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Combining Computational Effects: Commutativity and Sum
[chapter]
2002
Foundations of Information Technology in the Era of Network and Mobile Computing
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We give a theory of the commutative combination of effects, which in particular yields Maggi's side-effects monad transformer. ...
And we give a theory for the sum of computational effects, which in particular yields Maggi's exceptions monad transformer. ...
Theorem 6 There is a natural equivalence between Mod* ( L + L', C) and Mod*(L,Mod*(L', C)).
483 As in previous sections, the analysis of this section all enriches without fuss, with the sum again being ...
doi:10.1007/978-0-387-35608-2_39
dblp:conf/ifipTCS/HylandPP02
fatcat:da2dra2oejd5zo6sdlxgeh56qi
Sums of Commutators in Free Probability
[article]
2020
arXiv
pre-print
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We study the linear span of commutators of free random variables and show that these are the only quadratic forms which satisfy the following equivalent properties: * preservation free infinite divisibility ...
for sums of commutators of arbitrary noncommutative random variables. ...
The second result is presented in this section and concerns sums of commutators of semicircular elements for which the sum (2.16) simplifies considerably. ...
arXiv:2002.06051v2
fatcat:fhb7wtcjjzgyfbzjczdhm2ylia
Anomalous commutator corrections to sum rules
1995
Physical Review D, Particles and fields
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In this paper we consider the contributions of anomalous commutators to various QCD sum rules. ...
Using a combination of the BJL limit with the operator product expansion the results are presented in terms of the vacuum condensates of gauge invariant operators. ...
Similar effects have also been shown to modify the (canonically obtained) properties of the electroproduction sum rules [3] . ...
doi:10.1103/physrevd.52.5194
pmid:10019740
fatcat:4rqrf2gyjba63gc6r7dmk3kj64
Anomalous commutator corrections to sum rules
1996
Physical Review D, Particles and fields
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In this paper we consider the contributions of anomalous commutators to various QCD sum rules. ...
Using a combination of the BJL limit with the operator product expansion the results are presented in terms of the vacuum condensates of gauge invariant operators. ...
Similar effects have also been shown to modify the (canonically obtained) properties of the electroproduction sum rules [3] . ...
doi:10.1103/physrevd.53.4112.2
pmid:10021679
fatcat:vn2nwuxkh5fnlboyzrsiw2a6pi
A multiple commutator formula for the sum of Feynman diagrams
1997
Nuclear Physics B
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We present an exact combinatorial formula, involving multiple commutators of the vertices, which can be used to compute such cancellations. ...
In the presence of a large parameter, such as mass or energy, leading behavior of individual Feynman diagrams often get cancelled in the sum. ...
Theorem 5 can also be used to compute such cancellations. ...
doi:10.1016/s0550-3213(96)00548-2
fatcat:pf5wgdz4sbbf3acqsn4avxzl5i
Association schemes, non-commutative polynomial concentration, and sum-of-squares lower bounds for planted clique
[article]
2013
arXiv
pre-print
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2013 pre-print arXiv:1307.7615v1 fatcat:6ngelofvgvh6jkpughp5pigoraOther Versions
programming algorithms we know of: r rounds of the sum-of-squares hierarchy can only solve the planted clique for t > sqrt(n)/(C log n)^(r^2). ...
Our proof is formulated as a degree lower bound in the Positivstellensatz algebraic proof system, which is equivalent to the sum-of-squares hierarchy. ...
In Section 8.2.2 we compute the eigenvalues of the expectation of M ′ r . ...
arXiv:1307.7615v3
fatcat:wuvgunyw4beghpibycl5zzznue
An operational construction of the sum of two non-commuting observables in quantum theory and related constructions
[article]
2020
arXiv
pre-print
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., the requirement that the linear combination of two generally non-commuting observables A,B is an observable as well – is a fundamental postulate of the quantum theory yet before introducing any structure ...
We present such a construction with a formula which is valid for generally unbounded selfadjoint operators A and B, whose spectral measures may not commute, and a wide class of functions f: ℝ→ℂ. ...
A direct computation yields ν n L 1 ([0,1],dx) . ...
arXiv:1909.10974v4
fatcat:vuglce3gtzhi7etjzmytoigslq
Combining effects: Sum and tensor
2006
Theoretical Computer Science
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We further give a theory of the commutative combination of effects, their tensor, which yields Moggi's side-effects monad transformer. ...
We give a theory for the sum of computational effects, which in particular yields Moggi's exceptions monad transformer and an interactive input/output monad transformer. ...
In Section 7, we propose a canonical formula for combining the main computational effects we treat in the paper, and discuss several other issues concerning the combination of effects by sum and tensor ...
doi:10.1016/j.tcs.2006.03.013
fatcat:5pdjg635prgppjfkxian467gvu
Direct-sum behavior of modules over one-dimensional rings
[chapter]
2010
Commutative Algebra
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Moreover, a given finitely generated module can have many different representations as a direct sum of indecomposable modules. ...
With submodules and direct sums defined in the obvious way, we get an additive category in which every object has finite length. ...
Direct-sum cancellation Let R be a commutative Noetherian ring. ...
doi:10.1007/978-1-4419-6990-3_10
fatcat:c5mbbnnncjbi7lshbycjxbpeo4
Combining algebraic effects with continuations
2007
Theoretical Computer Science
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We consider the natural combinations of algebraic computational effects such as side-effects, exceptions, interactive input/output, and nondeterminism with continuations. ...
Continuations are not an algebraic effect, but previously developed combinations of algebraic effects given by sum and tensor extend, with effort, to include commonly used combinations of the various algebraic ...
way of combining effects [6] . ...
doi:10.1016/j.tcs.2006.12.026
fatcat:3uidveoyxnac7pwcvkfkaoa2jy
The optimal All-Partial-Sums algorithm in commutative semigroups and its applications for image thresholding segmentation
2011
Theoretical Computer Science
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The design and analysis of multidimensional All-Partial-Sums (APS) algorithms are considered. ...
With this criterion, we propose the piling algorithm to minimize the sequence length, then we show this algorithm is an optimal APS algorithm in commutative semigroups in the worst case. ...
Under the straight-line computation model, we will define the nD APS problems in the different universes, especially in the commutative semigroup. ...
doi:10.1016/j.tcs.2010.11.039
fatcat:hpco5ic3njbmxh6izo625qjyym
An operational construction of the sum of two non-commuting observables in quantum theory and related constructions
2020
Letters in Mathematical Physics
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., the requirement that the linear combination of two generally non-commuting observables A, B is an observable as well—is a fundamental postulate of the quantum theory yet before introducing any structure ...
We present such a construction with a formula which is valid for general unbounded self-adjoint operators A and B, whose spectral measures may not commute, and a wide class of functions $$f: {{\mathbb ...
If assumed, they, however, promote the theory to a very high level of effectiveness in physics a posteriori. ...
doi:10.1007/s11005-020-01332-7
fatcat:h7ezld466ratrh65mgntiuokry
Combining dynamical decoupling with fault-tolerant quantum computation
2011
Physical Review A. Atomic, Molecular, and Optical Physics
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We study how dynamical decoupling (DD) pulse sequences can improve the reliability of quantum computers. ...
Our accuracy estimates depend on the dynamics of the bath that couples to the quantum computer, and can be expressed either in terms of the operator norm of the bath's Hamiltonian or in terms of the power ...
Note that the last of these results bounds the sum of all high-order Magnus terms with n 5. Combining Eqs. ...
doi:10.1103/physreva.84.012305
fatcat:tjdfhtfsbzbjzdhkbrkwfocm3i
Parallel Algorithmic Techniques For Combinational Computation
1988
Annual Review of Computer Science
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The binary operation need not be commutative. The result of the computation is a sequence of prefix sums P1 = Vl, P' 2 = Vl 0 V2, ••• Pn = Vl 0 V2 0 '··0 v n . ...
[h,jj) , wruch by induction is the sum of the labels of all ways of combining two paths of length at most 2k-l. ...
doi:10.1146/annurev.cs.03.060188.001313
fatcat:lrel5pskwba7xeu4wufx75jj4e
Confidence level computation for combining searches with small statistics
1999
Nuclear Instruments and Methods in Physics Research Section A : Accelerators, Spectrometers, Detectors and Associated Equipment
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The effects of systematic uncertainty in the signal and background models are incorporated in the confidence levels. The procedure described allows efficient computation of expected confidence levels. ...
The results of many independent searches for the same particle may be combined easily, regardless of the discriminating variables which may be measured for the candidate events. ...
Summary An efficient technique for computing confidence levels for exclusion of small signals when combining a large number of counting experiments has been presented. ...
doi:10.1016/s0168-9002(99)00498-2
fatcat:k4wz2yunavd67px7tcvol45rcq
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