scholarly journals New Generalized Projection Speeds Up Audio Declipping

2019 ◽  
Author(s):  
Pavel Rajmic ◽  
Pavel Záviška ◽  
Vítězslav Veselý ◽  
Ondřej Mokrý
Keyword(s):  
Signal Processing ◽  
Explicit Formula ◽  
Convex Sets ◽  
The Other ◽  
Generalized Projection ◽  
Other Hand ◽  
Linear Transforms ◽  
Speed Up ◽  
Linear Transform

In theory and applications, it is often inevitable to work with projectors onto convex sets, where a linear transform is involved. In this article, a novel projector is presented, which generalizes previous results in that it admits a broader family of linear transforms, but on the other hand it is limited to box-type convex sets in the transformed domain. The new projector has an explicit formula and it can be interpreted within the framework of proximal optimization. The benefit of the new projector is demonstrated on an example from signal processing, where it was possible to speed up the convergence of a signal declipping algorithm by a factor of more than two.

scholarly journals A New Generalized Projection and Its Application to Acceleration of Audio Declipping

Axioms ◽  
2019 ◽  
Vol 8 (3) ◽  
pp. 105
Author(s):  
Pavel Rajmic ◽  
Pavel Záviška ◽  
Vítězslav Veselý ◽  
Ondřej Mokrý
Keyword(s):  
Signal Processing ◽  
Convex Optimization ◽  
Linear Operator ◽  
Explicit Formula ◽  
Convex Sets ◽  
State Of The Art ◽  
Computational Cost ◽  
The Other ◽  
Speed Up ◽  
Low Computational Cost

In convex optimization, it is often inevitable to work with projectors onto convex sets composed with a linear operator. Such a need arises from both the theory and applications, with signal processing being a prominent and broad field where convex optimization has been used recently. In this article, a novel projector is presented, which generalizes previous results in that it admits to work with a broader family of linear transforms when compared with the state of the art but, on the other hand, it is limited to box-type convex sets in the transformed domain. The new projector is described by an explicit formula, which makes it simple to implement and requires a low computational cost. The projector is interpreted within the framework of the so-called proximal splitting theory. The convenience of the new projector is demonstrated on an example from signal processing, where it was possible to speed up the convergence of a signal declipping algorithm by a factor of more than two.

On Gaussian Correlation Inequalities for Rectangles and Symmetric Sets

2002 ◽  
Vol 53 (3-4) ◽  
pp. 245-248
Author(s):  
Subir K. Bhandari ◽  
Ayanendranath Basu
Keyword(s):  
Recent Result ◽  
Convex Sets ◽  
Convex Set ◽  
Correlation Inequalities ◽  
The Other ◽  
Symmetric Convex ◽  
Complete Proof ◽  
Other Hand

Pitt's conjecture (1977) that P( A ∩ B) ≥ P( A) P( B) under the Nn (0, In) distribution of X, where A, B are symmetric convex sets in IRn still lacks a complete proof. This note establishes that the above result is true when A is a symmetric rectangle while B is any symmetric convex set, where A, B ∈ IRn. We give two different proofs of the result, the key component in the first one being a recent result by Hargé (1999). The second proof, on the other hand, is based on a rather old result of Šidák (1968), dating back a period before Pitt's conjecture.

scholarly journals Quantum Mechatronics

Electronics ◽  
2021 ◽  
Vol 10 (20) ◽  
pp. 2483
Author(s):  
Lucas Lamata ◽  
Marco B. Quadrelli ◽  
Clarence W. de Silva ◽  
Prem Kumar ◽  
Gregory S. Kanter ◽  
...  
Keyword(s):  
Quantum Effects ◽  
Review Article ◽  
The Other ◽  
Highly Efficient ◽  
Other Hand ◽  
Educational Initiatives ◽  
Speed Up ◽  
Macroscopic Domain ◽  
Promising Avenue

Mechatronics systems, a macroscopic domain, aim at producing highly efficient engineering platforms, with applications in a variety of industries and situations. On the other hand, quantum technologies, a microscopic domain, are emerging as a promising avenue to speed up computations and perform more efficient sensing. Recently, these two fields have started to merge in a novel area: quantum mechatronics. In this review article, we describe some developments produced so far in this respect, including early steps into quantum robotics, macroscopic actuators via quantum effects, as well as educational initiatives in quantum mechatronics.

scholarly journals Implementation of Prototyping Method on Website Development of Land use Mapping

2019 ◽  
Author(s):  
Ginanjar Wiro Sasmito
Keyword(s):  
Land Use ◽  
Urban Areas ◽  
Limited Resource ◽  
The Other ◽  
Land Supply ◽  
Website Development ◽  
Other Hand ◽  
Speed Up ◽  
Urban Activity

Increasing diversity of urban activity attracts many people to try their fate in urban areas so as to heighten the flow of urbanization. This resulted in a large demand for land supply to accommodate the increasing number of city dwellers. On the other hand, land is a very limited resource and cannot be created or renewed, so the problem that often arises is the proliferation of slum and squatter areas in urban areas. The solution to the problem is to produce a land use website. By using the prototyping method of land use website is generated in order to speed up the development of website and to really fit with the wishes and needs of the client

Quantitative aspects of speed-up and gap phenomena

2010 ◽  
Vol 20 (5) ◽  
pp. 707-722 ◽  
Author(s):  
KLAUS AMBOS-SPIES ◽  
THORSTEN KRÄLING
Keyword(s):  
Quantitative Analysis ◽  
Computable Function ◽  
Complexity Measure ◽  
The Other ◽  
Effective Measure ◽  
Fast Growing ◽  
Gap Theorem ◽  
Other Hand ◽  
Speed Up

We show that, for any abstract complexity measure in the sense of Blum and for any computable function f (or computable operator F), the class of problems that are f-speedable (or F-speedable) does not have effective measure 0. On the other hand, for sufficiently fast growing f (or F), the class of non-speedable computable problems does not have effective measure 0. These results answer some questions raised by Calude and Zimand. We also give a quantitative analysis of Borodin and Trakhtenbrot's Gap Theorem, which corrects a claim by Calude and Zimand.

scholarly journals Discrepancy of Matrices of Zeros and Ones

10.37236/1447 ◽  
1999 ◽  
Vol 6 (1) ◽  
Author(s):  
R. A. Brualdi ◽  
J. Shen
Keyword(s):  
Explicit Formula ◽  
The Other ◽  
Column Vector ◽  
Other Hand ◽  
Minimum Discrepancy ◽  
Positive Integers ◽  
Maximum Discrepancy ◽  
Sum Vector

Let $m$ and $n$ be positive integers, and let $R=(r_1,\ldots, r_m)$ and $ S=(s_1,\ldots, s_n)$ be non-negative integral vectors. Let ${\cal A} (R,S)$ be the set of all $m \times n$ $(0,1)$-matrices with row sum vector $R$ and column vector $S$, and let $\bar A$ be the $m \times n$ $(0,1)$-matrix where for each $i$, $1\le i \le m$, row $i$ consists of $r_i$ $1$'s followed by $n-r_i$ $0$'s. If $S$ is monotone, the discrepancy $d(A)$ of $A$ is the number of positions in which $\bar A$ has a $1$ and $A$ has a $0$. It equals the number of $1$'s in $\bar A$ which have to be shifted in rows to obtain $A$. In this paper, we study the minimum and maximum $d(A)$ among all matrices $A \in {\cal A} (R,S)$. We completely solve the minimum discrepancy problem by giving an explicit formula in terms of $R$ and $S$ for it. On the other hand, the problem of finding an explicit formula for the maximum discrepancy turns out to be very difficult. Instead, we find an algorithm to compute the maximum discrepancy.

scholarly journals Monomial multiplicities in explicit form

2019 ◽  
Vol 19 (09) ◽  
pp. 2050181
Author(s):  
Guillermo Alesandroni
Keyword(s):  
Explicit Formula ◽  
Explicit Form ◽  
Complete Intersection ◽  
Polynomial Ring ◽  
Monomial Ideal ◽  
The Other ◽  
Complete Intersections ◽  
New Class ◽  
Other Hand ◽  
The Family

Denote by [Formula: see text] a polynomial ring over a field, and let [Formula: see text] be a monomial ideal of [Formula: see text]. If [Formula: see text], we prove that the multiplicity of [Formula: see text] is given by [Formula: see text] On the other hand, if [Formula: see text] is a complete intersection, and [Formula: see text] is an almost complete intersection, we show that [Formula: see text] We also introduce a new class of ideals that extends the family of monomial complete intersections and that of codimension 1 ideals, and give an explicit formula for their multiplicity.

Bounds on the quantity of entanglement in parallel quantum computing of a single ensemble quantum computer

2014 ◽  
Vol 92 (2) ◽  
pp. 159-162
Author(s):  
M. Ávila Aoki ◽  
Guo Hua Sun ◽  
Shi Hai Dong
Keyword(s):  
Quantum Computing ◽  
Upper Bound ◽  
Quantum Computer ◽  
Quantum Algorithms ◽  
Point Of View ◽  
The Other ◽  
Quantum Computers ◽  
Other Hand ◽  
Speed Up ◽  
Parallel Mode

Speeding up of the processing of quantum algorithms has been focused on from the point of view of an ensemble quantum computer (EQC) working in a parallel mode. As a consequence of such efforts, additional speed up has been achieved for processing both Shor’s and Grover’s algorithms. On the other hand, in the literature there is scarce concern about the quantity of entanglement contained in EQC approaches, for this reason in the present work we study such a quantity. As a first result, an upper bound on the quantity of entanglement contained in EQC is imposed. As a main result we prove that equally weighted states are not appropriate for EQC working in parallel mode. In order that our results are not exclusively purely theoretical, we exemplify the situation by discussing the entanglement on an ensemble of n1 = 3 diamond quantum computers.

scholarly journals A stochastic Prékopa–Leindler inequality for log-concave functions

2020 ◽  
pp. 2050019
Author(s):  
Peter Pivovarov ◽  
Jesus Rebollo Bueno
Keyword(s):  
Stochastic Dominance ◽  
Convex Sets ◽  
Minkowski Inequality ◽  
The Other ◽  
Concave Functions ◽  
Compact Sets ◽  
Stochastic Approximations ◽  
Random Polytopes ◽  
Other Hand ◽  
Integrable Functions

The Brunn–Minkowski and Prékopa–Leindler inequalities admit a variety of proofs that are inspired by convexity. Nevertheless, the former holds for compact sets and the latter for integrable functions so it seems that convexity has no special signficance. On the other hand, it was recently shown that the Brunn–Minkowski inequality, specialized to convex sets, follows from a local stochastic dominance for naturally associated random polytopes. We show that for the subclass of log-concave functions and associated stochastic approximations, a similar stochastic dominance underlies the Prékopa–Leindler inequality.

scholarly journals On mathematical instrumentalism

2005 ◽  
Vol 70 (3) ◽  
pp. 778-794 ◽  
Author(s):  
Patrick Caldon ◽  
Aleksandar Ignjatović
Keyword(s):  
Equational Theory ◽  
Reverse Mathematics ◽  
The Other ◽  
Conservative Extension ◽  
Philosophical View ◽  
Other Hand ◽  
Primitive Recursive Arithmetic ◽  
Speed Up ◽  
Primitive Recursive

AbstractIn this paper we devise some technical tools for dealing with problems connected with the philosophical view usually called mathematical instrumentalism. These tools are interesting in their own right, independently of their philosophical consequences. For example, we show that even though the fragment of Peanos Arithmetic known as IΣ1 is a conservative extension of the equational theory of Primitive Recursive Arithmetic (PRA). IΣ1 has a super-exponential speed-up over PRA. On the other hand, theories studied in the Program of Reverse Mathematics that formalize powerful mathematical principles have only polynomial speed-up over IΣ1.

Sign in / Sign up

Export Citation Format

Share Document