diff --git a/docs/examples/notebooks/basic_quantum.ipynb b/docs/examples/notebooks/basic_quantum.ipynb new file mode 100644 index 0000000..078a78e --- /dev/null +++ b/docs/examples/notebooks/basic_quantum.ipynb @@ -0,0 +1 @@ +{"cells":[{"cell_type":"text","text":"

Basic Symbolic Quantum Mechanics

"},{"code":"%load_ext sympy_printing","cell_type":"code","prompt_number":1},{"code":"from sympy import sqrt, symbols, Rational\nfrom sympy import expand, Eq, Symbol, simplify, exp, sin\nfrom sympy.physics.quantum import *\nfrom sympy.physics.quantum.qubit import *\nfrom sympy.physics.quantum.gate import *\nfrom sympy.physics.quantum.grover import *\nfrom sympy.physics.quantum.qft import QFT, IQFT, Fourier\nfrom sympy.physics.quantum.circuitplot import circuit_plot","cell_type":"code","prompt_number":2},{"code":"phi, psi = Ket('phi'), Ket('psi')\nalpha, beta = symbols('alpha beta', complex=True)","cell_type":"code","prompt_number":3},{"code":"state = alpha*psi + beta*phi; state\n","cell_type":"code","prompt_number":4},{"code":"ip = Dagger(state)*state; ip\n","cell_type":"code","prompt_number":5},{"code":"qapply(expand(ip))\n","cell_type":"code","prompt_number":6},{"code":"A = Operator('A')\nB = Operator('B')\nC = Operator('C')","cell_type":"code","prompt_number":7},{"code":"A*B == B*A\n","cell_type":"code","prompt_number":8},{"code":"expand((A+B)**2)","cell_type":"code","prompt_number":9},{"code":"comm = Commutator(A,B); comm\n","cell_type":"code","prompt_number":10},{"code":"comm.doit()","cell_type":"code","prompt_number":11},{"code":"comm = Commutator(A*B,B+C); comm","cell_type":"code","prompt_number":12},{"code":"comm.expand(commutator=True)","cell_type":"code","prompt_number":13},{"code":"_.doit().expand()\n","cell_type":"code","prompt_number":14},{"code":"Dagger(_)","cell_type":"code","prompt_number":15},{"code":"%notebook save basic_quantum.ipynb","cell_type":"code","prompt_number":16}]} \ No newline at end of file diff --git a/docs/examples/notebooks/decompose.ipynb b/docs/examples/notebooks/decompose.ipynb new file mode 100644 index 0000000..1aba5d5 --- /dev/null +++ b/docs/examples/notebooks/decompose.ipynb @@ -0,0 +1 @@ +{"cells":[{"cell_type":"text","text":"

Gate Decomposition

"},{"code":"%load_ext sympy_printing","cell_type":"code","prompt_number":1},{"code":"from sympy import sqrt, symbols, Rational\nfrom sympy import expand, Eq, Symbol, simplify, exp, sin\nfrom sympy.physics.quantum import *\nfrom sympy.physics.quantum.qubit import *\nfrom sympy.physics.quantum.gate import *\nfrom sympy.physics.quantum.grover import *\nfrom sympy.physics.quantum.qft import QFT, IQFT, Fourier\nfrom sympy.physics.quantum.circuitplot import circuit_plot","cell_type":"code","prompt_number":2},{"code":"CY10 = CGate(1, Y(0)); CY10\n","cell_type":"code","prompt_number":3},{"code":"CY10.decompose()\n","cell_type":"code","prompt_number":4},{"code":"circuit_plot(CY10.decompose(), nqubits=2)","cell_type":"code","prompt_number":5},{"code":"CZ01 = CGate(0, Z(1)); CZ01\n","cell_type":"code","prompt_number":6},{"code":"CZ01.decompose()\n","cell_type":"code","prompt_number":7},{"code":"circuit_plot(CZ01.decompose(), nqubits=2)","cell_type":"code","prompt_number":8},{"code":"SWAP10 = SWAP(1, 0); SWAP10\n","cell_type":"code","prompt_number":9},{"code":"SWAP10.decompose()","cell_type":"code","prompt_number":10},{"code":"circuit_plot(SWAP10.decompose(), nqubits=2)","cell_type":"code","prompt_number":11},{"code":"gates = [CGate(1,Y(0)), CGate(0,Z(1)), SWAP(1, 0)]","cell_type":"code","prompt_number":12},{"code":"for g in gates:\n dg = g.decompose()\n display(Eq(g, dg))\n circuit_plot(g, nqubits=2)\n circuit_plot(dg, nqubits=2) ","cell_type":"code","prompt_number":16},{"code":"%notebook save decomposition.ipynb","cell_type":"code","prompt_number":30}]} \ No newline at end of file diff --git a/docs/examples/notebooks/dense_coding.ipynb b/docs/examples/notebooks/dense_coding.ipynb new file mode 100644 index 0000000..75f7c0c --- /dev/null +++ b/docs/examples/notebooks/dense_coding.ipynb @@ -0,0 +1 @@ +{"cells":[{"cell_type":"text","text":"

Dense Coding\n

"},{"code":"%load_ext sympy_printing","cell_type":"code","prompt_number":2},{"code":"from sympy import sqrt, symbols, Rational\nfrom sympy import expand, Eq, Symbol, simplify, exp, sin\nfrom sympy.physics.quantum import *\nfrom sympy.physics.quantum.qubit import *\nfrom sympy.physics.quantum.gate import *\nfrom sympy.physics.quantum.grover import *\nfrom sympy.physics.quantum.qft import QFT, IQFT, Fourier\nfrom sympy.physics.quantum.circuitplot import circuit_plot","cell_type":"code","prompt_number":3},{"code":"psi = Qubit('00')/sqrt(2) + Qubit('11')/sqrt(2); psi\n","cell_type":"code","prompt_number":4},{"code":"circuits = [H(1)*CNOT(1,0), H(1)*CNOT(1,0)*X(1), H(1)*CNOT(1,0)*Z(1), H(1)*CNOT(1,0)*Z(1)*X(1)]","cell_type":"code","prompt_number":20},{"code":"for circuit in circuits:\n circuit_plot(circuit, nqubits=2)\n display(Eq(circuit*psi,qapply(circuit*psi)))","cell_type":"code","prompt_number":21},{"code":"%notebook save dense_coding.ipynb","cell_type":"code","prompt_number":28}]} \ No newline at end of file diff --git a/docs/examples/notebooks/grovers.ipynb b/docs/examples/notebooks/grovers.ipynb new file mode 100644 index 0000000..3f3cd62 --- /dev/null +++ b/docs/examples/notebooks/grovers.ipynb @@ -0,0 +1 @@ +{"cells":[{"cell_type":"text","text":"

Grover's Algorithm

"},{"code":"%load_ext sympy_printing","cell_type":"code","prompt_number":1},{"code":"from sympy import sqrt, symbols, Rational\nfrom sympy import expand, Eq, Symbol, simplify, exp, sin\nfrom sympy.physics.quantum import *\nfrom sympy.physics.quantum.qubit import *\nfrom sympy.physics.quantum.gate import *\nfrom sympy.physics.quantum.grover import *\nfrom sympy.physics.quantum.qft import QFT, IQFT, Fourier\nfrom sympy.physics.quantum.circuitplot import circuit_plot","cell_type":"code","prompt_number":2},{"code":"nqubits = 3\n","cell_type":"code","prompt_number":4},{"code":"def black_box(qubits):\n return True if qubits == IntQubit(1, qubits.nqubits) else False\n","cell_type":"code","prompt_number":3},{"code":"psi = superposition_basis(nqubits); psi\n","cell_type":"code","prompt_number":5},{"code":"v = OracleGate(nqubits, black_box)\n","cell_type":"code","prompt_number":6},{"code":"iter1 = qapply(grover_iteration(psi, v)); iter1\n","cell_type":"code","prompt_number":7},{"code":"iter2 = qapply(grover_iteration(iter1, v)); iter2\n","cell_type":"code","prompt_number":8},{"code":"measure_all_oneshot(iter2)\n","cell_type":"code","prompt_number":12},{"code":"%notebook save grovers.ipynb","cell_type":"code","prompt_number":28}]} \ No newline at end of file diff --git a/docs/examples/notebooks/qerror.ipynb b/docs/examples/notebooks/qerror.ipynb new file mode 100644 index 0000000..7ff0a3d --- /dev/null +++ b/docs/examples/notebooks/qerror.ipynb @@ -0,0 +1 @@ +{"cells":[{"cell_type":"text","text":"

Quantum Error Correction

"},{"code":"%load_ext sympy_printing","cell_type":"code","prompt_number":1},{"code":"from sympy import sqrt, symbols, Rational\nfrom sympy import expand, Eq, Symbol, simplify, exp, sin\nfrom sympy.physics.quantum import *\nfrom sympy.physics.quantum.qubit import *\nfrom sympy.physics.quantum.gate import *\nfrom sympy.physics.quantum.grover import *\nfrom sympy.physics.quantum.qft import QFT, IQFT, Fourier\nfrom sympy.physics.quantum.circuitplot import circuit_plot","cell_type":"code","prompt_number":2},{"code":"M0 = Z(1)*X(2)*X(3)*Z(4); M0\n","cell_type":"code","prompt_number":3},{"code":"M1 = Z(2)*X(3)*X(4)*Z(0); M1\n","cell_type":"code","prompt_number":4},{"code":"M2 = Z(3)*X(4)*X(0)*Z(1); M2\n","cell_type":"code","prompt_number":5},{"code":"M3 = Z(4)*X(0)*X(1)*Z(2); M3\n","cell_type":"code","prompt_number":6},{"code":"gate_simp(Commutator(M0,M1).doit())\n","cell_type":"code","prompt_number":7},{"code":"for o in [M0,M1,M2,M3]:\n display(gate_simp(o*o))\n","cell_type":"code","prompt_number":8},{"code":"zero = Rational(1,4)*(1+M0)*(1+M1)*(1+M2)*(1+M3)*IntQubit(0, 5); zero\n","cell_type":"code","prompt_number":9},{"code":"qapply(4*zero)\n","cell_type":"code","prompt_number":10},{"code":"one = Rational(1,4)*(1+M0)*(1+M1)*(1+M2)*(1+M3)*IntQubit(2**5-1, 5); one\n","cell_type":"code","prompt_number":11},{"code":"qapply(4*one)\n","cell_type":"code","prompt_number":12},{"code":"encoding_circuit = H(3)*H(4)*CNOT(2,0)*CNOT(3,0)*CNOT(4,0)*H(1)*H(4)*\\\n CNOT(2,1)*CNOT(4,1)*H(2)*CNOT(3,2)*CNOT(4,2)*H(3)*\\\n H(4)*CNOT(4, 3)*Z(4)*H(4)*Z(4)\n","cell_type":"code","prompt_number":13},{"code":"circuit_plot(encoding_circuit, nqubits=5, scale=0.5)","cell_type":"code","prompt_number":14},{"code":"represent(4*encoding_circuit, nqubits=5)","cell_type":"code","prompt_number":16},{"code":"%notebook save qerror.ipynb","cell_type":"code","prompt_number":23},{"code":"","cell_type":"code","prompt_number":23}]} \ No newline at end of file diff --git a/docs/examples/notebooks/qft.ipynb b/docs/examples/notebooks/qft.ipynb new file mode 100644 index 0000000..39abd12 --- /dev/null +++ b/docs/examples/notebooks/qft.ipynb @@ -0,0 +1 @@ +{"cells":[{"cell_type":"text","text":"

Teleportation

"},{"code":"%load_ext sympy_printing","cell_type":"code","prompt_number":1},{"code":"from sympy import sqrt, symbols, Rational\nfrom sympy import expand, Eq, Symbol, simplify, exp, sin\nfrom sympy.physics.quantum import *\nfrom sympy.physics.quantum.qubit import *\nfrom sympy.physics.quantum.gate import *\nfrom sympy.physics.quantum.grover import *\nfrom sympy.physics.quantum.qft import QFT, IQFT, Fourier\nfrom sympy.physics.quantum.circuitplot import circuit_plot","cell_type":"code","prompt_number":2},{"code":"fourier = QFT(0,3).decompose(); fourier\n","cell_type":"code","prompt_number":3},{"code":"circuit_plot(fourier, nqubits=3)","cell_type":"code","prompt_number":4},{"code":"m = represent(fourier, nqubits=3)","cell_type":"code","prompt_number":12},{"code":"m","cell_type":"code","prompt_number":13},{"code":"represent(Fourier(0,3), nqubits=3)*4/sqrt(2)\n","cell_type":"code","prompt_number":5},{"code":"state = (Qubit('000') + Qubit('010') + Qubit('100') + Qubit('110'))/sqrt(4); state\n","cell_type":"code","prompt_number":6},{"code":"qapply(fourier*state)\n","cell_type":"code","prompt_number":7},{"code":"%notebook save qft.ipynb","cell_type":"code","prompt_number":23}]} \ No newline at end of file diff --git a/docs/examples/notebooks/quantum_computing.ipynb b/docs/examples/notebooks/quantum_computing.ipynb new file mode 100644 index 0000000..96c58c2 --- /dev/null +++ b/docs/examples/notebooks/quantum_computing.ipynb @@ -0,0 +1 @@ +{"cells":[{"cell_type":"text","text":"

Symbolic Quantum Computing

"},{"code":"%load_ext sympy_printing","cell_type":"code","prompt_number":2},{"code":"from sympy import sqrt, symbols, Rational\nfrom sympy import expand, Eq, Symbol, simplify, exp, sin\nfrom sympy.physics.quantum import *\nfrom sympy.physics.quantum.qubit import *\nfrom sympy.physics.quantum.gate import *\nfrom sympy.physics.quantum.grover import *\nfrom sympy.physics.quantum.qft import QFT, IQFT, Fourier\nfrom sympy.physics.quantum.circuitplot import circuit_plot","cell_type":"code","prompt_number":3},{"code":"alpha, beta = symbols('alpha beta',real=True)","cell_type":"code","prompt_number":4},{"code":"psi = alpha*Qubit('00') + beta*Qubit('11'); psi\n","cell_type":"code","prompt_number":5},{"code":"Dagger(psi)\n","cell_type":"code","prompt_number":6},{"code":"qapply(Dagger(Qubit('00'))*psi)\n","cell_type":"code","prompt_number":7},{"code":"for state, prob in measure_all(psi):\n display(state)\n display(prob)\n","cell_type":"code","prompt_number":8},{"code":"represent(psi, nqubits=2)\n","cell_type":"code","prompt_number":9},{"code":"g = X(0); g\n","cell_type":"code","prompt_number":10},{"code":"represent(g, nqubits=2)\n","cell_type":"code","prompt_number":11},{"code":"c = H(0)*Qubit('00'); c\n","cell_type":"code","prompt_number":12},{"code":"qapply(c)\n","cell_type":"code","prompt_number":13},{"code":"for g1 in (Y,Z,H):\n for g2 in (Y,Z,H):\n e = Commutator(g1(0),g2(0))\n if g1 != g2:\n display(Eq(e,e.doit()))\n","cell_type":"code","prompt_number":14},{"code":"c = H(0)*X(1)*H(0)**2*CNOT(0,1)*X(1)**3*X(0)*Z(2)**2*S(3)**3; c\n","cell_type":"code","prompt_number":24},{"code":"circuit_plot(c, nqubits=4)","cell_type":"code","prompt_number":25},{"code":"gate_simp(c)\n","cell_type":"code","prompt_number":16},{"code":"circuit_plot(gate_simp(c),nqubits=5)","cell_type":"code","prompt_number":23},{"code":"%notebook save quantum_computing.ipynb","cell_type":"code","prompt_number":35}]} \ No newline at end of file diff --git a/docs/examples/notebooks/teleportation.ipynb b/docs/examples/notebooks/teleportation.ipynb new file mode 100644 index 0000000..bd4d471 --- /dev/null +++ b/docs/examples/notebooks/teleportation.ipynb @@ -0,0 +1 @@ +{"cells":[{"cell_type":"text","text":"

Teleportation

"},{"code":"%load_ext sympy_printing","cell_type":"code","prompt_number":1},{"code":"from sympy import sqrt, symbols, Rational\nfrom sympy import expand, Eq, Symbol, simplify, exp, sin\nfrom sympy.physics.quantum import *\nfrom sympy.physics.quantum.qubit import *\nfrom sympy.physics.quantum.gate import *\nfrom sympy.physics.quantum.grover import *\nfrom sympy.physics.quantum.qft import QFT, IQFT, Fourier\nfrom sympy.physics.quantum.circuitplot import circuit_plot","cell_type":"code","prompt_number":2},{"code":"a,b = symbols('ab', real=True)\nstate = Qubit('000')*a + Qubit('001')*b; state","cell_type":"code","prompt_number":3},{"code":"entangle1_2 = CNOT(1,2)*HadamardGate(1); entangle1_2\n","cell_type":"code","prompt_number":4},{"code":"state = qapply(entangle1_2*state); state\n","cell_type":"code","prompt_number":5},{"code":"entangle0_1 = HadamardGate(0)*CNOT(0,1); entangle0_1\n","cell_type":"code","prompt_number":6},{"code":"circuit_plot(entangle0_1*entangle1_2, nqubits=3)\n","cell_type":"code","prompt_number":7},{"code":"state = qapply(entangle0_1*state); state\n","cell_type":"code","prompt_number":8},{"code":"result = measure_partial(state, (0,1))\n","cell_type":"code","prompt_number":10},{"code":"state = (result[2][0]*2).expand(); state","cell_type":"code","prompt_number":11},{"code":"state = qapply(XGate(2)*state); state\n","cell_type":"code","prompt_number":12},{"code":"%notebook save teleportation.ipynb","cell_type":"code","prompt_number":13},{"code":"","cell_type":"code","prompt_number":18}]} \ No newline at end of file diff --git a/docs/examples/notebooks/text_analysis.ipynb b/docs/examples/notebooks/text_analysis.ipynb new file mode 100644 index 0000000..0250cc7 --- /dev/null +++ b/docs/examples/notebooks/text_analysis.ipynb @@ -0,0 +1 @@ +{"cells":[{"cell_type":"text","text":"

Text Analysis Using NetworkX

"},{"cell_type":"text","text":"

This notebook will analyze a plain text file treating it as a list of\nnewline-separated sentences (e.g. a list of paper titles).

\n
\n

It computes word frequencies (after doing some naive normalization by\nlowercasing and throwing away a few overly common words). It also computes,\nfrom the most common words, a weighted graph of word co-occurrences and\ndisplays it, as well as summarizing the graph structure by ranking its nodes in\ndescending order of eigenvector centrality.

\n
\n

This is meant as an illustration of text processing in Python, using matplotlib\nfor visualization and NetworkX for graph-theoretical manipulation. It should\nnot be considered production-strength code for serious text analysis.

\n
\n

Author: Fernando Perez

"},{"code":"%run text_analysis.py","cell_type":"code","prompt_number":3},{"code":"default_url = \"http://bibserver.berkeley.edu/tmp/titles.txt\"\nn_words = 15\nn_nodes = 15\nurl = default_url\n ","cell_type":"code","prompt_number":4},{"cell_type":"text","text":"Fetch text and do basic preprocessing."},{"code":"text = get_text_from_url(url).lower()\nlines = text.splitlines()\nwords = text_cleanup(text)","cell_type":"code","prompt_number":5},{"cell_type":"text","text":"Compute frequency histogram."},{"code":"wf = word_freq(words)\nsorted_wf = sort_freqs(wf)","cell_type":"code","prompt_number":6},{"cell_type":"text","text":"Build a graph from the n_nodes most frequent words."},{"code":"popular = sorted_wf[-n_nodes:]\npop_words = [wc[0] for wc in popular]\nco_occur = co_occurrences(lines, pop_words)\nwgraph = co_occurrences_graph(popular, co_occur, cutoff=1)\ncentrality = nx.eigenvector_centrality_numpy(wgraph)\n","cell_type":"code","prompt_number":7},{"cell_type":"text","text":"Print summaries of single-word frequencies and graph structure."},{"code":"summarize_freq_hist(sorted_wf)\nsummarize_centrality(centrality)","cell_type":"code","prompt_number":8},{"cell_type":"text","text":"Plot histogram and graph."},{"code":"plot_word_histogram(sorted_wf, n_words,\"Frequencies for %s most frequent words\" % n_words)","cell_type":"code","prompt_number":9},{"code":"plot_word_histogram(sorted_wf, 1.0, \"Frequencies for entire word list\")\n","cell_type":"code","prompt_number":10},{"code":"plot_graph(wgraph)","cell_type":"code","prompt_number":11},{"code":"%notebook save text_analysis.ipynb","cell_type":"code","prompt_number":10}]} \ No newline at end of file diff --git a/docs/examples/notebooks/text_analysis.py b/docs/examples/notebooks/text_analysis.py new file mode 100644 index 0000000..9b1950c --- /dev/null +++ b/docs/examples/notebooks/text_analysis.py @@ -0,0 +1,373 @@ +#!/usr/bin/env python +"""Simple text analysis: word frequencies and co-occurrence graph. + +Usage: + + text_analysis.py [text_file] + +This script will analize a plain text file treating it as a list of +newline-separated sentences (e.g. a list of paper titles). + +It computes word frequencies (after doing some naive normalization by +lowercasing and throwing away a few overly common words). It also computes, +from the most common words, a weighted graph of word co-occurrences and +displays it, as well as summarizing the graph structure by ranking its nodes in +descending order of eigenvector centrality. + +This is meant as an illustration of text processing in Python, using matplotlib +for visualization and NetworkX for graph-theoretical manipulation. It should +not be considered production-strength code for serious text analysis. + +Author: Fernando Perez +""" + +#----------------------------------------------------------------------------- +# Imports +#----------------------------------------------------------------------------- + +# From the standard library +import os +import re +import sys +import urllib2 + +# Third-party libraries +import networkx as nx +import numpy as np + +from matplotlib import pyplot as plt + +#----------------------------------------------------------------------------- +# Function definitions +#----------------------------------------------------------------------------- + +def rescale_arr(arr,amin,amax): + """Rescale an array to a new range. + + Return a new array whose range of values is (amin,amax). + + Parameters + ---------- + arr : array-like + + amin : float + new minimum value + + amax : float + new maximum value + + Examples + -------- + >>> a = np.arange(5) + + >>> rescale_arr(a,3,6) + array([ 3. , 3.75, 4.5 , 5.25, 6. ]) + """ + + # old bounds + m = arr.min() + M = arr.max() + # scale/offset + s = float(amax-amin)/(M-m) + d = amin - s*m + + # Apply clip before returning to cut off possible overflows outside the + # intended range due to roundoff error, so that we can absolutely guarantee + # that on output, there are no values > amax or < amin. + return np.clip(s*arr+d,amin,amax) + + +def all_pairs(items): + """Make all unique pairs (order doesn't matter)""" + pairs = [] + nitems = len(items) + for i, wi in enumerate(items): + for j in range(i+1, nitems): + pairs.append((wi, items[j])) + return pairs + + +def text_cleanup(text, min_length=3, + remove = set(['for', 'the', 'and', 'with'])): + """Clean up a list of lowercase strings of text for simple analysis. + + Splits on whitespace, removes all 'words' less than `min_length` characters + long, and those in the `remove` set. + + Returns a list of strings. + """ + return [w for w in text.lower().split() + if len(w)>=min_length and w not in remove] + + +def print_vk(lst): + """Print a list of value/key pairs nicely formatted in key/value order.""" + + # Find the longest key: remember, the list has value/key paris, so the key + # is element [1], not [0] + longest_key = max([len(word) for word, count in lst]) + # Make a format string out of it + fmt = '%'+str(longest_key)+'s -> %s' + # Do actual printing + for k,v in lst: + print fmt % (k,v) + + +def word_freq(text): + """Return a dictionary of word frequencies for the given text. + + Input text should be given as an iterable of strings.""" + + freqs = {} + for word in text: + freqs[word] = freqs.get(word, 0) + 1 + return freqs + + +def sort_freqs(freqs): + """Sort a word frequency histogram represented as a dictionary. + + Parameters + ---------- + freqs : dict + A dict with string keys and integer values. + + Return + ------ + items : list + A list of (count, word) pairs. + """ + items = freqs.items() + items.sort(key = lambda wc: wc[1]) + return items + ## words,counts = freqs.keys(),freqs.values() + ## # Sort by count + ## items = zip(counts,words) + ## items.sort() + ## return items + + +def summarize_freq_hist(freqs, n=10): + """Print a simple summary of a word frequencies dictionary. + + Paramters + --------- + freqs : dict or list + Word frequencies, represented either as a dict of word->count, or as a + list of count->word pairs. + + n : int + The number of least/most frequent words to print. + """ + + items = sort_freqs(freqs) if isinstance(freqs, dict) else freqs + print 'Number of unique words:',len(freqs) + print + print '%d least frequent words:' % n + print_vk(items[:n]) + print + print '%d most frequent words:' % n + print_vk(items[-n:]) + + +def get_text_from_url(url): + """Given a url (local file path or remote url), read its contents. + + If it's a remote URL, it downloads the file and leaves it locally cached + for future runs. If the local matching file is found, no download is made. + + Returns + ------- + text : string + The contents of the file. + """ + if url.startswith('http'): + # remote file, fetch only if needed + fname = os.path.split(url)[1] + if os.path.isfile(fname): + with open(fname, 'r') as f: + text = f.read() + else: + with open(fname, 'w') as f: + text = urllib2.urlopen(url).read() + f.write(text) + else: + with open(url, 'r') as f: + text = f.read() + return text + + +def co_occurrences(lines, words): + """Return histogram of co-occurrences of words in a list of lines. + + Parameters + ---------- + lines : list + A list of strings considered as 'sentences' to search for co-occurrences. + + words : list + A list of words from which all unordered pairs will be constructed and + searched for co-occurrences. + """ + wpairs = all_pairs(words) + + # Now build histogram of co-occurrences + co_occur = {} + for w1, w2 in wpairs: + rx = re.compile('%s .*%s|%s .*%s' % (w1, w2, w2, w1)) + co_occur[w1, w2] = sum([1 for line in lines if rx.search(line)]) + + return co_occur + + +def co_occurrences_graph(word_hist, co_occur, cutoff=0): + """Convert a word histogram with co-occurrences to a weighted graph. + + Edges are only added if the count is above cutoff. + """ + g = nx.Graph() + for word, count in word_hist: + g.add_node(word, count=count) + for (w1, w2), count in co_occur.iteritems(): + if count<=cutoff: + continue + g.add_edge(w1, w2, weight=count) + return g + + +def plot_graph(wgraph, pos=None): + """Conveniently summarize graph visually""" + # Plot nodes with size according to count + sizes = [] + degrees = [] + for n, d in wgraph.nodes_iter(data=True): + sizes.append(d['count']) + degrees.append(wgraph.degree(n)) + sizes = rescale_arr(np.array(sizes, dtype=float), 100, 1000) + + # Compute layout and label edges according to weight + pos = nx.spring_layout(wgraph) if pos is None else pos + labels = {} + width = [] + for n1, n2, d in wgraph.edges_iter(data=True): + w = d['weight'] + labels[n1, n2] = w + width.append(w) + + # remap width to 1-10 range + width = rescale_arr(np.array(width, dtype=float), 1, 15) + + # Create figure + fig, ax = plt.subplots() + fig.subplots_adjust(0,0,1) + nx.draw_networkx_nodes(wgraph, pos, node_size=sizes, node_color=degrees, + alpha=0.8) + nx.draw_networkx_labels(wgraph, pos, font_size=15, font_weight='bold') + nx.draw_networkx_edges(wgraph, pos, width=width, edge_color=width, + edge_cmap=plt.cm.Blues) + nx.draw_networkx_edge_labels(wgraph, pos, edge_labels=labels) + ax.set_title('Node color:degree, size:count, edge: co-occurrence count') + + +def plot_word_histogram(freqs, show=10, title=None): + """Plot a histogram of word frequencies, limited to the top `show` ones. + """ + sorted_f = sort_freqs(freqs) if isinstance(freqs, dict) else freqs + + # Don't show the tail + if isinstance(show, int): + # interpret as number of words to show in histogram + show_f = sorted_f[-show:] + else: + # interpret as a fraction + start = -int(round(show*len(freqs))) + show_f = sorted_f[start:] + + # Now, extract words and counts, plot + n_words = len(show_f) + ind = np.arange(n_words) + words = [i[0] for i in show_f] + counts = [i[1] for i in show_f] + + fig, ax = plt.subplots() + if n_words<=20: + # Only show bars and x labels for small histograms, they don't make + # sense otherwise + ax.bar(ind, counts) + ax.set_xticks(ind) + ax.set_xticklabels(words, rotation=45) + fig.subplots_adjust(bottom=0.25) + else: + # For larger ones, do a step plot + ax.step(ind, counts) + + # If it spans more than two decades, use a log scale + if float(max(counts))/min(counts) > 100: + ax.set_yscale('log') + + if title: + ax.set_title(title) + return ax + + +def summarize_centrality(centrality): + c = centrality.items() + c.sort(key=lambda x:x[1], reverse=True) + print '\nGraph centrality' + for node, cent in c: + print "%15s: %.3g" % (node, cent) + +#----------------------------------------------------------------------------- +# Main script +#----------------------------------------------------------------------------- + +# if __name__ == '__main__': + + # # Configure user variables here + # # Specify the url (can be a local file path) of the text file to analyze. + # # If not given, it's read from the command line as the first argument + # + # # 11226 titles of recent articles in arxiv/math/prob + # default_url = "http://bibserver.berkeley.edu/tmp/titles.txt" + # # Number of words to display in detailed histogram + # n_words = 15 + # # Number of words to use as nodes for co-occurrence graph. + # n_nodes = 15 + # + # # End of user configuration + # + # # Actual code starts here + # try: + # url = sys.argv[1] + # except IndexError: + # url = default_url + # + # # Fetch text and do basic preprocessing + # text = get_text_from_url(url).lower() + # lines = text.splitlines() + # words = text_cleanup(text) + # + # # Compute frequency histogram + # wf = word_freq(words) + # sorted_wf = sort_freqs(wf) + # + # # Build a graph from the n_nodes most frequent words + # popular = sorted_wf[-n_nodes:] + # pop_words = [wc[0] for wc in popular] + # co_occur = co_occurrences(lines, pop_words) + # wgraph = co_occurrences_graph(popular, co_occur, cutoff=1) + # centrality = nx.eigenvector_centrality_numpy(wgraph) + # + # # Print summaries of single-word frequencies and graph structure + # summarize_freq_hist(sorted_wf) + # summarize_centrality(centrality) + # + # # Plot histogram and graph + # plt.close('all') + # plot_word_histogram(sorted_wf, n_words, + # "Frequencies for %s most frequent words" % n_words) + # plot_word_histogram(sorted_wf, 1.0, "Frequencies for entire word list") + # plot_graph(wgraph) + # + # # Display figures + # plt.show() diff --git a/docs/examples/notebooks/titles.txt b/docs/examples/notebooks/titles.txt new file mode 100644 index 0000000..2f7ad0a --- /dev/null +++ b/docs/examples/notebooks/titles.txt @@ -0,0 +1,11226 @@ +Achlioptas process phase transitions are continuous +Representing filtration consistent nonlinear expectations as $g$-expectations in general probability spaces +Uniqueness in law for parabolic SPDEs and infinite-dimensional SDEs +Gradient flows of the entropy for finite Markov chains +How to hedge Asian options in fractional Black-Scholes model +Detection of objects in noisy images based on percolation theory +Randomized algorithms for statistical image analysis and site percolation on square lattices +Approximations of Fractional Stochastic Differential Equations by Means of Transport Processes +A two cities theorem for the parabolic Anderson model +Rates of convergence in the strong invariance principle under projective criteria +Algebraic polynomials and moments of stochastic integrals +Positive speed for high-degree automaton groups +Brownian Motions on Metric Graphs +Occupation Times for Jump Processes +Multiple testing, uncertainty and realistic pictures +Robust nonparametric detection of objects in noisy images +Detection of objects in noisy images and site percolation on square lattices +Fractional diffusion equations and processes with randomly varying time +A Parallel Algorithm for solving BSDEs - Application to the pricing and hedging of American options +Characteristic Polynomials of Random Matrices and Noncolliding Diffusion Processes +Dependence on the initial condition for equilibrium last-passage percolation models +The right tail exponent of the Tracy-Widom-beta distribution +Cycle structure of random permutations with cycle weights +On the transience of random interlacements +First-passage percolation on ladder-like graphs with heterogeneous exponential times +Limit theorems for stochastic approximation algorithms +On The L\u007b2\u007d-Solutions of Stochastic Fractional Partial Differential Equations; Existence, Uniqueness and Equivalence of Solutions +The exact asymptotic for the stationary distribution of some unreliable systems +On a space discretization scheme for the Fractional Stochastic Heat Equations +Effect of scale on large-scale mutations +A note on the abelian sandpile in Z^d +A Markov chain on the symmetric group which is Schubert positive? +A note on higher dimensional $p$-variation +The shape of a random affine Weyl group element, and random core partitions +Gradient Bounds for Solutions of Stochastic Differential Equations Driven by Fractional Brownian Motions +Construction of the Paths of Brownian Motions on Star Graphs +Word-Induced Measures on Compact Groups +General alpha-Wiener bridges +Stein's method and locally dependent point process approximation +Moments of Traces for Circular Beta-ensembles +The Brownian Cactus I. Scaling limits of discrete cactuses +The Weitzenbock formula on the Wiener space and its application to the asymptotic estimate of entropy +On $L_p$-estimates for a class of non-local elliptic equations +Transforming fixed-length self-avoiding walks into radial SLE_8/3 +Sparse recovery for spherical harmonic expansions +Random Tight Frames +Approximate Gaussian isoperimetry for k sets +Parisian ruin probability for spectrally negative L\'evy processes +Some linear SPDEs driven by a fractional noise with Hurst index greater than 1/2 +Ruin probabilities in tough times - Part 2 - Heavy-traffic approximation for fractionally differentiated random walks in the domain of attraction of a nonGaussian stable distribution +A Note on Feller Semigroups and Resolvents +XOR-Ising Loops and the Gaussian Free Field +Perturbation of Burkholder's martingale transform and Monge--Amp\`ere equation +Levy stable two-sided distributions: exact and explicit densities for asymmetric case +Approximate Lifshitz law for the zero-temperature stochastic Ising in any dimension +Stochastic porous media equations and self-organized criticality: convergence to the critical state in all dimensions +Isoperimetry and Stability of Hyperplanes for Product Probability Measures +The growth constants of lattice trees and lattice animals in high dimensions +A definition of conditional probability distribution with non-stochastic information +Strong law of large number of a class of super-diffusions +Stochastic variational inequalities with oblique subgradients +Multimodality of the Markov binomial distribution +On random surface area +Large volatility-stabilized markets +Stratonovich's Signatures of Brownian Motion Determine Brownian Sample Paths +Modified Curvatures on Manifolds with Boundary and Applications +On distribution of zeros of random polynomials in complex plane +Smooth approximations for fractional and multifractional fields +Projections of random vectors via the generic chaining +Mixing Times for the Mean-Field Blume-Capel Model via Aggregate Path Coupling +The Length of the Longest Increasing Subsequence of a Random Mallows Permutation +Brownian motion on R trees +Decentralized Restless Bandit with Multiple Players and Unknown Dynamics +The decimation process in random k-SAT +$L^\u007bp\u007d-$solutions of the stochastic transport equation +Stochastic derivatives and generalized h-transforms of Markov processes +Backward Stochastic Variational Inequalities Driven by Fractional Brownian Motion +Flow level convergence and insensitivity for multi-class queueing networks +A Gaussian mixture ensemble transform filter +The Complete Convergence Theorem Holds for Contact Processes in a Random Environment on $Z^d\times Z^+$ +Large deviations for the largest eigenvalue of an Hermitian Brownian motion +Interference Networks with Point-to-Point Codes +Weak error analysis of approximate simulation methods for multi-scale stochastic chemical kinetic systems +Contingency tables with uniformly bounded entries +Phase Transition in Limiting Distributions of Coherence of High-Dimensional Random Matrices +On a link between a species survival time in an evolution model and the Bessel distributions +Estimating and Understanding Exponential Random Graph Models +Generalized Self Intersection Local Time for a Superprocess over a Stochastic Flow +Convergence rates for the one-dimensional three state contact process +The Height fluctuations of an off-critical dimer model on the square grid +Perturbed Toeplitz operators and radial determinantal processes +Strong spatial mixing of $4$-colorings on binary trees +A unitary extension of virtual permutations +Comments on the floating body and the hyperplane conjecture +Exact Simulation of One-dimensional Stochastic Differential Equations involving the local time at zero of the unknown process +Lower bounds on Information Divergence +The total path length of split trees +Extension of Lyapunov's Convexity Theorem to Subranges +Universality in bipartite mean field spin glasses +Spectra of Symmetrized Shuffling Operators +The role of space in the exploitation of resources +Complete integrability of shock clustering and Burgers turbulence +Picturing classical and quantum Bayesian inference +Approximating European Options by Rebate Barrier Options +Gaussian upper bounds for heat kernels of continuous time simple random walks +Classical and Quantum Probabilities as Truth Values +On stochastic calculus related to financial assets without semimartingales +Comparison Theorem for Stochastic Differential Delay Equations with Jumps +Competitive Lotka-Volterra Population Dynamics with Jumps +Random Interlacements and the Gaussian free field +CLTs and asymptotic variance of time-sampled Markov chains +Spectral properties of a class of random walks on locally finite groups +Regularity conditions in the realisability problem in applications to point processes and random closed sets +Row products of random matrices +Concentration bounds for entropy estimation of one-dimensional Gibbs measures +A characterisation of superposable random measures +Multivariate piecewise linear interpolation of a random field +Lognormal scale invariant random measures +Central limit theorem for Markov processes with spectral gap in Wasserstein metric +On the least singular value of random symmetric matrices +On a fractional linear birth-death process +Nucleation and growth for the Ising model in d dimensions at very low temperatures +Path correlations in a randomly oriented complete bipartite graph +On the embeddability of certain infinitely divisible probability measures on Lie groups +Characterization of tails through hazard rate and convolution closure properties +Patterns in Sinai's walk +Reachability and recurrence in a modular generalization of annihilating random walks (and lights-out games) on hypergraphs +A Discrete Choquet Integral for Ordered Systems +Stochastic Optimal Multi-Modes Switching with a Viscosity Solution Approach +Global Heat Kernel Estimates for $\Delta+\Delta^\u007b\alpha/2\u007d$ in Half-space-like domains +Mean-field limit for the stochastic Vicsek model +Potential Theory of Subordinate Brownian Motions Revisited +Passing to the Limit in a Wasserstein Gradient Flow: From Diffusion to Reaction +Optimal consumption and investment for markets with randoms coefficients +Lambda-coalescents with dust component +Simultaneous concentration of order statistics +A Modified log-Harnack inequality and asymptotically strong Feller property +Law of large numbers for a transient random walk driven by a symmetric exclusion process +A non-linear model of limit order book dynamics +Tail behaviour of the area under a random process, with applications to queueing systems, insurance and percolations +Evidence Feed Forward Hidden Markov Model: A New Type of Hidden Markov Model +Prisoner's Dilemma on Graphs with Large Girth +On explosions in heavy-tailed branching random walks +Convex minorants of random walks and L\'evy processes +The tamed Milstein method for stochastic differential equations with commutative noise +Geometry and Combinatorics of Crystal Melting +Matchings on infinite graphs +Noncommutative Independence in the Infinite Braid and Symmetric Group +Attractivity, invariance and ergodicity for SDEs on Riemannian manifolds +PDEs satisfied by extreme eigenvalues distributions of GUE and LUE +Rice formulas and Gaussian waves +Fractal Dimensions for Continuous Time Random Walk Limits +A comparison principle for functions of a uniformly random subspace +Percolation of even sites for random sequential adsorption +CKP Hierarchy, Bosonic Tau Function and Bosonization Formulae +Asymptotics for Weighted Random Sums +Invertibility of symmetric random matrices +Limit theorems for empirical Fr\'echet means of independent and non-identically distributed manifold-valued random variables +Martingale ratio convergence in the branching random walk +Martin Gardner's Mistake +Expected signature of two dimensional Brownian Motion up to the first exit time of the domain +On the chromatic number of random geometric graphs +Critical sets of random linear combinations of eigenfunctions +Metastability for Kawasaki dynamics at low temperature with two types of particles +Stochastic Homogenization for Some Nonlinear Integro-Differential Equations +Shape-Driven Nested Markov Tessellations +On some Brownian functionals and their applications to moments in lognormal and Stein stochastic volatility models +Parameter estimation for alpha-fractional bridges +On the scaling limits of planar percolation +Persistence of iterated partial sums +A Nonconventional Invariance Principle for Random Fields +L\'evy flights in ecology +The Wigner-Dyson-Mehta bulk universality conjecture for Wigner matrices +Greedy random walk +A representation of exchangeable hierarchies by sampling from real trees +Stochastic Integrate and Fire Models: a review on mathematical methods and their applications +Large deviation principle for stochastic integrals and stochastic differential equations driven by infinite-dimensional semimartingales +Partial functional quantization and generalized bridges +Diffusion approximation of a multilocus model with assortative mating +Longest path distance in random circuits +On the reversibility of the observed process of three-state hidden Markov model +Monotone stability of quadratic semimartingales with applications to general quadratic BSDEs and unbounded existence result +Central Limit for the Products of Free Random Variables +Finite n Largest Eigenvalue Probability Distribution Function of Gaussian Ensembles +Exit problems for oscillating compound Poisson process +On Painleve Related Functions Arising in Random Matrix Theory +A New Condition for the Invariance Principle for Stationary Random Fields +Kalman filtering for linear wave equations with model error +A double-ended queue with catastrophes and repairs, and a jump-diffusion approximation +An optimal stopping problem for fragmentation processes +Analytical Evaluation of Fractional Frequency Reuse for OFDMA Cellular Networks +The rank 1 real Wishart spiked model +The Symmetry Group of Gaussian States in $L^2 (\mathbb\u007bR\u007d^n)$ +Pseudo Differential Operators and Markov Semigroups on Compact Lie Groups +On the one-sided exit problem for fractional Brownian motion +On a flow of transformations of a Wiener space +Characterization of exponential distribution via regression of one record value on two non-adjacent record values +Stochastic geometric wave equations with values in compact Riemannian homogeneous spaces +A Maximum Entropy solution of the Covariance Extension Problem for Reciprocal Processes +Prior Ordering and Monotonicity in Dirichlet Bandits +Sample Path Properties of Volterra Processes +A multivariate Gnedenko law of large numbers +The one-sided exit problem for weighted random walks +Distance between two skew Brownian motions as a SDE with jumps and law of the hitting time +Binary jumps in continuum. I. Equilibrium processes and their scaling limits +A new approach to quantitative propagation of chaos for drift, diffusion and jump processes +Scaling limits of random trees and planar maps +Some circumstances where extra updates can delay mixing +Sloane's Gap. Mathematical and Social Factors Explain the Distribution of Numbers in the OEIS +Stein's method in high dimensions with applications +Ruin probabilities in tough times - Part 1 - Heavy-traffic approximation for fractionally integrated random walks in the domain of attraction of a nonGaussian stable distribution +Responding to traffic surges: Stochastic networks under time-space-priority scalings +Exponents, symmetry groups and classification of operator fractional Brownian motions +On non-ergodic solutions of generalized Langevin equation +Efficient and fast estimation of the geometric median in Hilbert spaces with an averaged stochastic gradient algorithm +Bridges of L\'evy processes conditioned to stay positive +Asymptotic results for tail probabilities of sums of dependent heavy-tailed random variables +Multiple sums and integrals as neutral BKP tau functions +Continuum Random Combs and Scale Dependent Spectral Dimension +Mixing times of monotone surfaces and SOS interfaces: a mean curvature approach +Marked metric measure spaces +Epidemics and vaccination on weighted graphs +Determinantal Correlations of Brownian Paths in the Plane with Nonintersection Condition on their Loop-Erased Parts +Distribution of the Relative Density of Central Similarity Proximity Catch Digraphs Based on One Dimensional Uniform Data +Series Expansion for Interference in Wireless Networks +On the Order of Magnitude of Sums of Negative Powers of Integrated Processes +Stable limit laws for randomly biased walks on supercritical trees +Randomly biased walks on subcritical trees +A host-parasite multilevel interacting process and continuous approximations +Killed multidimensional random walks and multinomial sequential estimation +The area of a self-similar fragmentation +Girsanov theory under a finite entropy condition +Gamma Limit for Transition Paths of Maximal Probability +A Lower Bound for the First Passage Time Density of the Suprathreshold Ornstein-Uhlenbeck Process +Three Random Tangents to a Circle +Stable Poisson Graphs in One Dimension +On the Height Profile of a Conditioned Galton-Watson Tree +An ensemble related to discrete orthogonal polynomials and its application to tilings of a half-hexagon +Integration without points +Snake representation of a superprocess in random environment +Modeling microstructure noise with mutually exciting point processes +Maximal $L^p$-regularity for stochastic evolution equations +Quasi-Stationary distributions for Randomly perturbed dynamical systems +Lyapunov Exponents of Brownian Motion: Decay Rates for Scaled Poissonian Potentials and Bounds +On the Spectral Gap of Brownian Motion with Jump Boundary +Almost Sure Convergence for Angelesco Ensembles +On Stratonovich and Skorohod stochastic calculus for Gaussian processes +GPGPUs in computational finance: Massive parallel computing for American style options +Stochastic coalescence in logarithmic time +Exact bounds on the closeness between the Student and standard normal distributions +Central Limit Theorem for linear eigenvalue statistics of the Wigner and sample covariance random matrices +Dimensional behaviour of entropy and information +Tail monotonicity properties of Student's family of distributions +On the Berry--Esseen bound for the Student statistic +On the resilience of Hamiltonicity and optimal packing of Hamilton cycles in random graphs +Sharpness in the k-nearest neighbours random geometric graph model +Freedman's inequality for matrix martingales +Inverse Littlewood-Offord problems and The Singularity of Random Symmetric Matrices +Hunt's hypothesis (H) and Getoor's conjecture for L\'\u007be\u007dvy Processes +Continued fraction solution of Krein's inverse problem +Duality in Robust Utility Maximization with Unbounded Claim via a Robust Extension of Rockafellar's Theorem +A H\"older--Young--Lieb inequality for norms of Gaussian Wick products +Progressive enlargement of filtrations and Backward SDEs with jumps +Weak coupling limits in a stochastic model of heat conduction +Random walks on Galton-Watson trees with random conductances +Randomized Urn Models revisited using Stochastic Approximation +On Free Stochastic Differential Equations +Understanding the non-Gaussian nature of reactive solute transport. From particle dynamics to the partial differential equations +Dynamically defined measures and equilibrium states +Small components in k-nearest neighbour graphs +Formulas and Asymptotics for the Asymmetric Simple Exclusion Process +Spectral Analysis of Diffusions with Jump Boundary +On the asymptotic internal path length and the asymptotic Wiener index of random split trees +A Note on the Central Limit Theorem for the Eigenvalue Counting Function of Wigner Matrices +Quadratic Semimartingale BSDEs under an Exponential Moments Condition +The coalescent point process of branching trees and spine decompositions at the first survivor +Tokunaga and Horton self-similarity for level set trees of Markov chains +Equilibria in Quitting Games - Basics +Perturbation of strong Feller semigroups and well-posedness of semilinear stochastic equations on Banach spaces +Cram\'er theorem for Gamma random variables +On the splitting method for some complex-valued quasilinear equations +Ergodic Properties of weak Asymptotic Pseudotrajectories for Set-valued Dynamical Systems +Deterministic and stochastic aspects of single-crossover recombination +On tails of perpetuities +Optimal stopping for the predictive maintenance of a structure subject to corrosion +Exponential return times in a zero-entropy process +Activity phase transition for constrained dynamics +Suficient conditions of standardness for filtrations of stationary processes taking values in a finite space +Asymptotic sampling formulae and particle system representations for $\Lambda$-coalescents +Exclusion Sensitivity of Boolean Functions +Ergodicity and stability of the conditional distributions of nondegenerate Markov chains +Optimal stopping for predictive maintenance +Critical window for the vacant set left by random walk on random regular graphs +The uniform measure on a Galton-Watson tree without the XlogX condition +The Mean First Rotation Time of a planar polymer +The Filtration of the split-words process +Numerical Schemes for Multivalued Backward Stochastic Differential Systems +Convergence in law of the minimum of a branching random walk +Discrete approximation to solution flows of Tanaka SDE related to Walsh Brownian motion +Concentration for noncommutative polynomials in random matrices +Stochastic flows related to Walsh Brownian motion +Multilevel Monte Carlo algorithms for L\'\u007be\u007dvy-driven SDEs with Gaussian correction +Interacting Urn Models +Asymptotic first exit times of the Chafee-Infante equation with small heavy-tailed L\'evy noise +Geometry of the random interlacement +Large deviations for the current and tagged particle in 1D nearest-neighbor symmetric simple exclusion +Rate of convergence estimates for the zero dissipation limit in Abelian sandpiles +Convergence of stochastic gene networks to hybrid piecewise deterministic processes +Subgaussian rates of convergence of means in directed first passage percolation +Boundary conditions for the single-factor term structure equation +On the Riemann surface type of Random Planar Maps +Almost sure central limit theorem for branching random walks in random environment +The first returning speed and the last exit speed of a type of Markov chain +Abstract, Classic, and Explicit Turnpikes +On the Ruin Probability of the Generalised Ornstein-Uhlenbeck Process in the Cram\'er Case +Is a Brownian skew? +Gaussian free field and conformal field theory +A Robbins-Monro procedure for estimation in semiparametric regression models +The C_\ell-free process +Tree-valued Fleming-Viot dynamics with mutation and selection +Quantum invariant families of matrices in free probability +Alternative approach to the optimality of the threshold strategy for spectrally negative Levy processes +One-dimensional general forest fire processes +Convexity of ruin probability and optimal dividend strategies for a general Levy process +On optimality of the barrier strategy for a general Levy risk process +Internal DLA and the Gaussian free field +Brownian motion, reflection groups and Tanaka formula +Some exact joint laws associated with spectrally negative Levy processes and applications to insurance risk theory +A definition for second-order freeness in the real case and the asymptotic real second-order freeness of several real matrix ensembles +Large deviations of empirical measures of zeros on Riemann surfaces +On the speed of convergence to stationarity via spectral gap: queueing networks with breakdowns and repairs +Strong Stationary Duality for M\"obius Monotone Markov Chains: Unreliable Networks +Aleksandrov-Bakelman-Pucci Type Estimates For Integro-Differential Equations +Generalised Wishart Processes +A measure-theoretic version of the Dragomir-Jensen inequality +Quantum stochastic cocycles and completely bounded semigroups on operator spaces +On quantum stochastic differential equations +Truncated Stochastic Approximation with Moving Bounds: Convergence +Multivariate supOU processes +A general framework for waves in random media with long-range correlations +Conditional central limit theorem via martingale approximation Conditional central limit theorem via martingale approximation +Delayed feedback causes non-Markovian behavior of neuronal firing statistics +Universal Behavior of Connectivity Properties in Fractal Percolation Models +A simpler proof of the Boros--F\"uredi--B\'ar\'any--Pach--Gromov theorem +Central limit theorem for triangular arrays of Non-Homogeneous Markov chains +Finite Variation of Fractional Levy Processes +Superdiffusive bounds on self-repellent Brownian polymers and diffusion in the curl of the Gaussian free field in d=2 +Dynamic risk measuring under model uncertainty: taking advantage of the hidden probability measure +High order weak approximation schemes for L\'evy-driven SDEs +On L_p theory for Zakai equation with discontinuous observation process +Exponential Convergence Rates of Second Quantization Semigroups and Applications +Harnack Inequalities for Functional SDEs with Multiplicative Noise and Applications +Coupling and Applications +Equivalent Semigroup Properties for Curvature-Dimension Condition +Second order discretization of Backward SDEs +Vertices of high degree in the preferential attachment tree +Concentration of the information in data with log-concave distributions +Particle approximation of the intensity measures of a spatial branching point process arising in multi-target tracking +Hitting distributions of simple random walks on Sierpinski graphs +Poincar\'e inequalities and hitting times +Asymptotics of visibility in the hyperbolic plane +Topological expanders +A short Proof of the Doob-Meyer Theorem +A remark on the two-point Schramm formula +Giant vacant component left by a random walk in a random d-regular graph +Information-Theoretic Capacity and Error Exponents of Stationary Point Processes under Random Additive Displacements +Aging through hierarchical coalescence in the East model +Moderate deviations via cumulants +The foundational inequalities of D.L. Burkholder and some of their ramifications +On some ergodicity properties for time inhomogeneous Markov processes with $T$-periodic semigroup +Generalized Fibonacci Numbers and Blackwell's Renewal Theorem +Fourier multipliers for non-symmetric L\'evy processes +Donald Burkholder's work in martingales and analysis +Outliers in the spectrum of iid matrices with bounded rank perturbations +Schramm Loewner Evolution and Liouville Quantum Gravity +Connectivity properties of random interlacement and intersection of random walks +Outliers in the spectrum of iid matrices with bounded rank permutations +Conformal weldings of random surfaces: SLE and the quantum gravity zipper +Some properties of skew-symmetric distributions +The discrete-time parabolic Anderson model with heavy-tailed potential +Heterogeneous-k-core versus Bootstrap Percolation on Complex Networks +Bit recycling for scaling random number generators +Existence of random gradient states +Products of Independent Non-Hermitian Random Matrices +On backward stochastic differential equations approach to valuation of American options +The largest eigenvalue of real symmetric, Hermitian and Hermitian self-dual random matrix models with rank one external source, part I +Systems with large flexible server pools: Instability of "natural" load balancing +The spectrum of random lifts +A New Formula for the BER of Binary Modulations with Dual-Branch Selection over Generalized-K Composite Fading Channels +Maximising functionals of the joint law of the maximum and terminal value in the Skorokhod embedding problem +From constructive field theory to fractional stochastic calculus. (I) An introduction: rough path theory and perturbative heuristics +Non-Parametric Maximum Likelihood Density Estimation and Simulation-Based Minimum Distance Estimators +Efficient Exact Sampling for the Ising Model at all Temperatures +Continuity correction for barrier options in jump-diffusion models +Optimal Transport from Lebesgue to Poisson +On approximation of functions satisfying defective renewal equations +Linearization effect in multifractal analysis: Insights from Random Energy Model analysis +Bootstrap percolation on the random graph G_\u007bn,p\u007d +Stein's method and the multivariate CLT for traces of powers on the classical compact groups +The Topology of Scaling Limits of Positive Genus Random Quadrangulations +A sharp correlation inequality with an application to almost sure local limit theorem +On Small deviations of Gaussian processes using majorizing measures +The asymptotical error of broadcast gossip averaging algorithms +Sharp rate for the dual quantization problem +On the speed of biased random walk in translation invariant percolation +Stability of Random Admissible-Set Scheduling in Spatial Wireless Systems +Two Pinning Models with Markov disorder +On the distribution of angles between the N shortest vectors in a random lattice +On invariant Gibbs measures conditioned on mass and momentum +Fast transport asymptotics for stochastic RDEs with boundary noise +Internal DLA in Higher Dimensions +Occupation times of spectrally negative L\'evy processes with applications +On the Combinatorial Multi-Armed Bandit Problem with Markovian Rewards +Cooperation under Incomplete Information on the Discount Factors +The Fundamental Theorem of Asset Pricing, the Hedging Problem and Maximal Claims in Financial Markets with Short Sales Prohibitions +Perfect Sampling of Markov Chains with Piecewise Homogeneous Events +Time scales in large systems of Brownian particles with stochastic synchronization +An $f$-divergence approach for optimal portfolios in exponential Levy models +Comparisons and asymptotics for empty space hazard functions of germ-grain models +Statistical mechanics on isoradial graphs +Penalisation of the symmetric random walk by several functions of the supremum +On the Asymptotic Spectrum of Products of Independent Random Matrices +Finitely additive equivalent martingale measures +Lamplighter Random Walks and Entropy-Sensitivity of Languages +On the asymptotic distribution of the singular values of powers of random matrices +On the asymptotic of spectrum of products of independent random matrices +Random Gaussian sums on trees +Quasi-stationary workload in a L\'evy-driven storage system +A nonconventional strong law of large numbers and fractal dimensions of some multiple recurrence sets +Low noise limit for the invariant measure of a multi-dimensional stochastic Allen-Cahn equation +Numerical methods for the exit time of a piecewise-deterministic Markov process +Support convergence in the single ring theorem +A strong invariance principle for nonconventional sums +Weak and strong moments of random vectors +Extended Generalized-K (EGK): A New Simple and General Model for Composite Fading Channels +Classical and quantum behavior of the integrated density of states for a randomly perturbed lattice +Large Deviations Principle by viscosity solutions: the case of diffusions with oblique Lipschitz reflections +Poisson--Dirichlet branching random walks +Moment asymptotics for the parabolic Anderson problem with a perturbed lattice potential +On the asymptotic distribution of singular values of products of large rectangular random matrices +Quenched limit theorems for nearest neighbour random walks in 1D random environment +Generalized covariation for Banach valued processes and It\^o formula +Poincar\'e inequality for Markov random fields via disagreement percolation +Singularity of Random Matrices over Finite Fields +A Lamperti type representation of Continuous-State Branching Processes with Immigration +Implicit Renewal Theorem for Trees with General Weights +The component sizes of a critical random graph with pre-described degree sequence +On the quasi-regularity of non-sectorial Dirichlet forms by processes having the same polar sets +Existence of Gibbs measure for a model of T-tessellations +Nonconventional Limit Theorems in Discrete and Continuous Time via Martingales +Diffusion and Cascading Behavior in Random Networks +On hitting times of affine boundaries by reflecting Brownian motion and Bessel processes +Annealed and quenched fluctuations for ballistic random walks in random environment on Z +Entropy Rate for Hidden Markov Chains with rare transitions +Limit theorems for bifurcating autoregressive processes with missing data +On noise limited cellular networks +Uniqueness of the representation for $G$-martingales with finite variation +Rational term structure models with geometric Levy martingales +On the moments and the interface of the symbiotic branching model +A generalization of Osgood's test and a comparison criterion for integral equations with noise +Central limit theorems for Hilbert-space valued random fields satisfying a strong mixing condition +Harmonic deformation of Delaunay triangulations +Shell Model of Turbulence Perturbed by L\'\u007be\u007dvy Noise +Quasi-polynomial mixing of the 2D stochastic Ising model with "plus" boundary up to criticality +Eigenvalues of the fractional Laplace operator in the interval +Random Sequences and Pointwise Convergence of Multiple Ergodic Averages +Rough Burgers-like equations with multiplicative noise +A simple proof of a generalization of the Chu-Vandermonde identity +Pricing of barrier options by marginal functional quantization +Subordination by orthogonal martingales in $L^\u007bp\u007d, 1