Degenerate flag varieties: moment graphs and Schr\"oder numbers

We study geometric and combinatorial properties of the degenerate flag varieties of type A. These varieties are acted upon by the automorphism group of a certain representation of a type A quiver, containing a maximal torus T. Using the group action, we describe the moment graphs, encoding the zero- and one-dimensional T-orbits. We also study the smooth and singular loci of the degenerate flag varieties. We show that the Euler characteristic of the smooth locus is equal to the large Schr\"oder number and the Poincar\'e polynomial is given by a natural statistics counting the number of diagonal steps in a Schr\"oder path. As an application we obtain a new combinatorial description of the large and small Schr\"oder numbers and their q-analogues.Comment: 25 page

IMPACT OF WII-FIT TRAINING ON NEURO-MUSCULAR CONTROL

INTRODUCTION: In the past year, the interactive exercise video game Wii Fit (Nintendo, Tokyo, Japan) has achieved worldwide popularity. This system could be a potential asset for both training and physical therapy purposes; however, there is a lack of scientific validation to justify such applications. As a first step in ascertaining the advantages of the Wii Fit system, the present study is focused on the neuromuscular control changes that occur after 8 weeks of daily training. METHOD: Two healthy subjects (25.5±2.1 years, 177.8±14.37 cm, 71.5±16.26 kg) trained for 30 minutes a day for 8 consecutive weeks using standard Wii Fit strength training, aerobic, and yoga exercises. Before and after the training period, a series of tests were performed (gait, hop, isometric, and one leg stability) while collecting EMG data from the quadriceps (rectus femoris, vastus lateralis, vastus medialis), the hamstrings (biceps femoris and semitendinosus), and the grastrocnemii (lateralis and medialis). The EMG data was linear-enveloped and normalized by a maximum isometric voluntary contraction (MVIC). Similarly to Lloyd et al. (2005), the electromyographic activations were then summed by muscle group to calculate the co-contraction ratio (CCR), which is a value between 0 and 1 that indicates equalizing activation as it increases. RESULTS: Only the right leg data is being reported in this paper. Table 1 displays the CCR for the antagonist coactivations of the hamstrings and quadriceps and also the synergistic activations of the knee flexor muscle groups. It is worth noting that during gait and hopping motions, the ratios are decreased after training, while during the stability tests they increased. Finally, no trend emerged for the isometric data. Table 1 Co-contraction Ratio Maximums (Ext 60 and Flex 60 refer to isometric extesion and flexion at 60°)– values in italics are reciprocals Ext 60 Flex 60 Gait Hop Stability Ham/Quad Coactivation Pre 0.21 0.41 0.17 0.20 0.06 Post 0.46 0.47 0.02 0.06 0.88 Ham/Gast Synergy Pre 0.34 0.47 0.02 0.08 0.04 Post 0.47 0.28 0.01 0.08 0.35 DISCUSSION: After training, the CCR data for dynamic activity indicated more focused muscle control. During the stability tests, much higher CCR values were reported, indicating the muscles were doing a better job achieving a intra-articular equilibrium. CONCLUSION: These preliminary results indicate a promising use of the Wii Fit system for training and physical therapy as on a small population they demonstrated neuromuscular control improvement during dynamic and static trials. REFERENCES: Lloyd, D. G., Buchanan, T. S., and Besier, T. F. (2005). Neuromuscular Biomechanical Modeling to Understand Knee Ligament Loading. Medicine & Science in Sports & Exercise, 37, 1939-1947

Improving ADMMs for solving doubly nonnegative programs through dual factorization

Alternating direction methods of multipliers (ADMMs) are popular approaches to handle large scale semidefinite programs that gained attention during the past decade. In this paper, we focus on solving doubly nonnegative programs (DNN), which are semidefinite programs where the elements of the matrix variable are constrained to be nonnegative. Starting from two algorithms already proposed in the literature on conic programming, we introduce two new ADMMs by employing a factorization of the dual variable. It is well known that first order methods are not suitable to compute high precision optimal solutions, however an optimal solution of moderate precision often suffices to get high quality lower bounds on the primal optimal objective function value. We present methods to obtain such bounds by either perturbing the dual objective function value or by constructing a dual feasible solution from a dual approximate optimal solution. Both procedures can be used as a post-processing phase in our ADMMs. Numerical results for DNNs that are relaxations of the stable set problem are presented. They show the impact of using the factorization of the dual variable in order to improve the progress towards the optimal solution within an iteration of the ADMM. This decreases the number of iterations as well as the CPU time to solve the DNN to a given precision. The experiments also demonstrate that within a computationally cheap post-processing, we can compute bounds that are close to the optimal value even if the DNN was solved to moderate precision only. This makes ADMMs applicable also within a branch-and-bound algorithm

Foundations of Fully Dynamic Group Signatures

Group signatures are a central cryptographic primitive that has received a considerable amount of attention from the cryptographic community. They allow members of a group to anonymously sign on behalf of the group. Membership is overseen by a designated group manager. There is also a tracing authority that can revoke anonymity by revealing the identity of the signer if and when needed, to enforce accountability and deter abuse. For the primitive to be applicable in practice, it needs to support fully dynamic groups, i.e. users can join and leave at any time. In this work we take a close look at existing security definitions for fully dynamic group signatures. We identify a number of shortcomings in existing security definitions and fill the gap by providing a formal rigorous security model for the primitive. Our model is general and is not tailored towards a specific design paradigm and can therefore, as we show, be used to argue about the security of different existing constructions following different design paradigms. Our definitions are stringent and when possible incorporate protection against maliciously chosen keys. In the process, we identify a subtle issue inherent to one design paradigm, where new members might try to implicate older ones by means of back-dated signatures. This is not captured by existing models. We propose some inexpensive fixes for some existing constructions to avoid the issue

Foundations of Fully Dynamic Group Signatures

Group signatures allow members of a group to anonymously sign on behalf of the group. Membership is administered by a designated group manager. The group manager can also reveal the identity of a signer if and when needed to enforce accountability and deter abuse. For group signatures to be applicable in practice, they need to support fully dynamic groups, i.e., users may join and leave at any time. Existing security definitions for fully dynamic group signatures are informal, have shortcomings, and are mutually incompatible. We fill the gap by providing a formal rigorous security model for fully dynamic group signatures. Our model is general and is not tailored toward a specific design paradigm and can therefore, as we show, be used to argue about the security of different existing constructions following different design paradigms. Our definitions are stringent and when possible incorporate protection against maliciously chosen keys. We consider both the case where the group management and tracing signatures are administered by the same authority, i.e., a single group manager, and also the case where those roles are administered by two separate authorities, i.e., a group manager and an opening authority. We also show that a specialization of our model captures existing models for static and partially dynamic schemes. In the process, we identify a subtle gap in the security achieved by group signatures using revocation lists. We show that in such schemes new members achieve a slightly weaker notion of traceability. The flexibility of our security model allows to capture such relaxation of traceability

Linear degenerations of flag varieties: partial flags, defining equations, and group actions

We continue, generalize and expand our study of linear degenerations of flag varieties from Cerulli Irelli et al. (Math Z 287(1–2):615–654, 2017). We realize partial flag varieties as quiver Grassmannians for equi-oriented type A quivers and construct linear degenerations by varying the corresponding quiver representation. We prove that there exists the deepest flat degeneration and the deepest flat irreducible degeneration: the former is the partial analogue of the mf-degenerate flag variety and the latter coincides with the partial PBW-degenerate flag variety. We compute the generating function of the number of orbits in the flat irreducible locus and study the natural family of line bundles on the degenerations from the flat irreducible locus. We also describe explicitly the reduced scheme structure on these degenerations and conjecture that similar results hold for the whole flat locus. Finally, we prove an analogue of the Borel–Weil theorem for the flat irreducible locus

IS PRINCIPAL COMPONENT ANALYSIS MORE EFFICIENT TO DETECT DIFFERENCES ON BIOMECHANICAL VARIABLES BETWEEN GROUPS?

The biomechanical analysis investigates variables such as angles, inter-segmental forces and moments at the joints. When the relevant parameters (e.g., range of motion, peak values) are selected a priori from these variables, they could not perfectly represent the information content of the original dataset. Therefore, in this study we want to validate the efficacy of the Principal Component Analysis (PCA) in overcoming the limitations of the a priori selection of the parameters. An application study is reported; the lower-limb joint mechanics between patients operated with two different surgical techniques for a total hip arthroplasty are analyzed with both the traditional analysis and the PCA. The findings from the two methods converged, but the PCA identified new sources of variability not previously detected

Respiratory muscle training in patients recovering recent open cardio-thoracic surgery: a randomized-controlled trial.

Objectives- To evaluate the clinical efficacy and feasibility of an expiratory muscle training (EMT) device (Respilift™) applied to patients recovering from recent open cardio-thoracic surgery (CTS). Design- Prospective, double-blind, 14-day randomised-controlled trial. Participants and setting- 60 inpatients recovering from recent CTS and early admitted to a pulmonary rehabilitation program. Interventions- Chest physiotherapy plus EMT with a resistive load of 30 cm H2O for active group and chest physiotherapy plus EMT with a sham load for control group. Measures- Changes in maximal expiratory pressure (MEP) was considered as primary outcome, while maximal inspiratory pressures (MIP), dynamic and static lung volumes, oxygenation, perceived symptoms of dyspnoea, thoracic pain and well being (evaluated by visual analogic scale-VAS) and general health status were considered secondary outcomes. Results- All outcomes recorded showed significant improvements in both groups; however, the change of MEP (+34.2 mmHg, p<0.001 and +26.1%, p<0.001 for absolute and % of predicted, respectively) was significantly higher in Active group. Also VAS-dyspnoea improved faster and more significantly (p<0.05) at day 12 and 14 in Active group when compared with Control. The drop out rate was 6%, without differences between groups. Conclusions- In patients recovering from recent CTS specific EMT by Respilift™ is feasible and effective

Changes in clinical characteristics and outcomes of patients admitted to inpatient cardiac rehabilitation

Aims: Cardiac rehabilitation (CR) have proven to be effective and beneficial in middle-aged and older patients. However, solid data in large cohorts of elderly individuals are yet to be explored. This retrospective study investigated the general characteristics, outcomes, and the level of re-sponse of patients referred to CR over 13 consecutive years. Methods: We reviewed the medical records of patients admitted to Villa Pineta Rehabilitation Hospital for exercise-based CR from 2006 to 2018. Patients’ baseline characteristics and changes following CR in upper limb weight-lifting test (ULW), 30-second sit-to-stand test (30STS), and the 6-minute walking test (6MWT) with associated Borg-related dyspnea (D) and fatigue (F) were collected. We also calculated the number of individuals reaching the minimal clinically relevant change (MCRC) following CR for each outcome. Results: 1551 patients (70.2 ± 9.7 years, 66% men) with complete data set were in-cluded in the analysis. Coronary artery bypass graft and cardiac valve replacement surgery were the most frequent surgical procedures leading to CR referral (41.1% and 35.8%, respectively). The patients’ age (p = 0.03), number of total comorbidities (p &lt; 0.0001), and post-surgical complica-tions (p = 0.02) significantly increased over time. In contrast, the average absolute changes in ULW, 30STS and 6MWT with associated D and F, and the proportion of patients reaching the re-spective MCRC, remained constant over the same period. Conclusion: Patients admitted to exer-cise-based CR were older and had more comorbidities and complications over time. Outcomes, however, were not influenced in terms of absolute change nor clinically meaningful response