2 XXZ chain. This formula is valid for any temperature and any longitudinal magnetic field.Comment: 12 pages, Late

From multiple integrals to Fredholm determinants

We consider a multiple integral representation for the finite temperature density-density correlation functions of the one-dimensional Bose gas with delta function interaction in the limits of infinite and vanishing repulsion. In the former case a known Fredholm determinant is recovered. In the latter case a similar expression appears with permanents replacing determinants.Comment: 11 pages, section on the free Boson limit adde

Measuring highly accurate foot position and angle trajectories with foot-mounted IMUs in clinical practice

Background: Gait analysis using foot-mounted IMUs is a promising method to acquire gait parameters outside of laboratory settings and in everyday clinical practice. However, the need for precise sensor attachment or calibration, the requirement of environments with a homogeneous magnetic field, and the limited applicability to pathological gait patterns still pose challenges. Furthermore, in previously published work, the measurement accuracy of such systems is often only validated for specific points in time or in a single plane. Research question: This study investigates the measurement accuracy of a gait analysis method based on foot-mounted IMUs in the acquisition of the foot motion, i.e., position and angle trajectories of the foot in the sagittal, frontal, and transversal plane over the entire gait cycle. Results: A comparison of the proposed method with an optical motion capture system showed an average RMSE of 0.67° for pitch, 0.63° for roll and 1.17° for yaw. For position trajectories, an average RMSE of 0.51 cm for vertical lift and 0.34 cm for lateral shift was found. The measurement error of the IMU-based method is found to be much smaller than the deviations caused by the shoes. Significance: The proposed method is found to be sufficiently accurate for clinical practice. It does not require precise mounting, special calibration movements, or magnetometer data, and shows no difference in measurement accuracy between normal and pathological gait. Therefore, it provides an easy-to-use alternative to optical motion capture and facilitates gait analysis independent of laboratory settings

Early Changes in Pain Acceptance Predict Pain Outcomes in Interdisciplinary Treatment for Chronic Pain

Studies have shown that pain acceptance is associated with a better pain outcome. The current study explored whether changes in pain acceptance in the very early treatment phase of an interdisciplinary cognitive-behavioral therapy (CBT)-based treatment program for chronic pain predict pain outcomes. A total of 69 patients with chronic, non-malignant pain (at least 6 months) were treated in a day-clinic for four-weeks. Pain acceptance was measured with the Chronic Pain Acceptance Questionnaire (CPAQ), pain outcomes included pain intensity (Numeric Rating Scale, NRS) as well as affective and sensory pain perception (Pain Perception Scale, SES-A and SES-S). Regression analyses controlling for the pre-treatment values of the pain outcomes, age, and gender were performed. Early changes in pain acceptance predicted pain intensity at post-treatment measured with the NRS (B = -0.04 (SE = 0.02); T = -2.28; p = 0.026), affective pain perception at post-treatment assessed with the SES-A (B = -0.26 (SE = 0.10); T = -2.79; p = 0.007), and sensory pain perception at post-treatment measured with the SES-S (B = -0.19 (SE = 0.08); T = -2.44; p = 0.017). Yet, a binary logistic regression analysis revealed that early changes in pain acceptance did not predict clinically relevant pre-post changes in pain intensity (at least 2 points on the NRS). Early changes in pain acceptance were associated with pain outcomes, however, the impact was beneath the threshold defined as clinically relevant

Emptiness formation probability at finite temperature for the isotropic Heisenberg chain

We present an integral formula for a special correlation function of the isotropic spin-1/2 antiferromagnetic Heisenberg chain. The correlation function describes the probability for the occurrence of a string of consecutive up-spins as a function of temperature, magnetic field and length of the string.Comment: 3 pages, 1 figure, submitted to SCES'0

A Kernel Two-sample Test for Dynamical Systems

Evaluating whether data streams were generated by the same distribution is at the heart of many machine learning problems, e.g. to detect changes. This is particularly relevant for data generated by dynamical systems since they are essential for many real-world processes in biomedical, economic, or engineering systems. While kernel two-sample tests are powerful for comparing independent and identically distributed random variables, no established method exists for comparing dynamical systems. The key problem is the critical independence assumption, which is inherently violated in dynamical systems. We propose a novel two-sample test for dynamical systems by addressing three core challenges: we (i) introduce a novel notion of mixing that captures autocorrelations in a relevant metric, (ii) propose an efficient way to estimate the speed of mixing purely from data, and (iii) integrate these into established kernel-two sample tests. The result is a data-driven method for comparison of dynamical systems that is easy to use in practice and comes with sound theoretical guarantees. In an example application to anomaly detection from human walking data, we show that the test readily applies without the need for feature engineering, heuristics, and human expert knowledge

Investigation of masking concepts for influencing the austenitization process during press hardening

One possibility to adjust tailored properties in hot stamping is the application of a masking concept to prevent a complete austenitization. In this study different concepts were investigated in order to use them as a suitable masking. A simulation model of the heating phase was developed for the purpose of predicting the resulting microstructure and hardness. Experimentally determined temperature profiles were used for the numerical model. The numerical results of the temperature profile and hardness were validated by experimental investigations and non-destructive hardness measurements. The simulated hardness is in adequate agreement with the measured hardness

Integral representations for correlation functions of the XXZ chain at finite temperature

We derive a novel multiple integral representation for a generating function of the \s^z-\s^z correlation functions of the spin-\2 XXZ chain at finite temperature and finite, longitudinal magnetic field. Our work combines algebraic Bethe ansatz techniques for the calculation of matrix elements with the quantum transfer matrix approach to thermodynamics.Comment: 33 pages, 2 figures, v2: 2 typos corrected, 1 figure adde

Calibration-free gait assessment by foot-worn inertial sensors

Walking is a central activity of daily life, and there is an increasing demand for objective measurement-based gait assessment. In contrast to stationary systems, wearable inertial measurement units (IMUs) have the potential to enable non-restrictive and accurate gait assessment in daily life. We propose a set of algorithms that uses the measurements of two foot-worn IMUs to determine major spatiotemporal gait parameters that are essential for clinical gait assessment: durations of five gait phases for each side as well as stride length, walking speed, and cadence. Compared to many existing methods, the proposed algorithms neither require magnetometers nor a precise mounting of the sensor or dedicated calibration movements. They are therefore suitable for unsupervised use by non-experts in indoor as well as outdoor environments. While previously proposed methods are rarely validated in pathological gait, we evaluate the accuracy of the proposed algorithms on a very broad dataset consisting of 215 trials and three different subject groups walking on a treadmill: healthy subjects (n = 39), walking at three different speeds, as well as orthopedic (n = 62) and neurological (n = 36) patients, walking at a self-selected speed. The results show a very strong correlation of all gait parameters (Pearson's r between 0.83 and 0.99, p < 0.01) between the IMU system and the reference system. The mean absolute difference (MAD) is 1.4 % for the gait phase durations, 1.7 cm for the stride length, 0.04 km/h for the walking speed, and 0.7 steps/min for the cadence. We show that the proposed methods achieve high accuracy not only for a large range of walking speeds but also in pathological gait as it occurs in orthopedic and neurological diseases. In contrast to all previous research, we present calibration-free methods for the estimation of gait phases and spatiotemporal parameters and validate them in a large number of patients with different pathologies. The proposed methods lay the foundation for ubiquitous unsupervised gait assessment in daily-life environments.DFG, 414044773, Open Access Publizieren 2021 - 2022 / Technische Universität Berli