The depth structure of motivic multiple zeta values

In this paper, we construct some maps related to the motivic Galois action on depth-graded motivic multiple zeta values. And from these maps we give some short exact sequences about depth-graded motivic multiple zeta values in depth two and three. In higher depth we conjecture that there are exact sequences of the same type. And we will show from three conjectures about depth-graded motivic Lie algebra we can nearly deduce the exact sequences conjectures in higher depth. At last we give a new proof of the result that the modulo zeta(2)$ version motivic double zeta values is generated by the totally odd part. And we reduce the well-known conjecture that the modulo zeta (2) version motivic triple zeta values is generated by the totally odd part to an isomorphism conjecture in linear algebra.Comment: 25 page

Depth-graded motivic Lie algebra

Consider the neutral Tannakian category mixed Tate motives over Z, in this paper we suggest a way to understand the structure of depth-graded motivic Lie subalgebra generated by the depth one part. We will show that from an isomorphism conjecture proposed by K. Tasaka we can deduce the F. Brown matrix conjecture and the non-degenerated conjecture about depth-graded motivic Lie subalgebra generated by the depth one part.Comment: 13 page

Motivic multiple zeta values reletive to \mu_2

We establish a short exact sequence about depth-graded motivic double zeta values of even weight relative to $\mu_2$. We find a basis for the depth-graded motivic double zeta values relative to $\mu_2$ of even weight and a basis for the depth-graded motivic triple zeta values relative to $\mu_2$ of odd weight. As an application of our main results, we prove Kaneko and Tasaka's conjectures about the sum odd double zeta values and the classical double zeta values. We also prove an analogue of Kaneko and Tasaka's conjecture in depth three. At last we formulate a conjecture which is related to sum odd multiple zeta values in higher depth.Comment: 27 page

Motivic double zeta values of odd weight

For odd $N\geq 5$, we establish a short exact sequence about motivic double zeta values $\zeta^{\mathfrak{m}}(r,N-r)$ with $r\geq3$ odd, $N-r\geq2$. From this we classify all the relations among depth-graded motivic double zeta values $\zeta^{\mathfrak{m}}(r,N-r)$ with $r\geq3$ odd, $N-r\geq2$. As a corollary, we confirm a conjecture of Zagier on the rank of a matrix which concerns relations among multiple zeta values of odd weight.Comment: 15 page

Strategically Simple Mechanisms

We define and investigate a property of mechanisms that we call "strategic simplicity," and that is meant to capture the idea that, in strategically simple mechanisms, strategic choices require limited strategic sophistication. We define a mechanism to be strategically simple if choices can be based on first-order beliefs about the other agents' preferences and first-order certainty about the other agents' rationality alone, and there is no need for agents to form higher-order beliefs, because such beliefs are irrelevant to the optimal strategies. All dominant strategy mechanisms are strategically simple. But many more mechanisms are strategically simple. In particular, strategically simple mechanisms may be more flexible than dominant strategy mechanisms in the bilateral trade problem and the voting problem

CERIAS Tech Report 2004-11 OACERTS: OBLIVIOUS ATTRIBUTE CERTIFICATES

We propose Oblivious Attribute Certificates (OACerts), an attribute certificate scheme in which a certificate holder can select which attributes to use and how to use them. In particular, a user can use attribute values stored in an OACert obliviously, i.e., the user obtains a service if and only if the attribute values satisfy the policy of the service provider, yet the service provider learns nothing about these attribute values. To build OACerts, we propose a new cryptographic primitive called Oblivious Commitment Based Envelope (OCBE). In an OCBE scheme, Bob has an attribute value committed to Alice and Alice runs a protocol with Bob to send an envelope (encrypted message) to Bob such that: (1) Bob can open the envelope if and only if his committed attribute value satisfies a predicate chosen by Alice. (2) Alice learns nothing about Bob’s attribute value. We develop provably secure and efficient OCBE protocols for the Pedersen commitment scheme and predicates such as =, ≥, ≤,>,<, ̸ = as well as logical combinations of them.

Minimal zero-sum sequence of length five over finite cyclic groups of prime power order

Let $G$ be a finite cyclic group. Every sequence $S$ of length $l$ over $G$ can be written in the form $S=(x_1g)\cdot\ldots\cdot(x_lg)$ where $g\in G$ and x_1, \ldots, x_l\in[1, \ord(g)], and the index \ind(S) of $S$ is defined to be the minimum of (x_1+\cdots+x_l)/\ord(g) over all possible $g\in G$ such that $\langle g \rangle =G$. Recently the second and the third authors determined the index of any minimal zero-sum sequence $S$ of length 5 over a cyclic group of a prime order where $S=g^2(x_2g)(x_3g)(x_4g)$. In this paper, we determine the index of any minimal zero-sum sequence $S$ of length 5 over a cyclic group of a prime power order. It is shown that if $G=\langle g\rangle$ is a cyclic group of prime power order $n=p^\mu$ with $p \geq 7$ and $\mu\geq 2$, and $S=(x_1g)(x_2g)(x_2g)(x_3g)(x_4g)$ with $x_1=x_2$ is a minimal zero-sum sequence with $\gcd(n,x_1,x_2,x_3,x_4,x_5)=1$, then \ind(S)=2 if and only if $S=(mg)(mg)(m\frac{n-1}{2}g)(m\frac{n+3}{2}g)(m(n-3)g)$ where $m$ is a positive integer such that $\gcd(m,n)=1$

Causality Extraction based on Self-Attentive BiLSTM-CRF with Transferred Embeddings

Causality extraction from natural language texts is a challenging open problem in artificial intelligence. Existing methods utilize patterns, constraints, and machine learning techniques to extract causality, heavily depending on domain knowledge and requiring considerable human effort and time for feature engineering. In this paper, we formulate causality extraction as a sequence labeling problem based on a novel causality tagging scheme. On this basis, we propose a neural causality extractor with the BiLSTM-CRF model as the backbone, named SCITE (Self-attentive BiLSTM-CRF wIth Transferred Embeddings), which can directly extract cause and effect without extracting candidate causal pairs and identifying their relations separately. To address the problem of data insufficiency, we transfer contextual string embeddings, also known as Flair embeddings, which are trained on a large corpus in our task. In addition, to improve the performance of causality extraction, we introduce a multihead self-attention mechanism into SCITE to learn the dependencies between causal words. We evaluate our method on a public dataset, and experimental results demonstrate that our method achieves significant and consistent improvement compared to baselines.Comment: 39 pages, 11 figures, 6 table

An upper bound for Davenport constant of finite groups

Let $G$ be a finite (not necessarily abelian) group and let $p=p(G)$ be the smallest prime number dividing $|G|$. We prove that $d(G)\leq \frac{|G|}{p}+9p^2-10p$, where $d(G)$ denotes the small Davenport constant of $G$ which is defined as the maximal integer $\ell$ such that there is a sequence over $G$ of length $\ell$ contains no nonempty one-product subsequence.Comment: arXiv admin note: text overlap with arXiv:1211.2614 by other author

Iterated integrals on products of one variable multiple polylogarithms

In this paper we show that the iterated integrals on products of one variable multiple polylogarithms from 0 to 1 are actually multiple zeta values if they are convergent. In the divergent case, we define regularized iterated integrals from 0 to 1. By the same method, we show that the regularized iterated integrals are also multiple zeta values. As an application, we give new series representations for multiple zeta values and calculate some interesting examples of iterated integrals.Comment: 18 page