Main Result Research Articles

Characterising Modal Formulas with Examples

We study the existence of finite characterisations for modal formulas. A finite characterisation of a modal formula φ is a finite collection of positive and negative examples that distinguishes φ from every other, non-equivalent modal formula, where an example is a finite pointed Kripke structure. This definition can be restricted to specific frame classes and to fragments of the modal language: a modal fragment ℒ admits finite characterisations with respect to a frame class ℱ if every formula φ ∈ ℒ has a finite characterisation with respect to ℒ consisting of examples that are based on frames in ℱ. Finite characterisations are useful for illustration, interactive specification and debugging of formal specifications, and their existence is a precondition for exact learnability with membership queries. We show that the full modal language admits finite characterisations with respect to a frame class ℱ only when the modal logic of ℱ is locally tabular. We then study which modal fragments, freely generated by some set of connectives, admit finite characterisations. Our main result is that the positive modal language without the truth-constants ⊤ and ⊥ admits finite characterisations w.r.t. the class of all frames. This result is essentially optimal: finite characterisability fails when the language is extended with the truth constant ⊤ or ⊥ or with all but very limited forms of negation.

Local Independence Testing for Point Processes.

Constraint-based causal structure learning for point processes require empirical tests of local independence. Existing tests require strong model assumptions, e.g., that the true data generating model is a Hawkes process with no latent confounders. Even when restricting attention to Hawkes processes, latent confounders are a major technical difficulty because a marginalized process will generally not be a Hawkes process itself. We introduce an expansion similar to Volterra expansions as a tool to represent marginalized intensities. Our main theoretical result is that such expansions can approximate the true marginalized intensity arbitrarily well. Based on this, we propose a test of local independence and investigate its properties in real and simulated data.

Visco-energetic solutions for a model of crack growth in brittle materials

Visco-energetic solutions have been recently advanced as a new solution concept for rate-independent systems, alternative to energetic solutions/quasistatic evolutions and balanced viscosity solutions. In the spirit of this novel concept, we revisit the analysis of the variational model proposed by Francfort and Marigo for the quasi-static crack growth in brittle materials, in the case of antiplane shear. In this context, visco-energetic solutions can be constructed by perturbing the time incremental scheme for quasistatic evolutions by means of a viscous correction inspired by the term introduced by Almgren, Taylor, and Wang in the study of mean curvature flows. With our main result we prove the existence of a visco-energetic solution with a given initial crack. We also show that, if the cracks have a finite number of tips evolving smoothly on a given time interval, visco-energetic solutions comply with Griffith's criterion.

Robust estimation of a regression function in exponential families

We observe n pairs of independent (but not necessarily i.i.d.) random variables X1=(W1,Y1),…,Xn=(Wn,Yn) and tackle the problem of estimating the conditional distributions Qi⋆(wi) of Yi given Wi=wi for all i∈{1,…,n}. Even though these might not be true, we base our estimator on the assumptions that the data are i.i.d. and the conditional distributions of Yi given Wi=wi belong to a one parameter exponential family Q¯ with parameter space given by an interval I. More precisely, we pretend that these conditional distributions take the form Qθ(wi)∈Q¯ for some θ that belongs to a VC-class Θ¯ of functions with values in I. For each i∈{1,…,n}, we estimate Qi⋆(wi) by a distribution of the same form, i.e. Qθ̂(wi)∈Q¯, where θ̂=θ̂(X1,…,Xn) is a well-chosen estimator with values in Θ¯. We establish non-asymptotic exponential inequalities for the upper deviations of a Hellinger-type distance between the true conditional distributions of the data and the estimated one based on the exponential family Q¯ and the class of functions Θ¯ we chose. We show that our estimation strategy is robust to model misspecification, contamination and the presence of outliers. Besides, when the data are truly i.i.d., the exponential family Q¯ is suitably parametrized and the conditional distributions Qi⋆(wi) of the form Qθ⋆(wi)∈Q¯ for some unknown Hölderian function θ⋆ with values in I, we prove that the estimator θ̂ of θ⋆ is minimax (up to a logarithmic factor). Finally, we provide an algorithm for calculating θ̂ when Θ¯ is a VC-class of functions of low or moderate dimension and we carry out a simulation study to compare its performance to that of the MLE and median-based estimators. The proof of our main result relies on an upper bound, with explicit numerical constants, on the expectation of the supremum of an empirical process over a VC-subgraph class. This bound can be of independent interest.

Lowness properties for strong reducibilities and the computational power of maximal sets

We introduce the notion of eventually uniformly weak truth table array computable (e.u.wtt-a.c.) sets. As our main result, we show that a computably enumerable (c.e.) set has this property iff it is weak truth table ( wtt-) reducible to a maximal set. Moreover, in this equivalence we may replace maximal sets by quasi-maximal sets, hyperhypersimple sets or dense simple sets and we may replace wtt-reducibility by identity-bounded Turing reducibility (or any intermediate reducibility). Here, a set A is e.u.wtt-a.c. if there is an effective procedure which, for any given partial wtt-functional Φ ˆ, yields a computable approximation g ( x , s ) of the domain of Φ ˆ A together with a computable indicator function k ( x , s ) and a computable order h ( x ) such that, once the indicator becomes positive, i.e., k ( x , s ) = 1, the number of the mind changes of the approximation g on x after stage s is bounded by h ( x ) where, for total Φ ˆ A , the indicator eventually becomes positive on almost all arguments x of Φ ˆ A . In addition to our main result, we show several properties of the computably enumerable e.u.wtt-a.c. sets. For instance, the class of these sets is closed downwards under wtt-reductions and closed under join. Moreover, we relate this class to – and separate it from – well known classes in the literature. On the one hand, the class of the wtt-degrees of the c.e. e.u.wtt-a.c. sets is strictly contained in the class of the array computable c.e. wtt-degrees. On the other hand, every bounded low set is e.u.wtt-a.c. but there are e.u.wtt-a.c. c.e. sets which are not bounded low. Here a set A is bounded low if A † ⩽ wtt ∅ † , i.e., if A † is ω-c.a., where A † is the wtt-jump of A (Anderson, Csima and Lange (Archive for Mathematical Logic 56(5–6) (2017) 507–521)). Finally, we prove that there is a strict hierarchy within the class of the bounded low c.e. sets A depending on the order h that bounds the number of mind changes of a computable approximation of A † , and we show that there exists a Turing complete set A such that A † is h-c.a. for any computable order h with h ( 0 ) > 0.

Religious and mythological ideas of Karelians about smallpox, rubella, measles and chicken-pox diseases

about smallpox, rubella, measles and chickenpox diseases Traditional medicine has always triggered genuine interest among researchers. It reflects not only medical practice, ra-tional and irrational, but also prognostics of diseases, beliefs, conspiracy traditions, ritual magic, etc. Mythology occupies a significant place in ethnomedicine as well, affecting not only the cause-effect relationship between the occurrence of an ailment and abolition of it, but also the designation of some diseases, the nomination of which is motivated by the mythological percep-tions of the people. Christianization of Karelians, which took place in the 13th century, had a major influence on the Karelian culture. Christian and pagan views became closely intertwined, making a dual impact on such cultural layer of the ethnic group as traditional medicine. The problematics of scientific research is determined by the lack of a complex analysis of the issue. The information about the ethnomedicine of the proper Karelians, Livvik Karelians and Ludikov Karelians was collected from pub-lished sources (Karelian speech samples, dialect dictionaries of the Karelian language, periodicals) and by the means of gather-ing materials from respondents living on the territory of the Republic of Karelia. The author addresses the religious and mytho-logical ideas of the Karelians on the example of such diseases as smallpox, rubella, and chickenpox. The identification of an entire complex of common ideas about these diseases — their personification, family relationships, methods of treatment and nomination of diseases — became the main result of the research. Karelians believed that smallpox, measles, rubella and chickenpox are related, they are sisters. The reason of their invasion was seen in not honoring them or insulting them with an action or word. When patients with these diseases appeared in the house, various forms of coaxing were used towards them, and a solemn reception was held, aiming at propitiation of these ailments. In the treatment of smallpox, rubella and measles, the main emphasis was placed on the use of red matter in healing rituals, as this color was believed to have protective function. Proba-bly, this method was based on the “like cures like” or “like repels like” principle, typical for Karelian folk medicine. Engaging the data on folk medicine of Vepsians and Russians showed the similarity of the religious and mythological ideas of these peoples with Kare-lians, which is explained by their long-term contact and interinfluence of cultures while living on the same territory.

Strong convergence theorem for split null point, split variational inequality and fixed point problems for a non-expansive semigroup

The primary goal of this paper is to find a common solution of a split null point problem, split variational inequality problem and fixed point problem for a non-expansive semigroup with the help of new type of iterative algorithm. We construct that the sequences induced by the proposed iterative method to solve the above stated problems in the setting of real Hilbert spaces and obtain a strong convergence theorem. We also deduce certain consequences from the main convergence result. At the end, we provide a numerical experiment to demonstrate the convergence analysis of proposed iterative method. The methodology and conclusion described in this work extend and unify previously published findings in this field.

Closed 𝑘-Schur Katalan functions as 𝐾-homology Schubert representatives of the affine Grassmannian

Recently, Blasiak–Morse–Seelinger introduced symmetric func- tions called Katalan functions, and proved that the K K -theoretic k k -Schur functions due to Lam–Schilling–Shimozono form a subfamily of the Katalan functions. They conjectured that another subfamily of Katalan functions called closed k k -Schur Katalan functions is identified with the Schubert structure sheaves in the K K -homology of the affine Grassmannian. Our main result is a proof of this conjecture. We also study a K K -theoretic Peterson isomorphism that Ikeda, Iwao, and Maeno constructed, in a nongeometric manner, based on the unipotent solution of the relativistic Toda lattice of Ruijsenaars. We prove that the map sends a Schubert class of the quantum K K -theory ring of the flag variety to a closed K K - k k -Schur Katalan function up to an explicit factor related to a translation element with respect to an antidominant coroot. In fact, we prove this map coincides with a map whose existence was conjectured by Lam, Li, Mihalcea, Shimozono, and proved by Kato, and more recently by Chow and Leung.

The Covid Shock, The Rise of Defi, and Bitcoin's Increasing Market Risk

This paper aims to determine whether Bitcoin’s market risk increased in response to the COVID-19 shock. Our analysis employs familiar asset pricing models used by investment managers. Our main result is that Bitcoin’s market risk increased after the lockdown in March 2020. Wavelet analysis that captures both time and scale changes is introduced, and risk estimates that allow for both time and scale changes are provided, consistent with our main finding. From the standpoint of traditional investments, we find that the market risk of a Bitcoin investment after March 2020 is similar to that of a risky tech stock.

Almost spanning distance trees in subsets of finite vector spaces

AbstractFor and an odd prime power , consider the vector space over the finite field , where the distance between two points and is defined as . A distance graph is a graph associated with a nonzero distance to each of its edges. We show that large subsets of vector spaces over finite fields contain every nearly spanning distance tree with bounded degree in each distance. This quantitatively improves results by Bennett, Chapman, Covert, Hart, Iosevich, and Pakianathan on finding distance paths, and results by Pham, Senger, Tait, and Thu on finding distance trees. A key ingredient in proving our main result is to obtain a colorful generalization of a classical result of Haxell about finding nearly spanning bounded‐degree trees in an expander.

Technical Note—On the Convergence Rate of Stochastic Approximation for Gradient-Based Stochastic Optimization

Finite-Time Performance of Gradient-Based Stochastic Approximation Algorithms Stochastic approximation (SA) algorithms are among the most commonly used methods for addressing stochastic optimization problems. In “Technical Note: On the Convergence Rate of Stochastic Approximation for Gradient-Based Stochastic Optimization,” J. Hu and M. C. Fu provide a new error bound for SA algorithms when applied to a class of problems with convex differentiable structures. The bound allows a detailed characterization of an algorithm’s finite-time performance through directly analyzing the bias and variance of the employed gradient estimator. The main result is then applied to study and compare the efficiency of traditional Kiefer-Wolfowitz algorithms and those based on random direction finite-difference gradient estimators such as simultaneous perturbation SA. The analysis leads to new insights into when it may be advantageous to use such randomized gradient estimates under various problem and algorithm parameter settings.

Parametric Semidefinite Programming: Geometry of the Trajectory of Solutions

In many applications, solutions of convex optimization problems are updated on-line, as functions of time. In this paper, we consider parametric semidefinite programs, which are linear optimization problems in the semidefinite cone whose coefficients (input data) depend on a time parameter. We are interested in the geometry of the solution (output data) trajectory, defined as the set of solutions depending on the parameter. We propose an exhaustive description of the geometry of the solution trajectory. As our main result, we show that only six distinct behaviors can be observed at a neighborhood of a given point along the solution trajectory. Each possible behavior is then illustrated by an example. Funding: This work was supported by OP RDE [Grant CZ.02.1.01/0.0/0.0/16_019/0000765].

Bidding Combinatorial Games

Combinatorial Game Theory is a branch of mathematics and theoretical computer science that studies sequential 2-player games with perfect information. Normal play is the convention where a player who cannot move loses. Here, we generalize the classical alternating normal play to infinitely many game families, by means of discrete Richman auctions (Develin et al. 2010, Larsson et al. 2021, Lazarus et al. 1996). We generalize the notion of a perfect play outcome, and find an exact characterization of outcome feasibility. As a main result, we prove existence of a game form for each such outcome class; then we describe their lattice structures. By imposing restrictions to the general families, such as impartial and symmetric termination, we find surprising analogies with alternating play.

Scattering over Varying Amplification Grating

The scattering pattern from a narrow absorbing/amplifying grating is investigated. A simple model of a narrow amplifying grating is solved exactly numerically and approximately analytically for the regime where the beam’s wavelength is much shorter than the grating’s wavelength. The main result is that the incident angle divides the scattering pattern into two regimes: below and above the incident angles. The former regime has a weak dependence on the incident angle but has a strong dependence on the scattering one. In this regime, a new grating formula is derived. The opposite occurs in the latter regime, which is very sensitive to the incident angle but has only weak dependence on the scattering angle. Consequently, at certain incident angles, all of the scattering is concentrated in the first regime, i.e., all scattering angles are lower than the incident angle.

Scaling and instantaneous blow up

The main result is a simple proof of the Baras-Goldstein (1984) instantaneous blow up result for the heat equation with the inverse square potential. The proof relies heavily, indeed mainly, on scaling. Remarks are also given concerning the case when the underlying space ℝ N is replaced by the Heisenberg group ℍ N .

Narrow operators on [formula omitted]-complete lattice-normed spaces

We extend some of main results of Abasov et al., 2016, Fotiy et al., (2020), Mykhaylyuk et al., (2015), Pliev and Fang, (2017), Pliev and Popov, (2014) to the setting of orthogonally additive operators on lattice-normed spaces. We introduce a new class of C-complete lattice-normed spaces which strictly includes a class of Banach–Kantorovich spaces. The first main result of the paper asserts that every laterally-to-norm continuous C-compact orthogonally additive operator T:X→Y from an atomless C-complete lattice-normed space X to a Banach space Y is narrow. As a non expecting consequence of the first main result we obtain necessary and sufficient conditions for a nonlinear superposition operator TN:E(X)→E(X) to be C-compact. We also show that the sum of two orthogonally additive operators G and T, where G is narrow and T is laterally-to-norm continuous and C-compact, is a narrow operator. In the last part of the article we investigate dominated orthogonally additive operators. In particular we show the narrowness of dominated operators taking values in a Banach sequence space Y or in a separable symmetric operator space CE.

Complete convergence for the maximal partial sums without maximal inequalities

This work provides the necessary and sufficient conditions for complete convergence for the maximal partial sums of dependent random variables. The results are proved without using maximal inequalities. The main theorems can be applied to sequences of (i) m-pairwise negatively dependent random variables and (ii) m-extended negatively dependent random variables. While the result for case (i) unifies and improves many existing ones, the result for case (ii) complements the main theorem of Chen et al. [J. Appl. Probab., 2010]. Affirmative answers to open questions raised by Chen et al. [J. Math. Anal. Appl., 2014], and Wu and Rosalsky [Glas. Mat. Ser. III, 2015] are also given. Two examples illustrating the sharpness of the main result are presented.

Experimental Monitoring of Dynamic Parameters of the Sub-Ballast Layers as a Prerequisite for a High-Quality and Sustainable Railway Line

Monitoring dynamic load transfer from train traffic to sub-ballast layers is crucial for verifying the reliability and safety of railway lines, assessing the design cost-effectiveness and achieving minimum environmental impact. For this purpose, measurements in labs, in situ or modeling the influence of dynamic loads on the immediate and long-term roadway quality are often performed using suitable software. The available test sections enabled monitoring of the dynamic loads and optimizing the critical spots where increased dynamic effects from railway traffic may occur. The subject of this paper is the calibration of the sensors installed in the different test sections of the trans-European corridor number V. As a result, the necessary input parameters for the subsequent numerical modeling of the dynamic effects on the track substructure and vibration propagation on the available sections of the upgraded railway line were obtained. The sensor calibration was carried out on the experimental field, part of the Experimental Basis of the Department of Railway Engineering and Track Management. As part of the calibration, the sensitivity of the sensors embedded in the track bed to the applied dynamic loads resulting from the impact effects of the lightweight deflectometer was assessed. The result of the calibration was the demonstration of sufficient sensitivity of the sensors and their suitability for implementation in an actual railway track structure, with the aim of obtaining relevant values of the response of the sub-ballast layers to dynamic loads and assessing the operational impacts on the sustainable environment. Also, the main result of the research was the possibility of using the theoretical–experimental route to optimize the layers of the railway body.

Post-abortion needs-based education via the WeChat platform to lessen fear and encourage effective contraception: a post-abortion care service intervention-controlled trial

ObjectiveOur study aims to investigate post-abortion needs-based education via the WeChat platform for women who had intended abortion in the first trimester, whether they are using effective contraception or becoming pregnant again.DesignThis single hospital intervention-controlled trial used a nearly 1:1 allocation ratio. Women who had intended abortions were randomly assigned to a Wechat group (needs-based education) and a control group (Traditional education). The women's ability to use effective contraception was the main result. Whether they unknowingly became pregnant again was the second result. Another result was patient anxiousness. Before and after education, women filled out questionnaires to assess their contraception methods and anxiety.MethodsBased on the theoretical framework of contraceptions of IBL (inquiry-based learning), post-abortion women were included in WeChat groups. We use WeChat Group Announcement, regularly sending health education information, one-on-one answers to questions, and consultation methods to explore the possibilities and advantages of WeChat health education for women after abortion. A knowledge paradigm for post-abortion health education was established: From November 2021 until December 2021, 180 women who had an unintended pregnancy and undergone an induced or medical abortion were recruited, their progress was tracked for four months, and the PAC service team monitored the women's speech, discussed and classified the speech entries and summarized the common post-abortion needs in 8 aspects. At least 2 research group members routinely extracted records and categorized the outcomes.ResultsBefore education, there were no appreciable variations between the two groups regarding sociodemographic characteristics, obstetrical conditions, abortion rates, or methods of contraception (P > 0.05). Following education, the WeChat group had a greater rate of effective contraception (63.0%) than the control group (28.6%), and their SAS score dropped statistically more than that of the control group (P < 0.05). Following the education, there were no unwanted pregnancies in the WeChat group, whereas there were 2 in the traditional PAC group. Only 5 participants in the WeChat group and 32 in the conventional PAC group reported mild anxiety after the education.

DYNAMICS OF PLASMA IN A DUAL-FREQUENCY CAPACITIVE DISCHARGE IN AN AR/XE MIXTURE

The spatiotemporal dynamics of the plasma of a symmetrical dual-frequency 81 MHz/1.76 MHz capacitive discharge under the in uence of a low-frequency eld of 1.76 MHz has been studied.Using the method of phase-resolved optical emission spectroscopy, the dynamics of the radiation intensity of argon and xenon in plasma was obtained.The electron energy distribution function at the center of the discharge was measured using a Langmuir probe and the electron density was measured using a microwave probe. The main result is the dynamics of the intensity ratios of the selected argon and xenon lines depending on di erent conditions: at pressures of 40, 200 and 400 mTorr, LF voltage amplitude of 100, 200 and 400 V, input power at 81 MHz of 3 W and 15 W. The dynamics of high-energy electrons is studied based on a two-temperature approximation of the electron energy distribution function.