Showing papers on "Prime (order theory) published in 2020"

Cache Telepathy: Leveraging Shared Resource Attacks to Learn DNN Architectures.

Abstract: Deep Neural Networks (DNNs) are fast becoming ubiquitous for their ability to attain good accuracy in various machine learning tasks. A DNN's architecture (i.e., its hyper-parameters) broadly determines the DNN's accuracy and performance, and is often confidential. Attacking a DNN in the cloud to obtain its architecture can potentially provide major commercial value. Further, attaining a DNN's architecture facilitates other, existing DNN attacks. This paper presents Cache Telepathy: a fast and accurate mechanism to steal a DNN's architecture using the cache side channel. Our attack is based on the insight that DNN inference relies heavily on tiled GEMM (Generalized Matrix Multiply), and that DNN architecture parameters determine the number of GEMM calls and the dimensions of the matrices used in the GEMM functions. Such information can be leaked through the cache side channel. This paper uses Prime+Probe and Flush+Reload to attack VGG and ResNet DNNs running OpenBLAS and Intel MKL libraries. Our attack is effective in helping obtain the architectures by very substantially reducing the search space of target DNN architectures. For example, for VGG using OpenBLAS, it reduces the search space from more than $10^{35}$ architectures to just 16.

Efficient generation of mouse models with the prime editing system.

Abstract: Dear Editor, Most genetic diseases in humans are caused by singlenucleotide mutations. Although genome editing with either the CRISPR-based cytosine base editor (CBE) or the adenine base editor (ABE) holds great promise for gene correction of C-to-T and A-to-G base substitutions in some genetic diseases, both editors are useless for correction of other variants such as base transversion, small insertions and deletions (indels). The prime editing system, a “search-and replace” genome editing technology, was recently added to the genome editing toolkit. The prime editors (PEs) combine an exogenous CRISPR/Cas9 system and endogenous DNA repair system to achieve an increased range of editing versatility, induces all types of base-to-base conversions out of CBE and ABE (C→T, G→A, A→G, and T→C), small indel, and their combinations. The prime editing system evolved from PE1 to PE3 (PE3b) with stepwise efficiency improvement. The executor of PE1 was constructed by fusing an engineered Cas9 nickase with a reverse transcriptase (M-MLV RTase), which can target genome sites, nick DNA, and trigger reverse transcription (RT). The executor combining with the engineered prime editing guide RNA (pegRNA) searches for and nicks the target DNA, and thus, new genetic information is encoded into genome by RT. Then, mutations were introduced to M-MLV RTase to improve the editing efficiency of PE1, which is referred to as PE2. Subsequently, in the PE3 system, to further improve editing efficiency, an additional sgRNA is used to induce nick on the non-edited strand to trigger the endogenous mismatch repair pathway. In comparison with base editors, PE induces base institutions in more extended regions with fewer bystander mutations. With its unique versatility and accuracy, this technology broadens the scope of genome editing and opens a new avenue for targeted mutagenesis and gene correction in many organisms. However, the efficiency of PE was reported only in five different cell types; it has not been investigated in animals. Here, we demonstrate that PE can be employed to generate mutant mice with singlenucleotide substitutions. We first validated the editing versatility of PEs in human HEK293T cells at eight loci (Supplementary Table S1), including two loci (RUNX1 and RNF2) that were reported by Anzalone et al. PE3 was selected for gene targeting validation, due to its higher editing efficiency compared with PE2. Sanger sequencing revealed that PE3 induced significant base conversions at six (RUNX1, RNF2, EMX1, VEGFA, SRD5A3, and KCNA1) out of eight targeted sites (Supplementary Fig. S1a, b). PE3 was then used to induce point mutations in the X-linked androgen receptor (Ar) gene and the homeobox protein Hox-D13 (Hoxd13) gene in mouse neuro-2a (N2a) cells. Both targeted mutations in mice are homologous to human variants associated with clinical diseases in ClinVar. pegRNAs and nick-editing sgRNAs targeting these two genes were designed (Supplementary Table S2). We designed pegRNAs starting with a primer binding site (PBS) length of 13 nt and an RT template length of ~13–15 nt. Nicks were positioned 3′ of the edit ~40–60 bp from the pegRNA-induced nick. Sanger sequencing revealed that PE3 efficiently (~8–40%) mediated base transversions at three target sites of Hoxd13 and Ar (pegHoxd13-1 for G to C, pegHoxd13-2 for G to T, pegAr-2 for G to T) (Fig. 1a;

Prime editing efficiently generates W542L and S621I double mutations in two ALS genes in maize.

Abstract: Prime editing is a novel and universal CRISPR/Cas-derived precision genome-editing technology that has been recently developed. However, low efficiency of prime editing has been shown in transgenic rice lines. We hypothesize that enhancing pegRNA expression could improve prime-editing efficiency. In this report, we describe two strategies for enhancing pegRNA expression. We construct a prime editing vector harboring two pegRNA variants for W542L and S621I double mutations in ZmALS1 and ZmALS2. Compared with previous reports in rice, we achieve much higher prime-editing efficiency in maize. Our results are inspiring and provide a direction for the optimization of plant prime editors.

Precision genome engineering in rice using prime editing system

Abstract: Making precise changes in the genomes of organisms is challenging for most genome editing tools. Recently, a search-and-replace method, also known as prime editing, was developed that can introduce user-defined sequence into a target site without requiring double-stranded breaks (DSBs) or repair templates (Anzalone et al., 2019). The prime editor contains a Moloney murine leukemia virus reverse transcriptase (M-MLV RT) fused to the C terminus of SpCas9 (H840A) nickase (Anzalone et al., 2019). This fusion protein is guided by a prime editing guide RNA (pegRNA) to the target site.

Some congruences involving fourth powers of central q-binomial coefficients

Abstract: We prove some congruences on sums involving fourth powers of central q-binomial coefficients. As a conclusion, we confirm the following supercongruence observed by Long [Pacific J. Math. 249 (2011), 405–418]: where p⩾5 is a prime and r is a positive integer. Our method is similar to but a little different from the WZ method used by Zudilin to prove Ramanujan-type supercongruences.

A q-analogue of the (A.2) supercongruence of Van Hamme for any prime p ≡ 3(mod4)

Abstract: Inspired by the recent work of Guo and Zudilin, we establish several results on q-supercongruences by using a q-analogue of Watson’s 3F2 summation formula. In particular, we give a q-analogue of th...

Prime Inner Product Encoding for Effective Wildcard-based Multi-Keyword Fuzzy Search

Abstract: With the prevalence of cloud computing, a growing number of users are delegating clouds to host their sensitive data. To preserve user privacy, it is suggested that data is encrypted before outsourcing. However, data encryption makes keyword-based searches over ciphertexts extremely difficult. This is even challenging for fuzzy search that allows uncertainties or misspellings of keywords in a query. In this paper, we propose a prime inner product encoding (PIPE) scheme, which makes use of the indecomposable property of prime numbers to provide efficient, highly accurate, and flexible multi-keyword fuzzy search. Our main idea is to encode either a query keyword or an index keyword into a vector filled with primes or reciprocals of primes, such that the result of vectors' inner product is an integer only when two keywords are similar. Specifically, we first construct PIPE0 that is secure in the known ciphertext model. Unlike existing works that have difficulty supporting AND and OR semantics simultaneously, PIPE0 gives users the flexibility to specify different search semantics in their queries. Then, we construct PIPES that subtly adds random noises to a query vector to resist linear analyses. Both theoretical analyses and experiment results demonstrate the effectiveness of our scheme.

Arcs in finite projective spaces

Abstract: This is an expository article detailing results concerning large arcs in finite projective spaces. It is not strictly a survey but attempts to cover the most relevant results on arcs, simplifying and unifying proofs of known old and more recent theorems. The article is mostly self-contained and includes a proof of the most general form of Segre's lemma of tangents and a short proof of the MDS conjecture over prime fields based on this lemma.

New types of finite groups and generated algorithm to determine the integer factorization by Excel

Abstract: In this work, new types of finite subgroups are given, they are called prime gaps additive subgroups (S, +p) of Zp and prime gaps multiplication subgroups (S, p) of Zp*. Also, new practical algorithm to track prime factors for any composite numbers is introduced. This new method depends on the general rule for prime numbers that has one variable (n). The new rule is very important because it exactly gives the number of primes for any interval of integer numbers. Also, the large gaps between n-th primes are given in this paper. Next, this formula is used to make application by Excel in order to exhibit the results for any integer number if it is prime or not at polynomial time. By this new method, we can find straightforwardly more than (97.5%) of the composite numbers while the rest of the percentage needs polynomial-time. In addition, we can use this rule to exhibit all prime numbers between the smallest prim number and any number x in sequence list. Finally, by this work the following points are considered; The distribution for any sequence of prime numbers is given, Our results better than Riemann Hypothesis (see Tables 3 and 4), For any large integer we can find its factorization in polynomial time by a classical computer.

S -prime ideals of a commutative ring

Abstract: Let R be a commutative ring with identity and $$S\subseteq R$$ a multiplicative subset. In this paper we introduce the concept of S-prime ideal which is a generalization of prime ideal. Let P be an ideal of R disjoint with S. We say that P is an S-prime ideal of R if there exists an $$s\in S$$ such that for all $$a,b\in R$$ if $$ab\in P,$$ then $$sa\in P$$ or $$sb\in P$$ . We show that S-prime ideals enjoy analogs of many properties of prime ideals and we study them over S-Noetherian rings.

Quantum codes from a class of constacyclic codes over finite commutative rings

Abstract: Let p be an odd prime, and k be an integer such that gcd(k,p) = 1. Using pairwise orthogonal idempotents γ1,γ2,γ3 of the ring ℛ = 𝔽p[u]/〈uk+1 − u〉, with γ1 + γ2 + γ3 = 1, ℛ is decomposed as ℛ = γ1ℛ...

On the directions determined by a Cartesian product in an affine Galois plane.

Abstract: We prove that the number of directions contained in a set of the form $A \times B \subset AG(2,p)$, where $p$ is prime, is at least $|A||B| - \min\{|A|,|B|\} + 2$. Here $A$ and $B$ are subsets of $GF(p)$ each with at least two elements and $|A||B|

Redshift and multiplication for truncated Brown-Peterson spectra

Abstract: We equip $\mathrm{BP} \langle n \rangle$ with an $\mathbb{E}_3$-$\mathrm{BP}$-algebra structure, for each prime $p$ and height $n$. The algebraic $K$-theory of this $\mathbb{E}_3$-ring is of chromatic height exactly $n+1$. Specifically, it is an fp-spectrum of fp-type $n+1$, which can be viewed as a higher height version of the Lichtenbaum-Quillen conjecture.

Monoidal categorification and quantum affine algebras

Abstract: We introduce and investigate new invariants of pairs of modules $M$ and $N$ over quantum affine algebras $U_{q}^{\prime }(\mathfrak{g})$ by analyzing their associated $R$ -matrices. Using these new invariants, we provide a criterion for a monoidal category of finite-dimensional integrable $U_{q}^{\prime }(\mathfrak{g})$ -modules to become a monoidal categorification of a cluster algebra.

Explicit expanders of every degree and size

Abstract: An $(n,d,\lambda)$-graph is a $d$ regular graph on $n$ vertices in which the absolute value of any nontrivial eigenvalue is at most $\lambda$. For any constant $d \geq 3$, $\epsilon>0$ and all sufficiently large $n$ we show that there is a deterministic poly(n) time algorithm that outputs an $(n,d, \lambda)$-graph (on exactly $n$ vertices) with $\lambda \leq 2 \sqrt{d-1}+\epsilon$. For any $d=p+2$ with $p \equiv 1 \bmod 4$ prime and all sufficiently large $n$, we describe a strongly explicit construction of an $(n,d, \lambda)$-graph (on exactly $n$ vertices) with $\lambda \leq \sqrt {2(d-1)} + \sqrt{d-2} +o(1) ( 0$, $d>d_0(\epsilon)$ and $n>n_0(d,\epsilon)$ we present a strongly explicit construction of an $(m,d,\lambda)$-graph with $\lambda < (2+\epsilon) \sqrt d$ and $m=n+o(n)$. All constructions are obtained by starting with known ones of Ramanujan or nearly Ramanujan graphs, modifying or packing them in an appropriate way. The spectral analysis relies on the delocalization of eigenvectors of regular graphs in cycle-free neighborhoods.

Optimizing Design of Fuzzy Model for Software Cost Estimation Using Particle Swarm Optimization Algorithm

Abstract: Estimation of software cost and effort is of prime importance in software development process. Accurate and reliable estimation plays a vital role in successful completion of the project. To estima...

On the anticyclotomic Iwasawa theory of rational elliptic curves at Eisenstein primes

Abstract: Let $E/\mathbb{Q}$ be an elliptic curve, and $p$ a prime where $E$ has good reduction, and assume that $E$ admits a rational $p$-isogeny. In this paper, we study the anticyclotomic Iwasawa theory of $E$ over an imaginary quadratic field in which $p$ splits, which we relate to the anticyclotomic Iwasawa theory of characters following the method of Greenberg--Vatsal. As a result of our study, we obtain a proof, under mild hypotheses, of Perrin-Riou's Heegner point main conjecture, as well as a $p$-converse to the theorem of Gross--Zagier and Kolyvagin and the $p$-part of the Birch--Swinnerton-Dyer formula in analytic rank $1$ for Eisenstein primes $p$.

Primality of multiply connected polyominoes

Abstract: It is known that the polyomino ideal of simple polyominoes is prime. In this paper, we focus on multiply connected polyominoes, namely polyominoes with holes, and observe that the nonexistence of a certain sequence of inner intervals of the polyomino, called zig-zag walk, gives a necessary condition for the primality of the polyomino ideal. Moreover, by computational approach, we prove that for all polyominoes with rank less than or equal to 14 , the above condition is also sufficient. Lastly, we present an infinite new class of prime polyomino ideals.

Remarks on $K(1)$-local $K$-theory

Abstract: We prove two basic structural properties of the algebraic $K$-theory of rings after $K(1)$-localization at an implicit prime $p$. Our first result (also recently obtained by Land--Meier--Tamme by different methods) states that $L_{K(1)} K(R)$ is insensitive to inverting $p$ on $R$; we deduce this from recent advances in prismatic cohomology and $\mathrm{TC}$. Our second result yields a Kunneth formula in $K(1)$-local $K$-theory for adding $p$-power roots of unity to $R$.

On the directions determined by Cartesian products and the clique number of generalized Paley graphs

Abstract: It is known that the number of directions formed by a Cartesian product $A \times B \subset AG(2,p)$ is at least $|A||B| - \min\{|A|,|B|\} + 2$, provided $p$ is prime and $|A||B|

On a diophantine inequality involving prime numbers (III)

Abstract: Let 1 0 such that for each real numberN>N(c) the inequality\(|p_1^c + p_2^c + p_3^c - N|< N^{ - \tfrac{1}{c}(\tfrac{{11}}{{10}} - c)} \log ^{c_1 } N\) is solvable in prime numbersp 1,p 2,p 3, wherec 1 is some absolute positive constant.

On the clique number of Paley graphs of prime power order

Abstract: Finding a reasonably good upper bound for the clique number of Paley graph is an old and open problem in additive combinatorics. A recent breakthrough by Hanson and Petridis using Stepanov's method gives an improved upper bound on $\mathbb{F}_p$, where $p \equiv 1 \pmod 4$. We extend their idea to the finite field $\mathbb{F}_q$, where $q=p^{2s+1}$ for a prime $p\equiv 1 \pmod 4$ and a non-negative integer $s$. We show the clique number of the Paley graph over $\mathbb{F}_{p^{2s+1}}$ is at most $\min \bigg(p^s \bigg\lceil \sqrt{\frac{p}{2}} \bigg\rceil, \sqrt{\frac{q}{2}} + \frac{p^s+1}{4} + \frac{\sqrt{2p}}{32} p^{s-1}\bigg)$.

Post-reform gender politics: How do Chinese Internet users portray Theresa May on Zhihu

Abstract: This article analyses Chinese Internet users’ discussions about the former UK Prime Minister—Theresa May We gathered data from China’s most popular community question-answering (CQA) site—Zhihu an

Rescue-Prime: a Standard Specification (SoK).

Abstract: This document provides a simple standard specification for the Rescue-Prime family of arithmetization-oriented hash functions.