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Alex D. Bird, Magnus J. E. Richardson
Transmission of temporally correlated spike trains through synapses with short-term depression
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389.9339 480.2457 l
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10 0 0 10 369.7511 484.7244 cm
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Q
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-0.0053 Tc
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 523.4456 476.674 cm
BT
/F5 1 Tf
1 TL
-0.004 Tc
0 0 Td
(})Tj
0.5612 0 Td
(but)Tj
1.5534 0 Td
(aver-)Tj
-34.4577 -1.2982 Td
(aged)Tj
2.0693 0 Td
(over)Tj
1.9786 0 Td
(all)Tj
1.1452 0 Td
(possible)Tj
3.4072 0 Td
(patterns)Tj
3.4753 0 Td
(of)Tj
1.0148 0 Td
(restock)Tj
3.101 0 Td
(and)Tj
1.7292 0 Td
(release)Tj
2.9026 0 Td
(events.)Tj
2.9537 0 Td
(Consider)Tj
3.8891 0 Td
(the)Tj
1.474 0 Td
(expected)Tj
3.719 0 Td
(occupancy)Tj
ET
Q
q
1 j
1 J
0 w
200.0126 456.7748 m
205.3984 456.7748 l
205.3984 456.378 l
200.0126 456.378 l
f*
10 0 0 10 200.0125 450.7086 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 205.3984 448.2141 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 212.7685 450.7086 cm
BT
/F5 1 Tf
1 TL
-0.004 Tc
0 0 Td
(immediately)Tj
5.2043 0 Td
(before)Tj
2.7383 0 Td
(the)Tj
/F10 1 Tf
1.4683 0 Td
[()]TJ
/F5 1 Tf
(th)Tj
1.8255 0 Td
(spike)Tj
2.2847 0 Td
(at)Tj
0.9525 0 Td
(time)Tj
/F10 1 Tf
2.0296 0 Td
[(\n)]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 380.8062 449.0078 cm
BT
/F10 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 388.8 450.7086 cm
BT
/F5 1 Tf
1 TL
-0.004 Tc
0 0 Td
(as)Tj
1.0147 0 Td
(a)Tj
0.652 0 Td
(function)Tj
3.6283 0 Td
(of)Tj
1.0148 0 Td
(the)Tj
1.474 0 Td
(expected)Tj
3.7191 0 Td
(occupancy)Tj
ET
Q
q
1 j
1 J
0 w
548.674 456.7748 m
554.0598 456.7748 l
554.0598 456.378 l
548.674 456.378 l
f*
10 0 0 10 548.674 450.7086 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 554.0598 448.2141 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()]TJ
/F14 1 Tf
( )Tj
/F16 1 Tf
1.5496 0 Td
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 200.0125 437.6125 cm
BT
/F5 1 Tf
1 TL
-0.004 Tc
0 0 Td
(immediately)Tj
5.1987 0 Td
(before)Tj
2.7439 0 Td
(the)Tj
1.4683 0 Td
(\()Tj
/F10 1 Tf
[()]TJ
/F12 1 Tf
1.338 0 Td
[()]TJ
/F5 1 Tf
0.788 0 Td
(1\)th)Tj
1.8652 0 Td
(spike:)Tj
2.5058 0 Td
(this)Tj
1.6781 0 Td
(obeys)Tj
2.4718 0 Td
(the)Tj
1.4683 0 Td
(recursion)Tj
4.0195 0 Td
(equation)Tj
ET
Q
q
1 j
1 J
0 w
292.1386 424.5732 m
297.5244 424.5732 l
297.5244 424.1764 l
292.1386 424.1764 l
f*
10 0 0 10 292.1385 418.507 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 297.5244 416.0125 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 312.7181 418.507 cm
BT
/F14 1 Tf
1 TL
0 0 Td
()Tj
ET
Q
q
1 j
1 J
0 w
330.4063 424.5732 m
335.7921 424.5732 l
335.7921 424.1764 l
330.4063 424.1764 l
f*
10 0 0 10 330.4062 418.507 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 335.7921 416.0125 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()]TJ
/F14 1 Tf
( )Tj
/F16 1 Tf
1.5591 0 Td
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 348.6047 418.507 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()3()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 357.3354 422.1354 cm
BT
/F14 1 Tf
1 TL
0 0 Td
( )Tj
/F21 1 Tf
0.7748 0 Td
(l)Tj
/F14 1 Tf
()Tj
/F10 1 Tf
[(\n)]TJ
ET
Q
q
1 j
1 J
0 w
5 0 0 5 369.411 420.6614 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 373.833 422.1354 cm
BT
/F14 1 Tf
1 TL
0 0 Td
( )Tj
/F10 1 Tf
0.7748 0 Td
[(\n)]TJ
ET
Q
q
1 j
1 J
0 w
5 0 0 5 380.296 420.6614 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()]TJ
/F14 1 Tf
( )Tj
/F16 1 Tf
1.5533 0 Td
(1)Tj
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 391.0677 422.1354 cm
BT
/F14 1 Tf
1 TL
0 0 Td
()Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 396.0566 418.507 cm
BT
/F14 1 Tf
1 TL
0 0 Td
()Tj
0.9977 0 Td
()Tj
/F16 1 Tf
(1)Tj
/F14 1 Tf
1.1055 0 Td
( )Tj
/F10 1 Tf
0.9922 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 430.9795 422.1354 cm
BT
/F14 1 Tf
1 TL
0 0 Td
( )Tj
/F21 1 Tf
0.7748 0 Td
(l)Tj
/F14 1 Tf
()Tj
/F10 1 Tf
[(\n)]TJ
ET
Q
q
1 j
1 J
0 w
5 0 0 5 443.0551 420.6614 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 447.4771 422.1354 cm
BT
/F14 1 Tf
1 TL
0 0 Td
( )Tj
/F10 1 Tf
0.7748 0 Td
[(\n)]TJ
ET
Q
q
1 j
1 J
0 w
5 0 0 5 453.9401 420.6614 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()]TJ
/F14 1 Tf
( )Tj
/F16 1 Tf
1.5533 0 Td
(1)Tj
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 464.7118 422.1354 cm
BT
/F14 1 Tf
1 TL
0 0 Td
()Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 467.4897 418.507 cm
BT
/F14 1 Tf
1 TL
0 0 Td
()Tj
9.598 0.0283 Td
()Tj
/F5 1 Tf
(6)Tj
/F14 1 Tf
()Tj
/F5 1 Tf
-0.004 Tc
-36.3455 -2.1826 Td
(where)Tj
/F10 1 Tf
2.6475 0 Td
[()]TJ
/F5 1 Tf
0.6974 0 Td
(=)Tj
0.7993 0 Td
(1)Tj
/F12 1 Tf
0.6973 0 Td
[()]TJ
/F10 1 Tf
0.7881 0 Td
[()]TJ
/F5 1 Tf
(.)Tj
0.9184 0 Td
(This)Tj
1.9899 0 Td
(can)Tj
1.6271 0 Td
(be)Tj
1.1508 0 Td
(solved,)Tj
2.9651 0 Td
(with)Tj
1.9955 0 Td
(the)Tj
1.4684 0 Td
(initial)Tj
2.5511 0 Td
(condition)Tj
ET
Q
q
1 j
1 J
0 w
444.1323 403.0299 m
449.5181 403.0299 l
449.5181 402.6331 l
444.1323 402.6331 l
f*
10 0 0 10 444.1322 396.9637 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 449.5181 394.4692 cm
BT
/F16 1 Tf
1 TL
0 0 Td
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 455.7543 396.9637 cm
BT
/F14 1 Tf
1 TL
0 0 Td
()Tj
/F16 1 Tf
1.0488 0 Td
(1)Tj
/F5 1 Tf
-0.004 Tc
(,)Tj
0.9467 0 Td
(to)Tj
1.0262 0 Td
(give)Tj
ET
Q
q
1 j
1 J
0 w
323.6031 375.5339 m
328.989 375.5339 l
328.989 375.137 l
323.6031 375.137 l
f*
10 0 0 10 323.6031 369.4677 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 328.9889 366.9732 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 336.9259 369.4677 cm
BT
/F14 1 Tf
1 TL
0 0 Td
()Tj
/F16 1 Tf
1.0544 0 Td
(1)Tj
/F14 1 Tf
0.72 0 Td
( )Tj
ET
Q
q
1 j
1 J
0 w
364.5921 372.189 m
369.411 372.189 l
369.411 371.7921 l
364.5921 371.7921 l
f*
10 0 0 10 364.5921 376.2708 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()]TJ
0 -1.3662 Td
[()]TJ
/F15 1 Tf
0.8163 1.6326 Td
(X)Tj
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 373.7763 380.9196 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()]TJ
/F14 1 Tf
( )Tj
/F16 1 Tf
1.5496 0 Td
(1)Tj
/F10 1 Tf
-1.3985 -3.6568 Td
[()]TJ
/F14 1 Tf
()Tj
/F16 1 Tf
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 388.7433 369.4677 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 393.5622 373.6062 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 396.8503 369.4677 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 400.8188 373.6062 cm
BT
/F14 1 Tf
1 TL
0 0 Td
( )Tj
/F21 1 Tf
0.7748 0 Td
(l)Tj
/F14 1 Tf
()Tj
/F10 1 Tf
[(\n)]TJ
ET
Q
q
1 j
1 J
0 w
5 0 0 5 412.8944 372.1322 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 417.3165 373.6062 cm
BT
/F14 1 Tf
1 TL
0 0 Td
( )Tj
/F10 1 Tf
0.7748 0 Td
[(\n)]TJ
ET
Q
q
1 j
1 J
0 w
5 0 0 5 423.7795 372.1322 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()]TJ
/F14 1 Tf
( )Tj
/F10 1 Tf
1.5533 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 434.3811 373.6062 cm
BT
/F14 1 Tf
1 TL
0 0 Td
()Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 437.159 369.4677 cm
BT
/F20 1 Tf
1 TL
0 0 Td
(:)Tj
/F14 1 Tf
12.6311 0 Td
()Tj
/F5 1 Tf
(7)Tj
/F14 1 Tf
()Tj
/F5 1 Tf
-0.004 Tc
-36.3455 -3.05 Td
(Taking)Tj
3.0387 0 Td
(expectations)Tj
5.1873 0 Td
(over)Tj
1.9786 0 Td
(all)Tj
1.1452 0 Td
(realisations)Tj
4.7395 0 Td
(of)Tj
1.0148 0 Td
(presynaptic)Tj
4.8359 0 Td
(spike)Tj
2.2846 0 Td
(times,)Tj
2.6192 0 Td
(as)Tj
/F10 1 Tf
1.0148 0 Td
[()]TJ
/F14 1 Tf
0 Tc
0.9978 0 Td
(!)Tj
1.2189 0 Td
(1)Tj
/F5 1 Tf
-0.004 Tc
(,)Tj
1.4456 0 Td
(gives)Tj
2.194 0 Td
(the)Tj
-33.7149 -1.3039 Td
(expected)Tj
3.719 0 Td
(occupancy)Tj
4.4844 0 Td
(before)Tj
2.7382 0 Td
(the)Tj
1.4684 0 Td
(arrival)Tj
2.8006 0 Td
(of)Tj
1.0148 0 Td
(a)Tj
0.6519 0 Td
(presynaptic)Tj
4.8359 0 Td
(action)Tj
2.6985 0 Td
(potential)Tj
3.7644 0 Td
(in)Tj
1.0318 0 Td
(the)Tj
1.4683 0 Td
(steady-state)Tj
/F14 1 Tf
0 Tc
-17.9204 -2.6079 Td
(h)Tj
/F10 1 Tf
[()]TJ
/F14 1 Tf
0.873 0 Td
(i)Tj
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 340.1574 297.1842 cm
BT
/F14 1 Tf
1 TL
0 0 Td
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 349.4551 299.8488 cm
BT
/F14 1 Tf
1 TL
0 0 Td
()Tj
/F16 1 Tf
1.0488 0 Td
(1)Tj
/F14 1 Tf
0.7256 0 Td
( )Tj
ET
Q
q
1 j
1 J
0 w
377.1213 302.5701 m
381.9402 302.5701 l
381.9402 302.1732 l
377.1213 302.1732 l
f*
10 0 0 10 377.1212 306.6519 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()]TJ
0 -1.3662 Td
[()]TJ
/F15 1 Tf
0.8107 1.6326 Td
(X)Tj
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 389.4236 311.3007 cm
BT
/F14 1 Tf
1 TL
0 0 Td
(1)Tj
/F10 1 Tf
-0.3685 -3.6568 Td
[()]TJ
/F14 1 Tf
()Tj
/F16 1 Tf
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 401.2724 299.8488 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 406.0913 303.9874 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 409.3795 299.8488 cm
BT
/F14 1 Tf
1 TL
0 0 Td
(h)Tj
/F10 1 Tf
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 417.2031 303.9874 cm
BT
/F14 1 Tf
1 TL
0 0 Td
( )Tj
/F21 1 Tf
0.7748 0 Td
(l)Tj
/F10 1 Tf
[()]TJ
ET
Q
q
1 j
1 J
0 w
5 0 0 5 428.7118 302.4566 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 432.0566 299.8488 cm
BT
/F14 1 Tf
1 TL
0 0 Td
(i)Tj
13.1413 -0.0737 Td
()Tj
/F5 1 Tf
(8)Tj
/F14 1 Tf
()Tj
/F5 1 Tf
-0.004 Tc
-36.3455 -2.9763 Td
(where)Tj
/F10 1 Tf
2.6475 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 232.3842 267.6472 cm
BT
/F10 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 238.0535 269.348 cm
BT
/F5 1 Tf
1 TL
-0.004 Tc
0 0 Td
(is)Tj
0.8503 0 Td
(the)Tj
1.4684 0 Td
(sum)Tj
1.9275 0 Td
(of)Tj
1.0148 0 Td
(the)Tj
1.4684 0 Td
(last)Tj
/F10 1 Tf
1.559 0 Td
[()]TJ
/F5 1 Tf
0.686 0 Td
(ISIs.)Tj
1.9615 0 Td
(This)Tj
1.99 0 Td
(result)Tj
2.4491 0 Td
(is)Tj
0.8447 0 Td
(quite)Tj
2.245 0 Td
(general)Tj
3.1294 0 Td
(and)Tj
1.7292 0 Td
(holds)Tj
2.3924 0 Td
(for)Tj
1.3833 0 Td
(arbitrarily)Tj
4.2463 0 Td
(corre-)Tj
-35.1493 -1.3039 Td
(lated)Tj
2.1486 0 Td
(spike)Tj
2.2846 0 Td
(trains;)Tj
2.7269 0 Td
(however,)Tj
3.8381 0 Td
(we)Tj
1.3266 0 Td
(now)Tj
1.9616 0 Td
(consider)Tj
3.6453 0 Td
(the)Tj
1.474 0 Td
(specific)Tj
3.1862 0 Td
(case)Tj
1.8651 0 Td
(of)Tj
1.0148 0 Td
(spike-times)Tj
4.8019 0 Td
(generated)Tj
4.1386 0 Td
(by)Tj
1.1792 0 Td
(a)Tj
-35.5915 -1.2982 Td
(renewal)Tj
3.3505 0 Td
(process.)Tj
3.4071 0 Td
(In)Tj
1.1112 0 Td
(this)Tj
1.6724 0 Td
(case)Tj
1.8652 0 Td
(the)Tj
1.4684 0 Td
(ISIs)Tj
1.7348 0 Td
(will)Tj
1.6667 0 Td
(be)Tj
1.1509 0 Td
(independent)Tj
5.2724 0 Td
(so)Tj
1.0885 0 Td
(that)Tj
1.7801 0 Td
(the)Tj
1.4684 0 Td
(expectation)Tj
4.8245 0 Td
(over)Tj
1.9786 0 Td
(the)Tj
1.4683 0 Td
(expo-)Tj
-35.308 -1.4911 Td
(nential)Tj
2.9877 0 Td
(term)Tj
2.1315 0 Td
(factorises)Tj
/F14 1 Tf
0 Tc
3.9515 0 Td
(h)Tj
/F10 1 Tf
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 298.5448 232.044 cm
BT
/F14 1 Tf
1 TL
0 0 Td
( )Tj
/F21 1 Tf
0.7748 0 Td
(l)Tj
/F10 1 Tf
[()]TJ
ET
Q
q
1 j
1 J
0 w
5 0 0 5 310.0535 230.5133 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 313.3984 228.4157 cm
BT
/F14 1 Tf
1 TL
0 0 Td
(i)Tj
0.6633 0 Td
()Tj
1.0488 0 Td
(h)Tj
/F10 1 Tf
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 338.3433 232.044 cm
BT
/F14 1 Tf
1 TL
0 0 Td
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