Present Proof Research Articles

Dealing with Student Mistakes in Mathematics at Primary School

The article focuses on how teachers deal with student mistakes during mathematics instruction at primary school. The theoretical framework encompasses a constructivist culture of teaching and learning and dialogic teaching. Two general strategies are distinguished: avoiding mistakes and using mistakes as opportunities to learn. The presented qualitative study is based on 24 audio recordings of mathematics instruction, supplemented by interviews with six teachers. Through axial coding, we arrived at seven categories that describe specific ways of dealing with mistakes: not responding; making students aware of a mistake; encouraging students to present proofs; leading students to a level where they do not fail; expanding the student network of mathematical knowledge; creating opportunities for presenting content to clarify mistakes; and providing opportunities for students to find the cause of their mistakes. The findings are discussed in the context of the constructivist approach to instruction.

HERV-W ENV transcription in B cells predicting symptomatic COVID-19 and risk for long COVID can express a full-length protein despite stop codon in mRNA from chromosome X via a ribosome readthrough.

The human genome comprises 8% of endogenous retroviruses (HERVs). Though HERVS contribute to physiological functions, copies retained pathogenic potential. The HERV-W ENV protein was shown expressed in patients with worse COVID-19 symptoms and post-COVID syndrome. A significant detection of the mRNA encoding HERV-W ENV from patients with COVID-19 in B cells from RNAseq reads obtained from peripheral blond mononuclear cells. This data stratified with increased COVID-19 symptoms or with post-acute sequelae of COVID-19 (long COVID) after 3 months. The HERV-W ENV-U3R RNA was confirmed to display the best alignment with chromosome X ERVWE2 locus. However, a stop codon precluding its translation was re-addressed after recent understandings of ribosome readthrough mechanisms. Experimental results evidenced that this HERV gene can effectively express a full-length protein in the presence of molecules allowing translation via a readthrough mechanism at the ribosome level. Results not only confirm HERV-W ENV RNA origin in these patients but show for the first time how a defective HERV copy can be translated into a complete protein when specific factors make it possible at the ribosome level. The present proof of concept now requires further studies to identify the factors involved in this newly understood mechanism, following SARS-CoV-2 exposure.

Group incentive compatibility in a market with indivisible goods: A comment

We note that the proofs of Bird (1984), the first to show group strategy-proofness of top trading cycles (TTC), require correction. We provide a counterexample to a critical claim and present corrected proofs in the spirit of the originals. We also present a novel proof of strong group strategy-proofness using the corrected results.

ω-Groundedness of argumentation and completeness of grounded dialectical proof procedures

Dialectical proof procedures in assumption-based argumentation are in general sound but not complete with respect to both the credulous and skeptical semantics (due to non-terminating loops). This raises the question of whether we could describe exactly what such procedures compute. In a previous paper, we introduce infinite arguments to represent possibly non-terminating computations and present dialectical proof procedures that are both sound and complete with respect to the credulous semantics of assumption-based argumentation with infinite arguments. In this paper, we study whether and under what conditions dialectical proof procedures are both sound and complete with respect to the grounded semantics of assumption-based argumentation with infinite arguments. We introduce the class of ω-grounded and finitary-defensible argumentation frameworks and show that finitary assumption-based argumentation is ω-grounded and finitary-defensible. We then present dialectical procedures that are sound and complete wrt finitary assumption-based argumentation.

A novel Adomian natural decomposition method with convergence analysis of nonlinear time-fractional differential equations

ABSTRACT The objective of the current article is to use the Banach fixed point theorem to present proofs for the existence and uniqueness theorems for a nonlinear time-fractional differential equation, namely, the linear and nonlinear, homogeneous and nonhomogeneous time-fractional diffusion equations. In addition, we explore exact solutions to nonlinear time fractional partial differential equations using an effective method called the Adomian natural decomposition method (ANDM), which is a combination of the Adomian decomposition method (ADM) and the natural transform method (NTM). To demonstrate the effectiveness of the suggested scheme, three examples are provided along with graphs and numerical tables to support our work. The outcomes demonstrate how effortless and effective the ANDM is for addressing fractional partial differential equations in multi-dimensional spaces, some of which we examined in this study as special cases. AMS Classifications 34A08, 65P99, 49J15, 35R11, 26A33, 74G10.

From GTC to : Generating reset proof systems from cyclic proof systems

We consider cyclic proof systems in which derivations are graphs rather than trees. Such systems typically come with a condition that isolates which derivations are admitted as proofs, known as the soundness condition. This soundness condition frequently takes the form of either a global trace condition, a property dependent on all infinite paths in the proof-graph, or a reset condition, a ‘local’ condition depending on the simple cycles only which, as a result, is typically stable under more proof transformations.In this article we present a general method for constructing cyclic proof systems with reset conditions from systems with global trace conditions. In contrast to previous approaches, this method of generation is entirely independent of logic's semantics, only relying on combinatorial aspects of the notion of ‘trace’ and ‘progress’. We apply this method to present reset proof systems for three cyclic proof systems from the literature: cyclic arithmetic, cyclic Gödel's T and cyclic tableaux for the modal μ-calculus.

Study of cyclic codes from low differentially uniform functions and its consequences

Cyclic codes have many applications in consumer electronics, communication and data storage systems due to their efficient encoding and decoding algorithms. An efficient approach to constructing cyclic codes is the sequence approach. In their articles (Ding and Zhou 2014 [11]) and (Ding, 2013 [7]), Ding and Zhou constructed several classes of cyclic codes from almost perfect nonlinear (APN) functions and planar functions over finite fields and presented some open problems on cyclic codes from highly nonlinear functions. This article focuses on these exciting works by investigating new insights in this research direction. Specifically, its objective is twofold. The first is to provide a complement with some former results and present correct proofs and statements on some known ones on the cyclic codes from the APN functions. The second is studying the cyclic codes from some known functions processing low differential uniformity. Along with this article, we shall answer some open problems presented in the literature. The first concerns Open Problem 1, proposed by Ding and Zhou (2014) [11]. The others are Open Problems 5.16 and 5.25, raised by Ding (2013) [7].

Spectral exponent assessment and neurofilament light chain: a comprehensive approach to describe recovery patterns in stroke.

Understanding the residual recovery potential in stroke patients is crucial for tailoring effective neurorehabilitation programs. We propose using EEG and plasmatic Neurofilament light chain (NfL) levels as a model to depict longitudinal patterns of stroke recovery. We enrolled 13 patients (4 female, mean age 74.7 ± 8.8) who underwent stroke in the previous month and were hospitalized for 2-months rehabilitation. Patients underwent blood withdrawal, clinical evaluation and high-definition EEG at T1 (first week of rehabilitation) and at T2 (53 ± 10 days after). We assessed the levels of NfL and we analyzed the EEG signal extracting Spectral Exponent (SE) values. We compared our variables between the two timepoint and between cortical and non-cortical strokes. We found a significant difference in the symmetry of SE values between cortical and non-cortical stroke at both T1 (p = 0.005) and T2 (p = 0.01). SE in the affected hemisphere showed significantly steeper values at T1 when compared with T2 (p = 0.001). EEG measures were consistently related to clinical scores, while NfL at T1 was related to the volume of ischemic lesions (r = 0.75; p = 0.003). Additionally, the combined use of NfL and SE indicated varying trends in longitudinal clinical recovery. We present proof of concept of a promising approach for the characterization of different recovery patterns in stroke patients.

A control theoretic framework for adaptive gradient optimizers

Gradient-based optimization and control frameworks have been utilized in several applications. The learning rate parameter is typically chosen following a schedule or using methods such as line search to enhance the convergence rate. Recently, the machine learning community has developed methodologies for automated tuning of the learning rate, known as adaptive gradient methods. This paper develops a control theory-inspired framework for modeling adaptive gradient methods that solve non-convex optimization problems. We first model the adaptive gradient methods in a state–space framework, which allows us to present simpler convergence proofs of prominent adaptive optimizers, such as AdaGrad, Adam, and AdaBelief. The proposed framework is constructive because it allows synthesizing new adaptive optimizers. To illustrate this fact, we then utilize the transfer function paradigm from classical control to propose a new variant of Adam, coined AdamSSM, and prove its convergence. We add an appropriate pole-zero pair in the transfer function from squared gradients to the second moment estimate. Applications on benchmark machine learning tasks of image classification using CNN architectures and language modeling using LSTM architecture demonstrate that the AdamSSM algorithm improves the gap between generalization accuracy and faster convergence than the recent adaptive gradient methods.

Measures of contextuality in cyclic systems and the negative probabilities measure CNT3.

Several principled measures of contextuality have been proposed for general systems of random variables (i.e. inconsistently connected systems). One such measure is based on quasi-couplings using negative probabilities (here denoted by [Formula: see text], Dzhafarov & Kujala, 2016 Quantum interaction). Dzhafarov & Kujala (Dzhafarov & Kujala 2019 Phil. Trans. R. Soc. A 377, 20190149. (doi:10.1098/rsta.2019.0149)) introduced a measure of contextuality, [Formula: see text], that naturally generalizes to a measure of non-contextuality. Dzhafarov & Kujala (Dzhafarov & Kujala 2019 Phil. Trans. R. Soc. A 377, 20190149. (doi:10.1098/rsta.2019.0149)) additionally conjectured that in the class of cyclic systems these two measures are proportional. Here we prove that conjecture is correct. Recently, Cervantes (Cervantes 2023 J. Math. Psychol. 112, 102726. (doi:10.1016/j.jmp.2022.102726)) showed the proportionality of [Formula: see text] and the Contextual Fraction measure introduced by Abramsky & Brandenburger (Abramsky & Brandenburger 2011 New J. Phys. 13, 113036. (doi:10.1088/1367-2630/13/11/113036)). The present proof completes the description of the interrelations of all contextuality measures proposed within or translated into the Contextuality-by-Default framework so far as they pertain to cyclic systems. This article is part of the theme issue 'Quantum contextuality, causality and freedom of choice'.

A New Approach to the Existence of Best Proximity Points With R‐Functions in the Framework of w‐Distances

In this paper, we present a new approach to check the existence of best proximity points for R‐proximal contractions in the framework of metric spaces equipped with a w0‐distance and present elementary proofs of recent results by using the corresponding fixed point problems without the continuity assumption of the considered self‐mapping. We also discuss on cyclic Geraghty contractions and resolve the problem of the existence and convergence of the best proximity point for such a class of mappings.

Anthelmintic Activity of Ethanolic and Aqueous Extracts of Khaya grandifoliola Stem Bark against Heligmosomoides polygyrus: In Vitro and In Silico Approaches.

Parasitic infection remains a serious health trade for humans and livestock. The purpose of this study was to present scientific proof of the anthelmintic properties of Khaya grandifoliola, which the native population uses to cure helminthiasis. Fresh Heligmosomoides polygyrus eggs were isolated from faecal samples of experimentally infected mice. The faecal material was cultured, and L1 and L2 larval stages were recovered after 48 and 120 hours, respectively. Using the worm microtracker, the anthelminthic efficacy of the extracts against H. polygyrus was assessed. Two different extracts (aqueous and ethanol extracts) were prepared. For the ovicidal and larvicidal activities, 100 µL of various concentrations of plant extracts, levamisole and 1.5% dimethyl sulfoxide (DMSO), were introduced into a 96-well microplate titer followed by the addition of 100 µL of embryonated eggs (60 eggs) for the ovicidal activity and 100 µL of L 1 or L 2 larvae (50 larvae) for the larvicidal activity. The movement of the worm was monitored for 24 hours in the worm microtracker at 27°C. The Glide module of the Schrodinger Maestro software was used to perform docking studies. For the aqueous extracts, the highest percentage of inhibition of hatching was 42.77 ± 12% at 7.5 mg/mL. The IC50 values for the ethanol (0.36 mg/mL) extract showed that the ethanol extract had a good inhibitory effect on the ability of parasites to hatch from eggs. The inhibition percentage of L1 larvae motility at 7.5 mg/mL was 98.0 ± 1.66% and 83.33 ± 1.66% for ethanol and aqueous extracts, respectively. The negative controls, distilled water and 1.5% DMSO, had no inhibitory impact on larvae. On L1-larvae, the drug of choice levamisole (positive control) had the highest percentage effect (100.0%). Six compounds had the highest docking score and their interactions with the receptor as well. Grandiamide A interacts most with tyrosine, glycine, phenylalanine, asparagine, and serine, and its benzene ring and oxygens inhibit these receptors. Carbonyl and hydroxyl (OH) groups connect grandiamide D to asparagine, isoleucine, and phenylalanine, respectively. By donating hydrogen to the receptor through OH groups, D-glucopyranose-6-phosphate also forms relatively strong hydrogen bonds with its oxygen-bound phosphorus and the receptor. 1-O-deacetylkhayanolide E interacts most with serine and glutamic acid. The carbamic acid benzyl ester of carbamic acid [(1S)-1-phenyl-2-[(4-methylphenyl) sulfinyl] ethyl] interacts most with the receptor with carbonyl groups and with asparagine and serine. With its abundant hydroxide, D-mannitol acts as a hydrogen donor and acceptor and interacts most strongly with amino acids such as glycine, asparagine, aspartic acid, alanine, and glutamic acid. K. grandifoliola extracts possess anthelminthic properties. However, in vivo studies are still necessary to demonstrate the effectiveness of this plant for the treatment of helminthiasis.

In Situ Capture and Real-Time Enrichment of Marine Chemical Diversity.

Analyzing the chemical composition of seawater to understand its influence on ecosystem functions is a long-lasting challenge due to the inherent complexity and dynamic nature of marine environments. Describing the intricate chemistry of seawater requires optimal in situ sampling. Here is presented a novel underwater hand-held solid-phase extraction device, I-SMEL (In Situ Marine moleculELogger), which aims to concentrate diluted molecules from large volumes of seawater in a delimited zone targeting keystone benthic species. Marine benthic holobionts, such as sponges, can impact the chemical composition of their surroundings possibly through the production and release of their specialized metabolites, hence termed exometabolites (EMs). I-SMEL was deployed in a sponge-dominated Mediterranean ecosystem at a 15 m depth. Untargeted MS-based metabolomics was performed on enriched EM extracts and showed (1) the chemical diversity of enriched seawater metabolites and (2) reproducible recovery and enrichment of specialized sponge EMs such as aerothionin, demethylfurospongin-4, and longamide B methyl ester. These EMs constitute the chemical identity of each targeted species: Aplysina cavernicola, Spongia officinalis, and Agelas oroides, respectively. I-SMEL concentrated sponge EMs from 10 L of water in a 10 min sampling time. The present proof of concept with I-SMEL opens new research perspectives in marine chemical ecology and sets the stage for further sustainable efforts in natural product chemistry.

A Prussian-blue analogue (PBA) ion-chromatography-based technique for selective separation of Rb+ (as RbCl) from brines

A new general method is presented for separating pure RbCl(s) from solutions rich in Na+ and K+. The method relies on Rb+ adsorption via ion exchange performed by self-synthesized PES coated Zn-Hexa-Cyanoferrate material. The procedure starts by passing the wastewater through an ion exchange column, which is thereafter regenerated with 1 M NH4Cl. If the Rb+ absorbed on the column does not reach a minimal predetermined value (e.g., 8%, eq-based), the ammonia is removed by sublimation and the remaining salts are passed again through a Na+-preadsorbed column. Once the adsorbed Rb+ is substantial (>8%), a chromatography-based separation between Rb+ and Na+/K+ is performed, using a 2nd column, fully pre-adsorbed with NH4+. First, 0.05M NH4+-solution is used to extract Na+ and K+ out of the first column, along with a small Rb+ mass, which is thereafter partly re-adsorbed on the second column, while Na+/K+ ions are not. Once the exiting eluent solution is devoid of the competing ions, 1M NH4+-solution is used to extract all the remaining Rb+ into the regeneration solution, which is thereafter subjected to water evaporation followed by NH3/HCl sublimation to result in pure RbCl(s) product. We used theoretical simulations corroborated by empirical results to present proof of concept for the suggested approach. A detailed cost analysis (Capex and Opex) reveals that the RbCl(s) production cost does not exceed ∼25% of the current salt price.

Cantorův diagonální důkaz

Cantor's diagonal proof is sig­nificant both because the central method of proof used in it has been subsequently applied in a number of other proofs, and because it is considered to confirm the existence of infinite sets whose size fun­ damentally and by an order of magnitude exceeds the size of the "classical" infinite set represented by all natural numbers, while their size can theoretically exceed every conceivable limit. Although Can­tor's proof is generally accepted by the scientific community, some experts are somewhat reserved about it. The aim of this paper is to present Cantor's proof in an accessible way, while pointing out its (hidden) assumptions and possible problematic points, and pointing out that some of its underlying assumptions are not indisputable mathematical truths, but rather postulated propositions that may or may not be accepted.

Distributed Predefined-Time Secondary Frequency and Average Voltage Control for Islanded AC Microgrids

The frequency and voltage restoration along with power sharing is imperative for the safe, reliable and stable operation of the islanded AC microgrids (MGs). In this paper, a novel distributed fractional-order predefined-time sliding mode controller (DFOPTSMC) is proposed as a secondary controller for the islanded AC MGs. The proposed DFOPTSMC can ensure that frequency and estimated average voltage (EAV) converge to reference value along with accurate power sharing within a setting predefined time. The fractional calculus algorithm is implemented to design the DFOPTSMC, which increases the degree of freedom of parameter adjustment and greatly enhances the flexibility of the DFOPTSMC. In addition, a distributed predefined-time observer is presented to achieve the EAV within a setting predefined time. The upper bound convergence time of the islanded AC MGs under the proposed DFOPTSMC is directly equal to a tunable parameter, thus overcoming the disadvantages of finite-time control and fixed-time control. The Lyapunov function is applied to present rigorous proof to analyze the stability of the islanded AC MGs under the proposed DFOPTSMC. An islanded AC MG is taken into simulation on the Matlab/Simulink 2021a platform and the experimental platform to test and verify the effectiveness and superior performance of the proposed DFOPTSMC. The results indicate that the proposed DFOPTSMC can significantly enhance the dynamic performances of the islanded AC MGs.

Proof of concept of intracochlear drug administration by laser-assisted bioprinting in mice

Transtympanic administration is used clinically for the injection of gentamicin and/or corticosteroids. This atraumatic route is based on passive diffusion through the round window membrane (RWM). The main limitation of this method is related to the clearance through the Eustachian tube, making the concentration of the therapeutic agent at the intracochlear level uncertain and limited. Moreover, this technique remains unsuitable for molecules of high molecular weight or in the case of gene therapies. The purpose was to study a new technique of intracochlear administration in an atraumatic, direct and controlled manner by laser-assisted bioprinting (LAB). LAB was used to deliver dexamethasone phosphate with thermosensitive hydrogel on the mouse RWM. After validation of the regularity and homogeneity of the pattern, the diffusion in vivo of the dexamethasone into the perilymph after LAB has been confirmed by ELISA. Auditory function measurements showed no hearing impairment suggesting that bioprinting does not induce significant cochlear damage. Hence, the present proof of concept study introduces a promising approach for inner ear drug delivery.

Single and multiple illuminant estimation using convex functions

The lighting situation in which a picture was taken has an impact on its color. Illuminant estimation is crucial in computer vision because the colors of objects vary as illumination changes. For this reason, numerous methods for estimating the illuminant have been suggested. In this paper, we suggest a novel statistic-based method for estimating single and multiple illuminants using convex functions. In this respect, convex functions are used in the two subsequent steps of normalization and weight creation. After using weighted K-means to segment the picture, each segment’s associated illuminations are determined. The illumination map for the input image is estimated as a final stage. In this study, we also analyze the effect of convexity on color constancy algorithms and present proofs for the convexity of some statistic-based algorithms. Four different single and multi-illuminant datasets have been used to evaluate the proposed algorithm in terms of two evaluation metrics; recovery and reproduction angular error. We believe that the proposed method could be considered one of the statistical state-of-the-art algorithms. In addition, it has competitive results when compared to most learning-based and deep-learning methods. Further advantages of the proposed algorithm include its simplicity of implementation and low execution time.

The Meaning of Proofs: Mathematics as Storytelling by Gabriele Lolli

Reviewed by: The Meaning of Proofs: Mathematics as Storytelling by Gabriele Lolli Firdous Ahmad Mala GABRIELE LOLLI The Meaning of Proofs: Mathematics as Storytelling Trans. Bonnie McClellan-Broussard. Cambridge, Massachusetts. MIT Press. 2022. 176 pages. MATHEMATICS HAS BEEN FEARED by many and loved by some for its rigor, symbolism, and brevity. Literature on mathematics abounds with technical, biographical, historical, and recreational titles. This book, The Meaning of Proofs: Mathematics as Storytelling, is not about such things, however. It attempts to present mathematical proofs as forms of narrative. It is a philosophical rumination on why mathematical proofs are expressed the way they are. The purpose of the book, as singled out in the preface, is to convince the reader of the idea that a natural way to conceive and understand a proof is to present and see it as a narrative. However, by presenting mathematical proofs as narratives, one must not mistake that to understand a proof, it is essential to know the biographical details of the one who came up with it. Narrating a piece in mathematics does not involve summarizing what is known about it, nor does it involve an account of the lives of mathematicians or logicians. In essence, it means bringing to the discussion the content and subject matter of that piece in mathematics. The concepts of limits in calculus and the one-to-one correspondence between the whole numbers and natural numbers in set theory are best understood through stories such as Zeno's paradox and Hilbert's grand hotel. These are essentially narratives brought about to bring the notions of limits, bijections, and infinite sets home to readers and students. Narratives have not only been relevant but also instrumental in shaping the pedagogy of mathematics. As a matter of fact, mathematics education, a branch of applied mathematics, aims at a deliberate and extensive use of such narratives to realize its objectives. The book is not aimed at an only-mathematical audience, rather it envisages to address any intellectually curious one. The employment of literature as a proxy for mathematics is a beautiful idea aimed at making it evident that the two subjects are not, in reality, as different as many people think. This idea is, in fact, gaining unprecedented impetus in the form of publications such as this one and Statistical Universals of Language (2021), by Kumiko Tanaka-Ishii, which aims to make the statement that language has a lot more in common with statistics than we realize. Interestingly, the author shows how, contrary to the common belief, metaphors and images pervade the literature of mathematical proofs. In mathematical proofs, visual diagrams and mechanical devices serve a twofold purpose. On one hand, they bring to the fore how narrative tools were viewed in ancient times; and on the other, they are pivotal in the context of contemporary research on automated theorem-proving that attempts to prove theorems in mathematics using computer programs. If mathematics is confined to its symbols and diagrams, it is difficult to listen to it. However, if it is presented as narratives, it is likely to attract more of an audience and have a wider reach. Then, it is also very likely to be embraced with open arms and be held dearer. This book analyzes the narrative of proofs at two levels—the grand and the individual. The grand narratives influence the ramifications of the subject over a considerably long period of time and are brought about, usually, by a large number of authors and papers. A case in point is Klein's Erlangen program, in 1872, that advocated the study of mathematical objects in terms of their symmetries and transformations. This idea soon became the talk of the town in both modern mathematics and theoretical physics. The individual narratives include specific papers highlighting proofs that are written as narratives unique in style and presentation. Concerning the individual narratives, the book analyzes how some individual proofs are modeled on ancient Greek composition forms. As Bruce Springsteen once said, stories save lives. To him, writers tell stories with the aim of saving themselves. It has been critically observed that the ideas expressed in mathematical proofs are common to all [End Page 88] humans...

A developed eagle-strategy supply-demand optimizer for solving economic load dispatch problems

This article proposes a new effective technique, named eagle-strategy supply–demand based optimization algorithm with chaotic (ESCSDO), for achieving global solutions to economic load dispatch (ELD) problems in power systems. This improvement is suggested to enhance the population diversity, the balance between local and global search, and the premature convergence of the original supply–demand based optimization (SDO) algorithm. The proposed ESCSDO algorithm benefits from a strategy named eagle strategy (ES) search strategy with ten chaotic maps. The efficacy of the ESCSDO technique is tested on 23 benchmark functions. Also, the robustness of the ESCSDO algorithm to find precise results in various aspects is examined and proven on ELD problems including four cases, 6, 13, 15, and 40-unit test systems. Finally, the obtained results using the proposed technique are compared with the those obtained by several well-known techniques and results reported in the previous literature. The simulation results present proof of the efficacious performance of the proposed ESCSDO technique in solving great diversity of ELD problems.