Sign-rank Can Increase under Intersection

The communication class UPP cc is a communication analog of the Turing Machine complexity class PP . It is characterized by a matrix-analytic complexity measure called sign-rank (also called dimension complexity), and is essentially the most powerful communication class against which we know how to prove lower bounds. For a communication problem f , let f ∧ f denote the function that evaluates f on two disjoint inputs and outputs the AND of the results. We exhibit a communication problem f with UPP cc ( f ) = O (log n ), and UPP cc ( f ∧ f ) = Θ (log 2 n ). This is the first result showing that UPP communication complexity can increase by more than a constant factor under intersection. We view this as a first step toward showing that UPP cc , the class of problems with polylogarithmic-cost UPP communication protocols, is not closed under intersection. Our result shows that the function class consisting of intersections of two majorities on n bits has dimension complexity n Omega Ω(log n ) . This matches an upper bound of (Klivans, O’Donnell, and Servedio, FOCS 2002), who used it to give a quasipolynomial time algorithm for PAC learning intersections of polylogarithmically many majorities. Hence, fundamentally new techniques will be needed to learn this class of functions in polynomial time.

The Factors of Marriage Dissolution Between Hearing Impairment Couple at Melaka Syariah Court

The dissolution of marriage which occurs between Muslim married couple in Malaysia shall be referred to the Syariah Court either it is between typical couples or between couple with disabilities. However, couple with disabilities faces quite different challenges compared to typical couple in maintaining relationship. The article aims to identify the factors of marriage dissolution between hearing impairment couple registered at Malacca Syariah Court. The study uses the qualitative and interview research methodologies to identify conflicts in relationship confronted by hearing impairment couple which leads to dissolution of marriage. It is found that there are seven factors of marriage dissolution among hearing impairment couple which are the communication problem, lack of knowledge regarding Islamic Family Law, the intervention of family members in marital disputes, inadequate pre-marriage course, no specific marriage course through the period of marriage as well as post-marriage course for hearing impairment spouse. The implication of research discovers that all these courses shall be review in order to prevent escalated divorce rate among hearing impairment couple. Abstrak Setiap perceraian yang berlaku di antara pasangan berkahwin Muslim di Malaysia mestilah dirujuk kepada Mahkamah Syariah sama ada pasangan suami isteri tipikal ataupun pasangan Orang Kurang Upaya (OKU). Bagi golongan OKU pendengaran, cabaran yang dihadapi dalam meneruskan kehidupan rumahtangga walaubagaimanapun agak berbeza berbanding golongan tipikal. Tujuan artikel ini adalah untuk mengenalpasti faktor-faktor pembubaran perkahwinan antara pasangan OKU pendengaran yang didaftarkan di Mahkamah Syariah Negeri Melaka. Kajian menggunakan kaedah temu bual untuk mengenal pasti masalah pasangan OKU pendengaran yang membawa kepada pembubaran perkahwinan. Hasil kajian mendapati terdapat enam faktor pembubaran perkahwinan antara pasangan OKU pendengaran iaitu masalah komunikasi, kurang pendedahan tentang ilmu Undang-Undang Keluarga Islam, campur tangan ahli keluarga dalam masalah rumahtangga, kursus Pra-Perkahwinan yang dianjurkan tidak bersesuaian, tiada kursus khusus sepanjang tempoh perkahwinan dan tiada kursus pasca perkahwinan khusus bagi pasangan OKU Pendengaran. Implikasi dari kajian mendapati bahawa kursus-kursus khas tersebut perlu dikaji semula bagi mengurangkan kadar perceraian dalam kalangan pasangan OKU pendengaran.

Research and Application of Network Trusted Interconnection Technology

In order to solve the problem of reliable information transmission between data centers and data sources, between data sources and between data centers, as well as the "network island" communication problem, a dynamic MPLS VPN method is proposed, the principle and steps of the method are introduced, and how to apply the method to the supporting platform is explained in detail.

Hamy Mean Operators Based on Complex q-Rung Orthopair Fuzzy Setting and Their Application in Multi-Attribute Decision Making

To determine the connection among any amounts of attributes, the Hamy mean (HM) operator is one of the more broad, flexible, and dominant principles used to operate problematic and inconsistent information in actual life dilemmas. Furthermore, for the option to viably portray more complicated fuzzy vulnerability data, the idea of complex q-rung orthopair fuzzy sets can powerfully change the scope of sign of choice data by changing a boundary q, dependent on the distinctive wavering degree from the leaders, where ζ ≥ 1, so they outperform the conventional complex intuitionistic and complex Pythagorean fuzzy sets. In genuine dynamic issues, there is frequently a communication problem between credits. The goal of this study is to initiate the HM operators based on the flexible complex q-rung orthopair fuzzy (Cq-ROF) setting, called the Cq-ROF Hamy mean (Cq-ROFHM) operator and the Cq-ROF weighted Hamy mean (Cq-ROFWHM) operator, and some of their desirable properties are investigated in detail. A multi-attribute decision-making (MADM) dilemma for investigating decision-making problems under the Cq-ROF setting is explored with certain examples. Finally, a down-to-earth model for big business asset-arranging framework determination is provided to check the created approach and to exhibit its reasonableness and adequacy. The exploratory outcomes show that the clever MADM strategy is better than the current MADM techniques for managing MADM issues.

The hardest halfspace

We study the approximation of halfspaces $$h:\{0,1\}^n\to\{0,1\}$$ h : { 0 , 1 } n → { 0 , 1 } in the infinity norm by polynomials and rational functions of any given degree. Our main result is an explicit construction of the “hardest” halfspace, for which we prove polynomial and rational approximation lower bounds that match the trivial upper bounds achievable for all halfspaces. This completes a lengthy line of work started by Myhill and Kautz (1961). As an application, we construct a communication problem that achieves essentially the largest possible separation, of O(n) versus $$2^{-\Omega(n)}$$ 2 - Ω ( n ) , between the sign-rank and discrepancy. Equivalently, our problem exhibits a gap of log n versus $$\Omega(n)$$ Ω ( n ) between the communication complexity with unbounded versus weakly unbounded error, improving quadratically on previous constructions and completing a line of work started by Babai, Frankl, and Simon (FOCS 1986). Our results further generalize to the k-party number-on-the-forehead model, where we obtain an explicit separation of log n versus $$\Omega(n/4^{n})$$ Ω ( n / 4 n ) for communication with unbounded versus weakly unbounded error.

Parent-Child Dyadic Coping and Quality of Life in Chronically Diseased Children

Different forms of dyadic coping are associated with positive outcomes in partner relationships, yet little is known about dyadic coping in parent-child relationships. The current research explored the association between parent-child dyadic coping and children’s quality of life in 12–18-year old children with a chronic disease (i.e., cystic fibrosis, autoimmune diseases, and children post-cancer treatment). In a sample of 105 parent-child dyads, self-reported forms of dyadic coping (i.e., stress communication, problem-oriented, emotion-oriented, and negative dyadic coping) and children’s quality of life were assessed. Children reported more stress communication and negative dyadic coping than their parents, while parents reported more problem-oriented dyadic coping and emotion-oriented dyadic coping than their children. More stress communication of the child was associated with more emotion-oriented dyadic coping and less negative dyadic coping of the parent. More negative dyadic coping of the child was associated with less stress communication, problem-oriented dyadic coping and emotion-oriented dyadic coping of the parent. Additionally, both children’s and parents’ negative dyadic coping were associated with lower self-reported pediatric quality of life and parents’ emotion-oriented dyadic coping was associated with higher pediatric quality of life. These findings emphasize that children and their parents mutually influence each other and that dyadic coping is associated with children’s quality of life. Theoretical and practical implications are discussed.

Attenuation of Microwaves Received From a Drone Owing to Smoke Obscuration

The objective of this study is to analyze the effect of smoke obscuration on the signal sensitivity of microwaves received from a drone. A spectrum analyzer and a directional antenna were employed for analyzing the received signal sensitivity and measuring the mean received power, both before and after the drone entered the smoke layer for one min in the fire training area. The drone operated in the range of 2.4 GHz to 2.48 GHz. It is found that the received power before entering the smoke layer is –39.3 dBm, at which signals and image data can be received. However, upon entering the smoke layer, the received power is reduced to –47 dBm, at which signals and image data cannot be received. Hence, the received power undergoes an attenuation of approximately 7.7 dBm (5.9 mW) owing to smoke obscuration, which causes communication outage. Based on this study, it can be concluded that the received power undergoes attenuation owing to smoke obscuration during fires. Furthermore, if a communication problem occurs due to microwave attenuation, it affects the drone’s operation.