The Experts below are selected from a list of 105 Experts worldwide ranked by ideXlab platform
Jinkao Hao - One of the best experts on this subject based on the ideXlab platform.
-
a Multiple search Operator heuristic for the max k cut problem
Annals of Operations Research, 2017Co-Authors: Jinkao HaoAbstract:The max-k-cut problem is to partition the vertices of an edge-weighted graph G=(V,E) into k≥2 disjoint subsets such that the weight sum of the edges crossing the different subsets is maximized. The problem is referred as the max-cut problem when k=2. In this work, we present a Multiple Operator heuristic (MOH) for the general max-k-cut problem. MOH employs five distinct search Operators organized into three search phases to effectively explore the search space. Experiments on two sets of 91 well-known benchmark instances show that the proposed algorithm is highly effective on the max-k-cut problem and improves the current best known results (lower bounds) of most of the tested instances for k∈[3,5]. For the popular special case k=2 (i.e., the max-cut problem), MOH also performs remarkably well by discovering 4 improved best known results. We provide additional studies to shed light on the key ingredients of the algorithm.
-
a Multiple search Operator heuristic for the max k cut problem
arXiv: Discrete Mathematics, 2015Co-Authors: Jinkao HaoAbstract:The max-k-cut problem is to partition the vertices of a weighted graph $G = (V,E)$ into $k\geq2$ disjoint subsets such that the weight sum of the edges crossing the different subsets is maximized. The problem is referred as the max-cut problem when $k=2$. In this work, we present a Multiple Operator heuristic (MOH) for the general max-k-cut problem. MOH employs five distinct search Operators organized into three search phases to effectively explore the search space. Experiments on two sets of 91 well-known benchmark instances show that the proposed algorithm is highly effective on the max-k-cut problem and improves the current best known results (new lower bounds) of most of the tested instances. For the popular special case $k=2$ (i.e., the max-cut problem), MOH also performs remarkably well by discovering 6 improved best known results. We provide additional studies to shed light on the alternative combinations of the employed search Operators.
Nikitopoulos, Evangelos A. - One of the best experts on this subject based on the ideXlab platform.
-
It\^{o}'s Formula for Noncommutative $C^2$ Functions of Free It\^{o} Processes with Respect to Circular Brownian Motion
2021Co-Authors: Nikitopoulos, Evangelos A.Abstract:In a recent paper, the author introduced a rich class $NC^k(\mathbb{R})$ of "noncommutative $C^k$" functions $\mathbb{R} \to \mathbb{C}$ whose Operator functional calculus is $k$-times differentiable and has derivatives expressible in terms of Multiple Operator integrals (MOIs). In the present paper, we explore a connection between free stochastic calculus and the theory of MOIs by proving a free It\^{o} formula for noncommutative $C^2$ functions of self-adjoint free It\^{o} processes with respect to circular Brownian motion. To do this, we extend P. Biane and R. Speicher's theory of free stochastic calculus to allow free It\^{o} processes involving circular Brownian motion and its adjoint -- instead of only semicircular Brownian motion -- and then reinterpret the quantities in the resultant It\^{o}-type formulas as MOIs. Along the way, we also obtain a useful "traced" free It\^{o} formula for arbitrary $C^2$ scalar functions of self-adjoint free It\^{o} processes. Finally, as motivation, we study an It\^{o} formula for $C^2$ scalar functions of $n \times n$ Hermitian matrix It\^{o} processes.Comment: 49 pages, changes from v1: significant reorganization, improved exposition/motivation, expanded examples, addition of more background, change in convention for NC derivatives, minor simplification
-
It\={o}'s Formula for Noncommutative $C^2$ Functions of Free It\={o} Processes with Respect to Circular Brownian Motion
2020Co-Authors: Nikitopoulos, Evangelos A.Abstract:In a recent paper, the author introduced a rich class $NC^k(\mathbb{R})$ of "noncommutative $C^k$" functions $\mathbb{R} \to \mathbb{C}$ whose Operator functional calculus is $k$-times differentiable and has derivatives expressible in terms of Multiple Operator integrals (MOIs). In this paper, we explore a connection between free stochastic calculus and the theory of MOIs by proving a "functional free It\={o} formula" for noncommutative $C^2$ functions of self-adjoint free It\={o} processes with respect to circular Brownian motion. To do this, we extend P. Biane and R. Speicher's theory of free stochastic calculus to allow free It\={o} processes involving circular Brownian motion and its adjoint -- instead of only semicircular Brownian motion -- and then reinterpret the quantities in the resultant It\={o}-type formulas as MOIs. As motivation, we also prove a "functional It\={o} formula" for $C^2$ functions of It\={o} processes with respect to $n \times n$ matrix Brownian motion
Hermann Bujard - One of the best experts on this subject based on the ideXlab platform.
-
co regulation of two gene activities by tetracycline via a bidirectional promoter
Nucleic Acids Research, 1995Co-Authors: Udo Baron, Sabine Freundlieb, Manfred Gossen, Hermann BujardAbstract:Recently, we have described a regulatory system that allows the stringent control of individual gene activities in higher eukaryotic cell lines (1), in plants (2) and in animals (3,4). The essential components of this system are (i) an RNA polymerase II minimal promoter placed downstream of Multiple Operator sequences (tetO) of the Escherichia coli TnlO tetracycline resistance operon and (ii) a fusion between the Tet repressor (TetR) and the herpes simplex virus protein 16 (VP16), named tTA (1). In the absence of tetracycline (Tc), tTA binds to the tet Operators to activate transcription from the minimal promoter, whereas in the presence of Tc its association and consequently its transcription activation is prevented. After the binding of tTA, minimal promoters derived from the cytomegalovirus IE promoter (PhCMv; 5) and fused to seven tetO sequences reach the remarkable strength of the parent promoter in HeLa cells when compared in transient expression assays (6). This high activation potential of tTA and the arrangement of its binding sites within PhCMV*-i [(!)'»see Fig. 1A] suggested the design of a bidirectional promoter which would allow the simultaneous regulation of two transcriptional units from centrally located Multiple tetO sequences (Fig. 1A). Such a promoter should be useful for a number of experimental approaches. First, it may allow the co-regulation of the synthesis of two gene products in stoichiometric amounts, frequently a prerequisite for the production of heterodimeric (or hetero-oligomeric) proteins. Second, by fusing minimal promoters of differing efficiencies to the centrally located tetO sequences, two gene products may be co-regulated at different but defined levels. Third, by integrating an appropriate reporter gene at one side of the bidirectional promoter, the regulation of a not-readily-assayable gene of interest may be monitored via the reporter function. This latter possibility may also facilitate—at the cellular as well as at the organismal level—the screening for properly integrated expression units controlling the gene of interest.
Vladimir Peller - One of the best experts on this subject based on the ideXlab platform.
-
Multiple Operator integrals haagerup and haagerup like tensor products and Operator ideals
Bulletin of The London Mathematical Society, 2017Co-Authors: A B Aleksandrov, Vladimir PellerAbstract:We study Schatten–von Neumann properties of Multiple Operator integrals with integrands in the Haagerup tensor product of L∞ spaces. We obtain sharp, best possible estimates. This allowed us to obtain sharp Schatten–von Neumann estimates in the case of Haagerup-like tensor products.
-
Multiple Operator integrals in perturbation theory
arXiv: Functional Analysis, 2015Co-Authors: Vladimir PellerAbstract:We start with the Birman--Solomyak approach to define double Operator integrals and consider applications in estimating Operator differences $f(A)-f(B)$ for self-adjoint Operators $A$ and $B$. We present the Birman--Solomyak approach to the Lifshits--Krein trace formula that is based on double Operator integrals. We study the class of Operator Lipschitz functions, Operator differentiable functions, Operator H\"older functions, obtain Schatten--von Neumann estimates for Operator differences. Finally, we consider in Chapter 1 estimates of functions of normal Operators and functions of $d$-tuples of commuting self-adjoint Operators. In Chapter 2 we define Multiple Operator integrals with integrands in the integral projective tensor product of $L^\infty$ spaces. We consider applications of such Multiple Operator integrals to the problem of the existence of higher Operator derivatives and to the problem of estimating higher Operator differences. We also consider connections with trace formulae for functions of Operators under perturbations of class $\boldsymbol{S}_m$, $m\ge2$. In the last chapter we define Haagerup-like tensor products of the first kind and of the second kind and we use them to study functions of noncommuting self-adjoint Operators under perturbation. We show that for functions $f$ in the Besov class $B_{\infty,1}^1({\Bbb R}^2)$ and for $p\in[1,2]$ we have a Lipschitz type estimate in the Schatten--von Neumann norm $\boldsymbol{S}_p$ for functions of pairs of noncommuting self-adjoint Operators, but there is no such a Lipschitz type estimate in the norm of $\boldsymbol{S}_p$ with $p>2$ as well as in the Operator norm. We also use triple Operator integrals to estimate the trace norms of commutators of functions of almost commuting self-adjoint Operators and extend the Helton--Howe trace formula for arbitrary functions in the Besov space $B_{\infty,1}^1({\Bbb R}^2)$.
-
Multiple Operator integrals and higher Operator derivatives
arXiv: Spectral Theory, 2005Co-Authors: Vladimir PellerAbstract:In this paper we consider the problem of the existence of higher derivatives of the function $t\mapsto\f(A+tK)$, where $\f$ is a function on the real line, $A$ is a self-adjoint Operator, and $K$ is a bounded self-adjoint Operator. We improve earlier results by Sten'kin. In order to do this, we give a new approach to Multiple Operator integrals. This approach improves the earlier approach given by Sten'kin. We also consider a similar problem for unitary Operators.
P Sadayappan - One of the best experts on this subject based on the ideXlab platform.
-
on optimizing machine learning workloads via kernel fusion
ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming, 2015Co-Authors: Arash Ashari, Shirish Tatikonda, Matthias Boehm, Berthold Reinwald, Keith M Campbell, John Keenleyside, P SadayappanAbstract:Exploitation of parallel architectures has become critical to scalable machine learning (ML). Since a wide range of ML algorithms employ linear algebraic Operators, GPUs with BLAS libraries are a natural choice for such an exploitation. Two approaches are commonly pursued: (i) developing specific GPU accelerated implementations of complete ML algorithms; and (ii) developing GPU kernels for primitive linear algebraic Operators like matrix-vector multiplication, which are then used in developing ML algorithms. This paper extends the latter approach by developing fused kernels for a combination of primitive Operators that are commonly found in popular ML algorithms. We identify the generic pattern of computation (alpha * X^T (v * (X * y)) + beta * z) and its various instantiations. We develop a fused kernel to optimize this computation on GPUs -- with specialized techniques to handle both sparse and dense matrices. This approach not only reduces the cost of data loads due to improved temporal locality but also enables other optimizations like coarsening and hierarchical aggregation of partial results. We also present an analytical model that considers input data characteristics and available GPU resources to estimate near-optimal settings for kernel launch parameters. The proposed approach provides speedups ranging from 2 to 67 for different instances of the generic pattern compared to launching Multiple Operator-level kernels using GPU accelerated libraries. We conclude by demonstrating the effectiveness of the approach in improving end-to-end performance on an entire ML algorithm.