Mountain Mouse-warbler

Mountain mouse-warbler

The mountain mouse-warbler (Origma robusta) is a species of bird in the family Acanthizidae. It is found in Indonesia and Papua New Guinea, where its natural habitat is subtropical or tropical moist montane forests. This species was formerly placed in the genus Crateroscelis, but following the publication of a molecular phylogenetic study of the scrubwrens and mouse-warblers in 2018, it was moved to the genus Origma.

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Fawn hopping mouse

The fawn hopping mouse (Notomys cervinus) is a rodent native to the central Australian desert. Like all hopping mice it has strong front teeth, a long tail, dark eyes, big ears, well-developed haunches and very long, narrow hind feet. It weighs between 30 and 50 g (1.1 and 1.8 oz). (Compare with the common house mouse, at 10 to 25 g (0.35 to 0.88 oz).) The coloration of the fawn hopping mouse varies from pale pinkish-fawn to grey on the upper parts, and white underneath. The tail is 120 to 160 mm (4.7 to 6.3 in) long, bicoloured (white underneath, darker below), and ends in a dark brush. The ears and round, dark eyes are particularly large, and the whiskers even more so: 65 mm (2.6 in) in a creature that is only 95 to 120 mm (3.7 to 4.7 in) long. The favoured habitat is the sparsely vegetated arid gibber plains and claypans of the Lake Eyre Basin, including parts of northern South Australia, far south-western Queensland and possibly the Northern Territory, though this last is uncertain. Records from the late 19th century show that its former range was more extensive including western New South Wales. Breeding is thought to be opportunistic. In captivity, gestation is about 40 days and between one and five fully furred young are born. Fawn hopping mice live in small family groups of two to four individuals. During the day, they shelter in burrows which are simpler and shallower than those of the sand-dwelling dusky hopping mouse but nevertheless up to a metre deep with between one and three entrances. At night, they forage outwards for hundreds of metres, searching for seeds, and also taking green shoots and insects if the opportunity presents itself. As with other hopping mice, they do not need to drink, though they can metabolise highly saline water if it is available. The fawn hopping mouse is classified as vulnerable. The causes of its decline are unknown, but assumed to be habitat degradation, competition for food with introduced species, and predation by introduced cats and foxes.

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Cyprus spiny mouse

The Cyprus spiny mouse (Acomys nesiotes) is a little-known rodent endemic to Cyprus. These nocturnal animals are generally found in arid areas. After the last reliable record in 1980 no considerable effort has been made until 2007 when four individuals were rediscovered. Due to the insufficient data of its population the IUCN considers it as data deficient

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Chaco grass mouse

The Chaco grass mouse (Akodon toba) is a species of rodent in the family Cricetidae. It is found in Argentina, Bolivia, and Paraguay.

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Shortridge's multimammate mouse

Shortridge's multimammate mouse (Mastomys shortridgei) is a rodent species in the family Muridae. It is native to Angola, Botswana and Namibia. Its natural habitats are moist savanna, subtropical or tropical seasonally wet or flooded lowland grassland, and swamps.

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Luzon giant forest mouse

The Luzon giant forest mouse (Apomys magnus) is a forest mouse endemic to Luzon, Philippines.

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My kitten just ate a mouse help!!?

It's her natural instinct to hunt and kill. Do not worry about her eating the mouse, she should be ok

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Example: the cat and mouse

Suppose there are a timer and a row of five adjacent boxes, with a cat in the first box and a mouse in the fifth box at time zero. The cat and the mouse both jump to a random adjacent box when the timer advances. E.g. if the cat is in the second box and the mouse in the fourth one, the probability is one fourth that the cat will be in the first box and the mouse in the fifth after the timer advances. If the cat is in the first box and the mouse in the fifth one, the probability is one that the cat will be in box two and the mouse will be in box four after the timer advances. The cat eats the mouse if both end up in the same box, at which time the game ends.

The random variable K gives the number of time steps the mouse stays in the game. The Markov chain that represents this game contains the following five states specified by the combination of positions (cat,mouse). Note that while a naive enumeration of states would list 25 states, many are impossible either because the mouse can never have a lower index than the cat (as that would mean the mouse occupied the cat's box and survived to move past it), or because the sum of the two indices will always have even parity. In addition, the 3 possible states that lead to the mouse's death are combined into one: State 1: (1,3) State 2: (1,5) State 3: (2,4) State 4: (3,5) State 5: game over: (2,2), (3,3) & (4,4).We use a stochastic matrix, P displaystyle P (below), to represent the transition probabilities of this system (rows and columns in this matrix are indexed by the possible states listed above, with the pre-transition state as the row and post-transition state as the column).:1-8 For instance, starting from state 1 - 1st row - it is impossible for the system to stay in this state, so P 11 = 0 displaystyle P_11=0 ; the system also cannot transition to state 2 - because the cat would have stayed in the same box - so P 12 = 0 displaystyle P_12=0 , and by a similar argument for the mouse, P 14 = 0 displaystyle P_14=0 . Transitions to states 3 or 5 are allowed, and thus P 13 , P 15 0 displaystyle P_13,P_15

eq 0 . P = [ 0 0 1 / 2 0 1 / 2 0 0 1 0 0 1 / 4 1 / 4 0 1 / 4 1 / 4 0 0 1 / 2 0 1 / 2 0 0 0 0 1 ] . displaystyle P=beginbmatrix0&0&1/2&0&1/20&0&1&0&01/4&1/4&0&1/4&1/40&0&1/2&0&1/20&0&0&0&1endbmatrix. Long-term averagesNo matter what the initial state, the cat will eventually catch the mouse (with probability 1) and a stationary state = (0,0,0,0,1) is approached as a limit.:55-59 To compute the long-term average or expected value of a stochastic variable Y, for each state Sj and time tk there is a contribution of Yj,kP(S=Sj,t=tk). Survival can be treated as a binary variable with Y=1 for a surviving state and Y=0 for the terminated state. The states with Y=0 do not contribute to the long-term average. Phase-type representationAs State 5 is an absorbing state, the distribution of time to absorption is discrete phase-type distributed.

Suppose the system starts in state 2, represented by the vector [ 0 , 1 , 0 , 0 , 0 ] displaystyle ,1,0,0, . The states where the mouse has perished do not contribute to the survival average so state five can be ignored. The initial state and transition matrix can be reduced to, = [ 0 , 1 , 0 , 0 ] , T = [ 0 0 1 2 0 0 0 1 0 1 4 1 4 0 1 4 0 0 1 2 0 ] , displaystyle boldsymbol tau =,1,0,,qquad T=beginbmatrix0&0&frac 12&00&0&1&0frac 14&frac 14&0&frac 140&0&frac 12&0endbmatrix, and ( I T ) 1 1 = [ 2.75 4.5 3.5 2.75 ] , displaystyle (I-T)^-1boldsymbol 1=beginbmatrix2.754.53.52.75endbmatrix, where I displaystyle I is the identity matrix, and 1 displaystyle mathbf 1 represents a column matrix of all ones that acts as a sum over states. Since each state is occupied for one step of time the expected time of the mouse's survival is just the sum of the probability of occupation over all surviving states and steps in time, E [ K ] = ( I T T 2 ) 1 = ( I T ) 1 1 = 4.5. displaystyle E[K]=boldsymbol tau left(ITT^2cdots

ight)boldsymbol 1=boldsymbol tau (I-T)^-1boldsymbol 1=4.5. Higher order moments are given by E [ K ( K 1 ) ... ( K n 1 ) ] = n ! ( I T ) n T n 1 1 . displaystyle E[K(K-1)dots (K-n1)]=n!boldsymbol tau (I-T)^-nT^n-1mathbf 1 ,..