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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Stable commutator length and linear programming
换向器长度 线性规划 曲面 拓扑优化
2023/4/18
Several topological optimization problems involving surfaces can be turned into linear programming problems. In the case of stable commutator length, this was first discovered by Danny Calegari in the...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Topological optimization and the stable commutator length
拓扑优化 稳定换向器 长度
2023/4/19
It is a relatively recent discovery in geometric topology that optimization problems of certain topological complexity are connected to important geometric and topological information. One example is ...
Estimator for Number of Sources using Minimum Description Length Criterion for Blind Sparse Source Mixtures
Minimum Description Length Criterion Blind Sparse Source Mixtures
2015/9/29
In this paper I present a Minimum Description Length Estimator for number of sources in an anechoic mixture of sparse signals.The criterion is roughly equal to the sum of negative normalized maximum l...
The filling length of an edge-circuit \eta in the Cayley 2-complex of a finite presentation of a group is the minimal integer length L such that there is a combinatorial null-homotopy of \eta down to ...
The gallery length filling function and a geometric inequality for filling length
filling length filling function
2015/8/26
We exploit duality considerations in the study of singular combinatorial 2-discs ("diagrams") and are led to the following innovations concerning the geometry of the word problem for finite presentati...
How to Find Good Finite-Length Codes: From Art Towards Science
LDPC coding transmission binary probability
2015/8/21
We explain how to optimize finite-length LDPC codes for transmission over the binary erasure channel. Our approach relies on an analytic approximation of the erasure probability. This is in turn...
FINITE-LENGTH SCALING FOR ITERATIVELY DECODED LDPC ENSEMBLES
low-density parity-check codes iterative decoding density evolution binary erasure channel finite-length analysis error probability curve
2015/8/21
In this paper we investigate the behavior of iteratively decoded low-density paritycheck codes over the binary erasure channel in the so-called “waterfall region.” We show that the performance curves ...
Ordered Partitions Avoiding a Permutation Pattern of Length 3
pattern avoidance ordered partition descent
2014/6/3
An ordered partition of [n]={1, 2,..., n} is a partition whose blocks are endowed with a linear order. Let OPn,k be set of ordered partitions of [n] with k blocks and OPn,k(σ) be set of ordered partit...
q-Hook Length Formulas for Signed Labeled Forests
statistic forest q-hook length formula Coxeter groups of types B and D (P w)-partition
2014/6/3
A signed labeled forest is defined as a (plane) forest labeled by {1, 2,..., n} along with minus signs associated to some vertices. Signed labeled forests can be viewed as an extension of signed permu...
Permutations all of whose patterns of a given length are distinct
Permutations a given length distinct Combinatorics
2012/6/21
For each integer k >= 2, let F(k) denote the largest n for which there exists a permutation \sigma \in S_n, all of whose patterns of length k are distinct. We prove that F(k) = k + \lfloor \sqrt{2k-3}...
On the length of one-dimensional reactive paths
one-dimensional reactive paths Probability
2012/6/21
Motivated by some numerical observations on molecular dynamics simulations, we analyze metastable trajectories in a very simplecsetting, namely paths generated by a one-dimensional overdamped Langevin...
The Ghost length, levels and shriek maps on classifying spaces
Level ghost length Gorenstein space shriek map
2012/4/17
We give a lower bound of the cochain type level of the diagonal map on the classifying space of a Lie group by using the ghostness of a shriek map. Moreover, in a derived category, we discuss the triv...
Monotonicity in the Sample Size of the Length of Classical Confidence Intervals
Gamma function Location and scale parameters Stochastic monotonicity
2012/3/1
It is proved that the average length of standard confidence intervals for parameters of gamma and normal distributions monotonically decrease with the sample size. The proofs are based on fine propert...
The asymptotic distribution of the length of Beta-coalescent trees
Beta-coalescent coupling, point process stable distribution Probability
2011/9/6
Abstract: We derive the asymptotic distribution of the total length $L_n$ of a Beta($2-\alpha,\alpha$)-coalescent tree for $1<\alpha < 2$, starting from $n$ individuals. There are two regimes: If $\al...
The Preimage Security of Double-Block-Length Compression Functions
Hash Function Preimage Resistance Block Cipher Beyond Birthday Bound Foundations
2012/12/4
We present new techniques for deriving preimage resistance bounds for block cipher based double-block-length, double-call hash functions. We give improved bounds on the preimage security of the three ...