Strict convexity of the objective function and uniqueness of the maximum point in a model with three arbitrary random priorities

The main result of this paper is the proof of the strict concavity of some function of integral form depending on three random variables, which we call priorities. This function is an objective function in the so-called model with priorities, in which the arbiter, following expert opinions, distributes funds among the enterprises and institutions under his jurisdiction. This result implies an important corollary about the existence and uniqueness of a local maximum point (which is also a global maximum point) of the objective function. This is a significant generalization of the corresponding result of N.V. Neumezhitskaia, S.I. Uglich and T.A. Volosatova, published in December 2020.

Bootstrapping BPS spectra of 5d/6d field theories

We propose a systematic approach to computing the BPS spectrum of any 5d/6d supersymmetric quantum field theory in Coulomb phases, which admits either gauge theory descriptions or geometric descriptions, based on the Nakajima-Yoshioka’s blowup equations. We provide a significant generalization of the blowup equation approach in terms of both properly quantized magnetic fluxes on the blowup $$ \hat{\mathrm{\mathbb{C}}} $$ ℂ ̂ 2 and the effective prepotential for 5d/6d field theories on the Omega background which is uniquely determined by the Chern-Simons couplings on their Coulomb branches. We employ our method to compute BPS spectra of all rank-1 and rank-2 5d Kaluza-Klein (KK) theories descending from 6d $$ \mathcal{N} $$ N = (1, 0) superconformal field theories (SCFTs) compactified on a circle with/without twist. We also discuss various 5d SCFTs and KK theories of higher ranks, which include a few exotic cases such as new rank-1 and rank-2 5d SCFTs engineered with frozen singularity as well as the 5d SU(3)8 gauge theory currently having neither a brane web nor a smooth shrinkable geometric description. The results serve as non-trivial checks for a large class of non-trivial dualities among 5d theories and also as independent evidences for the existence of certain exotic theories.

Fixed point theorems for a new generalization of contractive maps in incomplete metric spaces and its application in boundary value problems

In this paper, we obtain some fixed point theorems for multivalued mappings in incomplete metric spaces. Moreover, as motivated by the recent work of Olgun, Minak and Altun [M. Olgun, G. Minak and I. Altun, A new approach to Mizoguchi–Takahashi type fixed point theorems, J. Nonlinear Convex Anal. 17 2016, 3, 579–587], we improve these theorems with a new generalization contraction condition for multivalued mappings in incomplete metric spaces. This result is a significant generalization of some well-known results in the literature. Also, we provide some examples to show that our main theorems are a generalization of previous results. Finally, we give an application to a boundary value differential equation.

Hierarchical Microbial Functions Prediction by Graph Aggregated Embedding

Matching 16S rRNA gene sequencing data to a metabolic reference database is a meaningful way to predict the metabolic function of bacteria and archaea, bringing greater insight to the working of the microbial community. However, some operational taxonomy units (OTUs) cannot be functionally profiled, especially for microbial communities from non-human samples cultured in defective media. Therefore, we herein report the development of Hierarchical micrObial functions Prediction by graph aggregated Embedding (HOPE), which utilizes co-occurring patterns and nucleotide sequences to predict microbial functions. HOPE integrates topological structures of microbial co-occurrence networks with k-mer compositions of OTU sequences and embeds them into a lower-dimensional continuous latent space, while maximally preserving topological relationships among OTUs. The high imbalance among KEGG Orthology (KO) functions of microbes is recognized in our framework that usually yields poor performance. A hierarchical multitask learning module is used in HOPE to alleviate the challenge brought by the long-tailed distribution among classes. To test the performance of HOPE, we compare it with HOPE-one, HOPE-seq, and GraphSAGE, respectively, in three microbial metagenomic 16s rRNA sequencing datasets, including abalone gut, human gut, and gut of Penaeus monodon. Experiments demonstrate that HOPE outperforms baselines on almost all indexes in all experiments. Furthermore, HOPE reveals significant generalization ability. HOPE's basic idea is suitable for other related scenarios, such as the prediction of gene function based on gene co-expression networks. The source code of HOPE is freely available at https://github.com/adrift00/HOPE.

Refinements of the integral Jensen’s inequality generated by finite or infinite permutations

There are a lot of papers dealing with applications of the so-called cyclic refinement of the discrete Jensen’s inequality. A significant generalization of the cyclic refinement, based on combinatorial considerations, has recently been discovered by the author. In the present paper we give the integral versions of these results. On the one hand, a new method to refine the integral Jensen’s inequality is developed. On the other hand, the result contains some recent refinements of the integral Jensen’s inequality as elementary cases. Finally some applications to the Fejér inequality (especially the Hermite–Hadamard inequality), quasi-arithmetic means, and f-divergences are presented.

The Phenomenon of Values in the Axiology and in the History

The article offers a version of understanding values as elements of culture. As a fundamental idea, Adam Smith accepted the classical theory of labor value, but with a significant generalization of this idea from the economic context as a special case to the general theoretical level of social philosophy, in which values are understood as products of both practical and intellectual activity. The principle of social egocentrism and interpretation of the main categories of values, versions of the philosophy of history as a process in which the values of culture arise and are modified are also proposed are also considered.

Decision-Making Based on q-Rung Orthopair Fuzzy Soft Rough Sets

Recently, Yager presented the new concept of q-rung orthopair fuzzy (q-ROF) set (q-ROFS) which emerged as the most significant generalization of Pythagorean fuzzy set (PFS). From the analysis of q-ROFS, it is clear that the rung q is the most significant feature of this notion. When the rung q increases, the orthopair adjusts in the boundary range which is needed. Thus, the input range of q-ROFS is more flexible, resilient, and suitable than the intuitionistic fuzzy set (IFS) and PFS. The aim of this manuscript is to investigate the hybrid concept of soft set ( S t S) and rough set with the notion of q-ROFS to obtain the new notion of q-ROF soft rough (q-ROF S t R) set (q-ROF S t RS). In addition, some averaging aggregation operators such as q-ROF S t R weighted averaging (q-ROF S t RWA), q-ROF S t R ordered weighted averaging (q-ROF S t ROWA), and q-ROF S t R hybrid averaging (q-ROF S t RHA) operators are presented. Then, the basic desirable properties of these investigated averaging operators are discussed in detail. Moreover, we investigated the geometric aggregation operators, such as q-ROF S t R weighted geometric (q-ROF S t RWG), q-ROF S t R ordered weighted geometric (q-ROF S t ROWG), and q-ROF S t R hybrid geometric (q-ROF S t RHG) operators, and proposed the basic desirable characteristics of the investigated geometric operators. The technique for multicriteria decision-making (MCDM) and the stepwise algorithm for decision-making by utilizing the proposed approaches are demonstrated clearly. Finally, a numerical example for the developed approach is presented and a comparative study of the investigated models with some existing methods is brought to light in detail which shows that the initiated models are more effective and useful than the existing methodologies.

PROPERTY AS A MODE OF INDIVIDUALIZATION OF A COMMON PRODUCT

The article discusses the problem of property as a social relationship. The idea of Adam Smith in the classical theory of labor value is accepted as fundamental, but with a significant generalization of this idea from the economic context as a special case to the general theoretical level of social philosophy, at which values are understood as products of both practical and spiritual activity. In this context, property is interpreted not as a person's relationship to things, but as the relationship of people to each other about things. Forms of property are not considered historically, as in Marx, but functionally – as the author sees it. In this version, capitalism and communism turn out to be economic myths, and forms of ownership are determined by the means of individualization of the jointly produced product.

Augmentasi Data Pengenalan Citra Mobil Menggunakan Pendekatan Random Crop, Rotate, dan Mixup

Deep convolutional neural networks (CNNs) have achieved remarkable results in two-dimensional (2D) image detection tasks. However, their high expression ability risks overfitting. Consequently, data augmentation techniques have been proposed to prevent overfitting while enriching datasets. In this paper, a Deep Learning system for accurate car model detection is proposed using the ResNet-152 network with a fully convolutional architecture. It is demonstrated that significant generalization gains in the learning process are attained by randomly generating augmented training data using several geometric transformations and pixel-wise changes, such as image cropping and image rotation. We evaluated data augmentation techniques by comparison with competitive data augmentation techniques such as mixup. Data augmented ResNet models achieve better results for accuracy metrics than baseline ResNet models with accuracy 82.6714% on Stanford Cars Dataset.

Density Functional Hydrodynamics in Multiscale Pore Systems: Chemical Potential Drive

We use the method of density functional hydrodynamics (DFH) to model compositional multiphase flows in natural cores at the pore-scale. In previous publications the authors demonstrated that DFH covers many diverse pore-scale phenomena, starting from those inherent in RCA and SCAL measurements, and extending to much more complex EOR processes. We perform the pore-scale modelling of multiphase flow scenarios by means of the direct hydrodynamic (DHD) simulator, which is a numerical implementation of the DFH. In the present work, we consider the problem of numerical modelling of fluid transport in pore systems with voids and channels when the range of pore sizes exceed several orders of magnitude. Such situations are well known for carbonate reservoirs, where narrow pore channels of micrometer range can coexist and interconnect with vugs of millimeter or centimeter range. In such multiscale systems one cannot use the standard DFH approach for pore-scale modeling, primarily because the needed increase in scanning resolution that is required to resolve small pores adequately, leads to a field of view reduction that compromises the representation of large pores. In order to address this challenge, we suggest a novel approach, in which transport in small-size pores is described by an upscaled effective model, while the transport in large pores is still described by the DFH. The upscaled effective model is derived from the exact DFH equations using asymptotic expansion in respect to small-size characterization parameter. This effective model retains the properties of DFH like chemical and multiphase transport, thus making it applicable to the same range of phenomena as DFH itself. The model is based on the concept that the transport is driven by gradients of chemical potentials of the components present in the mixture. This is a significant generalization of the Darcy transport model since the proposed new model incorporates diffusion transport in addition to the usual pressure-driven transport. In the present work we provide several multiphase transport numerical examples including: a) upscaling to chemical potential drive (CPD) model, b) combined modeling of large pores by DFH and small pores by CPD.