scholarly journals Quantum prescriptions are more ontologically distinct than they are operationally distinguishable

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 345
Author(s):  
Anubhav Chaturvedi ◽  
Debashis Saha
Keyword(s):  
Lower Bounds ◽  
Additional Assumption ◽  
Quantum Measurements ◽  
Two Dimensional ◽  
Identity Of Indiscernibles ◽  
Unitary Transformations ◽  
Additional Assumptions

Based on an intuitive generalization of the Leibniz principle of `the identity of indiscernibles', we introduce a novel ontological notion of classicality, called bounded ontological distinctness. Formulated as a principle, bounded ontological distinctness equates the distinguishability of a set of operational physical entities to the distinctness of their ontological counterparts. Employing three instances of two-dimensional quantum preparations, we demonstrate the violation of bounded ontological distinctness or excess ontological distinctness of quantum preparations, without invoking any additional assumptions. Moreover, our methodology enables the inference of tight lower bounds on the extent of excess ontological distinctness of quantum preparations. Similarly, we demonstrate excess ontological distinctness of quantum transformations, using three two-dimensional unitary transformations. However, to demonstrate excess ontological distinctness of quantum measurements, an additional assumption such as outcome determinism or bounded ontological distinctness of preparations is required. Moreover, we show that quantum violations of other well-known ontological principles implicate quantum excess ontological distinctness. Finally, to showcase the operational vitality of excess ontological distinctness, we introduce two distinct classes of communication tasks powered by excess ontological distinctness.

scholarly journals Encoding Two-Dimensional Range Top-k Queries

Algorithmica ◽  
2021 ◽  
Author(s):  
Seungbum Jo ◽  
Rahul Lingala ◽  
Srinivasa Rao Satti
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Upper Bound ◽  
Total Order ◽  
Two Dimensional ◽  
Information Theoretic ◽  
Cartesian Tree ◽  
Dimensional Range

AbstractWe consider the problem of encoding two-dimensional arrays, whose elements come from a total order, for answering $${\text{Top-}}{k}$$ Top- k queries. The aim is to obtain encodings that use space close to the information-theoretic lower bound, which can be constructed efficiently. For an $$m \times n$$ m × n array, with $$m \le n$$ m ≤ n , we first propose an encoding for answering 1-sided $${\textsf {Top}}{\text {-}}k{}$$ Top - k queries, whose query range is restricted to $$[1 \dots m][1 \dots a]$$ [ 1 ⋯ m ] [ 1 ⋯ a ] , for $$1 \le a \le n$$ 1 ≤ a ≤ n . Next, we propose an encoding for answering for the general (4-sided) $${\textsf {Top}}{\text {-}}k{}$$ Top - k queries that takes $$(m\lg {{(k+1)n \atopwithdelims ()n}}+2nm(m-1)+o(n))$$ ( m lg ( k + 1 ) n n + 2 n m ( m - 1 ) + o ( n ) ) bits, which generalizes the joint Cartesian tree of Golin et al. [TCS 2016]. Compared with trivial $$O(nm\lg {n})$$ O ( n m lg n ) -bit encoding, our encoding takes less space when $$m = o(\lg {n})$$ m = o ( lg n ) . In addition to the upper bound results for the encodings, we also give lower bounds on encodings for answering 1 and 4-sided $${\textsf {Top}}{\text {-}}k{}$$ Top - k queries, which show that our upper bound results are almost optimal.

scholarly journals Structural bounds on the dyadic effect

2017 ◽  
Vol 5 (5) ◽  
pp. 694-711 ◽  
Author(s):  
Matteo Cinelli ◽  
Giovanna Ferraro ◽  
Antonio Iovanella
Keyword(s):  
Lower Bounds ◽  
Network Topology ◽  
Dimensional Space ◽  
Upper Bounds ◽  
Feasible Region ◽  
Two Dimensional ◽  
Independent Parameters

AbstractThe dyadic effect is a phenomenon that occurs when the number of links between nodes sharing a common feature is larger than expected if the features are distributed randomly on the network. In this article, we consider the case when nodes are distinguished by a binary characteristic. Under these circumstances, two independent parameters, namely dyadicity and heterophilicity are able to detect the presence of the dyadic effect and to measure how much the considered characteristic affects the network topology. The distribution of nodes characteristics can be investigated within a two-dimensional space that represents the feasible region of the dyadic effect, which is bound by two upper bounds on dyadicity and heterophilicity. Using some network structural arguments, we are able to improve such upper bounds and introduce two new lower bounds, providing a reduction of the feasible region of the dyadic effect as well as constraining dyadicity and heterophilicity within a specific range. Some computational experiences show the bounds effectiveness and their usefulness with regards to different classes of networks.

scholarly journals Improved lower bounds on the connective constants for two-dimensional self-avoiding walks

2004 ◽  
Vol 37 (48) ◽  
pp. 11521-11529 ◽  
Author(s):  
Iwan Jensen
Keyword(s):  
Lower Bounds ◽  
Two Dimensional ◽  
Self Avoiding Walks

A PROCESSOR-TIME-MINIMAL DESIGN FOR 3D RECTILINEAR MESH ALGORITHMS

1996 ◽  
Vol 06 (04) ◽  
pp. 539-550 ◽  
Author(s):  
CHRIS SCHEIMAN ◽  
PETER CAPPELLO
Keyword(s):  
Lower Bounds ◽  
Systolic Array ◽  
Directed Acyclic Graph ◽  
Two Dimensional ◽  
Processor Time ◽  
Acyclic Graph ◽  
Multiprocessor Schedule ◽  
Minimal Design ◽  
Dag Model

The paper, using a directed acyclic graph (dag) model of algorithms, investigates precedence constrained multiprocessor schedules for the nx×ny×nz directed rectilinear mesh. Its completion requires at least nx+ny+nz−2 multiprocessor steps. Time-minimal multiprocessor schedules that use as few processors as possible are called processor-time-minimal. Lower bounds are shown for the nx×ny×nz directed mesh, and these bounds are shown to be exact by constructing a processor-time-minimal multiprocessor schedule that can be realized on a systolic array whose topology is either a two dimensional mesh or skewed cylinder.

SIGNATURE AND RELIABILITY OF CONDITIONAL THREE-DIMENSIONAL CONSECUTIVE-(s, s, s)-OUT-OF-(s, s, m):F SYSTEM

2014 ◽  
Vol 21 (02) ◽  
pp. 1450009 ◽  
Author(s):  
MADHURI G. KULKARNI ◽  
AKANKSHA S. KASHIKAR
Keyword(s):  
Lower Bounds ◽  
Three Dimensional ◽  
Upper And Lower Bounds ◽  
System Failure ◽  
Three Dimension ◽  
Two Dimensional ◽  
Math Model ◽  
The Moment ◽  
Appl Math ◽  
F System

A three-dimensional consecutive (r1, r2, r3)-out-of-(m1, m2, m3):F system was introduced by Akiba et al. [J. Qual. Mainten. Eng.11(3) (2005) 254–266]. They computed upper and lower bounds on the reliability of this system. Habib et al. [Appl. Math. Model.34 (2010) 531–538] introduced a conditional type of two-dimensional consecutive-(r, s)-out-of-(m, n):F system, where the number of failed components in the system at the moment of system failure cannot be more than 2rs. We extend this concept to three dimension and introduce a conditional three-dimensional consecutive (s, s, s)-out-of-(s, s, m):F system. It is an arrangement of ms2 components like a cuboid and it fails if it contains either a cube of failed components of size (s, s, s) or 2s3 failed components. We derive an expression for the signature of this system and also obtain reliability of this system using system signature.

Aprioribounds for a class of nonlinear elliptic equations and applications to physical problems

1981 ◽  
Vol 88 (1-2) ◽  
pp. 75-81 ◽  
Author(s):  
Catherine Bandle
Keyword(s):  
Dirichlet Problem ◽  
Lower Bounds ◽  
Elliptic Equations ◽  
Nonlinear Elliptic Equations ◽  
Upper And Lower Bounds ◽  
Two Dimensional ◽  
Nonlinear Dirichlet Problem ◽  
Nonlinear Elliptic ◽  
Physical Problems ◽  
Maximal Pressure

SynopsisUpper and lower bounds for the solutions of a nonlinear Dirichlet problem are given and isoperimetric inequalities for the maximal pressure of an ideal charged gas are constructed. The method used here is based on a geometrical result for two-dimensional abstract surfaces.

Value preserving quantum measurements: Impossibility theorems and lower bounds for the distortion

1983 ◽  
Vol 24 (10) ◽  
pp. 2454-2460 ◽  
Author(s):  
G. C. Ghirardi ◽  
A. Rimini ◽  
T. Weber
Keyword(s):  
Lower Bounds ◽  
Quantum Measurements
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