Strict Regularity Research Articles

Gamma-convergence of a nonlocal perimeter arising in adversarial machine learning

In this paper we prove Gamma-convergence of a nonlocal perimeter of Minkowski type to a local anisotropic perimeter. The nonlocal model describes the regularizing effect of adversarial training in binary classifications. The energy essentially depends on the interaction between two distributions modelling likelihoods for the associated classes. We overcome typical strict regularity assumptions for the distributions by only assuming that they have bounded BV densities. In the natural topology coming from compactness, we prove Gamma-convergence to a weighted perimeter with weight determined by an anisotropic function of the two densities. Despite being local, this sharp interface limit reflects classification stability with respect to adversarial perturbations. We further apply our results to deduce Gamma-convergence of the associated total variations, to study the asymptotics of adversarial training, and to prove Gamma-convergence of graph discretizations for the nonlocal perimeter.

МІЖСТИЛЬОВІ ПРИСЛІВНИКОВІ ЕКВІВАЛЕНТИ СЛОВА СУЧАСНОЇ УКРАЇНСЬКОЇ МОВИ

In recent times, in Slavic linguistics, great attention is paid to the bound disjointed compounds that are on the border between the word and the phraseologism mostly called the equivalents of the word. Scholars have studied semantics, the form of expression, and some aspects of functional-stylistic features of these units on text materials of different functional styles, but, at the same time, no comprehensive research into the functioning of interdisciplinary equivalents of the word has not been done yet. The author of the article identifies the composition of adverbial equivalents of the word that are actively operating in all or most functional styles of the modern Ukrainian language. The research employed the integral extract method, the distributive analysis method, the methods of component and contextual analysis, the methods of functional and stylistic analysis, as well as the matrix method, the method of opposition relations, and the quantitative calculations method. The sources of the research material were texts published during 2010–2021, including translations, of six functional styles of the modern Ukrainian language — confessional, scientific, official-business, journalistic, colloquial, and artistic. An interdisciplinary character most often has adverbial equivalents of the word with generalized semantics of time and method of action. The most frequent among them were the compounds tak samo — same, vse (use) odno — anyway, chas vid (od) chasu — from time to time, ves chas — all the time, z (iz) chasom — with time, na sohodni — for today. For this time, there is no strict regularity in using the adverbial equivalents of the word in texts of different functional styles of the modern Ukrainian language. It all depends on the writer, the author of a specific text, or the predilection of the speaker. However, the official-business style significantly differs in this case, due to the distinct conventional presentation form of specific information. The study of units used in different functional styles will make it possible to trace the extent to which the boundaries of these styles are changing, as well as to determine the role of differently designed, but semantically coherent lexical elements at the current stage of the Ukrainian language system development.

Aristotle and Natural Justice

In Nicomachean Ethics V Aristotle outlines a framework with three elements, political, natural and conventional/legal justice. The paper aims to offer a more detailed picture of their relation and argues that natural and conventional justice are linked together. By distinguishing two phases of conventional justice, those before and after enactment, the first phase expresses a general rule that can be enacted in different ways. Such a general rule may also correspond to natural justice. The paper is about to show also that, on Aristotle’s view, natural justice does not imply strict regularity since nature itself allows for variations and natural laws apply only for the most part, which gives room for equity.

A note on second derivative estimates for Monge-Ampère-type equations

Abstract In this article, we revisit previous Pogorelov-type interior and global second derivative estimates of N. S. Trudinger, F. Jiang, and J. Liu for solutions of Monge-Ampère-type partial differential equations. Taking account of recent strict convexity regularity results of Guillen-Kitagawa and Rankin and following our earlier work in the optimal transportation case, we remove the monotonicity assumptions in the more general case of generated Jacobian equations and consequently in the subsequent application to classical solvability and global regularity for second boundary value problems.

Spectroscopic characterization of a new series of bismuth tantalate pyrochlores doped with 3d-ions

X-ray spectroscopy methods (XPS, NEXAFS) were used to study the electronic state of the ions that make up pyrochlores (sp. gr. Fd-3m, No. 227) Bi2Mg1-xMxTa2O9+Δ (M − Cr,Mn,Fe,Co,Ni,Cu). It has been established that doping of bismuth magnesium tantalate pyrochlore with 3d-ions does not affect the electronic state of bismuth and magnesium ions, which are found in the ionic form Bi(+3), Mg(+2). Tantalum ions are in the same charge state Ta(+5-δ) due to the characteristic shift of the energy position of peaks towards the lower energies compared to the binding energy in pentavalent tantalum oxide. An energy shift in the Ta4f and Ta5p spectra is observed for all transition ions without a strict regularity in the magnitude of the signal shift depending on the nature of the dopant. Ions of some 3d-elements in the composition of pyrochlores, according to X-ray spectroscopy, have several oxidation states, for example, Cu(+1,+2), Co(+2,+3), Mn(+2,+3), Cr(+3,+6). The iron and nickel ions predominantly have the +3 and + 2 oxidation states, respectively.

SANS Studies of the Gallium-Indium Alloy Structure within Regular Nanopores.

Potential applications of nanolattices often require filling their empty space with eutectic metallic alloys. Due to confinement to nanolattices, the structure of phase segregates in eutectic alloys can differ from that in bulk. These problems are poorly understood now. We have used small angle neutron scattering (SANS) to study the segregation in the Ga-In alloy confined to an opal template with the regular pore network, created by a strict regularity of opal constituents in close similarity with nanolattices. We showed that SANS is a powerful tool to reveal the configuration of segregated phases within nanotemplates. The In-rich segregates were found to have specific structural features as small sizes and ordered arrangement.

Convergence and Optimality of Policy Gradient Methods in Weakly Smooth Settings

Policy gradient methods have been frequently applied to problems in control and reinforcement learning with great success, yet existing convergence analysis still relies on non-intuitive, impractical and often opaque conditions. In particular, existing rates are achieved in limited settings, under strict regularity conditions. In this work, we establish explicit convergence rates of policy gradient methods, extending the convergence regime to weakly smooth policy classes with L2 integrable gradient. We provide intuitive examples to illustrate the insight behind these new conditions. Notably, our analysis also shows that convergence rates are achievable for both the standard policy gradient and the natural policy gradient algorithms under these assumptions. Lastly we provide performance guarantees for the converged policies.

Necessarily the Old Riddle Necessary Connections and the Problem of Induction

Abstract In this paper, I will discuss accounts to solve the problem of induction by introducing necessary connections. The basic idea is this: if we know that there are necessary connections between properties F and G such that F -ness necessarily brings about G-ness, then we are justified to infer that all, including future or unobserved, F s will be Gs. To solve the problem of induction with ontology has been proposed by David Armstrong and Brian Ellis. In this paper, I will argue that these attempts to solve the problem of induction fail. Necessary connections fail to reliably imply the respective regularities for two main reasons: Firstly, according to an argument originally presented by Helen Beebee, the respective necessary connections might be time-limited, and hence do not warrant inferences about future cases. As I will discuss, arguments against the possibility or explanatory power of time-limited necessary connections fail. Secondly, even time-unlimited necessary connections do not entail strict or non-strict regularities, and nor do they allow inferences about individual cases, which is an important function of inductive reasoning. Moreover, the proposed solution to the problem of induction would only apply to a tiny minority of inductive inferences. I argue that most inductive inferences are not easily reducible to the proposed inference pattern, as the vast majority of everyday inductive inferences do not involve necessary connections between fundamental physical properties or essences.

An iterative heuristic for passenger-centric train timetabling with integrated adaption times

In this paper we present a method to construct a periodic timetable from a tactical planning perspective. We aim at constructing a timetable that is feasible with respect to infrastructure constraints and minimizes total perceived passenger travel time. In addition to in-train and transfer times, our notion of perceived passenger time includes the adaption time (waiting time at the origin station). Adaption time minimization allows us to avoid strict frequency regularity constraints and, at the same time, to ensure regular connections between passengers’ origins and destinations. The combination of adaption time minimization and infrastructure constraints satisfaction makes the problem very challenging.The described periodic timetabling problem can be modelled as an extension of a Periodic Event Scheduling Problem (PESP) formulation, but requires huge computing times if it is directly solved by a general-purpose solver for instances of realistic size. In this paper, we propose a heuristic approach consisting of two phases that are executed iteratively. First, we solve a mixed-integer linear program to determine an ideal timetable that minimizes the total perceived passenger travel time but neglects infrastructure constraints. Then, a Lagrangian-based heuristic makes the timetable feasible with respect to infrastructure constraints by modifying train departure and arrival times as little as possible. The obtained feasible timetable is then evaluated to compute the resulting total perceived passenger travel time, and a feedback is sent to the Lagrangian-based heuristic so as to possibly improve the obtained timetable from the passenger perspective, while still respecting infrastructure constraints. We illustrate the proposed iterative heuristic approach on real-life instances of Netherlands Railways and compare it to a benchmark approach, showing that it finds a feasible timetable very close to the ideal one.

Impact of Sm3+ and Er3+ Cations on the Structural, Optical, and Magnetic Traits of Spinel Cobalt Ferrite Nanoparticles: Comparison Investigation.

In this study, we investigated a comparison of the structure, morphology, optic, and magnetic (room temperature (RT)) features of Er3+ and Sm3+ codoped CoFe2O4 (CoErSm) nanospinel ferrite (NSFs) (x ≤ 0.05) synthesized via hydrothermal (H-CoErSm NSFs) and sonochemical (S-CoErSm NSFs) approaches. The formation of all products via both synthesis methods has been validated by X-ray powder diffraction (XRD) and scanning electron microscopy (SEM), along with energy-dispersive X-ray (EDX) and transmission electron microscopy (TEM) techniques. The single phase of the spinel structure (except for the Hyd sample with x = 0.03) was evidenced by XRD analysis. The DXRD (crystallite size) values of H-CoErSm and S-CoErSm NSFs are in the 10–14.7 and 10–16 nm ranges, respectively. TEM analysis presented the cubic morphology of all products. A UV–visible percent diffuse reflectance (DR %) study was performed on all products, and Eg (direct optical energy band gap) values varying in the 1.32–1.48 eV range were projected from the Tauc plots. The data of RT magnetization demonstrated that all prepared samples are ferromagnetic in nature. M–H data revealed that rising the contents of cosubstituent elements (Sm3+ and Er3+ ions) caused an increase in Ms (saturation magnetization) and Hc (coercive field) in comparison to pristine samples. Although concentration dependence is significant (x > 0.02), no strict regularity (roughly fluctuating) has been ruled out in Ms values for doped samples prepared via the hydrothermal method. However, sonochemically prepared samples demonstrated that Ms values increase with increasing x up to x = 0.04 and then decrease with the further rise in cosubstituent Sm3+ and Er3+ ions. The calculated values of Ms and Hc were found to be greater in H-CoErSm NSFs compared to those in S-CoErSm NSFs. The present investigation established that the distribution of cations and the variation in crystallite/particle sizes are efficient to control the intrinsic properties of all samples.

Analogies of Genetic and Chemical Code. Supplement 1

In the original work, for which this is a Supplement, I presented analogies of the genetic and chemical code (Rakocevic 2018b, in relation to the source work from 1991). (Further: instead of Rakocevic I use the abbreviation MMR.) There I gave three Tables of the Periodic System of the Elements (PSE) in which I dealt with the problem of stable and unstable elements; in the sense that an unstable element is one that possesses at least one primordially unstable isotope, while elements that do not possess such isotopes are stable. I have shown that for the number of stable and the number of unstable elements there are strict regularities and a strict law; the same law that is valid for the association of codons to more complex and to less complex amino acids in the genetic code. I have not dealt with the question of the number of stable and the number of unstable isotopes, what I do now in this Supplement.

An Iterative Heuristic for Passenger-Centric Train Timetabling with Integrated Adaption Times

In this paper we present a method to construct a periodic timetable from a tactical planning perspective. We aim at constructing a timetable that is feasible with respect to infrastructure constraints and minimizes average perceived passenger travel time. In addition to in-train and transfer times, our notion of perceived passenger time includes the adaption time (waiting time at the origin station). Adaption time minimization allows us to avoid strict frequency regularity constraints and, at the same time, to ensure regular connections between passengers’ origins and destinations. The combination of adaption time minimization and infrastructure constraints satisfaction makes the problem very challenging. The described periodic timetabling problem can be modelled as an extension of a Periodic Event Scheduling Problem (PESP) formulation, but requires huge computing times if it is directly solved by a general-purpose solver for instances of realistic size. In this paper, we propose a heuristic approach consisting of two phases that are executed iteratively. First, we solve a mixed-integer linear program to determine an ideal timetable that mini- mizes the average perceived passenger travel time but neglects infrastructure constraints. Then, a Lagrangian-based heuristic makes the timetable feasible with respect to infra- structure constraints by modifying train departure and arrival times as little as possible. The obtained feasible timetable is then evaluated to compute the resulting average per- ceived passenger travel time, and a feedback is sent to the Lagrangian-based heuristic so as to possibly improve the obtained timetable from the passenger perspective, while still respecting infrastructure constraints. We illustrate the proposed iterative heuristic approach on real-life instances of Netherlands Railways and compare it to a benchmark approach, showing that it finds a feasible timetable very close to the ideal one.

Reflections of Lev Shestov on the essence of freedom in the context of theology, philosophy and modern science

In his reflections on freedom, Lev Shestov considered any definition of freedom insufficient, which excludes the concept of arbitrariness, causeless action. Although he raises the source of the idea of freedom as arbitrariness (an arbitrary desire of a person violating the laws of nature) to the Jewish prophets, in reality it was taken by him from the reasoning of the hero of the novel by F. Dostoevsky, “Notes from the Underground.” The article proves that in the words of his hero, Dostoevsky objects to A. Schopenhauer in the concept of which all human actions are subject to strict causal laws, and freedom refers to the transcendental act of “choosing” one’s character, which determines the actions and remains unchanged throughout life. However, recognizing the strict regularity of all phenomena (and actions) within the world,one can see the highest human freedom in the ability to arbitrarily change the world as a whole. This is precisely what the hero of Dostoevsky, “not reconciling” with the laws of nature, has in mind, and it is precisely to this concept of freedom that Shestov comes to. The article shows that such an understanding of freedom has parallels in theology (in Kabbalah, in Sufism and in Christian Gnosticism), and also has some foundations in modern science: the quantum theory claims that the macroscopic world is the result of many acts of observation made jointly by all people.

Investigating Interdisciplinary Practice: Methodological Challenges (Introduction)

Investigating Interdisciplinary Practice: Methodological Challenges (Introduction)

The Distribution of the Antarctic Limpet Nacella concinna (Nacellidae) on Underwater Landscapes of the Meek Channel, Argentine Islands, Graham Land

Objective(s). To clarify the patterns of Nacella concinna (Nacellidae) distribution in the water area of the Argentine Islands Archipelago (Meek Channel). Methods. Morphometric, statistical, cartographic methods as well as geoinformation technologies were used. Results. Analyzed the patterns of mollusc distribution on different transects, taking into account their morphometric characteristics — the length of the shell, the mollusс weight, the population density. It is determined that the distribution of Nacella concinna subpopulations does not have any visible strict regularity. At different transects with an insignificant exception the morphometric characteristics of the mollusсs are distributed both in classical and non-classical models. At the MK1 transect is shown the classical model of the distribution of morphometric characteristics, namely with an increase in the mollusс population density, the morphometric characteristics (shell length and weight of the mollusс) tend to decrease. At the MK2 transect is shown non-classical distribution model. The morphometric characteristics (shell length, mollusс weight) increase with an increase in the population density of the molluscs. At the MK3 transect is shown the classical distribution model, but a characteristic feature is an increase in the population density up to 5 m depth and a gradual decrease in the population density from 5 to 20 m. Geoinformation models of the Nacella concinna distribution by depth in the water area of the Ukrainian Antarctic Akademik Vernadsky station were constructed. Conclusions. Maps of the distribution of the Nacella concinna population were created for this region for the first time. The dimensional classes of the Nacella concinna subpopulation from selected water areas of the Argentine Islands were described.

Social Assistance of Women in Prison

Life in the penitentiary is absolutely a life in a group where all intimacy is annulled, everything is done in front of others, and this leads to the censorship of sensitivity, to the conviction that everything is privative, that here the interpersonal relationship is a drain, a waste and can not hide from the evil side of the conduct of those around. The penitentiary is a closed space, a field of forces in an eternal misunderstanding based on a strict regularity, with psychological consequences on the detainee and the penitentiary staff. The community of each penitentiary, taken apart, is an anonymous world of people preserved by social prestige. The objective of the research was to conduct an analysis of the consequences of deprivation of liberty on women as well as their behavior. An original questionnaire of 10 questions was applied to a sample of 23 women aged 20 to 60. It took into account: profession, studies, civil status, committed deed, activities carried out in the penitentiary, the need for counseling, the level of integration into prison life. The consequences of deprivation of liberty and the influence of the penitentiary environment on women call for specialists to develop educational programs aimed at rebalancing and socially recovering detainees, preparing for social reintegration, and preventing the passing on of future generations of violent behavioral patterns.

Urban Planning by Le Corbusier According to Praxeological Knowledge

The city is formed as a mosaic of various elements which affect its attractiveness. These elements range from location attributes, through economic opportunities, to social aspects. Therefore, urbanity and urban planning should be considered in a multi-dimensional context. In the paper we address the problem of urban planning by Le Corbusier according to praxeological and system knowledge. From praxeological point of view an active human being takes his/her choice between various possibilities by preferring one of these possibilities to the others, and by manifesting it by her actions. The same applies to the design process. Due to this fact, the scientific design process can be treated as a systematic rational reconstruction of the designer’s behaviour. Such a reconstruction requires previous reflection on designer’s work, as well as some consideration and design experience, thus know-how knowledge based on methodological knowledge. In the paper several city visions of Le Corbusier, as well as the characteristics and organisation of his design process are analysed. Le Corbusier’s innovative design ideas resulted from industrialisation changes and motorisation accelerating progress, which gave foundation to a new urban array. This array based on strict geometric forms, regularity and repetition determining standard. Thanks to his theories, Le Corbusier established principles of modern city construction and planning. Although some doubts were expressed as to the scale of centralisation of the cities designed by him and his class-based conception, he was awarded that overall welfare of the individual living in a city was the quality of built environment. Therefore, his designed creations were not only functional but they also produced emotions. The analysis of his prolific design activities allows us to state that the organisation of his architectural and urban planning process was very efficient and complex. The city concepts proposed by him were the subject of analysis by generations of designers. Also now, they can still be the basis for modelling virtual and navigable cities by modern planners. Le Corbusier’s comprehensive approach to modern city planning showed that research activities, that is theoretical thinking, and production activities, that is practice, are linked methodically. Therefore, urban planning should be understood not only as a projection of the possibilities of architecture, but as a multidisciplinary process. Due to this fact, an urban plan, as a result of that process, should be a synthesis of various social, industrial and economic aspects.

Multi-periodic train timetabling using a period-type-based Lagrangian relaxation decomposition

To provide passengers with strict regularity of train operation, this research is devoted to modeling and solving the multi-periodic train timetabling problem to simultaneously optimize operation periods, arrival times, and departure times of all period types of trains on a double-track rail network. Based on the construction of a weighted directed graph, a multi-path searching model, namely, a 0-1 linear programming model, is built to minimize the total travel time of all period-types of trains subject to many operational constraints, including station parking capacity and train minimum load factors. After decomposing this model by introducing some Lagrangian multipliers to relax its complicated constraints, a solution algorithm, including a multi-path simultaneous searching sub-algorithm for each period-type of train, is designed to optimize both the feasible and dual solutions, which correspond to the upper and lower bounds, respectively. Finally, the performance, convergence, sensitivity, and practicability of our method are analyzed using many instances on both a small rail network and the high-speed railway between Beijing and Shanghai in China.

Kritický realismus a ekologická ekonomie: neintuitivní protivníci nebo zřejmí spojenci?

The paper questions the compatibility of critical realism with ecological economics. In particular, it is argued that there is radical dissonance between ontological presuppositions of ecological economics and critical realist perspective. The dissonance lies in the need of ecological economics to state strict causal regularities in socio-economic realm, given the environmental intuitions about the nature of economy and the role of materiality and non-human agency in persistence of economic systems. Using conceptual apparatus derived from Andrew Brown’s critique of critical realism and Bruno Latour’s actor-network theory, the paper refuses ontological nature/society dualism employed by critical realism, and stresses the role of non-humans in practical production and reproduction of socio-economic networks on the one hand, and in broadly defined ecological economic research on the other hand.

A unified approach to error bounds for structured convex optimization problems

Error bounds, which refer to inequalities that bound the distance of vectors in a test set to a given set by a residual function, have proven to be extremely useful in analyzing the convergence rates of a host of iterative methods for solving optimization problems. In this paper, we present a new framework for establishing error bounds for a class of structured convex optimization problems, in which the objective function is the sum of a smooth convex function and a general closed proper convex function. Such a class encapsulates not only fairly general constrained minimization problems but also various regularized loss minimization formulations in machine learning, signal processing, and statistics. Using our framework, we show that a number of existing error bound results can be recovered in a unified and transparent manner. To further demonstrate the power of our framework, we apply it to a class of nuclear-norm regularized loss minimization problems and establish a new error bound for this class under a strict complementarity-type regularity condition. We then complement this result by constructing an example to show that the said error bound could fail to hold without the regularity condition. Consequently, we obtain a rather complete answer to a question raised by Tseng. We believe that our approach will find further applications in the study of error bounds for structured convex optimization problems.