The Surjective Mapping Conjecture and the Measurement Problem in Quantum Mechanics

Accepting a time-symmetric quantum dynamical world with ontological wave functions or fields, we follow arguments that naturally lead to a two-boundary interpretation of quantum mechanics. The usual two boundary picture is a valid superdeterministic interpretation. It has, however, one unsatisfactory feature. The random selection of a chosen measurement path of the universe is far too complicated. To avoid it, we propose an alternate two-boundary concept called surjective mapping conjecture. It takes as fundamental a quantum-time running forward like the usual time on the wave-function side and backward on the complex conjugate side. Unrelated fixed arbitrary boundary conditions at the initial and the final quantum times then determine the measurement path of the expanding and contracting quantum-time universe in the required way.

Shannon Entropy Loss in Mixed-Radix Conversions

This paper models a translation for base-2 pseudorandom number generators (PRNGs) to mixed-radix uses such as card shuffling. In particular, we explore a shuffler algorithm that relies on a sequence of uniformly distributed random inputs from a mixed-radix domain to implement a Fisher–Yates shuffle that calls for inputs from a base-2 PRNG. Entropy is lost through this mixed-radix conversion, which is assumed to be surjective mapping from a relatively large domain of size 2J to a set of arbitrary size n. Previous research evaluated the Shannon entropy loss of a similar mapping process, but this previous bound ignored the mixed-radix component of the original formulation, focusing only on a fixed n value. In this paper, we calculate a more precise formula that takes into account a variable target domain radix, n, and further derives a tighter bound on the Shannon entropy loss of the surjective map, while demonstrating monotonicity in a decrease in entropy loss based on increased size J of the source domain 2J. Lastly, this formulation is used to specify the optimal parameters to simulate a card-shuffling algorithm with different test PRNGs, validating a concrete use case with quantifiable deviations from maximal entropy, making it suitable to low-power implementation in a casino.

A Remark for the Hyers–Ulam Stabilities on n-Banach Spaces

In this article, we deal with stabilities of several functional equations in n-Banach spaces. For a surjective mapping f into a n-Banach space, we prove the generalized Hyers–Ulam stabilities of the cubic functional equation and the quartic functional equation for f in n-Banach spaces.

Partition: a surjective mapping approach for dimensionality reduction

Motivation Large amounts of information generated by genomic technologies are accompanied by statistical and computational challenges due to redundancy, badly behaved data and noise. Dimensionality reduction (DR) methods have been developed to mitigate these challenges. However, many approaches are not scalable to large dimensions or result in excessive information loss. Results The proposed approach partitions data into subsets of related features and summarizes each into one and only one new feature, thus defining a surjective mapping. A constraint on information loss determines the size of the reduced dataset. Simulation studies demonstrate that when multiple related features are associated with a response, this approach can substantially increase the number of true associations detected as compared to principal components analysis, non-negative matrix factorization or no DR. This increase in true discoveries is explained both by a reduced multiple-testing challenge and a reduction in extraneous noise. In an application to real data collected from metastatic colorectal cancer tumors, more associations between gene expression features and progression free survival and response to treatment were detected in the reduced than in the full untransformed dataset. Availability and implementation Freely available R package from CRAN, https://cran.r-project.org/package=partition. Supplementary information Supplementary data are available at Bioinformatics online.

A Study of Cyclic Codes Via a Surjective Mapping

In this article, cyclic codes of length $n$ over a formal power series ring and cyclic codes of length $nl$ over a finite field are studied. By defining a module isomorphism between $R^n$ and $(Z_4)^{2^kn}$, Dinh and Lopez-Permouth proved that a cyclic shift in $(Z_4)^{2^kn}$ corresponds to a constacyclic shift in $R^n$ by $u$, where $R=\frac{Z_4[u]}{<u^{2^k}-1>}$. We have defined a bijective mapping $\Phi_l$ on $R_{\infty}$, where $R_{\infty}$ is the formal power series ring over a finite field $\mathbb{F}$. We have proved that a cyclic shift in $(\mathbb{F})^{ln}$ corresponds to a $\Phi_l-$cyclic shift in $(R_{\infty})^n$ by defining a mapping from $(R_{\infty})^n$ onto $(\mathbb{F})^{ln}$. We have also derived some related results.

Properties of Complete Metric Spaces and their Applications to Computer Security, Information and Communication Technology

Information and Communication Technology has faced a lot of challenges in terms of security of data and information. The aim of this paper is to prove some common fixed point theorems for expansive type mappings, firstly for a continuous mapping and secondly for a surjective mapping. These theorems are generalizations of some recent results in complete b-dislocated metric space. The methodology involved is purely mathematical in nature with applications in computing. Moreover, we give various applications of these results in computer security, forensics and Information and Communication Technology.

On the Aleksandrov-Rassias Problems on Linearn-Normed Spaces

This paper generalizes T. M. Rassias' results in 1993 ton-normed spaces. IfXandYare two realn-normed spaces andYisn-strictly convex, a surjective mappingf:X→Ypreserving unit distance in both directions and preserving any integer distance is ann-isometry.

A Coordinate-Free Approach to Tracing the Coupler Curves of Pin-Jointed Linkages

In general, high-order coupler curves of plane mechanisms cannot be properly traced by standard predictor-corrector algorithms due to drifting problems and the presence of singularities. Instead of focusing on finding better algorithms for tracing curves, a simple coordinate-free method that first traces these curves in a distance space and then maps them onto the mechanism workspace is proposed. Tracing a coupler curve in the proposed distance space is much simpler because (a) the equation of this curve in this space can be straightforwardly obtained from a sequence of bilaterations; and (b) the curve in this space naturally decomposes into branches in which the signs of the oriented areas of the triangles involved in the aforementioned bilaterations remain constant. A surjective mapping permits to map the thus traced curves onto the workspace of the mechanism. The advantages of this two-step method are exemplified by tracing the coupler curves of a double butterfly linkage, curves that can reach order 48.