Hirzebruch-Milnor classes and Steenbrink spectra of certain projective hypersurfaces

We show that the Hirzebruch-Milnor class of a projective hypersurface, which gives the difference between the Hirzebruch class and the virtual one, can be calculated by using the Steenbrink spectra of local defining functions of the hypersurface if certain good conditions are satisfied, e.g. in the case of projective hyperplane arrangements, where we can give a more explicit formula. This is a natural continuation of our previous paper on the Hirzebruch-Milnor classes of complete intersections.Comment: 15 pages, Introduction is modifie

Study protocol subacromial impingement syndrome: the identification of pathophysiologic mechanisms (SISTIM)

<p>Abstract</p> <p>Background</p> <p>The Subacromial Impingement Syndrome (SIS) is the most common diagnosed disorder of the shoulder in primary health care, but its aetiology is unclear. Conservative treatment regimes focus at reduction of subacromial inflammatory reactions or pathologic scapulohumeral motion patterns (<it>intrinsic </it>aetiology). Long-lasting symptoms are often treated with surgery, which is focused at enlarging the subacromial space by resection of the anterior part of the acromion (based on <it>extrinsic </it>aetiology). Despite that acromionplasty is in the top-10 of orthopaedic surgical procedures, there is no consensus on its indications and reported results are variable (successful in 48-90%). We hypothesize that the aetiology of SIS, i.e. an increase in subacromial pressure or decrease of subacromial space, is multi-factorial. SIS can be the consequence of pathologic scapulohumeral motion patterns leading to humerus cranialisation, anatomical variations of the scapula and the humerus (e.g. hooked acromion), a subacromial inflammatory reaction (e.g. due to overuse or micro-trauma), or adjoining pathology (e.g. osteoarthritis in the acromion-clavicular-joint with subacromial osteophytes).</p> <p>We believe patients should be treated according to their predominant etiological mechanism(s). Therefore, the objective of our study is to identify and discriminate etiological mechanisms occurring in SIS patients, in order to develop tailored diagnostic and therapeutic strategies.</p> <p>Methods</p> <p>In this cross-sectional descriptive study, applied clinical and experimental methods to identify intrinsic and extrinsic etiologic mechanisms comprise: MRI-arthrography (eligibility criteria, cuff status, 3D-segmented bony contours); 3D-motion tracking (scapulohumeral rhythm, arm range of motion, dynamic subacromial volume assessment by combining the 3D bony contours and 3D-kinematics); EMG (adductor co-activation) and dynamometry instrumented shoulder radiographs during arm tasks (force and muscle activation controlled acromiohumeral translation assessments); Clinical phenotyping (Constant Score, DASH, WORC, and SF-36 scores).</p> <p>Discussion</p> <p>By relating anatomic properties, kinematics and muscle dynamics to subacromial volume, we expect to identify one or more predominant pathophysiological mechanisms in every SIS patient. These differences in underlying mechanisms are a reflection of the variations in symptoms, clinical scores and outcomes reported in literature. More insight in these mechanisms is necessary in order to optimize future diagnostic and treatment strategies for patients with SIS symptoms.</p> <p>Trial registration</p> <p>Dutch Trial Registry (Nederlands Trial Register) <a href="http://www.trialregister.nl/trialreg/admin/rctview.asp?TC=2283">NTR2283</a>.</p

Gait stability in response to platform, belt, and sensory perturbations in young and older adults

Perturbation-based gait assessment has been used to quantify gait stability in older adults. However, knowledge on which perturbation type is most suitable to identify poor gait stability is lacking. We evaluated the effects of ipsi- and contra-lateral sway, belt acceleration and deceleration, and visual and auditory perturbations on medio-lateral (ML) and anterior-posterior (AP) margins of stability (MoS) in young and older adults. We aimed to evaluate (1) which perturbation type disturbed the gait pattern substantially, (2) how participants recovered, and (3) whether recovery responses could discriminate between young and older adults. Nine young (25.1 ± 3.4 years) and nine older (70.1 ± 7.6 years) adults walked on the CAREN Extended (Motek BV, The Netherlands). The perturbation effect was quantified by deviation in MoS over six post-perturbation steps compared to baseline walking. Contra-lateral sway and deceleration perturbations resulted in the largest ML (1.9–4 times larger than other types) and AP (1.6–5.6 times larger than other types) perturbation effects, respectively. After both perturbation types, participants increased MoS by taking wider, shorter, and faster steps. No differences between young and older adults were found. We suggest to evaluate the potential of using contra-lateral sway and deceleration perturbations for fall risk identification by including both healthy and frail older adults.MP (NWO VIDI grant #917-14-344) and SB (NWO grant #451-12-041) were financially supported by the Netherlands Organization for Scientific Research.https://doi.org/10.1007/s11517-018-1855-756pubpub1

Differential Forms on Log Canonical Spaces

The present paper is concerned with differential forms on log canonical varieties. It is shown that any p-form defined on the smooth locus of a variety with canonical or klt singularities extends regularly to any resolution of singularities. In fact, a much more general theorem for log canonical pairs is established. The proof relies on vanishing theorems for log canonical varieties and on methods of the minimal model program. In addition, a theory of differential forms on dlt pairs is developed. It is shown that many of the fundamental theorems and techniques known for sheaves of logarithmic differentials on smooth varieties also hold in the dlt setting. Immediate applications include the existence of a pull-back map for reflexive differentials, generalisations of Bogomolov-Sommese type vanishing results, and a positive answer to the Lipman-Zariski conjecture for klt spaces.Comment: 72 pages, 6 figures. A shortened version of this paper has appeared in Publications math\'ematiques de l'IH\'ES. The final publication is available at http://www.springerlink.co

A real-time system for biomechanical analysis of human movement and muscle function

Mechanical analysis of movement plays an important role in clinical management of neurological and orthopedic conditions. There has been increasing interest in performing movement analysis in real-time, to provide immediate feedback to both therapist and patient. However, such work to date has been limited to single-joint kinematics and kinetics. Here we present a software system, named human body model (HBM), to compute joint kinematics and kinetics for a full body model with 44 degrees of freedom, in real-time, and to estimate length changes and forces in 300 muscle elements. HBM was used to analyze lower extremity function during gait in 12 able-bodied subjects. Processing speed exceeded 120 samples per second on standard PC hardware. Joint angles and moments were consistent within the group, and consistent with other studies in the literature. Estimated muscle force patterns were consistent among subjects and agreed qualitatively with electromyography, to the extent that can be expected from a biomechanical model. The real-time analysis was integrated into the D-Flow system for development of custom real-time feedback applications and into the gait real-time analysis interactive lab system for gait analysis and gait retraining. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1007/s11517-013-1076-z) contains supplementary material, which is available to authorized users

Landau-Ginzburg/Calabi-Yau correspondence, global mirror symmetry and Orlov equivalence

We show that the Gromov-Witten theory of Calabi-Yau hypersurfaces matches, in genus zero and after an analytic continuation, the quantum singularity theory (FJRW theory) recently introduced by Fan, Jarvis and Ruan following ideas of Witten. Moreover, on both sides, we highlight two remarkable integral local systems arising from the common formalism of Gamma-integral structures applied to the derived category of the hypersurface {W=0} and to the category of graded matrix factorizations of W. In this setup, we prove that the analytic continuation matches Orlov equivalence between the two above categories.Comment: 72pages, v2: Appendix B and references added. Typos corrected, v3: several mistakes corrected, final versio

A Metaheuristic Framework for Bi-level Programming Problems with Multi-disciplinary Applications

Bi-level programming problems arise in situations when the decision maker has to take into account the responses of the users to his decisions. Several problems arising in engineering and economics can be cast within the bi-level programming framework. The bi-level programming model is also known as a Stackleberg or leader-follower game in which the leader chooses his variables so as to optimise his objective function, taking into account the response of the follower(s) who separately optimise their own objectives, treating the leader’s decisions as exogenous. In this chapter, we present a unified framework fully consistent with the Stackleberg paradigm of bi-level programming that allows for the integration of meta-heuristic algorithms with traditional gradient based optimisation algorithms for the solution of bi-level programming problems. In particular we employ Differential Evolution as the main meta-heuristic in our proposal.We subsequently apply the proposed method (DEBLP) to a range of problems from many fields such as transportation systems management, parameter estimation and game theory. It is demonstrated that DEBLP is a robust and powerful search heuristic for this class of problems characterised by non smoothness and non convexity