Online Bin Packing with Advice

We consider the online bin packing problem under the advice complexity model where the 'online constraint' is relaxed and an algorithm receives partial information about the future requests. We provide tight upper and lower bounds for the amount of advice an algorithm needs to achieve an optimal packing. We also introduce an algorithm that, when provided with log n + o(log n) bits of advice, achieves a competitive ratio of 3/2 for the general problem. This algorithm is simple and is expected to find real-world applications. We introduce another algorithm that receives 2n + o(n) bits of advice and achieves a competitive ratio of 4/3 + {\epsilon}. Finally, we provide a lower bound argument that implies that advice of linear size is required for an algorithm to achieve a competitive ratio better than 9/8.Comment: 19 pages, 1 figure (2 subfigures

Single meson photoproduction and IR renormalons

Single pseudoscalar and vector mesons inclusive photoproduction $\gamma h\rightarrow MX$ via higher twist mechanism is calculated using the QCD running coupling constant method. It is proved that in the context of this method a higher twist contribution to the photoproduction cross section cannot be normalized in terms of the meson electromagnetic form factor. The structure of infrared renormalon singularities of the higher twist subprocess cross section and the resummed expression (the Borel sum) for it are found. Comparisons are made with earlier results, as well as with leading twist cross section. Phenomenological effects of studied contributions for $\pi, K, \rho$-meson photoproduction are discussed.Comment: 20 pages, 8 figure

On the List Update Problem with Advice

We study the online list update problem under the advice model of computation. Under this model, an online algorithm receives partial information about the unknown parts of the input in the form of some bits of advice generated by a benevolent offline oracle. We show that advice of linear size is required and sufficient for a deterministic algorithm to achieve an optimal solution or even a competitive ratio better than $15/14$. On the other hand, we show that surprisingly two bits of advice are sufficient to break the lower bound of $2$ on the competitive ratio of deterministic online algorithms and achieve a deterministic algorithm with a competitive ratio of $5/3$. In this upper-bound argument, the bits of advice determine the algorithm with smaller cost among three classical online algorithms, TIMESTAMP and two members of the MTF2 family of algorithms. We also show that MTF2 algorithms are $2.5$-competitive

High-frequency Oscillations in Small Magnetic Elements Observed with Sunrise/SuFI

We characterize waves in small magnetic elements and investigate their propagation in the lower solar atmosphere from observations at high spatial and temporal resolution. We use the wavelet transform to analyze oscillations of both horizontal displacement and intensity in magnetic bright points found in the 300 nm and the Ca II H 396.8 nm passbands of the filter imager on board the Sunrise balloon-borne solar observatory. Phase differences between the oscillations at the two atmospheric layers corresponding to the two passbands reveal upward propagating waves at high frequencies (up to 30 mHz). Weak signatures of standing as well as downward propagating waves are also obtained. Both compressible and incompressible (kink) waves are found in the small-scale magnetic features. The two types of waves have different, though overlapping, period distributions. Two independent estimates give a height difference of approximately 450+-100 km between the two atmospheric layers sampled by the employed spectral bands. This value, together with the determined short travel times of the transverse and longitudinal waves provide us with phase speeds of 29+-2 km/s and 31+-2 km/s, respectively. We speculate that these phase speeds may not reflect the true propagation speeds of the waves. Thus, effects such as the refraction of fast longitudinal waves may contribute to an overestimate of the phase speed.Comment: 14 pages, 7 figure

PRP and BMAC for Musculoskeletal Conditions via Biomaterial Carriers.

Platelet-rich plasma (PRP) and bone marrow aspirate concentrate (BMAC) are orthobiologic therapies considered as an alternative to the current therapies for muscle, bone and cartilage. Different formulations of biomaterials have been used as carriers for PRP and BMAC in order to increase regenerative processes. The most common biomaterials utilized in conjunction with PRP and BMAC clinical trials are organic scaffolds and natural or synthetic polymers. This review will cover the combinatorial strategies of biomaterial carriers with PRP and BMAC for musculoskeletal conditions (MsCs) repair and regeneration in clinical trials. The main objective is to review the therapeutic use of PRP and BMAC as a treatment option for muscle, bone and cartilage injuries