Machine learning with tree tensor networks, CP rank constraints, and tensor dropout

Tensor networks developed in the context of condensed matter physics try to approximate order-N tensors with a reduced number of degrees of freedom that is only polynomial in N and arranged as a network of partially contracted smaller tensors. As we have recently demonstrated in the context of quantum many-body physics, computation costs can be further substantially reduced by imposing constraints on the canonical polyadic (CP) rank of the tensors in such networks. Here, we demonstrate how tree tensor networks (TTN) with CP rank constraints and tensor dropout can be used in machine learning. The approach is found to outperform other tensor-network-based methods in Fashion-MNIST image classification. A low-rank TTN classifier with branching ratio b = 4 reaches a test set accuracy of 90.3% with low computation costs. Consisting of mostly linear elements, tensor network classifiers avoid the vanishing gradient problem of deep neural networks. The CP rank constraints have additional advantages: The number of parameters can be decreased and tuned more freely to control overfitting, improve generalization properties, and reduce computation costs. They allow us to employ trees with large branching ratios, substantially improving the representation power.

Criticality and Phase Classification for Quadratic Open Quantum Many-Body Systems

We study the steady states of translation-invariant open quantum many-body systems governed by Lindblad master equations, where the Hamiltonian is quadratic in the ladder operators, and the Lindblad operators are either linear or quadratic and Hermitian. These systems are called quasifree and quadratic, respectively. We find that steady states of one-dimensional systems with finite-range interactions necessarily have exponentially decaying Green's functions. For the quasifree case without quadratic Lindblad operators, we show that fermionic systems with finite-range interactions are noncritical for any number of spatial dimensions and provide bounds on the correlation lengths. Quasifree bosonic systems can be critical in D>1 dimensions. Last, we address the question of phase transitions in quadratic systems and find that, without symmetry constraints beyond invariance under single-particle basis and particle-hole transformations, all gapped Liouvillians belong to the same phase.

The 3-triangle method preserves the posterior tibial slope during high tibial valgus osteotomy: first preliminary data using a mathematical model

PURPOSE

Despite much improved preoperative planning techniques accurate intraoperative assessment of the high tibial valgus osteotomy (HTO) remains challenging and often results in coronal over- and under-corrections as well as unintended changes of the posterior tibial slope. Noyes et al. reported a novel method for accurate intraoperative coronal and sagittal alignment correction based on a three-dimensional mathematical model. This is the first study examining preliminary data via the proposed Noyes approach for accurate intraoperative coronal and sagittal alignment correction during HTO.

METHODS

From 2016 to 2020 a total of 24 patients (27 knees) underwent HTO applying the proposed Noyes method (Noyes-Group). Radiographic data was analyzed retrospectively and matched to patients that underwent HTO using the conventional method, i.e., gradual medial opening using a bone spreader under fluoroscopic control (Conventional-Group). All operative procedures were performed by an experienced surgeon at a single orthopaedic university center.

RESULTS

From the preoperative to the postoperative visit no statistically significant changes of the posterior tibial slope were noted in the Noyes-Group compared to a significant increase in the Conventional-Group (p = 0.01). Regarding the axial alignment no significant differences between both groups were observed pre- and postoperatively. The number of over- and under-corrections did not differ significantly between both groups. Linear regression analysis showed a significant correlation of the postoperative medial proximal tibial angle (MPTA) with the position of the weightbearing line on the tibial plateau.

CONCLUSION

The 3-triangle method by Noyes seems to be a promising approach for preservation of the posterior tibial slope during HTO.

Focal cartilage defects of the lateral compartment do influence the outcome after high tibial valgus osteotomy

INTRODUCTION

High tibial medial open-wedge valgus osteotomy (HTO) is a well-established procedure for unicompartimental medial osteoarthritis of the young and active patient. However, the influence of cartilage defects of the lateral compartment on the total outcome remains obscure.

METHODS

From 2005 to 2012, a total of 63 patients underwent HTO for medial osteoarthritis of the knee at a single university orthopaedic center. Baseline data as well as intraoperative findings, including the grade and location of cartilage lesions, were evaluated retrospectively. Two groups were formed regarding the integrity of the lateral tibiofemoral compartment as measured by the Outerbridge score (group A: no lateral cartilage defects, group B: mild to moderate lateral cartilage defects). Functional outcome was assessed using the Knee and Osteoarthritis Outcome Score (KOOS), including its five subscores.

RESULTS

Comparing pre- and postoperative data, we identified an overall benefit of the HTO procedure as measured by the KOOS. Group A (no lateral cartilage defects) showed an increase in all five KOOS subscores (p = 0.00-0.01), whereas for group B (mild to moderate lateral cartilage defects), only two KOOS subscores revealed a significant increase (p = 0.03-0.04). There was also a statistically significant difference in the total KOOS score with higher values for group A at the postoperative visit. Cartilage defects with a higher Outerbridge score were associated with lower postoperative KOOS subscores.

DISCUSSION

Mild to moderate cartilage defects of the lateral compartment humble the total outcome after HTO procedure. Thus, indication for HTO should be made very carefully if any degree of lateral cartilage degeneration is present.

Eigenstate Entanglement: Crossover from the Ground State to Volume Laws

For the typical quantum many-body systems that obey the eigenstate thermalization hypothesis (ETH), we argue that the entanglement entropy of (almost) all energy eigenstates is described by a single crossover function. The ETH implies that the crossover functions can be deduced from subsystem entropies of thermal ensembles and have universal properties. These functions capture the full crossover from the ground-state entanglement regime at low energies and small subsystem size (area or log-area law) to the extensive volume-law regime at high energies or large subsystem size. For critical one-dimensional systems, a universal scaling function follows from conformal field theory and can be adapted for nonlinear dispersions. We use it to also deduce the crossover scaling function for Fermi liquids in d>1 dimensions. The analytical results are complemented by numerics for large noninteracting systems of fermions in d≤3 dimensions and have also been confirmed for bosonic systems and nonintegrable spin chains.

Correction to: Is debridement beneficial for focal cartilage defects of the knee: data from the German Cartilage Registry (KnorpelRegister DGOU)

A correction to this paper has been published: https://doi.org/10.1007/s00402-021-03905-0

Is debridement beneficial for focal cartilage defects of the knee: data from the German Cartilage Registry (KnorpelRegister DGOU)

INTRODUCTION

Focal cartilage defects of the knee are often treated with arthroscopic debridement. Existing literature discussing the benefit of debridement for small articular cartilage lesions is scarce, especially if the debridement was not part of a combined operative cartilage procedure including meniscal and ligament repair. The purpose of this study was to examine the patients´ benefit after arthroscopic debridement for the treatment of isolated focal chondral defects with or without partial meniscus resection.

MATERIALS AND METHODS

Baseline (preoperative data) and 12-month follow-up of the five Knee Osteoarthritis Outcome Score (KOOS) subscores and the Numeric Rating Scale (NRS) for pain were analyzed in 126 patients undergoing debridement for focal chondral defects of the knee from the German Cartilage Registry. Sub-analysis for patients receiving isolated debridement and debridement with concomitant partial resection of meniscal pathologies was performed. Thus, four subgroups were created according to the treated defect size and presence of meniscal pathologies: "debridement-only < 2 cm²", "debridement-only > 2 cm²", "debridement and partial meniscus resection < 2 cm²" and "debridement and partial meniscus resection > 2 cm²".

RESULTS

KOOS-subscores showed a significant increase from baseline to follow-up evaluation (p = 0.017-0.037) within the 126 patients. Sub-analysis showed significant improvement of all five KOOS-subscores in all three subgroups, except for the "debridement and partial meniscus resection > 2 cm²"-group: in this group the KOOS subscores symptoms and sports showed no significant improvement. The NRS scores revealed no significant changes from baseline to 12-month follow-up within the four subgroups.

CONCLUSION

An overall benefit of arthroscopic debridement for focal cartilage lesions of the knee could be conducted. Isolated cartilage defects seem to benefit from debridement irrespectively of size. In patients with large cartilage defects (> 2 cm²) and concurrent meniscal pathology expectation to improvement should be humbled. Effective reduction of pain by arthroscopic debridement remains unclear.

[Indications and techniques of arthroscopic anterior and lateral acromioplasty]

OBJECTIVE

Arthroscopic anterior acromioplasty (AAAP) for treatment of symptomatic subacromial spur. Arthroscopic lateral acromioplasty (ALAP) to reduce a pathological critical shoulder angle (CSA) and prevent rotator cuff re-tear after reconstruction.

INDICATIONS

AAAP is indicated for acromial impingement due to an anterolateral acromial spur with or without bursa-sided rotator cuff lesion. ALAP is indicated concomitant to arthroscopic rotator cuff repair if the CSA is pathologically increased.

RELATIVE CONTRAINDICATIONS

Irreparable rotator cuff tear with acetabularization of the acromion due to anterosuperior escape of the humeral head or symptomatic os acromiale can contraindicate for AAAP. Dehiscence of the origin of the deltoid muscle or symptomatic os acromiale can contraindicate for ALAP.

SURGICAL TECHNIQUE

To preform AAAP, arthroscopic subacromial decompression is followed by anterolateral resection of an acromion spur or ossification of the coracoacromial ligament. To perform ALAP, arthroscopic subacromial decompression and reconstruction of a rotator cuff-tear is followed by reduction of a pathologically increased CSA by resection of the lateral edge of the acromion.

POSTOPERATIVE MANAGEMENT

After isolated AAAP, physiotherapy can be performed without restriction. After AAAP or ALAP combined with rotator cuff repair, immobilization in a brace is recommended. The use of pain medication should be standardized and adapted to individual pain levels.

Mesenchymal Stem Cells Isolated from the Anterior Cruciate Ligament: Characterization and Comparison of Cells from Young and Old Donors

Purpose

Mesenchymal stem cells (MSCs) isolated from the anterior cruciate ligament (ACL) share multiple characteristics of bone marrow-derived mesenchymal stem cells (BMSCs), allowing their use for regenerative therapies. Injuries to the ACL can affect people of all ages. This study assesses whether the regenerative potential of ACL-derived MSCs (ACL-MSCs) from old donors is as high as the potential of ACL-MSCs from young donors.

Materials and Methods

ACL-MSCs were isolated from ACL tissues obtained from young and old donors at the time of ACL reconstruction or arthroplasty. Proliferative capacity, multilineage differentiation potential (chondrogenic, osteogenic, and adipogenic lineages), and transcriptome-wide gene expression were assessed and compared between young and old donors. BMSCs of middle-aged donors served as an additional comparator.

Results

No substantial differences between ACL-MSCs from young and old donors were observed in their proliferative capacity and multilineage differentiation potential. The latter did not substantially differ between both ACL-MSC groups and BMSCs. Differential expression of genes related to the cytoskeleton and to protein dephosphorylation amongst other pathways was detected between ACL-MSCs from young and old donors.

Conclusions

Regenerative potential of ACL-MSCs from old donors was not substantially lower than that from young donors, suggesting that regenerative therapies of ACL tears are feasible in both age groups. In vivo studies of the effect of age on the efficacy of such therapies are needed.

Fundamental Limitations for Measurements in Quantum Many-Body Systems

Dynamical measurement schemes are an important tool for the investigation of quantum many-body systems, especially in the age of quantum simulation. Here, we address the question whether generic measurements can be implemented efficiently if we have access to a certain set of experimentally realizable measurements and can extend it through time evolution. For the latter, two scenarios are considered: (a) evolution according to unitary circuits and (b) evolution due to Hamiltonians that we can control in a time-dependent fashion. We find that the time needed to realize a certain measurement to a predefined accuracy scales in general exponentially with the system size-posing a fundamental limitation. The argument is based on the construction of ϵ-packings for manifolds of observables with identical spectra and a comparison of their cardinalities to those of ϵ-coverings for quantum circuits and unitary time-evolution operators. The former is related to the study of Grassmann manifolds.

Surgical technique and clinical outcome of arthroscopic shoulder stabilization via suture anchors using the lasso-loop stitch

During arthroscopic Bankart-repair the lasso-loop-stitch can be used. The clinical outcome of this technical modification to a broadly used procedure is not known. We followed-up 24 patients treated with this technique over 30 months. We found an excellent clinical outcome in 96% of all cases. The average Rowe-score was 96.3 points. The mean QuickDash was 2.8 points. Using the lasso-loop-stitch in arthroscopic Bankart-repair is safe and results in very good clinical outcomes. It might lead to an accentuated labral bump and enables secure knot-tying with knot-positioning away from the articular cartilage while avoiding the suture cutting through the tissue.

Matrix product algorithm for stochastic dynamics on networks applied to nonequilibrium Glauber dynamics

We introduce and apply an efficient method for the precise simulation of stochastic dynamical processes on locally treelike graphs. Networks with cycles are treated in the framework of the cavity method. Such models correspond, for example, to spin-glass systems, Boolean networks, neural networks, or other technological, biological, and social networks. Building upon ideas from quantum many-body theory, our approach is based on a matrix product approximation of the so-called edge messages-conditional probabilities of vertex variable trajectories. Computation costs and accuracy can be tuned by controlling the matrix dimensions of the matrix product edge messages (MPEM) in truncations. In contrast to Monte Carlo simulations, the algorithm has a better error scaling and works for both single instances as well as the thermodynamic limit. We employ it to examine prototypical nonequilibrium Glauber dynamics in the kinetic Ising model. Because of the absence of cancellation effects, observables with small expectation values can be evaluated accurately, allowing for the study of decay processes and temporal correlations.

[Refixation of the biceps tendon onto the radial tuberosity using two suture anchors]

OBJECTIVE

Reinsertion of the distal biceps tendon onto the radial tuberosity restoring full force of flexion and supination.

INDICATIONS

Distal biceps tendon avulsion from the radial tuberosity. Acute and chronic tears with a tendon stump, which can be mobilized and reduced to the radial tuberosity in flexion and supination.

CONTRAINDICATIONS

Tears of the musculotendinous junction. Chronic distal biceps tendon tears with wide retraction and the need for tendon graft augmentation. Severe atrophy of the biceps muscle.

SURGICAL TECHNIQUE

In supination, the skin is incised longitudinally for 4 cm, centered over the medial border of the radial tuberosity. Incision starts 2 cm distal from the humeroradial joint line. Bluntly the distal biceps tendon stump is found and mobilized. Preparation and debriding of the radial tuberosity sparing neurovascular structures. Crossing vessel branches are ligated, if needed. Positioning of two spreading anchors into the radial tuberosity and reinsertion of the tendon stump.

POSTOPERATIVE MANAGEMENT

Adjustable elbow movement orthosis adapted to tendon quality and tissue tension for 6 weeks without active flexion or supination. Degree of extension is gradually increased by 20° every 2 weeks. After orthosis treatment is finished after 6 weeks, flexion and supination with weights is not allowed for another 6 weeks.

RESULTS

In a retrospective study of 30 patients with a mean follow-up of 45 months (range 15-80 months), the clinical outcome was good or excellent in 99% of cases. On average, a Mayo Elbow Performance Score of 93 points (range 65-100 points) and a QuickDash of 5 points (range 0-39 points) were achieved.

Arthroskopische Therapie bei spinoglenoidalem Ganglion

Aims and Indications A paralabral ganglion cyst of the shoulder can cause neuropathy of the inferior branches of the suprascapular nerve. This can lead to atrophy of the infraspinatus muscle. Arthroscopic decompression of the cyst in combination with repair of the associated labrum tear appears to be an effective treatment option. Methods Initially the connection of the cyst to the joint in the area of the posterior rim of the glenoid is identified arthroscopically. Following the decompression of the cyst the labrum tear is repaired to avoid recurrence. The goal is the complete decompression of the ganglion cyst carefully protecting the infraspinatus branch. Concomitant intraarticular pathologies are also addressed. Conclusions In the literature arthroscopic treatment is superior to open surgical treatments. The degree of muscle atrophy at the time of surgery determines the prognosis for functional recovery. There is a lack of long-term outcome studies and publications of larger case series.

Case report - calcification of the medial collateral ligament of the knee with simultaneous calcifying tendinitis of the rotator cuff

BACKGROUND

Calcification of the medial collateral ligament (MCL) of the knee is a very rare disease. We report on a case of a patient with a calcifying lesion within the MCL and simultaneous calcifying tendinitis of the rotator cuff in both shoulders.

CASE PRESENTATION

Calcification of the MCL was diagnosed both via x-ray and magnetic resonance imaging (MRI) and was successfully treated surgically. Calcifying tendinitis of the rotator cuff was successfully treated applying conservative methods.

CONCLUSION

This is the first case report of a patient suffering from both a calcifying lesion within the medial collateral ligament and calcifying tendinitis of the rotator cuff in both shoulders. Clinical symptoms, radio-morphological characteristics and macroscopic features were very similar and therefore it can be postulated that the underlying pathophysiology is the same in both diseases. Our experience suggests that magnetic resonance imaging and x-ray are invaluable tools for the diagnosis of this inflammatory calcifying disease of the ligament, and that surgical repair provides a good outcome if conservative treatment fails. It seems that calcification of the MCL is more likely to require surgery than calcifying tendinitis of the rotator cuff. However, the exact reason for this remains unclear to date.

Nail-patella-syndrome in a young patient followed up over 10 years: relevance of the sagittal trochlear septum for patellofemoral pathology

INTRODUCTION

Nail-patella-syndrome (NPS) is a rare autosomal-dominant inherited disease with pathologies of nails, skeleton, kidneys, and eyes. Linkage to a mutated gene was found. It codes for the transcription-factor LMX1B. In most cases knees are symptomatic. Patients have hypoplastic patellae, which are laterally subluxated. In those individuals a sagittal trochlear fibrous septum was found, dividing the anterior knee-joint-space. In the literature the etiology and clinical significance of this anatomic abnormality is unclear. Based on clinical and intraoperative findings we developed a theory regarding knee pathology in nail-patella-syndrome. Successful treatment via early resection of the septum with sustained good outcome is presented.

METHODS

In a symptomatic six-year-old boy with nail-patella-syndrome we resected the fibrous sagittal septum adherent to the trochlea femoris and we balanced the patella via lateral release and medial plication in both knee joints. We analyzed the clinical outcome of this procedure prospectively over 10 years.

RESULTS

Postoperatively the hypoplastic patellae stayed centered and stable during further skeletal development. The patient was still pain free with normal range of motion of both operated knee joints after 10 years of follow-up.

DISCUSSION

In patients with nail-patella-syndrome and a subluxated or dislocated patella we recommend diagnostics with magnetic-resonance-imaging and early surgical treatment via resection of the trochlear septum and soft-tissue-balancing of the patella. When the septum displaces the patella and prevents physiological articulation of the patella with the trochlea femoris, early septum resection is likely to be important for a good functional outcome and proper development of the patellofemoral joint during growth.

No significant difference in clinical outcome and knee stability between patellar tendon and semitendinosus tendon in anterior cruciate ligament reconstruction

INTRODUCTION

ACL reconstruction with either patellar tendon or semitendinosus tendon autografts are standard procedures. Between these two grafts might be differences in stability, morbidity, or long-term changes. This study investigates outcomes of ACL reconstruction with patellar tendon versus semitendinosus tendon autografts. We hypothesize no significant differences in clinical outcome and knee stability between both groups.

METHODS

In a randomized prospective trial, we operated 62 ACL-deficient patients, 45 males and 17 females with a mean age of 29.8 years (min. 18, max. 44). We reconstructed the ligament using either autologous patellar tendon (n = 31) or semitendinosus tendon (n = 31). After 10 years of follow-up, we investigated 47 patients of the study. For evaluation we used a standard clinical examination including one-leg jump test and KT-1000 instrumental translation measure, visual analog pain scale, IKDC subjective knee form, Lysholm score, Tegner activity scale, and standard X-rays of the knee.

RESULTS

The data did not show any significant differences between the two groups. Between 5 and 10 years after ACL reconstruction both groups started to develop degenerative arthritic changes, which were detectable in standard radiographs of the knee. At 10-year follow-up mean IKDC for the BPTB group was 1.8 (min. 1, max. 3) and for the ST group it was 2.2 (min 1, max. 4), p = 0.35. Regarding Tegner activity scale after 10 years, the BPTB group showed a mean score of 5.9 (min. 4, max. 9) versus 5.1 (min. 3, max. 7) in the ST group, p = 0.53. For the Lysholm score the BPTB group reached a mean of 92.0 (min. 63, max. 98) and the ST group 91.8 (min. 62, max. 98) points, p = 0.66. There is a tendency for higher donor site morbidity in the BPTB group than in the ST group, p = 0.07.

CONCLUSIONS

Both, patellar tendon and semitendinosus tendon are safe autografts for ACL reconstruction. Regarding graft selection, individual patient-dependent factors should be considered. ACL reconstruction cannot fully restore pre-injury status of knee joint function in the majority of cases.

Phase Diagram of an Extended Quantum Dimer Model on the Hexagonal Lattice

We introduce a quantum dimer model on the hexagonal lattice that, in addition to the standard three-dimer kinetic and potential terms, includes a competing potential part counting dimer-free hexagons. The zero-temperature phase diagram is studied by means of quantum Monte Carlo simulations, supplemented by variational arguments. It reveals some new crystalline phases and a cascade of transitions with rapidly changing flux (tilt in the height language). We analyze perturbatively the vicinity of the Rokhsar-Kivelson point, showing that this model has the microscopic ingredients needed for the "devil's staircase" scenario [Eduardo Fradkin et al. Phys. Rev. B 69, 224415 (2004)], and is therefore expected to produce fractal variations of the ground-state flux.

[Sliding osteotomy of the tibial tuberosity in patellofemoral instability]

OBJECTIVE

The development of a stable patellofemoral joint by distal realignment with normal positioning of the patella.

INDICATIONS

Patellofemoral instability with increased tibial tubercle to trochlear groove (TT-TG) distance ≥ 20 mm and higher Caton-Deschamps patellar height index ≥ 1.3.

CONTRAINDICATIONS

Open epiphyseal and apophyseal plates of the proximal tibia, normal TT-TG distance with normal patellar height, and high-grade chondral lesions of the patellofemoral joint (ICRS grades 3 and 4).

SURGICAL TECHNIQUE

Examination of the knee joint under anesthesia and evaluation of stability and mediolateral translation of the patella. Diagnostic knee arthroscopy and treatment of chondral or osteochondral lesions. Lateral approach to the tibial tuberosity with soft tissue mobilization and exposure of the patellar tendon. Osteotomy is performed in the frontal plane, creating a fragment at least 6 cm long. The tuberosity is slid into the desired position, medially and distally, if necessary, according to preoperative analysis and planning, followed by careful drilling of the posterior tibial cortex and lag screw osteosynthesis.

POSTOPERATIVE MANAGEMENT

Partial weight-bearing of 20 kg in a MECRON knee brace for 6 weeks. Mobilization 0/0/90° from the MECRON knee brace without active knee extension. Isometric training of the thigh muscles with the knee fully extended.

RESULTS

With meticulous planning and implementation, and in cases of severe trochlear dysplasia combined with medial patellofemoral ligament reconstruction, the technique of sliding osteotomy of the tibial tuberosity has a high success rate.

Algebraic versus Exponential Decoherence in Dissipative Many-Particle Systems

The interplay between dissipation and internal interactions in quantum many-body systems gives rise to a wealth of novel phenomena. Here we investigate spin-1/2 chains with uniform local couplings to a Markovian environment using the time-dependent density matrix renormalization group. For the open XXZ model, we discover that the decoherence time diverges in the thermodynamic limit. The coherence decay is then algebraic instead of exponential. This is due to a vanishing gap in the spectrum of the corresponding Liouville superoperator and can be explained on the basis of a perturbative treatment. In contrast, decoherence in the open transverse-field Ising model is found to be always exponential. In this case, the internal interactions can both facilitate and impede the environment-induced decoherence.

Multispinon continua at zero and finite temperature in a near-ideal Heisenberg chain

The space-and time-dependent response of many-body quantum systems is the most informative aspect of their emergent behavior. The dynamical structure factor, experimentally measurable using neutron scattering, can map this response in wave vector and energy with great detail, allowing theories to be quantitatively tested to high accuracy. Here, we present a comparison between neutron scattering measurements on the one-dimensional spin-1/2 Heisenberg antiferromagnet KCuF3, and recent state-of-the-art theoretical methods based on integrability and density matrix renormalization group simulations. The unprecedented quantitative agreement shows that precise descriptions of strongly correlated states at all distance, time, and temperature scales are now possible, and highlights the need to apply these novel techniques to other problems in low-dimensional magnetism.

Quasilocality and efficient simulation of markovian quantum dynamics

We consider open many-body systems governed by a time-dependent quantum master equation with short-range interactions. With a generalized Lieb-Robinson bound, we show that the evolution in this very generic framework is quasilocal; i.e., the evolution of observables can be approximated by implementing the dynamics only in a vicinity of the observables' support. The precision increases exponentially with the diameter of the considered subsystem. Hence, time evolution can be simulated on classical computers with a cost that is independent of the system size. Providing error bounds for Trotter decompositions, we conclude that the simulation on a quantum computer is additionally efficient in time. For experiments and simulations in the Schrödinger picture, our result can be used to rigorously bound finite-size effects.

Solving condensed-matter ground-state problems by semidefinite relaxations

We present a generic approach to the condensed-matter ground-state problem which is complementary to variational techniques and works directly in the thermodynamic limit. Relaxing the ground-state problem, we obtain semidefinite programs (SDP). These can be solved efficiently, yielding strict lower bounds to the ground-state energy and approximations to the few-particle Green's functions. As the method is applicable for all particle statistics, it represents, in particular, a novel route for the study of strongly correlated fermionic and frustrated spin systems in D>1 spatial dimensions. It is demonstrated for the XXZ model and the Hubbard model of spinless fermions. The results are compared against exact solutions, quantum Monte Carlo calculations, and Anderson bounds, showing the competitiveness of the SDP method.

[Minimally invasive retrograde drilling of osteochondral lesions of the femur using an arthroscopic drill guide]

OBJECTIVE

Retrograde drilling for penetration of subchondral sclerotic bone in osteochondrosis dissecans (OCD) of the femoral condyle with preserved cartilage integrity. Hereby, revascularization of the OCD and immigration of bone marrow cells to achieve stable reintegration of the OCD into the surrounding subchondral bone.

INDICATIONS

Stable juvenile and adult osteochondrosis dissecans (stage I-II of the International Cartilage Repair Society (ICRS) classification) of the medial and lateral femoral condyle with an intact articular surface and surrounding sclerosis zone, which is visible in the x-ray.

CONTRAINDICATIONS

OCD stage III-IV of the ICRS grading scale. Relative contraindication: preceding retrograde drilling.

SURGICAL TECHNIQUE

Arthroscopic inspection and palpation of the cartilage defect. Minimal incision over the M. vastus medialis (when the defect is located in the medial condyle) or the M. vastus lateralis (when the defect is located in the medial condyle). Preparation and dissection of the fascia of the vastus muscle. Insertion of retractors underneath the vastus muscle to expose the metaphysis of the distal femur. Intraarticular positioning of the arthroscopic drill guide, placement of the wire guide and a Kirschner(K) wire on the femur metaphysis and retrograde drilling with a 2.0-2.2 mm K wire under radiographic visualization. Length measurement of the intraosseous wire distance. Switch the guide mechanism to a multiple hole drill guide and, depending on the defect size, insertion of a further 7-10 K wires of same thickness and defined length.

POSTOPERATIVE MANAGEMENT

Sterile bandage and slightly compressive dressing. Continuous active and passive knee motion. Weight bearing of 20 kg for 6 weeks, with subsequent transition to continuous weight bearing. Radiographic controls at 6 and 12 weeks postoperatively. In case of a persistent sclerosis zone in the control x-ray or clinical abnormalities, control MRI is indicated.

RESULTS

A total of 55 patients with a mean age of 19.6 years were treated using the described technique: 49 patients (89.1%), and 54 knees respectively (35 juvenile OCD, 19 adult OCD), were seen with a mean follow-up of 37.9 months. An improvement was observed in 81.6% of the knees using the radiographic score, i.e., a mean improvement of 1.13 of the radiographic score published by Rodegerdts and Gleissner (preoperative 3.04 vs. postoperative 1.91). Juvenile OCD showed better radiographic results overall (88.2% healing) than adult OCD (66.7% healing).

A prospective multicenter study on the outcome of type I collagen hydrogel-based autologous chondrocyte implantation (CaReS) for the repair of articular cartilage defects in the knee

BACKGROUND

The Cartilage Regeneration System (CaReS) is a novel matrix-associated autologous chondrocyte implantation (ACI) technique for the treatment of chondral and osteochondral lesions (Outerbridge grades III and IV). For this technology, no expansion of the chondrocytes in a monolayer culture is needed, and a homogeneous cell distribution within the gel is guaranteed.

PURPOSE

To report a prospective multicenter study of matrix-associated ACI of the knee using a new type I collagen hydrogel (CaReS).

STUDY DESIGN

Case series; Level of evidence, 4.

METHODS

From 2003 to 2008, 116 patients (49 women and 67 men; mean age, 32.5 ± 8.9 years) had CaReS implantation of the knee in 9 different centers. On the basis of the International Cartilage Repair Society (ICRS) Cartilage Injury Evaluation Package 2000, the International Knee Documentation Committee (IKDC) score, pain score (visual analog scale [VAS]), SF-36 score, overall treatment satisfaction and the IKDC functional status were evaluated. Patient follow-up was performed at 3, 6, and 12 months after surgery and annually thereafter. Mean follow-up was 30.2 ± 17.4 months (range, 12-60 months). There were 67 defects of the medial condyle, 14 of the lateral, 22 of the patella/trochlea, and 3 of the tibial plateau, and 10 patients had 2 lesions. The mean defect size was 5.4 ± 2.4 cm(2). Thirty percent of the defects were <4 cm(2) and 70% were >4 cm(2).

RESULTS

The IKDC score improved significantly from 42.4 ± 13.8 preoperatively to 70.5 ± 18.7 (P < .001) at latest follow-up. Global pain level significantly decreased (P < .001) from 6.7 ± 2.2 preoperatively to 3.2 ± 3.1 at latest follow-up. There also was a significant increase of both components of the SF-36 score. The overall treatment satisfaction was judged as very good or good in 88% by the surgeon and 80% by the patient. The IKDC functional knee status was grade I in 23.4%, II in 56.3%, III in 17.2%, and IV in 3.1% of the patients.

CONCLUSION

Matrix-associated ACI employing the CaReS technology for the treatment of chondral or osteochondral defects of the knee is a safe and clinically effective treatment that yields significant functional improvement and improvement in pain level. However, further investigation is necessary to determine the long-term viability and clinical outcome of this procedure.

Dissipative quantum Church-Turing theorem

We show that the time evolution of an open quantum system, described by a possibly time dependent Liouvillian, can be simulated by a unitary quantum circuit of a size scaling polynomially in the simulation time and the size of the system. An immediate consequence is that dissipative quantum computing is no more powerful than the unitary circuit model. Our result can be seen as a dissipative Church-Turing theorem, since it implies that under natural assumptions, such as weak coupling to an environment, the dynamics of an open quantum system can be simulated efficiently on a quantum computer. Formally, we introduce a Trotter decomposition for Liouvillian dynamics and give explicit error bounds. This constitutes a practical tool for numerical simulations, e.g., using matrix-product operators. We also demonstrate that most quantum states cannot be prepared efficiently.

Mesenchymal stem cell characteristics of human anterior cruciate ligament outgrowth cells

When ruptured, the anterior cruciate ligament (ACL) of the human knee has limited regenerative potential. However, the goal of this report was to show that the cells that migrate out of the human ACL constitute a rich population of progenitor cells and we hypothesize that they display mesenchymal stem cell (MSC) characteristics when compared with adherent cells derived from bone marrow or collagenase digests from ACL. We show that ACL outgrowth cells are adherent, fibroblastic cells with a surface immunophenotype strongly positive for cluster of differentiation (CD)29, CD44, CD49c, CD73, CD90, CD97, CD105, CD146, and CD166, weakly positive for CD106 and CD14, but negative for CD11c, CD31, CD34, CD40, CD45, CD53, CD74, CD133, CD144, and CD163. Staining for STRO-1 was seen by immunohistochemistry but not flow cytometry. Under suitable culture conditions, the ACL outgrowth-derived MSCs differentiated into chondrocytes, osteoblasts, and adipocytes and showed capacity to self-renew in an in vitro assay of ligamentogenesis. MSCs derived from collagenase digests of ACL tissue and human bone marrow were analyzed in parallel and displayed similar, but not identical, properties. In situ staining of the ACL suggests that the MSCs reside both aligned with the collagenous matrix of the ligament and adjacent to small blood vessels. We conclude that the cells that emigrate from damaged ACLs are MSCs and that they have the potential to provide the basis for a superior, biological repair of this ligament.

Real-space renormalization yields finite correlations

Real-space renormalization approaches for quantum lattice systems generate certain hierarchical classes of states that are subsumed by the multiscale entanglement renormalization Ansatz (MERA). It is shown that, with the exception of one spatial dimension, MERA states are actually states with finite correlations, i.e., projected entangled pair states (PEPS) with a bond dimension independent of the system size. Hence, real-space renormalization generates states which can be encoded with local effective degrees of freedom, and MERA states form an efficiently contractible class of PEPS that obey the area law for the entanglement entropy. It is further pointed out that there exist other efficiently contractible schemes violating the area law.

Snapping elbow caused by hypertrophic synovial plica in the radiohumeral joint: a report of three cases and review of literature

The snapping elbow caused by hypertrophic synovial radiohumeral plica is a rare form of lateral elbow impingement. In this article we report on hypertrophic radiohumeral synovial folds in three male patients, aged 54, 65 and 27 years. All three patients suffered isolated lateral elbow pain, painful snapping and unsuccessful conservative treatment over at least 5 months (range 5-9 months, mean 7.7 months) prior to surgical treatment. None of the patients had lateral epicondylitis, instability, osteochondrosis dissecans, loose bodies, arthritis or neurological disorders. Upon clinical examination the range of motion in the respective painful elbows was found to be normal in all three cases, but a painful snapping occurred between 80 degrees and 100 degrees of flexion with the forearm in pronation. While there were no pathologic findings in standard radiographs, magnetic resonance imaging (MRI) revealed hypertrophic synovial plicae in the radiohumeral joints associated with effusion in each of the diseased elbows. Arthroscopic examinations confirmed the presence of a hypertrophic synovial plica in all three radiocapitellar joints, and revealed a transient interposition and compression of the folds in the articulation from extension until 90 degrees -100 degrees elbow flexion, with replacement beyond 90 degrees elbow flexion with a visible jump. Surgical management in all three cases comprised arthroscopic diagnosis confirmation and removal of the synovial plicae, leading to excellent outcomes at 6-12 months follow-up.

Predictive formula for the length of tibial tunnel in anterior crucitate ligament reconstruction

BACKGROUND

The anterior cruciate ligament (ACL) reconstruction using bone-patellar tendon bone graft is a common procedure in orthopedics. One challenging problem found is a graft-tunnel mismatch. Previous studies have reported the mathematic formula to predict the tibial angle length and angle to avoid graft-tunnel mismatch but these formulas have shown limited predictability.

OBJECTIVE

To propose a predictive formula for the length of tibial tunnel and to examine its predictability.

MATERIAL AND METHOD

Thirty six patients (26 males, 14 females) with ACL injury were included in this study. The preoperativemedial proximal tibial angle was measured. Intraoperatively, the tibial tunnel length and tibial entry point were measured. The postoperative coronal and saggital angle of tibial tunnel were measured from knee radiograph. The data were analysed by using trigonometry correlation and formulate the predictive formula of tibial tunnel length.

RESULTS

We found that tibial tunnel length (T) has trigonometric correlation between the location of tibial tunnel entry point (w), coronal angle of tibial tunnel (b), saggital angle of tibial tunnel (a) and the medial proximal tibial slope (c) by using this formula T = Wcos(c)tan(b)/sin(a)

CONCLUSION

This proposed predictive formula can well predict the length of the tibial tunnel at preoperative period to avoid graft-tunnel mismatch.

Influence of phosphatidylserine on cognitive performance and cortical activity after induced stress

The aim of this study was to investigate the effect of phosphatidylserine (PS) on cognition and cortical activity after mental stress. After familiarization, 16 healthy subjects completed cognitive tasks after induced stress in a test-re-test design (T1 and T2). Directly after T1, subjects were assigned double-blind to either PS or placebo groups followed by T2 after 42 days. At T1 and T2, cortical activity was measured at baseline and immediately after stress with cognitive tasks using electro-encephalography (EEG). EEG was recorded at 17 electrode positions and fast Fourier transforms (FFT) determined power at Theta, Alpha-1, Alpha-2, Beta-1 and Beta-2. Statistics were calculated using ANOVA (group x trial x time). The main finding of the study was that chronic supplementation of phosphatidylserine significantly decreases Beta-1 power in right hemispheric frontal brain regions (F8; P < 0.05) before and after induced stress. The results for Beta-1 power in the PS group were connected to a more relaxed state compared to the controls.

Dephasing and the steady state in quantum many-particle systems

We discuss relaxation in bosonic and fermionic many-particle systems. For integrable systems, time evolution can cause a dephasing effect, leading for finite subsystems to steady states. We explicitly derive those steady subsystem states and devise sufficient prerequisites for the dephasing to occur. We also find simple scenarios, in which dephasing is ineffective and discuss the dependence on dimensionality and criticality. It follows further that, after a quench of system parameters, entanglement entropy will become extensive. This provides a way of creating strong entanglement in a controlled fashion.

VAP-1, Eotaxin3 and MIG as potential atherosclerotic triggers of severe calcified and stenotic human aortic valves: Effects of statins

Sclerotic calcification of the aortic valve is a common disease in advanced age. Its pathophysiology is unclear. However, pathobiological similarities to atherosclerosis have been shown in several studies. The current study assesses gene profiling of severe calcified stenotic human aortic valves identifying transforming growth factor (TGF)-beta, Eotaxin3, vascular adhesion protein-1 (VAP-1) and monokine induced by interferon-gamma (MIG) as potential atherosclerotic target genes in severe calcified and stenotic aortic valves, and analyzes the effects of statins on their expression as part of an anti-inflammatory treatment strategy. We collected human severe calcified and stenotic aortic valves with (CSAV+) or without (CSAV-) statin pre-treatment prior to valve replacement and investigated gene profiling by using micro-array technique and real-time PCR for the TGF-beta, Eotaxin3, VAP-1 and MIG expression. In comparison to atherosclerotic plaques of carotid arteries, immunohistochemical staining was investigated. Results were contrasted to human normal non-calcified aortic valves as controls (C). As compared to C, TGF-beta, Eotaxin3, MIG or VAP-1 was significantly upregulated in CSAV-. In CSAV+ no significant change in gene expression was found for Eotaxin3 and MIG. In contrast, VAP-1 and TGF-beta were still upregulated. Corresponding gene expression was confirmed on atherosclerotic plaque formations of carotid arteries. Monocyte/Macrophage infiltration (presence of CD68) on aortic valves (CSAV+, CSAV-, or C) confirmed inflammatory nature of the disease. Our data support further evidence for atherosclerotic inflammation as a trigger for sclerosis in end-stage calcified stenotic aortic valves by showing upregulation of gene expression for TGF-beta, VAP-1, MIG and Eotaxin3, which is only partially inhibited by previous statin therapy. Potent benefits of statin treatment on early stages of valve disease are still propagated.

9- to 11-year results of cemented titanium mueller straight stem in total hip arthroplasty

This retrospective study reviewed 9- to 11-year results after total hip arthroplasty (THA) with cemented titanium stems (Mueller-Straight-Stem). Ninety-one patients (110 hips) were examined clinically and radiologically at an average 9.5-year follow-up. Revisions for aseptic loosening were performed in 4 (4%) patients. Subsidence or varus position could only be observed in one of these patients. Radiolucent lines were found in 37 patients, mainly located around the proximal zones of the stem (zone 1, 7, 8, and 14). Harris scores were good or excellent in 78% and satisfactory in 20% of patients. The 9.5-year survival rate of the cemented titanium stem with regard to aseptic loosening was 96.4%. Body weight was significantly higher (88 +/- 5.4 kg) in the 4 patients with aseptic loosening, compared to patients without radiolucent lines (75 +/- 15 kg). The body weight to stem surface ratio showed a significant difference (1.5 kg/cm2 versus 1 kg/cm2; P < .05). No significant differences were found in other factors, including sex, size or type of stem, Harris score, heterotopic ossification, or body mass index. Good long-term results can be achieved with cemented titanium stem implants. This titanium implant is recommended for patients with hypersensitivity to chrome, cobalt, and nickel. mplanting the biggest possible stem seems to be most beneficial.

Entanglement entropy beyond the free case

We present a perturbative method to compute the ground state entanglement entropy for interacting systems. We apply it to a collective model of mutually interacting spins in a magnetic field. At the quantum critical point, the entanglement entropy scales logarithmically with the subsystem size, the system size, and the anisotropy parameter. We determine the corresponding scaling prefactors and evaluate the leading finite-size correction to the entropy. Our analytical predictions are in perfect agreement with numerical results.

Anterior cruciate ligament constructs fabricated from human mesenchymal stem cells in a collagen type I hydrogel

BACKGROUND

Disruptions of the anterior cruciate ligament (ACL) of the knee joint are common and are currently treated using ligament or tendon grafts. In this study, we tested the hypothesis that it is possible to fabricate an ACL construct in vitro using mesenchymal stem cells (MSC) in combination with an optimized collagen type I hydrogel, which is in clinical use for autologous chondrocyte transplantation (ACT).

METHODS

ACL constructs were molded using a collagen type I hydrogel containing 5 x 10(5) MSC/mL and non-demineralized bone cylinders at each end of the constructs. The constructs were kept in a horizontal position for 10 days to allow the cells and the gel to remodel and attach to the bone cylinders. Thereafter, cyclic stretching with 1 Hz was performed for 14 days (continuously for 8 h/day) in a specially designed bioreactor.

RESULTS

Histochemical analysis for H and E, Masson-Goldner and Azan and immunohistochemical analysis for collagen types I and III, fibronectin and elastin showed elongated fibroblast-like cells embedded in a wavy orientated collagenous tissue, together with a ligament-like extracellular matrix in the cyclic stretched constructs. No orientation of collagen fibers and cells, and no formation of a ligament-like matrix, could be seen in the non-stretched control group cultured in a horizontal position without tension. RT-PCR analysis revealed an increased gene expression of collagen types I and III, fibronectin and elastin in the stretched constructs compared with the non-stretched controls.

DISCUSSION

In conclusion, ACL-like constructs from a collagen type I hydrogel, optimized for the reconstruction of ligaments, and MSC have been fabricated. As shown by other investigators, who analyzed the influence of cyclic stretching on the differentiation of MSC, our results indicate a ligament-specific increased protein and gene expression and the formation of a ligament-like extracellular matrix. The fabricated constructs are still too weak for animal experiments or clinical application and current investigations are focusing on the development of a construct with an internal augmentation using biodegradable fibers.

Ultrasonography for intraoperative control of the amount of bone resection in arthroscopic acromioclavicular joint resection

Remaining superior osteophytes or osseous spurs after arthroscopic lateral clavicle resection can cause persistent pain and could lead to revision surgery. A new method of intraoperative ultrasonographic imaging of the result of the operation during arthroscopic lateral clavicle resection is presented. In 10 patients with acromioclavicular arthritis, standardized arthroscopic lateral clavicle resection was performed. Intraoperatively, the space between the clavicle and the acromion was measured before and after arthroscopic acromioclavicular resection using a Sonosite 180 plus (SonoSite, Bothell, WA) with a 10-MHz broadband linear array in a sterile bag. The width of the joint space between the clavicle and the acromion was between 0.38 and 0.56 cm before operation and 0.92 cm and 1.28 cm after operation (nine cases). In one case, the anticipated minimum resection of 0.5 cm was not achieved at the sonographic measurement and further resection was required. Real-time ultrasonography allows exact measurement of the amount of resected bone during arthroscopic lateral clavicle resection. This could avoid revision surgery resulting from persisting disability caused by insufficient or extensive bone resection.

[Anatomy of the glenoid labrum]

Most instabilities or pain syndromes are associated with injuries or morphologic changes in the glenoid labrum complex or long head of the biceps tendon origin. The first anatomic descriptions go back to Fick in 1910 and since then many authors have described the anatomy of these structures. It was Snyder who introduced the term SLAP lesions, classifying superior, anterior, posterior labrum changes into four grades. It is still unclear whether all of the described and arthroscopically observed changes are due to a post-traumatic, acquired lesion or whether anatomic variations can be present as well. In order to elucidate this problem, 36 cadaver shoulder joints were inspected macroscopically and sectioned for microscopic evaluation. Here the glenoid could be divided into an superior and an anterior- superior area demonstrating a wide variety of morphologic labral glenoid changes, while the dorsal and inferior sectors of the glenoid showed a relatively uniform anatomy of a firm labrum-glenoid bond. Four types of biceps tendon attachments could be identified similar to the description given by Vangsness. In addition, a variety of anterior-superior changes could be found. The sublabral hole as described by Esch in the clinical setting was found to be a physiologic variant. Precise knowledge of the anatomic morphology of the normal glenoid in its variations seems to be necessary to understand variants and allow for distinguishing between physiologic anatomic variants and pathoanatomic changes in imaging and the clinical setting.

Prophylaxis of heterotopic ossification after total hip arthroplasty: a prospective randomized study comparing indomethacin and meloxicam

We performed a randomized, prospective study on the prophylaxis of heterotopic ossification (HO) after total hip arthroplasty (THR), comparing indomethacin and the selective COX-2 inhibitor meloxicam. From the day after surgery, 272 patients were treated with 7.5 mg meloxicam, 15 mg meloxicam, or 2 x 50 mg indomethacin a day, for 14 days. After 6 months, radiographs of patients treated with 7.5 mg meloxicam showed that HO had occurred in one third. This treatment was therefore stopped after 26 patients have been assigned to this group. According to the intention-to-treat principle, patients given 15 mg meloxicam developed HO in 25% (20% Brooker grade I, 4% grade II and 1% grade III) and those given indomethacin in 10% (7% Brooker grade I, 1% grade II and 2% grade III), a statistically significant difference.

Biomechanical evaluation of braces used for the treatment of epicondylitis

The purpose of the study was to investigate the biomechanical effects of different types of braces that are used in the treatment of patients with epicondylitis radialis. Vibration and acceleration of the forearm and the elbow were measured with sensors taped to defined anatomic points on the skin surface. The impact-induced vibration of the racket-arm system was analyzed while the subjects were playing tennis. Different designed brace systems were investigated with respect to acceleration amplitudes and acceleration integrals. Clasp-based brace systems showed a slight reduction of acceleration amplitudes (-6%) and acceleration integrals (-8%). Braces with pads at the lateral epicondyle reduced acceleration amplitudes by 20% and acceleration integrals by 22%. Braces with pads placed at the forearm showed the highest reduction of acceleration amplitudes (-46%) and acceleration integrals (-42%). Overload of the wrist extensors, which is considered to be a major pathogenic factor in lateral epicondylitis, can be reduced by braces. There is a significant difference in the effects among different biomechanical principles of braces.

Arthroscopic treatment of septic joints: prognostic factors

From 1987 to 1993, 88 patients (average age 48 years, range 3 months to 83 years) with septic arthritis were treated at the orthopaedic clinic König Ludwig Haus of the University of Würzburg by arthroscopic means consisting of joint debridement and application of suction drains, combined with appropriate antibiotics and early functional treatment. The series consisted of 78 knees, 8 shoulders and 3 ankles. At the first visit to our clinic, patients typically presented with fever, leucocytosis, elevated sedimentation rate and localized findings in almost every joint involved (generalized tenderness, swelling, effusion, painful and limited range of motion). All the patients were taken to the operating room on an emergency basis. Broad-spectrum antibiotics were given before the initial culture was evaluated, and its sensitivity was determined. Recovery from arthritis by elimination of joint effusion and disappearance of the inflammatory syndrome occurred in all the joints except for 3 (1 knee joint and 2 shoulders). The number of arthroscopic procedures needed to become free from infection depended on the one hand on the time between onset of symptoms and arthroscopic surgery and on the other on the kind of microorganism discovered. At the average follow-up evaluation after 2.5 years (range 6 months to 5 years), the functional results were excellent or good in 61% of the patients, satisfactory in 20% and poor in 19% from our series. This functional outcome depends on the degenerative changes of the joint before infection, patient's age, and the time interval between onset of symptoms and surgical intervention; indirectly, the time lapse between the onset of infection and surgical intervention also had an influence on the intraoperative macroscopic appearance.

Readiness potential in different states of physical activation and after ingestion of taurine and/or caffeine containing drinks

To investigate the influence of taurine and caffeine containing drinks and physical stress on the cortical movement-preparation, the readiness potentials or "Bereitschaftspotentiale" (BPs), preceding voluntary self-placed pedalling movements, were examined after different states of exhaustion on an ergometer. 15 (13 right-handed) healthy men, aged between 22-30, participated in a randomised, cross over, double-blind, placebo controlled study. BPs were averaged out of artefact free EEG-segments from more than 90 triggered events, measured at 17 electrodes of the 10:20 system. With increasing effort the BPs were enlarged differently depending on the drink consumed. In placebo trials after exhaustive exercise premovement negative potential curves could be seen even in frontal areas. With caffeine the BPs increased after lower workload, achieving a level, which was reached in the placebo trials only after submaximal physical activation. Furthermore a significant shortening of premovement-brain-potentials in frontal and parietal regions could be seen in the caffeine trials at rest. Taurine admixture seems to inhibit this effects.