Can grid cell ensembles represent multiple spaces?

The way grid cells represent space in the rodent brain has been a striking discovery, with theoretical implications still unclear. Di\u21b5erently from hippocampal place cells, which are known to encode multiple, environment-dependent spatial maps, grid cells have been widely believed to encode space through a single low dimensional manifold, in which coactivity relations between di\u21b5erent neurons are preserved when the environment is changed. Does it have to be so? Here, we compute \u2013 using two alternative mathematical models \u2013 the storage capacity of a population of grid-like units, embedded in a continuous attractor neural network, for multiple spatial maps. We show that distinct representations of multiple environments can coexist, as existing models for grid cells have the potential to express several sets of hexagonal grid patterns, challenging the view of a universal grid map. This suggests that a population of grid cells can encode multiple non-congruent metric relationships, a feature that could in principle allow a grid-like code to represent environments with a variety of di\u21b5erent geometries and possibly conceptual and cognitive spaces, which may be expected to entail such context-dependent metric relationships

Tibia, Diaphysis

Fractures of the tibia are brought on by a variety of high-energy injury mechanisms and are prone to complications. The lack of a circumferential soft tissue envelope around the bone makes the bone ends more likely to fail to unite. The soft-tissue envelope is the most important component in the evaluation and subsequent care of tibia fractures. Surgeons have moved away from plates and external fixators in favor of intramedullary nails in the operative treatment of both closed and open tibia diaphyseal fractures. Nailing is done with the patient in the supine position on a radiolucent table or on a fracture table with the knee flexed at least 90°. Experimental data suggest that reamed nails offer greater biomechanical stability and increased soft tissue blood flow, while non-reamed nails preserve blood flow to the bone. Locking with bolts or interlocking screws is mandatory for small-diameter nails in order to improve stability in a wide medullary canal and is recommended in all other situations. Poller screws aid in obtaining satisfactory alignment during surgery and provide additional stability. When strategically placed, these screws guide the reamers and the nail to a suitable trajectory, thereby achieving indirect reduction. Fibula fixation will provide good landmarks for the length of the tibia and add stability. The most common complication of intramedullary nailing of tibia fractures is anterior knee pain, which has been reported in more than half of patients. Malalignment, malunion and nonunion can be avoided by a meticulous surgical technique

Femoral neck pseudoarthrosis in a polio patient treated with closed reduction and cell therapy

Poliomyelitis disease affects the anterior horns cells of the spinal cord and certain motor nuclei of the brain stem. Paralysis type is flaccid and asymmetrical and result in muscular imbalance.Due to this, in case of having a hip muscles involvement, degenerative or posttraumatic, total hip arthroplasty is normally contraindicated because of the excessive risk of hip dislocation. In cases of subcapital femoral neck fractures the femoral head vascularization is a main concern, and in cases of neglected fracture with pseudoarthrosis the vascular status to the head must be investigated prior to further decisions.We report the case of a femoral neck fracture non-union after a missed femoral neck fracture in a polio affected leg treated with cannulated screws and percutaneous autologous injection of processed total nuclear cells (TNC) mixed with putty demineralized bone matrix. Keywords: Pseudoarthrosis, Poliomyelitis, Cell therapy, Femoral nec

Bounds for list-decoding and list-recovery of random linear codes

A family of error-correcting codes is listdecodable from error fraction p if, for every code in the family, the number of codewords in any Hamming ball of fractional radius p is less than some integer L. It is said to be list-recoverable for input list size ℓ if for every sufficiently large subset of at least L codewords, there is a coordinate where the codewords take more than ℓ values. In this work, we study the list size of random linear codes for both list-decoding and list-recovery as the rate approaches capacity. We show the following claims hold with high probability over the choice of the code (below q is the alphabet size, and ε > 0 is the gap to capacity). (1) A random linear code of rate 1 - logq(ℓ)-ε requires list size L ≥ ℓΩ(1/ε) for list-recovery from input list size ℓ. (2) A random linear code of rate 1 - hq(p) - ε requires list size L ≥ ⌊hq(p)/ε + 0.99⌋ for list-decoding from error fraction p. (3) A random binary linear code of rate 1 - h2(p) - ε is list-decodable from average error fraction p with list size with L ≤ ⌊h2(p)/ε⌋ + 2. Our lower bounds follow by exhibiting an explicit subset of codewords so that this subset—or some symbol-wise permutation of it—lies in a random linear code with high probability. Our upper bound follows by strengthening a result of (Li, Wootters, 2018)

Demineralized bone matrix-induced ectopic bone formation in rats: in vivo study with follow-up by magnetic resonance imaging, magnetic resonance angiography, and dual-energy X-ray absorptiometry.

Contains fulltext : 57929.pdf (publisher's version ) (Open Access)The aim of this study was to further explore the use of magnetic resonance imaging (MRI), magnetic resonance angiography (MRA), and dual-energy X-ray absorptiometry (DEXA) to assess bone formation and blood circulation in a pedicled bone graft substitute. In 14 Wistar rats, initially 10 weeks old, heterogeneous demineralized femur bone matrix implants were wrapped in pedicled adductor thigh muscle flaps. One rat died after surgery. Subsequently, bone formation and maintenance of blood vessel functionality were evaluated in six rats 6 weeks postimplantation by means of in vivo MRI/MRA and postmortem histomorphometry. The other seven rats were left for 12 weeks, whereafter bone formation was evaluated by in vivo DEXA and postmortem histomorphometry. The results demonstrated that after 6 weeks bone formation was present in four of six animals, quantified as 42 (+/-35)% and 25 (+/-19)% by means of MRI and histomorphometry, respectively. MRA was able to show patency of the pedicles of these four rats only, which suggests that the lack of blood supply in the other two rats is the cause of the failure to form bone. In the 12-week group, histology showed increased bone formation without signs of osteolysis, which was quantified histomorphometrically to be as high as 48 (+/-15)%. DEXA failed to show bone formation. It is concluded that in vivo MRI proved to be a reliable method for monitoring ectopic bone formation in a rat model, whereas in vivo DEXA was unable to detect the implants. Furthermore, in vivo MRA proved to be a useful technique for studying the circulation of muscle flaps in this animal model