Linear-time list recovery of high-rate expander codes

We show that expander codes, when properly instantiated, are high-rate list recoverable codes with linear-time list recovery algorithms. List recoverable codes have been useful recently in constructing efficiently list-decodable codes, as well as explicit constructions of matrices for compressive sensing and group testing. Previous list recoverable codes with linear-time decoding algorithms have all had rate at most 1/2; in contrast, our codes can have rate $1 - \epsilon$ for any $\epsilon > 0$. We can plug our high-rate codes into a construction of Meir (2014) to obtain linear-time list recoverable codes of arbitrary rates, which approach the optimal trade-off between the number of non-trivial lists provided and the rate of the code. While list-recovery is interesting on its own, our primary motivation is applications to list-decoding. A slight strengthening of our result would implies linear-time and optimally list-decodable codes for all rates, and our work is a step in the direction of solving this important problem

Comparison of total ankle replacement and ankle arthrodesis in patients with haemophilia using gait analysis : two case reports

BACKGROUND: Severe hemophilia is an inherited, lifelong bleeding disorder characterized by spontaneous bleeding, which results in painful joint deformities. Currently two surgical treatments are available to treat haemophilia-related ankle joint destruction: ankle arthrodesis and total ankle replacement. The aim of the present study was to compare these two surgical procedures in haemophiliac subjects. CASE PRESENTATION: Kinematic and dynamic parameters were quantified using a three-dimensional gait-analysis system in two similar clinical cases. In Caucasian case 1, ankle arthrodesis was chosen because of a kinematic ankle flexion defect and lack of dynamic power regeneration. The defect in energy absorption was compensated for by the contralateral side. Total ankle replacement in Caucasian case 2 allowed sparing the ipsilateral knee (maximum 0.27 preoperatively vs. 0.71 W/kg postoperatively) and hip joints powers (maximum 0.43 preoperatively vs. 1.25 W/kg postoperatively) because of the small ankle dorsiflexion motion. CONCLUSIONS: Total ankle replacement is recommended for haemophiliac patients who present with a preserved ankle range of motion

Random subcubes as a toy model for constraint satisfaction problems

We present an exactly solvable random-subcube model inspired by the structure of hard constraint satisfaction and optimization problems. Our model reproduces the structure of the solution space of the random k-satisfiability and k-coloring problems, and undergoes the same phase transitions as these problems. The comparison becomes quantitative in the large-k limit. Distance properties, as well the x-satisfiability threshold, are studied. The model is also generalized to define a continuous energy landscape useful for studying several aspects of glassy dynamics.Comment: 21 pages, 4 figure

Understanding Mechanical Response of Elastomeric Graphene Networks

Ultra-light porous networks based on nano-carbon materials (such as graphene or carbon nanotubes) have attracted increasing interest owing to their applications in wide fields from bioengineering to electrochemical devices. However, it is often difficult to translate the properties of nanomaterials to bulk three-dimensional networks with a control of their mechanical properties. In this work, we constructed elastomeric graphene porous networks with well-defined structures by freeze casting and thermal reduction, and investigated systematically the effect of key microstructural features. The porous networks made of large reduced graphene oxide flakes (>20 μm) are superelastic and exhibit high energy absorption, showing much enhanced mechanical properties than those with small flakes (<2 μm). A better restoration of the graphitic nature also has a considerable effect. In comparison, microstructural differences, such as the foam architecture or the cell size have smaller or negligible effect on the mechanical response. The recoverability and energy adsorption depend on density with the latter exhibiting a minimum due to the interplay between wall fracture and friction during deformation. These findings suggest that an improvement in the mechanical properties of porous graphene networks significantly depend on the engineering of the graphene flake that controls the property of the cell walls