On the structure of non-full-rank perfect codes

The Krotov combining construction of perfect 1-error-correcting binary codes from 2000 and a theorem of Heden saying that every non-full-rank perfect 1-error-correcting binary code can be constructed by this combining construction is generalized to the $q$-ary case. Simply, every non-full-rank perfect code $C$ is the union of a well-defined family of $\mu$-components $K_\mu$, where $\mu$ belongs to an "outer" perfect code $C^*$, and these components are at distance three from each other. Components from distinct codes can thus freely be combined to obtain new perfect codes. The Phelps general product construction of perfect binary code from 1984 is generalized to obtain $\mu$-components, and new lower bounds on the number of perfect 1-error-correcting $q$-ary codes are presented.Comment: 8 page

Taylor approximations of operator functions

This survey on approximations of perturbed operator functions addresses recent advances and some of the successful methods.Comment: 12 page

Quantum Phase Shift in Chern-Simons Modified Gravity

Using a unified approach of optical-mechanical analogy in a semiclassical formula, we evaluate the effect of Chern-Simons modified gravity on the quantum phase shift of de Broglie waves in neutron interferometry. The phase shift calculated here reveals, in a single equation, a combination of effects coming from Newtonian gravity, inertial forces, Schwarzschild and Chern-Simons modified gravity. However the last two effects, though new, turn out to be too tiny to be observed, and hence only of academic interest at present. The approximations, wherever used, as well as the drawbacks of the non-dynamical approach are clearly indicated.Comment: 16 pages, minor errors corrected. Accepted for publication in Phys. Rev.

Unsupervised Video Summarization via Attention-Driven Adversarial Learning

This paper presents a new video summarization approach that integrates an attention mechanism to identify the signi cant parts of the video, and is trained unsupervisingly via generative adversarial learning. Starting from the SUM-GAN model, we rst develop an improved version of it (called SUM-GAN-sl) that has a signi cantly reduced number of learned parameters, performs incremental training of the model's components, and applies a stepwise label-based strategy for updating the adversarial part. Subsequently, we introduce an attention mechanism to SUM-GAN-sl in two ways: i) by integrating an attention layer within the variational auto-encoder (VAE) of the architecture (SUM-GAN-VAAE), and ii) by replacing the VAE with a deterministic attention auto-encoder (SUM-GAN-AAE). Experimental evaluation on two datasets (SumMe and TVSum) documents the contribution of the attention auto-encoder to faster and more stable training of the model, resulting in a signi cant performance improvement with respect to the original model and demonstrating the competitiveness of the proposed SUM-GAN-AAE against the state of the art

Fragmentation of a Circular Disc by Impact on a Frictionless Plate

The break-up of a two-dimensional circular disc by normal and oblique impact on a hard frictionless plate is investigated by molecular dynamics simulations. The disc is composed of numerous unbreakable randomly shaped convex polygons connected together by simple elastic beams that break when bent or stretched beyond a certain limit. It is found that for both normal and oblique impacts the crack patterns are the same and depend solely on the normal component of the impact velocity. Analysing the pattern of breakage, amount of damage, fragment masses and velocities, we show the existence of a critical velocity which separates two regimes of the impact process: below the critical point only a damage cone is formed at the impact site (damage), cleaving of the particle occurs at the critical point, while above the critical velocity the disc breaks into several pieces (fragmentation). In the limit of very high impact velocities the disc suffers complete disintegration (shattering) into many small fragments. In agreement with experimental results, fragment masses are found to follow the Gates-Gaudin-Schuhmann distribution (power law) with an exponent independent of the velocity and angle of impact. The velocity distribution of fragments exhibit an interesting anomalous scaling behavior when changing the impact velocity and the size of the disc.Comment: submitted to J. Phys: Condensed Matter special issue on Granular Medi

Transition from damage to fragmentation in collision of solids

We investigate fracture and fragmentation of solids due to impact at low energies using a two-dimensional dynamical model of granular solids. Simulating collisions of two solid discs we show that, depending on the initial energy, the outcome of a collision process can be classified into two states: a damaged and a fragmented state with a sharp transition in between. We give numerical evidence that the transition point between the two states behaves as a critical point, and we discuss the possible mechanism of the transition.Comment: Revtex, 12 figures included. accepted by Phys. Rev.

Summarizing Videos with Attention

In this work we propose a novel method for supervised, keyshots based video summarization by applying a conceptually simple and computationally efficient soft, self-attention mechanism. Current state of the art methods leverage bi-directional recurrent networks such as BiLSTM combined with attention. These networks are complex to implement and computationally demanding compared to fully connected networks. To that end we propose a simple, self-attention based network for video summarization which performs the entire sequence to sequence transformation in a single feed forward pass and single backward pass during training. Our method sets a new state of the art results on two benchmarks TvSum and SumMe, commonly used in this domain.Comment: Presented at ACCV2018 AIU2018 worksho

Acute leukaemoid reaction following cardiac surgery

Chronic myelomonocytic leukaemia is an atypical myeloproliferative disorder with a natural history of progression to acute myeloid leukaemia, a complex and poorly understood response by the bone marrow to stress. Cardiac surgery activates many inflammatory cascades and may precipitate a systemic inflammatory response syndrome. We present a case of undiagnosed chronic myelomonocytic leukaemia who developed rapidly fatal multi-organ dysfunction following cardiac surgery due to an acute leukaemoid reaction

Outer-Sphere Contributions to the Electronic Structure of Type Zero Copper Proteins

Bioinorganic canon states that active-site thiolate coordination promotes rapid electron transfer (ET) to and from type 1 copper proteins. In recent work, we have found that copper ET sites in proteins also can be constructed without thiolate ligation (called “type zero” sites). Here we report multifrequency electron paramagnetic resonance (EPR), magnetic circular dichroism (MCD), and nuclear magnetic resonance (NMR) spectroscopic data together with density functional theory (DFT) and spectroscopy-oriented configuration interaction (SORCI) calculations for type zero Pseudomonas aeruginosa azurin variants. Wild-type (type 1) and type zero copper centers experience virtually identical ligand fields. Moreover, O-donor covalency is enhanced in type zero centers relative that in the C112D (type 2) protein. At the same time, N-donor covalency is reduced in a similar fashion to type 1 centers. QM/MM and SORCI calculations show that the electronic structures of type zero and type 2 are intimately linked to the orientation and coordination mode of the carboxylate ligand, which in turn is influenced by outer-sphere hydrogen bonding