Unsolvable Problems Research Articles

Kernels, data & physics

Abstract Lecture notes from the course given by Professor Julia Kempe at the summer school ‘Statistical physics of Machine Learning’ in Les Houches. The notes discuss the so-called NTK approach to problems in machine learning, which consists of gaining an understanding of generally unsolvable problems by finding a tractable kernel formulation. The notes are mainly focused on practical applications such as data distillation and adversarial robustness, examples of inductive bias are also discussed.

Issues of social justice in the development of personalised therapy for paediatric SIRS patients

Abstract Background Systemic Inflammatory Response Syndrome (SIRS) is an often-emergent condition, which lacks specific diagnostic tools. Personalised therapy could fill this gap but as every new technology, it raises issues of social justice. Our report aims at identification and analysis of social justice implications within the bigger ERA PerMed funded project of development of tailored immunotherapy for paediatric SIRS patients (TIPS) coordinated by Prof. Catharina Schütz from Technic University Dresden. Methods Qualitative research methodology thought 10 semi-structured interviews. Systematic literature review grounded the interview questionnaire. Transcripts were subjected to thematic analysis by two independent researchers. Results Social justice was seen as equal chances of inclusion of different population groups in research. Socioeconomic differences were perceived as a challenge to ensure justice across various populations (N = 7). Two interviewees saw discrimination as inherent to precision medicine, which is focused on personalised treatment. Two experts viewed the exclusion of specific patients’ groups as an unsolvable problem, that only advocates for the inclusion of as many patients as possible. On the opinion of six experts individual and ethnocultural factors may influence outcomes in personalised treatment, especially considering the small sample size and the diverse populations. One medical expert, on the contrary, perceived no significant challenges associated with the heterogeneity of patients. Whether socioeconomic injustices should be addressed by guidelines and how these correspond to the rights of the patient were further discussed. Conclusions The issues of social justice accompany research in personalised medicine, including SIRS. In general, there is sensitivity to this issue, but current guidelines are too vague. As with other ethical problems, so with social justice we seem to have a rethinking of the concept, that needs further study. Key messages • In the context of SIRS personalised therapy research, there is a sensitivity to the issue of social justice, but no consensus how to ensure it. • Issues of social justice are often boiled down to equal chances of inclusion in research and equal access to treatment. In the case of personalised therapy, there seems to be more to it.

Uncloneable Quantum Advice

The famous no-cloning principle has been shown recently to enable a number of uncloneable cryptographic primitives, including the copy-protection of certain functionalities. Here we address for the first time unkeyed quantum uncloneablity, via the study of a complexity-theoretic tool that enables a computation, but that is natively unkeyed: quantum advice. Remarkably, this is an application of the no-cloning principle in a context where the quantum states of interest are not chosen by a random process. We establish unconditional constructions for promise problems admitting uncloneable quantum advice and, assuming the feasibility of quantum copy-protecting certain functions, for languages with uncloneable advice. Along the way, we note that state complexity classes, introduced by Rosenthal and Yuen (ITCS 2022) — which concern the computational difficulty of synthesizing sequences of quantum states — can be naturally generalized to obtain state cloning complexity classes. We make initial observations on these classes, notably obtaining a result analogous to the existence of undecidable problems. Our proof technique defines and constructs ingenerable sequences of finite bit strings, essentially meaning that they cannot be generated by any uniform circuit family with non-negligible probability. We then prove a generic result showing that the difficulty of accomplishing a computational task on uniformly random inputs implies its difficulty on any fixed, ingenerable sequence. We use this result to derandomize quantum cryptographic games that relate to cloning, and then incorporate a result of Kundu and Tan (arXiv 2022) to obtain uncloneable advice. Applying this two-step process to a monogamy-of-entanglement game yields a promise problem with uncloneable advice, and applying it to the quantum copy-protection of pseudorandom functions with super-logarithmic output lengths yields a language with uncloneable advice.

Environmental noise protection problems of Hungary's old heavy industrial areas

Hungary's first domestic environmental noise regulation entered into force in 1984. Several heavy industrial areas operate in the country, which were established in the first half of the last century or in the decades following the Second World War. During this period, aspects of environmental noise protection were not yet considered. These heavy industry plants are usually located in huge industrial areas, operate thousands of diverse technological equipment and still remain significant factors of the Hungarian national economy. The reason for the development of the environmental noise problem is that during the intensive socialist industrialization, to satisfy the huge demand for labor, they developed residential areas around the industrial areas. This led to a situation, when environmental noise protection legislation came into force, these heavy industry plants found themselves in violation without any changes in their operations. The plants implemented noise reductions and attempted to comply with the limits, but mostly with little success. This presented an unsolvable problem to the plants, the authorities, and the residents too. The solution to the problem is the introduction of regulations on the designated highly noisy areas and several additional measures, following the international practice of designating noise protection zones.

The Hermite-Birkhoff Problem and Local Spline Approximation

This paper discusses the use of local spline approximations to solve the Hermite-Birkhoff problem. The solution to a specific problem using polynomial and non-polynomial local splines of the third order of approximation is considered. Here we discuss the case when the values of the function 𝑢(𝑥) and its derivative 𝑢’(𝑥) are given at the nodes of the grid in an alternative way: … , 𝑢(𝑥𝑗), 𝑢′(𝑥𝑗+1), 𝑢(𝑥𝑗+2), … . Note that when using polynomial and non-polynomial spline approximations, it is possible to obtain acceptable solutions in several interesting cases that are impossible when we use the classical approach. In the case of using local basis splines, many previously unsolvable problems turn out to be solvable. The results of the numerical experiments are presented.

Counting vanishing matrix-vector products

Consider the following parameterized counting variation of the classic subset sum problem, which arises notably in the context of higher homotopy groups of topological spaces. Let v∈Qd be a rational vector, (T1,T2…,Tm) a list of d×d rational matrices, S∈Qh×d a rational matrix not necessarily square and k a parameter. The goal is to compute the number of ways one can choose k matrices Ti1,Ti2,…,Tik from the list such that STik⋯Ti1v=0∈Qh.In this paper, we show that this problem is #W[2]-hard for parameter k. As a consequence, computing the k-th homotopy group of a d-dimensional 1-connected topological space for d>3 is #W[2]-hard for parameter k. We also discuss a decision version of the problem and its several modifications for which we show W[1]/W[2]-hardness. This is in contrast to the parameterized k-sum problem, which is only W[1]-hard (Abboud-Lewi-Williams, ESA'14). In addition, we show that the decision version of the problem without parameter is an undecidable problem, and we give a fixed-parameter tractable algorithm for matrices of bounded size over finite fields, parameterized by the matrix dimensions and the order of the field.

A Commentary. Another Unsolvable Problem and Axiom of Biology: It Is Impossible to Deduce Cell Properties in an Organism from the Properties of Its Constituent Cells

A Commentary. Another Unsolvable Problem and Axiom of Biology: It Is Impossible to Deduce Cell Properties in an Organism from the Properties of Its Constituent Cells

Asymptomatic Cholecystitis Presents a New Challenge for Correcting Treatment Tactics in Patients with Gallstone Disease Rather Than Being an Unsolvable Problem of Biliary Surgery

Gallbladder stones, or cholelithiasis, represent a significant public health concern, particularly in Russia, with an incidence of 5-6 per 1,000 people annually. Western countries report a prevalence of 10%-20%, which has nearly tripled in the last three decades due to advancements in diagnostic techniques. Notably, the condition disproportionately affects women and the elderly, with a marked increase in prevalence after the age of 70. Approximately 80% of cases are asymptomatic, and the clinical manifestations develop in only 1-4% of patients annually. Despite the rising identification of asymptomatic cases through enhanced imaging, management strategies remain unclear, leading to hesitancy among surgeons regarding surgical intervention. Current guidelines from various national and international bodies, including NICE and ESGE, advocate for a watch-and-wait approach for asymptomatic patients, citing spontaneous stone clearance. However, the treatment of asymptomatic choledocholithiasis remains contentious, with some guidelines supporting intervention. This ambiguity is compounded by the recognition that complications can arise from unnecessary cholecystectomy, with 10-40% of patients experiencing ongoing symptoms post-surgery. The article emphasizes the need for a comprehensive understanding of asymptomatic cholecystitis, advocating for a meticulous diagnostic approach that considers the potential underlying causes of gallstone formation. The lack of consensus in current literature regarding management strategies highlights the necessity for further research into the natural history of asymptomatic gallstones and the implications of various treatment options. By addressing these complexities, clinicians can enhance patient outcomes and reduce the incidence of post-cholecystectomy syndrome, ultimately leading to more individualized and effective management strategies for patients with asymptomatic cholecystitis.

Able and willing: Infants selectively seek help from competent and benevolent others.

Young children often encounter unsolvable problems with which they require others' help. To receive adequate assistance, children must be savvy about whom they seek help from: Effective helpers must possess both the ability to help (e.g., competence) and a willingness to do so (e.g., benevolence). Although past work suggests that information about competence and benevolence can inform young children's help-seeking behavior, it remains unclear how and whether children utilize said factors independently of each other. Furthermore, it is unclear whether they can generalize potential helpers' competence from one task to another. The current experiments examined whether 22- to 23-month-olds confronted with a broken toy selectively sought help from agents who had previously demonstrated either competence (Experiment 1) or benevolence (Experiment 2). In Experiment 1, infants preferred to seek help from a competent agent who successfully opened a closed box over one who failed to do so. In Experiment 2, infants selectively sought help from a benevolent agent who helped a third party by returning a lost ball, over an agent who stole the ball instead. These patterns of selectivity were not driven by associative valence matching; in Experiment 3, infants showed no preference for an agent who was itself helped versus an agent who was hindered. These results suggest that before their second birthday, infants independently utilize cues to both competence and benevolence to inform their help seeking, using information generalized from novel contexts. We discuss the potential nature of this generalization as well as directions for future work. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Certified algorithms for equilibrium states of local quantum Hamiltonians

Predicting observables in equilibrium states is a central yet notoriously hard question in quantum many-body systems. In the physically relevant thermodynamic limit, certain mathematical formulations of this task have even been shown to result in undecidable problems. Using a finite-size scaling of algorithms devised for finite systems often fails due to the lack of certified convergence bounds for this limit. In this work, we design certified algorithms for computing expectation values of observables in the equilibrium states of local quantum Hamiltonians, both at zero and positive temperature. Importantly, our algorithms output rigorous lower and upper bounds on these values. This allows us to show that expectation values of local observables can be approximated in finite time, contrasting related undecidability results. When the Hamiltonian is commuting on a 2-dimensional lattice, we prove fast convergence of the hierarchy at high temperature and as a result for a desired precision ε, local observables can be approximated by a convex optimization program of quasi-polynomial size in 1/ε.

Covert Communications in Active-RIS-Aided NOMA Systems: Element Grouping or Not?

This paper investigates the impacts of element grouping on the covert communication performance of an active reconfigurable intelligent surface (ARIS)-aided uplink non-orthogonal multiple access (NOMA) system. Through element grouping, each element of the ARIS works in either the reflecting mode to reflect the information signal or the jamming mode to generate a jamming signal. Optimizing the NOMA transmit power, ARIS beamforming, and receive beamforming jointly is necessary to maximize the covert communication rate. To tackle the unsolvable covert communication rate maximization problem, we decouple the original problem into three sub-problems of optimizing the NOMA transmit power, ARIS beamforming, and receive beamforming, respectively. To tackle the mixed-integer non-linear programming for the element grouping, we introduce the arithmetic- and geometric-mean-based penalty term and apply the Dinkelbach transform to reformulate the optimization problem. Next, we propose an alternating optimization algorithm to optimize the system parameters. The numerical results demonstrate the effectiveness of the element grouping in improving the covert communication rate. However, the element grouping scheme achieves a lower covert communication rate performance compared to the scheme without element grouping, indicating that using element grouping for covert communications in the ARIS-aided uplink NOMA system is not the preferred option.

Behavior, long-term stress and relationship to owner in relinquished dogs

Dog ownership gained popularity during the pandemic. However, there was also a corresponding increase in the number of dogs being relinquished and rehomed. The rehoming procedure is known to be stressful to the dog, but the short- and long-term effects still need to be better understood. This study aimed to enhance our understanding of the short- and long-term challenges dogs encounter during the rehoming process by combining behavioral and physiological measures. The study included 20 relinquished dogs from a Swedish shelter and 30 rehomed dogs, comparing them to 33 control dogs that have been with their owner since leaving the breeder as puppies. All participants performed an unsolvable problem task, eye-contact test, and memory test and hair samples were obtained to analyze cortisol concentrations. Furthermore, dog owners (of rehomed and control dogs) completed a questionnaire assessing their perceived human-dog relationship. These owner-dog dyads also participated in a behavioral synchronization test. The result indicated that shelter dogs had the shortest eye-contact duration in both an eye-contact test and an unsolvable problem task, but there was no difference between the three groups in the short-term memory test or in stress-related behaviors. Analysis of hair cortisol concentrations in the dogs revealed that the shelter dogs had higher long-term stress levels than rehomed dogs, but they did not differ significantly from control dogs. Both rehomed and control dogs synchronized their behavior with their owner, but, interestingly, the owners of rehomed dogs reported a higher emotional closeness to their dogs than owners of control dogs. Consequently, despite the observed short-term effects during the rehoming procedure, this study suggests that rehomed dogs can adapt to their new life and develop a strong relationship with their owner.

High Rates of Honey Bee Colony Losses and Regional Variability in Ethiopia Based on the Standardised COLOSS 2023 Survey.

The COLOSS research association has been assessing honey bee colony losses, associated risk factors and management, focusing on Western countries but with a progressive international expansion. Here, we report the first survey on the loss rates of colonies in 2022/2023 in Ethiopia using COLOSS monitoring survey tools. A face-to-face interview questionnaire survey was conducted on 64 beekeepers selected from Oromia and Tigray regions. This covered 1713 honey bee colonies distributed in 68 apiaries. The percentages of colonies lost were significantly different between Oromia (24.1%) and Tigray (66.4%) regions. Colony losses were attributed as unsolvable queen problems (8% in Oromia; 10% in Tigray), natural disaster (32%; 82%), and empty hives or dead colonies (60%; 8%). The loss rate was significantly affected by queen replacement (p < 0.0001), use of natural comb (p < 0.0001), feed supplementation (p < 0.0001), region (p < 0.0001), varroa treatment (p < 0.0001), colony splitting (p < 0.01), and merging (p < 0.01). Beekeepers in Oromia managed more colonies and implemented improved practices compared to those in Tigray. However, all beekeepers in Oromia detected at least some bees with signs of deformed wing virus, compared to 76% of beekeepers in Tigray. In conclusion, the colony loss rate was significantly different between Oromia and Tigray regions due to differences in natural disasters, management, environment and health factors.

A simple undecidable problem for free groups

Let Fn denote the free group on n generators. It is shown to be undecidable for two morphisms g,h:Fn→F2 and a generator element a of F2, whether or not there exists an element w∈Fn such that g(w)=a and h(w)=1, where 1 is the identity element.

An optimal energy efficient routing in WSN using adaptive entropy bald eagle search optimization and density based adaptive soft clustering

Wireless Sensor Network (WSN) uses soft computing techniques to reduce task time consuming and unsolvable energy consumption problems. This study used soft-computing-based methods to demonstrate the best data transfer in WSN. Nodes in a network are initially clustered using density-based Adaptive Soft (DAS) clustering. Afterward, the cluster head (CH) is selected using a modified beetle swarm optimization technique. Distance, energy, trust, and throughput are all considered when deciding on the ideal CH. The node with the highest entropy for data transmission is then determined by calculating each node’s entropy weight values based on these factors. The CH carries out the data aggregation after the data collection from the sensor nodes. Finally, entropy value based bald eagle search (EBES) optimization with an adaptive entropy value is used to perform the finest energy efficient routing, a strategy for the best possible data transmission. The proposed approach attains improved performance than the compared existing approaches in terms of delay (6.5 ms), throughput (320.1 kbps), energy (1.92j), and packet delivery ratio (218.7%), the work provided is contrasted to the various current methods. The performance of the proposed approach is compared to existing approaches to prove its effectiveness, and it has been proven to perform better than the existing routing approaches.

Autonomous Marine Vehicle Operations

The world has witnessed the rapid development of autonomous marine vehicles,such as surface vehicles and underwater vehicles, which have created fruitful innovative approaches to previously unsolvable problems in marine and ocean engineering [...]

THE TWO LETTERS W.H. IN THE DEDICATION TO W. SHAKESPEARE’S SONNETS AND THE CUMULATIVE EFFECT OF DIRECT AND CIRCUMSTANTIAL EVIDENCE IN SHAKESPEAROLOGY

William Shakespeare’s works had been written more than 4 centuries ago; since then scholars had enough time to subject his texts and the facts of his biography to the interpretations which are so numerous and so diversified that many Shakespearologists have come to believe that it is simply impossible to give indisputable answers to quite a number of highly significant questions. To these unsolvable problems one might attribute the identification of the addressee of Shakespeare’s sonnets and of Mr W.H. who is mentioned in the dedication to these poetic texts. Syntactically the text of the dedication may be interpreted either as one sentence with “Mr W.H.” acting in the capacity of an indirect object or as a subject in the first of the two independent clauses. The choice of either of these two variants of reading (in the article the second variant is accepted as the only possible one) influences the direction of the further discussion of the sonnets. The article is aimed at showing that through studying the literary texts by Shakespeare and his contemporaries and through closely analyzing the relevant direct and circumstantial evidence one may arrive at the inherently sound and noncontroversial interpretations of Shakespeare’s life and work. When applied to Shakespeare’s sonnets, such an approach allows one 1) to corroborate certain theories concerning the time when most of the sonnets were created and 2) to prove that the addressee of the sonnets and Mr W.H. were two different people who may be identified with a fair degree of certainty.

TRI HITA KARANA: MODAL SPIRITUAL UNTUK MEWUJUDKAN PARIWISATA REGENERATIF DI BALI

Discussion on regenerative sustainability results from understanding that previous concepts of sustainability, the conventional and the contemporary sustainability, failed to achieve the sustainability agenda. The failure results from human behavior that considers themselves as having the right to use the environment to fulfill their needs. The urgency to satisfy their basic needs and, finally, their greed has resulted in an unsolvable problem: unsustainability. Sustainability is a behavioral matter, and behavior is a product of someone's understanding, attitude, value, beliefs, paradigm, or worldview. Therefore, to achieve sustainability, there should be a mindset change. As a form of contemporary spirituality, Tri Hita Karana can initiate change in the mindset concerning sustainability (inner-sustainability) through character education, so that regenerative sustainability and regenerative tourism in Bali can be achieved.

The Arctic potential: cutting the Gordian knot of EU–Russia relations?

ABSTRACT The relationship between the European Union (EU) and Russia in the past 30 years has been complex, encompassing periods of hope, optimism and cooperation but also elements of competition, conflict and complicated geopolitical tensions. There is an omnipresent pattern of intertwined conflict and cooperation that has run through the core of the relationship, until reaching a stalemate following the 2022 Russian aggression in Ukraine. We identify the current state of EU–Russia relations to resemble a Gordian knot or a deeply entrenched and unsolvable problem. Nevertheless, a site where the EU and Russia meet face to face to pursue interests on a plethora of issues is the Arctic. We examine whether the EU–Russia relations have been qualitatively different there, and whether it might hold lessons for cutting the identified Gordian knot. We employ discourse analysis to the official EU documents on the Arctic from the European Parliament, the European Commission and the Council of the European Union, and examine how Russia has been presented in these documents – as a competitor or a cooperation partner. We discover more cooperation rather than conflict language, indicating the Arctic might hold some lessons about the future EU–Russia relations after a Russian withdrawal from Ukraine.

СИНТЕЗ ЗНАНИЯ КАК ЦЕННОСТЬ НАУКИ

The article seeks to answer whether it is legitimate to assert that «synthesis of knowledge» is the value of science. The identification of the value content of the process and result of synthesis of new knowledge determines the actual development of human civilization. However, there is a reasonable assumption that the explanation of the nature of values goes beyond the methodological possibilities of modern science since value covers the area of both the known and the unknown, which limits the possibility of constructing a sufficiently complete model of the development of humanity within the framework of the worldview of its life form. The article explores the possibilities of axiological constructivism for constructing logical and semiotic structures describing synthesis of knowledge and making it possible to objectify its value bases. The context of the reasoning is given by the decomposition of the basic statement that synthesis of knowledge is the value of science. The article shows the process of transformation of the understanding of value in various axiological approaches (axiological normativism, subjectivism, normativism). The ontological, epistemological, and logical foundations of the development of the theory of values are considered. The study substantiates the need to rethink the logical-semiotic approach to reading cultural texts as a type of synthetic knowledge, up to the necessary reconstruction of iconic forms and semiotic structures, while taking into account the value aspects of meaning- and text-generation. The research is based on the methodology of synergetics of complexity, the model-theoretic approach is used to describe the nature of value, the method of ontosemiotic modeling — to provide understanding of the value-driven boundaries of cognition. The introduction of the element «feeling» into the structure of the semiotic construction — a modal sign, allows us to identify the boundaries of extra-textual and extralinguistic areas of scientific knowledge. To do this, the text model has been expanded to the sphere of the dynamic subject’s activity, which is set in the form of a three-level cultural text (pre-linguistic, linguistic, and post-linguistic levels). The modal sign forms a space of semiosis and text generation, based on the «idea» of communication and the activity of the subject of cognition. The idea, as a generative element of the text, has a personality-colored character, can be represented as a unit of «implicit knowledge» according to M. Polani. The article shows that, unlike solvable problems, unsolvable problems that are significant for the subject affect the value domain of knowledge construction, activating archetypal manifestations, unconscious, mythological thinking and attitudes. Embodied, value-based thinking introduces nonrational relationships into the resulting constructs, ensuring its coherence through personal knowledge.