An infinite step billiard

A class of non-compact billiards is introduced, namely the infinite step billiards, i.e. systems of a point particle moving freely in the domain Ω = ∪n∈ℕ[n,n + 1] × [0, p_n], with elastic reflections on the boundary; here p_0 = 1, p_n > 0 and pn ↘ 0. After describing some generic ergodic features of these dynamical systems, we turn to a more detailed study of the example p_n = 2^{-n}. Playing an important role in this case are the so-called escape orbits, that is, orbits going to +∞ monotonically in the X-velocity. A fairly complete description of them is given. This enables us to prove some results concerning the topology of the dynamics on the billiard

Non-Hamiltonian dynamics in optical microcavities resulting from wave-inspired corrections to geometric optics

We introduce and investigate billiard systems with an adjusted ray dynamics that accounts for modifications of the conventional reflection of rays due to universal wave effects. We show that even small modifications of the specular reflection law have dramatic consequences on the phase space of classical billiards. These include the creation of regions of non-Hamiltonian dynamics, the breakdown of symmetries, and changes in the stability and morphology of periodic orbits. Focusing on optical microcavities, we show that our adjusted dynamics provides the missing ray counterpart to previously observed wave phenomena and we describe how to observe its signatures in experiments. Our findings also apply to acoustic and ultrasound waves and are important in all situations where wavelengths are comparable to system sizes, an increasingly likely situation considering the systematic reduction of the size of electronic and photonic devices.Comment: 6 pages, 4 figures, final published versio

Treatment of an aneurysmal bone cyst in a young dog: A case report

Background: An aneurysmal bone cyst (ABC) is a rare benign lytic lesion affecting the medullary canal of long bones. It has been widely reported in human medicine, but rarely described in domestic animals. Objective: To report the surgical treatment and long term follow-up of a dog affected by ABC. Methods: An 8-month-old, intact female Weimaraner was presented with lameness affecting the left front limb and progressive swelling of the mid-distal radius. Survey radiographs revealed a mid-distal diaphyseal radial lesion. Fine needle aspirates, biopsy, CT scan and histopathology results supported the diagnosis of ABC. Treatment consisted of partial corticotomy of the affected radius, filling of the cystic cavity with demineralised bone matrix and autologous bone graft and stabilisation using lag screws and a neutralisation plate. Results: The long-term follow-up, at 36 post-operative months, showed no recurrence of the cyst and bone modelling. Comparing preoperative radiographs with those at 36 months, bone modelling reduced the radial area by 23.3% in the craniocaudal radiographic view and 30% in the mediolateral projection. Conclusions: This treatment was sucessful in the case here described, with a 3 years follow-up

Dura mater marsupialisation and outcome in a cat with a spinal subarachnoid pseudocyst: a case report

A six-month-old male domestic shorthair cat was referred with a history of acute-onset paraplegia, over the previous two months. The neurological examination revealed a thoracolumbar lesion. After myelography and myelo-computed tomography (myelo-CT), the diagnosis of a T13\u2013L1 subarachnoid pseudocyst potentially related to a previous L1 vertebral body fracture or malformation was made. Surgical decompression consisted in dorsal laminectomy followed by durotomy and marsupialisation. Immediately after surgery the cat improved neurologically and showed progressive improvement of his neurological signs over the next few months, until he died, from unrelated causes, approximately 18 months after surgery

Prevalence and patterns of antimicrobial resistance among escherichia coli and staphylococcus spp. In a veterinary university hospital

The occurrence of antimicrobial resistance in commensal strains of Escherichia coli and Staphylococcus spp. was investigated in 320 samples collected from patients and the environment of a veterinary university hospital—specifically, the consultation area (CA) and intensive care unit (ICU). E. coli was isolated in 70/160 samples (44%), while Staphylococcus spp. were isolated in 110/160 (69%) samples. The occurrence of multidrug-resistant (MDR) isolates from CA and ICU admission were similar for E. coli (1/12 (8%) versus 4/27 (15%), respectively) and Staphylococcus spp. (10/19 (53%) versus 26/50 (52%), respectively). MDR E. coli isolates increased significantly at hospital discharge (18/31; 58%; p = 0.008). Antimicrobial treatment administered during hospitalization was a risk factor for carriage of MDR E. coli (OR, 23.9; 95% CI: 1.18–484.19; p = 0.04) and MDR Staphylococcus spp. (OR, 19.5; 95% CI 1.30–292.76; p = 0.02), respectively. The odds ratio for MDR E. coli was 41.4 (95% CI 2.13–806.03; p = 0.01), if the administration of fluoroquinolones was evaluated. The mecA gene was detected in 19/24 (79%) coagulase-positive Staphylococcus spp. isolates resistant to oxacillin. High rates of MDR Staphylococcus spp. were reported. Hospitalization in the ICU and antimicrobial treatment were risk factors for colonization by MDR commensal bacteria

The comparison of latero-medial versus dorso-palmar/plantar drilling for cartilage removal in the proximal interphalangeal joint

The aims of the present study were to compare the percentages of articular cartilage removed using a lateral drilling approach of the proximal interphalangeal joint (PIPJ) and a dorsal drilling approach, and to assess the usefulness of digital fluoroscopy when performing a lateral drilling approach. Sixty cadaveric PIPJs were drilled using a surgical drill bit to remove the articular cartilage. The limbs were divided into three groups containing 10 forelimbs and 10 hindlimbs each. One group received the dorsal drilling approach, the second one received the lateral drilling approach and the last one received the lateral drilling approach under digital fluoroscopy guidance. The percentage of articular cartilage removed from each articular surface was assessed using Adobe Photoshop® software. The percentages of removed cartilage turned out to be significantly higher with lateral approach, especially under fluoroscopic guidance, both in the forelimbs (p = 0.00712) and hindlimbs (p = 0.00962). In conclusion, the lateral drilling approach seems to be a minimally invasive technique with which to perform PIPJ arthrodesis, even more efficient than the previously reported dorsal approach

Escape orbits and Ergodicity in Infinite Step Billiards

In a previous paper we defined a class of non-compact polygonal billiards, the infinite step billiards: to a given decreasing sequence of non-negative numbers $\{p_{n}$, there corresponds a table \Bi := \bigcup_{n\in\N} [n,n+1] \times [0,p_{n}]. In this article, first we generalize the main result of the previous paper to a wider class of examples. That is, a.s. there is a unique escape orbit which belongs to the alpha and omega-limit of every other trajectory. Then, following a recent work of Troubetzkoy, we prove that generically these systems are ergodic for almost all initial velocities, and the entropy with respect to a wide class of ergodic measures is zero.Comment: 27 pages, 8 figure

Track billiards

We study a class of planar billiards having the remarkable property that their phase space consists up to a set of zero measure of two invariant sets formed by orbits moving in opposite directions. The tables of these billiards are tubular neighborhoods of differentiable Jordan curves that are unions of finitely many segments and arcs of circles. We prove that under proper conditions on the segments and the arcs, the billiards considered have non-zero Lyapunov exponents almost everywhere. These results are then extended to a similar class of of 3-dimensional billiards. Finally, we find that for some subclasses of track billiards, the mechanism generating hyperbolicity is not the defocusing one that requires every infinitesimal beam of parallel rays to defocus after every reflection off of the focusing boundary.Comment: 7 figure

Influence of Nanoparticle Size and Shape on Oligomer Formation of an Amyloidogenic Peptide

Understanding the influence of macromolecular crowding and nanoparticles on the formation of in-register $\beta$-sheets, the primary structural component of amyloid fibrils, is a first step towards describing \emph{in vivo} protein aggregation and interactions between synthetic materials and proteins. Using all atom molecular simulations in implicit solvent we illustrate the effects of nanoparticle size, shape, and volume fraction on oligomer formation of an amyloidogenic peptide from the transthyretin protein. Surprisingly, we find that inert spherical crowding particles destabilize in-register $\beta$-sheets formed by dimers while stabilizing $\beta$-sheets comprised of trimers and tetramers. As the radius of the nanoparticle increases crowding effects decrease, implying smaller crowding particles have the largest influence on the earliest amyloid species. We explain these results using a theory based on the depletion effect. Finally, we show that spherocylindrical crowders destabilize the ordered $\beta$-sheet dimer to a greater extent than spherical crowders, which underscores the influence of nanoparticle shape on protein aggregation

Cause of Death and Predictors of All-Cause Mortality in Anticoagulated Patients With Nonvalvular Atrial Fibrillation : Data From ROCKET AF

M. Kaste on työryhmän ROCKET AF Steering Comm jäsen.Background-Atrial fibrillation is associated with higher mortality. Identification of causes of death and contemporary risk factors for all-cause mortality may guide interventions. Methods and Results-In the Rivaroxaban Once Daily Oral Direct Factor Xa Inhibition Compared with Vitamin K Antagonism for Prevention of Stroke and Embolism Trial in Atrial Fibrillation (ROCKET AF) study, patients with nonvalvular atrial fibrillation were randomized to rivaroxaban or dose-adjusted warfarin. Cox proportional hazards regression with backward elimination identified factors at randomization that were independently associated with all-cause mortality in the 14 171 participants in the intention-to-treat population. The median age was 73 years, and the mean CHADS(2) score was 3.5. Over 1.9 years of median follow-up, 1214 (8.6%) patients died. Kaplan-Meier mortality rates were 4.2% at 1 year and 8.9% at 2 years. The majority of classified deaths (1081) were cardiovascular (72%), whereas only 6% were nonhemorrhagic stroke or systemic embolism. No significant difference in all-cause mortality was observed between the rivaroxaban and warfarin arms (P=0.15). Heart failure (hazard ratio 1.51, 95% CI 1.33-1.70, P= 75 years (hazard ratio 1.69, 95% CI 1.51-1.90, P Conclusions-In a large population of patients anticoagulated for nonvalvular atrial fibrillation, approximate to 7 in 10 deaths were cardiovascular, whereasPeer reviewe