Probabilistic algorithm of professional pedagogical teaching for the students of “music art” specialty

2018 ◽  
Vol 2 (31) ◽  
pp. 16-21
Author(s):  
Bronyslav Goleschevich
Keyword(s):  
Probabilistic Algorithm

Short paths in PU(2)

2021 ◽  
Vol 21 (9-10) ◽  
pp. 771-780
Author(s):  
Zachary Stier
Keyword(s):  
Recent Work ◽  
Probabilistic Algorithm

Parzanchevski--Sarnak \cite{PS} recently adapted an algorithm of Ross--Selinger \cite{RS16} for factorization of $\PU(2)$-diagonal elements to within distance $\eps$ into an efficient probabilistic algorithm for any $\PU(2)$-element, using at most $3\log_p(\nicefrac{1}{\eps^3})$ factors from certain well-chosen sets. The Clifford+$T$ gates are one such set arising from $p=2$. In that setting, we leverage recent work of Carvalho Pinto--Petit \cite{CPP} to improve this to $\frac{7}{3}\log_2(\nicefrac{1}{\eps^3})$, and implement the algorithm in Haskell.

A Novel Dynamic Noise-Dependent Probabilistic Algorithm for Route Discovery in MANETs

2013 ◽  
pp. 52-68
Author(s):  
Hussein Al-Bahadili ◽  
Alia Sabri
Keyword(s):  
Noise Level ◽  
Ad Hoc ◽  
Network Services ◽  
Route Discovery ◽  
Probabilistic Algorithm ◽  
Dynamic Noise ◽  
Wide Range ◽  
Simulation Results ◽  
Hoc Networks ◽  
Broadcasting Algorithm

In mobile ad hoc networks (MANETs), broadcasting is widely used in route discovery and other network services. The most widely used broadcasting algorithm is simple flooding, which aggravates a high number of redundant packet retransmissions, causing contention and collisions. Proper use of dynamic probabilistic algorithm significantly reduces the number of retransmissions, which reduces the chance of contention and collisions. In current dynamic probabilistic algorithm, the retransmission probability (pt) is formulated as a linear/non-linear function of a single variable, the number of first-hop neighbors (k). However, such algorithm is suffers in the presence of noise due to increasing packet-loss. In this paper, the authors propose a new dynamic probabilistic algorithm in which ptis determined locally by the retransmitting nodes considering both k and the noise-level. This algorithm is referred to as the dynamic noise-dependent probabilistic (DNDP) algorithm. The performance of the DNDP algorithm is evaluated through simulations using the MANET simulator (MANSim). The simulation results show that the DNDP algorithm presents higher network reachability than the dynamic probabilistic algorithm at a reasonable increase in the number of retransmissions for a wide range of noise-level. The effects of nodes densities and nodes speeds on the performance of the DNDP algorithm are also investigated.

DEEP CLASSES

2016 ◽  
Vol 22 (2) ◽  
pp. 249-286 ◽  
Author(s):  
LAURENT BIENVENU ◽  
CHRISTOPHER P. PORTER
Keyword(s):  
Mutual Information ◽  
Initial Segment ◽  
Computability Theory ◽  
Binary Sequences ◽  
Algorithmic Randomness ◽  
Positive Probability ◽  
Probabilistic Algorithm ◽  
Image Position ◽  
The Relationship ◽  
Mass Problems

AbstractA set of infinite binary sequences ${\cal C} \subseteq 2$ℕ is negligible if there is no partial probabilistic algorithm that produces an element of this set with positive probability. The study of negligibility is of particular interest in the context of ${\rm{\Pi }}_1^0 $ classes. In this paper, we introduce the notion of depth for ${\rm{\Pi }}_1^0 $ classes, which is a stronger form of negligibility. Whereas a negligible ${\rm{\Pi }}_1^0 $ class ${\cal C}$ has the property that one cannot probabilistically compute a member of ${\cal C}$ with positive probability, a deep ${\rm{\Pi }}_1^0 $ class ${\cal C}$ has the property that one cannot probabilistically compute an initial segment of a member of ${\cal C}$ with high probability. That is, the probability of computing a length n initial segment of a deep ${\rm{\Pi }}_1^0 $ class converges to 0 effectively in n.We prove a number of basic results about depth, negligibility, and a variant of negligibility that we call tt-negligibility. We provide a number of examples of deep ${\rm{\Pi }}_1^0 $ classes that occur naturally in computability theory and algorithmic randomness. We also study deep classes in the context of mass problems, examine the relationship between deep classes and certain lowness notions in algorithmic randomness, and establish a relationship between members of deep classes and the amount of mutual information with Chaitin’s Ω.

Efficient Probabilistic Calculation of a Thermal Transient on a 3D FE Model With Variable Heat Exchange Coefficient

2013 ◽  
Author(s):  
Thibault Demol ◽  
Jean-Pierre Izard ◽  
Nicolas Tartare
Keyword(s):  
Transfer Functions ◽  
Physical Problem ◽  
Nuclear Industry ◽  
Fe Model ◽  
Probabilistic Algorithms ◽  
Heat Exchange Coefficient ◽  
Probabilistic Algorithm ◽  
Constant Heat ◽  
Element Analysis ◽  
Reactor Pressure

Probabilistic calculations are often used to evaluate reliability in nuclear industry. One of their main difficulties is that failure probabilities are, in this domain, very low and therefore their computations are very long. The speed of the calculations depends on the probabilistic algorithm and the complexity of the physical problem (usually modeled by a finite element analysis). The optimization of the probabilistic algorithms benefits from a wealth of literature but the physical problem is often very simplified by a lot of approximations. This paper develops a methodology to avoid some approximations. The geometry of the problem is often brought back to a 1D or 2D problem. Here, large 3D mesh can still be used thanks to transfer functions. This requires the linearity of the problem and especially a constant heat transfer coefficient for a thermo-elastic analysis. This limitation has been removed. This article’s focus is on methodology but qualitative results of a probabilistic brittle fracture application of a reactor pressure vessel (RPV) in ferritic steel are given. Other kinds of analysis can benefit from similar methodology.

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