Decoding Hidden Markov Models Faster Than Viterbi Via Online Matrix-Vector (max, +)-Multiplication

In this paper, we present a novel algorithm for the maximum a posteriori decoding (MAPD) of time-homogeneous Hidden Markov Models (HMM), improving the worst-case running time of the classical Viterbi algorithm by a logarithmic factor. In our approach, we interpret the Viterbi algorithm as a repeated computation of matrix-vector $(\max, +)$-multiplications. On time-homogeneous HMMs, this computation is online: a matrix, known in advance, has to be multiplied with several vectors revealed one at a time. Our main contribution is an algorithm solving this version of matrix-vector $(\max,+)$-multiplication in subquadratic time, by performing a polynomial preprocessing of the matrix. Employing this fast multiplication algorithm, we solve the MAPD problem in $O(mn^2/ \log n)$ time for any time-homogeneous HMM of size $n$ and observation sequence of length $m$, with an extra polynomial preprocessing cost negligible for $m > n$. To the best of our knowledge, this is the first algorithm for the MAPD problem requiring subquadratic time per observation, under the only assumption -- usually verified in practice -- that the transition probability matrix does not change with time.Comment: AAAI 2016, to appea

The Rhombi-Chain Bose-Hubbard Model: geometric frustration and interactions

We explore the effects of geometric frustration within a one-dimensional Bose-Hubbard model using a chain of rhombi subject to a magnetic flux. The competition of tunnelling, self-interaction and magnetic flux gives rise to the emergence of a pair-superfluid (pair-Luttinger liquid) phase besides the more conventional Mott-insulator and superfluid (Luttinger liquid) phases. We compute the complete phase diagram of the model by identifying characteristic properties of the pair-Luttinger liquid phase such as pair correlation functions and structure factors and find that the pair-Luttinger liquid phase is very sensitive to changes away from perfect frustration (half-flux). We provide some proposals to make the model more resilient to variants away from perfect frustration. We also study the bipartite entanglement properties of the chain. We discover that, while the scaling of the block entropy pair-superfluid and of the single-particle superfluid leads to the same central charge, the properties of the low-lying entanglement spectrum levels reveal their fundamental difference.Comment: 12 pages, 11 figure

Defects at Silica Surfaces and crack-tip shielding - A Finite Element Study

The prediction of strength in silica needs knowledge of failure behaviour of defects in the surface region. Pores and cracks are studied by using the Finite Element method. The results for pores are given in terms of stresses, the results for cracks by stress intensity factors

Finite Element study on semi-elliptical surface cracks in a cylinder

Different types of test specimens were applied in the past for the measure-ment of subcritical crack growth in silica. The rather large scatter of crack-growth curves calls for re-analysis of stress intensity factors. In the present note semi-elliptical surface cracks in long cylinders are addressed. In addition the first regular stress term (T-stress) is considered

Effect of annealing temperature on microstructure and high-temperature tensile behaviour of Ti-6242S alloy produced by Laser Powder Bed Fusion

This work is focussed at investigating the properties of additive manufactured Ti-6242S, a Ti alloy with excellent mechanical strength and stability up to 550 °C. Special attention is given to the effect of different heat treatment routes on microstructure and high-temperature mechanical behaviour of the Ti-6242S alloy produced by Laser Powder Bed Fusion. Annealing was performed in the α/β field (at 940 °C, 960 °C, 980 °C) or above the β transus (at 1050 °C). Annealing step was followed by Ar gas cooling and ageing at 595 °C. The as-built material exhibits high strength and anisotropic behaviour, showing lower fracture elongation in the direction parallel to the build platform. Heat treatments are responsible for a reduction of material strength but an increase in fracture elongation. Tensile tests at high temperature show that the best heat treatment for applications up to 300 °C is the annealing at 940 °C followed by Ar cooling and ageing. For applications at higher temperatures (namely 550 °C, 750 °C) the annealing step should be performed above the β transus temperature, at 1050 °C, to achieve the best tensile properties

FE-study on maximum swelling anisotropy in silica

Strength of silica fibers heat treated in humid air is affected by swelling strains. In the absence of externally applied stresses swelling is isotropic. Under uniaxial stress an anisotropy of swelling strains has to be expected with maximum expansion in stress direction. In order to compute the maximum possible anisotropy, a Finite Element analysis is carried out. Under the assumption of a spherical nano-pore generated by a single bond breaking event, an averaged axial swelling strain was computed that is by a factor of >2 larger than the volume swelling strain

Error sources and geometry effects in DCDC-tests

The main advantages of DCDC-specimens are the completely stable crack extension after spontaneous crack initiation due to the decreasing stress intensity factor with increasing crack length and a very high path stability due to the strongly negative T-stress term. In this report, several possible error sources occurring in DCDC-tests are addressed: end effects in short specimens, differently long cracks at both sides of the drill hole, slight offset of the hole and the crack, non-symmetrical loading