Video learning is an important task in computer vision and has experienced increasing interest over the recent years. Since even a small amount of videos easily comprises several million frames, methods that do not rely on a frame-level annotation are of special importance. In this work, we propose a novel learning algorithm with a Viterbibased loss that allows for online and incremental learning of weakly annotated video data. We moreover show that explicit context and length modeling leads to huge improvements in video segmentation and labeling tasks and include these models into our framework. On several action segmentation benchmarks, we obtain an improvement of up to 10% compared to current state-of-the-art methods.

In economics duopoly is a market dominated by two firms large enough to influence the market price. Stackelberg presented a dynamic form of duopoly that is also called `leader-follower' model. We give a quantum perspective on Stackelberg duopoly that gives a backwards-induction outcome same as the Nash equilibrium in static form of duopoly also known as Cournot's duopoly. We find two qubit quantum pure states required for this purpose.Comment: Revised in the light of referee's comments. Latex, 16 pages, 2 figures, To appear in Phy. Rev.

Evolutionarily Stable Strategy (ESS) in classical game theory is a refinement of Nash equilibrium concept. We investigate the consequences when a small group of mutants using quantum strategies try to invade a classical ESS in a population engaged in symmetric bimatrix game of Prisoner's Dilemma.Secondly we show that in an asymmetric quantum game between two players an ESS pair can be made to appear or disappear by resorting to entangled or unentangled initial states used to play the game even when the strategy pair remains a Nash equilibrium in both forms of the game.when |b| 2 = 0 i.e. when the initial state becomes unentangled. NE inequalities are thenThe parameters of the initial entangled state a and b may decide some of the possible NE. Three symmetric NE are 1.The first two NE are independent of the parameters a and b of the initial state. However, the third NE depends on these. We now ask which of these NE can be ESS's assuming that a particular NE exists with reference to a particular set of initial states |ψ in for which it can be found. The payoff to a player using I with probability p when the opponent uses I with probability q is9For the first case ⋆ p = ⋆ q = 0. The payoff P (0, 0) > P (p, 0) when 3 |b| 2 < 1 and P (0, 0) = P (p, 0) imply 3 |b| 2 = 1. Also P (q, q) = −q 2 + 5 3 (q + 1) and P (0, q) = 5 3 (q + 1). Now P (0, q) > P (q, q) when q = 0.Therefore, ⋆ p = ⋆ q = 0 is an ESS when 3 |b| 2 ≤ 1.Consider ⋆ p = ⋆ q = 1 now. P (1, 1) > P (p, 1) means 3 |b| 2 > 2 if p = 1. And P (1, 1) = P (p, 1) means for p = 1 we have 3 |b| 2 = 2. In such case P (q, q) = −q 2 + 1 3 (q + 7) and P (1, q) = 5 3 (2 − q). Now P (1, q) > P (q, q) because (1 − q) 2 > 0 for q = 1. Therefore ⋆ p = ⋆ q = 1 is an ESS when 3 |b| 2 ≥ 2.The third case ⋆ p = ⋆ q = 3 |b| 2 − 1. Here P (3 |b| 2 − 1, 3 |b| 2 − 1) = −36 |b| 6 + 36 |b| 4 − 5 |b| 2 + 6.Also we find P (p, 3 |b| 2 − 1) = −21 |b| 4 + 21 |b| 2 − 3. Therefore, the condition P (3 |b| 2 − 1, 3 |b| 2 − 1) > P (p, 3 |b| 2 − 1) holds and ⋆ p = ⋆ q = 3 |b| 2 − 1 is an ESS too for 1 < 3 |b| 2 < 2.All three possible symmetric NE definable for different ranges of |b| 2 turn out ESS's. Each of the three sets of initial states |ψ in give a unique NE that is an ESS too. Switching from one to the other sets of initial states also changes the NE and ESS accordingly. A question rises here: is it possible that a particular NE switches over between 'ESS' and 'not ESS' when the initial state changes between certain possible choices?. The transition between classical and quantum game is also controlled by a change in the initial state. For example classical payoffs can be obtained when the initial state is unentangled. It implies that it may be possible to switch over between 'ESS' and 'not ESS' by a change between 'classical' and 'quantum' forms of a game i.e. when the initial state is unentangled and entangled respectively. This possibility makes ESS interesting for the quantum game theory as well.Because PD does not allow such a possibility we now investigate asymmetric games to look for ...

In 2008, researchers at the Hewlett-Packard (HP) laboratories published a paper in Nature reporting the development of a new basic circuit element that completes the missing link between charge and flux linkage, which was postulated by Chua in 1971(Chua 1971 IEEE Trans. Circuit Theory 18, 507-519 (doi:10.1109/TCT.1971). The HP memristor is based on a nanometre scale TiO 2 thin film, containing a doped region and an undoped region. Further to proposed applications of memristors in artificial biological systems and non-volatile RAM, they also enable reconfigurable nanoelectronics. Moreover, memristors provide new paradigms in application-specific integrated circuits and field programmable gate arrays. A significant reduction in area with an unprecedented memory capacity and device density are the potential advantages of memristors for integrated circuits. This work reviews the memristor and provides mathematical and SPICE models for memristors. Insight into the memristor device is given via recalling the quasi-static expansion of Maxwell's equations. We also review Chua's arguments based on electromagnetic theory.

We consider a slightly modified version of the Rock-Scissors-Paper (RSP) game from the point of view of evolutionary stability. In its classical version the game has a mixed Nash equilibrium (NE) not stable against mutants. We find a quantized version of the RSP game for which the classical mixed NE becomes stable.Comment: Revised on referee's criticism, submitted to Physical Review